Suppose z varies directly with x and inversely with the square of y. If z = 16 when x = 4 and y = 1 , what is z when x = 8 and y = 9 ?

Step-by-step explanation:

z

=

32 /27  

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

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

now, put y=a(n) and x=n,

hence, option d is correct.

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