Question

QUESTION 7

If y varies inversely with,
square root|x^2 + 2

(i) Write an equation involving y, square root|x^2 + 2 and a constant of proportionality k.

(ii) Given that y = 3, When x = 2, find the value of the constant of proportionality k. Leave your answer in surd form.

(iii) Hence calculate the value of y when x = 5. Express your answer in simplified surd form.

Answer 1

(i) $y=\frac{k}{\sqrt{x^2+2}}$

(ii) $3=\frac{k}{\sqrt{2^2+2}}$, $k=3\sqrt{6}$

(iii) $y(5)=\frac{3\sqrt{6}}{\sqrt{5^2+2}}=\sqrt{2}$