Question

for the statement, find the constant of variation and the variation equationy varies inversely as the square of x; y=0.054 when x=5

Answer 1

Answer

Constant of variation is

k = 1.35

We can write the variation equation by inserting k = 1.35

y = (k/x²)

y = (1.35/x²)

Explanation

We are told that y varies inversely as the square of x, which can be written as

y ∝ (1/x²)

Introducing the constant of variation, k, we have

y ∝ (1/x²)

y = k(1/x²)

y = (k/x²)

We can then solve for k knowing that

y = 0.054 when x = 5

y = (k/x²)

0.054 = (k/5²)

(k/25) = 0.054

Multiply both sides by 25

(k/25) × 25 = 0.054 × 25

k = 1.35

Hope this Helps!!!