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Variable y varies directly with x2, and y = 96 when x = 4.


What is the value of y when x = 2?


y =_________


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Variable y varies directly with x2, and y = 180 when x = 6.


Enter the constant of variation in the quadratic variation equation?



y = ________x2


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Verified Answer :

nobrains

Direct variation is y = kx, where k is the constant of variation.

 But now it says y varies directly with x2 (or 2x), so now the x in the equation is 2x.


The equation is y = k(2x)

 Now you find k.

y = 96 when x = 4.

(96) = k(24)

96 = k(8)

k = 12

 
The equation is now y = 12(2x)

To find the value of y when x=2, plug 2 into the equation you made.
y = 12(22)
y = 48
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Now it's with a "quadratic variation," which is the same thing except x is squared.

The equation is y = kx^2

 
But y varies directly with x2 (same thing as 2x), so now it's y = k(2x)^2.

 
Now you find k by substituting y and x values that were given.

y = 180 when x = 6

(180) = k(2*6)^2

180 = k(12)^2

180 = k(144)

k = 1.25

k, 1.25, is the constant of variation.

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