Question

Suppose z varies directly with x and inversely with the square of y. If z = 12 when x what is z when x = 7 and y = 8?

what is z?

Answer 1

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