f(z) = z^2 + 1 has an antiderivative on the domain G = C \ {i, -i}.
(b) Hence, we cannot determine whether f(z) = z^2 + 1 has an antiderivative on the domain G = {z in C | Re(z) > 0} based on the Cauchy-Goursat theorem alone.
(a) To determine whether f(z) = z^2 + 1 has an antiderivative on the domain G = C \ {i, -i}, we can check if f(z) satisfies the Cauchy-Riemann equations on G.
The Cauchy-Riemann equations state that for a function f(z) = u(x, y) + iv(x, y) to have a derivative at a point, its real and imaginary parts must satisfy the partial derivative conditions:
∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x.
For f(z) = z^2 + 1, we have u(x, y) = x^2 - y^2 + 1 and v(x, y) = 2xy.
Calculating the partial derivatives, we find:
∂u/∂x = 2x, ∂v/∂y = 2x,
∂u/∂y = -2y, ∂v/∂x = 2y.
Since ∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x hold for all (x, y) in the domain G, f(z) satisfies the Cauchy-Riemann equations on G. Hence, f(z) has an antiderivative on G = C \ {i, -i}.
(b) Now, let's consider the domain G = {z in C | Re(z) > 0}. To determine if f(z) = z^2 + 1 has an antiderivative on G, we can utilize the Cauchy-Goursat theorem, which states that a function has an antiderivative on a simply connected domain if and only if its line integral around every closed curve in the domain is zero.
For f(z) = z^2 + 1, we can calculate its line integral over a closed curve C in G. However, since G is not simply connected (it has a "hole" at Re(z) = 0), the Cauchy-Goursat theorem does not apply, and we cannot conclude whether f(z) has an antiderivative on G based on this theorem.
To provide a definitive answer, further analysis or techniques such as the residue theorem may be required.
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Write a polynomial of least degree with roots 2 and – 7
Answer: x^2+5x-14
Step-by-step explanation:
2 and -7 are the roots of the polynomial then we have to write them as
x=2 ,x=-7
To convert these as factors, we have to write them as
( x-2) (x+7)
The product of those factors will give the polynomial. Because we have two factors, we will get a quadratic polynomial.
x^2+7x-2x-14
x^2+5x-14
Number of factors = Highest exponent of the polynomial
Answer:
y = x² + 5x - 14
Step-by-step explanation:
Given roots x = a, x = b, then the corresponding factors are
(x - a) and (x - b) and the polynomial is the product of the factors
y = (x - a)(x - b)
Here the roots are x = 2 and x = - 7, then the factors are
(x - 2) and (x - (- 7)) = (x + 7), so
y = (x - 2)(x + 7) ← expand using FOIL
y = x² + 5x - 14
Find the absolute maximum and minimum values of the given function on the indicated inter- val. (a) f(x) = 31/3 - 3:2/3, on 11-,3).
The absolute maximum value of the function on the interval [-3, 1] is approximately 28.97, and the absolute minimum value is approximately 3.84.
To find the absolute maximum and minimum values of the function f(x) = 31/3 - 3x2/3 on the interval [-3, 1], we need to evaluate the function at its critical points and endpoints.
First, let's find the critical points by taking the derivative of the function:
f'(x) = (2/3)(31/3)(-3x^(-1/3)) = -2(31/3)(1/x^(1/3)) = -62/x^(1/3)
To find the critical points, we set f'(x) equal to zero and solve for x:
-62/x^(1/3) = 0
This equation has no solutions since the numerator is always non-zero.
Next, we evaluate the function at the endpoints of the interval:
f(-3) = 31/3 - 3(-3)^(2/3) ≈ 3.84
f(1) = 31/3 - 3(1)^(2/3) ≈ 28.97
Finally, we compare the values of the function at the critical points and endpoints to determine the absolute maximum and minimum:
Absolute maximum: f(1) ≈ 28.97
Absolute minimum: f(-3) ≈ 3.84
Therefore, the absolute maximum value of the function on the interval [-3, 1] is approximately 28.97, and the absolute minimum value is approximately 3.84.
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Manny invested $8,000 in an account that pays 6.5% simple
interest. Manny will not make any additional deposits or
withdrawals. How many years must the money stay invested for
before the investment has a balance of $13,200?
