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2 years ago

(85 x 255) / 289 + 15 - 70 =

Mathematics

2 answers:

Alex777 [14]2 years ago

7 0

The answer to your question is 20

ANEK [815]2 years ago

5 0

I do believe its twenty

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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

Harry reads that a particular element has an atom with a mass of 0.000000000012 grams. What is the weight of the atom expressed

Arlecino [84]

1.2 e⁻¹¹

Because you need a number between 1 and 10 for scientific notation. So you move the decimal over 11 places. Since you move it to the right, it becomes a negative exponent.

8 0

2 years ago

Krutika and Natasha win some money and share it in the ratio 3:4. Krutika gets £39. How much did Natasha get?

grin007 [14]

Answer:

22.28 Pounds

Step-by-step explanation:

Add 3+4=7

39 ÷ 7=5.57

Because Natasha has the ratio of 4 she would get

5.57 × 4=22.28

Answer=22.28

4 0

2 years ago

Use substitution to solve each system of equations<br> 2x -y = 6 <br> -3y = -6x + 18

vichka [17]

Hope this helps
Step are all below

3 0

2 years ago

What is the circumference of a circle with a diameter of 5 feet? Use 3.14 for pie.

sammy [17]

Answer:

A. 15.7 ft

Step-by-step explanation:

circumference = 2πr

radius= half the diameter 5/2=2.5

2(3.14)(2.5)=15.7 ft

8 0

2 years ago