The contour integral of the function f(z) over the contour C is zero because the function f(z) is analytic inside and on the contour C.
How to determine contour integral?In this case, the function f(z) = (8² - 16)5 = 64 × 5 = 320 is a constant function. Constant functions are always analytic within their domain. Therefore, f(z) is analytic within the region enclosed by the contour C.
According to Cauchy's Integral Formula, the contour integral of a function over a closed contour C is given by:
∮C f(z) dz = 2πi × sum of the residues of f(z) at its isolated singularities within C.
Since f(z) is a constant function, it does not have any singularities. Therefore, all the residues of f(z) are zero.
Hence, the contour integral of f(z) over the contour C is zero:
∮C f(z) dz = 0.
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Consider the curve given by the parametric equations x=t(t2−192),y=8(t2−192) a.) Determine the point on the curve where the tangent is horizontal. t= b.) Determine the points t1,t2 where the tangent is vertical and t1
a) The point on the curve where the tangent is horizontal is at t = 0.
b) The points where the tangent is vertical are at t₁ = -5 and t₂ = 5.
To find the points on the curve where the tangent is horizontal, we need to find the values of t that satisfy dy/dt = 0.
a.) Differentiating y = 3(t² - 75) with respect to t, we get:
dy/dt = 6t
Setting dy/dt = 0, we have:
6t = 0
t = 0
Therefore, when t = 0, the tangent is horizontal.
b.) To find the points where the tangent is vertical, we need to find the values of t that satisfy dx/dt = 0.
Differentiating x = t(t² - 75) with respect to t, we get:
dx/dt = 3t² - 75
Setting dx/dt = 0, we have:
3t² - 75 = 0
t² = 25
t = ±5
Therefore, the points where the tangent is vertical are when t = -5 and t = 5, with t₁ = -5 and t₂ = 5.
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The question is -
Consider the curve given by the parametric equations
x = t (t²-75) , y = 3 (t²-75)
a.) Determine the point on the curve where the tangent is horizontal.
t=
b.) Determine the points t_1,t_2 where the tangent is vertical and t_1 < t_2.
t_1=
t_2=
number 8 please help me
Answer:
15.9??
Step-by-step explanation:
Make up any linear equation with two variables the solution to which will be these pairs of numbers. x=2, y=4.5 PLS HELP
Answer:
[tex]y = 0.25x + 4[/tex]
[tex](x,y) = (2,4.5)[/tex]
Step-by-step explanation:
Given
[tex]x = 2[/tex]
[tex]y = 4.5[/tex]
Required
Make up a linear function
A linear function is represented as:
[tex]y = mx + b[/tex]
Assume [tex]b = 4[/tex]
The equation becomes
[tex]y = mx + 4[/tex]
Substitute [tex]x = 2[/tex] and [tex]y = 4.5[/tex] to solve for m
[tex]4.5 = m*2 + 4[/tex]
[tex]4.5 = 2m + 4\\[/tex]
Solve for m
[tex]2m = 4.5 - 4[/tex]
[tex]2m = 0.5[/tex]
[tex]m = 0.5/2[/tex]
[tex]m = 0.25[/tex]
So, we have:
[tex]m = 0.25[/tex], [tex]b = 4[/tex], [tex]x = 2[/tex] and [tex]y = 4.5[/tex]
[tex]y = mx + b[/tex] becomes
[tex]y = 0.25x + 4[/tex]
[tex](x,y) = (2,4.5)[/tex]
The current in a stream moves at a speed of 5 km/h. A boat travels 20 km upstream and 20 km downstream in a total of 3 hours. Find the speed of the boat in still water.
Answer:
14
Step-by-step explanation:
im right
area = ___ square units
Answer:
9 square units
Step-by-step explanation:
Area of a square = base * height
= 3*3
= 9
What is the interquartile range The following data points represent the volume of gas in each race car driver's tank (in liters) Sort the data from least to greatest: 2.8 43 7.5 8.5 11.6 12 12.1 Find the interquartile range
The interquartile range of the data set is 4.7 liters.
To find the interquartile range, we first need to sort the data from least to greatest. This gives us the following data set:
2.8, 7.5, 8.5, 11.6, 12, 12.1
The first quartile (Q1) is the median of the lower half of the data set. In this case, the lower half of the data set is {2.8, 7.5, 8.5}. The median of this data set is 7.5. Therefore, Q1 = 7.5.
