Question

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

Answer 1

hnjmmm

Explanation:

m,,\

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Answer 2

x = 2
`√(10)`

Explanation:

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

y =
`(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 =
`(32)/(x^2)` ← equation of variation

When y =
`(4)/(5)`, then

`(4)/(5)` =
`(32)/(x^2)` ( cross- multiply )

4x² = 160 ( divide both sides by 4 )

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

x =
`√(40)` =
`√(4(10))` = 2
`√(10)`