Answers
Answer:
Your answer is absolutely correct
Step-by-step explanation:
The work would be as follows:
[tex]\int _0^{\sqrt{\pi }}4x^3\cos \left(x^2\right)dx,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=> 4\cdot \int _0^{\sqrt{\pi }}x^3\cos \left(x^2\right)dx\\\\\mathrm{Apply\:u-substitution:}\:u=x^2\\=> 4\cdot \int _0^{\pi }\frac{u\cos \left(u\right)}{2}du\\\\\mathrm{Apply\:Integration\:By\:Parts:}\:u=u,\:v'=\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\int \sin \left(u\right)du\right]^{\pi }_0\\\\[/tex]
[tex]\int \sin \left(u\right)du=-\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0\\\\\mathrm{Simplify\:}4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0:\quad 2\left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0\\\\\mathrm{Compute\:the\:boundaries}:\quad \left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0=-2\\=> 2(-2) = - 4[/tex]
Hence proved that your solution is accurate.
Answer:
[tex]\int\limits^{\sqrt{\pi}}_0 {4x^3\cos(x^2)} \, dx=-4[/tex]
Step-by-step explanation:
So we have the integral:
[tex]\int\limits^{\sqrt{\pi}}_0 {4x^3\cos(x^2)} \, dx[/tex]
As told, let's use u-substitution first and then use integration by parts.
For the u-substitution, we can let u to be equal to x². So:
[tex]u=x^2[/tex]
Differentiate:
[tex]du=2x\, dx[/tex]
We can rewrite our integral as:
[tex]\int\limits^{\sqrt{\pi}}_0 {2x(2x^2)\cos(x^2)} \, dx[/tex]
Therefore, by making our u-substitution, our integral is now:
[tex]\int\limits {2u\cos(u)} \, du[/tex]
We also need to change our bounds. Substitute them into u. So:
[tex]u=\sqrt{\pi}^2=\pi\\u=(0)^2=0[/tex]
Therefore, our integral with our new bounds is:
[tex]\int\limits^{\pi}_{0} {2u\cos(u)} \, du[/tex]
Now, let's use integration by parts. Integration by parts is given by:
[tex]\int\limits {v}\, dy=vy-\int y\, dv[/tex]
(I changed the standard u to y because we are already using u).
Let's let v be 2u and let's let dy be cos(u). Thus:
[tex]v=2u\\dv=2\,du[/tex]
And:
[tex]dy=\cos(u)\\y=\sin(u)[/tex]
So, do integration by parts:
[tex]=2u\sin(u)-\int \sin(u)2\,du[/tex]
Simplify:
[tex]=2u\sin(u)-2\int \sin(u)\,du[/tex]
Evaluate the integral:
[tex]=2u\sin(u)+2\cos(u)[/tex]
Now, use the bounds. So:
[tex](2(\pi)\sin(\pi)+2\cos(\pi))-(2(0)\sin(0)+2\cos(0))[/tex]
Evaluate:
[tex]=(2\pi(0)+2(-1))-(0(0)+2(1))[/tex]
Simplify:
[tex]=(-2)-(2)[/tex]
Subtract:
[tex]=-4[/tex]
And we're done!
Related Questions
How would you do this question?
Answers
Answer:
1) ∫ x² e^(x) dx
4) ∫ x cos(x) dx
Step-by-step explanation:
To solve this problem, eliminate the choices that can be solved by substitution.
In the second problem, we can say u = x², and du = 2x dx.
∫ x cos(x²) dx = ∫ ½ cos(u) du
In the third problem, we can say u = x², and du = 2x dx.
∫ x e^(x²) dx = ∫ ½ e^(u) du
Please help me out!!!!!
Answers
Inverse of [tex] {12}^{2} [/tex] is [tex] {12}^{ \frac{1}{2} } [/tex]
Explanation:Because [tex] {12}^{ \frac{1}{2} } = \sqrt[2]{12} [/tex]Which is the inverse of [tex] {12}^{2} [/tex]
Answer:Option C. Is the correct answer.
