Question

If a varies directly as the square of b and a=6 when b=5 Find a when b=2

Answer 1

If a varies directly as the square of b, then, you can write the following equation:

`a=kb^2`

where k is the constant of proportionality.

a = 6 when b = 5. Use this information to find the value of k, as follow:

`\begin{gathered} 6=k(5)^2 \\ k=(6)/((5)^2)=(6)/(25) \end{gathered}`

Then, the equation that relates a and b becomes:

`a=(6)/(25)b^2`

Now, if b=2, you obtain for a:

`\begin{gathered} a=(6)/(25)(2)^2 \\ a=(6)/(25)\cdot4 \\ a=(24)/(25) \end{gathered}`

Hence, a = 24/25 when b = 2