Functions Word Problems
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An airplane is sighted at the same time by two ground observers who are 4 miles apart and both directly west of the airplane. They report the angles of elevation as 11° and 22°. How high is the airplane?

Frank is standing 110 yards from 32yard high waterfall. What angle does he look at to see the top?

AB=1000 straight N and turn 127 degree to the left. Calculate the bears of BC.

Four boys are playing with their marbles. Two boys have the same number of marbles and they both have 1 more marble than the 3rd boy. The 4th boy has 1 marble less than the 3rd boy. If all the number of marbles of each boy is multiplied, the product would be 18. How many marbles does each boy have?

A rectangular shipping container has a volume of 2500 cm3. The container is 4 times as wide as it is deep, and 5cm taller than it is wide. What are the dimensions of the contaner?

A satellite, travelling in a circular orbit 700 km above Earth, will pass directly over a tracking station at noon. The satellite takes 95 mins to complete an orbit. a) If the antenna for a tracking station is aimed at an angle of elevation of 30 degrees, at what time will the satelite pass through the beam of the antenna? The radius of Earth is 6378km.

It costs $1.50 per day to place a oneline ad in the classifieds plus a flat service fee. One day costs $3.50 and four days costs $8.00. Write a linear equation in point slope form that gives the cost in dollars, y, in terms of the number of days the ad appears, x.

A crow is on the ground 80 feet from the base of a 45 foot tall tree. It then flies straight through the air to the top of the tree. What is the angle of the crow`s flight path relative to the ground?

Suppose the Population of D.C. in January of 2006 was 580,000 and 2 percent of them moved every 6 months. How many people would be left on January 2009?

A 10ft ladder leans against a wall at an angle with the horizontal. The top of the ladder is x feet above the ground. If the bottom of the ladder is pushed toward the wall, find the rate at whih x changes with respect to the angle when the angle is 60 degrees.

Beth owns her own candle making business. The cost to create and buy your own candle is $475. In addition to these one time charges, the cost of putting your own picture on the candle is $1.75. Let "x" equal the average cost per candle for Beth`s business to make. Find the average cost per candle when x=100.

A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs^{2}(3Ls) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long. a) If the deflection at the end of the board is 1 ft, find c b) Show that the deflection is .5 foot somewhere between s=6.5 and s=6.6

How do you graph trig tangents?

f(x)= sqrt(x)  sqrt(x+4) find the domain

A company produces a product for $9.45 per unit, plus a fixed cost of $5200. The company sells the product for $15.80 per unit. a) determine a function, c(x), to represent the cost production x units b) determine a function, r(x) to represent the revenue from selling x units c) determine a fucntion to represent profit d) caculate break even point

What is the slope of the line joining (5,9) and (2,9)

Mia has a temperature of 101 degrees. Her temperature is rising at the rate of 1 degree every 5 hours. If her temperature reaches 108 degrees, Mia`s parents will take her to the emergency room. Write and solve an equation to determine how long it will be before Mia goes to the emergency room.

You need to determine the length of a tunnel drilled through a lunar peak at the center of a crater. From a point on the crater floor, you run ropes to the ends of the tunnel. The first rope`s distance covered is 24.5 meters and the second rope`s distance is 21.2 meters. The two ropes meet at an angle of 68 degrees. a) What is the length of the tunnel? b) At what angle with the 1st rope should the tunnel be drilled so that it comes out at the correct exit point?

A biologist is researching a newlydiscovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Round k to two decimal places.)


The rat population in a major metropolitan city is given by the formula n(t)= 73 e^{0.015 t} where t is measured in years since 1990 and n(t) is measured in millions. What was the rat population in 1990 ? What is the rat population going to be in the year 2005 ?

A 25 m tower standing vertically on a hillside casts a shadow down the hillside that is 27 m long. The angle at the tip of the shadow S, subtended by the tower is 26. What is the angle of elevation of the sun at S?

If you put 25 cents in a bank and your money doubles each year, how long will it take to have a billion dollars?

To obtain a retail price, a dress shop adds $20 to the wholesale cost of every dress. When the shop has a sale, every dress is sold for 75% of the retail price. Write functions f(x), g(x), and [g◦f ](x) to describe the situation.

A new FDA diet claims that a person weighing 140 pounds should consume 1560 daily calories and that a 180 pound person should consume 1700 calories. Let y represent the calories and x the weight of the person in pounds.

m=2 for every increase of 1 year in age, there will be a corresponding increase of $2000 in the median income.

A linear cost function is C(x) = 5x + 250 What are the slope and the C intercept?


From an airplane, Janara looked down to see a bit. If she looked down at an angle of 9 degrees and the airplane was half a mile above the ground, what was the horizontal distance to the city?

Together Steve and Heather`s ages add up to be ten. If we let "x" be Steve`s age, setup the polynomial describing Heather`s age.

Due to wind, a tree grew so that it leaned 8 degrees from the vertical. From a point on the ground 28 meters from the base of the tree, the angle of elevation to the top of the tree is 24.6 degrees. What is the height of the tree?

Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation: C(g)=3.03(g) a) What does the number 3.03 represent? b) Find C(2) c) Find C(9) d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did. e) If you were to graph C(g), what would be an appropriate domain? Range? Explain your reasoning.

Mary invested $1400 in two mutual funds. One fund earned interest at 7% per year and the other earned interest at 8% per year. If she receives $104 in interest after one year, how much did she invest in each fund?


In 1995, the number of families with cable television was 20.0 million. By the year 2008, there will be 27.6 families with cable television and enjoying every minute of it. Find the slope and describe what the slope represents.

Two observers,who are 2 miles apart on a horizontal plane,observe a balloon the same vertical plane with themselves. The angles of elevation are 50` and 65` respectively. Find the height of the balloon ,(a) if it is between the observers (b) if it is on the same side of both of them.

A ladder 39 feet long leans against a building and reaches the ledge of a window. If the foot of the ladder is 15 feet from the foot of the building, how high is the window ledge about the ground?

One particularly large ant hill found in1997 measured 40 inches wide at the base and 18 inches high. What was the slope of the ant hill?

What is an equation for a slope of zero?

f(x) computes the height in inches of a cylinder with radius x inches and volume 60 cubic inches. What is the domain? Justify your answer.

Greenshield`s Formula can be used to determine the amount of time a traffic light at an intersection should remain green. G = 2.1n + 3.7 G= green time in seconds n = average number of vehicles traveling in each lane per light cycle. Write a simplified expression to represent the average green light time per vehicle

Two ships leave port at 4 p.m. One is headed at a bearing of N 38 E and is traveling at 11.5 miles per hour. The other is traveling 13 miles per hour at a bearing of S 47 E. How far apart are they when dinner is served at 6 p.m.?

From the top of a lighthouse 160 feet above sea level, the angle of depression to a boat at sea is 25 degree. To the nearest foot, what is the horizontal distance from the boat to the base of the lighthouse?

Mr. Gregg is giving each of her students 3 apples. Find the function rule.


The total sales for a new camera equipment store were 200,500 for the second year and 500,000 for the fourth year a) find a linear equation for the above model b) estimate the total sales for the 6th year

A rectangular box is (2x + 7) feet wide, (5x + 2) feet long, and (x  4) feet high. Find the volume of this box.



The linear equation y=30x describes how far from home Deena is as she drives from Dallas to Miama. Let x represent the number if hours and y represent the number of miles. How far from home Deena in 12 hours? Graph the equation and tell whether it is linear.


If there are 45 rats in a New York deli and the number of rats doubles every 7 days how long will it take for the deli to have 100,000 rats?

What is the area of triangle ABC given that a = 4 , b = 7 , and B = 75°



A ramp is at an angle of elevation of 30 degrees. The distance from the top of the slope to the ground is 900 meters. What is the lenght of the ramp?

Liselle is flying her kite with 62 feet of string attached to the ground. She measures 5 feet of string from the ground to a point of 4 feet high. How high is her kite?

A tree on a hillside casts a shadow 215 ft down the hill. If the angle of inclination of the hillside is 22 degrees to the horizontal and the angle of elevation of the sun is 52 degrees, find the height of the tree.

A plane flies 1.3 hours at 110 miles per hour at a bearing or North 40 degrees East. It then turns and flies on a bearing of South 50 degrees East at the same rate for 1.5 hours. How far is the plane from the starting point, and at what bearing is the plane from the original site?

While fishing, you spot a fish below the water at a 25 degree angle with the surface. It is producing air bubbles 20 feet ahead. How far away is the fish from the boat?

You are driving from Grand Rapids, Michigan, to Detroit, Michigan. You leave Grand Rapids at 4:00 p.m. At 5:10 p.m. you pass through Lansing, Michigan, a distance of 65 miles. Write a linear equation that gives the distance in miles, d, in terms of time, t. Let t represent the number of minutes since 4:00 p.m.


