Direct, Inverse & Joint Variation Review

Direct

Are the given values direct, inverse, or neither?

Inverse

Are the given values direct, inverse, or neither?

Neither

Are the given values direct, inverse, or neither?

Increases

If x and y vary inversely, as x decreases, what happens to the value of y?

Decreases

If x and y vary inversely, as y increases, what happens to the value of x?

1/2

If y varies directly as x and inversely as w, and y = 55, x = 100 when w = 2, then find w when y = 44, x = 20.

12/7

If y varies directly as x and inversely as z, and y = 42, x = 14 when z = 7, then find x when y = 12, z = 3.

k=2; y = 40

If y varies directly with x, find the constant of variation if x = -7 when y = -14, then find y when x = 20.

2

If y varies inversely with x and x=-5 when y=-4.1, find x if y=10.25.

15

If y varies inversely with x, and x = 9 when y = 45, then find y when x = 27.

32

If y varies inversely with x, determine the constant of variation. (-4, -8) (5, 6.4)

-50

If y varies inversely with x, determine the constant of variation. (-5, 10) (1, -50) (2, -25)

k = 3800; y = 50

If y varies inversely with x, find the constant of variation if x = 38 when y = 100, then find y when x = 76.

-3.5

If y varies inversely with x, find y. (-7, 2) (4, y)

3

If y varies jointly as w and the square of z, and y = 75, w = 1/4 when z = 10, then find w when y = 36, z = 2.

16

If y varies jointly as x and the square of z, and y = 18, x = 10 when z = 3, then find y when x = 5, z = 4.

±5

If y varies jointly as x and z and inversely as the square of w, and y = 192, x = 2, z = 3 when w = 1/4, then find w when y = 4, x = 5, and z = 10.

8

If y varies jointly as x and z and inversely as the square of w, and y = 27, x = 15, z = 45 when w = 5, then find x when y = 32, z = 16, and w = 2.

3/2

If y varies jointly with x and z and inversely with a, and y = 18, x = 6, z = 3, when a = 3 then find y when x = 2, z = 7, and a = 28

6

If y varies jointly with x and z and inversely with w, and y = 15, x = 4, z = 25, when w = 20, then find w when x, y, and z all equal 2.

45

If y varies jointly with x and z, and y = 18, x = 3, when z = 2, then find y when x = 5 and z = 3.

k = 3/4; y = 36

If y varies jointly with x and z, find the constant of variation if y = 6, x = 4, and z = 2 then find y when x = 6 and z = 8.

Direct

Is the equation direct, inverse or neither?

Inverse

Is the equation direct, inverse or neither?

Neither

Is the equation direct, inverse or neither?

Direct

Is the graph direct, inverse, or neither?

Inverse

Is the graph direct, inverse, or neither?

Neither

Is the graph direct, inverse, or neither?

1000

The number of boxes that a warehouse can store varies inversely with the average size of the box. A warehouse can store 3000 boxes when the average size of a box is 2 cubic meters. If the box size is reduced by 25%, how many more boxes can the warehouse store?

20

The number of hours needed to assemble computers varies directly with the number of computers. If 12 computers can be assembled in 9 hours, how many computers can be assembled in 15 hours?

75

The number of revolutions made by a tire traveling over a fixed distance varies inversely with the radius of the tire. A 12-inch radius tire makes 100 revolutions to travel a certain distance. How many revolutions would a 16-inch radius tire require to travel the same distance?

12

The volume, V, of a gas kept at a constant temperature varies inversely with the pressure, p. If the pressure is 24 pounds per square inch, the volume is 15 cubic feet. What will the volume be when the pressure is 30 pounds per square inch?

-128

y varies inversely with x. If y = 40 when x = 16, find x when y = -5

-5.6

y varies inversely with x. If y = 7 when x = -4, find y when x = 5