Question

Y is inversely proportional to the square root of x if y=3 when x=25 find y when x is 9

Answer 1

Answer:

$y=5$

Step-by-step explanation:

$\textsf{If }y \textsf{ is \underline{inversely proportional} to the square root of }x, \textsf{ then}:$

$y \propto\dfrac{1}{\sqrt{x}} \implies y=\dfrac{k}{\sqrt{x}}\quad \textsf{(where k is some constant)}$

$\textsf{When }x=25, y = 3:$

$\implies 3=\dfrac{k}{\sqrt{25}}$

$\implies 3=\dfrac{k}{5}$

$\implies k=15$

Inputting the found value of k into the equation:

$\implies y=\dfrac{15}{\sqrt{x}}$

To find the value of y when x is 9, substitute x = 9 into the found equation:

$\implies y=\dfrac{15}{\sqrt{9}}$

$\implies y=\dfrac{15}{3}$

$\implies y=5$