How do you do both questions?
Answers
1. We have all the information we need here to set up our 'least-squares regression equation.'
Given: r = 0.68, x = 260, y = 70, s₁ = 33, s₂ = 6, remember that the general equation for our least-squares line is in the form y = a + bx. The slope of the regression equation is the linear correlation coefficient multiplied by the standard deviation for x:
b = r(s₂ / s₁) = 0.68(6 / 33) = 0.12363...
Remember that the constant of the regression equation is the mean of y decreased by the product of the slope and the mean of x:
a = y - bx = 70 - 0.12363(260) = 37.8562
The equation of the least-squares regression line would then be y = 37.8562 + 0.12363x. We know that the Jane's previous score was 279, so if we plug that into our equation as 'x' we will receive Jane's final score. The set up will be y = 37.8562 + 0.12363(279) = 72.34897. Your solution for the first part is absolutely correct!
2. Actually the values of 'y' could have been much larger. r^2 = 0.4624, thus the proportion of y explained by x is only about 46%. It would negatively affect her final course grade.
10 [12 2+ (4 x 2)] ÷ 8 2
Answers
20x+60
Urgent Fast!!!!!!!??????
Answers
If he has 484 plants and there are as many rows as there are plants in each row, his field is a square.
The area of a square = (side)^2
In this problem,
Area = 484
side = # of rows
Let's plug our values into the formula above
484 plants = (side)^2
Take the sqrt of both sides.
22 rows = side.
Answer:
This is the answer..........
SD and SG are tangent to ⊙ K. Identify SG. HELP!!
Answers
Answer:
63
Step-by-step explanation:
Tangents drawn from external point to a circle are congruent.
Therefore,
SG = SD
8x - 9 = 5x + 18
8x - 5x = 9 + 18
3x = 27
[tex]x = \frac{27}{3} \\ x = 9 \\ SG = 8x - 9 \\ SG =8 \times 9 - 9\\ SG =72 - 9 \\ \huge \red{ \boxed{SG =63}}[/tex]
Answer: 63
Tangents drawn from external point to a circle are congruent.
SG = SD
8x - 9 = 5x + 18
8x - 5x = 9 + 18
3x = 27
Step-by-step explanation: 63
ASAP! Question 3: The following data give the weights (in pounds) lost by 15 members of a health club at the end of 2 months after joining the club. 3 22 9 19 12 3 9 13 12 17 7 3 7 17 14 a. Compute the values of the three quartiles and the interquartile range. Q1 = Q2 = Q3 = IQR = b. Calculate the approximate value of the 82nd percentile. Enter an exact value: c. Find the percentile rank of 14. Round your answer to the nearest integer: %
Answers
Answer:
First arrange the data in an order
3, 3, 3, 7, 7, 10, 10, 12, 12, 13, 14, 17, 17, 18, 21
a.) Q1 = (N + 1)/4th item = (15 + 1)/4 = 4th item = 7
Q2 = 2(16)/4 = 16/2 = 8th item = 12
Q3 = 3(16)/4 = 3(4) = 12th item = 17
IQR = (Q3 - Q1)/2 = (17 - 7)/2 = 10/2 = 5
b.) 82nd percentile = 82(16)/100 = 13th item = 17
c.) 12 is the 8th item which is in the middle of the data set, so the percentile rank is 50%
Step-by-step explanation:
Express the ratio BC/EF in simplest form
Answers
Answer:
bc/ef =48/32
divide by 16 you will get
3/2
Step-by-step explanation:
x/3 - 15 = -7 solve for x
Answers
Answer:
[tex]x=24[/tex]
Step-by-step explanation:
[tex]\frac{x}{3}-15=-7[/tex]
Add 15 to both sides:
[tex]\frac{x}{3}-15+15=-7+15[/tex]
[tex]\frac{x}{3} =8[/tex]
Multiply both sides by 3:
[tex]\frac{3x}{3}=8\times3[/tex]
[tex]x=24[/tex]
The length of a rectangle is 5 centimeters longer than twice its width. If the perimeter of the rectangle is 88 centimeters, what is the width?