An airplane flying at an altitude of 6 miles, is on a flight path that goes directly over you. If angle is the angle of elevation, find the distance from the observer to plance at 30, 75 degree.

Natali is 5 feet 3 inches tall. She walks from the base of a broadcasting tower directly toward the tip of the shadow cast by the tower. When she is 130 feet from the tower and 3 feet from the tip of the tower`s shadow, her shadow starts to appear beyond the tower`s shadow. What is the height of the tower?


The diagonal of a rectangle is 25 and the angle formed by the shorter side and the diagonal is 71 degrees. Find the length of the shorter side to the nearest whole number.

An antenna is atop of a 80 foot building, 12 feet from the edge. From a point 60 feet from the base of the building, the angle from the ground level to the top of the building is 68 degrees. Find the height of the antenna to the nearest foot?

X and Y are two lighthouses, Y being 20 Km due east of X. From a ship due south of X, the bearing of Y was 055 degrees. Find the distance of the ship from Y. Find the distance of the ship from X.

A mass suspended from a spring is pulled down a distance of 2 feet from its rest position. The mass is released at time t=0 and allowed to oscillate. If the mass returns to this position after 1 second, find an equation that describes its motion.

From a glider 200 feet above the ground, two sightings of a stationary object directly in front are taken 1 minute apart. What is the speed of the glider?

Two people leave from the same point. Their paths diverge by 95 degrees. If one walks 5 miles and the other walks 3.5 miles, how far apart are they at that time?

Coast Guard Station Able is located 150 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located N55°E; the call to Station Baker indicates that the ship is located S60°E. (a) How far is each station from the ship? (b) If a helicopter capable of flying 200 miles per hour is dispatched from the nearest station to the ship, how long will it take to reach the ship?

Find a polynomial for the perimeter and for the area using d+4 and d

A ski slope at a mountain has an angle of elevation of 25.2 degrees. The vertical height of the slope is 1808 feet. How long is the ski slope?

If angle B = 25 degrees 30`, angle A = 90 degrees, what is angle C of a triangle?

Two firetowers are 30 kilometers apart, tower A being due west of tower B. A fire is spotted from the towers and the bearings from A and B are E 14 degreesN and W 34 degreesN, respectivly. Find the distance D of the fire from the line segment AB.

A train is traveling up a slight grade with an angle of inclination of only 2 degrees. After traveling 1 mile what is the vertical change in feet?

The length of a tree`s shadow is 15 m. The angle of elevation of the sun is 38 degrees. What is the height of the tree?

A pilot flies in a straight path for 1 hour and 30 minutes. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 hours in the new direction. If she maintatins a constant speed of 620 miles per hour, how far is she from her starting position?

Julio works as a quality control expert in a beverage factory. The assembly line that he monitors produces about 20,000 bottles in a 24hour period. Julio samples about 120 bottles an hour and rejects the line if he finds more than 1/50 of the sample to be defective. About how many defective bottles should Julio allow before rejecting the entire line?

You are driving at a speed of 55 miles per hour to your sisters house. At 1 pm, you are 150 miles from her house. Write an equation that models the distance from your sister`s house in terms of the number of hours since 1 pm.

A 95ft tree casts a shadow that is 45 ft long. What is the angle of elevation of the sun?

A straight road makes an angle of 15 degrees with the horizontal. When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road. Find the length of the pole.


Tyler is flying a kite on 1700 feet of string. How high is it above the ground if the horizontal distance between Tyler and the kite is 800 feet?

A ferris wheel is built such that the height (h) in feet above the ground of a seat on the wheel at time (t) in sec can be modeled by: H(t)=53+50sin(π/10tπ/2) Find the angular speed in radians and the linear speed in feet?

The right angle of the triangle is 1808 feet the slope is 25,2 degrees, how long is the slope?

A roof rises 9.75 ft over a horizontal distance of 17.24 ft. What is the slope of the roof to the nearest hundredth?

From a point on the ground, a person notices a 110foot antenna on the top of a hill subtends an angle of 1.5 deg. If the angle of elevation on the bottom of the antenna is 25 deg, find the height of the hill.

Company produced 45,000 tons of steel in March at a cost of 1,150,000. In April the company produced 35,000 tons at a cost of 950,000. using only those two data points, determine the cost function.

The cost of an ice cream sundae is given by the formual C(s) = 1.25s + 5.00. In this formula, C(s) represents the cost of the ice cream sundae and s is the number of scoops of ice cream. What does the slope represent?

In high school baseball, the front of the pitcher`s rubber is 60.5 feet away from the back end of the home plate, and the first base bag is 90 ft fromhome place. The home plate and each of the bases makes a 90 degree angle with the next one, and the pitcher`s rubber is aligned between home place and second base. Find the distance from the front of the pitching rubber to first base.

A ladder leans against a building forming an angle of 50 degrees with the ground. The base of the ladder is 8 feet from the building. Use the cosine to determine the length of the ladder.

An airplane takes off from a field with an 8 degree angle with the horizontal ground. Find the horizontal distance covered when it had flown 2000 meters.

The world population in 1950 was estimated to be 2.5 bilion. The population has grown exponentially so that in 2008 there were an estimated 6.8 billion. Determine the yearly growth factor.


At noon, a tree having a height of 10 feet casts a shadow 15 feet in length. Find, to the nearest degree, the angle of elevation of the sun at this time.


A straight road slopes upward at 15 degrees from the horizontal. How long is the section of the road that rises a vertical distance of 250 feet? ( Express the answer to the nearest 10 feet.)

Rose Street is perpendicular to Oak Lane. on your map. Draw Rose Street so that it is perpendicular to Oak Lane. { Oak Lane is a line going straight ahead.}

One afternoon your family goes out to pick strawberries. At 1:00P.M., your family has picked 3 quarts. Your family finishes picking at 3:00P.M. and has 28 quarts of strawberries. At what rate was your family picking?

A pig at Papas Barn just had a litter of piglets. The whole barn is about 12 miles long. In the middle of the night one piglet ran out of the barn a traveled down to the Bray Ranch which is about 13.5 miles away. When viewed on the towns map the two barns make a 115 degree angle. How far does the mama pig have to travel to get to her piglet.

You want to shoot and make 25 shots per day. If you shoot in sets of ten and make 50%. how many sets will it take to make 25 shots

( 1,2 ) ( 7,9 ) What is the slope?

A man on a 135ft vertical cliff looks down at an angle of 16 degrees and sees his friend. How far away is the man from his friend? How far is the friend from the base of the cliff?

Amelia sees a jet heading south away from her at 42 degree angle of elevation. Twenty seconds later the jet is still moving away from her, heading south at a 15 degree angle of elevation. If the jets elevation is constantly 6.3 km, how fast is it flying in kilometers per hour?

A ladder rests against a wall. the top of the ladder reaches 15 feet up the wall, and makes an angle of 53 with the wall. how long is the ladder?

High tide at Fisherman`s Cove occurs at 3am and is 2.1m. Low tide occurs at 9am and is 0.7m. A simple model for such tides could be a cosine function of the form; d(t)=A Cos(Bt+C)+D Determine the equation for the above model where "t" represents the numbers of hours since midnight.

What is the value of arcsin ( √2 / 2)?

Write an equation in standard form for a line that contains the points (2, 8) and (2, 5)

Island A is 230 miles from island B. A ship captain travels 270 miles from island A and then finds that he is off course and 180 miles from island B. What angle, in degrees, must he turn through to head straight for island B? Round the answer to two decimal places.

A ship at sea, the Admiral, spots two other ships, the Barstow and the Cauldrew and measures the angle between them to be 65° . They radio the Barstow and by comparing known landmarks, the distance between the Admiral and the Barstow is found to be 236 meters. The Barstow reports an angle of 36° between the Admiral and the Cauldrew. To the nearest meter, what is the distance between the Barstow and the Cauldrew?

The course for a bike race follows a triangular shaped trail. The first leg is a straight 6 kilometre ride. After that, the biker must turn 283 degrees to the left and follow the train to the next turn. Turning 269 degrees again to the left will take the biker to the finish line, which is exactly where he started. How long is the entire race?



Three students in an outdoor pursuits program collaborated to write an adventure travel guidebook for Alberta and BC. Two local publishers are interested in marketing and publishing it and both anticipate retailing the book for $20. Publisher "A" offers a straight royalty of 10% (on the retail price) on all book sales. Publisher "B" offers an 8% royalty for any books sold up to 5000 copies and will then increase the royalty to 15% for any copies sold in excess of 5000. a) Describe the type of function b) Find the functions A(x) and B(x)  notice that function A(x) is apiecewise defined function. c) Let x be the number of books sold and let A(x) give the income under plan "A" and B(x) give the income under plan "B". Graph functions on the interval 0,10000

Supppose an investment of $8,100 doubles in value every 7 years. How much is the investment worth after 28 years?

what is an equation for a zero slope?

