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agasfer [191]
3 years ago
5

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

Mathematics
2 answers:
Mars2501 [29]3 years ago
6 0

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

fiasKO [112]3 years ago
6 0

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

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