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lisov135 [29]
2 years ago
14

A cyclist rides 14 miles in 47 minutes.What is the speed of the cyclist in miles per hour

Mathematics
1 answer:
DedPeter [7]2 years ago
3 0

Step-by-step explanation:

20miles per hour HAVE A GOOD DAY

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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
Please answer the question and leave an explanation on how to solve each part. Thank you in advance!
horsena [70]

The solutions are

  • it is going to take 15.9 months to raise 10000 dollars
  • You will have $37.31 after you have bought the car
  • The money deficit would be $37.31

<h3>How to solve the question</h3>

a. 10000 = 9359.08e(0.05)

e⁰⁰⁵ = 10000/9359.08

= 0.05 = ln(10000/9359.08)

= 1.325 years

convert to months = 15.9 months

Hence it is going to take 15.9 months to raise 10000 dollars

b. 9359.08 x e^(0.05 x1.25)

= 9962.69

10000 - 9962.69

= $37.31

You will have $37.31 after you have bought the car

c. The money loss and the deficit would be same as above $37.31

d. ln(e^a) = a

We can clearly see that the money cannot be raised in the 15 months from $ 9359.08. there is a deficit amount of $37.31

Read more on compound interest here: brainly.com/question/24924853

#SPJ1

3 0
1 year ago
523 x = 523 x = last one
Sphinxa [80]

Answer:

X has an infinite number of solutions

or

0 = 0

Step-by-step explanation:

<em>Hey there!</em>

Given,

523x = 523x

Simplify

523x = 523x

-523x to both sides

0 = 0

<u>So x has an infinite number of solutions.</u>

<em>Hope this helps :)</em>

5 0
3 years ago
Read 2 more answers
What is the slope of the line?<br> m=
telo118 [61]

Answer:

m = 1/4

Step-by-step explanation:

slope = rise / run

rise = 1 (red arrow)

run = 4 (dotted line)

3 0
2 years ago
Which table represents a function?
Anastaziya [24]

Answer:

The first box

Step-by-step explanation:

In a linear function you cannot have 2 of the same X numbers. Ex) You cannot have 2 -4's in the X row. In the Y, you may. But never the X.

3 0
3 years ago
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