Question

Find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.

Answer 1

Answer: b.

Step-by-step explanation:

Based on the information given, you can write the following expression:

$y=\frac{k}{x^2}$

Where k is the the constant of variation

If y=4/63 when x=3, then you can substitute these values into the expression and solve for k:

$\frac{4}{63}=\frac{k}{3^2}\\k=9*\frac{4}{63}\\k=\frac{4}{7}$

Substitute k into the expression. Then the equation is:

$y=\frac{4}{7x^{2}}$

Substitute x=5  into the equation. Then, y is:

$y=\frac{4}{7(5)^{2}}=\frac{4}{175}}$

Answer 2

Answer:

Final answer is choice B.$y=\frac{4}{7x^2}$, $y(5)=\frac{4}{175}$

Step-by-step explanation:

Given that if y varies inversely as square of x, and $y=\frac{4}{63}$ when x=3, then we need to find out y-value when x=5.

We also need to find the constant of variation and the equation.

Since y varies inversely as square of x, so we can write equation

$y=\frac{k}{x^2}$

where k is constant of variation.

Plug given values $y=\frac{4}{63}$  and x=3

$y=\frac{k}{x^2}$

$\frac{4}{63} =\frac{k}{3^2}$

$\frac{4}{63} =\frac{k}{9}$

$\frac{4}{63}*9 =k$

$\frac{4}{7} =k$

Hence constant of variation is $k=\frac{4}{7}$

Now plug the value of k into formula

we get required equation as  $y=\frac{4}{7x^2}$

Now plug the value of x=5 into above formula

$y=\frac{4}{7x^2}$

$y=\frac{4}{7(5)^2}$

$y=\frac{4}{7(25)}$

$y=\frac{4}{175}$

Hence final answer is choice B.$y=\frac{4}{7x^2}$, $y(5)=\frac{4}{175}$