Answer:
The answer is "[tex]\bold{\frac{ \ e^{9x}}{9} (x-1)+C}\\[/tex]"
Step-by-step explanation:
Taking the integral [tex]\int x^{2x} \ dx[/tex]
Evaluating the integral by using integration:
[tex]u=x\\\\dv=e^{9x} \ dx[/tex]
Let
[tex]u=x\\\\ dv=e^{9x} dx[/tex]
Then,
[tex]\to \frac{du}{dx}= 1 \ and\ v =\int e^{9X} \ dx \\\\\to du = 1 \ dx \\\\\to v = \frac{e^{9x}}{9}\\\\\text{integrate the above value}:\\\\\int\ u \ dv = uv - \int v du \\\\Now, \\\\\to \int x e^{9X} \ dx = x \frac{e^{9x}}{9} - \int \frac{e^{9x}}{9} dx[/tex]
[tex]= \frac{ x \ e^{9x}}{9} - \frac{e^{9x}}{9}\\\\= \frac{ \ e^{9x}}{9} (x-1)+C\\[/tex]
Answer:
[tex]\displaystyle \int {xe^{9x}} \, dx = e^{9x} \bigg( \frac{x}{9} - \frac{1}{81} \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
Integrals[Indefinite Integrals] Integration Constant CIntegration 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^{9x}} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = x[/tex][u] Differentiate: [tex]\displaystyle du = dx[/tex]Set dv: [tex]\displaystyle dv = e^{9x} \ dx[/tex][dv] Integrate [Exponential Integration]: [tex]\displaystyle v = \frac{e^{9x}}{9}[/tex]Step 3: Integrate Pt. 2
[Integral] Integration by parts: [tex]\displaystyle \int {xe^{9x}} \, dx = \frac{xe^{9x}}{9} - \int {\frac{e^{9x}}{9}} \, du[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xe^{9x}} \, dx = \frac{xe^{9x}}{9} - \frac{1}{9} \int {e^{9x}} \, du[/tex]Step 4: Integrate Pt. 3
Identify variables for u-substitution.
Set u: [tex]\displaystyle u = 9x[/tex][u] Differentiate [Derivative Properties, Basic Power Rule]: [tex]\displaystyle du = 9 \ dx[/tex]Step 5: Integrate Pt. 4
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xe^{9x}} \, dx = \frac{xe^{9x}}{9} - \frac{1}{81} \int {9e^{9x}} \, du[/tex][Integral] U-Substitution: [tex]\displaystyle \int {xe^{9x}} \, dx = \frac{xe^{9x}}{9} - \frac{1}{81} \int {e^u} \, du[/tex][Integral] Exponential Integration: [tex]\displaystyle \int {xe^{9x}} \, dx = \frac{xe^{9x}}{9} - \frac{e^u}{81} + C[/tex][u] Back-Substitute: [tex]\displaystyle \int {xe^{9x}} \, dx = \frac{xe^{9x}}{9} - \frac{e^{9x}}{81} + C[/tex]Factor: [tex]\displaystyle \int {xe^{9x}} \, dx = e^{9x} \bigg( \frac{x}{9} - \frac{1}{81} \bigg) + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Mhanifa please help me with this! I need it done ASAP! I will mark brainliest
Answer:
[tex]1) \to \: B \\ 2) \to A[/tex]
Answer:
The third one
Step-by-step explanation:
Find the area of the figure shown below and choose the appropriate result.
4 cm
6 cm
5 cm
3 cm
Two weeks ago price was $220 now it's $325. What is the percent increase? What is percent increase if there is an additional $50 baggage fee with the new ticket price?
Answer:
68.18%
Step-by-step explanation:
325+50=375
375-220=155
155÷220×100%
≈68.18%
Pls help me with math ASAP
Answer:
y = 5/2x - 5
Step-by-step explanation:
y-int = -5
slope = 5/2
rise/run
alright my friend i've gotta go but i think you can solve these on your own.
just use the number that's on the Y vertical line to find y-int
and then use 2 points and count up to find the rise and then count across to fine thet run.
use the formula y=mx+b
good luck my friend <3
Answer:
Step-by-step explanation:
(0,-5) (4,5)
(5+5)/(4-0)= 10/4 = 5/2
y + 5 = 5/2(x - 0)
y + 5 = 5/2x - 0
y = 5/2x - 5
ice cream is served for dessert if Gio serves himself and 3 friends half a cup of ice cream how many total pints did Gio and his friends eat?
Answer:
0.25 pints
Step-by-step explanation:
To find how many pints they ate, find the number of pints in half a cup.
In 1 cup, there are 0.5 pints.
This means in half a cup, there will be 0.25 pints.
So, Gio and his friends ate 0.25 pints
Determine the center of the circle whose equation is (x – 5)2 + (y + 7) = 14
Answer:58 approximately c
Step-by-step explanation:
Do
5 cm
5 cm
20 cm
form a triangle
Answer:
Step-by-step explanation:
No. If two sides are 5cm the third side must be less than 2(5)=10cm
Answer: No, a triangle cannot be formed with these side lengths.
