Question

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 simplest form

Answer 1

Answer:

y = 16/25x³

Step-by-step explanation:

If y is inversely proportional to a^3, this is expressed as;

y∝1/a³

y = k/a³ where k is the proportionality constant

Given a=2, y=10, then 10 = k/2³

k = 10*2³

k = 80

Substituting k = 80 back into the formula;

y = 80/a³ ............. 1

Similarly, if a is directly proportional to x, then a ∝ x i.e a = kx

If x=4, a=20 then;

20 = 4k

k = 20/4

k = 5

Substituting k = 5 back into the formula;

a = 5x ....... 2

Substitute equation 2 into 1;

y = 80/a³

y = 80/(5x)³

y = 80/125x³

y = 16/25x³

Hence the formula for y in terms of x is y = 16/25x³