Answers
First integral:
Parameterize -C (the reverse of C) by [tex]z = e^{it}[/tex] where [tex]0\le t \le\frac\pi2[/tex]. Then the contour integral is
[tex]\displaystyle \int_{-C} (z^2 - z + 2) \, dz = \int_0^{\frac\pi2} \left(e^{2it} - e^{it} + 2\right) i e^{it} \, dt[/tex]
[tex]\displaystyle = i \int_0^{\frac\pi2} \left(e^{3it} - e^{2it} + 2e^{it}\left) \, dt[/tex]
[tex]\displaystyle = i \left(\frac1{3i} e^{3it} - \frac1{2i} e^{2it} + \frac2i e^{it}\right) \bigg|_0^{\frac\pi2}[/tex]
[tex]\displaystyle = \left(\frac13 e^{3it} - \frac12 e^{2it} + 2 e^{it}\right) \bigg|_0^{\frac\pi2}[/tex]
[tex]\displaystyle = -\frac43 + \frac53i[/tex]
Then
[tex]\displaystyle \int_C (z^2-z+2) \, dz = -\int_{-C} (z^2+z-2) \, dz = \boxed{\frac43 - \frac53i}[/tex]
Second integral:
The integrand has a pole of order 2 at z = 3i which is contained in C. By the residue theorem,
[tex]\displaystyle \int_C \frac{z^2+z}{(z-3i)^2} \, dz = 2\pi i\, \mathrm{Res}\left(\frac{z^2+z}{(z-3i)^2}, z=3i\right)[/tex]
Compute the residue:
[tex]\displaystyle \mathrm{Res}\left(\frac{z^2+z}{(z-3i)^2},z=3i\right) = \lim_{z\to3i} \frac{d}{dz}\left[z^2+z\right] = \lim_{z\to3i} (2z+1) = 1 + 6i[/tex]
Then the value of the integral is
[tex]\displaystyle \int_C \frac{z^2+z}{(z-3i)^2} \, dz = 2\pi i (1 + 6i) = \boxed{-12\pi + 2\pi i}[/tex]
Related Questions
Describe a set of transformations that would map Triangle FGH onto Triangle F’G’H’
Answers
1) reflection over the x-axis
2) translation of (-6,0)
find the derivative pls !!
Answers
=5/2s(5s^3-3s+10)
To make a small vase, Elisa uses no more than 4.5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, c, that Elisa uses to make one vase of either size?
4.5 < c < 12
4.5 ≤ c ≤ 12
c < 4.5 or c > 12
c ≤ 4.5 or c ≥ 12
Answers
Answer:
last one is the answer of the following question
Answer:
D
Step-by-step explanation:
whats 1 added up to 1?
Answers
Trey plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months.
Answers
Answer:
2n*m. when there is a one in front of a letter, it is immediately just the letter
2x +2y-16x+4y+20=0 solve by completing the square
Answers
Answer
7/3
Step-by-step explanation:
Find f of x and f of y
F(x,y) = 2x + 27 - 16x + 4y + 20, f of x = -14
F(x,y) = 2x + 2y - 16x + 4y + 20, f of y = 6
Find the fist partial derivative
f of x = -14
f of y = 6
Subsitude f of x = 14 and f of y = 6 into dy/dx = - f of x / f of y
reduce the fraction
dy/dx = - 14/6 = - - 7/3 = 7/3
What is the best next step in the construction of the perpendicular bisector of AB?
Answers
Answer:
B
Step-by-step explanation:
Out of all the answers given as a choice B makes the most sense because the triangle AB and point of intersection of the two circles form an equilateral triangle.
In general to construct a perpendicular bisector after we drew the two circles we have to ...draw a straight line trough the points where the two circles intersect and that is our perpendicular bisector of AB.
Solve the following equation
Answers
Answer:
Write it down in comments i can barely see
Step-by-step explanation:
What is the length of the hypotenuse of the triangle below?
45
h
45°
5√2
90⁰
5√2
Answers
Answer:
10
Step-by-step explanation:
find the square root of the sum of the squares
The length of the hypotenuse for the given right angled triangle is 10 units.
What is a Pythagoras theorem?Pythagoras theorem states that the square of the hypotenuse is equivalent to the square of the base and perpendicular.
We can write the formula for Pythagoras theorem as -
(hypotenuse)² = (base)² + (perpendicular)²
Given is to find the length of the hypotenuse in the right angled triangle shown.
Using the Pythagoras theorem, we can write that -
(hypotenuse)² = (base)² + (perpendicular)²
(hypotenuse)² = (5√2)² + (5√2)²
(hypotenuse)² = 2 x (5√2)²
(hypotenuse)² = 2 x 25 x 2
(hypotenuse)² = 100
(hypotenuse) = 10
Therefore, the length of the hypotenuse for the given right angled triangle is 10 units.