A periodic function f has a period of 15. if f(3)=5 and f (11) =11, determine the value of f(72)

The angle of elevation from point A to the top of a cliff is 38 degrees, if point a is 80 feet from the base of the cliff how high is the cliff?

If you let 100 feet of string out on a kite and fly it how high can the kite go?


(3, 3) that is perpendicular to the line 2x+y=1.

Two observers 200 feet apart are in line with the base of flagpole. The measurement of the angle of elevation of the top from one observer is 30 degrees and other 60 degrees. How far is the flagpole from each observer?

During an air show, a stunt pilot flies over a crown at an altitude of 2500 feet. One minute later the angle of elevation of the plane is 15 degrees. How high is the plane flying?


Express the area A of an equilateral triangle as a function of the length x of a side.

Brandon gets a 40% discount on loose diamonds where he works. The cost of the setting is $250. If he plans to spend at most $1450, then what is the price range (list price) of the diamonds that he can afford?

what is the graph of the radical function F(x) = √3x+5

A triangle has three sides of 7,4,8 what is the measurement?

bill jogged for 5 min. and then sprinted for 400 m in 64 s. a) At what rate did he sprint?

ABCD is a rectangle on a coordinate grid with side AB parallel to side CD and side BC parallel to side AD. If the slope of side AB is 2/7, what is the slope of side BC?

In 2006, the population of a town was 15,139 and growing by 75 people per year. Find a formula for P, the town`s population, in terms of t, the number of years since 2006.

hicks owns a local ice cream parlor and yogurt stand. his single scoop cone sells for 89 cents and the "giant earthquake" of eight scoops sells for $6.07. The cost of the ice cream cone varies linearly with the number of scoops

Two temperature scales are established, one, the R scale where water under fixed conditions freezes at 15 degrees and boils at 405 degrees, and the other, the S scale where water freezes at 5 degrees and boils at 70 degrees. If the R and S scales are linearly related, find an expression for any temperature R in terms of a temperature S.

an airplane flies due north from ft myers to sarasota, a distance of 150 miles, and then turns through an angle of 50 degrees and flies to orlando, a distance of 100 miles. how far is it directly from ft. myers to orlando?

When moving, how many boxes are needed for each room of the house.

Different weights. ProfessorWilliamson counts his midterm as 2 3 of the grade and his final as 1 3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the final exam would put Wendy’s average between 70 and 79 inclusive? Compare to the previous

A mountain peak C is 4130 ft above sea level, and from c the angle of elevation of the second peak B is 5 degree. An aviator at directly over peak c, find angle CAB is 43.8 degree where his altimeter show that he is 8460 ft above sea level. find the height of peak b?

After the mill closed, Steeltown PA started losing people exponentially. If Steeltown`s population was 100,000 in 1970, and 59,874 people in 1980, model the population with an exponential function.

tunnel word problem on laws of sines : a rectangular tunnel is cut through a mountain side. The upeer vertices of the rectagle are on circle x2+y2 = 400 cross sectional area of tunnel is 400sin2x. the dimension of this tunnel will be what?

cos²x 1+sinx both sides have to equal each other ___________ = ________ 1+3sinx  4sin²x 1+4sinx

1. Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation: a) What does the number 3.03 represent? b) Find C(2) c) Find C(9) d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did. e) If you were to graph C(g), what would be an appropriate domain? Range? Explain your reasoning.

Business and finance. Julio works as a quality control expert in a beverage factory. The assembly line that he monitors produces about 20,000 bottles in a 24hour period. Julio samples about 120 bottles an hour and rejects the line if he finds more than of the sample to be defective. About how many defective bottles should Julio allow before rejecting the entire line?

find the standard and slopeintercapt form with a line that has an undefined slope and contains the point (3/7, 1/8)

math question: a helicopter takes off and flies 5 miles south then turns east and flies 4 miles then turns again toward the south and flies 3 miles how far away is the helicopter from where it took off?

linear function w/ solution and word problem

A dress that is size x in France is size s(x) in the United States, where s(x) = x  32. A dress that is size x in the United States is size y(x) in Italy, where y(x)  2(x + 12). Find a function that will convert French dress sizes to Italian dress sizes.



given is:c is 26,a is 15,and angle C is 29 degrees.

A man standing at the top of a 65m lighthouse observes two boats. Using the data given in the picture, determine the distance between the two boats. how would you set up this problem

John is a salesperson who must decide between two monthly income options: Option A: Salary of $1412 per month, plus 10% of monthly sales or Option B: Salary of $2000 per month, plus 6% of monthly sales What must the monthly sales amount be so that Option A is a better choice for Bob than Option B?

Catering charges a basic fee of $100 to cater a banquet plus an additional charge of $2 per person invited to the banquet


A ball is dropped out of a window of a tall building. If it hits the ground 3.5 seconds later, how high above ground is the window?

The afrrican bush elephant is the largest land animal and weighs eight tons. Write the amount in exponetual form

The afrrican bush elephant is the largest land animal and weighs eight tons. Write the amount in exponential form

A small dog (neglect its physical dimensions) is spotted from a 16th floor window 160 ft high, and a ledge of width, d, 50 ft below the 16th floor window. The angles of elevation subtended by the dog at the two observers are as shown in the diagram. Determine the width, d of the ledge.

C(G)=3.03 d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did.

how many miles can you get off of a gallon of gas if you were driving 55 miles per hour. I do not even know if that problem makes sense.

translate the verbal phrase into an expression: the quotient of 8 and twice a number z

slope intercept form x 7y = 13

A saleperson receives a base salary of $200 per week and commission of 10% on sales over $3000. Find the weekly earning for weekly sales of $2000 and for weekly sales of $5000.


a 10ft ladder leans against a wall at an angle with the horizontal.The top of the ladder is x feet above the ground.If the bottom of the ladder is pushed toward the wall,find the rate at which x changes with respect to the angle is 60 degrees.

the period of a simple pendulum varies directly as the square root of its length. If a pendulum three feet long has a period of 4.8 seconds, find the period of a pendulum half as long.

The manager of a furniture factory finds that is costs $3000 to manufacture 100 chairs in one day and $4800 to produce 3000 chairs in one day. Express the cost C (in dollars) as a function of the number of chairs X produced, assuming that it is linear.

graph the function, not by plotting points, but by starting from the graphs in figures 2 and 5. state the domain , range ,and asymptote. g(x)=2^x3

erin opened a savings account with $15.then every week she deposited $ 5.write an equationin slope intercept form that represnts the data

find the domain of the following: f(t)=4.5e^t


c=2.85n+30.52 where n is the number of years since 1990. Find and interpret the cintercept of the line.

How do I find the free radicals in the square root of 200?

f(x)=x^3+5, g(x)= x^2  10 and h(x)= 5x + 7 find the rule for the function fg

Jason leaves Detroit at 6:00 PM and drives at a constant speed west along I96. He passes Ann Arbor, 40 mi from Detroit, at 6:50 PM. (a) Express the distance traveled in terms of the time (in hours) elapsed.

wendy, a loan officer at a bak has $1000000 to lend and is required to obtain an average return of 18% per year. if she can lend at the rate of 19% or at the rate of 16%, how much can she lend at the 16% rate and till meet her requirmeents?

anna needed to let everyone in the music club know the time of its next meeting. she called two people and asked each of them to call two other people, and so on. if each phone call takes one minute, how many phone calls were made during the fifth minute?


Write an equation in slopeintercept form for the following info. slope=.25, xintercept=24

56  14y divided by 24x to the 3rd power  54x


In 1999, the world`s population reached 6 billion and was increasing at a rate of 1.3% per year. Assume that this growth rate remains constant. Write a formula for the world population (in billions) as a function of the number of years since 1999.




Joe has two pay receipts that he earned $58.00 for 12 hours work one week and $92.50 for 18 hours work another week. Express his pay as a linear equation in slopeintercept form

The population of a certain city was 199000 in 1998, and the observed relative growth rate is 6 percent per year. (a) Find a function that models the population after t years

T(h)=0.8^217.6h+93.6 t= temp h=hours since storm began what was the temp as the storm began? how many hours until the temp dropped below 0 how many hours did the temp remain below 0 coldest temp recorded during the storm round if necessary

An air freshener starts with 31 grams and evaporates. In each of the following cases, write a formula for the quantity, Q grams, of air freshener remaining t days after the start

The air in a factory is being filtered so that the quantity of a pollutant, P, is decreasing according to the function P=Poa^t, where t is time in hours. If 10% of the pollution is removed in the first 5 hours, what percentage is left after 10 hours?


passes through (1,2) and is parallel to the graph of y= 3x+7


give me examples and their illustrations with the correct solution




give me examples and their illustrations

The cost of carpeting a room is 4$ per square yard plus $100. Each square yard is equal to 9 square feet. What is teh composite function of carpeting a room that covers x feet.

