Answer
a) The required value is $k=16$.
b) The resulting equation is $y=16{{x}^{2}}$.
c) The required value of $y=400$.
Work Step by Step
a)
As provided
$y=k{{x}^{2}}$
$x=2\ \text{ and }\ y=64$
Now, put the value of $x$ and $y$ in $y=k{{x}^{2}}$.
$\begin{align}
& y=k{{x}^{2}} \\
& 64=k{{\left( 2 \right)}^{2}} \\
& k=\frac{64}{4} \\
& k=16
\end{align}$
Therefore, the value of k is $16$.
b)
Consider the provided equation,
$y=k{{x}^{2}}$.
As, $k=16$
So,
$y=16{{x}^{2}}$
Therefore, the resulting equation is $y=16{{x}^{2}}$.
c)
Putting the value of $x=5$ in $y=16{{x}^{2}}$ , we get,
$\begin{align}
& y=16{{x}^{2}} \\
& y=16{{\left( 5 \right)}^{2}} \\
& y=16\times 25 \\
& y=400
\end{align}$
Therefore, the value of $y=400$ when $x=5$.
