38. Evaluate f (3x +4y)dx + (2x --3y)dy where C, a circle of radius two with center at the origin of the xy
C plane, is traversed in the positive sense.
please i need real time help
It looks like the integral is
[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy[/tex]
where C is the circle of radius 2 centered at the origin.
You can compute the line integral directly by parameterizing C. Let x = 2 cos(t ) and y = 2 sin(t ), with 0 ≤ t ≤ 2π. Then
[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \int_0^{2\pi} \left((3x(t)+4y(t))\dfrac{\mathrm dx}{\mathrm dt} + (2x(t)-3y(t))\frac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt \\\\ = \int_0^{2\pi} \big((6\cos(t)+8\sin(t))(-2\sin(t)) + (4\cos(t)-6\sin(t))(2\cos(t))\big)\,\mathrm dt \\\\ = \int_0^{2\pi} (12\cos^2(t)-12\sin^2(t)-24\cos(t)\sin(t)-4)\,\mathrm dt \\\\ = 4 \int_0^{2\pi} (3\cos(2t)-3\sin(2t)-1)\,\mathrm dt = \boxed{-8\pi}[/tex]
Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on C nor in the region bounded by C, so
[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \iint_D\frac{\partial(2x-3y)}{\partial x}-\frac{\partial(3x+4y)}{\partial y}\,\mathrm dx\,\mathrm dy = -2\iint_D\mathrm dx\,\mathrm dy[/tex]
where D is the interior of C, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: [tex]-2\times \pi\times2^2 = -8\pi[/tex].
3.0040916 to the nearest hundred thousandth
Answer:
3.004
Step-by-step explanation:
If you were to round it like this: 3.0041, the thousands place would still be 4, so it would come out to be 3.004. Hope that helps!!
A display case of plastic bracelets are marked 13 for $3. If Nate has $60, how many plastic bracelets can Nate get? (assume no other taxes or fees)
Answer:
$4
Step-by-step explanation:
We can write a ratio to solve
15 stickers 30 stickers
----------------- = -------------
2 dollars x stickers
Using cross products
15x = 2*30
15x = 60
Divide by 15
15x/15 = 60/15
x = 4
4. Use the properties of exponents to simplify the expression: y ^ -4 (y ^ 3) ^2
Answer:
y^2
Step-by-step explanation:
See the image for solution
Hope it helps
Have a great day
A salesman's salary is $18,500 per year. In addition, the salesman earns 5% commission on the year's sales. Last year the salesman earned $25,400. How much was sold that year?
Answer:
138000
Step-by-step explanation:
25,400 - 18,500
6900
5% = 6900
100% = ?
cross multiplication
5x6900 / 100
yearly sale = 138000
at what point do the increasing and decreasing parts of the graphs in Part A intersect?
Evaluate the expression 2−7+15
pls somone help
Answer:
answer is -20
BODMAS
So we do addition First, then subtraction so 7+15 = 22
2- 22= -20
Determine the largest positive integer N such that 1005! is divisible by 10N.
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Answer:
N = 250
Step-by-step explanation:
The way your question is written, the answer is a number of 2582 digits, much too large to show here. We assume you actually want N such that 10^N is the largest power of 10 that will divide 1005!.
__
That factor is limited by the number of factors of 2 and 5 in 1005!. Of those, there are far more factors of 2, so the actual limit is the number of factors of 5 in 1005!.
Every 5th number is divisible by 5, so there are 1005/5 = 201 numbers divisible by 5 in 1005!.
Every 5th one of those is divisible by another factor of 5, so an additional 201/5 ≈ 40.
Every 5th one of those is divisible by another factor of 5, so an additional 40/5 = 8.
Finally, every 5th one of those has yet another factor of 5, so an additional 8/5 ≈ 1.
Then the total number of factors of 5 in 1005! is 201 +40 +8 + 1 = 250.
That is, the number 1005! will end in 250 zeros. It will be divisible by 10^250.
N = 250
A total of 574 tickets were sold for the school play. They were either adult tickets or student tickets. There were 74 more student tickets sold than adult tickets. How many adult tickets were sold?
411 is not correct
The answer is: 250 adult tickets were sold.
To be safe, prove that your answer is correct.
If there are 74 more student tickets than adult tickets, the amount of adult tickets must obviously be less.
Explanation:
74 more than 250, or 250+74 is 324.
