Question

If y varies inversely as the square of x and y=2 when x=4.Find x when y=4/5

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

x = 2$\sqrt{10}$

Step-by-step explanation:

Given that y varies inversely as the square of x then the equation relating them is

y = $\frac{k}{x^2}$ ← k is the constant of variation

To find k use the condition y = 2 when x = 4

k = yx² = 2 × 4² = 2 × 16 = 32

y = $\frac{32}{x^2}$ ← equation of variation

When y = $\frac{4}{5}$, then

$\frac{4}{5}$ = $\frac{32}{x^2}$ ( cross- multiply )

4x² = 160 ( divide both sides by 4 )

x² = 40 ( take the square root of both sides )

x = $\sqrt{40}$ = $\sqrt{4(10)}$ = 2$\sqrt{10}$