Y is inversely proportional to a^3

When a = 2, y = 10

a is directly proportional to x

When x = 4, a = 20

Find a formula for y in terms of x.

Give your answer in its simplest form.

y = 0.64/x^3

Step-by-step explanation:

If y is inversely proportional to a^3, we can write the equation:

y * a^3 = k

Using a = 2 and y = 10, we have:

10 * 2^3 = k

k = 80

If a is directly proportional to x, we can write the equation:

a = c * x

Using x = 4 and a = 20, we have:

20 = c * 4

c = 5

Now, using the value of a = 5*x in the equation y * a^3 = 80, we have:

y * (5x) ^3 = 80

y * 125x3 = 80

y = 80 / (125x3) = 0.64/x^3