Main answer: f(z) = Reſiz is differentiable at every point of the complex plane where partial derivative with respect to x exists and the Cauchy-Riemann equations are satisfied.
Supporting answer: Given f(z) = ReſizLet z = x + iy∴ f(z) = Re(x + iy)z = x - iyi.e. x = ½ (z + z¯)and y = -½i(z - z¯)Hence f(z) = ½ (z + z¯ ) Differentiating f(z) partially with respect to x, we get,fx = ∂(x + y)/∂x = 1And differentiating f(z) partially with respect to y, we get,fy = ∂(x + y)/∂y = 1Now, for f(z) to be differentiable, it is necessary thatfx = uxx + ivxxandfy = uyx + ivyxwhere u = Re (f(z)) and v = Im(f(z))i.e. uxx = vyyanduyx = -vxy These equations are known as the Cauchy-Riemann equations. On substituting, we get uxx = vyy∴ 1 = 0which is not true. Hence f(z) is not differentiable when partial derivative with respect to y exists. So f(z) is differentiable at every point of the complex plane where partial derivative with respect to x exists and the Cauchy-Riemann equations are satisfied.
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please help, is it x = 6, y = 6, y = x, or y = 2?
01:08:55
B
O
B
А
A'
2
D
C
ci
D'
Х
6
8
10
2
O x = 6
O y = 6
O y = x
O y=2
The equation for the line of reflection is x = 6
What is reflection?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given that, a graph, we need to find the equation of the reflection of the polygon graphed,
We can see, all the vertices on the polygon are being mirrored across the line x = 6.
So, we can say the line of reflection is x = 6.
Hence, the equation for the line of reflection is x = 6
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What is the percent of change from 10 to 8?
use Laplace transforms to solve the following differential equation
y' + 3y = f(t), y(0) = α, α is a constant.
The solution to the differential equation y' + 3y = f(t), y(0) = α using Laplace transforms is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).
We use the Laplace transform on both sides of the problem in order to solve the given differential equation. Let Y(s) and F(s) represent the Laplace transforms of y(t) and f(t), respectively. Taking the Laplace transform of both sides of the equation, we have:
sY(s) - y(0) + 3Y(s) = F(s)
Substituting y(0) = α, we get,
sY(s) - α + 3Y(s) = F(s)
Rearranging the equation and solving for Y(s), we have,
Y(s) = (F(s) + α)/(s + 3)
Now, we need to find the inverse Laplace transform of Y(s) to obtain y(t). Using the properties of Laplace transforms, we know that the inverse Laplace transform of Y(s) is y(t) = L⁻¹{Y(s)}. Applying the inverse Laplace transform, we find,
y(t) = αe⁻³ᵗ + L⁻¹{F(s)/(s+3)}
The term αe⁻³ᵗ corresponds to the initial condition y(0) = α. The remaining term L⁻¹{F(s)/(s+3)} represents the inverse Laplace transform of F(s)/(s+3), which depends on the specific function f(t) and its Laplace transform.
Therefore, the solution to the differential equation is y(t) = αe⁻³ᵗ + F(s)/(s+3), where F(s) is the Laplace transform of f(t).
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4x^2+2x-1=0 in quaratic equations
Answer:
Step-by-step explanation:
"quaratic" should be "quadratic."
The coefficients of this quadratic are 4, 2 and -1. Thus, the discriminant is
b^2 - 4ac, or here, 4 - 4(4)(-1) = 20
Since the discriminant is positive, our quadratic has two real, different roots.
-2 ± (√4)(√5)
The roots are: x = ---------------------
2(4)
-1 ± √5
This reduces to x = ---------------
8
Which expressions are equivalent to 6 + 12x
A 3(2+4x)
B. 3(2+6x)+2x
C. 5(1+2x)+1+2x
D7(1+2x)-2x-1
E 7 (1+2x)+2x-1
Answer:
A,C and D
Step-by-step explanation:
A: 3x2=6
3x4X=12X
6+12X
C: 5x1=5
5x2X=10X
5+10X+1+2X
6+12X
D: 7x1=7
7x2X=14X
7+14X-2X-1
6+14X-2X
6+12X
Solve the system of equations shown below?
What is the equation of the line that passes through (0, 2) and (3, - 4)
i'll give brainiest to who answers this pls help
Answer:
The answer is 126 square inches.
Step-by-step expalation
Please help me anyone any other answers would be reported
Answer:
Wait So...
Step-by-step explanation:
What Kind of Math is this?
