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
The population of Afghanistan is growing at a rate of 1.3% per year. In 2014 there were 30 million people in Afghanistan. The population (in millions) of Afghanistan x years after 2014 can be approximated by the function
f(x)=30(1.013)^x
a. Use the function to predict the population in Afghanistan in 2024.
b. Use the function to predict the population in Afghanistan in 2100.
c. Use the function to predict when (during what year) the population of Afghanistan will reach 50 million. (Feel free to use the online equation solver and/or grapher for this one.)
Answers
The graph shows the speed of sally the sloth. How long would it take Sally to travel 9 feet
Answers
Answer:
dude wheres the choices
Step-by-step explanation:
Solve the equation 3(x + 4.5) = 36.
If you get stuck, use the diagram. first one and with an explanation will get brainllest
Answers
Answer:
.75
Step-by-step explanation:
there is prof
Plz answer fast I’m on a timer !!!
Answers
Answer:
option b is your correct answer
hy if it help you then mark me brilliant
.............
What is the distance between these set of points?
(0,5) and (-3,0)
sorry i cant add the graph photo but please helppp
Answers
Step-by-step explanation:
applying the distance formula,
±√(0-5)^2 + (-3-0)^2 = ±√34 (rej -√34 since distance > 0)
Topic: coordinate geometry
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
Dennis has made a purchase of $50,000
Answers
Really? On what? Man thats a lot of money.
Choose an equivalent expression for 10^6 divided by 10^4
10^2
10^3
10^10
10^24
Answers
Answer:
10^2
Step-by-step explanation:
When dividing by powers you subtract the exponent, so 6-4
Answer:
stuff and stuff
Step-by-step explanation:
7 4/10 greater than 7.421
Answers
Answer:
False
Step-by-step explanation:
7 4/10= 7.4
7.4<7.421
Jill is factoring the expression 13 x y minus 52 y. Her work is shown below.
Factors of 13 x y: 1, 13, x, y
Factors of 52y: 1, 2, 26, 52, y
GCF: y
Factored expression: y (13 x minus 52)
Which best describes the accuracy of Jill’s solution?
Jill’s solution is accurate.
Jill omitted a factor pair, which affected the GCF and factored expression.
Jill made an error when determining the GCF from her list of factors.
Jill made an error when writing the factored expression.
Answers
Answer:
the answer is the last choice
Answer:
d
Step-by-step explanation:
X intercept for -3x+10
Answers
Answer:
(10/3, 0)
Step-by-step explanation:
how this helps
Find the average rate of change of h(x) = - x ^ 2 + 3x + 3 from x = 2 to x = 6 .
Answers
Answer:
The average rate of change is
Δy ÷ Δx = -20 ÷ 4
Δy/Δx = -20/4
= -5
Step-by-step explanation:
Given the function
[tex]h\left(x\right)\:=\:-x^2\:+\:3x\:+\:3[/tex]
Putting x = 6
[tex]h\left(6\right)\:=\:-\left(6\right)^2\:+\:3\left(6\right)\:+\:3[/tex]
[tex]=-36+18+3[/tex]
[tex]=-15[/tex]
Putting x = 2
[tex]h\left(2\right)\:=\:-\left(2\right)^2\:+\:3\left(2\right)\:+\:3[/tex]
[tex]= -4 + 6 +3[/tex]
[tex]= 5[/tex]
The change in y from 2 to 6 is
Δy = -15 - 5
= -20
The interval from 2 to 6 has a width of
Δx = 6 - 2
= 4
Therefore, the average rate of change is
Δy ÷ Δx = -20 ÷ 4
Δy/Δx = -20/4
= -5
if a sprinkler waters 1/14 of a lawn in 1/2 hour, how much time will it take to water the entire lawn
Answers
Answer:
7 hours
Step-by-step explanation:
1/14 * 14 = 1 whole lawn
1/2 hours = 30 minutes
14 * 30 = 420 minutes to water entire lawn
420 minutes = 7 hours
Find the derivative of the function.
