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If p varies inversely as q^2, and p=4 when q=1/2, find p when q=3/2.

Sagot :

skylarbeard801

if p varies Inversely as q.2, AND P=4 WHEN q=1\2, find p when q=3\2.

Answer:

p = [tex]\frac{4}{9}[/tex]

Step-by-step explanation:

Given p varies inversely as q² then the equation relating them is

p = [tex]\frac{k}{q^2}[/tex] ← k is the constant of variation

To find k use the condition p = 4 when q = [tex]\frac{1}{2}[/tex] , that is

4 = [tex]\frac{1}{(\frac{1}{2}) ^{2} }[/tex] = [tex]\frac{1}{\frac{1}{4} }[/tex] ( multiply both sides by [tex]\frac{1}{4}[/tex] )

1 = k

p = [tex]\frac{1}{q^2}[/tex] ← equation of variation

When q = [tex]\frac{3}{2}[/tex] , then

p = [tex]\frac{1}{(\frac{3}{2})^2 }[/tex] = [tex]\frac{1}{\frac{9}{4} }[/tex] = [tex]\frac{4}{9}[/tex]

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