Ben conducted an experiment to determine the association between the number of hours spent studying per day with GPA. The line of best fit for his data has a slope of 1, with time, in hours, as the independent variable x and GPA as the dependent variable, y. What does a slope of 1 mean in this context?
A) GPA is 1 point every hour.
B) GPA of 1 point is at zero hours.
C) GPA increases by 1 additional point per hour.
D) Time decreases by 1 hour for every GPA point increase.
Answer:
C.
Step-by-step explanation:
Since the slope is 1 meaning it goes up and over by 1 the GPA would increase by 1 every hour
Answer:
c
Step-by-step explanation:
A study looked at n=256 adolescents, where subjects wore a wrist actigraph, which allowed the researchers to estimate sleep patterns. Those subjects classified as having low sleep efficiency had an average systolic blood pressure that was 5.6 millimeters of mercury (mm Hg) higher than that of other adolescents. The standard deviation of this difference is 1.8 mm Hg. Based on the results, test whether this difference is significant at the 0.01 level. 2. An SRS of 100 incoming freshman was taken to look at their college anxiety level. The mean score of the sample was 87.3 (on a 0 to 100 scale with a higher score indicating mores stress). Assuming population o = 8.1, construct a 95% confidence interval for the population mean. What sample size is required to get a margin of error less than or equal to .15?
There is a significance at the level 0.01.
We can use a two-sample t-test for this purpose.
A two-sample t-test is used to examine whether two data samples have a mean difference that is statistically significant.The null hypothesis for this test is that there is no significant difference between the mean systolic blood pressure of those adolescents classified as having low sleep efficiency and that of other adolescents.
Hence, H0: μ1 = μ2
where μ1 is the mean systolic blood pressure of those adolescents classified as having low sleep efficiency and μ2 is the mean systolic blood pressure of other adolescents.
The alternative hypothesis is that there is a significant difference between the two means:
H1: μ1 ≠ μ2
The level of significance (α) is 0.01, so the critical value of t can be found using a t-distribution table with 254 degrees of freedom (n1+n2-2=254).
The critical value at a 0.01 level of significance is ±2.576.
From the question, we know that the mean difference between the two groups is 5.6 mm Hg and the standard deviation of this difference is 1.8 mm Hg.
Therefore, the t-statistic can be calculated as:
t = (5.6 - 0) / (1.8 / sqrt(256))
= 56 / 1.8 = 31.11
Since the calculated t-statistic (31.11) is greater than the critical value (±2.576), we reject the null hypothesis.
Thus, we can conclude that there is a significant difference in systolic blood pressure between the two groups at the 0.01 level of significance.
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population grows according to an exponential growth model: The initial population is Po 10, and the growth rate is r 0.2_ Then: Pi 10.2 Pz 10.4 Find an explicit formula for Pn: Your formula should involve n. Pn 10 ( 1.02) n Use your formula to find P9 Pg 11.95 Give all answers accurate to at least one decimal place
The population at time n=9 is approximately 11.95. The term "population" refers to the entire set of individuals, objects, or events that are of interest to a researcher or analyst.
Based on the given information, we have:
Initial population (P0) = 10
Growth rate (r) = 0.2
To find an explicit formula for Pn, we can use the formula for exponential growth:
Pn = P0 * (1 + r)^n
Substituting the given values:
Pn = 10 * (1 + 0.2)^n
Simplifying the formula, we have:
Pn = 10 * 1.2^n
Using this formula, we can find P9:
P9 = 10 * 1.2^9 ≈ 11.95
Therefore, the population at time n=9 is approximately 11.95.
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What is the sample space for a spinner with four equal sections, numbered 1 to 4?
1, 2, 3, 4
4-1. 4-2. 4-3. 4-4
1-1,1-2, 1-3, 1-4
1, 2, 3, 4, 5
Answer:
the answer is 1-1, 1-2, 1-3, 1-4
Step-by-step explanation:
which statement is true?
Answer:
B is the answer
because if you observe very well the angles look similar in a way when you turn it the other way round ...
How much water can a sponge filter in one minute?
2 quarts
3 quarts
4 quarts
1 quart
Answer:
It would be 4 quarts.
Step-by-step explanation:
The answer is 2 quarts
um just testing 157x124
Answer:
Step-by-step explanation:
Advertisements for the train claim it is on time 90% of the time. The bus has a record of being on time 56 out of 64 days. Which form of transportation provides more reliable service???
Answer:
The train is more reliable.
Step-by-step explanation:
The train is more reliable. The bus is on-time 87.5% of the time, while the train is on-time 90% of the time.
How much can this water
tank hold?