Answer:
10 years
Step-by-step explanation:
Simple interest formula:
AV=PV(1+it)
13200=8000(1+.065t)
1.65=1+.065x
.65=.065x
10=x
The lengths of three line segments are shown above. Which of the following statements is true?
Determine the number of ways 7 books can be arranged on a shelf if a) there are no restrictions?
The number of ways seven books can be arranged on a shelf if there are no restrictions is 7! = 5040.Why? As there are no restrictions, any of the seven books can occupy any of the seven places on the shelf. Therefore, there are 7 ways to place the first book. After the first book has been placed, there are 6 ways to place the second book (as one place is now occupied).Then, after the first and second books have been placed, there are 5 ways to place the third book (since two places are now occupied). Similarly, there are 4 ways to place the fourth book after the first four have been placed. There are 3 ways to place the fifth book after the first five have been placed.
There are 2 ways to place the sixth book after the first six have been placed. There is only one way to place the last book after the first six have been placed.
So, using the Multiplication Principle, the number of ways 7 books can be arranged on a shelf is:7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
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A set H in R² is displayed on the right. Assume the set includes the bounding lines. Determine whether H is a subspace of R² and justify.
To determine whether set H is a subspace of R², we need to check if H satisfies the three requirements for a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.
To determine if set H is a subspace of R², we need to check if it satisfies the three properties of a subspace.
Closure under addition: For any two vectors u and v in H, their sum u + v should also be in H. If the lines forming the boundary of H extend infinitely, then any two vectors u and v in H can be added to form a vector that lies within H. Thus, H is closed under addition.
Closure under scalar multiplication: For any vector u in H and any scalar c, the scalar multiple cu should also be in H. Similarly to the closure under addition, if the lines forming the boundary of H extend infinitely, then any vector u in H can be multiplied by a scalar to obtain a vector that lies within H. Hence, H is closed under scalar multiplication.
Contains the zero vector: The zero vector (0, 0) is part of R² and is also part of H since it lies within the boundary of H.
Since H satisfies all three requirements, it is a subspace of R².
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When a number is multiplied by 5 before subtracting from 78 the result obtained is the same as three times the sum of the number and 5 find the number
Answer:
x = 7.875
Step-by-step explanation:
Let the number = x
When a number is multiplied by 5 before subtracting from 78 the result obtained is the same as three times the sum of the number and 5 find the number
Hence,
78 -(x × 5) = 3(x + 5)
Expand the brackets
78 - 5x = 3x + 15
Collect like terms
78 -15 = 3x + 5x
63 = 8x
x = 63/8
x = 7.875
Which describes the difference between the two sequences?
First Sequence: 3, 6, 9, 12, ...
Second Sequence: 3, 12, 48, 192, ...
The first sequence is geometric because there is a common difference of 3. The second sequence is arithmetic
because there is a common ratio of 4.
O The first sequence is arithmetic because there is a common difference of 3. The second sequence is geometric
because there is a common ratio of 4.
The first sequence is arithmetic because there is a common ratio of 3.
The second sequence is geometric because there is a common difference of 4.
O The first sequence is arithmetic because there is a common difference of 4. The second sequence is geometric
because there is a common ratio of 3.
Answer:
the sequence is geometric sequence with common ratio (-2).
Option : D is correct.
Step-by-step explanation:
In this question table is given as
n 1 2 3 4 5
f(n) 48 -96 192 -385 768
We have to find out if the sequence is arithmetic or geometric.
For Arithmetic sequence :
Difference should be common in each term of fees.
common difference = f(2) - f(1)
= -96 -48 = -144
similarly = f(3) - f (2) = 192 + 96 = 288
Here, ≠ so the sequence is not an arithmetic sequence.
For Geometric sequence :
Ratio should be common in each term of f(n)
Common ratio =
Therefore, the sequence is geometric sequence with common ratio (-2).
Option : D is correct.
Please Answer This, the question is on the picture. it needs to be a fraction
will mark brainllest if its right, no links!
Answer:
x = 19.48 or 19 12/25
Step-by-step explanation:
cos 41° = 14.7/x
x = 19.48 or 19 12/25
let f be a continuous function on the interval [a,b]. select the answer that correctly completes each sentence. the area between the graph of y=f(x) and the x-axis on the interval [a,b]
A continuous function the graph of y = f(x) and the x-axis on the interval [a, b] evaluating the definite integral of f(x) over that interval, the changes of f(x) if applicable.
