Answer:
[tex]\displaystyle \int {xe^{7x}} \, dx = \frac{e^{7x}}{7} \bigg( x - \frac{1}{7} \bigg) + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {xe^{7x}} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = x[/tex][u] Basic Power Rule: [tex]\displaystyle du = dx[/tex]Set dv: [tex]\displaystyle dv = e^{7x} \ dx[/tex][dv] Exponential Integration [U-Substitution]: [tex]\displaystyle v = \frac{e^{7x}}{7}[/tex]Step 3: integrate Pt. 2
[Integral] Integration by Parts: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \int {\frac{e^{7x}}{7}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{1}{7} \int {e^{7x}} \, dx[/tex]Step 4: Integrate Pt. 3
Identify variables for u-substitution.
Set u: [tex]\displaystyle u = 7x[/tex][u] Basic Power Rule [Derivative Property - Multiplied Constant]: [tex]\displaystyle du = 7 \ dx[/tex]Step 5: Integrate Pt. 4
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{1}{49} \int {7e^{7x}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{1}{49} \int {e^u} \, dx[/tex][Integral] Exponential Integration: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{e^u}{49} + C[/tex][u] Back-Substitute: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{xe^{7x}}{7} - \frac{e^{7x}}{49} + C[/tex]Factor: [tex]\displaystyle \int {xe^{7x}} \, dx = \frac{e^{7x}}{7} \bigg( x - \frac{1}{7} \bigg) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Function C gives the cost, in dollars, of buying n apples. What does this equation represent in this situation?
C(5)=4.50
help pls
Answer:
The cost of 5 apples.
Step-by-step explanation:
Typically the equation would be written as C(n) = 4.50
Since 5 is where 'n' should be, then that means the number of apples in the equation is five.
C(5) = 4.50
Means, that 5 apples cost $4.50
For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price.
p = −0.3x + 6 and p = 0.05x + 2.5
equilibrium quantity
units
equilibrium price $
9514 1404 393
Answer:
(x, p) = (10, 3)
Step-by-step explanation:
Equating the expressions for p, we have ...
-0.3x +6 = 0.05x +2.5
3.5 = 0.35x . . . . . add 0.3x-2.5
10 = x . . . . . . . . . . divide by 0.35
p = -0.3(10) +6 = 3
The equilibrium quantity is 10 units.
The equilibrium price is $3.
can somebody please help
a. 44.5
b. 15
c. 37.5
d. 26.25
Answer:
I think c
Step-by-step explanation:
not completely sure cant see question
Convert 6.3 m to millimeters
Hi. 6.3 meters to millimetres is 6300
Eric is x years old. Eric's sister is 5 years older than Eric. His mother is 3 times his sister's age. His father is x years older than his mother. How old is Eric's father if he was 8 years old? How old is Eric's mother is he was 8 years old?
Answer:
Eric´s mother is 39 years old.
Step-by-step explanation:
Eric is 8, so 8+5 = 13 then 13x3 = 39
Answer:
Eric mother was 39 years old and the father is 47 years old.
Step-by-step explanation:
I hope this helped.
What do you get when you simplify 12/8
Answer:
3/2
Step-by-step explanation:
You can divide both 12 and 8 by four. Dividing 12 by four gives you 3 and dividing 8 by 4 gives you 2. This makes the simplified fraction 3/2
:)
Please i need help thank you!..
How many minutes in 255 seconds A)2 11/12 B)3 5/12 C)3 3/4 D) 4 1/4
Answer:
4 1/4
Step-by-step explanation:
divide 255 by 60
I need help ASAP have a picture
If I have 41 red mechanical pencils and each pencil has 3 pieces of lead in it. How many pieces of lead are there in all
Answer:
there are 123 pieces of lead in all
SOMEONE HELP I'LL MARK CORRECT ANSWER BRAINLY
Answer:
B
Step-by-step explanation:
what percent is 25 out of 72
Answer:
35%
Step-by-step explanation:
It’s 34.722222222222%, but if you round it up, it’s about 35%.
while shopping for clothes jacklyn spent $38 less than 2 times what Daniel spent. Jacklyn spent $10. Write and solve an equation to find out how much daniiel spent. Let x trepresent what daniel spent.
HELP A B OUT HELP A B OUT HELP A B OUT HELP A B OUT
PLEAE HELP I WILL GIVE BRAINLIST can someone please help with 4,5,6 and use the box method on a paper please I need this ( show work ) please!
evaluate f(x)=x/x-5 when x=3
Answer:
Step-by-step explanation:
3/3-5=3/-2
The maroon team and the orange team played a game of football. The maroon team scored 20 points and the orange team scored 6 points. What is the ratio of points scored by the maroon team to points scored by the orange team?
