Question

f x and y varies inversely as each other and x = 8 when y = 32. Find y when x = 16. *

Answer 1

Answer:

y= 16

Step-by-step explanation:

X ~1/y

X=k/y

k=x×y

k= 8×32

k= 256

According to given condition

k= x× y

y= k/X

y= 256/16

y=16

Answer 2

The value of y = 16

Given :

• x and y varies inversely as each other

• x = 8 when y = 32

To find :

The value of y when x = 16

Solution :

Step 1 of 3 :

Form the equation

Here it is given that x and y varies inversely as each other

$\displaystyle \sf{x \propto \: \frac{1}{y} }$

$\displaystyle \sf{ \implies \: x = \: \frac{k}{y} }$

$\displaystyle \sf{ \implies \: xy = k } \: \: \: \: - - - (1)$

Where k is a non zero real number

Step 2 of 3 :

Find the value of k

$\displaystyle \sf{ \implies \: xy = k } \: \: \: \: - - - (1)$

x = 8 when y = 32 gives

$\displaystyle \sf{ \implies \: (8 \times 32) = k }$

$\displaystyle \sf{ \implies \: k = 256 }$

Equation 1 gives

$\displaystyle \sf{ \implies \: xy = 256}$

Step 3 of 3 :

Find value of y when x = 16

$\displaystyle \sf{ \implies \: xy = 256}$

For x = 16 we have

$\displaystyle \sf{ \implies \: 16y = 256}$

$\displaystyle \sf{ \implies \: y = 16}$

Hence the required value of y = 16

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ if x varies directly as y the complete the following table

https://brainly.in/question/12901438

2. If 2x and y vary inversely and x = 10 when y = 25, find x when y = 50.

https://brainly.in/question/36601868