A. To obtain the Cartesian and polar forms of the function f(z) = z², we square the complex number z and express it in both forms.
B. To verify if u(x, y) = (x y³ -x³y) is a harmonic function, we check if it satisfies Laplace's equation. We can then construct the analytic function w = f(z) = u(x, y) + iv(x, y) by introducing a harmonic conjugate.
C. To find the poles and classify their orders for the given functions, we analyze the denominators and determine the values of z for which the functions become singular.
A. The function f(z) = z² can be expressed in Cartesian form as f(z) = (x + iy)² = x² - y² + 2ixy. In polar form, we write z as z = re^(iθ), where r represents the magnitude and θ is the argument. Squaring z gives f(z) = r²e^(2iθ).
B. To verify if u(x, y) = (x y³ - x³y) is harmonic, we calculate its second-order partial derivatives with respect to x and y. If Laplace's equation (∂²u/∂x² + ∂²u/∂y² = 0) holds true, then u is harmonic.
Next, we introduce a harmonic conjugate v(x, y) such that vₓ = -uₓ and vᵧ = -uᵧ. Solving these partial differential equations gives us v(x, y) = -(x³ + 3xy²) + C, where C is a constant.
Thus, the analytic function w = f(z) = u(x, y) + iv(x, y) is given by w = (x y³ - x³y) - i(x³ + 3xy²) + C.
C. To find the poles and classify their orders for the given functions:
f(z) = ²1: There is no denominator, so the function has no poles.
f(z) = z¹ + 2z² + 1: The denominator is z² + z + 1, which can be factored as (z - ω)(z - ω²), where ω is a complex cube root of unity. The function has simple poles at z = ω and z = ω², with orders 1.
f(z) = z² + z + 1: The denominator is z² + z + 1, which does not factor further. The function has no poles.
By analyzing the denominators of the functions, we determine the poles and classify their orders accordingly.
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help please right answer oonnnly
Answer:
domain(-3,\infty )range(-\infty ,\infty )
Step-by-step explanation:
D
-2 (x + 3) > 9 + 3x.
inequality
Answer:
x<-3
Step-by-step explanation:
-2(x+3)>9+3x - Distribute
-2x-6 > 9+3x - Subtract 3x to both sides
-5x-6 > 9 - Add 6 to both side
-5x > 15 - Divide -5 to both sides
Integer switches: x < -3 - Answer
Source: MathPapa
the lengths of songs on the radio are normally distributed with a mean length of 210 seconds. if 38.2% of all songs have lengths between 194 and 226 seconds, then the standard deviation of this distribution is
Answer:
Step-by-step explanation:
Rick is setting up a model train track that is 5 and 3 over 5 feet long. No telephone pole is needed at the start of the track. However, along the track, he places a telephone pole every 4 over 5 foot apart. How many telephone poles does he need? (Input number values only) (3 points)_ (01.06) Rick is setting up a model train track that is 5 and 3 over 5 feet long. No telephone pole is needed at the start of the track. However, along the track, he places a telephone pole every 4 over 5 foot apart. How many telephone poles does he need? (Input number values only)
Answer:
7 telephone poles
Step-by-step explanation:
Given that:
Length of track = 5(3/5) feet long
No pole is needed at the atart of the track
Poles are however placed every 4/5 foot apart
Number of telephone poles needed :
Length of track / distance between each placed poles
= length of track = 5(3/5) = 28/5 feet
Distance between poles = 4/5 foot
Hence,
(28 /5) ÷ (4 /5)
= 28 /5 × 5 / 4
= (28 * 5) / 20
= 140 / 20
= 7
Number of poles required = 7
Step-by-step explanation:
5 5/6 / 5/12
Keep Change Flip
35/6 * 12/5
cross simplify
7/1 * 2/1= 14/1= 14
If I was asked to think of a number and multiply it by 2, I could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, multiply it by 3 and add 1 to the result."
