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:
z = [tex]\frac{4x}{y}[/tex]
Step-by-step explanation:
Given z varies directly with x and inversely with y then the equation relating them is
z = k × [tex]\frac{x}{y}[/tex] ← k is the constant of variation
To find k use the condition z = 10 when x = 5 and y = 2, then
10 = k × [tex]\frac{5}{2}[/tex] ( multiply both sides by 2 to clear the fraction
20 = 5k ( divide both sides by 5 )
4 = k
z = [tex]\frac{4x}{y}[/tex] ← equation of variation
