<< Chapter < Page Chapter >> Page >

y varies jointly as the square of x and of z and inversely as the square root of w and of t  . When x = 2 , z = 3 , w = 16 , and t = 3 , then y = 1. Find y when x = 3 , z = 2 ,   w = 36 , and t = 5.

Got questions? Get instant answers now!

Technology

For the following exercises, use a calculator to graph the equation implied by the given variation.

y varies directly with the square of x and when x = 2 ,   y = 3.

y = 3 4 x 2

Graph of y=3/4(x^2).
Got questions? Get instant answers now!

y varies directly as the cube of x and when x = 2 ,   y = 4.

Got questions? Get instant answers now!

y varies directly as the square root of x and when x = 36 ,   y = 2.

y = 1 3 x

Graph of y=1/3sqrt(x).
Got questions? Get instant answers now!

y varies inversely with x and when x = 6 ,   y = 2.

Got questions? Get instant answers now!

y varies inversely as the square of x and when x = 1 ,   y = 4.

y = 4 x 2

Graph of y=4/(x^2).
Got questions? Get instant answers now!

Extensions

For the following exercises, use Kepler’s Law, which states that the square of the time, T , required for a planet to orbit the Sun varies directly with the cube of the mean distance, a , that the planet is from the Sun.

Using Earth’s time of 1 year and mean distance of 93 million miles, find the equation relating T and a .

Got questions? Get instant answers now!

Use the result from the previous exercise to determine the time required for Mars to orbit the Sun if its mean distance is 142 million miles.

1.89 years

Got questions? Get instant answers now!

Using Earth’s distance of 150 million kilometers, find the equation relating T and a .

Got questions? Get instant answers now!

Use the result from the previous exercise to determine the time required for Venus to orbit the Sun if its mean distance is 108 million kilometers.

0.61 years

Got questions? Get instant answers now!

Using Earth’s distance of 1 astronomical unit (A.U.), determine the time for Saturn to orbit the Sun if its mean distance is 9.54 A.U.

Got questions? Get instant answers now!

Real-world applications

For the following exercises, use the given information to answer the questions.

The distance s that an object falls varies directly with the square of the time, t , of the fall. If an object falls 16 feet in one se c ond, how long for it to fall 144 feet?

3 seconds

Got questions? Get instant answers now!

The velocity v of a falling object varies directly to the time, t , of the fall. If after 2 seconds, the velocity of the object is 64 feet per second, what is the velocity after 5 seconds?

Got questions? Get instant answers now!

The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 24 inches long and vibrates 128 times per second, what is the length of a string that vibrates 64 times per second?

48 inches

Got questions? Get instant answers now!

The volume of a gas held at constant temperature varies indirectly as the pressure of the gas. If the volume of a gas is 1200 cubic centimeters when the pressure is 200 millimeters of mercury, what is the volume when the pressure is 300 millimeters of mercury?

Got questions? Get instant answers now!

The weight of an object above the surface of Earth varies inversely with the square of the distance from the center of Earth. If a body weighs 50 pounds when it is 3960 miles from Earth’s center, what would it weigh it were 3970 miles from Earth’s center?

49.75 pounds

Got questions? Get instant answers now!

The intensity of light measured in foot-candles varies inversely with the square of the distance from the light source. Suppose the intensity of a light bulb is 0.08 foot-candles at a distance of 3 meters. Find the intensity level at 8 meters.

Got questions? Get instant answers now!

The current in a circuit varies inversely with its resistance measured in ohms. When the current in a circuit is 40 amperes, the resistance is 10 ohms. Find the current if the resistance is 12 ohms.

33.33 amperes

Got questions? Get instant answers now!

Questions & Answers

0.037 than find sin and tan?
Jon Reply
cos24/25 then find sin and tan
Deepak Reply
tan20?×tan40?×tan80?
Santosh Reply
At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?
Kimberly Reply
-3 and -2
Julberte Reply
tan(?cosA)=cot(?sinA) then prove cos(A-?/4)=1/2?2
Chirag Reply
tan(pi.cosA)=cot(?sinA) then prove cos(A-?/4)=1/2?2
Chirag Reply
sin x(1+tan x)+cos x(1+cot x) = sec x +cosec
Ankit Reply
let p(x)xq
Sophie Reply
To the nearest whole number, what was the initial population in the culture?
Cheyenne Reply
do posible if one line is parallel
Fran Reply
The length is one inch more than the width, which is one inch more than the height. The volume is 268.125 cubic inches.
Vamprincess Reply
Using Earth’s time of 1 year and mean distance of 93 million miles, find the equation relating ?T??T? and ?a.?
James Reply
cos(x-45)°=Sin x ;x=?
Samaresh Reply
10-n ft
Nalin Reply
Practice Key Terms 7

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask