Question

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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Answer 1

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.