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anonymous
 one year ago
Let $ABCD$ be a square of side length 4. Let $M$ be on side $\overline{BC}$ such that $CM = 1$, and let $N$ be on side $\overline{AD}$ such that $DN = 1$. We draw the quartercircle centered at $A$. Find xy.
anonymous
 one year ago
Let $ABCD$ be a square of side length 4. Let $M$ be on side $\overline{BC}$ such that $CM = 1$, and let $N$ be on side $\overline{AD}$ such that $DN = 1$. We draw the quartercircle centered at $A$. Find xy.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So i know how to find the cuarter circle, and i know the samll rectangle is 4, but i cant figure out the white part of the quarter circle we remove...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0are you allowed to use calculus?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2is the answer \(4\pi4\) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no i cant use calculus @jayzdd and im supposed to write a proof so i dont have the answer @ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2let \(a\) be the area of unshaded region in quarter circle. then we have \(x+a = \frac{\pi 4^2}{4}\) \(y+a = 4\times 1\) subtract

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just for the fun of it , using integration $$ \large x= \large \int_{0}^{3}\sqrt{ 4^2  t^2}~dt \\~\\ \large y = \large \int_{3}^{4} \left( 4 \sqrt{ 4^2  t^2 } \right) ~dt $$ we see that if we subtract x  y, we get a nice expression $$ \large x  y = \large \int_{0}^{3}\sqrt{ 4^2  t^2}~dt  \int_{3}^{4}\left( 4 \sqrt{ 4^2  t^2 } \right) ~dt \\ \large = \large \int_{0}^{3}\sqrt{ 4^2  t^2}~dt  \int_{3}^{4} 4 ~ dt + \int_{3}^{4}\sqrt{ 4^2  t^2 } ~dt \\ ~\\ = \large \int_{0}^{4}\sqrt{ 4^2  t^2}~dt  4\cdot 1 \\ = \large \pi ~\frac{4^2}{4}  4 = 4\pi  4 $$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Emeyluv99 did you follow ganeshie's solution?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 thanks so much!, i feel so stupid now, it was staring me in the face! @jayzdd Yes, thanks for the calculus solution!

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Haha It is so simple yeah :)
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