(a)whats is the value of x (b) what is the measure of angle B

Mathematics

1 answer:

natulia [17]2 years ago

3 0

$cdb = 8 \\ x = 4 \\ by \: pythagoras \: theorem \\ 8 {}^{2} = 4 {}^{2} + x{}^{2} \\ 64 = 16 + x {}^{2} \\ 64 - 16 = x {}^{2} \\ 48 = x{}^{2} \\ \sqrt{48 } = x\\ angle \: b = 60 \\ angle \: of \: equilateral \: triangle \: equal \: 60$

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Let

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For the remaining integral, we can integrate by parts, taking

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$\implies\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx=-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{a(n-3)}{3a}\int\sin^{n-4}ax\cos^4ax\,\mathrm dx$

For this next integral, we rewrite the integrand

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$I(n,a)=I(n-2,a)-\left(-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{n-3}3\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx\right)$
$I(n,a)=I(n-2,a)-\dfrac{n-3}3\bigg(I(n-4,a)-2I(n-2,a)+I(n,a)\bigg)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax$
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$\implies I(n,a)=\dfrac{2n-3}nI(n-2,a)-\dfrac{n-3}nI(n-4,a)+\dfrac1{na}\sin^{n-3}ax\cos^3ax$