A clothing store offers a 10% discount sale on its blue jeans. Lulu has a $10 off coupon for any item in the store. How much would lulu pay?

domain=0,1,2,3,4 Range=9,7,5,3,1 FInd the rule

If you plot the distance that a car travels on the graph traveling at a speed of 60 miles per hour, what is the slope of the graph?

from the cliff 250 feet, the angle of depression of a boat s 10 degrees.how far out is the boat to the cliff?.

The price of a 2hour plumbing repair job is $130 and the price of a 5hour job is $250. Explain in a complete sentence what the yintercept and slope mean as they relate to the problem.

A cone circumscribes a sphere with radius 1. Express the volume V of the cone as a function of the base radius r.

A 2mi. cab ride cost $4.30. A 5 mi. cab ride cost $7.60. Find a linear equation that models cost c as a function of distance d.

A crow is on the ground 80 feet from the base of a 45 foot tall tree. It then flies straight through the air to the top of the ...

If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000100p shirts at a tournament. Find a polynomial R(p) that represents the total revenue when the shirts are p dollars each

what does 3.03 equal when c(g)=3.03(g)


A tree casts a 75 foot shadow when the angle of elevation of the sun is 39 degrees. How tall is the tree?

Suppose a population of initial size 100 grows at the rate of 8% per year forever. What is the size of the population at the end of year 1? What is the size of the population at the end of year 2? What is the size of the population at the end of year 3? What is the size of the population at the end of year n (for any integer n)? What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200?


Write the equation in slopeintercept form of the line that passes through the point (6,2) and has a slope of 3. Show your work.

A baby weighing 7 pounds at birth may increase in weight by 11% per month. How much will the baby weigh after 1 year?


Please find the equation of the line in slope intercept form and convert it to standard form (0,3) and (3,9)


If we have a rock concert, someone will faint.

in triangle ABC, m < C = 6, and AB = 10. Find tan A

adjacent 8 with an opposite angle of 32 degrees. whats the hypotenuse?

Wholesales of bottled water in the United States in 2006 were $10.6 billion. This was an increase of about 54% over sales in 2001. Find the wholesale sales of bottled water in the United States in 2001.

find an equation of the line with slope 1/2 that passes through the point (2,5)

A lighthouse is located on a small island, 3 km away from the nearest point P on a straight shoreling, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline whin it is 1 km from P?


A wheelchair ramp is to be built at the town library. If the entrance to the library is 18 inches above ground, and the slope of the ramp is1/15, how far out from the building will the ramp start?

If a woman in an average dance class burms 353 calories per hour, express the number of calories burned, C, as a function of the number of hours danced,n.

whats the rule of function (0,3) (3,9)

Write an equation of the form y=mx+b for your line. Explain what the values of m and b tell you about this situation.

The function that gives the temperature for time on a normal day.


lines always have a slope of zero

a person standing 19m from the base of a tree notices that the angle of elevation to the top of the tree is 42 degrees

Sarah has a longdistance plan where she pays 10 cents for each minute or part of a minute that she talks, regardless of the time of day. Graph a step function that represents this situation.

jessica wants to enclose a rectangular feed area in her backyard using a barbed wire fence. she only has 64 feet of fencing, and wants to maximize the area of the rectangle. express the area as a function of x.


pam has $25 and is earning $4 per week for doing chores. If she does not spend any money, write an equation to represent how much money (y) she has after (x) weeks.

1. The pitch of a roof is the slope of a roof. If the roof of a house rises vertically a distance of 9 feet through a horizontal distance of 15 feet, what is the pitch of the roof?

The pitch of a roof is the slope of a roof. If the roof of a house rises vertically a distance of 8 feet through a horizontal distance of 20 feet, what is the pitch of the roof?

One hundred feet of fencing is used to enclose three sides of a rectangular pasture. The side of a barn closes off the fourth side. let x be one of the sides perpendicular to the barn.

F(x)= 2X^2+4=3x fins F(x) is (2a+7)


bob and donna leave their home .they travel in opposite drections. bob travels 65 mph and donna travels 75 mph . in how many hours will they be 420 miles apart?

Soppose a supermarket pays its cashiers a regular hourly wage if they worked up to eight ho

At a local airport, a light that produces a powerful whitegreen beam is placed on the top of a 45foot tower. If the tower is at one end of the runway, find the angle of depression needed so that the light extends to the end of the 2200foot runway.

You are designing a rectangular flower bed that you will border using brick pavers. The width of the border around the bed will be the same on every side. The flower be is 6ft by 5ft.

Suppose that a fungal disease originates in the middle of an orchard, initially affecting only one tree. The disease spreads out radially at a constant rate of 10 feet per day. What area will be affected after 2 days, 4 days, and 8 days? Write an equation that expresses that affected area as a function of time measured in days, and show that this function is a polynomial of degree 2.

a rectangular shipping container has a volume of 2500cm3. the container is 4 times as wide as nit is deep, and 5cm taller than it is?

John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33º. This particular tree grows at an angle of 83º with respect to the ground rather than vertically (90º). How tall is the tree?

a communications tower is located at the top of a steep hill. The angle of inclination of the hill is 45 degrees. A guy wire is to be attached to the top of the tower and the ground, 134 meters downhill from the base of the tower. the angle is determined to be 15 degrees. what is the length of the angle required for the guy wire.

claire has a job selling sports cars. she gets a base salary of $30000 per year plus 2% of her sales

A 120 Ib inline skater burns 7.4 Cal/min skating at 10 mph. For every extra 20 Ib of weight, a skater skating at 10 mph burns an extra 0.9 Cal/min. a. Write a pointslope equation giving c, the number of calories burned per minute, as a function of w, the weight of the skater.


you are driving at a constant 50 mph along a straight road at a constant speed between cities A and B. Along the way you pass through city C. The cities B and C are 100 and 25 miles, respectively, from city A. a.)Draw a graph that indicates your distance from city C as a function of time, measured from the time you leave city A.


Suppose an absolute value graph that opens up has a vertex (h,k) in Quadrant II. This graph is reflected across the xaxis and then translated down c units. What is the range of the new graph?

what is the absolute value function shifted nine units to the left?

A 5mi cab ride costs $4.40. A 8mi cab ride costs $6.20. Find a linear equation that models cost c as a function of distance d.

Sapose the number of cars, c, on first ave. in a city over a perould of time t, in months is greater on a rectangular cordnent system where time is on the horazonal axis. sapose the number of cars on first ave. can be modified by an exponential function C=p(a)^t where p is the munber of cars on the road on the first day recorded. If you commuted to work each day along first ave. would you prefer that the value of "a" be between 0,1 or larger than 1?

use a calculator to evaluate csc (0.6)


Tom has $8.00. He wants to by oranges which cost $.75 a piece.

Betty`s Phone Service has been calling you to join their service to enjoy low rates. With her plan, for 25 minutes of use per month, you pay $7.95. If you use 40 minutes, you monthly charge is $10.35. find the rate of change for this phone plan. how much do you pay per minute?

f(x) = 2 ; x<.2 f(x) = x + 3 ; x>.2

Write the equation in slopeintercept form of the line that has a slope of 3 and contains the point (1, 1).


a pilot is flying over a straight highway. The angles of depression are 5 miles apart and are 32 degees and 48 degrees. Find the elevation of the plane.

sample problem in algebraic function chain rule, sum & product,

WATER LEVEL IN A HARBOR: the water level (in feet) in Boston Harbor during a certain 24hr period is approimated by the formula: H= 4.8sin Pi/6 (t10) + 7.6 (0 < t < 24) when t=0 corresponds to 12 am. When is the water level rising and when is falling? Find the relative extrema of H and interpret the results

A group of scuba divers are diving in Hawaii at Hanama Bay. The pressure on a diver at a depth of d feet is given by the formula P = 64d + 2112 where P represents the pressure in pounds per square foot. Amongst the divers the pressures range from 4032 pounds per square foot to 3552 pounds per square foot. Find the range of depths of the divers.

A rectangular lawn measures 7m by 5m. A uniform border of flowers is to be planted along two adjacent sides of the lawn. If the flowers that have been purchased will cover an area of 6.2m2, how wide is the border?


the half life of radioactive cesium 137 is 30.2 years. If we have 750 poiunds of radioactive cesium, how much will be lost over the next 500 years?

as the time increases by 0.2 seconds,by how much does the distance change?does the distance change by the same amount over each time interval?

the graphs of the equations y3x=3, 2y+x=11 and 2y4x=8 form three sides of a parallelogram.complete the parallelogram by writing an equation for the graph that forms the fourth side. explaiin how to determin whether the parallelogram is a rectangle. is it a rectangle?

Write an equation in slopeintercept from that describes the number of kilocalories remaining from a meal of 420 calories at the end of each minute of exercise. Exercise burns 6.75 kilocalories per minute

The number of cases of dysentery in an African village has steadily been around 100 cases per month. For every new well built, the number of cases will drop by 12.

