9.1 Inverse Variation

k = xy or

0

ky

xk

Ex 1Suppose that x and y vary inversely. If x = 7

and y = 4, write a function.

Ex 2

Direct, inverse, or neither?

x y

3 0.7

6 0.35

21 0.1

Ex 3

Direct, inverse, or neither?

x y

-2 6

-1.3 5

7 -4

Ex 4

Direct, inverse or neither?

x y

-2 5

4 -10

6 -15

Combined variation

y varies directly with the square of x: y = kx2

y varies inversely with the cube of x: y = k/x3

z varies jointly with x and y and inversely with w: z = kxy/w

z varies directly with x and inversely with the product of w and y: z = kx/wy

Ex 5Mass m of a moving object is related to its

kinetic energy k and its velocity v by m = 2k/v2. Describe the relationship using combined variation.

Ex 6

Describe using combined variation: 1 2

1( )

2A h b b

Ex 7

The area of an equilateral triangle varies directly with the square of the radius r of its circumscribed circle. The area of an equilateral triangle for which r =2 is 3 3 . Find the formula for the area A

of an equilateral triangle in terms of r.