Expand f(z) into partial fractions:
[tex]\dfrac1{z(z-2)} = \dfrac12 \left(\dfrac1{z-2} - \dfrac1z\right)[/tex]
Recall that for |z| < 1, we have the power series
[tex]\displaystyle \frac1{1-z} = \sum_{n=0}^\infty z^n[/tex]
Then for |z| > 2, or |1/(z/2)| = |2/z| < 1, we have
[tex]\displaystyle \frac1{z-2} = \frac1z \frac1{1 - \frac2z} = \frac1z \sum_{n=0}^\infty \left(\frac 2z\right)^n = \sum_{n=0}^\infty \frac{2^n}{z^{n+1}}[/tex]
So the series expansion of f(z) for |z| > 2 is
[tex]\displaystyle f(z) = \frac12 \left(\sum_{n=0}^\infty \frac{2^n}{z^{n+1}} - \frac1z\right)[/tex]
[tex]\displaystyle f(z) = \frac12 \sum_{n=1}^\infty \frac{2^n}{z^{n+1}}[/tex]
[tex]\displaystyle f(z) = \sum_{n=1}^\infty \frac{2^{n-1}}{z^{n+1}}[/tex]
[tex]\displaystyle \boxed{f(z) = \frac14 \sum_{n=2}^\infty \frac{2^n}{z^n} = \frac1{z^2} + \frac2{z^3} + \frac4{z^4} + \cdots}[/tex]
Which compound inequality has a solution set of all real numbers?
Question 5 options:
a) x > -2 or x < 1
b) x < -1 and x > 2
c) x < -1 and x > 2
d) x < -3 or x > -2
Answer:
If the number on the other side of the inequality sign is negative
Step-by-step explanation:
I just know okay
Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,4802).
[tex]y = ab^x \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=14 \end{cases}\implies 14~~ = ~~ab^0\implies 14=a(1)\implies 14=a~\hfill \underline{y=14b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=4802 \end{cases}\implies 4802~~ = ~~14b^3\implies \cfrac{4802}{14}=b^3 \\\\\\ 343=b^3\implies \sqrt[3]{343}=b\implies 7=b~\hfill \underline{y=14(7)^x}[/tex]
please help me im stuck
Answer: The mean is 6, mean also means the constence.
Step-by-step explanation:
6 is able to go into 10,20,30,40. But I maybe wrong, sorry if I am.
need help fast! 100 POINTS
Answer:
100 points ??? I see 5 points :]
Orlando is mixing nuts and cereal squares to make a party mix. Nuts sell for $7 a pound and cereal squares sell for $4 a pound. If Orlando wants to make 30 pounds of party mix at a cost of $6.50 a pound, how many pounds of nuts and how many pounds of cereal squares should he use?
Answer:
5 lbs cereal squares.
25 Ibs nuts.
Step-by-step explanation:
Let x be the weight of nuts in pounds and y be the weight of cereal squares in pounds.
Total weight of the party mix is 30 pounds.
[tex]x+y=30[/tex] ..... (1)
It is given that,
Cost of nuts = $7 per pound
Cost of cereal = $4 per pound
The cost of mix = $6.50 per pound.
[tex]7x+4y=6.50*30[/tex]
[tex]7x+4y=195[/tex] ..... (2)
Substitute the value of x in equation (2) from equation (1).
[tex]7(30-y)+4y=195[/tex]
[tex]210-7y+4y=195[/tex]
[tex]-3y=195-210[/tex]
[tex]-3y=-15[/tex]
Divide both sides by -3.
[tex]y=5[/tex]
Substitute y=5 in equation (1).
[tex]x+5=30[/tex]
Subtract both sides by 5.
[tex]x=30-5[/tex]
[tex]x=25[/tex]
Therefore, he use 25 lbs of nuts and 5 lbs cereal squares for party mix.
Pls help me and show work! Thank you <3
Answer: 27
Step-by-step explanation:
By the same-side interior angles theorem, [tex]x+72+3x=180 \longrightarrow x=\boxed{27}[/tex]
PLEASE HELP ME !!!!