The third quartile (Q3) is the median of the upper half of the data set. In this case, the upper half of the data set is {11.6, 12, 12.1}. The median of this data set is 12. Therefore, Q3 = 12.
The interquartile range (IQR) is calculated by subtracting Q1 from Q3. In this case, IQR = 12 - 7.5 = 4.7 liters.
The interquartile range is a measure of the variability of the middle 50% of the data. In this case, the interquartile range tells us that the middle 50% of the race car drivers have between 7.5 and 12 liters of gas in their tanks.
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Find the length of the diagonal of
rectangle whose length
is 12ft and whose
width 5 ft
Answer:
13 ft
Step-by-step explanation:
The formula to find the length of the diagonal of a rectangle =
Diagonal² = Length² + Width²
Diagonal = √Length² + Width²
Length = 12 ft
Width = 5ft
Diagonal = √12² + 5²
Diagonal = √144 + 25
Diagonal = √169
Diagonal = 13 ft
The length of the diagonal of the rectangle = 13 ft
[tex]2v^{2} +14=104[/tex]
Step-by-step explanation:
[tex]2 {v}^{2} + 14 = 104 \\ 2 {v}^{2} = 104 - 14 \\ 2 {v}^{2} = 90 \\ {v}^{2} = 90 \div 2 \\ {v}^{2} = 45 \\ v = \sqrt{45} [/tex]
I will leave the answer in square root form as i am not sure if you need to round your answer or not.
what differences can be found when contrasting the mood of third person acc with that of claudettes first person account?
Answer: The mood of the third-person account is less emotional and more matter-of-fact. The mood of Claudette's account is less emotional and more matter-of-fact.
Step-by-step explanation:
Jonah has two small bags of assorted doughnuts. Each bag contains exactly 8 powdered doughnuts.
Bag 1 contains 20 total doughnuts.
Bag 2 contains 24 total doughnuts.
What is the probability of Jonah grabbing
a powdered doughnut from
Bag 1?
Answer:
There is a 40% probability of Jonah grabbing a powdered doughnut from Bag 1.
Step-by-step explanation:
Total number of doughnuts in the bag 1 =20
Total powdered doughnuts in each bag = 8
Probability of selecting powdered doughnut from Bag 1 by Jonah =
[tex]\frac{8}{20} * 100\\40[/tex]%
16. You decide to drop a penny off the top of the Willis Tower (fromerly the Sears Tower) in Chicago, IL. The
height of the penny (in feet) can be represented by the equation h= -16t2 + 1451 where t is time (in seconds).
a) How long will it take for the penny to hit the ground? Show any work that leads to your answer.
Answer:
9.5 seconds.
Step-by-step explanation:
We know that the equation that represents the height of the penny as a function of time is:
h(t) = -16*t^2 + 1451
Where the height is in ft, and the time is in seconds.
a) We want to know how long takes the penny to hit the ground.
Well, the penny will hit the ground when its height is equal to zero.
Then we need to solve for t:
h(t) = 0 = -16*t^2 + 1451
0 = -16*t^2 + 1451
16*t^2 = 1451
t^2 = 1451/16 = 90.7
t = √90.7 = 9.5
This means that it takes 9.5 seconds to hit the ground.
Answer:9.5 seconds
Step-by-step explanation:you subtract
please help anybody it would help alot
Correct Given the sample data, find the mean (round to 2 decimals): 23, 27, 35, 44 1.00 points out of 1.00 Flag question Answer: 32.25 Check Correct Marks for this submission: 1.00/1.00 Question 6 Incorrect 0.00 points out of 1.00 Given the data from problem 5 (sample data: 23, 27, 35, 44), find the sum of the squared deviations (the numerator of the fraction under the square root in the formula). In finding the number, round all calculations to 2 decimals (if you carry more or fewer your answer may be off enough to be marked incorrect on this system).
The sum of the squared deviation for the given sample data (23, 27, 35, 44) is 212.00.
In statistics, the squared deviation is calculated by subtracting each data point from the mean and then squaring the result. The sum of these squared differences gives us a measure of how much the individual data points vary from the mean.
Find the sum of squared deviations, we first calculate the mean of the data set. In this case, the mean is found by adding up all the values (23 + 27 + 35 + 44) and dividing the sum by the number of data points (4).
