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Trava [24]
4 years ago
5

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).

Mathematics
1 answer:
USPshnik [31]4 years ago
3 0

Answer:

  (81 -20.25π) cm²

Step-by-step explanation:

The area of the 9 cm square is ...

  (9 cm)² = 81 cm²

The area of the 9 cm circle is ...

  (π/4)(9 cm)² = 20.25π cm²

The blue shaded region is the difference of these areas, so is ...

  shaded area = (81 -20.25π) cm²

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Following are the solution to the given point:

Step-by-step explanation:

Please find the comp[lete question in the attached file.

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\bold{ \lim_{n \to \ \infty} (1+ \frac{r}{n})^{nt} =e^{rt}}

In point 1:

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In point 2:

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In point 3:

Its key thing to understand, which would be that you consider the limit n to\infty,  in which r and t were constants!  

=lim_{n \to \ \infty}  \ln (y) =  lim_{n \to \ \infty}  nt \ln(1+\frac{r}{n})\\\\=  lim_{n \to \ \infty} \frac{\ln(1+\frac{r}{n})}{\frac{1}{nt}}\\\\=  lim_{n \to \ \infty} \frac{\frac{-r}{\frac{n^2}{(1+\frac{r}{n})}}}{- \frac{1}{n^2t}}\\\\=  lim_{n \to \ \infty} \frac{\frac{rn^2t}{n^2}}{(1+\frac{r}{n})}\\\\=  lim_{n \to \ \infty} \frac{rt}{(1+\frac{r}{n})}\\\\= \frac{rt}{(1+\frac{r}{0})}\\\\=rt

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