Question

F varies directly as the square of g. It is found that g = 100 when

f = 200.
a. Find f when g = 61.5
b. Given that g > 0, find the exact value of g when f = 14

Answer 1

To find f and g in a direct variation relationship, plug the values into the equation and solve. When g = 61.5, f is approximately 152.64. When f = 14, g is approximately 0.0839.

Step-by-step explanation:

To solve this problem, we need to use the concept of direct variation.

When two variables vary directly, it means that they have a constant ratio. In this case, f varies directly as the square of g, so we can write the equation as f = kg^2, where k is the constant of variation.

To find f when g = 61.5, we can plug in the values into the equation.

f = (200 / 100^2) * 61.5^2

= 0.04032 * 3782.25

= 152.64.

To find g when f = 14, we can rearrange the equation to solve for g. f = kg^2, so g^2 = f / k.

Substituting the values, we get g^2 = 14 / (200 / 100^2)

= 0.007.

Taking the square root, we find that g is approximately 0.0839.