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2 years ago

What is m ZDFC? O45° O 80° O 125° O 135

Mathematics

2 answers:

Yanka [14]2 years ago

5 0

I also believe it’s 80

Law Incorporation [45]2 years ago

4 0

I believe it’s 80 hope it helps

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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

Please help me find the answer!!<br><br> Picture ⬇️

expeople1 [14]

Answer:

(1) y≥-3x + 4

3 0

2 years ago

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Find the slope and y-intercept of the line that is parallel to y = -x - 3 and passes through the point (3, -2)

motikmotik

Use point slope formula y-y1=m(x-x1)
You are told that y=-x+3. This equation is of the form y=mx+b. Where m=-1. m is the slope. And you have a point (x1,y1) that is (3,-2). With all of this in mind, you then plug all of these details into the point slope formula y-y1=m(x-x1)

In point slope form, you have the following:

y-(-2)=-1(x-3).

To turn this into slope intercept form, simplify y-(-2) to get y+2 and distribute in the -1 to get:

y+2=-x+3

Subtract 2 from both sides to get

y=-x+1

In slope intercept form, the answer is
y=-x+1 and in point slope form, the answer is y+2=-x+3

Hope this helps!!!

3 0

2 years ago

Brainlist for best answer and 100 points

dexar [7]

Well, $920 multiplied by .15 would equal 138 and
since 138 divided by 138 would equal 920. 15% of his income aka $138 would go towards his taxes.
Hope this helped!
have a great day! (:

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2 years ago

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The first step in calculating the mean is to ____the numbers<br> add<br> group

Blababa [14]

The first step in calculating the mean is to add the numbers. After that you divide by the number of items in the data set. You don’t need to group the numbers to find the mean. Hope this helped!

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3 years ago

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