# Hotmath Practice Problems

Title:
Hotmath Algebra 2
Author:
Hotmath Team
Chapter:Rational Expressions, Equations and ExponentsSection:Direct, Inverse, and Joint Variation

Problem: 1

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

Problem: 3

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

Problem: 5

If s varies as r2, and s = 4 when r = 2, find s when r = 6.

Problem: 7

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

Problem: 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.

4 and 9

Problem: 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.

10 and 8

Problem: 13

Prove that ad = bc when

.

Problem: 15

Prove that

Problem: 17

Prove

.

Problem: 19

Prove

when and c d.

Problem: 21

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

Problem: 23

Show yzvaries directly as y2 + z2 when y and z varies directly as x.

Problem: 25

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

Problem: 27

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

Problem: 29

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

Problem: 31

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

Problem: 33

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

Problem: 35

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

Problem: 37

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.

Problem: 39

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

xy = 12

Problem: 41

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

y = x – 2

Problem: 43

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

Problem: 45

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

x = 7y

Problem: 47

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?

Problem: 49

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?

Problem: 51

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

Problem: 53

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?

Problem: 55

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?

Problem: 57

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?