Answer:
1,000
Step-by-step explanation:
just took the quiz
Expand: f(z) = z / (z-1) (2-z) as Laurent series for |z| < 1
Most problems like this can be done with two tools only: partial fractions, and the result 1/(1−w)=1+w+w2+⋯ for |w|<1. So first split your function f into 1/(z−2)−1/(z−1). I will show you how to cope with one of these factors, 1/(z−2). Writing this as −1211−z/2 is tempting but no good: the "1/(1−w)" expansion will converge only for |z/2|<1, not on the regions you are supposed to care about. So you take out a factor of z−1 instead:
1/(z−2)=z−111−2/z
The final term can be expanded with the 1/(1−w) series, valid for |2/z|<1 that is |z|>2. So that does give you a Laurent series valid in the right region (once you multiply bu z−1. These methods can be used to solve all of your problems.
Partial fractions:
[tex]f(z) = \dfrac z{(z-1)(2-z)} = -\dfrac1{1-z} + \dfrac2{2-z}[/tex]
For |z| < 1, we have
[tex]\displaystyle \frac1{1-z} = \sum_{n=0}^\infty z^n[/tex]
and
[tex]\displaystyle \frac2{2-z} = \frac1{1-\frac z2} = \sum_{n=0}^\infty \left(\frac z2\right)^n[/tex]
(The latter series is valid for |z/2| < 1 or |z| < 2, but |z| < 1 is a subset of this region.)
Then
[tex]\boxed{f(z) = \displaystyle \sum_{n=0}^\infty \left(\frac1{2^n} - 1\right) z^n}[/tex]
mr jones told his students they each need half of a piece of paper calvin cut his piece of paper horizontally and mathew cut his piece of paper diagonally which student has the larger area on his half piece of paper
Answer:
Both
Step-by-step explanation:
After cutting the paper, both Calvin and Matthew have the same area. Calvin cut his into two rectangles that are each half the area of the original piece of paper. Matthew cut his paper into two equivalent right triangles that are also half the area of the original piece of paper.
Solve for y: 5( 3y+4) = 6( 2y-2/3)
Answer: y= -8
Step-by-step explanation:
5( 3y+4) = 6( 2y-2/3)15y+20=12y-415y-12y=-4-203y=-24y=-24/3y= -8Solve the system of equations.
4x - 4y = 8
y + 4x = 2.5
x = -1.5
y = 8.5
hope it helps....!!!
[tex]4x-4y = 8~~~....(i)\\\\y+4x = 2.5~~~...(ii)\\\\(i)-(ii)\\\\~~~~4x-4y-y-4x = 8-2.5\\\\\implies -5y = 5.5\\\\\implies y = -\dfrac{5.5}5\\\\\implies y= -1.1\\\\\text{Substitute y= -1.1 in eq (i):}\\ \\~~~~4x-4(-1.1) = 8\\\\\implies 4x +4.4. =8\\ \\\implies 4x = 8-4.4\\\\\implies 4x = 3.6\\\\\implies x = \dfrac{3.6}4\\\\\implies x =0.9\\ \\\text{Hence,}~~ (x,y) = (0.9, ~-1.1)[/tex]
...............................................the problem below is so hard...................................
Answer:
16 cm
Step-by-step explanation:
Circumference of a circle
We are told that the string is wound symmetrically around a circular rod.
Now, the circumference of the rod is 4 cm and length is 12 cm.
Now, circumference is also the length of a circle. Thus, one wound of the string will be equal to the circumference of the rod.
Thus, one wound = 4 cm
Since the string makes 4 turns about the rod, then;
Length of string = 4 × 4 = 16 cm
hopes this helps ya out
34.321 greater than 34.3211
Answer:
It's not
Step-by-step explanation:
To know this, you have to put a zero to the right.
So it'd be 34.3210, and as you can see, 34.3211 is greater
The direct route from Marta's apartment to work is a road that is a straight line. The road is closed for repairs. Marta had to drive 8 miles west and then 6 miles south to get to work. She returned home by the same route. How many miles would she have saved round-trip if she had taken the direct route?
She would have to take 5.29 miles to save round-trip if she had taken the direct route.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
The direct route from Marta's apartment to work is a road that is a straight line. The road is closed for repairs.
Marta had to drive 8 miles west and then 6 miles south to get to work. She returned home by the same route.
Let's consider x to be the direct route.
By Pythagoras theorem, we can find the direct route
[tex]x^{2} = 8^{2} +6^{2} \\\\x^{2} = 64 - 36\\\\x^{2} = 28\\\\x= \sqrt{28} \\\\x= 5.29[/tex]
Thus, She would have to take 5.29 miles to save round-trip if she had taken the direct route.
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In the given figure x = 145°. What theorem can be used to prove the lines p and q are parallel?
A) Same side interior angles converse theorem
B) Corresponding angles converse theorem
C) Alternate exterior angles converse theorem
D) Alternate interior angles converse theorem
The graph below shows the exponential function and the linear function What is the minimum y-value after which the exponential function will always be greater than the linear function? y = 1 y = 2 y = 3 y = 4
Answer:
y = 1
Step-by-step explanation:
Write 8 statements and reasons for the proof
Answer:
Step-by-step explanation:
Analyze the diagram below and complete the instructions that follow.
