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3 years ago

Evaluate the expression below for x = 4, y = –5, and z = 2. 3x^2 -4y+xz

Mathematics

1 answer:

klio [65]3 years ago

5 0

3(4)^2 -4(-5) + (4)(2)
= 3(16) + 20 + 8
= 48 + 20 + 8
= 76 (d)

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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

3 years ago

PLEASE HELP WITH #3 i’ll give brainliest

tekilochka [14]

Step-by-step explanation:

Lets begin with this 4x-25=x+14, 3x=39, so x=13, than we plug it in to side NP because that is the most simple one to plug it into to and that side is 27 since the triangle is equilateral all sides are the same so it is 27, 27, 27, for the sides and x=13

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3 years ago

How many seconds are in 45 minutes?

fgiga [73]

45 minutes equal to 2700 seconds.

8 0

3 years ago

Read 2 more answers

(3x-4)^2 - (2x-1) ^2

Len [333]

Step-by-step explanation:

Hope it helps u

Plz mark as brainlist

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2 years ago

Pythagorean Theorem Worksheet. Round Each Number To The Nearest Tenth.

dybincka [34]

Answer:

1. 10

2. 5

3. 10

4. 8

Step-by-step explanation:

1. 8²+6² = 100

The square root of 100 = 10

2. 3²+4² = 25

The square root of 25 = 5

3. 26²-24²=100

The square root of 100 = 10

4. 10²-6² = 64

The square root of 64 = 8

4 0

2 years ago