The area between the graph of y = f(x) and the x-axis on the interval [a, b] by evaluating the definite integral of f(x) over that interval.
The definite integral of f(x) from a to b represents the signed area between the graph of f(x) and the x-axis. The sign of the area depends on the behavior of f(x) above and below the x-axis.
If f(x) is non-negative (greater than or equal to 0) on the interval [a, b], then the area between the graph of f(x) and the x-axis will be positive or zero.
If f(x) is non-positive (less than or equal to 0) on the interval [a, b], then the area between the graph of f(x) and the x-axis will be negative or zero.
If f(x) changes sign on the interval [a, b] (i.e., it is positive in some regions and negative in others), then the area between the graph of f(x) and the x-axis will be the sum of the positive areas minus the sum of the negative areas.
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what is the total lateral area of the square pyramid in square inches, 8 inches base and 9 inches height
can someone help me with this please
Answer:
x=4
Step-by-step explanation:
so there are two triangles in that shape and they are similar to each other because their angles are equal and the ratio of their sides it 1:2
so the ratio of the side 5x & 40 is 1:2
5x/40=1/2
10x=40
x=4
The tip of the second hand travels around the edge of the face of a clock. How far does the tip of the second hand travel
between the 6 and the 12, if the length of the second hand is 6 inches?
Arc length
Recall that Circumference
- 360°
3 inches
O 6 x inches
12 x inches
0 24 inches
Answer:A. 3 inches
Step-by-step explanation: :)
Answer:
b and c
Step-by-step explanation:
Ms. Padilla is ordering art supplies for 90 students. She
orders 8 jars of paint for every 5 students and 10 sketch
pads for every 3 students.
Determine whether each statement about Ms. Padilla's order is true or false.
Select True or False for each statement.
Ms. Padilla orders 40 sketch pads.
O True
O False
оо
Ms. Padilla orders 144 jars of paint.
O True
O False
The ratio of sketch pads to jars of paint in Ms. Padilla's order can be written as
25 : 12
O True
O False
The ratio of jars of paint to sketch pads in Ms. Padilla's order can be written as
4:5.
o
O True
O False
Answer:
1. False
Sketch pads ordered: 10(90/3) = 10×30 = 300
2. True
Painting jars ordered: 8(90/5) = 8×18 = 144
3. True
(25×12)/(12×12) = 300/144
or
25/12 = 300/144 = 2.083..
4. False
Since the previous statement isn't 5:4 and it's true, then this statement is false.
whats 3x+2 x 12.
.
.
.
.
.
music recommendations pls (unknown artist pls not like billie e. or lil nas x/ariana g and megan/cardi b/Justin b) Artist like ALI, Kikou/ mafumafu/set it off/K.flay/twice/ASTRO/taemin. artist like them? like name the artist and some of their songs.
Answer:
sheck wes, sam hunt, mainiac, petty level , lakeyah , doja cat, sawatiee
Step-by-step explanation:
Answer:
NF: Songs are kinda depressing sometimes but he is a really good rapper. Hear clouds
Kid Laroi: Listen to without you.
iann dior: rapper and really good
Mumford and sons: more of slow music but upbeat at the same time
Tracy chapman: She has really good music. Recommend listening to fast car
those are some of my favs
Step-by-step explanation:
w
Which value of x would make ASUV 2 ATUN by HI?
S
(4X-1
O 2
03
O 4
05
2x + 9
Answer:
fourth answer choice) 5
Step-by-step explanation:
2x + 9 = 4x - 1
9 = 2x - 1
10 = 2x
5 = x
x = 5
I would appreciate Brainliest, but no worries.
The value of x that would make ASUV = ATUN by HL is 4, the correct option is C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
SUV congruent to TUV
Now,
To solve for x in the equation 2x+9=4x+1, we need to isolate x on one side of the equation.
First, we can simplify both sides by subtracting 2x from each side:
2x+9-2x=4x+1-2x
Simplifying this gives us:
9=2x+1
Next, we can subtract 1 from each side:
9-1=2x+1-1
Simplifying this gives us:
8=2x
Finally, we can divide both sides by 2:
8/2=2x/2
Simplifying this gives us:
4=x
Therefore, by the algebra the answer will be x=4.
