How do you do this question?

How Do You Do This Question?

Answers

Answer 1

Step-by-step explanation:

Start with the series representation for eˣ.

eˣ = ∑ₙ₌₀°° xⁿ / n!

Substitute -x².

e^(-x²) = ∑ₙ₌₀°° (-x²)ⁿ / n!

e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ) / n!

Multiply by x².

x² e^(-x²) = x² ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ) / n!

x² e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ⁺²) / n!

Integrate both sides (use power rule).

∫ x² e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (x²ⁿ⁺³) / ((2n + 3) n!)

Evaluate between x=0 and x=0.5.

∫ x² e^(-x²) = ∑ₙ₌₀°° (-1)ⁿ (0.5²ⁿ⁺³) / ((2n + 3) n!)

This is an alternating series, so use alternating series estimation.

(0.5²⁽ⁿ⁺¹⁾⁺³) / ((2(n+1) + 3) (n+1)!) ≤ 0.001

(0.5²ⁿ⁺⁵) / ((2n + 5) (n+1)!) ≤ 0.001

n ≥ 1

So the estimate of the integral is the sum of the first two terms (n=0 and n=1).

I = (-1)⁰ (0.5³) / ((3) 0!) + (-1)¹ (0.5²⁺³) / ((2 + 3) 1!)

I = (0.5³) / 3 − (0.5⁵) / 5

I = 1/24 − 1/160

I = 17/480

I = 0.0354


Related Questions

A train travels at 45 mph for 3 h and then increases its speed to 55 mph for 2 more hours. How far does the train travel in the 5-hour period

Answers

Answer:

245miles

Step-by-step explanation:

Step one:

given that the first 3 hours the train travels at a speed of 45 mph.

i.e Time = 3 hours

    speed =45 mph

    distance=?

we know that speed = distance/time

distance= speed*time

distance= 45*3

distance=135miles

Step two:

For the nex two hours it travels at 55 mph

i.e time= 2hours

   speed= 55mph

  distance=?

distance= speed*time

distance= 2*55

 distance= 110mile

Step three:

Hence for a total of 5 hours drive, the total distance covered is

135+110= 245miles

Solve the following inequality using an algebraic approach:
-4 < 3x+5<11

Answers

Answer:

-3 < x < 2

Step-by-step explanation:

Move all terms not containing x from the center section of the inequality

-4x+6y=-7
-13x-2y=-4
Elimination or substitution

Answers

Answer:

substitution

Step-by-step explanation:

6 is the ______ root of 36​

Answers

6 is the square root of 36.

6(6) = 36

Answer:

6 is the square root of 36

If 1 inch represents 10 miles on a map then how many inches will represent 120 miles ?

Answers

Answer:

12 inches

Step-by-step explanation:

We can write this as a proportion:

inches/miles = inches/miles

1/10 = x/120

Solving for x, we get 12 inches.

ion f (x) = -2(x+8)+11
Standard form

Answers

-2x-5 is your answer I believe

Liam had a container of oatmeal that contained 5 and one-half cups of oatmeal. Liam ate StartFraction 4 over 9 EndFraction cup of oatmeal every morning before school for a week. Which is the best estimate of the number of cups of oatmeal that Liam had left in the container at the end of the five-day week?
2 and one-half
3
3 and one-half
5

Answers

3 and two half I hope you get a good answer

Answer:

3

Step-by-step explanation:

Consider the limaçon with equation r = 3 + 4cos(θ). How does the quotient of a and b relate to the existence of an inner loop?

Answers

A polar graph that is a limacon has a formula similar to [tex]r=a+bcos\theta[/tex]

Option B is correct.

A  limacon has a formula similar to [tex]r=a+bcos\theta[/tex]

Case 1 .  If  a < b  or  [tex]\frac{b}{a}>1[/tex]

Then the curve is limacon with an inner loop.

Case 2.  If  a>b   or   [tex]\frac{b}{a}<1[/tex]

Then the limacon does not have an inner loop.

Here, given that,  [tex]r=3+4cos\theta[/tex]

It is observed that,  a < b  or [tex]\frac{b}{a}>1[/tex]

Therefore, the curve is limacon with an inner loop.

Hence, option B is correct.

Learn more:

https://brainly.com/question/10381605

Convert 4B from hexadecimal to decimal.

Answers

Answer:

75

Step-by-step explanation:

Write the fractional equivalent (in reduced form) to each number
10
0.125 =
0.16

Answers

10 —> 10/1
0.125 —> 1/8
0.16 —> 4/25

WILL MARK AS BRAINLIEST!!!!!

Answers

answer: y=x-4
explanation: -1-4=-5 0-4=-4 1-4=-3 2-4=-2

What is the answer to
5 + 3 x 3x -2 X=2

Answers

Answer:

x = 1/6

Step-by-step explanation:

Consider the system of equations below. What could be the first step in solving by elimination?

