Direct Joint Combined Variation

Suppose y varies directly as x.
If  y = 22.5 when x = 15, find y when x = 20.

• 1.5

• 337.5

• 30

• 16.875

Suppose y varies directly as x, and y=39 when x=3.  Find the value of y when x=2.

• 26

• 3

• 58.5

• 2

Suppose y varies jointly as x & z. 
If y = -180 when z = 15
and x = -3,
then find y when x = 7 and z = -5.

• -140

• 140

• -4

• 4

Suppose p varies directly as r, and p varies inversely as t.
t = 20 when p = 4 and r = 2.
Find t when r = 10 and p = -5.

• 80

• -80

• 4

• -20

The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm)) and the cube of the diameter. If the shaft of a certain material 3 inches in diameter can transmit 45 hp at 100 rpm, what must the diameter be in order to transmit 60 hp at 150 rpm?

• 24

What type of variation is represented by this equation?

• Direct

• Inverse

• Joint

• None

• 12

• 24

• 36

• 48

A type of variation that involves 3 or more quantities that may vary directly.

• Direct Variation

• Inverse Variation

• Joint Variation

• Combined Variation

Y varies directly as x. If y = 12 when x = 15, what is y when x = 20?

• 4/5

• 17

• 16

• 25

What type of variation does this scenario represent?
The grade you earn in a class
and the number of assignments you complete
and the number of hours you study

• direct variation

• inverse variation

• joint variation

• none of these