Answers
Answer:
The length of a rectangle is 5 centimetres longer than twice its width. If the perimeter of the rectangle is 88 centimetres, what is the width?
width=x
length=2x+5
perimeter=88=2L+2W
so half perimeter=44=L+W
x+2x+5=44
3x=39
x=13 cm width ANSWER
2x+5=31 cm length
The width of the rectangle is Width, W = 13 centimeters.
Let the length of the rectangle be L. Let the width of the rectangle be W.Given the following data:
Perimeter of rectangle = 88 centimetersTranslating the word problem into an algebraic equation, we have;
[tex]L = 2W + 5[/tex]
To find the width of the rectangle;
Mathematically, the perimeter of a rectangle is given by the formula;
[tex]P = 2(L + W)[/tex]
Substituting the values into the formula, we have;
[tex]88 = 2(2W + 5 + W)\\\\88 = 2(3W + 5)\\\\88 = 6W + 10\\\\6W = 88 - 10\\6W = 78\\\\W = \frac{78}{6}[/tex]
Width, W = 13 centimeters.
Therefore, the width of the rectangle is Width, W = 13 centimeters.
Find more information: brainly.com/question/897975
I am genuinely so confused please help
Answers
Answer:
I hope it will help you :)
The sum of three consecutive integers is -216. List the numbers from smallest to largest:
Check Answer
Answers
Answer:
Step-by-step explanation:
One
Answer:
-73,-74 and -75
Step-by-step explanation:
1st No=x
2nd No=x+1
3rd No=x+2
x+(x+1)+(x+2)=-216
x+x+x+2+1=-216
3x+3=-216
3x=-216-3
3x=-219 (÷ b.s by 3)
x=-73
1st No=-73
2nd No=-73+1
3rd No=-73+2
4 customers entered a store over the course of 6 minutes. At what rate were the
customers entering the store in customers per minute?
Answers
50 seconds per minute
The rate of entering customers per minute, if 4 customers entered a store over the course of 6 minutes, is 2 / 3.
What is division?It is the basic arithmetic operation, in which you are separating the number into some parts. One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
Given:
4 customers entered a store over the course of 6 minutes,
Calculate the rate of entering customers per minute as shown below,
The rate of entering customers per minute = total number of customer / total time
The rate of entering customers per minute = 4 / 6
The rate of entering customers per minute = 2 / 3
Thus, the rate of entering is 2 / 3.
To know more about division:
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PLEASE HELP PLEASE PLEASE
Answers
Answer:
The second one is d. 13
Step-by-step explanation:
Add what you know first. 110+57= 167. Then, subtract what the angle is all together with the answer from what you know. 180-167= 13. X= 13. I'm bad at explaining so I hope that was clear.
I will give brainliest answer
Answers
Answer:
(-2,-1)
Step-by-step explanation:
Right now, P is at (3,-4). After the translation, it would be at
(-2,-1)
2. Graph the inequality.
y<- 3x-2
Answers
Answer:
(2,-8) (0,-2)
Step-by-step explanation:
M= slope
B= y-intercept
-2 is the y-intercept (0,-2), plot those coordinates
-3x is the slope
- slope is -3/1
- top number depicts if you go up or down, (-) go down and (+) go up
- the bottom number you go to the right
So, from (0,-2) go down three and to the right one
Graph a dotted line since it is
PLEASE HELP!! BEST ANSWER WILL BE MARKED BRAINIEST! The stadium is at (-2,3) and the high schools (1,8). What is the shortest driving distance (in blocks) between these two locations? Can you figure this out without looking a the grid
Answers
Answer:
Shortest distance is 5 blocks.
