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

Answer 1

Since y is directly proportional to x^2, this means that \[y/x ^{2}=k\] or \[y=kx^2\] for some constant k. Thus, plugging in y=10, we see that \[x=\pm \sqrt{10/k}\] We shall just consider the positive value of x for simplicity. Halving x gives us \[0.5\sqrt{10/k}\] We now just plug this into x in our initial equation gives us \[k(.5\sqrt{10/k})^{2}=2.5\] Thus, the answer is 2.5. Note that this can also be seen from the fact that, since y is directly proportional to the square of x, if you divide x by 2, you divide y by 2^2=4.