Three sides of a rectangular prism are to be constructed with 600ft. of fencing (one side is a river and pigs are not good swimmers). Write a function which represents the area as a function of the width.

In a study on the speed of muscle contraction in frogs under various loads,researchers found that the speed of contraction decreases with increasing loads.s(w)=(26+0.06w)


Suppose the ratio of 16yearolds to 15yearolds on a soccer team must be 2:3. If 10 of the players on the team are 15 years old, how many 16yearolds can be on one team?

The Acme carton company makes rectangular cardboard boxes. They were able to buy a large shipment of precut pieces of cardboard 20 cm by 10cm from a company that had gone out of business. They purchased the cardboard at a low cost and now want to make boxes by cutting a square piece out of each corner, folding up the sides and taping them. What dimensions should they make the boxes if they wish to maximize the volume?

Ken burns 425 calories per hour when he bikes. He bikes from 3 to 7 hours each weekend. Indentify the independent and dependent quantaties for this sutiation and find reasonable domain and range values

A flagpole 20ft. high was suited at the top of a hill. A string was tied from the top of the pole to the point P on the ground 150m. from the foot of the pole. If the flagpole measured an angle of 100 degree with the surface of the hill, find the length of the string.

find the slope between these points: (7/8, 3/4), (5/4, 1/4)

a video store charges $10 for a rental card plus $2 per rental

2. Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26 and in January 2006 the price of regular unleaded gasoline was $2.31 (Bureau of Labor Statistics, 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope (or rate of change) between the two points.

Michelle, a forestry officer on watch from a lookout 35m above the ground, notices a small brush fire at an angle of depression of 16°. How far , in meters, would a firefighting aircraft, directly over the lookout, need to fly to drop its load on the fire?

Write the equation in standard form 4xy+2y=9

math functions total construction cost as function of length of brick wall


whats the function rule for a line thaty is shifted 2 units down from Y=3x+5

how to find the cot 38 (degrees) without using a calculator


A decorator plans to place a rug in a room 9 m x 12 m in such a way that a uniforom strip of flooring around the rug will remain uncovered. If the rug is to cover half the floor space, what should the dimensions of the rug be?

two towers a and b are located 48 m apart. Rod who is standing at the base of tower B found that the angle of elevation of tower a is twice the angle elevation of tower B as observed by Alexandra who is also standing at the base of tower "A . At a point midway between their bases the angle elevation of two towers are complementary . Gind the heights of the two towers.

two towers a and b are located 48 m apart. Rod who is standing at the base of tower B found that the angle of elevation of tower a is twice the angle elevation of tower B as observed by Alexandra who is also standing at the base of tower \"A . At a point midway between their bases the angle elevation of two towers are complementary . find the heights of the two towers.

decide whether to use sine, cosine, tangent, or the Pythagorean relationship to find x. Solve for x.

how do i find c (2) in a domain of a function

AB is a line 652 feet long on one bank of a stream, and C is a point on the opposite bank. A = 58 degrees, and B = 48 degrees . find the width of the stream from C to AB.



When there are 22 apple trees pre acre, the average yield has been found to be 500 apples per tree. For each additional tree planted per acre, the yield per tree decreases by 15 apples per tree. How many additional trees per acre should be planted to maximize the yield?

Find the slope m of the line that passes through the points (4, 1) and (4, 10) if possible. m=

Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation: C(g)=3.03(g) a) What does the number 3.03 represent? b) Find C(2) c) Find C(9) d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did. e) If you were to graph C(g), what would be an appropriate domain? ...

One beautiful summer day, ___________ decided to do to Six Flags. Since they are afraid of heights, they decided to ride the MerryGoRound, which has a diameter of 14 meters. Around the carousel is a square gate, which has a perimeter of 72 meters. All along one side of this gate, their friends are lined up watching and notice that it is 20 seconds between times when ____, _______, and_____ are closest to their side of the gate.

From 1990 to 2000, the number of visits by people to Bryce Canyon National Park increased by about 23.9 thousand visits per year. In 2000, there were about 1102.4 thousand visits to the park.

A plane flies a straight course. On the ground directly below the flight path, observers 2 miles apart spot the plane at the same time. the plane`s angle of elevation is 46 degrees from one observation point and 71 degrees from the other. How high is the plane.

Write the slope intercept form of the equation of the line that has slope 4 and passes throughthe point (3,6)

Find the lines tangent to the curve y= x^3 + x, where the slope is equal to 4. What is the smallest value the slope of this curve can ever have and where on the curve does the slope equal this smallest value?



A tire with a 29.6 inch diameter traveling at a constant speed of 0.7 miles per hour over a nail at exactly 12 noon. The nail is stuck in the tire but does not deflate it. a. What is the speed of the tire in inches per second rounded to the nearest hundredth? b. How often does the nail hit the ground to the nearest hundredth of a second? c. Write a cosine equation in the form y = Acos(B(x – C)) + D that calculates the height that the nail is above the ground for any given time. Makes sure that A, B, C, D are exact values. d. How high above the ground will the nail be at: i. 12:00:08 ii. 12:00:15 iii. 12:01 iv. 12:15 e. Find the first 8 times the nail is 10 inched above the ground rounded to the nearest hundredth of a second.


rewrite the equations in slopeintercept form

rewrite the equations in slopeintercept form xy +5=0

find the area when a side of a squre measures 6 cm and 8 cm...using functional notations.

at rest, the human heart beats once every second. at the strongest part of the beat, a persons blood pressure peaks at 120mmHg. at the most relaxed part of the beat, a persons blood pressure drops to 80mmHg. supposing that t = 0 corresponds to the relaxed part of the beat write down a trigonometric function that captures this behavior. sketch the blood pressure over two heart beats.

when you are pricked with a pin, there is a short time delay before you say, "Ouch!" This reaction time varies linearly with the distance between you r brain and the place you are pricked. Dr. Hollers pricks Leslie Morley`s finger and toe, and measures reaction times of 15.2 and 22.9 milliseconds, respectively. (a millisecond is 1/1000 of a second.) Leslie`s finger is 100 cm from the brain, and her toe is 170 cm from the brain.

when you are pricked with a pin, there is a short time delay before you say, \"Ouch!\" This reaction time varies linearly with the distance between you r brain and the place you are pricked. Dr. Hollers pricks Leslie Morley\`s finger and toe, and measures reaction times of 15.2 and 22.9 milliseconds, respectively. (a millisecond is 1/1000 of a second.) Leslie\`s finger is 100 cm from the brain, and her toe is 170 cm from the brain.

there were 174 words typed in 3 minutes. There were 348 words typed in 6 minutes. how many words will be typed in 8 minutes.

The rat population in a major metropolitan city is given by the formula where is measured in years since 1990 and is measured in millions.

term 1,2,3,4,5,6,.... value 7,2,3,8,13,18,...

Ainsley`s school honors outstanding mathematics students at the end of their high school careers with the Mathematics Excellence Award. To earn this award, a student must achieve at least a 90% average in the mathematics sequence, which includes Geometry, Algebra II, Trigonometry, Precalculus, and Calculus. Trigonometry, which is a halfyear course taken concurrently with the second half of Algebra II or the first half of Precalculus (or during the summer), counts for 10% of the award. The other courses are weighted, starting with 15% for Geometry, with a 5 percentage point increase in weight for each fullyear course. Ainsley has earned 80%, 98%, and 85%, respectively, in the first three courses in the sequence. What is the maximum difference in scores she can earn in the remaining two courses and still receive the Mathematics Excellence Award? Extra: Ainsley`s experienced friends say that Precalculus averages five hours of homework per week while Calculus averages eight hours a week. How might this affect Ainsley`s plan? What advice would you offer?

My company has produced 45,000 tons of steel in March at a cost of $1,150,000. In April, we produced 35,000 tons at a cost of 950,000. Using only these two data points, determine the cost function.

A tank can be filled in 12 minutes by two pipes running simultaneously. By the larger pipe it can be filled in two minutes less time than by the smaller. Find the time required for each to fill it.

if `f` is a periodic function.The period of `f` is 5 and f(1)=2. find f(6);f(11);f(4)

1. Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation:

You are about to land your Cessna airplane in Salt Lake City. You are approaching the runway at a ground speed of 72 miles per hour and you are sinking at 240 feet per minute. (The ground speed is the speed of the point on the ground directly underneath your plane. You can also think of it as the horizontal component of your current velocity.) You are going to hit the runway at an angle of degrees. (Enter your answer as a mathematical expression, or with at least three digits beyond the decimal point.) Hint: Draw a triangle showing your descent and the horizontal distance you cover in one minute.