20 ft
40 ft
cubic feet
ETOOTC
Volume of Cylinder = 7r2 x h
Use 3.14 for .
Do NOT round your answer.
Answer:
15 i don't think it is right
PLZZZ HELPPP BRAINLIESTT
Answer:
1. 4 less than x
2. v = 15.00n
Answer:
4 minus x and v = 15.00n
Step-by-step explanation:
Find the probability of the indicated event if P(E)=0.20 and P(F)=0.45. Find P(E or F) i PE and F)=0.10. P(E or F)-
The probability of event E is 0.20, the probability of event F is 0.45, and the probability of both E and F occurring is 0.10. Therefore, the probability of either event E or event F occurring, denoted as P(E or F), is 0.65.
Given that P(E) = 0.20 and P(F) = 0.45, we also know that P(E and F) = 0.10. Using the formula P(E or F) = P(E) + P(F) - P(E and F), we can substitute the values and calculate the probability of either event E or event F occurring.
P(E or F) = P(E) + P(F) - P(E and F)
P(E or F) = 0.20 + 0.45 - 0.10
P(E or F) = 0.65
Therefore, the probability of either event E or event F occurring, denoted as P(E or F), is 0.65.
The concept behind this formula is that when we add the individual probabilities of E and F, we count their intersection (P(E and F)) twice. Since we want to avoid double-counting the intersection, we subtract P(E and F) from the sum of P(E) and P(F). This gives us the probability of either event E or event F occurring.
In this case, the probability of either event E or event F occurring is 0.65, indicating a relatively high likelihood of one of the events happening.
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Three friends ate 3/4 of a pizza. The 3 friends ate
equal amounts. How much of the pizza did each
friend eat?
Answer:
each friend ate 1/4 of pizza
Step-by-step explanation:
3/4 ÷ 3
= 1/4
Someone help me with this its in the picture!!!
Answer:
JK < KI < IJ
Step-by-step explanation:
The length of the side of a rectangle corresponds with the size of the angle opposite it.
m<K = 180 - (50 + 44) (sum of triangle)
m<K = 86°
IJ is opposite m<K = 86°
JK is opposite to m<1 = 44°
KI is opposite to m<J = 50°
The bigger the measure of an angle, the larger the side opposite it.
Therefore, form least to greatest, the side lengths of the triangle cam be ordered as follows:
JK < KI < IJ
surface area does anyonr know it im confused on the formula
Answer:
131.92ft²
Step-by-step explanation:
okay, so we have to find the area of both circles, and the circumference then multiply that with the height, it's confusing, so:
3² x 3.14 = 28.26 x 2 = 56.52 so that the area of the bases
3 x 2 x 3.14 = 18.85 x 4 = 75.4
75.4 + 56.52 = 131.92
So the surface area of the cylinder is 131.92ft²
What number equals 8 when its cubed?
Step-by-step explanation:
2 would be the answer .
hope it helps u .
2 cubed = 8
equasion; 2 Cubed = [tex]2^{3}[/tex] = 2 × 2 x 2 = 8
i hope this helps <3
help! rs - st + m - tv
Answer:
umm, i think the question is incomplete
Step-by-step explanation:
Kareem is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges $95 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0 80 for every mile driven.
For what mileages will Company A charge less than Company B7
Use m for the number of miles driven, and solve your inequality for m.
Answer:
95 < 75 + 0.80m 20 < m Company A will charge less than Company B for mileages less than 20.
Scott has a rope 8 metres long. He says, “I need 9 pieces each 0.89 metres long.’’ Will Scott have enough ribbon?
A. Yes B. No
Answer:
B
Step-by-step explanation:
How did it go from "rope" to "ribbon", therefore, the statement is incorrect. This is a man-made equation that clearly has a mistake. If it was to say, "Will Scott have enough rope?" then the answer will be "YES"
Answer:
the answer is NO
Step-by-step explanation:
0.89 x 889 = 8.01
Therefore, he is 1cm short
Since previous studies have reported that elite athletes are often deficient in their nutritional
intake (e.g., total calories, carbohydrates, protein), a group of researchers decided to evaluate
Canadian high performance athletes. A total of n = 324 athletes from eight Canadian sports
centers participated in the study. One reported finding was that the average caloric intake
among the n=201 women was 2403.7 kcal/day. The recommended amount is 2811.5 kcal/day.