Answers

Answer:

The first step would be to multiply the bottom equation by -1 to eliminate x, then you would combine like terms, like 5y + 2y, and 16 + 10.

Answer:

Subtracting the 2 equations

Step-by-step explanation:

3x + 5y = 16

3x + 2y = 10

Subtract it;

3y = 6

Divide both sides b 3;

y = 2

Substitute y;

3x + 5y = 16

3x + 5(2) = 16

3x + 10 = 16

Subtract 10 from both sides;

3x = 6

Divide both sides by 3;

x = 2

(x, y) = (2, 2)

Mr. Johnson listed each class’s average on a quiz in fraction form. Based on the chart, Which shows the classes ordered from the highest average to the lowest average?

A. C,D,A,B
B. C,A,D,B
C. B,D,A,C
D. B.A,D,C

Answers

Answer:

C

Step-by-step explanation:

I'm not sure if my picture made since because I'm not the best at drawing but that's how I'd explain it

-7*3^0.25x=-10 what is the solution of the equation

Answers

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 1.08547955

simplify (3x+2) (y-2) - (7y+3) (y-3)

Answers

Answer:

3 x y − 7 y 2 − 6 x + 20 y + 5

Step-by-step explanation:

A jogger is running home. His distance from home, as a function of time, is modeled by y=-7x +8.
Which statement best describes the function?
A. The function is nonlinear.
B. Not enough information is given.
C. The function is linear at some points and nonlinear at other points.
D. The function is linear.

Answers

Answer: the function is a liner

Step-by-step explanation: trust


Find the amount that results from investing $5000 at 3% compounded continuously for 5 years. Round your
answer to two decimal places.

Answers

Answer:

The amount that results from investing $5000 at 3% compounded continuously for 5 years is $5800

Step-by-step explanation:

We are given:

Principal Amount (P) = $5000

Years (t) = 5

Rate (r) = 3% or 0.03

We need to find New Amount (A)

The formula used is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Since amount is compounded continuously so n=1

Putting values and finding A

[tex]A=P(1+\frac{r}{n})^{nt}\\A=5000(1+\frac{0.03}{1})^{1*5}\\A=5000(1+0.03)^5\\A=5000(1.03)^5\\A=5000(1.16)\\A=5800[/tex]

So, New Amount (A) = $5800

The amount that results from investing $5000 at 3% compounded continuously for 5 years is $5800

josie walks 3/4 miles in 1/5 hour. what is josie’s speed in miles per hour

Answers

Answer:

Speed = 3.75 miles per hour.

Step-by-step explanation:

Speed can be defined as distance covered per unit time. Speed is a scalar quantity and as such it has magnitude but no direction.

Mathematically, speed is given by the equation;

[tex]Speed = \frac{distance}{time}[/tex]

[tex]S = \frac{d}{t}[/tex]

Given the following data;

Distance, d = 3/4 miles

Time, t = 1/5 hour

Substituting into the equation, we have;

[tex]Speed, S= \frac{3/4}{1/5}[/tex]

[tex]Speed, S = \frac{3}{4}*5[/tex]

[tex]Speed, S = \frac{15}{4}[/tex]

Speed, S = 3.75mph.

Therefore, Josie's speed is 3.75 miles per hour.

If I work four days from 6-4:30 and earn $600. How much of taxes is being taken off my check

Answers

Answer:

80$

Step-by-step explanation:

Which of the following choices will simplify (8 − 5)2 + 18/3+ 4 ?
19
13
22
None of these choices are correct.

Answers

Answer:

None of these choices are correct.

I have solved u can have a look :)

Answer:

(8-5)²+18/3+4

(3)²+6+4

9+6+4= 19

Follow P.E.M.D.A.S

Start with parenthesis first

(8-5) =3

second step exponents

3² = 9

Third step Division

3÷18 = 6

last step add all the numbers

9+6+4 = 19

19 is your answer!!!

Mrs.Rodriquez is purchasing trophies for each child that plays little league she wants to spend no more than $7.00 per thropy ​

Answers

Answer:

7 trophies for $49.00

5 trophies for $30.00

-----------------------------------

Explination:

It says that she wants to pay no more than 7 dollars for each trophy she buys, which means 7 and less. So we have to multiply 7 x the number of trophies, And if it gives you the excact number or less its correct.

