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]
