Evaluate the integral using integration by parts. ∫(7x^2−12x)e^2xdx
Answers
To evaluate the integral ∫(7x^2 - 12x)e^(2x) dx using integration by parts, we can follow the integration by parts formula:
∫u dv = uv - ∫v du
Let's assign u and dv as follows:
u = 7x^2 - 12x (choose the polynomial term to differentiate)
dv = e^(2x) dx (choose the exponential term to integrate)
Now, let's differentiate u and integrate dv:
du = (d/dx)(7x^2 - 12x) dx = 14x - 12
v = ∫e^(2x) dx = (1/2)e^(2x)
Applying the integration by parts formula, we have:
∫(7x^2 - 12x)e^(2x) dx = u * v - ∫v * du
Substituting the values:
∫(7x^2 - 12x)e^(2x) dx = (7x^2 - 12x) * (1/2)e^(2x) - ∫(1/2)e^(2x) * (14x - 12) dx
Simplifying, we get:
∫(7x^2 - 12x)e^(2x) dx = (7/2)x^2e^(2x) - 6xe^(2x) - ∫7xe^(2x) dx + 6∫e^(2x) dx
Now, we can integrate the remaining terms:
∫7xe^(2x) dx can be evaluated using integration by parts again. Let's assign u and dv:
u = 7x (choose the polynomial term to differentiate)
dv = e^(2x) dx (choose the exponential term to integrate)
Differentiating u and integrating dv:
du = (d/dx)(7x) dx = 7 dx
v = ∫e^(2x) dx = (1/2)e^(2x)
Applying integration by parts to ∫7xe^(2x) dx, we have:
∫7xe^(2x) dx = u * v - ∫v * du
= 7x * (1/2)e^(2x) - ∫(1/2)e^(2x) * 7 dx
= (7/2)xe^(2x) - (7/2)∫e^(2x) dx
= (7/2)xe^(2x) - (7/4)e^(2x)
Now, we can substitute this back into our original equation:
∫(7x^2 - 12x)e^(2x) dx = (7/2)x^2e^(2x) - 6xe^(2x) - 7/2xe^(2x) + 7/4e^(2x) + 6∫e^(2x) dx
Simplifying further:
∫(7x^2 - 12x)e^(2x) dx = (7/2)x^2e^(2x) - (11/2)xe^(2x) + (7/4)e^(2x) + 6(1/2)e^(2x) + C
Finally, the definite integral would involve substituting the limits of integration into this expression.
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Related Questions
How many unique triangles can be made when one angle measures 90° and another angle is half that measure? 1 2 More than 2 None
Answers
Answer:
1
Step-by-step explanation:
I'm not sure if I read your question right, but if one angle is 90 and the other should be half the angle 90, the other angle must be 45. Thus, this would create a 45-45-90 triangle. There is no other possibility if one of the angles must be half that of the 90 degree angle.
Answer:
1
Step-by-step explanation:
Suzie bought 17.75 lbs of flour. If the price for 1lb is $19.68, calculate the total amount she paid to the shopkeeper
Answers
( excluding the .75)
17 x 19.68 = $334.56
.75 = 3/4
19.68 / 4 = $4.92
($4.92 for every quarter of a pound)
4.92 x 3 = $14.76 ( .75 = 3/4)
334.56 + 14.76 = $349.32
CHECK
17.75 x 4 = 71 ( Figure out how many fourths make 17.75)
71 x 4.92 = $349.32
She paid the shopkeeper $349.32
Stress state is given as following.. σ
ij
=
⎣
⎡
20
−4
0
−4
−15
0
0
0
10
⎦
⎤
Calculate normal stress and shear stress acting on a plane perpendicular to direction inclined 30
∘
counter clockwise to σ
11
and direction of three principal stresses and maximum shear stress.
Answers
The normal stress and shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ 11 are σn = 16−15√3 and τ = 2+15√3/4. The maximum shear stress is 17.5.