So we multiply

7 x 7 = 49 (The excact number, correct)

9 x 7 = 63 (The price they are selling it at is higher, incorrect)

12 x 7 = 84 (The price they are selling it at is higher, incorrect)

5 x 7 = 35 (Paying less, Correct)

3 x 7 (The price they are selling it at is higher, incorrect)

---------------------------------------------------------------------------------------

Its really easy if you put your mind into it! Goodluck <3

At a bake sale, students sold 145 chocolate chip cookies, 95 oatmeal cookies, and 87 sugar cookies. What percent of the cookies sold were oatmeal? Round to the nearest tenth

Answers

Answer:

29.05% of cookies sold were oatmeal cookies.

Step-by-step explanation:

Students sold chocolate chip cookies = 145

Students sold oatmeal cookies = 95

Students sold sugar cookies = 87

Total cookies sold = 145+ 95 + 87

Total cookies sold= 327

The formula used to find percentage is : [tex]Percentage = \frac{part}{whole}*100[/tex]

Now, finding percent of the cookies sold that were oatmeal

Percentage of oatmeal cookies sold = [tex]\frac{95}{327}*100[/tex]

Percentage of oatmeal cookies sold = 29.05 %

So, 29.05% of cookies sold were oatmeal cookies.

what is 2.898989... as a mixed number?

Answers

Answer:

2 89/100

Step-by-step explanation:

its 289/100 as an improper fraction

Keep in mind that 0.89 means 89/100.

Now apply the whole number 2.

We get 2_(89/100).

A scientist needs 80 liters of a 30% solution of alcohol. She has a 20% solution and a 60% solution available. How many liters of the 20% solution and how many liters of the 60% solution should she mix to make the 30% solution?

Answers

Answer:

60 liters of 20% solution & 20 liters of 60% solution

Step-by-step explanation:

80*0.3=.2x+0.6(80-x)

24=0.2x+48-0.6x

-24=0.2x-0.6x

-24=0.4x

24=0.4x

60=x

Hope this helps!! This is step by step btw!

Juan got grades of 68 and 73 on his first two math tests. What grade must he get on the third test if all were weighted equally and he wants to raise his grade to a 75 average?

Answers

Answer: 84

Step-by-step explanation: Multiply 75 by 3. That is 225, and is the value the three numbers must add up to. 73+68=141. 225-141 is 84.

Does anyone know the solution to this question

Answers

Answer:

Graph A

Step-by-step explanation:

3x+y=5

y=-3x+5

4x-y=2

-y=-4x+2

4=2x-2

graph a is correct. hope this helps

A computer manufacturer built a new facility for assembling computers. There were construction and new equipment costs. The company paid for these costs and made combined profits of $40 million after 4 years, while profits increased $30 million per year. Select the correct graph of this function. (2 points)

A)There is a graph of a line that has a y intercept that is approximately $80 million and passes through the point of approximately x equals 2 years and y equals $140 million.

B)There is a graph of a line that has a y intercept that is approximately negative $80 million and an x intercept that is approximately 2.7 years.

C)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 2 years.

D)There is a graph of a line that has a y intercept that is approximately negative $45 million and an x intercept that is approximately 0.6 years.

Answers

Answer:

I am not really good at this but...if I had to choose the ones that make sense

A and B

Step-by-step explanation:

Your are incresing the amount is going up, so if you go backwards you woild have to the negatuves.

Then again I woild not trust my math for the second answer cause I am no good at math.

You finance a $500 car repair completely on credit, you will just pay the minimum payment each month for the next three months. The APR is 18.99% and the minimum payment each month is 4% of the balance. Determine the finance charge, carry-over balance, and minimum payment required for each of the next two months, and the starting balance for month 2 in the table below.

Answers

Answer:

Determination of the Finance Charge, Carry-over balance, Minimum Payment for each of the next two months:

Finance Charge:

First month = $7.91

Second month = $7.72

Carry-over balance:

First month = $487.59

Second month = $475.50

Minimum Payment:

First month = $20.32

Second month = $19.81

Starting balance (Carry-over balance + Finance charge):

First month = $507.91

Second month = $495.31

Step-by-step explanation:

a) Data and Calculations:

Credit Finance = $500

APR = 18.99%

Minimum monthly payment = 4% of the balance

Monthly rate of interest = 0.1899/12 = 0.015825

Finance Charge:

First month = $7.91 ($500 * 0.015825)

Second month = $7.72 ($487.59 * 0.015825)

Carry-over balance:

First month = $487.59($507.91 - $20.32)

Second month = $475.50 ($495.31 - $19.81)

Minimum Payment:

First month = $20.32 ($507.91 * 4%)

Second month = $19.81 ($495.31 * 4%)

Starting balance (Carry-over balance + Finance charge):

First month = $507.91 ($500 + $7.91)

Second month = $495.31 ($487.59 + $7.72)

Solve the following equation algebraically X^2=36
A. X=_+18
B. X=_+6
C. X=-6
D. X=-18

Answers

Answer:

I think the answer is C.

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