SOLUTION: if y varies directly as the square of x, and y = 32, when x = 2, find y when x = 5

Question 119281: if y varies directly as the square of x, and y = 32, when x = 2, find y when x = 5
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Since y varies directly as the square of x we can write the equation:
.

.
where k is just a constant that makes the equation true. Notice in this equation that if x
gets bigger, then y must also get bigger. This is what is meant by "y varies directly as"
.
We can find the value of k because we are told that when x = 2, then y = 32. Substitute these
two values into the above equation and you get:
.

.
Square the 2 on the right side and the equation is then:
.

.
Solve for k by dividing both sides by 4 to get:
.

.
Now we can return to the original equation and substitute 8 for k to get:
.

.
This the complete equation that relates x to y for this problem.
.
To find the value of y when x is 5 all we need to do is to substitute 5 for x in the equation
to get:
.

.
Squaring the 5 on the right side results in:
.

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and the right side multiplies out to:
.

.
So the answer to your problem is that when x = 5, y equals 200.
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Hope this helps you to understand the problem.
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