I assume the integral is
[tex]\displaystyle \int x^3 e^{-x} \, dx[/tex]
Integrate by parts with
[tex]u = x^3 \implies du = 3x^2 \, dx[/tex]
[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]
so that
[tex]\displaystyle \int u \, dv = uv - \int v \, du[/tex]
i.e.
[tex]\displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} + 3 \int x^2 e^{-x} \, dx[/tex]
Integrate by parts again, this time with
[tex]u = x^2 \implies du = 2x \, dx[/tex]
[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]
and so
[tex]\displaystyle \int x^2 e^{-x} \, dx = -x^2 e^{-x} + 2 \int x e^{-x} \, dx[/tex]
[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} + 3 \left(-x^2 e^{-x} + 2 \int x e^{-x} \, dx\right)[/tex]
[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} + 6 \int x e^{-x} \, dx[/tex]
Once more, with
[tex]u = x \implies du = dx[/tex]
[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]
[tex]\displaystyle \int x e^{-x} \, dx = -xe^{-x} + \int e^{-x} \, dx[/tex]
[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} + 6 \left(-xe^{-x} + \int e^{-x} \, dx\right)[/tex]
[tex]\implies \displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} -6xe^{-x} + 6 \int e^{-x} \, dx[/tex]
Finally,
[tex]\displaystyle \int e^{-x} \, dx = -e^{-x} + C[/tex]
and so
[tex]\displaystyle \int x^3 e^{-x} \, dx = -x^3 e^{-x} - 3x^2 e^{-x} -6xe^{-x} - 6 e^{-x} + C[/tex]
or equivalently,
[tex]\displaystyle \int x^3 e^{-x} \, dx = \boxed{-(x^3+3x^2+6x+6) e^{-x} + C}[/tex]
We can also approach the integral more generally by considering
[tex]I_n = \displaystyle \int x^n e^{-x} \, dx[/tex]
Integrate by parts with
[tex]u = x^n \implies du = nx^{n-1} \, dx[/tex]
[tex]dv = e^{-x} \, dx \implies v = -e^{-x}[/tex]
Then
[tex]\displaystyle I_n = -x^n e^{-x} + n \int x^{n-1} e^{-x} \, dx = -x^n e^{-x} + n I_{n-1}[/tex]
We can solve the recurrence using the initial "value" [tex]I_0 = -e^{-x}+C[/tex] to find a general formula for [tex]I_n[/tex]. Then we get the integral we want [tex]I_3[/tex] "for free".
Peter went to a store. He bought 6.4 pounds of onions, potatoes, and hamburger. If 1.18 pounds was hamburger and 4.75 pounds were potatoes, how many pounds of onions did
Peter buy?
Answer:
0.47 pounds
Step-by-step explanation:
Simple subtraction!
Total pounds = pounds of onions + pounds of potatoes + pounds of hamburger
Setting the pounds of onions to [tex]x[/tex] we get:
[tex]6.4 = x + 1.18 + 4.75[/tex]
[tex]x=0.47[/tex]
So we get 0.47 pounds of onions!
guy is half as old as Gerald, who is three times older than gill. If the sum of their ages is 99, what are their ages?
Answer:
Step-by-step explanation:
gerald=2x
guy=x
gill= aproximately 0.3x
2x+x+0.3x=99
2.3x=99
x=43.04
The age of the guy is 29.72 years, the age Gerald is 59.44 years and the age of gill is 9.8 years.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given data in the question,
The equation according to the given statement will be,
The age of Gerald is 2x,
The age of the guy is x and the age of the gill is 0.33x.
So, the equation will be,
x + 2x + 0.33x = 99
3.33x = 99
x = 99/3.33
x = 29.72
Age of Gerald, 2x = 2(29.72) = 59.44 years.
Age of guy, x = 29.72 years and,
Age of gill, 0.33x = 0.33(29.72) = 9.8 years.
To know more about arithmetic operations:
https://brainly.com/question/13585407
#SPJ2
Pls answer my math, thank u
Answer: question 1 equals 31 Over 8 or 3.875 .
question 2 equals 425 over 24 .
question 3 equals 41 over 6 or 6.83333333
question 4 equals 55 Over 14
Step-by-step explanation: hope it helps you .
Question 1a:
Compute the Laplace Transforms of
f(x) = { x² +2x +1 , x < 3
{ e⁻⁵ˣ , x ≥ 3
This is made easy if you know the Laplace transform pair
[tex]u(t - c) y(t - c) \mapsto e^{-cs} Y(s)[/tex]
where u(t) is the Heaviside step function and Y(s) is the Laplace transform of y(t).
