Inverse, Joint and Direct Variation

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

Determine the type of variation.

• Direct

• Inverse

• None

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

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

The time required to process a shipment of goods at Wal-Mart varies directly with the number of items in the shipment and inversely with the number of workers assigned. If 15,000 items can be processed by 8 workers in 10 hours, then how long would it take 12 workers to process 20,000 items?

• 6.5 hours

• 7.75 hours

• 8.9 hours

• 10.2 hours

HyVee found that the demand for Coke products varies inversely as the price of the product. When the price of a Coke product is $2.75, the weekly demand is 1250. Find the weekly demand if the price is raised to $4.00.

• 859.4

• 1818.2

• 1604.4

• 723.5

Determine the type of variation.

• Direct

• Inverse

• None

Is the given table a direct variation? If so, what is the constant of variation?

• Yes; 1/3

• Yes; 3

• Yes; 5

• No

Determine the type of variation:

• Direct

• Inverse

• Neither