Hotmath Practice Problems

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 r², 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.

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

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

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.

10 and 8

Prove that ad = bc when

.

Prove that

Prove

.

Prove

when and c d.

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

Show yzvaries directly as y² + z² 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

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 = 5, y = 1

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

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

xy = 12

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

y = x – 2

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

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

x = 7y

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?

The heat loss h (in watts) through a single–pane glass window varies jointly with A, the area (in square meters), and d, the difference between the temperatures on either side (in degrees Kelvin).

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?

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 r², 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.

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

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

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.

10 and 8

Prove that ad= bc when

.

Prove that

Prove

.

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 y² + z² 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

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 = 5, y = 1

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

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

xy = 12

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

y = x – 2

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

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

x = 7y

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?

The heat loss h (in watts) through a single–pane glass window varies jointly with A, the area (in square meters), and d, the difference between the temperatures on either side (in degrees Kelvin).

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?