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3 years ago

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I need help on these 3 questions. Please help. “Find the area of each figure. Round your answer to the nearest tenth, show your

work.

1 answer:

My name is Ann [436]3 years ago

6 0

The first one is 6x10+6x7/2=81

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"find the reduction formula for the integral" sin^n(18x)

dexar [7]

Let

$I(n,a)=\displaystyle\int\sin^nax\,\mathrm dx$
For demonstration on how to tackle this sort of problem, I'll only work through the case where $n$ is odd. We can write

$\displaystyle\int\sin^nax\,\mathrm dx=\int\sin^{n-2}ax\sin^2ax\,\mathrm dx=\int\sin^{n-2}ax(1-\cos^2ax)\,\mathrm dx$
$\implies I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx$

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

$u=\sin^{n-3}ax\implies\mathrm du=a(n-3)\sin^{n-4}ax\cos ax\,\mathrm dx$ $\mathrm dv=\sin ax\cos^2ax\,\mathrm dx\implies v=-\dfrac1{3a}\cos^3ax$

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

For this next integral, we rewrite the integrand

$\sin^{n-4}ax\cos^4ax=\sin^{n-4}ax(1-\sin^2ax)^2=\sin^{n-4}ax-2\sin^{n-2}ax+\sin^nax$
$\implies\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx=I(n-4,a)-2I(n-2,a)+I(n,a)$

So putting everything together, we found

$I(n,a)=I(n-2,a)-\displaystyle\int\sin^{n-2}ax\cos^2ax\,\mathrm dx$
$I(n,a)=I(n-2,a)-\left(-\dfrac1{3a}\sin^{n-3}ax\cos^3ax+\dfrac{n-3}3\displaystyle\int\sin^{n-4}ax\cos^4ax\,\mathrm dx\right)$
$I(n,a)=I(n-2,a)-\dfrac{n-3}3\bigg(I(n-4,a)-2I(n-2,a)+I(n,a)\bigg)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax$
$\dfrac n3I(n,a)=\dfrac{2n-3}3I(n-2,a)-\dfrac{n-3}3I(n-4,a)+\dfrac1{3a}\sin^{n-3}ax\cos^3ax$

$\implies I(n,a)=\dfrac{2n-3}nI(n-2,a)-\dfrac{n-3}nI(n-4,a)+\dfrac1{na}\sin^{n-3}ax\cos^3ax$

7 0

2 years ago

A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 60 oz. Twenty percent of all purchasers select a

ss7ja [257]

Answer:

Please find solution in the picture attached

Step-by-step explanation:

4 0

2 years ago

- 10x - 11 = -12x + 21

Helen [10]

-10x=-12x + 21 + 11
-10x= -12 + 32
-10x + 12x = 32
2x = 32
X = 32/2

4 0

2 years ago

Read 2 more answers

Plz i need help -8 = p -5

AveGali [126]

The answer is p = -3

7 0

3 years ago

Read 2 more answers

Find f(k - 1) when f(x) = 5x^2+ 4x – 5.

bekas [8.4K]

Plug in $k-1$ to each $x$ in the function.

$f(k-1)=5(k-1)^2+4(k-1)-5$

$f(k-1)=5(k^2-2k+1)+4k-4-5$

$f(k-1)=5k^2-10k+5+4k-4-5$

$f(k-1)=5k^2-6k-4$

Hope this helps.

頑張って!

5 0

3 years ago