Question

Let D={(x,y)∈R^2:−5≤x≤5 and 0≤y≤√(25−x^2)}. Then D


is the shape of a

Select one:

a. quarter circle in the second and first quadrant with radius 25.

b. semi-circle in the second and first quadrant with radius 5.

c. semi-circle in the second and first quadrant with radius 25.

d. quarter circle in the second and first quadrant with radius 5.

Answer 1

Lets consider a function $y= \sqrt{25-x^2}$. Then $y^2=25-x^2$ and $x^2+y^2=25$. It's a circle with the center in (0, 0) and radius 5.

As we have D={(x,y)∈R^2:−5≤x≤5 and 0≤y≤√(25−x^2)}, so our shape is semi-circle in the second and first quadrant with radius 5. The right answer is b.