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if y varies directly as the square if x. If y=27 when x=3, find x when y=81?

Sagot :

Answer:

x = 3[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Given y varies directly as x², then the equation relating them is

y = kx² ← k is the constant of variation

To find k use the condition y = 27 when x = 3 , then

27 = k × 3² = 9k ( divide both sides by 9 )

3 = k

y = 3x² ← equation of variation

When y = 81, then

81 = 3x² ( divide both sides by 3 )

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

x = [tex]\sqrt{27}[/tex] = [tex]\sqrt{9(3)}[/tex] = 3[tex]\sqrt{3}[/tex]

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