The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each
shaded part. Give your answer as a completely simplified exact value in terms of π (no approximations).
1 answer:
First compute the area of the square like this: 
There is two semi circles here, so the sum of the two white
spaces equate the area of a circle.
the radius of the circle is 9/2.
So compute the area of the like this:
And the area of the shaded region is the area of the square minus
the area of the two semi circles, like this:
We are done.
There is two semi circles here, so the sum of the two white
spaces equate the area of a circle.
the radius of the circle is 9/2.
So compute the area of the like this:
And the area of the shaded region is the area of the square minus
the area of the two semi circles, like this:
We are done.
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Answer:
- there are 4 complex solutions
- 3 real zeros and 2 complex zeros
Step-by-step explanation:
1. Descarte's rule of signs tells you there are 0 positive real roots and 0 or 2 negative real roots. (for positive x, signs are ++++ so have no changes; for negative x, signs are ++-+, so have 2 changes.) A graph shows no real roots.
2. There are 3 sign changes in the given polynomial, so 3 or 1 positive real roots. When the sign of x is changed, there are 2 sign changes, so 0 or 2 negative real roots. A graph shows 2 negative and one positive real root (for a total of 3), so the remaining 2 roots are complex.
