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Alina [70]
3 years ago
10

Need help fast will give brainliest! Please help me solves this equation!

Mathematics
1 answer:
kicyunya [14]3 years ago
8 0

Answer:

x = 15, y = 75

Step-by-step explanation:

hope it helps

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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
3 years ago
Tyler fills up his tank with 12 gallons of gas. If one trip, on average,takes 1/2 gallon of gas, how many trips will the Tyler b
Bingel [31]
24
Since each trip takes half a gallon of gas, you divide the amount of gas by how much per trip.
That gives you 24 trips he can make with the gas.
7 0
3 years ago
How many units apart are (-1,4) and (2,-1)
Serggg [28]

Answer:

Those points are \sqrt{34} units apart.

7 0
3 years ago
A basketball team sells tickets that costs $10, $20, or, for VIP seats $30. The team has sold 3188 tickets overall. It has sold
Drupady [299]
490 tickets is 1,230
8 0
3 years ago
If 9x x 3x+1 = 2187, what is the value of x?<br><br><br><br><br>​
Snezhnost [94]

Answer:

x = 80.96

Step-by-step explanation:

9x * 3x +1 = 2187

27x +1 = 2187

27x = 2187-1

27x = 2186

x = 2186/27 = 80.96(2dp)

7 0
3 years ago
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