Model Inverse and Joint Variation

Suppose f varies directly as g, and f varies inversely as h.
f = -12 when h = 4 and g = -3.
Find g when f = 28 and h = 8.

• 14

• -14

• 16

• -16

• direct variation
• inverse variation
• neither direct nor inverse variation

• direct variation
• inverse variation
• joint variation
• none of these

What type of variation does this scenario represent?
The outside temperature
and the number of layers of clothes you need to wear outside to feel comfortable 

• direct variation

• inverse variation

• joint variation

• none of these

What type of variation does this scenario represent?
You and some friends decide to buy 2 pizzas and split the cost evenly.
The number of friends who are sharing the cost of the pizzas
and the amount of money you pay for your share.

• direct variation

• inverse variation

• joint variation

• none of these

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

State what type of variation the equation represents.

• Direct

• Inverse

• Joint

• None

The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk is 3 feet, what is the volume of wood obtained from a tree that is 32 feet tall having a measurement of 4 feet around the trunk?

• 44.96 ft³

• 49.96 ft³

• 40.96 ft³

• 32.96 ft³

If x varies inversely as v, and x = 35 when v = 3, find x when v = 15.

• 7

• 9

• 5

• 21

The frequency of a vibrating string varies inversely as its length. A string 3 feet long vibrates 175 cycles per

second. Find the frequency of a 5 foot string.

• 105 cycles

• 291.7 cycles

• 2625 cycles

• 332 cycles