The stress tensor σ given in the problem is:
σ = 201504−400−1500−1010
The normal stress is given by
σn = σ11cos²θ+σ22sin²θ−2σ12sinθcosθ
where
θ = 30°
θ = 30° is the angle between the direction perpendicular to the plane and the direction of σ11
σ11 = 20
σ22 = −15
σ12 = −4
Here is a detailed calculation:
σn = 20cos²(30)+(-15)sin²(30)-2(-4)sin(30)cos(30)
σn = 20cos²(30)+(-15)sin²(30)+4sin(30)cos(30)
σn = 20(3/4)+(-15)(1/4)+4(1/2)(√3/2)
σn = 12−15√3+4√3
σn = 16−15√3
The normal stress is σn = 16−15√3
The shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ11
σ11 is given by:
τ = σ12(sin²θ−cos²θ)+0.5(σ11−σ22)sin2θ
where
θ = 30°
θ=30° is the angle between the direction perpendicular to the plane and the direction ofσ11.
σ11 = 20
σ22 = −15
σ12 = −4
Here is a detailed calculation:
τ = −4(sin²(30)−cos²(30))+0.5(20−(−15))sin(60)
τ = −4((1/4)−(3/4))+0.5(20+15)(√3/2)
τ = 4(1/2)+0.5(35)(√3/2)
τ = 2+15√3/4
The shear stress is τ = 2+15√3/4
Maximum shear stress
The maximum shear stress is given by
τmax = 0.5(σ1−σ2)
whereσ1σ1 andσ2σ2 are the first and second principal stresses.
The eigenvalues of the stress tensor σ are found by solving the characteristic equation:
det(σ−λI)=0
Here is a detailed calculation:
σ−λI = [20150−λ−400−1500−λ0−400−15−λ10−λ]
σ−λI = 0(20150−λ)[(−λ)(−λ−15)+0(−400)]−(−4)[0(−λ−15)+(−400)(−λ)]+0[0(−400)+(20150−λ)(−λ)]
σ−λI = 0λ³+35λ²−605λ−1875
σ−λI = 0
λ = −25,5,3
The maximum shear stress occurs on the plane of maximum shear stress which is at 45° 45° to the coordinate axes.
The maximum shear stress is found to be
τmax = 0.5(σ1−σ2)
τmax = 0.5(20−(−15))
τmax = 17.5.
Therefore, the maximum shear stress is τmax = 17.5.
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Which quadratic function has a y-intercept of 4?
y=x2−2x+4
y=x2+2x+9
y=−x2+3x
y=x2+13x+12
Answers
Answer:
This tells us that the vertex is at (−2, 9) and the equation of the axis of symmetry is x = −2. To find the x-intercepts, we put y = 0 to obtain
(x + 2)2 − 9 = 0
(x + 2)2 = 9
x + 2 = 3 or x + 2 = −3
x = 1 or x = −5.
Step-by-step explanation:
Image result for Which quadratic function has a y-intercept of 4? y=x2−2x+4 y=x2+2x+9 y=−x2+3x y=x2+13x+12
The standard form of a quadratic equation is written as y=ax2+bx+c, where x and y are variables and a, b, and c are known constants. To find the y-intercept from a quadratic equation, substitute 0 as the value for x and solve. The y-intercept is always equal to the value of c in the equation.
Answer:
X is the answer so ez lolololol is the first thing
You play a gambling game with a friend in which you win 25% of the time and lose 75% of the time. When you lose, you lose $1. What profit should you earn when you win, in order for the game to be fair?.
Answers
Therefore, to make the game fair, you should earn a profit of $3 when you win.
To determine the profit you should earn when you win in order for the game to be fair, we need to consider the overall expected value.
In this gambling game, you win 25% of the time and lose 75% of the time. Let's assume that when you win, you earn a profit of P dollars. When you lose, you lose $1.
