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2 years ago

Find the missing angle. 90 - 43 y = [???]

Mathematics

1 answer:

Stella [2.4K]2 years ago

6 0

Step-by-step explanation:

Here. ...the sum of interior angle of triangle is 180° so...

90° + 43° + y = 180°.

133° + y = 180°

y = 180° - 133°

y = 47°

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SCORPION-xisa [38]

I don't see a square root sign anywhere, so I'll assume the integral is

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Now in the integral, substitute

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so that

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Under this change of variables, we have

$7^2-(6-x)^2=7^2-7^2\sin^2t=7^2(1-\sin^2t)=7^2\cos^2t$

so that

$\displaystyle\int\sqrt{13+12x-x^2}\,\mathrm dx=-7\int\sqrt{7^2\cos^2t}\,\cos t\,\mathrm dt=-49\int|\cos t|\cos t\,\mathrm dt$

Under the right conditions, namely that cos(<em>t</em>) > 0, we can further reduce the integrand to

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$\displaystyle-49\int|\cos t|\cos t\,\mathrm dt=-\frac{49}2\int(1+\cos(2t))\,\mathrm dt=-\frac{49}2\left(t+\frac12\sin(2t)\right)+C$

Expand the sine term as

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Then

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So the integral is

$\displaystyle-\frac{49}2\left(\sin^{-1}\left(\dfrac{6-x}7\right)+\dfrac{6-x}7\sqrt{13+12x-x^2}\right)+C$

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