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y is inversely proportional to square of x when y=10 and x=3 find value of y when x=1/2

Sagot :

Answer:

y = 360

Step-by-step explanation:

Given y is inversely proportional to x² then the equation relating them is

y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of proportion

To find k use the condition y = 10 when x = 3 , then

10 = [tex]\frac{k}{3^2}[/tex] = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )

90 = k

y = [tex]\frac{90}{x^2}[/tex] ← equation of proportion

When x = [tex]\frac{1}{2}[/tex] , then

y = [tex]\frac{90}{(\frac{1}{2})^2 }[/tex] = [tex]\frac{90}{\frac{1}{4} }[/tex] = 90 × 4 = 360

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