What is 0 over 0 slope? Would it be undefined or a zero slope





given points of (0,4),(5,4) what do i do


solve (3,1) (23) y = (4/5)x + 7/5



Write a 250word summary of the above problem. Your written work should include, but not necessarily be limited to, the following: an explanation of the problem, a review of the mathematical concepts involved, a critique of the method used to obtain the solution, and an interpretation of the answer. Your summary should be written in APA format, demonstrate proper use of the English language, and be mathematically precise.


an earthquake occurred at 9:40 am and started a tsunami in the ocean. it produced waves that traveled more than 540 ft/sec (370mph) and reached a height of 60 ft. If the period of the waves was 30 min or 1800 sec., estimate the length L between the crests.


crabon14 decays at a rate of 11.4%every 1000 years. a. write a formula for the quantity,Q, with an initial 200gram sample as a function of time t, in years b. How much of the 200 grams will remain after 1500 years

an aerobic class is being offered once a week for 6 weeks. the registration fee is $15 and the cost for each class attended is $10. write a function rule to describe the total cost of the class. Find a reasonable domain and range for the function.

how do i find the range of a function

What is the period of the wave motion for a wave with a frequency of 0.50kHz?

A roof is 12 feet high at its edge and rises to a height of 20 feet at a point 10 feet horizontally from the edge. what is the slope of the roof?

slope = 2; yintercept = 5 find the slopeintercept form

x intercept =3/8 and y intercept = 6


A straight road makes an angle of 15 degrees with the horiontal/ When the angle of elevation of the sun is 57 degrees, a vertical pole at the side of the road casts a shadow 75 feet long directly down the road, as shown in the figure. approximate the length of the pole.


the milk price is $3 and goes up to $5.50 what is the slope?

An airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. They report the angles of elevation as 11° and 25°. How high is the airplane?

susan` sbowling scores have a range of 20 points. Dan`s scores are each 10 points greater than Susan`s scores. Will Dan`s range be greater than, less than, or equal to Susan`s range?.


in 1974, there were 86,821 people from other countries who immigrated to the state of California. In 2004, the number of immigrants was 252,920. If the change in foreign immigration to California is considered to be linear, write an equation in slopeintercept form expressing the number of immigrants, y, in terms of the number of years after 1974, x.

A rocket tracking station has two telescopes A and B placed 1.1 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket from telescope B at the moment when both tracking stations are directly east of the rocket telescope A reports an angle of elevation of 26° and telescope B reports an angle of elevation of 48°?

a triangle has angle A=35 degrees and angle B=40 degrees and side a=3.67x10^3 meters. what are the lengths of sides b and c?

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 9 mi apart, to be 32° and 48°, as shown in the figure. Round your answers to the nearest tenth mile. (a) Find the distance of the plane from point A. (b) Find the elevation of the plane.

A 50 foot tall tree casts a shadow that is 40 feet long. Draw a picture on your scratch paper, including the "ray of sunshine" causing the shadow. Now, find the angle (in degrees rounded to tenths) at the top of your picture (the one made by the tree and the sunshine).

an airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplanr. They report the angles of elevation as 11 degrees and 25 degrees.how high is the airplane?

A company produces a product (#687) A company produces a product for $9.45 per unit, plus a fixed cost of $5200. The company sells the product for $15.80 per unit. a) determine a function, c(x), to represent the cost production x units b) determine a function, r(x) to represent the revenue from selling x units c) determine a fucntion to represent profit d) caculate break even point

A plane flies 6000 km in the air and the pilor sees two cities directly to the right of the plane. The angle from the plane of one city is 32 degrees and the other is 76 degrees. What is the distance between the two cities?

A vendor can sell 300 trees for $15 each. The trees cost the vendor $5 each to cut and deliver to sell. If the trees are sold at a higher price, then for each $1 increase in price, 12 fewer trees will be sold

an airplane is sighted at the same time by two ground observers who are 5 miles apart and both directly west of the airplane. they report the angles of elevation as 11 degrees and 25 degrees. how high is the airplane?

an airplane is sighted at the same time two ground observers who are 5 miles apart and both directly west of the airplane. the angles of elevation are 11 and 25. how high is the airplane.

three times the sine of a certain in angle is twice of the square of the cosine of the same angle.Find the angle?


"A ferris wheel has a radius of 25 m, and its centre is 26 m above the ground. It rotates once every 50 s. Suppose you get on at the bottom at t=0. Draw a graph showing how your height above the ground changes during the first two minutes. Write an equation for this function"

A 20ft ladeer is leaning against a wall. The foot of the ladder is 7 feet from the base of the wall. What is the angle of measure that the ladder forms with the ground?

I`m an italin student .i want to know how can i write the hypothesis of zero slopes. is it the rigth way : H:Bo=B1=0

A boat is sailing due east parallel to the shoreline at a speed of 10 miles per hour. At a given time the bearing to the light house is S 70 degrees W and 15 minutes later the bearing is S 63 degrees. Find the distance from the boat the the shoreline if the lighthouse is at the shoreline.

a yard stick, held vertically on a level surface, cast a show 1 foot 8 inches long. Find the tangent of the angle that the raise of the sun make with the horizontal.


In 8 days, a sample of Vanadium48 decays to 1/ squareroot of 2 of its original amount. Determine the halflife of Vanadium48.


write a function rule for the cost of buying bananas at $.39 a pound

A video sore charges $10 for a rental card plus $2 per rental

An advertising blimp hover over a stadium at an altitude of 125m. The pilot sights a tennis court at 8 degree angle of depressio. Find the ground distance in a straight line between the stadium and the tennis court.

An advertising blimp hover over a stadium at an altitude of 125m. The pilot sights a tennis court at 8 degree angle of depression. Find the ground distance in a straight line between the stadium and the tennis court.

Two guy wires from the top of a tower are anchored in the ground 35m apart and in direct line with the tower. If the wires make angles of 36.4 degrees and 23.7 degrees with the ground, what is the height of the tower?


what is the slope of a ladeder that reaches a height of 30 feet and is places 5 feet away from the wall?

Write an exponential function to model the situation. Then predict the value of the function after 5 years. A population of 450 animals that decreases at an annual rate of 19%.

plane traveling 80 miles south, 95 miles east what bearing should they go to reach ground

the coast of 7 dance lessons is $82 and the coast of 11 dance lessons is $122

A certain radioactive substance decays half of itself everyday. Initially, there are 10 grams. How much substance will be left after 8 days?

TWO PLANES LEAVE AN AIRPORT AT THE SAME TIME, ONE FLYING DUE TO EAST AT 600KM/H AND OTHER FLYING DUE NORTHWEST AT 400 KM/H HOW FAR APART ARE THEY TWO HOURS LATER?


A store charges a flat fee of $6.75 plus $1.75 for every poung to mail packages. Write an equation in intercept form relating the cost of mailing a package, c, to the number of poins, p, the package weighs. Find the price of mailing a 3 lb package.

A parallelogram has sides of lengths 3 and 5, and one angle is 50 degrees. Find the lenghts of the diagonals.

At a car company the salesmen make $2,000 per month in addion to 1/5 of their sales. the maximum payment in one month is $15,000. a) Write a simplified function representing an employees income in one month based on the value of their sales.(define x and f(x))

a sporting goods store sells about 200 pairs of running shoes each month when it charges $6 per pair. For each $1 increase in price, 2 fewer pairs are sold each month.

a ladder rests against a wall the top of the ladder reaches 15 feet up the wall, and makes an angle of 53 with the wall. how long is the ladder?


10. Liselle is flying her kite with 62 feet of string attached to the ground. She measures 5 feet of string from the ground to a point 4 feet high. How high is her kite?

THE ANGLE OF ELEVATION TO THE SUN IS 65 DEGREES. A BUILDING CASTS A SHADOW THAT IS 16 M LONG. WHAT IS THE HEIGHT OF THE BUILDING?


From the top of a barn 25 feet tall, you see a cat on the ground. The angle of depression of the cat is 40 degrees. How many feet, to the nearest foot, must the cat walk to reach the barn?


Using unit circle properties, find the value of tan (  11 [pi] / 6 ) .


The pentagon has 5 side each of them are 921 feet long. find the greatest straightline distance from one point on the outside of the building to another outside point (the lenght of a diagonal).

Using unit circle properties, find the value of tan (  11 pi / 6 )

A ski slope drops 40 feet for every horizontal 90


exponential growth and their examples

a pool is being drained at a constant rate. the amount of water is a function of the number of minutes the pool has been draining, as shown in the table, write a equation in slpe intercept form that represents the function. then find the amount of water in the pool after two and a half hours

you are going on a trip to the natural history museum. at 9:00 am, you leave for the museum, which is 120 miles away. at 10:15 am, you are 63 miles away from the museum. write an equation in slopeintercept form that gives the distance from the museum in terms of x, where x is the number of minutes since 9:00 am.