250+324=574.
Now, you know the answer is correct. It satisfies all of the given conditions.
Also, note that the difference between the number of student tickets and adult tickets is 74.
So, there are 250 adult tickets and 324 student tickets.
3. Write a word phrase using 10x(14+11)
Answer:
10 multiplied by the sum of 14 and 11
Step-by-step explanation:
[tex].[/tex]
write all prime numbers from 20 to 50.
Answer:
So, 23, 29, 31, 37, 41, 43 and 47 these are the prime numbers between 20 and 50.
Step-by-step explanation:
plz mark me brainliest
Answer:
So the prime numbers between 20 and 50 are so easy
- 23, 29, 31, 37, 41, 43 and 47
these are the prime numbers between 20 and 50
Step-by-step explanation:
Hope it helps
The product of two whole numbers is 588 and their sum is 49. What are the two numbers?
Answer:
Here is your answer. HOPE THIS HELPS YOU! STAY BLESSED.
Answer:
28,21
Step-by-step explanation:
let the numbers be x and y
x+y=49
y=49-x
xy=588
x(49-x)=588
49x-x²=588
x²-49x+588=0
[tex]x=\frac{49 \pm \sqrt{49^2-4*1*588} }{2*1} \\=\frac{49 \pm \sqrt{2401-2352} }{2} \\=\frac{49 \pm\sqrt{49} }{2} \\=\frac{49 \pm 7}{2} \\=\frac{49+7}{2} ,\frac{49-7}{2} \\=28,21[/tex]
A. 5x-2+x=x-4 B. 5x+x=x-4
B. -4/6
Step-by-step explanation:
5x+x=-4
6x=-4
x=-4/6
Answer:
x= -2/5 or -0.4 x= -4/5 or -0.8Step-by-step explanation:
If you are solving for x then you should get something like this
A 5x-2+x=x- 4 B. 5x+x=x-4
6x-2=-4. 6x=x-4
6x-2-x=-4. 6x-x=-4
5x-2+2=-4+2. 5x=-4
5x/5=-2/5. 5x/5=-4/5
x=-2/5. x=-4/5
I hope this helped you out!
The ________ is the actual population of individuals, or clusters, from which a random sample will be drawn.
What is the y-intercept
Answer:
y-intercept is (0, 9)
Step-by-step explanation:
At y-intercept, x is 0
[tex]y = 9[/tex]
Answer: (0, 9)
Concept:
The y-intercept of a function is the point at which the graph of the function crosses the y-axis.
In other words, the y-intercept is the point when the x value is 0.
Solve:
Find the point where the x value is 0
It is the fourth from the left, where the x value is 0.
The y value is 9.
Finalize the point
x value is 0
y value is 9
Point = [tex]\boxed{(0, 9)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
You are looking at your power bill for the month, you pay 12 cents per kilowatt-hour. Running a 60 watt light bulb for 1 hour is .06 KWH, if you leave a light on all the time that has 5 light bulbs in it how much would that cost in a 30 day month? Answer in the form of $2.54 without the dollar sign.
Answer:
$25.92Step-by-step explanation:
1 bulb in 1 hour = 0.06 kWhUnit of cost = 12 cents per kWh = $0.12 per kWh5 bulbs in 30-day month will consume electricity:
5*0.06*30*24 = 216 kWhThe total cost is:
216 * 0.12 = $25.92Total electricity consumed per day
24(0.06)1.44KwhConsumed in 30days
30(1.44)43.2KwhFor 5bulbs
5(43.2)216kwHCost
216(0.12)$25.92FIRST TO ANSWER CORRECTLY GETS BRAINLIEST!!!
Answer:
6ft by 15ft
Explanation:
L1 = 10 ft
W1 = 4 ft
L2 = L1*(3/2)
W2 = W1*(3/2)
L2 = 10 ft times (3/2) = 15 ft
W2 = 4 ft times (3/2) = 6 ft
I hope this answer helps you out!
which statement best describes f(x)=-2√x-7+1
it is under mapping and function
f of x is equal to -2 root x-7 plus one
find the derivative of the function y= x^20
Answer:
Step-by-step explanation:
[tex]\frac{dy}{dx} =20x^{19}[/tex]
the length of a rectangle is 8cm and the height is 16cm find the answer of the above figures using this formular...