We rewrite f, g, and h in terms of u :
[tex]f(x) = (x^2+2x+1) (u(x) - u(x-3)) + e^{-5x} u(x-3)[/tex]
[tex]g(x) = \sin(3x) (u(x-5) - u(x-10))[/tex]
[tex]h(x) = (u(x) - u(x-4)) + 2(u(x-4)-u(x-8)) + 3 (u(x-8)-u(x-16))[/tex]
and we also rearrange terms to get the right shift in argument:
[tex]f(x) = (x^2+2x+1) u(x) - ((x-3)^2+8(x-3)+16) u(x-3) + e^{-15} e^{-5(x-3)} u(x-3)[/tex]
[tex]g(x) = [\cos(15) \sin(3(x-5)) + \sin(15) \cos(3(x-5))] u(x-5) \\\\ ~~~~~~~~~~- [\cos(30) \sin(3(x-10)) + \sin(30) \cos(3(x-10))] u(x - 10)[/tex]
[tex]h(x) = u(x) + u(x-4) + u(x-8) - 3 u(x - 16)[/tex]
Now we can apply the known transform pair, along with
[tex]x^n \mapsto \dfrac{n!}{s^{n+1}}[/tex]
[tex]e^{ax} \mapsto \dfrac1{s-a}[/tex]
[tex]\sin(ax) \mapsto \dfrac{a}{s^2+a^2}[/tex]
[tex]\cos(ax) \mapsto \dfrac{s}{s^2+a^2}[/tex]
The transforms of f, g, and h are then
[tex]F(s) = e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-15} e^{-3s}}{s + 5} \\\\ = \boxed{e^{-s} \left(\dfrac2{s^3} + \dfrac2{s^2} + \dfrac1s\right) - e^{-3s} \left(\dfrac2{s^3} + \dfrac8{s^2} + \dfrac{16}s\right) + \dfrac{e^{-3(s+5)}}{s + 5}}[/tex]
[tex]G(s) = \dfrac{3\cos(15) e^{-5s}}{s^2+9} + \dfrac{s \sin(15) e^{-5s}}{s^2+9} - \dfrac{3\cos(30)e^{-10s}}{s^2+9} - \dfrac{s \sin(30) e^{-10s}}{s^2+9} \\\\ ~~~~~~~ = \dfrac{3(\cos(15)-\cos(30)) + s(\sin(15) - \sin(30))}{s^2+9} \\\\ ~~~~~~~ = \boxed{\dfrac{6\sin\left(\frac{45}2\right)\sin\left(\frac{15}2\right) - 2s \cos\left(\frac{45}2\right)\sin\left(\frac{15}2\right)}{s^2+9}}[/tex]
[tex]H(s) = \boxed{\dfrac{e^{-s} + e^{-4s} + e^{-8s} - 3 e^{-16s}}s}[/tex]
Simplify the expression
Step-by-step explanation:
for me it is best as a first step to combine this all to one big fraction, and then simplify the whole expression.
you do know that when multiplying the same variable with exponent we simply add the exponents. and she we divide the same variable with exponents, we subtract them from each other (as the overlapping exponent parts cancel each other out).
(3ac³f³)/(8a²bcf⁴) × (12ab²c)/(18ab³c²f) =
= (3×12a²b²c⁴f³)/(8×18a³b⁴c³f⁵) =
= (3×12c)/(8×18ab²f²) = 12c / (8×6ab²f²) =
= 2c / (8ab²f²) = c / (4ab²f²)
While researching the industry she is interested in, Demi sees that the average unemployment rate is 6.3%. How many people, out of every 250, are unemployed? (2 points)
15.75
39.68
45.50
157.5
Answer:
15.75 is 6.3% of 250.
Formula:
[Percentage] x [Number Given] = [New number]
Kai randomly surveys eighth graders at his school and learns that 7 of 35 respondents own a video gaming system. Based on these data, how many of the 150 eighth-grade students in Kai's school would be expected to own a video gaming system? A 15 students B 25 students C 30 students D 50 students
The correct answer for this question is 30 students
Sure hope this helps you :)
-15(y2)4 divide 5y3y4
Answer:
-3y
Step-by-step explanation:
-15(y2)4 ÷5y3y4
Rewrite the division as a fraction
-15(y2)4
5y3y4
Multiply y3 by y4 by adding the exponents
-5(y2)4
5y7
Cancel the common factor of -15 and 5
-3(y2)4
y7
Multiply the exponents in (y2)4
-3y8
y7
Cancel the common factor of y8 and y7
Factor y7 out of -3y8
y7(-3y)
y7
Multiply by 1
y7(-3y)
y7 × 1
Cancel the common factor which is y7 and y7
Rewrite the expression
-3y
1
Divide -3y by 1
-3y
how do i solve this?