The mean turns out to be 32.25.Next, we subtract the mean from each data point:
(23 - 32.25) = -9.25
(27 - 32.25) = -5.25
(35 - 32.25) = 2.75
(44 - 32.25) = 11.75
Then, we square each of these differences:
(-9.25)² = 85.56
(-5.25)² = 27.56
(2.75)² = 7.56
(11.75)² = 138.06
Finally, we sum up these squared deviations:
85.56 + 27.56 + 7.56 + 138.06
= 212.00
Therefore, the sum of the squared deviations is 212.00 (rounded to two decimal places).
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Solve for x.
PLEASE ANSWER I WILL GIVE BRAINLIEST!!
Answer:
16 + 5 =21 21 is your answer
Step-by-step explanation:
plllleeeasssw help scams are reporteddd
In this class we considered a variety of problems, formulas, and theorems. For an extra credit problem, describe a concept that we covered in class in your own words. It can be a theorem or a question that we solved in class or in homework problems (please don't repeat problems above). State the concept, explain the details in your own words.
The Pythagorean Theorem is a concept in geometry that explains the relationship between the sides of a right-angled triangle. According to this theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of its two legs. This can be represented in the form of an equation as c² = a² + b², where c is the hypotenuse and a and b are the legs of the triangle. This theorem is widely used in various fields, including architecture, engineering, and physics. It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.
In simpler words, the Pythagorean theorem is used to find the length of the missing side of a right-angled triangle. For example, if we know the lengths of two sides of a triangle, we can use this theorem to find the length of the third side. This theorem is based on the fact that the hypotenuse is the longest side of a right-angled triangle, and that the square of a number is the product of that number multiplied by itself. It is also used to prove whether a triangle is a right-angled triangle or not. The Pythagorean Theorem is a fundamental concept in geometry and is an essential tool for solving various mathematical problems.
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BRAINLY TO WHOEVER HELPS AND GET IT RIGHT
~no links pls~
Answer:
4 yards saved
Step-by-step explanation:
two adjacent sides: 6 + 8 = 14
diagonal: √(6² + 8²) = √100 = 10
14 - 10 = 4
If an apple pie recipe calls for 3 pounds of candy apples then how many cups of canned apples required
Answer:
Seven cups of canned apples are required to make apple pie recipe
Step-by-step explanation:
The weight of one canned apple is 0.45 pounds
Weight of total canned apple required to make the apple pie recipe is 3 pounds.
Total number of cups of canned apples required
[tex]= \frac{3}{0.45} \\= \frac{300}{45} \\= \frac{20}{3} \\[/tex]
So approximately seven cups of canned apples are required to make apple pie recipe
Least:
Greatest:.
Median
Lower Quartile Range:
Upper Quartile Range:
thx :)
Answer:
Below :)
Step-by-step explanation:
Least/Minimum: 0
Greatest/Maximum: 6
Median: 2
Lower Quartile Range: 1
Upper Quartile Range: 3
Find median:
0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 6
Find Lower Quartile:
0, 1, 1, 1, 1, 1, 1, 2, 2, 2
Find Upper Quartile:
2, 2, 3, 3, 3, 3, 4, 4, 4, 6
look at photo to answer!
please help
Answer:
the answer is minus 2 ( -2)
Answer:
B
Step-by-step explanation:
This involves reading the coordinates of points from the graph
When x = 3 then y = - 2 , that is the point (3, - 2 )
12 × (3 + 2²) ÷ 2 - 10
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
This should help
A structural steel rod 1-1/2 in. in diameter and 20 ft long supports a balcony and is subjected to an axial tensile load of 30,000 lb. Compute: (a) the total elongation (b) the diameter of the rod required if the total elongation must not exceed 0.10 in. A. a. Elongation = 0.2358in. b. Use a1-1/2" dia. Rod B. a. Elongation = 1.1358in. b. Use a 1-1/4" dia. Rod C. a. Elongation = 0.1358in. b. Use a 1-3/4" dia. Rod D. a. Elongation = 0.1458in. b. Use a 3/4" dia. Rod
The diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.
(a) To compute the total elongation, we can use the formula:
Elongation = (P * L) / (A * E)
where P is the axial tensile load, L is the length of the rod, A is the cross-sectional area of the rod, and E is the modulus of elasticity for the material.
Given:
P = 30,000 lb
L = 20 ft = 240 in
Diameter of the rod = 1-1/2 in
First, we need to calculate the cross-sectional area:
Area = π * (diameter/2)^2
Area = π * (1.5/2)^2
Area ≈ 1.767 in^2
Next, we need to determine the modulus of elasticity for the material. Assuming it's a standard structural steel, we can use a typical value of 29,000,000 psi.