The expected value can be calculated as follows:
Expected Value = (Probability of Winning * Profit) + (Probability of Losing * Loss)
Since the game should be fair, the expected value should equal zero. Thus, we can set up the equation:
0 = (0.25 * P) + (0.75 * (-1))
Simplifying the equation:
0 = 0.25P - 0.75
0.75 = 0.25P
P = 0.75 / 0.25
P = 3
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If a parcel of land originally worth $35,000 increases in values 18% per year, what will the land be worth about in the eighth year?
Answers
Answer:
131560.072
Step-by-step explanation:
Because it is increase so we add humdred to the percent and then divide by hundred - 18+100/100 = 1.18
eight years - 1.18 raised to the pwer of 8
worth - 35000
hence it will be - 1.18 raised to the power of 8 x 35000
thank you
Byron earns $11.00 per hour. How many hours will Byron have to work to earn $143.00?
7.7 hours
13.0 hours
14.3 hours
15.7 hours
Answers
Answer:
13.0 hours
Step-by-step explanation:
$143 ÷ $11 (how he gets payed per hour) = 13 hours
Byron has to work 13 hours to earn $143 dollars
Answer:
\(Byron \: will \: have \: to \: work \: for \\ \: 13\: hrs \: to \: earn \: 143\)
\(let \: the \: number \: of \: hrs \: = x \\ then \\ for \: the \: salary \: of \: \: 143 \: \\ the \: earning \: \times \: the \: time \: (x) = 143 \\ so \: 11x \: = 143 \\ x = \frac{143}{11} = 13.\)
suppose that inches 23 of wire costs 92 cents .at the same rate, how much (in cents) will 34 inches of wire cost?
Answers
The required cost of 34 inches of wire as per the cost of 23 inches of wire is 92 cents is equals to 136 cents.
Let x be the cost (in cents) of 34 inches of wire.
We know that 23 inches of wire costs 92 cents,
Use a proportion to solve this problem,
23 inches / 92 cents = 34 inches / x cents
To solve for x, apply cross-multiply and simplify,
⇒ 23 inches × x cents = 92 cents × 34 inches
⇒ 23x = 3128
⇒ x = 3128/23
⇒ x ≈ 136.00 cents
Therefore, the cost of 34 inches of wire will be approximately 136 cents.
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What is the value of x?
Pls hurry!!!
Answers
Answer:
C. 120
Step-by-step explanation:
Hope it helps!
Last question find measure of arc Su
Answers
Check the picture below.
\(52x=\cfrac{154-50x}{2}\implies 104x=154-50x\implies 154x=154\implies x=\cfrac{154}{154} \\\\\\ x=1\hspace{9em}\stackrel{ 50(1) }{\widehat{SU}=50^o}\)
What is anti derivative of 1?
Answers
The general form of the anti-derivative of 1 is given by:
∫1dx = x + C
Where "x" represents the variable, "dx" represents the infinitesimal change in x, and "C" represents the constant of integration.
It's important to note that the constant of integration can take on any value, so the anti-derivative of 1 is not a unique function, but a family of functions.
The anti-derivative, also known as the indefinite integral, of a function is the reverse of finding the derivative. It gives us the original function given its derivative.
The anti-derivative of a constant function, such as 1, is a simple linear function. To find the anti-derivative of 1, we simply integrate it by adding a constant of integration, represented by "C".
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Curt and Melanie are mixing 70% of blue paint and 30% of yellow paint to make seafoam green paint in a 1. 5 quarts bucket. Use the percent equation to find out how much yellow paint they should use
Answers
The amount of yellow paint Curt and Melanie should use is 0.45 quarts so that they can make 1.5 quarts bucket of seafoam green paint.We can use per cent equation.
Given that to make 1.5 quarts bucket of seafoam green paint Curt and Melanie have to mix 70 parts blue paint and 30 parts yellow paint.If 100 percent represent total paint then for 1.5 quarts we have to find the proportion of yellow paint.Let it be x.
