Question

Y varies directly as x and inversely as the square of z. y=36 when x=75 and z=5. Find y when x=2 and z=8.

Answer 1

Answer:

${\boxed{y = 0.375}}$

Step-by-step explanation:

We are given that y varies directly as x and inversely as the square of z.

$y  \propto \: x$

$y \propto \dfrac{1}{ {z}^{2} }$

$y  = k \dfrac{x}{ {z}^{2} }$

where,

k is constant of proportionality

Let's solve for k:

If y = 36, x = 75 and z = 5.

$36  = k \dfrac{75}{ {(5)}^{2} }$

$36  = k \dfrac{75}{25}$

$36 = k \times 3$

$k =  \dfrac{36}{3}$

$k = 12$

Now using the value of k, we can find the value of y:

$y  = k \dfrac{x}{ {z}^{2} }$

To solve for y, substitute k = 12, x = 2 and z = 8

$y  = 12 \dfrac{2}{ {(8)}^{2} }$

$y  = 12 \dfrac{2}{ 64}$

$y  = \dfrac{24}{ 64}$

$y  = 0.375$

Therefore, when  x = 2 and z = 8  the value of y is 0.375.