Answer:
5.8
Step-by-step explanation:
I'm not 100% on this as the decimal in the answer makes me doubt myself. Here's the explanation anyways
A coin was tossed 60 times and the coin landed on Heads 35 times. What proportion of the time did the coin land on Heads?
Type your numeric answer and submit
Answers
Answer: Hence, the proportion of head lands obtained from the total number of tosses is 0.583
Step-by-step explanation:
Given the following :
Total number of coin tosses = 60
Total number of times coin landed on head = 35
Proportion of head landings obtained :
Total number of head landings obtained / total number of coin tosses
Proportion of head landing obtained :
= 35 / 60 = 7 / 12 = 0.5833
Approximtely how many 27cubic volume cabinets will a container98,000cbic volume hold?
Answers
Answer: 3630
Step-by-step explanation:
Given that:
Volume of container = 98,000 cubic volume
Volume of cabinet = 27 cubic volume
The number of cabinets which the container will. Hold equals:
Volume of container / volume of cabinet
= 98000 cubic volume / 27 cubic volume
= 3629.6296
The container will hold approximately 3630 27 cubic volume of cabinet.
Help me ASAP plssssssssss
Answers
Answer:
Community Parks
Step-by-step explanation:
Answer:
D
Step-by-step explanation: Because they are trying to reserve the parks and the animal life and plant life in it. Hope this helps :)
Crude oil Imports to one country from another for 2009-2013 could be approximated by the following model where t is time in years since the start of 2000,
(1) --33428001 - 1,000 thousand barrels per day (9 st s 13)
According to the model, approximately when were oil imports to the country greatest? HINT (See Example 1) (Round your answer to two decimal places.)
How many barrels per day were imported at that time? (Round your answer to two significant digits.)
thousand barrels
Answers
Answer:
Time = approximately mid 2012Oil import rate = 3600 barrelsStep-by-step explanation:
Unclear part of the questionI(t) = −35t² + 800t − 1,000 thousand barrels per day (9 ≤ t ≤ 13) According to the model, approximately when were oil imports to the country greatest? t = ? SolutionGiven the quadratic function
The vertex of a quadratic function is found by a formula: x = -b/2aAs per given function:
b = 800, a = -35Then
t = - 800/2*(-35) = 11.43 which is within given range of 9 ≤ t ≤ 13This time is approximately mid 2012.
Considering this in the function, to get oil import rate for the same time:
l(11.43) = -35*(11.43)² + 800*11.43 - 1000 = 3571.4285Rounded to two significant figures, the greatest oil import rate was:
3600 barrelsIn your part-time job, your hours vary each week. One week you worked 22 hours, the next 25 hours, the third 14 hours, and the fourth 19 hours. Your gross pay for the entire month was $960. How much money did you bring home during the second week?
Answers
Answer:
$300
Step-by-step explanation:
1 month =4 weeks
1 week=22 hrs
2 week= 25 hrs
3 week = 14 hrs
4 week = 19 hrs
Total of hrs in the month is 80 hrs
80 hrs = $960
25 hrs = ?
960×25÷80=300
Answer =$ 300
[
When a submarine starts at sea level, goes down
250 feet, rises 80 feet, and descends another 18
feet, how would this be shown mathematically?
Answers
Answer:
This should be shown as:
-250 + 80 - 18 = - 118
Step-by-step explanation:
Going down 250 feet will mean going down feet 250 so it will be -250. Rising 80 feet will mean going up 80 feet so it will be adding 80. Finally, descending 18 feet will mean going down 18 feet, so it will be -18. If you put them all together as one equation, you will get -250 + 80 - 18 which is -118.
Hope this helps!
The required mathematical expression would be shown as:
-250 + 80 - 18 = - 118
What is algebra?Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.
When a submarine starts at sea level, goes down 250 feet, rises 80 feet, and descends another 18 feet which are given in the question.
