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Vesna [10]
3 years ago
7

Triangle ABC is rotated clockwise to create triangle A’B’C’. What is the angle of rotation?

Mathematics
1 answer:
lukranit [14]3 years ago
5 0

Answer:

90 degrees counterclockwise (ccw)

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Estimate the solution to the system of equations.<br><br> y=−2x−5 <br> y=2x−2 ​
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Answer:

(-3/4, -7/2)

Step-by-step explanation:

y= −2x − 5

y= 2x − 2

2y = -7

y = -7/2

y= 2x − 2

-7/2 = 2x - 2

2x = -3/2

x = -3/4

(x,y) = (-3/4, -7/2)

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\displaystyle h(x)=\int\limits_{1}^{\sqrt{x}}~\cfrac{z^2}{z^4+1}dz~\hspace{10em}\cfrac{dh}{du}\cdot \stackrel{chain~rule}{\cfrac{du}{dx}\implies \cfrac{dh}{dx}} \\\\[-0.35em] ~\dotfill\\\\ u=\sqrt{x}\implies \cfrac{du}{dx}=\cfrac{1}{2\sqrt{x}} \\\\[-0.35em] ~\dotfill

\cfrac{dh}{dx}\implies \displaystyle \cfrac{d}{du}\left[ \int\limits_{1}^{u}~\cfrac{z^2}{z^4+1}dz \right]\cdot \cfrac{1}{2\sqrt{x}}\implies \left[ \cfrac{u^2}{u^4+1} \right]\cdot \cfrac{1}{2\sqrt{x}} \\\\\\ \stackrel{substituting~back}{\left[ \cfrac{(\sqrt{x})^2}{(\sqrt{x})^4+1} \right]\cdot \cfrac{1}{2\sqrt{x}}}\implies \cfrac{x}{x^2+1}\cdot \cfrac{1}{2\sqrt{x}}\implies \cfrac{\sqrt{x}}{2x^2+2}

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