Inverse Variations

Inverse Variations

Multiple Choice

If (4x⁵y⁷)ⁿ=64x¹⁵y²¹ what is the value of n?

• 2

• 3

• 10

• 16

Multiple Choice

The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 5 cm on a side is 250 g, find the weight of the liquid in a cubical container 3 cm on a side.

• 12 g

• 6 g

• 27 g

• 54 g

Multiple Choice

The amount of money earned on a job is directly proportional to the number of hours worked.  If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

• $2
• $308
• $1.57
• $265

Multiple Choice

If f varies jointly as q² and h, and f = 96 when q = 4 and h = 3, find q when f = 48 and h = 6.

• 4

• 2

• 6

• 3

Multiple Choice

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

Multiple Choice

a varies inversely as the square of b. If a is 1 when b is 3, find a when b is 5. 

• 0.36
• 9
• 25
• 36

Multiple Choice

The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

• 8 painters
• 10 painters
• 9 painters
• 11 painters