Going down 250 feet means going down 250 feet, thus it will be -250. Rising 80 feet will result in an increase of 80 feet. Finally, descending 18 feet means going down 18 feet, therefore the result is -18. When you add them all together, you get -250 + 80 - 18, which equals -118.
Therefore, the required mathematical expression would be shown as:
-250 + 80 - 18 = - 118
To learn more about the Algebra link is given below.
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I want to know-24 divided by -4
Answers
Answer: 6
Step-by-step explanation: -24/-4 = 6.
the answer is: 6
explanation: ...
2
If A=
4 3
find A1 using
elementary row operations.
Answers
Answer: [tex]A^{-1}=\left[\begin{array}{cc}\frac{3}{2}&-\frac{1}{2}\\-2&1\end{array}\right][/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{cc}2&1\\4&3\end{array}\right]=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
[tex]\dfrac{1}{2}Row\ 1\rightarrow\left[\begin{array}{cc}1&\frac{1}{2}\\4&3\end{array}\right]=\left[\begin{array}{cc}\frac{1}{2}&0\\0&1\end{array}\right][/tex]
[tex]Row\ 2 -4 \ Row\ 1\rightarrow \left[\begin{array}{cc}1&\frac{1}{2}\\0&1\end{array}\right]=\left[\begin{array}{cc}\frac{1}{2}&0\\-2&1\end{array}\right][/tex]
[tex]Row\ 1-\dfrac{1}{2}\ Row\ 2 \rightarrow \left[\begin{array}{cc}1&0\\0&1\end{array}\right]=\left[\begin{array}{cc}\frac{3}{2}&-\frac{1}{2}\\-2&1\end{array}\right][/tex]
Use the given conditions to write an equation in point-slope form. Keep parenthesis in point-slope form. passing through (3,5) and (8,15).
Answers
Answer:
Step-by-step explanation:
(15 -5)/(8 - 3)= 10/5 = 2
y - 5 = 2(x - 3)
y - 5 = 2x - 6
y = 2x - 1
A grocery store sells jelly beans in the bulk section for $2.75 a pound. If Wanda buys 1.8 pounds, how much will it cost?
Answers
Answer:
$4.95
Step-by-step explanation:
If jelly beans cost $2.75 per pound then multiplying the cost per pound by the amount of jelly beans purchased will give the answer of $4.95 per 1.8 pounds of jelly beans.
If Ben invests $3000 at 4% interest per year, how much additional money must he invest at 5.5 % annual interest to ensure that the interest he receives each year is 4.5 % of the total amount invested?
Answers
Answer:
$1500
Step-by-step explanation:
Investment 1 = $3000Interest 1 = 4%Investment 2 = xInterest 2 = 5.5%Total interest = 4.5%Total interest:
3000*0.04 + x*0.055 = (3000+ x)*0.045 ⇒ multiply by 100 both sides3000*4 + 5.5x = 3000*4.5 + 4.5x ⇒ parenthesis5.5x - 4.5x = 3000(4.5-4) ⇒ collect like termsx = 3000*0.5 ⇒ simplifyx = 1500 ⇒ answerAdditional money is $1500
State the domain and range and determine if its a function?
Answers
The Math 123 book includes about 230 pages (not including the back parts of the book). If you aim to complete 65% of all the pages, how many should you finish?
Answers
Answer:
149.5 pages excluding the back parts
150.8 pages including the back parts
Step-by-step explanation:
Total pages in Math 123 book = 230 pages
You aim to complete 65% of all the pages, how many should you finish
65 % of 230 pages
= 65 / 100 × 230 pages
= 0.65 × 230 pages
= 149.5 pages excluding the bark parts of the book
If you include the back parts, that is, the beginning and ending page
You have a total of 230 pages + 2 pages
= 232 pages
65 % of 232 pages
= 65 / 100 × 232 pages
= 0.65 × 232 pages
= 150.8 pages including the back parts