Question

If x varies directly as y and inversely as z and x = 12 when y = 9 and z = 16, find y when x = 9 and z = 24.​

Answer 1

Step-by-step explanation:

If x varies directly as y and inversely as z and x = 12 when y = 9 and z = 16, find y when x = 9 and z = 24.

I think answer is already given in question

please subscribe my channel vitality zdax

Answer 2

The value of y = 81/8

Given :

• x varies directly as y and inversely as z
• x = 12 when y = 9 and z = 16

To find :

The value of y when x = 9 and z = 24.

Solution :

Step 1 of 2 :

Find constant of variation

Here it is given that x varies directly as y and inversely as z

Thus we have

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

$\displaystyle \sf{ \implies x \propto \: \frac{ y }{z} }$

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

x = 12 when y = 9 and z = 16

This gives

$\displaystyle \sf{ \implies 12 = \: \frac{9k }{16} }$

$\displaystyle \sf{ \implies k = \frac{12 \times 16}{9} }$

Step 2 of 2 :

Find the value of y

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

$\displaystyle \sf{ \implies 9 = \: \frac{ky}{24} }$

$\displaystyle \sf{ \implies 9 = \: \frac{y}{24} } \times \frac{12 \times 16}{9}$

$\displaystyle \sf{ \implies 9 = \: \frac{8y}{9} }$

$\displaystyle \sf{ \implies y = \frac{81}{8} }$

The value of y = 81/8

━━━━━━━━━━━━━━━━

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