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k0ka [10]
3 years ago
5

Perimeter of triangle:20

Mathematics
1 answer:
EleoNora [17]3 years ago
4 0
What do you want me to do
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Eevaluate the expression 7x, if x=11.​
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4 years ago
Find the area of the region bounded by the curves y= sin^-1(x/6), y=0, and x=6 obtained by integrating with respect to y. Your w
Ahat [919]
Check the picture below.

let's check where the quadratic and x = 6 meet, bear in mind we're integrating by "y", so

\bf y=sin^{-1}\left( \frac{x}{6} \right)\implies sin(y)=\cfrac{x}{6}\implies \boxed{6sin(y)=x}
\\\\\\
\begin{cases}
6sin(y)=x\\
x=6\\
y=0\\
x=0\leftarrow y-axis
\end{cases}\\\\
-------------------------------\\\\
6sin(y)=6\implies sin(y)=\cfrac{6}{6}\implies sin(y)=1\implies \measuredangle \boxed{y=\frac{\pi }{2}}
\\\\\\
6sin(y)=0\implies sin(y)=0\implies \to  \boxed{\measuredangle y=0\ ,\ \pi }

\bf -------------------------------\\\\
\displaystyle \int\limits_{0}^{\frac{\pi }{2}}\ [6-6sin(y)]dy\implies \left. \cfrac{}{} 3y^2+6cos(y) \right]_{0}^{\frac{\pi }{2}}
\\\\\\
\left[ \cfrac{3\pi 2}{4}+0 \right]-[0+6]\implies \cfrac{3\pi^2}{4}-6\approx 1.4022033

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4 years ago
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