Answer:
D
Step-by-step explanation:
Exterior means outside which means it has to be one of the angles outside the triangle.
Options A, B, and C have angles inside the triangle.
Option D is the only angle outside the triangle
A shipping box in the shape of a rectangular prism has a volume of 15,000
cm3. The length of the box is 20 cm, and the width is 25 cm. What is the
height of the box?
A. 15 cm
B. 30 cm
C. 37.5 cm
D. 24 cm
Answer:
Option (B) 30cm.Step-by-Step explanation:
Given:
Volume of Rectangular Prism is 15,000cm³.
Length (l) ➠ 20 cm Width (w) ➠ 25 cmWe know that,
★ Volume of Rectangular Prism = whl ★
Let "h" be the height.
➛ 25 × h × 20 = 15,000
➛ h × 20 × 25 = 15,000
➛ h × 500 = 15,000
➛ h = 15,000 ÷ 500
➛ h = 30
Thus, height of the box is 30 cm.
If each student needs 1/3 of a stick of clay to do an art project,and there are 4 sticks of clay, how many students can do the art project?
Answer:
12 students
Step-by-step explanation:
Because the total is 4 sticks, and each student needs 1/3 of a stick, we would have to see how many 1/3 sticks fit into 4 sticks. Because 3 of the 1/3 sticks fit into 1 stick, then 4 sticks would be 4*3=12 of the 1/3 sticks, which means 12 students can do it.
We could also just do: 4/(1/3)= 4*(3/1)=12
This is fractional division. The second value of the division process, we switch the numerator and denominator's, and the expression turns to a multiplication expression, where we can just multiply.
What is the surface area of the cylinder with height 3 km and radius 3 km? Round your answer to the nearest thousandth.
Answer:
A≈113.1km²
Step-by-step explanation:
Joe can paint 2 yards of fence for $48.60. What is the price per foot.
Answer:
the price per foot = $8,1
Step-by-step explanation:
Note : 2 yards = 2 × 3 = 6 foot
Then
Joe can paint 6 foots of fence for $48.60
Then
Joe can paint 1 foot of fence for 48.60 ÷ 6 = $8,1
What is the area of the base of the cone below? A cone with height 12 feet and volume 90 feet cubed. 2.5 feet squared 4 feet squared 22.5 feet squared 26 feet squared
Answer:
its C or 22.5
Step-by-step explanation:
Im doing the test right now
Answer:
22.5
Step-by-step explanation:
Fred bought 3 shirts and a tie. He remembers each shirt was $25, and the total cost was $85. How much was the tie?
Answer:
The tie is $10
Step-by-step explanation:
3 shirts were bought, so 25*3 is 75. The total cost is $85, you take 85 and subtract 75 from it and you get the cost of the tie, $10.
What is the value of the expression below when a = 4?
6a + 7
A. 31
B. 41
C. 53
D. 71
Please help the distance formula
Answer:
7.8
Step-by-step explanation:
distance formula : [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where the x and y values are derived from the given points
here the given points are (11,3) and (6,9)
assigning variables
(x1,y1) = (11,3) so x1 = 11 and y1 = 3
(x2,y2) = (6,9) so x2 = 6 and y2 = 9
plugging in values into formula
recall formula [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
==> plug in x1 = 11 , y1 = 3 , x2 = 6 and y2 = 9
[tex]d=\sqrt{(6-11)^2+(9-3)^2}[/tex]
==> subtract values in parenthesis
[tex]d=\sqrt{(-5)^2+(6)^2}[/tex]
==> evaluate exponents
[tex]d=\sqrt{25+36}[/tex]
==> add 25 and 36
[tex]d=\sqrt{61}=7.8[/tex] ( approximately )
£6846 is shared equally between 7 people. How much does each person get?
