Suppose f varies inversely with g and that f=48 when g=3. What is the value of f when g=12?
48 * 3 = 144
f * 12 = 144
To find the value of f when g=12, we can use the concept of inverse variation. Inverse variation states that if two variables, f and g, are inversely proportional, their product remains constant. Mathematically, this can be represented as:
f ∝ 1/g
Now, let's use the given information to determine the constant of variation. We know that when g=3, f=48, which implies:
48 = k * (1/3)
To solve for k, we can multiply both sides of the equation by 3:
3 * 48 = k
k = 144
Now that we have the constant of variation, we can use it to find f when g=12:
f = k * (1/g)
f = 144 * (1/12)
Simplifying this expression gives us:
f = 12
Therefore, when g=12, the value of f is 12.