Algebra: Functions Word Problems
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Algebra: Functions WordProblems
A 25 m tower standing vertically
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...
Suppose you are at the gas station
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? ...
A ladder rests against a wall
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 ...
An airplane is sighted at the same time
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°...
A 10-ft ladder leans against a wall
A 10-ft 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 ...
A biologist is researching a newly-discovered species
A biologist is researching a newly-discovered 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.)
polynomial functions
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 pig at Papas Barn just had a litter of piglets
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 ...
A company produces a product
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 satellite, travelling in a circular orbit
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 ...
Beth owns her own candle making business
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 ...
Julio works as a quality control expert in a beverage factory
Julio works as a quality control expert in a beverage factory. The assembly line that he monitors produces about 20,000 bottles in a 24-hour period. Julio samples about 120 bottles an hour and rejects the line if he finds more than 1/50 of the sample to be ...
A rectangular shipping container
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 ...
The rat population in a major metropolitan city
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 ...
A new FDA diet claims that a person
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 ...
From the top of a lighthouse
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 ...
A diver stands at the very end of a diving board
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(3L-s) 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
A crow is on the ground
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 ...
Two ships leave port at 4 p.m.
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.?
Liselle is flying her kite
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 ...
A straight road makes an angle of 15 degrees
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 ...
Amelia sees a jet heading south away from her
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 ...
Mia has a temperature of 101 degrees
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 ...
Due to wind, a tree grew
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 ...
A ferris wheel is built such that
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/10t-π/2)
Find the angular speed in radians and the linear speed in feet?
Coast Guard Station Able is located
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 ...
Two observers,who are 2 miles apart
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 ...
SOHCAHTOA
The angle of elevation from point A to the top of a cliff is 38 ...
Greenshield`s Formula can be used
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
You need to determine the length
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 ...
A tree on a hillside casts a shadow
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 ...
The course for a bike race follows
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 ...
Three students in an outdoor pursuits program
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
A ship at sea, the Admiral, spots two other ships
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 ...
In 1995, the number of families
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 ...
The total sales for a new camera equipment store
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 straight road slopes upward
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.)
A pilot flies in a straight path
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 ...
To obtain a retail price, a dress shop
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)...
cosine
AB=1000 straight N and turn 127 degree to the ...
You are driving at a speed
You are driving at a speed of 55 miles per hour to your sisters house. At 1 pm, you are 150 miles from her ...
The cost of an ice cream sundae
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 ...
Zero Slope
m=2 for every increase of 1 year in ...
A plane flies 1.3 hours at 110 miles per hour
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 ...
Island A is 230 miles from island B
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 ...
Mary invested $1400 in two mutual funds
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 ...
Slope and Intercept
A linear cost function is C(x) = 5x + 250
What are the slope and the C intercept?
Two observers 200 feet apart
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 ...
A mass suspended from a spring
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 ...
The linear equation y=30x describes
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 ...
An airplane flying at an altitude of 6 miles
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...
It costs $1.50 per day
It costs $1.50 per day to place a one-line 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 ...
An antenna is atop of a 80 foot building
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 ...
X and Y are two lighthouses
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 ...
Two firetowers are 30 kilometers apart
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, ...
In high school baseball, the front of the pitcher`s rubber
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 ...
One afternoon your family goes out
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 ...
From a point on the ground
From a point on the ground, a person notices a 110-foot 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 ...
Natali is 5 feet 3 inches tall
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 ...
You are driving from Grand Rapids, Michigan
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 ...