=========================================================
Explanation:
Recall that the triangle inequality theorem says that for a triangle to be possible, the sum of any two sides must be larger than the third side.
With these given side lengths, we can see that 5+5 = 10 is not larger than 20, so a triangle is not possible here. I recommend you try it out with 3 slips of paper of these lengths. You should find that the two 5 cm sides are too short to be able to connect to the 20 cm side properly.
What are the coordinates of point A?
(8, –6)
(–6, 8)
(–5, 7)
(7, –5) marking brainiest
Answer:
Can you add an image of the points on a graph so I can help?
4 (n-4) + 14
n = 5 btw
Answer:
=18
Step-by-step explanation:
5-4=1
1x4=4
4+14=18
hope it helped
Which is greater, 0.28 or 0.205? Explain how you know.
Answer:
Step-by-step explanation:
0.28 is roughly the same as 0.280, which has 3 significant digits (same as 0.205 has 3 significant digits). It's easier when we compare numbers having the same number of decimal places.
Comparing 0.280 to 0.205, we see that the hundredths place of 0.280 (which is 8) is greater than the hundredths place of 0.205 (which is 0). Thus 0.28 is greateer than 0.205.
How to divide 8 by 3 the long way
The number 8 divided by 3 is 2 with a remainder of 2 (8 / 3 = 2 R.
Answer:
The steps are more or less the same, except for one new addition:
Divide the tens column dividend by the divisor.
Multiply the divisor by the quotient in the tens place column.
Subtract the product from the divisor.
Bring down the dividend in the ones column and repeat
Step-by-step explanation:
The number 8 divided by 3 is 2 with a remainder of 2 (8 / 3 = 2 R.
find the value of w and then x. round side lengths to the nearest tenth and angle measures to the nearest degree
Answer:
w = 7.7 units; x = 44°
Step-by-step explanation:
If the sum of 20 numbers is 440, find the mean of the numbers.
Answer:
22
Step-by-step explanation:
mean= sum of observations/no: of observations
mean=440/2=22
please mark me brainliest
use the two points and the line to find the y-intercept
a. (-1, -1)
b. (-2, -6)
c. (- 3/4, 0)
d. (0, 4)
Answer:
0,4, That is the y intercept.
Step-by-step explanation:
Hope I helped :)
Pleaseeee help meeeeeeeee
Answer:
A. m = -6
Step-by-step explanation:
What is the value of the number in the thousandths place of 1079.483?
Answer:
3
Step-by-step explanation:
Please help please please
Answer:
C. y = 2x + 8
Step-by-step explanation:
✔️First, find the slope of the line that goes through points (-2, 4) and (6, 20):
Slope (m) = ∆y/∆x = (20 - 4) / (6 - (-2))
Slope (m) = 16/8
m = 2
✔️Find the y-intercept (b):
To do this, substitute (x, y) = (6, 20) and m = 2 into y = mx + b
Thus:
20 = 2(6) + b
20 = 12 + b
20 - 12 = b
8 = b
b = 8
✔️Write the equation by substituting m = 2 and b = 8 into y = mx + b
Thus:
y = 2x + 8
Find the circumference of a circle that has a diameter of 5 inches. Use 22/7 for pi.
15 in.
22/35 in.
15 3/7 in.
15 5/7 in.
Answer:
step 1. The circumference (c) of a circle is equal to the diameter of a circle x pi. c = d(pi) = 5pi
step 2. c = 5pi = 5(22/7) = 110/7 = 15 5/7.
Hello, happy Friday, I am just here with some geometry questions.
Please only answer this if you know the answer. If you have a comment, please add it to the comment box. Only answer the question if you can explain your answer and why you think it is accurate. Thanks, good luck!
What is x? and how did you get it?
Answer:
x = 16
Step-by-step explanation:
step 1 - 64 + 100 + x = 180 (all triangles equals 180)
step 2 - 164 + x = 180
step 3 - 164 + x = 180
-164. -164
step 4 - 180 - 164 = 16
step 5 - 100 + 64 + 16 = 180
(I do this part to double check my work)
step 6 - x = 16
Answer:
x = 48Step-by-step explanation:
The ratio:
x/64 = (100 - 64)/xx² = 64*36x = 48i need help with this
The following table shows a proportional relationship between j and m.
write an equation to describe the relation between j and m
Answer:
m=3/4 j or m = .75j
Step-by-step explanation:
Lara draws some triangle models with the measurements she wants to use to construct them. Which of these
triangle constructions would NOT be possible?
a triangle with side measurements of 3, 4, and 6 inches
a triangle with side measurements of 2, 3, and 5 inches
a triangle with side measurements of 3, 3, and 4 inches
a triangle with side measurements of 5, 5, and 5 inches.
Answer:
a triangle with side measurements of 5, 5, and 5 inches
Step-by-step explanation:
I took the test.
Construction of triangle with side measurement 2 inch, 3 inch, 5 inch is not possible.
