I need help with this

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]

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

Answer:

0.25

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

3÷12=0.25

12 goldfish for $3

Given -

To find -

Explanation -

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.

Answer: y= -8

Step-by-step explanation:

Answer: go to the website

Step-by-step explanation:

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.

Answer:

Step-by-step explanation:

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

Take 4 common as GCF

Answer:Sure, what do you need help with

Step by step explanation:

Sure, what do you need help with

Answer:

10 times

Step-by-step explanation:

Answer:

2.36705065488

Answer:

Step-by-step explanation:

Remark

All you need do is find the radius and put it into the formula V = (4/3) pi r^3.

Givens

d = 12 yards

r = d/2

Solution

r = 12 yds/2 = 6 yds

V = 4/3 pi r^3

V = 4/3 * 3.14 * 6*6*6

V = 904.32

Answer 904.4 yd^3

Answer:

227

Step-by-step explanation:

Since they give you the hypotenuse length of 290in and they ask you to find the length os the adjacent angle, use the cosine to find side b.

So you do tan38=b/290 then calculate.

The true answer is 226.5728 but they ask you to round.

Answer:

y = 1

Step-by-step explanation:

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]

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

I think it's like this.

Hope this helps

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.

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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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

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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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.

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

Answer:

Larissa would spend a total of: $7,680 in 1 year

Step-by-step explanation:

The circular pan must have a radius of 6.68 inches.

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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She would have to take 5.29 miles to save round-trip if she had taken the direct route.

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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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

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.

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\°