Question

If y is proportional to the sqaure root of x and y equal x when x equal 5,evaluate y when x eqaul 9.​

Answer 1

Answer:

$y = 3\, \sqrt{5}$ when $x = 9$.

Step-by-step explanation:

The question states that $y$ is proportional to $\sqrt{x}$. In other words, there is a constant $a$ ($a \ne 0$) such that $y = a\, \sqrt{x}$ for all $x \ge 0$.

The question also states that $y = x$ when $x = 5$. Make use of this equality to find the value of $a$.

Since $x = 5$ and $y = x$, it must be true that $y = 5$. Substitute $x = 5\!$ and $y = 5\!$ into the equation $y = a\, \sqrt{x}$ and solve for $a$:

$5 = a\, \sqrt{5}$.

$\begin{aligned}a &= \frac{5}{\sqrt{5}} \\ &= \sqrt{5}\end{aligned}$.

Thus, $y = \sqrt{5}\, (\sqrt{x})$ for all $x \ge 0$.

Substitute in the value $x = 9$ to find the corresponding value of $y$:

$\begin{aligned} y &= \sqrt{5} \, (\sqrt{9}) \\ &= \sqrt{5} \times 3 \\ &= 3\, \sqrt{5}\end{aligned}$.