What is triangle equality theorem?This theorem simply states that the sum of two sides of a triangle must be greater than the third side. If this is true for all three combinations, then you will have a valid triangle.
If triangle has the sides, a , b and c then
a + b > c
b + c > a
a + c > b
Given length of the sides,
a) Triangle made with sides having length 3 inch, 4 inch, 6 inch.
3 + 4 > 6 ; 4 + 6 > 3 ; 3 + 6 > 4
= 7 > 6 ; 10 > 3 ; 9 > 4
Triangle inequality theorem is satisfied, hence triangle construction is possible
b) Triangle made with sides having length 2 inch, 3 inch, 5 inch.
2 + 3 > 5 ; 3 + 5 > 2 ; 2 + 5 > 3
= 5 = 5 ; 8 > 3 ; 7 > 3
Triangle inequality theorem is not satisfied, hence triangle construction is not possible
a) Triangle made with sides having length 3 inch, 3 inch, 4 inch.
3 + 3 > 4 ; 3 + 4 > 3 ; 3 + 4 > 3
= 6 > 4 ; 7 > 3 ; 7 > 3
Triangle inequality theorem is satisfied, hence triangle construction is possible
a) Triangle made with sides having length 5 inch, 5 inch, 5 inch.
5 + 5 > 5 ; 5 + 5 > 5 ; 5 + 5 > 5
= 10 > 5 ; 10 > 5 ; 10 > 5
Triangle inequality theorem is satisfied, hence triangle construction is possible.
Hence, Triangle with side measurements of 2 inch , 3 inch , and 5 inch is not possible to construct.
Learn more about triangle inequality theorem here:
https://brainly.com/question/30066983
#SPJ6
Select all that apply.
Which graphed lines represent direct variation functions?
line a
line 6
linec
lined
Answer:
C and D
Step-by-step explanation:
HELP PLEASE
ARM SPAM (INCHES) HEIGHT (INCHES)
58 60
49 47
51 55
19 25
37 39
44 45
47 49
36 35
41 40
46 50
58 61
65 68
1. Which variable did you plot on the x-axis and which variable did you plot on the y-axis? Explain why you assigned the variables in that way.
2. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
3. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
4. Test the residuals of two other points to determine how well the line of best fit models the data.
5. Use the line of best fit to help you to describe the data correlation.
6. Using the line of best fit that you found in Part Three, Question 2, approximate how tall is a person whose arm span is 66 inches?
7. According to your line of best fit, what is the arm span of a 74-inch-tall person?
Step-by-step explanation:
we have to write all things by which which x-axis is viraivil with you and y axis is variable with you and spleen in our right one formula X is equals to X is equals to y y - behind honey bunny i y is equals to x minus b right and right that formula and write if you don't know and I will tell you another this video is it was thank you so much
what is y=− 2/9 x+2 written in standard form?
Answer:
2x+9y=18
Step-by-step explanation:
Distribute the denominator
y=-2/9x+2
9y=-2x+2
9y+2x=2
im sorry if this is wrong
a license plate that has 3 numbers from 0 to 9 and 2 letters
Answer:
what's the question there
complete the equation ×1/12=5/12+5/12+5/12
Answer:
x/12=15/12
x=15it is the answer
5.7 is increased to 7.8
What is the percentage of increase?
Answer:
7.8%
Step-by-step explanation:
Answer:
The percentage of increase is 37%
Step-by-step explanation:
The way to find the percentage of increase is to divide The difference between the two numbers by the number before the increase
7.8 - 5.7 = 2.1
The difference between 7.8 and 5.7 is 2.1
So now we divided 2.1 by the number before the increase, in this case, 5.7
2.1 ÷ 5.7 = 0.3684
0.3684 rounded to the nearest hundredth is 0.37
Thus the percentage of increase is 37%
(x^2 - 4)(x^2 + x - 12) = 0
Answer:
is that a T or F
Step-by-step explanation:
a) Let P(t) be written as
P(t) = a cos[b(t - d)] + c
The minimum Pmin and the maximum Pmax of P(t) are given.
Pmin = 4
Pmax = 20
c = (Pmax + Pmin) / 2 = (20 + 4) / 2 = 12
|a| = (Pmax - Pmin) / 2 = (20 - 4) / 2 = 8
We now need to find the number of days t after January 1st at which P(t) is maximum by counting the days of the months from January to May and adding 21 days in June.
t = 31 + 28 + 31 + 30 + 31 + 21 = 172
We now use the period to find b (b > 0) as follows
period = 365 = 2π / b
hence b = 2π / 365
A cosine function without shift has a maximum at t = 0. P(t) has a maximum at t = 172. We can model P(t) by a cos(x) function shifted by 172 to the right as follows:
P(t) = 8 cos[(2π / 365)(t - 172)] + 12
check that P(t) is maximum at t = 172: P(172) = 8 cos[(2π / 365)(172 - 172)] + 12 = 8 cos[(0)] + 12 = 20
b) The graph of P(t) is shown below.
Answer:
perfect
Step-by-step explanation: