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2 years ago

Select the letter of the correct answer.

Mathematics

2 answers:

babymother [125]2 years ago

5 0

Answer:

D $11.63

Step-by-step explanation:

Pepsi [2]2 years ago

4 0

the answer is c) $14.12

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Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.

$I(5)=x^5e^x-5I(4)$

$I(5)=x^5e^x-5(x^4e^x-4I(3))=(x-5)x^4e^x+20I(3)$

$I(5)=(x-5)x^4e^x+20(x^3e^x-3I(2))=(x^2-5x+20)x^3e^x-60I(2)$

$I(5)=(x^2-5x+20)x^3e^x-60(x^2e^x-2I(1))=(x^3-5x^2+20x-60)x^2e^x+120I(1)$

$I(5)=(x^3-5x^2+20x-60)x^2e^x+120(xe^x-I(0))$

Finally,

$I(0)=\displaystyle\int e^x\,\mathrm dx=e^x+C$

so we end up with

$I(5)=(x^4-5x^3+20x^2-60x+120)xe^x-120e^x+C$

$I(5)=(x^5-5x^4+20x^3-60x^2+120x-120)e^x+C$

and the antiderivative is

$\displaystyle\int2x^5e^x\,\mathrm dx=(2x^5-10x^4+40x^3-120x^2+240x-240)e^x+C$

8 0

2 years ago

The equation K = mv2 represents the energy an object has based on its motion. The kinetic energy, K, is based on the mass of the

docker41 [41]

The answer is She should have multiplied by 2 instead of dividing by 2.
First one.

6 0

2 years ago

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A swimming pool had 2.5 liters of water in it. Some water evaporated, and then the pool only had 2 million liters of water in it

djyliett [7]

Hi!

If I have done this correctly, then the answer is:

2 million is 80% of 2.5

That means that 20% of the water evaported.

5 0

3 years ago

Subtract. 5x – 6x+2 - 1-2x - x - 2)

adell [148]

Answer:

7x^2 -5x + 4

Step-by-step explanation:

5x^2 – 6x+2

- (-2x^2 - x - 2)

We got 5x^2 - (-2x^2) = 5x^2 + 2x^2 = 7x^2

-6x - (-x) = -6x + x = -5x

2 - (-2) = 2+2 = 4

So the equation would be 7x^2 -5x + 4

Hope this help :3

3 0

2 years ago

Determine if the following functions are increasing or decreasing, and compare their rates of change. A. Both functions are incr

adoni [48]

Answer:

D is the answer

Step-by-step explanation:

The both are - 2 slopes hope this helps!:)

4 0

2 years ago

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