Question

The variable a is jointly proportional to the square of b and the cube of c. If a=306

when b=8
and c=7
, what is the value of a when b=4
and c=5
? Round your answer to two decimal places if necessary.

Answer 1

Explanation:

If a is jointly proportional to the square of b and the cube of c, we can write:

a = k b^2 c^3

where k is some constant of proportionality. We can solve for k using the values given:

306 = k 8^2 7^3

306 = k 3,136

k = 306 / 3,136 ≈ 0.0974

Now we can use this value of k to find a when b=4 and c=5:

a = k 4^2 5^3

a = 0.0974 * 16 * 125

a ≈ 194.79

Therefore, when b=4 and c=5, a is approximately 194.79. Rounded to two decimal places, we get:

a ≈ 194.79