Question

If r is inversely proportional to x² and r = 4 when x = 4 Find the formula for r in terms of x​

Answer 1

If r is inversely proportional to x², then we can represent this relationship as:

r = k / x²

where k is the constant of proportionality. We are given that r = 4 when x = 4. Let's use this information to find the value of k:

4 = k / (4²)

4 = k / 16

k = 4 × 16 = 64

Now that we have the value of k, we can write the formula for r in terms of x:

r = 64 / x²

Answer 2

r =
`(64)/(x^2)`

Explanation:

given that r is inversely proportional to x² then the equation relating them is

r =
`(k)/(x^2)` ← k is the constant of proportion

to find k use the condition r = 4 when x = 4

4 =
`(k)/(4^2)` =
`(k)/(16)` ( multiply both sides by 16 )

64 = k

r =
`(64)/(x^2)` ← equation of proportion