If x varies inversely as the square of y and if x=3 when y=-1, what is the value of x when y =3

Question

asked Oct 27, 2022 201k views

1 Answer

Daniel Rosenwasser · Answer 1 · 2022-11-01T02:56:34+0000

Answer:

would be
(1/3) when
y = 3 .

Explanation:

The question states that
varies "inversely" as
y^2 . In other words, there is a non-zero number
(a constant) such that:

$\displaystyle x = (a)/(y^2)$ .

The challenging part is to find the value of
in this equation.

Given that
x = 3 when
y = -1 , replace the
in this equation with
and
with
(-1) . This equation should still be valid:

$\displaystyle 3 = (a)/((-1)^(2))$ .

Solve for
:

a = 3 * (-1)^2 = 3 .

Hence, the relation between
and
becomes:

$\displaystyle x = (3)/(y^2)$ .

Find the value of
when
y = 3 by replacing the
in this equation with
.

$\displaystyle x = (3)/(3^2) = (1)/(3)$ .

In other words, the value of
would be
$\displaystyle (1)/(3)$ when
y = 3 .