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I need the answers 1-4
Answer:
hope this helps you out question 4 and 3 are the same
Do there exist subspaces S,T, and U of R3 such that SIT, SIU, and T 1 U? If so, provide an example of such an S, T, and U, and prove that SIT, SIU, and T 10. If not, prove why they do not exist.
There exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.
In order to answer the given question, we first need to understand the definition of subspaces of a vector space.A subspace of a vector space is a subset that meets three requirements:
i) It includes the zero element of the vector space.
ii) It is closed under addition (if u and v belong to the subspace, then u + v is also in the subspace).
iii) It is closed under scalar multiplication (if u is in the subspace and k is a scalar, then ku is also in the subspace).
there exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.
The reason is simple because if T∩U = Ø, then either SIT or SIU will be the trivial subspace {0}.
However, this contradicts the fact that both SIT and SIU have to contain a non-zero vector as they are subspaces that are generated by S, T, and U.
Therefore, it is proven that there exist no subspaces S, T, and U of R³ such that SIT, SIU, and T∩U.
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Simplify the ratio 7:21.
(OLD HW!!)
(TIPS FOR ALGEBRA TO PLS ^^)
Answer:
Simplified : 1:3
Step-by-step explanation:
7:21 is equal to 1:3
Also, for algebra tips. Algebra is literally practice. There aren't too many complicated equations or anything until you get into a higher math class so practicing problems is best.
Answer:
7:21 = 1:3
Tips for algebra...
just know the basics and related rules or theorams and practice as much as u can
good day mate
Please answer^^ I will give you brainlist!
Yes 5th grade math :clown face:
Answer:
Rhombuses
Step-by-step explanation:
It has four vertical lines, then draw a Venn Diagram, opposite to opposite.
Order from Venn Diagrams:
Quadrilaterals
Rectangles
Squares
Rhombuses.
Please solve these for me will give you brainiest please!!
2- y= -5
3- y= 2x
4- y= -4
5- y= 6x,,, 60
6- -4,,,,,,,,, 36
1/3 points Previous Answers TanApMath7 10.5.004. My Notes + Ask Your Teacher The owner of the Rancho Los Feliz has 3180 yd of fencing to enclose a rectangular piece of grazing land along the straight portion of a river and then subdivide it by means of a fence running parallel to the sides. No fencing is required along the river. (See the figure below.) What are the dimensions of the largest area that can be enclosed? x = X yd y = 1590 yd What is this area? x yd2 Need Help?
The dimensions of the largest area that can be enclosed is 1590 × 795= 1264050 yd² when no fencing is required along the river.
Given the owner of the Rancho Los Feliz has 3180 yd of fencing to enclose a rectangular piece of grazing land along the straight portion of a river and then subdivide it by means of a fence running parallel to the sides. No fencing is required along the river.
We need to find the dimensions of the largest area that can be enclosed.
Therefore, the length of the land is the perimeter of the rectangle minus the river front.
We have; 2x + 3y = 3180 yd
Also, we can rewrite this equation in terms of x;
2x = 3180 - 3yy = (3180 - 2x) / 3
Substituting y in terms of x in the area equation;
Area A = x y= x(3180 - 2x) / 3
Taking the derivative of the area equation to find the maximum value of A;
A' = 1060 - 2x / 3 When A' = 0, x = 1590 / 2 = 795 yd.
Substitute x = 795 into the equation for y;
2(795) + 3y = 3180y = (3180 - 1590) / 3 = 530 yd
Therefore, the dimensions of the largest area that can be enclosed are; Length = 1590 yd Width = 795 yd
Hence, the area is given by; Area = Length × Width= 1590 × 795= 1264050 yd².
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Astudent was asked to find a 99% confidence interval for the proportion of students who take notes using data from a random sample of size n - 83. Which of the following is a correct interpretation of the interval 0.14 « p<0.342?
The given confidence interval is 0.14 < p < 0.342, where p represents the proportion of students who take notes. To interpret this interval correctly, we can say: We are 99% confident that the true proportion of students who take notes lies between 0.14 and 0.342.
In other words, based on the data from the random sample of size 83, we estimate that the proportion of students who take notes falls within this range with a 99% level of confidence. This means that if we were to take multiple random samples of the same size and calculate confidence intervals, approximately 99% of those intervals would contain the true proportion of students who take notes.
Furthermore, the interval does not include the value of 0.5, which represents no preference or a 50% proportion. Since both 0.14 and 0.342 are less than 0.5, we can infer that the data suggests that a substantial proportion of students take notes, but we cannot conclude with certainty whether the majority or minority take notes without further information.