To solve more questions on triangles, visit the link-
https://brainly.com/question/2773823
#SPJ7
Please help I really need this
Answers
Answer:
(0 , 4)
Step-by-step explanation:
The Y-intercept is when a line crosses sector y at any point. This means x will be zero. Simply to find the y-intercept from this quadratic function, just look at where the line crosses the y-line.
This clearly passes at (0,4), therefore (0,4) is the y-intercept.
Find the time required for an investment of 4,000 dollars to grow to 9,000 dollars at an interest rate
of 5% per year, compounded monthly. Give your answer accurate to 2 decimal places.
years.
Answers
Answer:
25 years
Step-by-step explanation:
Pleaseeee answer I’ll give you pointsss
Answers
Answer:
Okay . That looks interesting. Can't help.
coulddd i be helped really quick?
Answers
Answer for 30 is x+56=y-$5.05
So
For every increase in cover price of x means 5x+0.5 decreases customers by 30
So
the expression is
5x+0.5=300y-305x=300y-30.5300y=5x-30.55x-300y-30.5=0
(a) Is the image
of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain.
Answers
please help !! I dont know what the awnser is, i put mean, medium, and mode for the first try adn it gave me partial
Answers
Answer:
All of them but the last one
Step-by-step explanation:
For two functions, f(x) and g(x), a statement is made that f(x) = g(x) at x = 5. What is definitely true about x = 5?
A. Both f(x) and g(x) cross the x-axis at 5.
B. Both f(x) and g(x) cross the y-axis at 5.
C. Both f(x) and g(x) have a maximum or minimum value at x = 5.
D. Both f(x) and g(x) have the same output value at x = 5
Answers
Answer:
D
Step-by-step explanation:
f(x) = g(x) at x=5
means
f(5) = g(5)
The regular price of a sofa, in dollars, is represented by . The sale price of the sofa is 30%off the regular price. Select alltrue statements.
A. The sale price of the sofa can be represented by −0.3.
B. The sale price of the sofa can be represented by 0.7.
C. The sale price of the sofa can be represented by 0.3
D. The dollar amount of the discount for the sale price can be represented by 0.3.
E. The dollar amount of the discount for the sale price can be represented by −0.3.
Answers
Answer:
BEStep-by-step explanation:
The sale price of the sofa is given as :
Original Price (100% - 30%)Original Price (70%)Original Price (0.7)The dollar amount for the discount
- 30% [discount]-0.38 ≤ 2m Find variable of m
Please show your work
Answers
Answer:
m ≥ 4
Step-by-step explanation:
8 ≤ 2m
8/2 ≤ m
4 ≤ m
m ≥ 4
Molly's alarm clock fell to the floor and the glass face was broken. Molly measured the glass face so that she could order a new one.
The radius of the circle-shaped glass face is 8 centimeters. What is the approximate area of the glass face? (Use 3.14 for .)
Answers
Answer:
200.96 cm^2
Step-by-step explanation:
πr^2 is the formula for the area of a circle
π*8^2
64π
substitute pi with 3.14
64 * 3.14 = 200.96
200.96
mark brainliest please!
Simplify this expression . With each step. please (x2 - x - 2)/(x2 + 5x + 4)
Answers
Answer:
I hope dis helps
Step-by-step explanation:
Simplify
x2 + 5x + 4
Trying to factor by splitting the middle term
1.1 Factoring x2 - x - 2
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is -1 .
-2 + 1 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 1
x2 - 2x + 1x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-2)
Add up the last 2 terms, pulling out common factors :
1 • (x-2)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-2)
Which is the desired factorization
Trying to factor by splitting the middle term
1.2 Factoring x2+5x+4
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is 5 .
-4 + -1 = -5
-2 + -2 = -4
-1 + -4 = -5
1 + 4 = 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 4
x2 + 1x + 4x + 4
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+1)
Add up the last 2 terms, pulling out common factors :
4 • (x+1)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x+1)
Which is the desired factorization
Canceling Out :
1.3 Cancel out (x+1) which appears on both sides of the fraction line.
Final result :
x - 2
—————
x + 4
Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.