30% / 100% =30 / 100 = x / 1.5 quarts.
We can reduce the equation further,
0.3 = x / 1.5.
0.3 * 1.5 = x
x = 0.45
We can also find blue paint proportion similar by substituting 30 per cent to 70 per cent.
As a result of our calculation, we found the amount of yellow paint to be 0.45 quarts.
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5,376 divided by 24 explanation
Answers
Your answer should be 224.
Hope you get this right.
At the school book sale Michael brought 3 books for $6 Darnell by 5 books for $10 are these rates equivalent explain your reasoning
Answers
Answer:
=2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
3 times 2 is 6 and 5 times 2 is 10
One of the worlds largest crocodiles weighed 38,400 ounces how many tons did the crocodile weigh
Answers
Answer: 1.2 tons
Step-by-step explanation:
Answer: 1,777
Step-by-step explanation:
Help me with this. I'll give brainiest
Answers
Answer:
I would say C
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
You can simplify it into 3 and 2.25. This can be averaged into 2. So, 2 feet for every second. :)
I don't know the choices for the bottom questions, but the answer is x>2, meaning any number higher than 2 works, or any number below 2 doesn't work.
Let A={7,8,9,10,11,13,14). a. How many subsets does A have? b. How many proper subsets does A have? a. A has subsets. (Type a whole number.) b. A has proper subsets. (Type a whole number.)
Answers
a. A has 2^7 = 128 subsets.
b. A has 2^7 - 1 = 127 proper subsets.
a. To determine the number of subsets of set A, we can use the concept of the power set. The power set of a set A is the set of all possible subsets of A, including the empty set and A itself. Since set A has 7 elements, the number of subsets can be calculated as 2^7 = 128. This is because for each element in A, we have two choices: either include it in a subset or exclude it. Therefore, we multiply 2 by itself 7 times to get the total number of subsets.
b. Proper subsets are subsets that do not include the entire set A. In other words, proper subsets of A are subsets of A that exclude at least one element from A. To calculate the number of proper subsets, we subtract 1 from the total number of subsets. This is because the empty set is not considered a proper subset. Therefore, 128 - 1 = 127 proper subsets exist for set A.
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for an independent-samples t test where group 1 has 23 participants, a mean of 11.6, and a standard deviation of 3.1, and group 2 has 19 participants, a mean of 13.24, and a standard deviation of 2.9, what is the proper way to report the groups' means and standard deviations using apa formatting?
Answers
The proper way to report the groups' mean and standard deviation of independent sample t test is
Group 1 (M = 11.6, SD = 3.1) Group 2 (M = 13.24, SD = 2.9).
The APA style guide provides detailed instructions for referencing statistical test results, so in addition to following the basic format correctly, you must pay attention to details like punctuation, bracket placement, italicization, and other formatting elements.
Given, that the independent samples t test is conducted, where we have two groups.
Group 1- mean= 11.6 and SD=3.1
Group 2- mean=19 and SD=2.9
We have to write the values in the APA format for a report.
The APA formatting to represent the mean and SD of two groups is as follows, Mean and standard deviation are denoted by the letters M and SD, respectively.
Group 1 (M = 11.6, SD = 3.1) Group 2 (M = 13.24, SD = 2.9).
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80 divided by 192.0!!!!!!!!!!!!!!!
Answers
Answer: .416666667
Step-by-step explanation: Take 80 and divide it by 192.0= .416666667
Add 3/5+3/10. 1/5 3/10 2/5 9/10
Answers
Answer:
9/10
Step-by-step explanation:
hope this helps:)
5. suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x
Answers
If a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1
The mean of the normal distribution = 4
Standard deviation of the normal distribution = 1.5
The value of x = 5.5
The z-score of the normal distribution = The mean of the normal distribution / Standard deviation of the normal distribution
Substitute the values in the equation
The z-score of the normal distribution = (5.5 - 4) / 1.5
Substract the terms
= 1.5 / 1.5
= 1
Hence, if a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1
The complete question is:
suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x = 5.5
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One player on the team wants to emphasize that his
team generally scored a lot of points. Which measure
of center should he report: the mean or the median?