Is there evidence that female Canadian athletes are deficient in the caloric intake? (Assume
?=0.05 and the data comes from a normal population)
a. State the appropriate null and alternative hypotheses to test this.
b. Which n should be used (201 or 324)? What key word in the last sentence of the paragraph
above led you to this decision?
c. Assuming a population standard deviation of 880 kcal/day, what is the value of the test
statistic?
d. Sketch the normal curve, label your test statistic and shade the appropriate area related to
the p-value.
e. What is the p-value?
f. Do you reject or fail to reject the null hypothesis? Why?
g. Write a conclusion in terms of language related to the given problem.
a. Null hypothesis (H0): The average caloric intake among female Canadian athletes is equal to or greater than the recommended amount (µ ≥ 2811.5 kcal/day).
Alternative hypothesis (H1): The average caloric intake among female Canadian athletes is less than the recommended amount (µ < 2811.5 kcal/day).
b. The value of n that should be used is 201
c. SEM = 880 / √201
d. To sketch the normal curve and label the test statistic, we need the test statistic value and the critical region corresponding to the significance level α = 0.05
e. Without the test statistic or critical region, we cannot calculate the p-value.
f. Since we don't have the test statistic, critical region, or p-value, we cannot make a decision to reject or fail to reject the null hypothesis at this point.
g. Without the test statistic, critical region, or p-value, we cannot draw a conclusion regarding the evidence for or against the deficiency in caloric intake among female Canadian athletes.
a. The appropriate null and alternative hypotheses to test whether female Canadian athletes are deficient in caloric intake can be stated as follows:
Null hypothesis (H0): The average caloric intake among female Canadian athletes is equal to or greater than the recommended amount (µ ≥ 2811.5 kcal/day).
Alternative hypothesis (H1): The average caloric intake among female Canadian athletes is less than the recommended amount (µ < 2811.5 kcal/day).
b. The value of n that should be used is 201, which represents the number of female athletes in the study. The key word in the last sentence of the paragraph ("n=201 women") indicates that the information provided specifically pertains to the female athletes, not the entire sample of 324 athletes.
c. To calculate the test statistic, we need to determine the standard error of the mean (SEM) using the formula:
SEM = σ / √n
where σ is the population standard deviation and n is the sample size. In this case, the population standard deviation is given as 880 kcal/day, and the sample size is 201.
SEM = 880 / √201
d. To sketch the normal curve and label the test statistic, we need the test statistic value and the critical region corresponding to the significance level α = 0.05. However, the critical region is not provided in the given information.
e. The p-value represents the probability of obtaining a test statistic as extreme as or more extreme than the observed value, assuming the null hypothesis is true. Without the test statistic or critical region, we cannot calculate the p-value.
f. Since we don't have the test statistic, critical region, or p-value, we cannot make a decision to reject or fail to reject the null hypothesis at this point.
g. Without the test statistic, critical region, or p-value, we cannot draw a conclusion regarding the evidence for or against the deficiency in caloric intake among female Canadian athletes. Further analysis is required to obtain the missing information and make a conclusive statement.
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I need to know what is the given in this problem
well, the triangle is an isosceles with twin sides, and so twin sides stemming from a common vertex will make twin angles on the other sides, the heck all that means?
well, it means that the twin sides of BC and BD make twin angles at C and D, so
[tex]6x-9~~ = ~~3x+24\implies 3x-9=24\implies 3x=33 \\\\\\ x=\cfrac{33}{3} \implies x=11 \\\\[-0.35em] ~\dotfill\\\\ \underset{ C }{\stackrel{ 6(11)-9 }{\text{\LARGE 57}^o}}\hspace{5em}\underset{ D }{\stackrel{ 3(11)+24 }{\text{\LARGE 57}^o}}\hspace{5em}\underset{ B }{\text{\LARGE 66}^o}[/tex]
What must the values of x and y be so that the two houses are similar?
Answer:
x=12 and y=6
Step-by-step explanation:
because the angle are same and equal
The value of x is 12 and y is 6.
what is similarity?Similar figures mean when two figures are of the same shape but are of different sizes. In other words, two figures are called similar when they both have a lot of the same properties but still may not be identical. For example, the sun and moon might appear the same size but they are actually different in size. However, we are similar figures since both the figures are circular in nature.
Two triangles will be similar if the angles are equal (corresponding angles) and sides are in the same ratio or proportion(corresponding sides). Similar triangles may have different individual lengths of the sides of triangles but their angles must be equal and their corresponding ratio of the length of the sides or scale factor must be the same. If two triangles are similar that means,
All corresponding angle pairs of triangles are equal.All corresponding sides of triangles are proportional.As per the situation we have given that
The similarity in figures show that the angles are equal.
Also, the corresponding sides are also equal.
Hence, the value of x is 12 and y is 6.
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