Answer:
3x+1
Step-by-step explanation:
The algebraic expression is 3x+1
What is a polynomial?Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is defined as an expression that is composed of variables, constants, and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11
Given here let the number be x and we multiply it by 3 and add 1 to the result then we get 3x+1
Hence, the algebraic expression is 3x+1
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Write the complex number in standard form. (Simplify your answer completely.) (5+ √5) (6-√-10)
To write the complex number (5+√5)(6-√-10) in standard form, we simplify the expression by multiplying the terms and then combine the real and imaginary parts. The standard form of the complex number is 30 + 5√2.
To simplify the expression (5+√5)(6-√-10), we need to multiply the terms using the distributive property.
First, let's multiply the real parts:
5 * 6 = 30.
Next, we multiply the imaginary parts:
√5 * -√-10 = -√(5 * -10) = -√(-50) = -√(50)(-1) = -√(25 * 2)(-1) = -√25 * √2 * (-1) = -5√2.
Now, let's combine the real and imaginary parts to write the complex number in standard form:
(5+√5)(6-√-10) = 30 + 5√2.
Therefore, the complex number (5+√5)(6-√-10) can be written in standard form as 30 + 5√2. In standard form, the complex number is expressed as the sum of a real part and an imaginary part. The real part is 30, and the imaginary part is 5√2.
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||3x−4|−5|>1
Solve the inequality
:)
[tex]||3x-4|-5|>1\\|3x-4|-5>1 \vee |3x-4|-5<-1\\|3x-4|>6 \vee |3x-4|<4\\3x-4>6 \vee 3x-4<-6 \vee (3x-4<4 \wedge 3x-4>-4)\\3x>10 \vee 3x<-2 \vee (3x<8 \wedge 3x>0)\\x>\dfrac{10}{3} \vee x<-\dfrac{2}{3} \vee (x<\dfrac{8}{3} \wedge x>0)\\x\in\left(-\infty,-\dfrac{2}{3}\right)\cup\left(0,\dfrac{8}{3}\right)\cup\left(\dfrac{10}{3},\infty\right)[/tex]
[tex]\left \{ {{50x-2y=230} \atop {50x-3y=170} \right.[/tex]
combination method
Answer:
x = 7, y = 60
Step-by-step explanation:
Given the 2 equations
50x - 2y = 230 → (1)
50x - 3y = 170 → (2)
Subtract (2) from (1) term by term on both sides
y = 60
Substitute y = 60 into either of the 2 equations and evaluate for x
Substituting into (1)
50x - 2(60) = 230
50x - 120 = 230 ( add 120 to both sides )
50x = 350 ( divide both sides by 50 )
x = 7
Bro I need help explain what is meant by "it's okay for a student to not succeed right away" ima just put it as math:-P
Learning is a process that often involves unsuccessful attempts.
This is not failure since options are eliminated toward the correct solution.
Learning and problem solving require passing through a period of sorting through facts and options toward success.
From my understanding (what I think it means), is that it is okay for a student not to understand the problem automatically. They may need a minute or two to re-read it or look over the problem again. It's most likely a harder question than the other ones, or it is a common problem that people have trouble with.
A store is designing the space for rows of nested shopping carts.
Each row has a starting cart that is `4` feet long, followed by the nested carts. (`0` nested carts means there's just the starting cart.)
• A row of `13` nested carts is `23.5` feet long.
• A row of `18` nested carts is `31` feet long.
Enter the appropriate label and scale for each axis, and drag the movable points to create a graph of the situation.
By creating a graph that shows the relationship between the number of carts and the space required, the store can better design the space for rows of nested shopping carts.
To design the space for rows of nested shopping carts in a store, a graph can be created that shows the relationship between the number of carts and the amount of space required.
This can be done by plotting the number of carts on the x-axis and the space required on the y-axis.The appropriate labels for each axis are "Number of Carts" for the x-axis and "Space Required" for the y-axis.
The scale for the x-axis would depend on the maximum number of carts that the store wants to accommodate, while the scale for the y-axis would depend on the amount of space that each cart takes up.
The movable points on the graph can be used to illustrate different scenarios.
For example, if the store wants to know how much space would be required for 50 carts, the movable point can be placed at 50 on the x-axis, and the corresponding space required can be read off the y-axis.