8
Find the value of y.
A. y = 2
B. Y=4sqrt3/3
C. y = 4
D. Y=4sqrt3
Answer:
y = 4
Step-by-step explanation:
Thewtriangle on the right side has a 90° angle and a 30°, so the third angle is 60°. That makes the triangle a 30-60-90 right angle. The short leg is half the length of the hyptenuse.
y = 8/2 = 4
Answer: C. y = 4
Patricia was having fun playing a card game. To win the game, she
needed the next two cards dealt to be yellow cards. There are 12
cards left in the deck, and three are[yellow.
What is the probability that the two cards dealt to Patricia will both
be yellow?
Answer:
25
%
Step-by-step explanation:
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The probability that the two cards dealt to Patricia will both be yellow
is 1/4.
What is the probability?In mathematics, probability refers to the likelihood of an occurrence occurring. Simply put, how frequently the incidence occurs over a certain period of time.
Given, there are 12 cards left in the deck, and three are yellow.
To find the probability:
The probability= number of yellow cards in the deck / total number of cards in the deck.
= 3/12
= 1/4
Therefore, the probability is 1/4.
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Pls help i need an A my mom is going to get mad at me pls help i will give 62 points
Answer:
Both of those tables show a proportional relationship between x and y.
Step-by-step explanation:
In the second table the values all equal 0.75 when divided.
In the first table the values all equal 1.25 when divided.
A Ferris wheel has a diameter of 250 feet. What is
the distance, to the nearest whole foot, that riders
travel if they stay on it for 15 rotations?
The distance that riders travel round the Ferris wheel in 15 rotations is 11,786 feet.
What is the distance travelled by the riders in 15 rotations?The first step is to determine the distance travelled in one rotation. To do this, the circumference of the wheel has to be determined.
Circumference of a circle = π x 250
22/7 x 250 = 785.71 feet
Now, multiply the circumference by 15
785.71 feet x 15 = 11,786 feet
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Witch number is a common factor of 25 and 40?
A) 2
B) 4
C) 5
D) 10
I will give Brainlyest only for correct answers. :)
Answer:
The answer is 5.
Step-by-step explanation:
The answer is 5 because 5x8 and 5x5. find the greatest common factor by matching the biggest common factor of 25 and 40.This is why the answer is 5.
Step 1: 25 = 5[tex]^2[/tex]
Step 2: 40 = [tex]2^{3}[/tex] × [tex]5^{1}[/tex]
Step 3: List of positive integer factors of 25 that divides 25 without a remainder. That is 1 and 5
Step 4: List of positive integer factors of 40 that divides 25 without a remainder. 1, 2, 4, 5, 8, 10, 20
Step 5: We found the factors and prime factorization of 25 and 40. The biggest common factor number is the GCF number.
So the greatest common factor 25 and 40 is 5.
The equation of the trend line is y = −0.36x + 12.6.
Use the equation of the trend line to predict the wind chill for a wind speed of 33 mi/h. Round your answer to the nearest degree.
Answer:
−1\°
Step by step explation:
Let
x -----> the wind speed in mi/h
y ----> the wind chill in °F
we have
y=-0.36x+12.6y=−0.36x+12.6
so
For x=38 mi/h
substitute in the linear equation and solve for y
y=-0.36(38)+12.6=-1.08\°y=−0.36(38)+12.6=−1.08\°
Round to the nearest degree
-1.08=-1\°−1.08=−1\°
what does 30,000 divided by 12,674 equals?
Answer:
2.36705065488
Celia bought a bag of 12 goldfish for $3.
What is the cost of 1goldfish?
Answer:
0.25
Step-by-step explanation:
Answer:
0.25
Step-by-step explanation:
3÷12=0.25
12 goldfish for $3
Factor the expression using the greatest common factor 16x + 12y
Answer:
4(4x + 3y)
Step-by-step explanation:
Given expression: 16x + 12y
Factors of 16: 1, 2, 4, 8, 16
Factors of 12: 1, 2, 3, 4, 6, 12
Therefore, the greatest common factor of 16 and 12 is 4.
As the expression has two variables, the variables cannot be factored.
Therefore, factored expression: 4(4x + 3y)
16x+12y
Factor each
16x=4×4x12y=4×3yTake 4 common as GCF
16x+12y4(4x+3y)Estimate how many times larger 5*10^8 is than 24*10^6.
A) 10 times
B) 20 times
C) 50 times
D) 100 times
Answer:
10 times
Step-by-step explanation:
Brainliest for who can help!!
I think it's like this.
Hope this helps
A 2-cup bottle of glass cleaner costs $9.12. What is the price per fluid ounce
Answer:
$0.57
Step-by-step explanation:
In one cup there are eight fluid ounces
To find the cost per fluid ounce all you have to do is divide the price by how many ounces]
To find ounces= 2x8=16
To find price per ounce 9.12/16= .57
Ayden is 1.85 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 39.55 meters. He stands 35.4 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The height of the tree is 4.15m
We are given that
Height of Joshua, h=1.85 m
Length of tree's shadow, L=39.55 m
Distance between the tree and Joshua=35.4 m
We have to find the height of the tree.