3
f(x) = 4x + 20x4
f'(x)=
Answers
Answer:
f'(x) = 4 + 80x³
General Formulas and Concepts:
Calculus
The definition of a derivative is the slope of the tangent line.
We can take the derivative/distribute it over addition and subtraction.
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define function
f(x) = 4x + 20x⁴
Step 2: Find 1st derivative
Basic Power Rule (1st term): f'(x) = 4 · 1x¹⁻¹ + 20x⁴Basic Power Rule (2nd term): f'(x) = 4 · 1x¹⁻¹ + 20 · 4x⁴⁻¹Simplify: f'(x) = 4 + 80x³Please help
What is 1. answer abc
What is 2. abcd
What is E and F
Also what is x
Help
Answers
Answer:
Step-by-step explanation:
1 × a = a
a² = a*a ; a³ = a*a*a .....
[tex](\frac{a}{b}) ^{n} = \frac{a^{n} }{b^{n} }[/tex]
(1).
(a). [tex]7^{5}[/tex]
(b). [tex](\frac{1}{7}) ^{6}[/tex] = [tex]\frac{1}{7^{6} }[/tex]
(c). [tex](9.3)^{9}[/tex]
(2).
(e). [tex](\frac{1}{2} )^{4} =\frac{1}{2^{4} }[/tex] = [tex]\frac{1}{2*2*2*2}[/tex] = [tex]\frac{1}{16}[/tex]
(f). [tex](\frac{1}{3} )^{2}[/tex] = [tex]\frac{1}{3}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{1}{9}[/tex]
(3).
x² = 30² + 16² = 900 + 256 = 1156 = 34² ⇒ x = 34 units
Parábola donde su directriz eje x
Answers
Answer:
umm realmente no lo sé
Step-by-step explanation:
8^x=2 what is x please help
Answers
Answer:
Step-by-step explanation:
8 = 2^3
So 8^x =2 is 2^3x =2
Now they are same base.
So 3x =1 , x= 1/3
rewrite the function f(x)=3(x-1)^2+9 in the form f(x)=ax^2+bx+c
Answers
Answer:
f(x) = 3x² - 6x + 12
General Formulas and Concepts:
Order of Operations: BPEMDAS Expand by FOIL (First Outside Inside Last) Standard Form: f(x) = ax² + bx + c Vertex Form: f(x) = a(bx + c)² + dStep-by-step explanation:
Step 1: Define function
Vertex Form: f(x) = 3(x - 1)² + 9
Step 2: Find Standard Form
Expand by FOILing: f(x) = 3(x² - 2x + 1) + 9Distribute 3: f(x) = 3x² - 6x + 3 + 9Combine like terms (constants): f(x) = 3x² - 6x + 12If 1 inch = 2.54 centimeters, how many inches are in 328 centimeters? Round to the nearest hundredth.
Answers
Answer:
2.54 cm in 1 inch......how many inches in 51.78 cm...
51.78 / 2.54 = 20.4 inches <==
or this way...
2.54 / 1 = 51.78 / x....2.54 cm to 1 in = 51.78 cm to x inches
cross multiply
(2.54)(x) = 51.78)(1)
2.54x = 51.78
x = 51.78 / 2.54
x = 20.4 inches <==
Step-by-step explanation:
Answer:
129.134 rounded will be 129.1
Step-by-step explanation:
HOPE THIS HELPS :)
Can any of the experts help me on my new question for math? PLEASE!!!
Answers
Answer:
yes I can
but wheres the question
why dont you type it in the comments
Which of these equations represents the graph below?
y = 2x + 3
y = 3x - 2
y = 3x + 2
y=2x - 3
Answers
Explanation: y=mx+b
b is where the slope going over the y axis which is -3. mx is the slope which is rise over run, the line rises 2 and goes over 1 making it y=2x-3
kx^2+k=8x-2xk
Find the range of values of k- there are two distinct roots.
I’m pretty sure you need to use the discriminate but i’m stuck so pls could somebody show me step by step
Answers
Answer:
i cant understans the quedtoion its worng bro
solve...