O He should report the mean.
O He should report the median.
O He could report either because they are equal.
o The exact number of points per game are needed to
decide
Answers
If the player wants to emphasize that his team generally scored a lot of points, it might be best to report the median.
The median and the mean are both measures of center in statistics. They help to describe where the center of the data set is located, but they are not the same thing.
The mean is calculated by adding up all the values in the data set and then dividing by the number of values. It gives a good overall picture of the average of the data set, but it is sensitive to outliers or extreme values.
On the other hand, the median is the middle value in a data set when the values are arranged in order.
To find the median, you must first arrange the values in order and then identify the middle value. If there are an even number of values, the median is the average of the two middle values.
The median is not as sensitive to outliers or extreme values as the mean, so it gives a more accurate picture of the center of the data set when there are outliers or extreme values.
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Is the ratio 15:12 equivalent to the ratios above? Explain your reasoning.
Answers
Answer:
No
Step-by-step explanation:
the ratio of 15:12 is not equivalent to the ratios above. The ratios above have a common factor of 3, while 15:12 does not.
Write as an algebraic expression
Answers
Answer:
18.) 10x
20.) k - 24
22.) 12 - 9
Step-by-step explanation:
To simplify 8. 3 − 4 1 5 ( 6. 1 + 1 2 ) , which operation must be performed first? Which operation must be performed second? Which operation must be performed last? Which is the simplified expression in the decimal form?
its a mutilpy choice question the choices are addition, multiplication, and subtraction
Answers
Answer:
Step-by-step explanation:
Use PEMDAS to determine order of operations.
P = Parentheses
E = Exponents
M/D = Multiplication/Division
A/S = Addition/Subtraction
The operation in the parentheses must be performed first, which is the addition of 6.1 + 12.
The next operation to perform is multiplication, which is 415 times (6.1 + 12).
The last operation to perform is the subtraction of 415 times (6.1 + 12) from 8.3.
6.1 + 12 = 18.1
8.3 - 415(18.1)
8.3 - 7511.5 = -7503.2
geometric sequence with a ratio of 2 and a first term of 1/3.
Answers
Answer:
1/3, 2/3, 4/3, 8/3, 16/3, 32/3
or
1/3, 2/3, 1 1/3, 2 2/3, 5 1/3, 10 2/3
Step-by-step explanation:
i need help with this ASAP!!
Answers
Answer:
54 Degrees
Step-by-step explanation:
5 1/2 / x = 11/20
I need it ASAP!
Answers
Answer:
10
Step-by-step explanation:
I find it easier to work with decimals, so I'll start by converting to decimal form:
5 1/2 = 5.5
11/20 = 0.55
So the new version of this equation is 5.5/x=0.55
Now I can rearrange and solve for x:
\(\frac{5.5}{x}=0.55\\ 5.5=0.55x\\\frac{5.5}{0.55}=x\\ 10=x\)
1. Name the vertex of angle 2.
2. Name the sides of angle 4.
3. Write another name for angle 3.
4. Classify each angle.
-angle YTW
-angle XTU
-angle YTU
-angle WTX
5. Name an angle bisector.
Answers
Answer:
1) YTW
2) WT, TZ
3) UTZ
4) Right angle
Acute angle
Obtuse angle
Right angle
5) TU
Jamie has 2 dimes, 4 nickels and 8 pennies. in how many different ways can she make 26 cents?
Answers
Answer:
(2 dimes + 6 pennies)
(4 nickels + 6 pennies)
(1 dime + 2 nickels + 6 pennies)
( 2 dimes + 1 nickels + 1 penny)
(1 dime + 3 nickels + 1 penny)
5 different ways that Jamie can make 26 cents.