The number of recreational visits to national parks in the united states increases by about 9.3 million visits each year. In 1990 there were about 263 million visits. Write an equation to model the relationship between the number of visits and time in years. Let 90 correspond to 1990.



he has 50$ to spend. the movie costs 8$ per person. what is the range?

f(2)=7 and f(4)=10, find the slope of the function

mary beth is arranging a birthday party for her daughter.the pizza place has quoteda price of $180 for the first 20 and $12 per guest for each guest over 20.


Two airplanes leave an airport, and the angle between their flight paths is 40º. An hour later, one plane has traveled 300 miles while the other has traveled 200 miles. How far apart are the planes at this time?

y = 4x + 2; y = 2x + 1 ; y = 2x  3

nancu earns $200 per week plus 15% commission on the value of her sales. in the linear function representing nancu`s weekly earning, x represents the value of her sales, and y represents her total earnings for the week. what is the slope of this problem

In 1983, 57.5 % of students graduated in 5 or fewer years of study. In 1997, that number fell to 52.8%. whate was the rate of change for students within 5 year sfrom 1983 to 1997?

Perform each transformation on f(x)=IxI write transformed funcion,g(x) up 3 units

the short leg of a 30 degrees 60 dgrees and 90 degrees triangle is 7.4 meters long.find the perimeter

an airport parking lot charges an entry fee of $2.00 plus $2.50 for every hour that your car is parked. the total charge for parking is x hours is f(x)=2.5x+2. How will the graph of this function change if the entry fee is increased to $3.50? if the hourly rate is reduced to $2.25?

a website charges $12 to buy a hat and a shipping charge of $5 per order. find the cost of buying 7 hats

d) For the average motorist, name one value for g that would be inappropriate for this function’s purpose. Explain why you chose the number you did.

Find the variation constant and an equation of variation where y veries directly as y and x=60 whenx=6

find g(a1) when g(x) = 3x  5


a 62 inch tall person is 275 inches away from the base of a tree. using a clinometer, it shows a reading of 27 degrees. what is the height of a tree?



Two ships leave a port at 7:00 am. One travels at a bearing of N56 degrees West at 10 mph, and the other travels at a bearing of S65 degrees West at 14 mph. Approximate how far apart are the ships at 1:00 pm that day?

at 2 A.M. the tide is at 4 ft high and at 8:30 A.M. the tide is 12 ft high

fine the slope of the linear function X=2y6

A construction company charges $15 per hour for debris removal, plus a onetime fee for the use of a trash dumpster. Write the pointslope form of an equation to find the total fee y for any number of hours x.


Jack follows a 2200 calorie perday diet. He has 11 servings of bread and cereals, which average 140 calories each. Yesterday, he had a combined 9 servings of fruits and vegetables averaging 60 caloeries each. How many 180 calories servings of meat and milk did he have to complete his diet?


If a kid`s desk is 22 feet from the door and the principle is 70 inches tall, at what angle shouold the kid set his sling shot in order to hit him in the middle of his forehead, which is 2 inches below the top of his head?


A rocket tracking station has two telescopes A and B placed 1.6 miles apart. The telescopes lock onto a rocket and transmit their angles of elevation to a computer after a rocket launch. What is the distance to the rocket from telescope B at the moment when both tracking stations are directly east of the rocket telescope A reports an angle of elevation of 23 degrees and telescope B reports an angle of elevation of 49 degrees



if there are two candy and two children how much candy do each children get?

is a linear equation with an undefined slope a function

A bacteria culuture started with 8500 bacteria. In two hours, the number of bacteria had reached 9775. Find an expression for the number of bacteria t hours after it was first observed. Using your answer to (a), find the number of bacteria after 10 hours. When will the number of bacteria reach 4000?

A video store charges $10 for a rental card plus $2 per rental.


A water wheel with radius 2 m has 0.2 m submerged and rotates at 5 rev/min. Find the equation of the sine function describing the height above the water taking the point at which the wheel touches the water at t = 0.

a ship is sailing toward a small island 800 miles away. if the ship is 2 degrees of course, by how many miles will it miss he island

A ship is sailing toward a small island 800 miles away. If the ship is 2 degrees of course, by how many miles will it miss the island?

It costs $1.50 per day to place a oneline ad in teh classifieds plus a flat service fee. One da costs $3.50 and four days costs $8.

It costs $1.50 per day to place a oneline ad in the classifieds plus a flat service fee. One da costs $3.50 and four days costs $8.

A flashlight was focused on the mirror forming an angle of 80 degrees. The length of the light from the flashlight to the mirror was 8 meters and the lengthof the reflected light to the wall was 7 meters. Find the distance from the flashlight to the end of the reflected light.

As you walk on a straight level path toward a mountain the measure of the angle of elevation to the peak from one point is 33 degrees. From a point 1,000 feet closer, the angle of elevation is 35 degrees. How high is the mountain?

Four boys are playing with their marbles. Two boys have the same number of marbles and they both have 1 more marble than the 3rd boy. The 4th boy has 1 marble less than the 3rd boy. If all the number of marbles of each boy is multiplied, the product would be 18...


A plumber charged $110 for a threhour job and $160 for a fivehour job. At this rate, how much would he charge for an eighthour job?

b=3 (b to second power)2nd power

natalie who is 5ft tall walks away from a streetlight that is 12 ft high at a rate of 3ft per second. express the length of her shadow as a function of time


i need an example of a rational function equation


to find the distance from the house at A to the house at B, a surveyoor measures the anges BAC to be 40 degrees and then walks off a distance of 100 feet to C and measures the angle ACB to be 50 degrees. What is the distance from A to B?

Identify the domain and range of the relation: (5,0),(6,0),(7,6),(8,8),(8,10)

Ron is saving money for college. Each month he deposits 10% of his net income plus an additional $50 into a savings account. His net income, after taxes have been taken out, is 80% of his gross income. a. Write a composite function for the amount that Ron saves each month if his gross income is g. b. Find the amount that Ron saves in a month when his gross income is $2400

A ferris wheel has a radius of 30ft. A person gets on the ferris wheel and then the ferris wheel rotates 7pie/6 radians. How far above the ground is the person after the rotation?

The debate club needs $240 to attend a debate tournament. The club decides to sell cups of iced tea and lemonade at baseball games. Iced tea will be sold for $0.50/cup and lemonade will be sold for $0.80/cup.

Your are traveling home on a bus whose speed is 50 miles per hour. At noon, you are 200 miles away from home. Write an equation that models the distance y from home in terms of t, the number of hours since noon.

Grandpa Violente wishes to find the distance between two points A and B on the opposite side of the river. On his side of the river he locates two trees that are 472 feet apart at C and D. He measures the angles w=17, x=66, y=59 and z=20, as indicated. Determine the required distance A and B.

Mary invested $1400 in two mutual funds. One fund earned interest at 7% per year and the other earned interest at 8% per year. If she receives $104 in interest after one

An airplane flying on a straight line at a constant altitude was at a horizontal distance of 40 km from an airfield at an elevation of 30 degrees from an observer at the airfield. After another 6.4 minutes, its angle of elevation from the same point was 60 degrees. What was the planes`s speed in km/hr?

An airplane flying on a straight line at a constant altitude was at a horizontal distance of 40 km from an airfield at an elevation of 30 degrees from an observer at the airfield. After another 6.4 minutes, its angle of elevation from the same point was 60 degrees. What was the planes\`s speed in km/hr?

how many steps must stickman walk up to move to the right 3 units?

you are standing 30 meters from the base of a tree that is leaning 6 degrees vertical away from you. the angle of elevation from your feet to the top of the tree is 24 degrees. what is the height of the tree?

A construction company charges $15 per hour for debris removal, plus a onetime use of a trash dumpster. The total fee for 9 hours of service of service is $195.

below are the graphs of x=1 and y=7.Find the point at which the two graphs intersect

The school yearbook staff is purchasing a digital camera. Recently the staff received two ads in the mail. The ad for Store 1 states that all digital cameras are 25% off. The ad for Store 2 gives a $150 coupon to use when purchsing any digital camera. Assume that the lowest priced digital camera is $900. Write two equations that describes the prices at both stores.

In two minutes a plane descending at a constant angle of depression of 10.5 degrees travels 3800 m along its flight path. How much altitude has it lost?

To find the distance between two points A and B on opposite sides of a river, a surveyor measures out a base line AC that is 25 m long. He then measures angle A= 82 degree and angle C= 69 degree. Calculate the distance AB.

A baseball diamond is a square 90 feet on each side. The pitcher`s mound is 60. 5 feet from home plate. How far is it from the pitcher`s mound to first base?

