Answers
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
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
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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)
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Its really easy if you put your mind into it! Goodluck <3
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.
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
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:
245milesStep-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
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)
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!
-4x+6y=-7
-13x-2y=-4
Elimination or substitution
Answers
Answer:
substitution
Step-by-step explanation:
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.
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
Write the fractional equivalent (in reduced form) to each number
10
0.125 =
0.16
Answers
0.125 —> 1/8
0.16 —> 4/25
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.
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
Consider the system of equations below. What could be the first step in solving by elimination?
Answers
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)
-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
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
Answer:
3
Step-by-step explanation:
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
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
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!!!
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.
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:
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).
WILL MARK AS BRAINLIEST!!!!!
Answers
explanation: -1-4=-5 0-4=-4 1-4=-3 2-4=-2
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:
ion f (x) = -2(x+8)+11
Standard form
Answers
Convert 4B from hexadecimal to decimal.
Answers
Answer:
75
Step-by-step explanation:
6 is the ______ root of 36
Answers
6(6) = 36
Answer:
6 is the square root of 36
What is the answer to
5 + 3 x 3x -2 X=2
Answers
Answer:
x = 1/6
Step-by-step explanation:
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.
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
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.