Answer:
33
Step-by-step explanation:
For 4 triangles area 4*(1/2)*4*3=24
base square area 3*3=9
all together 24+9= 33
a] The area of a square is 200 cm² Find the length of its diagonal.
[tex]"20cm"[/tex]
Step-by-step explanation:[tex]Area\ of\ rq=a^2[/tex]
[tex]a=\sqrt{200}=10\bullet \sqrt{2}[/tex]
[tex]d\ iargul=\sqrt{2}9[/tex]
[tex]=10\times \sqrt{2}\times \sqrt{2}[/tex]
[tex]=20cm[/tex]
I hope this helps you
:)
Select all the fractions that are equivalent to each other.
(Choose 2)
[tex]hi \\answer \\the \\question[/tex]
Answer: You should try to multiply and divide try then question me back. But the answers are neither of them.
Step-by-step explanation:
Does 0 ÷ a =a ÷ a(assume a is not equal to 0)? explain
Answer:
A = 0
__________________________________________________________
SolveAlthough the question says not to assume A is 0, that is the only possible option, since any nor prime or composite is going to be the higher number, because it stays the same.
0 ÷ a(0) = 0
a(0) ÷ a(0) = 0
__________________________________________________________
Questions?Ask in the comments.
Tim has a checking account with $1,200 remaining after paying bills after several months. He wants to earn interest on
this money rather than keep extra money he does not need for monthly bills in his checking account. Over the next
year, he thinks he might need to withdraw $100 one or two times. His bank requires $250 to open a regular savings
account, $500 for a one-year CD, $750 for a two-year CD, and $1,000 to open a money market account. Decide which
choice would be the best for his situation
Assuming He wants to earn interest on this money rather than keep extra money he does not need. The choice that would be the best for his situation is $250 to open a regular savings.
What is regular savings account?A regular savings account is a saving acount that enables you to save and earn interest based on the amount saved because it is an interest bearing account.
Although this account gives you interest but the interest rate is low. Since Tim has $1200 in his checking account assuming he withdraw $100 twices, Tim will have $1,000 ($1,200-$200).
Now if he open a regular saving with $250 he will have $750 left ($1,000-$250) with which he can earn interest with.
Inconclusion the choice that would be the best for his situation is $250 to open a regular savings.
Learn more about regular account here:https://brainly.com/question/25787382
Determine the area of the following shapes.
a. 144 in
b. 154 in
c. 164 in
A) 144 in
is your answer. good luck
Tell if the slope is positive, negative, zero, or no slope.
Answer:
No slope.
Step-by-step explanation:
There is no such thing as a vertical slope, meaning that there is no slope. I hope this helps! :)
Answer:
No slope
Step-by-step explanation:
The line is going straight up :)
Brainliest pls?
find a quadratic polynomial each with the given number as the sum and product of its zeros respectively
1/4 and 1
Answer:
The answer is 4x² – x – 4 = 0
Step-by-step explanation:
1st Method Given;Sum of zeroes = α + β = (-b)/a = 1/4Product of zeros = αβ = c/a = 1Where,
a = 4b = 1c = 4So, one quadratic polynomial satisfying is given condition is 4x² – x – 4 = 0
2nd MethodSum of zeroes = 1/4
Product of zeros = 1
Remember this formula
x² – (α + β)x + αβ
x² – 1/4x + 1
4x² – x – 4 = 0
Thus, The quadratic polynomial is
4x² – x – 4 = 0.
How to simplify in laws of exponents
Answer:
You multiply the exponents and or to keep the base the same.
Step-by-step explanation:
I apologize if it is incorrect-
I hope it helps! Have a great day!
Anygays-
A rectangular box has a volume of 15 cubic feet. The length, width, and height of the box are each doubled.
What is the new volume of the rectangular box?
O A. 30 cubic feet
OB. 60 cubic feet
O c. 90 cubic feet
OD. 120 cubic feet
Answer:
I BELIEVE the answer would be 30
Question
The sum of the measures of the angles of a triangle is
180. The sum of the measures of the second and third angles is five
times the measure of the first angle. The third angle is 30 more than the second. Let T. y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.
Provide your answer below:
Answer:
t = 30°y = 60°z = 90°Step-by-step explanation:
The given relations can be used to write three equations for the angle values.