Answer:
20/6 or 10/3
Step-by-step explanation:
4 1/2 - 1 2/3 = ?
what is the question mark ?
Answer:
17/6 LMK if you need a different form.
Step-by-step explanation:
Estimate the sum to the nearest ten. 772 + 146 =
?
Answer:
920
Step-by-step explanation:
added up the original answer would be 918 but you have to round up to 920
Answer:
918.0
Step-by-step explanation:
6) 9x - 7y = -4
18x - 14 y = 10
A) (8, -1)
C) (-8,-8)
B) (-8,-1)
D) No solution
Answer:
D). No solution
Step-by-step explanation:
9x - 7y = -4
18x - 14 y = 10
9x - 7y = 5
9x - 7y = -4
9x - 7y = 5
__________--
0 = -9
No solution
y + 2x = -1
y = 1/2x + 4
Answer:
x = -1
y = 3
Step-by-step explanation:
y + 2x = -1
y = 1/2x + 4
(1/2x + 4) + 2x = -1
1/2x + 2x + 4 = -1
2 1/2x + 4 = -1
2 1/2x = -1 - 4
2 1/2x = -5
x = -5 / 2 1/2
x = -2
y + 2x = -1
y + 2(-2) = -1
y - 4 = -1
y = -1 + 4
y = 3
i need help asap do tonight
Answer:
The first one..
Step-by-step explanation:
Answer:
The top one
Step-by-step explanation:
If you minus 19-10 you get 9 then if you divide 9 by 3 you get 3 which means that each soda costs 3 bucks
Robertson builds 3 chairs every hour how many hours does he have to work to build 999 chairs
Answer:
333 hours
Step-by-step explanation:
you didvide 999by 3
The Franklins inherited $3,500, which they want to invest for their child's future college expenses. They use the following formula to calculate the value of their investment over time, where
A = value of the investment after years, P = principal invested, r = annual interest rate, and n = number of times compounded per year.
A = P(1 +
you
71
If they invest the inherited money at an annual rate of 8.25% with interest compounded monthly, what is the value of the account to the nearest dollar, after 5 years?
Answer:
1443.75 i think
Step-by-step explanation:
Thus, Franklin has $5011 after 5 years for an annual rate of 8.25% with interest compounded monthly.
The Franklins inherited $3,500, which they want to invest for their child's future college expenses. Using formula [tex]A = p(1+r/n)^{nt}[/tex]
where A is the value of the investment after t years, P is the principal invested, r is the annual interest rate and n is the number of times compounded per year.
an annual rate of 8.25% with interest compounded monthly, what is the value of the account to the nearest dollar, after 5 years is to be determined.
Statistic is the study of mathematics which deal with relations between comprehensive data.
Using formula [tex]A = p(1+r/n)^{nt}[/tex]
[tex]A = 3500*(1+0.0825/12)^{12*5}\\A = 3500*(1+0.006)^{60}\\A = 3500*(1.006)^{60}\\A = 5011.25\\[/tex]
A ≈ 5011
Thus, Franklin has $5011 after 5 years for an annual rate of 8.25% with interest compounded monthly.
Learn more about Statistics here:
https://brainly.com/question/23091366
#SPJ2
Plerson's science grades were 95,87, 75,78, 84, and 97.
What was the average of her grades?
Answer:
The average is 86
Step-by-step explanation:
so you have to take all the numbers and add them together, the answer of all the numbers together should be: 516. Then you divide 516 by 6 which equals 86.
So the average of 95,87,75,78,84, and 97 is 86
Hope this helps:)
-9(8x — 8) = 8(-7 - 10x)
Answer:
×=1/3
Step-by-step explanation:
8x –3(5x–2)=7–10x
Distribute
8x - 15x +6 = 7-10x
Combine like terms
-7x + 6 = 7- 10x
Add 10x to each side
-7x +10x+ 6 = 7- 10x+10x
3x+6 = 7
Subtract 6 from each side
3x+6-6 =7-6
3x = 1
Divide each side by 3
3x/3 = 1/3
x = 1/3
Which ordered pair is NOT included in a graph of y=x+5?
ANSWER GET BRAINLIEST
Step-by-step explanation:
Ay bro use photomath its really easy to awnsere with it just take a photo of the question and it'll give u steps
If a pound of coffee costs 12. How many ounces can be brought for 3.90
Find what the value of x.
60
15
30
45
Answer:
ANS;;;; 45 ...........................