Now we can plug the values into the formula:
Elongation = (30,000 * 240) / (1.767 * 29,000,000)
Elongation ≈ 0.2358 in
Therefore, the total elongation is approximately 0.2358 inches.
(b) If the total elongation must not exceed 0.10 inches, we need to determine the diameter of the rod that satisfies this requirement.
We can rearrange the formula for elongation to solve for the cross-sectional area:
A = (P * L) / (E * Elongation)
Using the given values:
A = (30,000 * 240) / (29,000,000 * 0.10)
A ≈ 2.069 in^2
To find the corresponding diameter, we use the formula:
Diameter = √(4 * A / π)
Diameter = √(4 * 2.069 / π)
Diameter ≈ 1.441 in
Therefore, the diameter of the rod required to limit the total elongation to 0.10 inches is approximately 1-1/2 inches (or 1.441 inches to be more precise). Hence, the correct answer is option (A) with an elongation of 0.2358 inches and using a 1-1/2" diameter rod.
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Sample mean = 5.5, 8=2.517. df-8 and confidence level 95% (corresponding test statistic value is 2303). Based on this information answer the following: Which test is appropriate, z-test or t-test? Type either "z-test" or "t-test" t-test Ą What was the sample size? A Calculate the margin of error. (Report two decimal point, #.##) A Calculate the confidence interval-write lower and uppler value using comma.(Report two decimal point: #.##, #.##) Ą If the df increases to 30 then what will impact on the margin of error? Write either "increase" or "decrease" or "no change decrease ^ If the df increases to 30 then what will impact on the confidence interval? Write either "wide" or "narrow" or "no change" decrease A/
The confidence interval is (4.25, 6.75). If the df increases to 30 then the impact on the margin of error will decrease.
The test that is appropriate for the given values is the t-test since the sample size is small. The sample size is not given in the question but it is necessary to find the margin of error. Hence, the sample size can be found using the formula of the t-test. Let us recall the formula of the t-test below:t = (sample mean - population mean) / (sample standard deviation / √n)
Where,t = test statistic sample mean = 5.5population mean = 8sample standard deviation = 2.517confidence level = 95%corresponding test statistic value = 2.303Let's plug in all the values in the formula and solve for the sample size,n = ((sample mean - population mean) / (sample standard deviation/test statistic value))²= ((5.5 - 8) / (2.517 / 2.303))²= 3.484²≈ 12.11Hence, the sample size is 12.11 or approximately 12.
Now, let's calculate the margin of error using the formula below: Margin of error = (t-critical value) × (standard deviation / √n)Since the confidence level is 95%, the alpha level is 5% which is divided equally between the two tails, so the area in each tail is 2.5%. Using the t-distribution table with df = n-1 = 11 and alpha/2 = 0.025, the t-critical value is 2.201.
Let's plug in all the values in the formula of the margin of error and solve it: Margin of error = (t-critical value) × (standard deviation / √n)= 2.201 × (2.517 / √12)= 1.245 ≈ 1.25Therefore, the margin of error is 1.25.
The confidence interval can be calculated using the formula below: Confidence interval = (sample mean - margin of error, sample mean + margin of error)Confidence interval = (5.5 - 1.25, 5.5 + 1.25)= (4.25, 6.75)Hence, the confidence interval is (4.25, 6.75).If the df increases to 30 then the impact on the margin of error will decrease. If the pdf increases to 30, then the impact on the confidence interval will be narrow.
So, the confidence interval is (4.25, 6.75).If the df increases to 30 then the impact on the margin of error will decrease.
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Convert the point from Cartesian to polar coordinates. Write your answer in radians. Round to the nearest hundredth.
(−10,1)
The point (-10, 1) in Cartesian-Coordinates can be represented in polar coordinates as approximately (10.05, 3.0416 radians).
To convert the point (-10, 1) from Cartesian-Coordinates to polar coordinates, we can use the formulas:
r = √(x² + y²)
θ = arctan(y / x)
We know that, the point is (-10, 1), we substitute the values into the formulas:
We get,
r = √((-10)² + 1²) = √(100 + 1) = √101 ≈ 10.05, and
The point lies in second-quadrant, so, the angle is measured counterclockwise from the positive x-axis, which means it is between π/2 and π radians.
