Question

The function, f(x), describes the height of a dome on top of a building, where f(x) is the height from the base of the dome and x is the horizontal distance from where the dome meets the building.
The domain of the function is __ ≤ x ≤ ___

I will give brainiest If correct!!!!!!!!!!!

Answer 1

The height of the dome of the building is given by

$f(x)=2\sqrt{-x^2+10x}$. The quantity in the square root should be greater than or equal to 0. We need

$-x^2+10x\geq 0\\ x(10-x)\geq 0\\ 0\leq x\leq 10$.

So the domain is $0\leq x\leq 10$

Answer 2

Answer:

0 ≤ x ≤ 10

Step-by-step explanation:

We cannot take the square root of a negative number.  This means we cannot use negative numbers in this equation; this means the lower end is 0.

We can only use x values until the value of the negative square is greater than the value of 10 times the x.

10(1) = 10, which is greater than -(1(1)) = -1.

10(2) = 20, which is greater than -(2(2)) = -4.

10(3) = 30, which is greater than -(3(3)) = -9.

10(4) = 40, which is greater than -(4(4)) = -16.

10(5) = 50, which is greater than -(5(5)) = -25.

10(6) = 60, which is greater than -(6(6)) = -36.

10(7) = 70, which is greater than -(7(7)) = -49.

10(8) = 80, which is greater than -(8(8)) = -64.

10(9) = 90, which is greater than -(9(9)) = -81.

10(10) = 100, which is equal to -(10(10)) = -100.  This means this is the cutoff point for this function.