# Inverse, Joint, and Combined Variation

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Inverse, Joint, and Combined Variation
Objective: To find the constant of variation for many types of problems and to solve real world problems.

Inverse Variation Two variables, x and y, have an inverse-variation relationship if there is a nonzero number k such that xy = k, y = k/x. The constant of variation is k.

Example 1

Example 1

Example 1

Try This The variable y varies inversely as x, and y = 120 when x = Find the constant of variation and write an equation for the relationship. Then, find y when x is 1.5, 4.5, 8, 12.5, and 14.

Try This The variable y varies inversely as x, and y = 120 when x = Find the constant of variation and write an equation for the relationship. Then, find y when x is 1.5, 4.5, 8, 12.5, and 14.

Try This The variable y varies inversely as x, and y = 120 when x = Find the constant of variation and write an equation for the relationship. Then, find y when x is 1.5, 4.5, 8, 12.5, and 14.

Joint Variation If y = kxz, then y varies jointly as x and z, and the constant of variation is k.

Example 2

Example 2

Squared Variation If , where k is a nonzero constant, then y varies directly as the square of x. Many geometric relationships involve this type of variation, as show in the next example.

Example 3

Example 3

Example 3

Try This Write the formula for the area A, of a circle whose radius is r. Identify the type of variation and the constant of variation. Find the area of the circle when r is 1.5, 2.5, 3.5, 4.5.

Try This Write the formula for the area A, of a circle whose radius is r. Identify the type of variation and the constant of variation. Find the area of the circle when r is 1.5, 2.5, 3.5, 4.5. The constant of variation is

Try This Write the formula for the area A, of a circle whose radius is r. Identify the type of variation and the constant of variation. Find the area of the circle when r is 1.5, 2.5, 3.5, 4.5. The constant of variation is

Combined Variation

Example 4

Example 4

Example 4

Homework Page 486 13-27 odd

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