2(a + b) Perimeter
(B×H) Area
[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(16+8)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(24)[/tex]
[tex]\\ \sf\longmapsto Perimeter=48cm[/tex]
Area:-
[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto Area=8(16)[/tex]
[tex]\\ \sf\longmapsto Area=128cm^2[/tex]
Any mathematician am giving brainliest for this question
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Answer:
(x, y) = (1/2, 1)
Step-by-step explanation:
Subtract twice the second equation from the first to eliminate the x-variable.
(2/x +3/y) -2(1/x -4/y) = (7) -2(-2)
11/y = 11 . . . . . . . simplify
y = 1 . . . . . . . . multiply by y/11
__
Substituting into the second equation gives ...
1/x -4/1 = -2
1/x = 2 . . . . . . add 4
1/2 = x . . . . . . multiply by x/2
The solution is (x, y) = (1/2, 1).
_____
Additional comment
The attached graph seems to show that the graphs of the two equations also intersect at (x, y) = (0, 0). However, careful consideration of these equations leads to the conclusion that x=0 and y=0 are not in the domain of either equation. (Division by 0 is undefined.) So, the only solution is (x, y) = (1/2, 1).
If you were to multiply both equations by xy to eliminate fractions, you would, indeed, arrive at the conclusion that (x, y) = (0, 0) is a solution. As we noted, that "solution" is extraneous. Whenever you multiply an equation by an expression that can have the value 0, you need to be careful to exclude any "solution" that makes that expression 0.
Solve the equation.
} (a + 2) = {(2-a)
WWW.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution is
(Type an integer or a simplified fraction.)
B. The solution is all real numbers.
O C. There is no solution.
(Answer quickly)
Need help with solving please
Answer:
x=8
Step-by-step explanation:
4 ^(1/2x) = 256
Rewriting 256 as a power of 4
4 ^(1/2x) = 4^4
Since the bases are the same, the exponents are the same
1/2x = 4
Multiply each side by 2
1/2x *2 = 4*2
x=8
Show Work! There are 380 students, teachers, and chaperones going on school buses for a field trip. Each school bus can hold 68 passengers. Everyone will ride on a school bus. How many school buses does this group need?
Answer:
6 buses
Step-by-step explanation:
i believe you just have to divide 380/68
then it'll give you 5.5 and then have to round to the nearest integer
Does this picture indicate that < JAC =
Answer:
No
Step-by-step explanation:
<JAC = 93
< DBE = 90
The two angles are not equal
Is square root of 11+10 a rational or irrational number
Answer:
Irrational Number is the answer
Answer:
[tex] \sqrt{11 + 10} = \sqrt{22} = 4.69041576 [/tex]
THIS IS IRRATIONAL
Step-by-step explanation:
The correct answer is irrational and the reason for that is the decimals for sqrt of 22 are non-recurring, are non-terminating and lastly it cannot be expressed in a form of a fraction.
I hope this makes sense
:)
The university of Michigan football stadium can hold 107,601 people. Michigan states football stadium can hold 75,001 people. 51,000 people can fit in the football stadium at the university of North Carolina and 40,004 people can fit in duke universities stadium which is also in North Carolina. How many more people can fit in the stadiums in Michigan combined than in the stadiums in North Carolina combined
Answer:
56,601
Step-by-step explanation:
Madura is 25 years younger than her father. Nadira's mother is two years younger than her father. Together Nadira, her mother and father have a combined age of 78. Work out their ages.
just solve by yourself
You are wrapping a gift box that is 16 inches long,
7 inches wide, and 9 inches tall. Find the amount of
wrapping paper you need to wrap the gift box to the
nearest square inch.
Answer:
1008 inches
Step-by-step explanation:
A car has been purchased for £5200 and is estimated to have an expected life driving 200,000
miles. At the end of that time its value is estimated to be £200. If the units-of-production
method is used to depreciate the car,
a) What is depreciation cost per mile?
b) What will be book value of the car after it has driven 55000 miles?
Answer:
a) 0.025£ b)3825£
Step-by-step explanation:
a) 5200-200=5000 - of the value will be lost after reaching the milleage of 200000 miles
200000-5000
1-x
200000=5000/x
x=5000/200000= 5/200=1/40=0.025£- the depreciation cost per mile
b)0.025*55000= 1375- the decreasing of the price
5200-1375=3825£- the book value of the car after it has driven 55000 miles
