Region q, shown here, is defined by (x-6)^2+(y-4)^2 \leq 100 ,(x−6) 2 +(y−4) 2 ≤100, y \geq 0, \text{ and } x \geq 0.y≥0, and x≥0.
Answers
Answer:
Step-by-step explanation:
This would be a very hard area to calculate directly. Fortunately, the question mentions the word "approximate," and the ranges in the answer choices are rather large. We can use rough approximation here and we will be OK.
The circle has a radius of r = 10. This means
A=\pi r^2=100\pi \approx 314A=πr2
=100π≈314
Part of the shaded area is the upper right quarter of the circle:
That has an area of
A1 = 314/4 = 78.5
We can approximate the areas below and to the right of this as rectangles. The lower rectangle has a height of exactly 4, and a width of approximately 15:
This leave a little extra in the curved part on the right, but that's OK. We'll just remember that this estimation is a little on the low side. This area is:
A2 = 4*15 = 60
The rectangle to the left of the quarter circle has a width of exactly 6, and height that goes from y = 4 to the y-intercept, y = 12:
This has an area of
A3 = 6*8 = 48
Again, this rectangle excludes a chunk of curved area above it. We could fit a little triangle, with a base of b = 6 and height of h = 2. The area of this triangle, 6, would account for much of that curved area.
Add all this up:
78.5 + 60 + 48 + 6 = 192.5