Therefore, The adjusted θ is : θ = π + arctan(1/-10) ≈ 3.0416 radians.
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Perform these steps: 1. State the hypotheses and identify the claim. 2. Find the critical value(s) 3. Compute the test value. 4. Make the decision. 5. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Assume all assumptions are met. 6. Game Attendance 10. Lottery Ticket Sales A lottery outlet owner hypothesizes that she sells 200 lottery tickets a day. She randomly sampled 40 days and found that on 15 days she sold fewer than 200 tickets. At a = 0.05, is there sufficient evidence to conclude that the median is below 200 tickets?
Hypotheses and Claim:Null Hypothesis (H0): The median number of lottery tickets sold per day is 200.Alternative Hypothesis (HA): The median number of lottery tickets sold per day is below 200.
Claim: There is sufficient evidence to conclude that the median is below 200 tickets.
Critical Value(s):
To determine the critical value for the hypothesis test, we need to specify the significance level (α). In this case, α is given as 0.05.
Since the sample size is relatively small (n = 40), we can use the t-distribution to find the critical value. The critical value corresponds to the lower tail because we are testing whether the median is below 200 tickets.
Using a t-table or a statistical software, we find the critical value tα/2 with (n - 1) degrees of freedom. For α = 0.05 and (n - 1) = 39, we find t0.025 = -1.685.
Compute the Test Value:
To compute the test value, we need to calculate the test statistic, which is the t-value.
Let's define X as the number of days the owner sold fewer than 200 tickets. In this case, X follows a binomial distribution with n = 40 and p = 0.5 (assuming equal probability of selling more or fewer than 200 tickets).
Since the sample size is large enough, we can approximate the binomial distribution using the normal distribution. The mean (μ) and standard deviation (σ) of the binomial distribution can be calculated as follows:
μ = np = 40 * 0.5 = 20
σ = sqrt(np(1-p)) = sqrt(40 * 0.5 * 0.5) = sqrt(10)
The test statistic t is given by:
t = (X - μ) / (σ / sqrt(n))
In this case, X = 15, μ = 20, σ = sqrt(10), and n = 40. Plugging these values into the formula:
t = (15 - 20) / (sqrt(10) / sqrt(40)) ≈ -2.24
Make the Decision:
In this step, we compare the test value to the critical value.
If the test value falls in the rejection region (t < tα/2), we reject the null hypothesis. Otherwise, if the test value does not fall in the rejection region, we fail to reject the null hypothesis.
In our case, the test value t = -2.24 is smaller than the critical value tα/2 = -1.685.
Therefore, we reject the null hypothesis.
Summarize the Results:
Based on the analysis, there is sufficient evidence to conclude, at the α = 0.05 level, that the median number of lottery tickets sold per day is below 200.
The lottery outlet owner's hypothesis that she sells 200 lottery tickets a day is not supported by the data, indicating that the median sales are lower than the claimed value.
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In the above figure, m∠AOC = 30° and m∠BOD = (2x + 39)°. If ∠AOC and ∠BOD are vertical angles, what is the value of x? A. x = 69 B. x = -9 C. x = 34.5 D. x = -4.5
i need help asap
Answer:
bestie thats hard
Step-by-step explanation:
Answer:
D. x=-4.5
Step-by-step explanation:
Since they are both vertical angles, m∠BOD must also be equal to 30 degrees, and if you input -4.5 as x, (2 x -4.5x) + 39, that is rewritten as -9 and 39. 39 - 9 is 30 degrees.
Consider the inequality x<1. Determine whether each value of x makes the inequality trueSelect Yes or No va Yes No 3/2 13/6
What is the equation of the line that passes through the point (7,-6) and has a slope of -2?
Answer:
y=-2+8
Step-by-step explanation:
The answer is y=-2+8 because of course the slope has to be -2 as you stated in your Question. So all you have to do is change the Y-Intercept until you reach the point. Since the Slope is negative, the Y-Intercept will rise until you reach your point. You may double check my answer to see if it is right, it is up to you. If you find any fault in my answer please let me know. Have a good day!
no links no links sssssdrerw
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Mr. Frederick teaches 4 math classes. Which class period has the most students? Use the bar graph to answer the question.
Answer:
The class in the second and longest bar graph (the one labeled 3) has the most students.
Step-by-step explanation:
When looking for the largest amount of something in bar graphs, the largest bar graph is correct. In this case the second bar graph is the longest, and we can see it indicates the class contains 28 students.