Variation question, URGENT

Question

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

Hello, Alexis,

I started with the equation a=b²/c³ and then found the value of a with b=8 and c=9, which we know is equal to 171. The calculation results in avery small number, 0.08779, which shouldn't have surprised us since we have a much smaller number on top (8²) than on bottom (9³). That means we need to multply the expression with a coefficient that brings 0.08779 to 171. I do the with (171/0.08779) or 1947.80. The expression then becomes c = (1947.80)*(b²/c³).

The new values of b and c yield a vaue of a of 730.42.

Not very nice numbers, so it's either wrong or simply unsatifying.

Bob

Answer 2

2 3

a = kb / c

2 3

171 = k (8) / (9)

171 = k (64)/729

171 * 729 / 64 = k

1947.8 = k

2 3

a = 1947.8 * (9) / (6) = 730.43