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

`y = 3\, √(5)` when
`x = 9`.

Explanation:

The question states that
`y` is proportional to
`√(x)`. In other words, there is a constant
`a` (
`a \\e 0`) such that
`y = a\, √(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\, √(x)` and solve for
`a`:

`5 = a\, √(5)`.

`\begin{aligned}a &= (5)/(√(5)) \\ &= √(5)\end{aligned}`.

Thus,
`y = √(5)\, (√(x))` for all
`x \ge 0`.

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

`\begin{aligned} y &= √(5) \, (√(9)) \\ &= √(5) * 3 \\ &= 3\, √(5)\end{aligned}`.