Y is directly proportional to x^2. It is known that y=10 for a particular value of x. Find the value of y when the value of x is halved

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Y is directly proportional to x^2. It could be represented by the expression:

y α x^2

We can make it into an equality by inserting the proportionality constant, k.

y = kx^2

k would be constant for any value of y with a corresponding value of x. We solve the problem by this concept as follows:

y1 / (x1) ^2 = y2 / (x2) ^2

10 / (x1) ^2 = y2 / (x1/2) ^2

10/4 = y2

Therefore, when the value of x is halved, y is equal to 10/4.