Question

Find the area of this region in the coordinate plane that satisfies both the inequalities:
𝑥^2 + 𝑦^2 ≤ 4 and 𝑥 + 𝑦 − 2 ≥ 0
A)2(𝜋– 1) B)2𝜋−1 C) 4(𝜋−2) D) 3𝜋+2 E)none

Answer 1

What good is it for the robot tutor just to state an answer, which btw is wrong
as is so often the case with the AI doing math ?

After making the sketch you should see that we want the segment of
the circle which lies totally in the first quadrant, and is above the line
x + y = 2
so we need (1/4) of the circle - the area of the triangle in quad I
= (1/4)π (2^2) = (1/2)(2)(2)
= π - 2

which is not the robot's answer, nor is it one of the given choices.
so E

Answer 2

of these

C) 4(𝜋−2)