Question

A rectangle is bounded by the x-axis and the semicircle
y = 36 − x2 (see figure). Write the area A of the rectangle as a function of x.
A = ___


Graphically determine the domain of the function.

A. 0 < x < 36

B.all real numbers


C. all real numbers except x = 6

D. 0 < x < 6

E. all real numbers except x = 36
Thanks!

Answer 1

I don't see any "figure below" , but I can surmise your figure shows a quarter circle in the first quadrant with a rectangle, whose base is along the x-axis, its height along the y-axis and it touches the quarter circle at (x,y)

Area = xy
= x√(36-x^2) or x(36-x^2)^(1/2)

for the domain, we have to make sure that the number under the √ does not become negative, so
0 < x < 6

Meaning the answer is D