It's important to note that the interpretation assumes the random sampling method was appropriate and the sample is representative of the population of interest.
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The area of the base is 7 cm. What is the surface area of the pyramid?
Answer: 34.5
Step-by-step explanation:
(Base · Height) ÷ 2 → (2 · 4.5) ÷ 2 = 5.5
5.5 · 5 = 27.5
27.5 + 7 = 34.5
fill in the missing justifications to the proof given: lm = np, lp = mn prove: lmn = npl
The justification for the proof based on the information will be:
lm = np (Given)
lp = mn (Given)
(1) lmn = lm * n
Justification: Associative property of multiplication
(2) lmn = np * n
Justification: Substitute lm = np
(3) lmn = n * np
Justification: Commutative property of multiplication
(4) lmn = npl
Justification: Substitute lp = mn
Therefore, lmn = npl.
How to explain the informationThe associative property of multiplication is one of the fundamental properties of arithmetic. It states that the grouping of factors does not affect the result of multiplication.
In other words, when you multiply three or more numbers, you can change the grouping of the factors without changing the product.
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A rectangular prism has a length of 18 meters, a height of 10 meters, and a width of 5
meters. What is its volume, in cubic meters?
Answer:
900
Step-by-step explanation:
A debt of $25,000 is to be amortized over 17 years at a 7% annual interest rate under monthly compounding. What value of monthly payments will achieve this? Please round your numerical answer to the nearest integer dollar.
After considering the given data we conclude that value of monthly payments will achieve this is $25,000 over 17 years at a 7% annual interest rate under monthly compounding is $203.
To evaluate the monthly payments that will amortize a debt of $25,000 over 17 years at a 7% annual interest rate under monthly compounding, we could apply the following steps:
Alter the annual interest rate to a monthly interest rate by applying division of 12. The monthly interest rate is 7% / 12 = 0.5833%.
Alter the number of years to the number of months by multiplying by 12. The number of months is 17 × 12 = 204.
Apply the formula for the monthly payment on an amortized loan:
[tex]P = (r * PV) / (1 - (1 + r)^{(-n))}[/tex]
Here,
P = monthly payment,
r = monthly interest rate,
PV = present value of the loan (which is $25,000),
n = total number of payments (which is 204).
Placing in the values, we get:
[tex]P = (0.005833 * 25000) / (1 - (1 + 0.005833)^{(-204))} = $202.91[/tex]
Hence, the monthly payments that will amortize the debt of $25,000 over 17 years at a 7% annual interest rate under monthly compounding is $203 (rounded to the nearest dollar).
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The figure is the net for a rectangular prism.
What is the surface area of the rectangular prism represented by the net?
PLS HELP!! I WILL GIVE BRAINLYIEST!!
Answer:
surface area = 544 cm²
Step-by-step explanation:
surface area = (16)(8 + 6 + 8 + 6) + (2)(8)(6) = 448 + 96 = 544 cm²
Help me guys. plz no Decimal please. Thank you!
Answer: 1,145,375cm^3
Step-by-step explanation:
The top of the cake to be triangular with one side length 10cm, one side length 12cm and a 90-degree angle between these sides
Answer:
See attachment
Step-by-step explanation:
Given
[tex]Side\ 1 = 10cm[/tex]
[tex]Side\ 2 = 12cm[/tex]
[tex]\theta = 90^\circ[/tex]
Required [Missing from the question]
Draw the top of the cake
See attachment for reference.
From the attachment,
[tex]2cm = 1\ unit[/tex]
So:
[tex]Side\ 1 = 10cm[/tex]
[tex]Side\ 1 = 5 * 2cm[/tex]
Substitute [tex]2cm = 1\ unit[/tex]
[tex]Side\ 1 = 5 * 1unit[/tex]
[tex]Side\ 1 = 5\ units[/tex]
[tex]Side\ 2 = 12cm[/tex]
[tex]Side\ 2 = 6 * 2cm[/tex]
Substitute [tex]2cm = 1\ unit[/tex]
[tex]Side\ 2 = 6 * 1unit[/tex]
[tex]Side\ 2 = 6\ units[/tex]
This means that, the given side lengths will be represented by 5 units and 6 units on the grid, respectively.
See attachment for drawing