A 600ft guy wire is attached to the top of a communications tower. If the wire makes an angle of 65degree with the ground,how tall is the communications tower?

a ship proceeds on a course of 300 for 2hrs at speed 15 knots .then it chnges course of 240 at 16 for 3hrs at this time how far is the ship from starting point


Ideal weight for someone who is 66 inches tall is 112 pounds and someone who is 66 inches tall is 136 lbs. Write an equation in slope intercept form

A tree growing on a hillside casts a 157ft shadow straight down the hill. Find the vertical height of the tree if relative to the horizontal, the hill slopes 11.0 and the angle of elevation of the sun is 42.

from the top of a 60 ft high bldg. the angle of elevation of the top of the vertical pole is 14 degrees. and of the bottom of the building the angle of elevation of the top of the pole is 28 degrees.. find a) height of the pole & b) the distance of the pole from the bldg

two rats, one male one female,


from the top of the building 60ft. high ,the angle of elevation of the top of a vertical pole is 14 degree.At the bottom of the building the angel of elevation of the top of the pole is 28 degree.Find the (a) the height of the pole and (b) the distance of the pole from the building.



find the slope. A 10 foot ladder leaning at a height of 8 feet against a wall.




Suppose one painter can paint the entire house in 12 hours, and the second painter takes 8 hours. How long would it take the two painters together to work the house?

Two rats were brought to an Island, where there are no any natural predators. The original female gives birth to 3 male and 3 female rats on January 1 and produces another liter (3 male & 3 female) every 40 days thereafter. Each born female will produce her first litter after 120 days of her birth and will continue producing every 40 days. Come up with general formula for the number of rats in one year.




evaluate the six trigonometric functions of the anle o

The cost of an ice cream sundae is given by the formula C(s)=1.25s+5.00. In this formula, C(s) represents the cost of the ice cream sundae and s is the number of scoops of ice cream. What does the slope represent?

Three ships a b and c are anchored in the ocean. the distance from a to b is 25.5 km, from b to c is 17.2 km and from c to a is 37.4 km. find the angle measurements of the triangle formed by the three ships.

find an equation of a line that passes through (13,17) and has a slope of zero


To service her car before a trip, Ms. Stein bought motor oil for $1.25 per quart and engine coolant for $2..50 a quart. Altogether she bought 10 quarts and spent $15. How many quarts of motor oil and coolant did Ms. Stein buy?

Write the equation in slopeintercept form of the line that has a slope of 5 and a yintercept of 2.

A clock pendulum completes one backandforth cycle every 2 seconds. The maximum mesure of the angle of the pendulum with the vertical is 12 degrees. a) Express the measure of the angle between the pendulum and the vertical as a function of time. Assume the relationship is a sine function. b) Draw a graph of the function for 0



An expedition starts at an altitude of 9056 ft and climbs at an average rate of 544 ft of elevation a day. Write an equation in slopeintercept form that describe`s the expedition`s climb.

An expedition starts at an altitude of 9056 ft and climbs at an average rate of 544 ft of elevation a day. Write an equation in slopeintercept form that describe\`s the expedition\`s climb.

a ski slope on a mountain has an angle of elevation of 25.2 degrees. the vertical height of the slope is 1808 feet. how long is the slope?

A tree cast a shadow that is 20 feet long. the angle of elevation of the sun is 29 degrees. How tall is the tree?

A piece of trash is caught on a paddle wheel. After watching for 2 seconds, you see the piece of trash at the top of the wheel. After 8 seconds you see the trash at the to of the wheel again.

Find a horizonal slope picture

The drama club sells 200lb of fruit to raise money. The fruit is sold in 5ib bags and 10lb bags

Suppose you give a salesperson $20 for a purchase. Write a function rule to express the amount if change a(c) that you receive as a function of the cost c.

a 20feet vertical pole casts a shadow of 32feet.what is the angle of elevation of the sun?

A wedding cake measures 2 feet high in the center, and the diameter of the bottom tier is 12 inches. What is the slope of the cake?

A 25 m tower standing vertically on a hillside casts a shadow down the hillside that is 27 m long. The angle at the tip of the shadow S, subtended by the tower is 26. What is the angle of elevation of the sun at S

An airplane is flying North at 500 mph when a wind of 20 mph comes up out of the East. What is the new speed and direction of the plane if no correction is made for the wind?

jacob has 50 dollars and spends 2.50 on hotdogs everyday for a week how much money does he have after one week

Two ships leave port on paths which form a 40` angle. The first ship is traveling at 25 km/hour, the second is traveling at 30 km/hour. Draw a diagram which shows the position of the two ships and their paths after 3 hours and solve for the distance between the two ships at this time.

The angle of depression from the top of the Smoketown Lighthouse 120ft above the surface of the water to a buoy is 10degrees. How far is the buoy from the lighthouse?

The number of trout in a lake was estimated to be 44.5 thousand in 1995. During the next 10 years, the trout population is expected to increase by about 3.2 thousand per year. Write an equation to model the trout population in any year between 1995 and 2005 where t is the number of years since 1995.


solve 5^3x1=500 for x to threesignificant digits


A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs2(3Ls) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long.

A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs2(3Ls) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long. wih answer

A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs2(3Ls) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long. a) If the deflection at the end of the board is 1 ft, find c b) Show that the deflection is .5 foot somewhere between s=6.5 and s=6.6

Liselle is flying her kite with 62 feet of string attached to the ground. She measures 5 feet of string from the ground to a point 4 feet high. How high is her kite?


a telephone company charges a fee of 29.99 per month for basic local service. A fee of 4.95 per month is added for customers wanting up to 500 minutes of long distance at .04 a minute.

polynomial functions related to economics


A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per camera for labor and materials. The cameras sell for $14 each. a. How many cameras must the company sell in one day to equal its daily costs? b. If the manufacturer can increase production by 50 cameras per day, what would their daily profit be?

adults $15 students $20 how much would it cost for 3 adults and 5 students

Cattle point is part of Victoria, B.C. Maynard Cove is 2.4 km from Cattle Point, on a bearing of 053 degrees. a sailboat leaves Cattle point on a bearing of 079 degrees. after sailing for 1.8 km the boat turns and heads directly to Maynard Cove, on a bearing of 008 degrees. a) What is the bearing of Cattle Point from Maynard Cove? b) Calculate the total distance the boat travels to get to maynard cove

a flagpole that is 6.6 yd tall casts a 30 ft shadow. a nearby tree casts a 45 ft shadow. what is the height of the tree?

Pizza Hut has a flat fee of $8.75 for a large pizza. And they charge $2.10 for each additional topping. If "x" is the $2.10. What is the "y"?

A ladder leans against a window in a twostory building. The window is 16 feet off the ground. The base of the ladder is 12 feet from the base of the building. How many feet long is the ladder?

What is the angle of an ant hill that is 18 inches high and has a base of 40 inches around

My mom has a cleaning business, She charge a flaterate of 50 and a 25 per room charge


a horizontal line passing through (5,8)

To find the length of the span of a proposed ski lift from A to B, a survey or measures the angle DAB to be 25 degrees and then walks off a distance of 1000ft to C and measures the angles ACB to 15 degrees. What is the distance from A to B?

Find cotangent if 5x3y=0 and x is less than or equal 0.

how do u know its has a zero slope?



the wheel of the car with a diameter of 50cm makes 750 revolution per minute . how fast is the car running in km/h.

Two families leave on a trip to visit friend in Burns, Oregon. one family, the Zolotoff`s, live in Newberg which is 290 miles from burns. the Zolotoff`s leave at 7:00am driving an avarage speed of 65 milies per hour. the second family, the Anderson`s also leave at 7:00 but they begin their journey from Mill City, and average 40 miles per hour. the distance from Mill City to Burns is 230 mils. Will the Zolotoff`s pass the Anderson`s before reaching burns? Ir they do, how long will it take untill they pass the Anderson`s and how far from burns will the families be?

A skier sees the top of a radio tower due south of him at at an angle of elevation of 32 degrees.He then skis on a bearing of 130 degrees for 560 m and finds himself due east of the tower. Calculate the height of the radio tower.

find to the nearest foot the height of a building that casts a shadow of 80 feet when the angle of elavation of the sun is 42

An advertiser goes to a printer and is charged $44 for 50 copies of one flyer and $59 for 241 copies of another flyer. The printer charges a fixed setup cost plus a charge for every copy of singlepage flyers. Find a function that describes the cost of a printing job, if x is the number of copies made. C(x)=


A helicopter 110 m from a person takes off vertically. Express the distance d from the person to the helicopter as a function of the height, f(h), of the helicopter.

calculate height when two angles of elevation are given

calculate height when two angles of elevation 42 degrees and 32 degrees are given

A ladder rests against a wall. the top of the ladder reaches 15 feet up the wall, and makes an angle of 53 with the ...

The wheels of a car have a 24in. diameter. When the car is being driven so that the wheels make 10 revolutions per second, how far with the car travel in one minute?

express the area of an equilateral triangle as a function of the length of aside.

A flagpole is situated on a hill that makes an angle of 18° with the horizontal. How tall is the flagpole if its shadow is 14 meters when the angle of elevation of the sun is 31°?