Similarly, if the store wants to know how many carts can be accommodated in a given amount of space, the movable point can be placed at the desired space on the y-axis, and the corresponding number of carts can be read off the x-axis.
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60 PTS PLEASE HELP ME!! I NEED AN ANSWER QUICK!!
Answer:
y = 4/3x + 1
Step-by-step explanation:
slope = rise over run
slope = 4 rise 3 run
slope = 4/3
Answer:
1st Option
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Find slope m
[tex]m=\frac{5-1}{3-0}[/tex]
[tex]m=\frac{4}{3}[/tex]
y = 4/3x + b
Step 2: Find y-intercept b
(0, 1)
Step 3: Write linear equation
y = 4/3x + 1
4=[(43-34-32)*0]+2-2+4-3+5-2
Is this True?
Answer: True
Step-by-step explanation:
Solve for the indicated variable
ab-ac= 2 for a
Given, the indicated variable is: ab - ac = 2, We have to solve the given equation for a. So the answer is a = 2/(b - c).
Let's do this: Factor out the a from the left-hand side of the equation.
Using the distributive property, we get: a(b - c) = 2
Now, we'll isolate a by dividing both sides by (b - c).
Thus, we get: a = 2/(b - c)
Therefore, the value of the variable a is 2 divided by the quantity of (b - c).
Let's have a look at the steps: ab - ac = 2
a(b - c) = 2
a = 2/(b - c). Hence, we have obtained the value of the variable a by solving the given equation.
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Find the domain of the function expressed by the formula: f(x)= 3x/(x−1)(x−2)
Answer:
Domain: x < 1 or 1 < x < 2 or x > 2
Step-by-step explanation:
Take the denominator(s) and compare to zero
(x-1)(x-2) = 0
Solve (x-1)(x-2)=0:
x = 1
x = 2
I need help with this pls
Answer:
make the picture more clear its hard to see.
Step-by-step explanation:
Answer:
4. y=-1x+1
5. y=-2x+27
Step-by-step explanation:
please help me solve...-5(-2-8x) = 10 + 5x
thank you,
Answer:
x=0
Step-by-step explanation:
−5(−2−8x)=10+5x
10+40x=10+5x
10+40x−5x=10
10+35x=10
35x=10−10
35x=0
x=0
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $68. A season ski pass costs $450. The skier would have to rent skis with either pass for $25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Answer:
Five days
Step-by-step explanation:
Because the skier has to pay $93 a day to ski (68 + 25), in five days of daily pay, the skier would end up paying $465. However, if he paid for a season pass for $450, he would only have to ski for five days in order to make the season pass less expensive than the daily pass.
Between which 2 whole numbers is the square root of 50?
Answer: It would be between 7 and 8
Please help with homework! I don't understand this
Answer:
B.
Step-by-step explanation:
Basic Power Rule: f'(x) = n · xⁿ⁻¹
Step 1: Define
[tex]\frac{dy}{dx} [6x^{\frac{-2}{3} }][/tex]
Step 2: Use Basic Power Rule
[tex]f'(x)=6(\frac{-2}{3})x^{\frac{-2}{3} -1}[/tex]
[tex]f'(x)=-4x^{\frac{-5}{3}}[/tex]
Step 3: Simplify
[tex]f'(x)=\frac{-4}{x^{\frac{5}{3} }}[/tex]
[tex]f'(x)=\frac{-4}{\sqrt[3]{x^5} }[/tex]
Consider the diagram below and Solve for x
Answer: I believe the answer is x = 38°
114° / 3
x = 38°
Hope this helps :)
What is the value of y when x = 5 in the equation y = 5x?
Consider a population with population proportion p, and a sample from the population with sample proportion p. Which of the following describes the purpose of the one-sample 2-test: (a) To estimate the value of Ô (b) To estimate the value of p (c) To estimate a margin of error for ø (d) To estimate the probability of observing a value as extreme as pe (e) To estimate the probability of observing a value as extreme as p given P
The purpose of the one-sample 2-test is to estimate the probability of observing a value as extreme as the sample proportion (p) given the population proportion (p). In light of this, the right response is (e) "To estimate the probability of observing a value as extreme as p given P."
