Question

a varies directly as b and inversely as the square of c. If a=113 when b=7 and c=8, find a if b=5 and c=3. Round your answer to two decimal places if necessary.

Answer 1

To find a when b=5 and c=3 in a equation where a varies directly as b and inversely as the square of c, substitute the values into the equation using the constant of variation.

Step-by-step explanation:

Given that a varies directly as b and inversely as the square of c, we can write the equation as a = k(b/c²), where k is the constant of variation.

To find the value of k, we can substitute the given values of a, b, and c into the equation. When a = 113, b = 7, and c = 8, we have: 113 = k(7/8²).

Solving for k, we get k = 113(8²/7) = 128.51.

Now, we can use the value of k to find a when b = 5 and c = 3. Substituting the values into the equation, we have: a = 128.51(5/3²) = 113.89.