BC=35.4 m
BD=39.55m
What is the height?CD=BD-BC
CD=-35.4 m=4.15 m
EC=1.45 m
All right triangles are similar. When two triangles are similar then the ratio of their corresponding sides is equal.
[tex]\triangle ABD=\triangle ECD[/tex]
[tex]\frac{AB}{EC}=\frac{BD}{CD}[/tex]
Substitute the values
[tex]\frac{AB}{1.45}=\frac{39.55\times 1.45}{4.15} \\\\AB=20.39[/tex]
Hence, the height of the tree=20.39 m
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John has 5 pairs of formal shoes, 2 pairs of traditional shoes, and 4 pairs of casual shoes. What is the probability that John selects a pair of formal shoes??? Write the answer as a fraction in the simplest form.
Answer:
5/11
Step-by-step explanation:
probability = # of favorable outcomes / # of total outcomes
favorable outcome = selecting a pair of formal shoes.
There are 5 pairs of formal shoes so # of favorable outcomes = 5
The total number of outcomes = sum of different pairs of shoes. There are 5 pairs of formal shoes, 2 pairs of traditional shoes, and 4 pairs of casual shoes, so total there are 5 + 2 + 4 = 11 pairs of shoes
so we have probability = # of favorable outcomes / # of total outcomes
and # of favorable outcomes = 5 and total # of outcomes = 11 so probability of selecting a pair of formal shoes is 5/11
Larissa spent $280 per month on
clothes and a total of $2,920 for food
and entertainment during the last
5 months. How much should Larissa
expect to pay for clothes, food, and
entertainment in 1 year?
Answer:
Larissa would spend a total of: $7,680 in 1 year
Step-by-step explanation:
Pleaseeeee help meee
Step-by-step explanation:
simplify the three equations to get the common (Y) and we get the following:
1. [tex]Y = \frac{-5}{2}x + \frac{1}{2}\\[/tex]
2. [tex]Y = \frac{2}{5}x - 8[/tex]
3. [tex]Y = \frac{2}{5}x + \frac{4}{5}[/tex]
Line 1 and 2 are perpendicular because for the gradient(m) the fraction in line 1 for x is the negative reciprocal to line 2.
Line 1 and 3 are also perpendicular because for the gradient(m) the negative reciprocal can also be seen
*note for perpendicular lines the +c or y-intercept is neglected as it does not affect the perpendicularity
Line 2 and Line 3 are parallel because they have the same gradient of [tex]\frac{2}{5}x[/tex]
So they will have the same slope, regardless of the y-intercept.
The directions on a box of Luigi’s Pizza Mix are as follows: Spread the dough to the edges of a circular pan or a 10-inch by 14-inches rectangular pan. You will need to use the following formulas to answer the questions below. For a circle: A = πr2 where π = 3.14C = 2πr For a rectangle: A = lw P = 2l + 2w a. If you used the same amount of dough, how large a circular pan would you need to make a pizza of the same area and thickness as one made in the rectangular pan? *
The circular pan must have a radius of 6.68 inches.
How large a circular pan would you need?
The area of the circular pan just be the same as the area of the rectangular pan.
The rectangular pan is 10in by 14 in, so its area is:
A = 10in*14in = 140in^2
Then the circular pan must have an area:
A' = 3.14*r^2 = 140in^2
We can solve this for r:
r = √(140in^2/3.14) = 6.68 in
The circular pan must have a radius of 6.68 inches.
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Can y’all help me pls
Answer:Sure, what do you need help with
Step by step explanation:
Sure, what do you need help with
The graph of a linear function is shown. A coordinate plane with a straight line. The line starts at (negative 5, negative 1) and continues up and to the right passing through (0, 0) and (5, 1). Which word describes the slope of the line? positive negative zero undefin
The linear function is represented by the straight line, and the word that describes the slope of the line is positive
What is a linear function?A linear function is an equation that has a constant rate or slope
The points on the lines are given as:
(x,y) = (-5,-1), (0,0) and (5,1)
The slope is then calculated using:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
This gives
m = (0 + 1)/(0 + 5)
Evaluate
m = 0.2
The above slope is positive.
Hence, the word that describes the slope of the line is positive
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Answer:
the answer is a
Step-by-step explanation:
A circle has a diameter of 32 ft. What is its circumference?
Use 3.14 for 1, and do not round your answer. Be sure to include the correct unit in your ans
0
32 ft
Given -
diameter of circle = 32ftTo find -
the circumference of the circleExplanation -
As we know, circumference of the circle = 2πr
where r signifies the radius of the circle. And radius if half of the diameter, i.e, r = d/2
Solution -
Circumference of the circle = 2πr
r = 32/2 = 6
Substituting the value of r,
Circumference of the circle = 2 × 3.14 × 6
Circumference of the circle = 12 × 3.14
Circumference of the circle = 37.6 ft
Therefore, the the circumference of the circle is 37.6 ft.