The one-sample 2-test, also known as the one-sample proportion test or z-test for proportions, is a statistical test used to determine if a sample proportion significantly differs from a hypothesized population proportion.
It helps assess whether the observed proportion in the sample is significantly different from what would be expected based on the hypothesized population proportion.
Therefore, the correct answer is (e) "To estimate the probability of observing a value as extreme as p given P."
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Evaluate each expression. (Simplify your answers completely.) (a) (9)°-2-1 (b) 2-3 30 -2 (3)?
(a) Evaluating the expression (9)°-2-1:(9)°-2-1 = (1/9)²-1 = (1/81) - 1 = -80/81. The solution for the given expression is -80/81. (b) Evaluating the expression 2-3 30 -2 (3):2-3 30 -2 (3) = 2-3 × 30-2 × 3= (1/8) × 1/900 × 3= 3/7200 = 1/2400.Therefore, the expression is 1/2400.
The first expression to be evaluated is (9)°-2-1. We know that an exponent is a number that tells how many times the base is multiplied by itself. In this expression, 9 is the base and 2-1 is the exponent. So the expression can be rewritten as 9²-1. Squaring 9 gives us 81. And 1 is subtracted from 81 to get 80. Hence, 9°-2-1 is equal to -80/81.Now let's look at the second expression, 2-3 30 -2 (3). We need to use the order of operations, which is a set of rules for carrying out operations in a particular sequence. According to the order of operations, we need to first solve the exponents, then multiplication, and finally division. So the expression can be written as 2-3 × 30-2 × 3.Using the formula aⁿ × aᵐ = aⁿ⁺ᵐ, we can simplify this expression as 2-3 × 900-1. Since 900 is a square of 30, we can write 900 as 30². So the expression becomes 2-3 × 30²-1. Simplifying this further, we get 2-3 × 900-1 = 2-3 × 1/900 × 3. Using the formula aⁿ ÷ aᵐ = aⁿ⁻ᵐ, we can simplify this expression as 3/2⁹ × 3. The denominator 2⁹ can be written as 512. Hence, the expression can be simplified as 3/7200 = 1/2400.
To summarize, we have evaluated the two expressions (9)°-2-1 and 2-3 30 -2 (3). The final answers are -80/81 and 1/2400 respectively. We used the order of operations and exponent rules to simplify the expressions.
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Question 16
QUICK
Please help me find out what d is
Answer:
864
Step-by-step explanation:
d/6=144
cross multiply
d=144×6
d=864
(1 point) Deshaun is a plumber who charges $40 per hour for his work. Another plumber, Silvio, charges based on the equation d = 60+ 20h, where h is the number of hours worked and d is the cost in dollars. Which statement is true? a b Deshaun's charge per hour is more expensive. Silvio's charge per hour is more expensive. Deshaun and Silvio charge the same amount. Deshaun's initial value is $20. C d
Answer:
A
Step-by-step explanation:
Deshaun charges $40 per hour.
So if Deshaun and Silvio work for 5 hours, then it would be $40(5) which would be more expensive than Silvio's with $60 + 20(5). Silvio gets $60 with $20 per hour.
Deshaun would get $200 while Silvio would get $160.
which ones are in scientific notation? 15 points
Last question ;-; i think...
10 pnts
Answer:
a) -11
b) 75
Step-by-step explanation:
a= -24-13=-11
b= 61-(-14)=75
El cuadrado de un número -17 es igual a 152 .Encuentra el número
Answer:
hajskshsjakalskksks
I'LL MARK YOU AS A BRAINLIEST PLZ ANSWER
is radical 43/2 rational or irrational
Answer:
i think its rational
Step-by-step explanation:
Answer:
i said rational on ur other post bc i know its rational hope this helps
Step-by-step explanation:
help please this is difficult
Answer:
(5,2)
Step-by-step explanation:
(5,2) is the same distance from the lone as point N
Answer:
N(2,5)
Step-by-step explanation:
