Question

Write the function that models the relationship. z varies directly with x and inversely with y, and z = 10 when x = 5, y = 2

Answer 1

Step-by-step explanation:

z=3227

Explanation:

the initial statement here is z∝xy2

to convert to an equation multiply by k the constant

of variation

⇒z=kxy2

to find k use the given condition

z=18 when x=6 and y=2

z=kxy2⇒k=y2zx=4×186=12

equation is ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯∣∣∣22z=12xy222∣∣∣−−−−−−−−−−−−−

when x=8 and y=9

z=12×881=3227

Answer 2

Answer:

z = $\frac{4x}{y}$

Step-by-step explanation:

Given z varies directly with x and inversely with y then the equation relating them is

z = k × $\frac{x}{y}$ ← k is the constant of variation

To find k use the condition z = 10 when x = 5 and y = 2, then

10 = k × $\frac{5}{2}$ ( multiply both sides by 2 to clear the fraction

20 = 5k ( divide both sides by 5 )

4 = k

z = $\frac{4x}{y}$ ← equation of variation