Question

Please include an explanation.

"a" varies directly as the square of "b" and inversely as the cube of "c". If a=171 when b=8 and c=9, find a if b=9 and c=6. Round your answer to two decimal places if necessary.

Answer 1

730.42

Explanation:

a varies directly with the square of b, and inversely with the cube of c. Therefore:

a = k b² / c³

where k is the constant of proportionality.

a = 171 when b = 8 and c = 9. So the value of k is:

171 = k (8)² / (9)³

k ≈ 1947.8

So the value of a when b = 9 and c = 6 is:

a = 1947.8 (9)² / (6)³

a ≈ 730.42

Answer 2

a = 730.43

Explanation:

The formula for this type of problem is [ a = kb²/c³ ].

We are given a = 171, b = 8 and c = 9.

Solve for k.

171 = k(8)²/(9)³

k = 1947.80

Solve for a since we found k using b = 9 and c = 6.

a = (1947.80)(9)²/6³

a = 730.425

Round to the nearest hundredth.

730.425 → 730.43

Best of Luck!