Question

Suppose z varies directly as the square of x and inversely as y. If z = 2 when x = ½ and y = ⅓, find z when x = 3 and y = 4.

Answer 1

Answer:

32/27

Step-by-step explanation:

the initial statement here is  

z

∝

x

y

2

 

to convert to an equation multiply by k the constant

of variation

⇒

z

=

k

x

y

2

to find k use the given condition

z

=

18

when  

x

=

6

and  

y

=

2

z

=

k

x

y

2

⇒

k

=

y

2

z

x

=

4

×

18

6

=

12

equation is  

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

∣

∣

∣

2

2

z

=

12

x

y

2

2

2

∣

∣

∣

−−−−−−−−−−−−−  

when  

x

=

8

and  

y

=

9

z

=

12

×

8

81

=

32

27