Answers
Step-by-step explanation:
[tex]4(2 - x) > - 2x - 3(4x + 1)[/tex]
[tex]8 - 4x > - 2x - 12x - 3[/tex]
[tex]8 - 4x > - 14x - 3[/tex]
[tex] - 4x + 14x > - 3 - 8[/tex]
[tex]10x > - 11[/tex]
[tex]x = - 1.1[/tex]
Answer:
[tex]x > \frac{-11}{10}[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]4(2 - x) > -2x - 3(4x + 1)[/tex]
[tex](4*2)+(4 * (-x)) > -2x + (-3 * 4x) + (-3 * 1)[/tex]
[tex]8 - 4x > -2x - 12x - 3[/tex]
Step 2: Combine like terms
[tex]8 - 4x > (-2x - 12x) - 3[/tex]
[tex]8 - 4x > -14x - 3[/tex]
Step 3: Add 14x to both sides
[tex]8 - 4x + 14x > -14x - 3 + 14x[/tex]
[tex]8 + 10x > -3[/tex]
Step 4: Subtract 8 from both sides
[tex]10x + 8 - 8 > -3 - 8[/tex]
[tex]10x > -11[/tex]
Step 5: Divide both sides by 10
[tex]\frac{10x}{10} > \frac{-11}{10}[/tex]
[tex]x > \frac{-11}{10}[/tex]
Answer: [tex]x > \frac{-11}{10}[/tex]
Multiplicaciones que den 35
Answers
Answer:
Estos pares de factores son (1, 35) y (5, 7).
espero que esto ayude.
➡ (1,35)
➡ (5,7)
How would I solve I need to know Asap and what is the answer
Answers
Answer:
All of them are true.
Step-by-step explanation:
The symbol ≅ is used to show congruence between two shapes.
Congruency means that the shapes have the same shape and size.
This means that the two shapes are the same.
This means that all sides are going to be the same, so the first two statements are true.
This also means that the angles are the same, so the last two statements are also true.
mark brainliest please!
Answer:
1 and 3 are correct.
Step-by-step explanation:
You can just look at the order of the letters in the triangle congruence statement and see if they correspond with the answer choices.
For example... OC is congruent to JA because for both segments, it's the first letter, then the second letter from the beginning triangle congruence statement.
Can any math experts please help me out with this? Thank you,
Answers
Answer:
13) x = 19
14) x = 12.4
Step-by-step explanation:
So, for 13, we know that the whole thing is 90 degrees, a right angle.
So, (4x - 17) + 31 = 90
Now, we'll subtract 31 from 90 to figure out the other angle.
4x - 17 = 59
Now, add seventeen to both sides to get 4x alone...
4x = 76
Divide each by four!
x = 19
Now, to check, we plug this x value into our first equation:
(4(19) - 17) + 31 = 90
(76 - 17) + 31 = 90
(59) + 31 = 90
90 = 90 :: true!
________________________________________
For 14, we know that the total must be 180, because it's a straight angle.
So, (5x + 22) + 96 = 180
Again, subtract the known angle from each side:
5x + 22 = 84
Subtract 22 from each side to get the exponent by itself...
5x = 62
Divide each side by 5:
x = 12.4
Now, plug it in to check.....
(5*12.4) + 22 + 96 = 180
62 + 22 + 96 = 180
84 + 96 = 180
180 = 180 :: true!
Can yall help me with this math
Answers
Answer:
2 the change in expected height for every additional centimeter of femur length
Step-by-step explanation:
1 and 4 have 55 is the starting point but is just there to throw you off and 3 has expected femur length, but the graph says expected height
the table shows the fees david charges for yard work
how much does david charge for yard work that takes 4.5 hours
Answers
Darcy pays $37.95 for a 25.3-kilometer taxi ride.
How much does Darcy pay, in dollars, per kilometer?
Answers
Answer:
1.5 per kilo
Step-by-step explanation:
Answer: That would be $1.50
Explanation: I took a test and I got it right
A coin tossed four times and a card is selected from a standard deck of cards
Answers
Probability of landing on tails = 1/2Probability of choosing a spade = 1/4, as there are 13 spades in a pack of 52 cardsSo the probability of both = 1/2 * 1/4 = 1/8.We are assuming the deck of cards does not contain jokers.
SOLVE PLSEEE I GIVE POINTS
Answers
Since the diameter for a segment is 68 centimeters long, we must divide that number by 4, since there are four circles. Next, we get 17.
Then, we use the formula for solving a circle, which is [tex]A = \pi r^2[/tex]. Plug in 8.5 (half of 17) for the radius, and then convert pi into 3.14. The equation should now look something like this: [tex]A = 3.14 * 8.5^2[/tex]. When solving, we get 265.865 for one circle only. We next multiply 256.856 by 4 since there are four circles. After multiplying you should get a total of 907.46 centimeters squared.
If this isn't correct, then do the same thing, but the radius is 34 centimeters.
Mrs. Murray wants to hang lights around the edge of the ceiling. The ceiling measures 14.5 feet by 9.6 feet. What is the perimeter, in feet, of Mrs. Murray's ceiling?
What is the perimeter of the ceiling in inches.
Answers
Answer:
48.2 feet
or
578.4 inches
Step-by-step explanation:
Perimeter is the distance around the shape or in this case the room. Assuming the room is a rectangle you would have two walls of the same length totaling 4 walls.
To find the perimeter add up 14.5 + 14.5 + 9.6 + 9.6 = 48.2 feet
Since it askes for the answer in inches you have to convert from feet to inches by multiplying your answer by twelve.