16= k/11
help
Answers
Answer:
k = 176
Step-by-step explanation:
16 = [tex]\frac{k}{11}[/tex]
11 × 16 = [tex]\frac{k}{11} *11[/tex]
176 = k
Answer:
k = 176
Step-by-step explanation:
16 = k/11
16x11 = k/11 x 11
176 = k
9a + 8 - 20-3-50
Answer
Answers
Answer:
9a-65
Step-by-step explanation:
simply write 9a+(add the remaining numbers all together)
Carter answered 5% of the questions
on a math test incorrectly, or 1
question. What fraction of the
questions did Carter answer correctly?
Answers
Answer:19/20
1-20=19
1÷20=0.05
0.05=5%
I hope this is good enough:
An ice cream factory makes 310 quarts of ice cream in 5 hours. How many quarts can they make per hour?
Answers
310/5
A recent telephone poll of 1000 randomly selected adults revealed that 2 in 10 adults believe there has been progress in finding a cure for cancer in the last 28 years. Describe the population, sample, population parameters, and sample statistics.
Answers
Answer:
Explained below.
Step-by-step explanation:
A population is the set of all the data that can be collected and from which a smaller set of data is drawn for further examination. A population may denote to a group of individuals, articles, trials or measurements. A population can thus be called as a collection of information regarding subjects combined together by a common characteristic.
In this case, the population consists of all people in the country.
A sample denotes a smaller, controllable form of a larger cluster. It is a subset comprising of the characteristics of a bigger population. Samples are used in statistical experiments when the population under consideration is too large for the test to include all the members.
In this case, the sample consists of 1000 randomly selected adults.
A parameter is a valuable element of statistical analysis. It denotes the characteristics that are used to define a given population. It is used to define a particular attribute of the population. For instance, population mean, population standard deviation, population proportion and so on.
In this case, the population parameter is the proportion of adults who believe there has been progress in finding a cure for cancer in the last 28years.
A statistic is the value of the characteristics that are computed using this sample. For instance, sample mean, sample standard deviation, sample proportion and so on.
In this case, the sample statistic is the 0.20 proportion of adults believe there has been progress in finding a cure for cancer in the last 28 years.
22. Find the slope and Y intercept of the line 3x+4y-9=0
Answers
hi there! here's my answer for you...
Answer:
slope:
m = -3/4
y-intercept:
y = −3x/4 + 9/4
hope this helped. have a good one!
PLEASE HELP ME! THANK YOU !!
Answers
Doamin of the function
inf
Simplify 3r(4r-5s)+2r(-6r-9s)
Answers
Answer:
-33rs
Step-by-step explanation:
First, distribute in the first part of the equation.
3r(4r-5s)=12r-15rs
Now, distribute in the first part of the equation.
2r(-6r-9s)=-12r-18rs
Combine this together.
12r-15sr-12r-18rs
Combine like terms. (12r and -12r will cancel out to 0.)
-33rs
Hope this helps! Have a wonderful day ^^
Answer:
[tex]\boxed {-33rs}[/tex]
Step-by-step explanation:
Simplify the expression:
[tex]3r(4r - 5s) + 2r(-6r - 9s)[/tex]
-Use Distributive Property:
[tex]3r(4r - 5s) + 2r(-6r - 9s)[/tex]
[tex]12r^{2} - 15rs - 12r^{2} - 18rs[/tex]
-Combine both [tex]12r^{2}[/tex] and [tex]-12r^{2}[/tex]:
[tex]12r^{2} - 15rs - 12r^{2} - 18rs[/tex]
[tex]-15rs - 18rs[/tex]
-Then, combine both [tex]15rs[/tex] and [tex]18rs[/tex]:
[tex]-15rs - 18rs[/tex]
[tex]\boxed {-33rs}[/tex] (final answer)
Terrence is learning how to play the piano. Each lesson costs $18.50, and he usually pays for a whole month in advance. If he has 4 lessons scheduled for next month, how much will he pay?
Answers
Answer:
$74
Step-by-step explanation:
If each lesson is 18.50 and he has 4 lessons next month, you multiply 18.50 by 4 which you will get 74. So he has to pay $74
Answer:
$74
Step-by-step explanation:
