Question

Find a formula for y in terms of x when y is inversely proportional to a, a = 2 when y = 10, and a is directly proportional to x, with a = 20 when x = 4. Provide your answer in its simplest form.

Answer 1

To find the formula for y in terms of x when y is inversely proportional to a and a is directly proportional to x, we combine the two proportionalities. The formula for y in terms of x is y = 5/x.

Step-by-step explanation:

To find the formula for y in terms of x when y is inversely proportional to a and a is directly proportional to x, we need to combine the two proportionalities. Let's start by writing the proportionality equations:

y ∝ 1/a

a ∝ x

We can rewrite the second equation as a = kx, where k is the constant of proportionality. Substituting this into the first equation, we get y ∝ 1/kx. To find the exact formula for y in terms of x, we need to determine the value of k. Using the given values, we have a = 20 when x = 4, so k = 20/4 = 5.

Therefore, the formula for y in terms of x is y = 5/x.