Setupt + y + z = 180 . . . . . sum of all angle measures
y + z = 5t . . . . . . . . second and third total 5 times the first
y + 30 = z . . . . . . third angle is 30 more than the second.
__
SolutionUsing the third equation to substitute for z in the first two equations gives ...
t + y + (y +30) = 180 ⇒ t +2y +30 = 180
y + (y +30) = 5t ⇒ 2y +30 = 5t
Using the second of these equations to substitute for (2y+30) in the first, we have ...
t +5t = 180
t = 180/6 = 30 . . . . . . divide by the coefficient of t
Using this value in our equation for 5t gives ...
2y +30 = 5(30)
2y = 120
y = 60
Then the value of angle z is ...
y +30 = z = 60 +30
z = 90
The first, second, and third angles are 30°, 60°, and 90°, respectively.
Hi, I need help. What is 4 1/12 + 5 3/12?
Answer:
9 4/12
Step-by-step explanation:
Just add the mixed numbers 4 + 5 = 9
Add the fraction numerators 1 +3 = 4
*Since the denominator is the same, we just add the numerators
9 4/12
Answer:
as decimal 9.33333
Step-by-step explanation:
4 1/12 + 5 3/12 = 28/3 = 9 1/3
f(x) = x^2. What is g(x)?
A. g(x) = 2x^2
B. g(x) = (1/4 x)^2
C. g(x) = 1/2 x^2
D. g(x) = (1/2 x)^2
help asap will give brainly .
A drawer is 5 feet wide, 4 feet deep. If the volume is 40, what is the height =
The diagram shows the shape of a schools auditorium stage. What is the area of the stage?
Do number 5
Answer:
100 square feet (100 ft²)
Step-by-step explanation:
Formula
Area (trapezoid) = 1/2 x sum of parallel sides x heightArea (parallelogram) = base x heightArea of stage
Area (trapezoid) + Area (parallelogram)1/2 x (8 + 12) x 4 + 4 x 152 x 20 + 6040 + 60100 square feetArea of trapezoid:-
1/2(Sum of parallel sides×Height)1/2(8+12)×42(20)40ft²Area of parallelogram
BH15(4)60ft²Total:-
60+40=100ft²BRAINLIEST!!!
Given the figure below, find the values of x and z.
Step-by-step explanation:
87 and z are opposite so the are equal. The x equation is on the same line as the 87 degree angle so those 2 added together have to equal 180 so subtract 87 from 180 and get 93 and set 93 equal to 9x-87 and solve to get x=20
Answer:
=> z = 87° { vertically opposite angle }
=> 87° + (9x-87) = 180° { linear pair }
=> 87 +9x-87 = 180
=> 9x = 180°
=> x = 180/9
=> x = 20°
What is the slope of a line perpendicular to the line whose equation is
3x – 3y = 63. Fully simplify your answer.
Find two integers whose sum is 11 and whose product is 30.
help please. I don't know it
Help me out please simple
A straight line is 180 degrees in measure
The straight line is made up of three angles
--> angle 1
--> angle 2
--> angle with a little square on it
(angle with a little square means it is 90 degrees in measure)
Let's set up an equation
[tex]angle1 + angle2 + 90 = 180\\angle1 + 87 + 90 = 180\\angle1 = 3[/tex]
Thus angle 1 is 3 degrees or the second choice
Hope that helps!
The graph of a system of two linear equations is a pair of
lines that intersect at the origin. Which statement is true of
the system?
Answer:
They both have a y intercept of 0
Step-by-step explanation:
Linear equations are written in the form y = mx + b. m is the slope and b is the y-intercept. It also states that they intersect at the origin, so they must have a y-intercept of 0.
What's the area of the composite figure?
Answer:
[tex]\huge\boxed{\bf\: 83 \: yd^{2}}[/tex]
Step-by-step explanation:
Consider rectangle ABCD.
Here,
AB = DC = 9 yd (length = l)
AD = BC = 7 yd (width = w)
Area of this rectangle:
= l * b
= 9 * 7
= 63 yd²
[tex]\rule{150pt}{2pt}[/tex]
Now, take rectangle DEGF.
Here,
DE = FG = 5 yd (length = l)
DF = EG = 4 yd (width = w)
Area of this rectangle:
= l * b
= 5 * 4
= 20 yd²
[tex]\rule{150pt}{2pt}[/tex]
Total area of the compisite figure:
= Area of rectangle ABCD + Area of rectangle DEGF
= 63 yd² + 20 yd²
= 83 yd²
[tex]\rule{150pt}{2pt}[/tex]
Refer to the attachment for the labelling of the figure.