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If x varies as y , and x = 4 when y = 8, find y when x = 15.

If p is directly proportional to q , and p = 5 when q = 30, find q when p = 15.

If s varies as r ^{ 2 } , and s = 4 when r = 2, find s when r = 6.

If p is proportional to ( r – 2), and p = 18 when r = 8, find p when r = 11.

If a , b , c are positive and , then b is called the mean proportional or the geometric mean.

Work out the geometric mean between each pair of numbers.

4 and 9

10 and 8

Prove that ad = bc when

.

Prove that

Prove

when and c d .

Show a + b varies directly as c when a and b vary directly as c .

Show yz varies directly as y ^{ 2 } + z ^{ 2 } when y and z varies directly as x .

Use the given values to write an equation relating x and y , where x and y vary inversely. Then find y when x = 3.

x = 7, y = –3

x = 5, y = 1

The variable z varies jointly with the product of x and y .

Find an equation that relates the variables x , y , and z .

The given values are

Use the given values to write an equation relating x , y and z , where z varies jointly with x and y . Then find z when x = –3 and y = 5.

x = 3/4, y = (2/9), z = 6

If c varies jointly with m and n , and n varies directly with s , show that c varies jointly with m and s .

Suppose t varies jointly with a and b , and t = 90 when a = 5 and b = 6. Find t when a = 6 and b = 5.

State whether x and y show direct variation , inverse variation , or neither .

xy = 12

y = x – 2

x = 7 y

A paycheck varies directly with the number of hours worked.

Suppose the pay for 20 hours of work is $238.25.

What is the pay for 500 hours of work?

A pump empties a swimming pool in 60 minutes at the rate of 1500 L/min.

If the rate of pumping is 2500 L/min, how long does it take to empty the swimming pool?

The curved surface area of a cylinder varies jointly with the radius of its base and its height. Find the constant of variation.

The work W (in joules) done when lifting an object varies jointly with the mass m (in kg) of the object and the height h (in meters) that the object is lifted. The work done when a 140 kg object is lifted 1.6 meters is 2060.8 joules. Write an equation that relates W , m and h . How much work is done when lifting a 100 kg object 1.5 meters?

Suppose a single pane window with an area of 1 sq meter and a temperature difference of 1 Kelvin has a heat loss of 6.4 watts. What is the heat loss through a single–pane window with an area of 2.5 meters and a temperature difference of 20 Kelvin?

The distance that an object falls from rest varies directly as the square of the time it has fallen. If the object fell 2 ft during the first half second, how far did it fall during the next two seconds?