Answer: Each person gets £978
Step-by-step explanation: £6846 divided by 7 is £978
Frankie wants to build a path from one corner of his yard to the opposite corner. His yard measures 20 ft. x 32 ft. What will be the length of his path to the nearest tenth of a foot? 21.5 ft 25.0 ft 32.6 ft 37.7 ft
Answer:
37.7 ft
Step-by-step explanation:
This is Pythagorean Theorem aka A^2+B^2=C^2
20^2+32^2=C^2
400+1024=C^2
1424=C^2 (now square root both sides)
37.7359…
Closest answer is 37.7 ft
Answer: [tex]37.7ft[/tex]
Step-by-step explanation:
[tex]a=32, b=20[/tex]
[tex]look[/tex] [tex]for~ the ~hypotenuse~ c[/tex]
[tex]a^2+b^2=c^2[/tex]
[tex]\sqrt{32^2+20^2} =37.7ft[/tex]
The point B (3, -1) has been translated from A by the Vector (4∗3) . What are the coordinates of A?
If point B (3, -1) has been translated from A by the Vector (4, 3). Then the coordinates of A will be (12, -3)
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
Point B (3, -1) has been translated from A by the Vector (4, 3).
Then the coordinates of A will be
Point B (3, -1) x (4, 3)
Point B (3 x 4, -1 x 3)
Point B (12, -3)
More about the transformation of a point link is given below.
https://brainly.com/question/27224339
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Use the three functions shown. 1. f(x)=x² II. f(x)=√x III. f(x) = ln x For which of the functions, if any, is a trapezoidal approximation for the area under the curve y = f(x) over the interval [1, 4] with 3 equal subintervals less than the midpoint approximation? none of the functions O I only II and III only all of the functions
II and III only
We split up the integration interval [1, 4] into 3 equally-spaced subintervals of length (4 - 1)/3 = 1 :
[1, 2], [2, 3], [3, 4]
The area over each subinterval [L, R] is either approximated by a trapezoid, whose area will be
1 • (f(L) + f(R))/2
or by a rectangle with height f((L + R)/2) and hence area
1 • f((L + R)/2)
For f(x) = x², the area under f(x) over [1, 4] is approximated by
• using trapezoids (T) :
[tex]\displaystyle \int_1^4 x^2 \, dx \approx \frac{4-1}{2\times3} (1^2 + 2\times2^2 + 2\times3^2 + 4^2) = \frac{43}2 = \frac{86}4[/tex]
• using midpoints (M) :
[tex]\displaystyle \int_1^4 x^2 \, dx \approx \frac{4-1}3 \left(\left(\frac32\right)^2 + \left(\frac52\right)^2 + \left(\frac72\right)^2\right) = \frac{83}4[/tex]
so T > M. (This eliminates "I only" and "all of the functions".)
For f(x) = √x, the area is approximated by
• T :
[tex]\displaystyle \int_1^4 \sqrt x \, dx \approx \frac{4-1}{2\times3} (\sqrt1 + 2\sqrt2 + 2\sqrt3 + \sqrt4) \approx 4.646[/tex]
• M :
[tex]\displaystyle \int_1^4 \sqrt x\, dx \approx \frac{4-1}3 \left(\sqrt{\frac32} + \sqrt{\frac52} + \sqrt{\frac72}\right) \approx 4.677[/tex]
so T < M. (This eliminates "none of the functions".)
What is the slope of a line through (-3, 4) and
(5, 6)?
Answer:
slope= x2- x1/y2 -y1
= 5-(-3)/6-4
8/2= 4
A standard NBA basketball has a diameter of 24.1 cm. What is the volume of a standard NBA basketball?
a.7,329 cm3
b.270 cm3
c.58,633 cm3
d.1,629 cm3
The volume of a standard NBA basketball is 7,329 cm³.
What is the volume of a sphere?The volume of a sphere is given by the formula,
V = 4/3×π×r³
Given the diameter of the ball is 24.1 cm, therefore, the radius of the ball will be 12.05cm (half the diameter of the ball). Thus, the volume of the NBA basketball will be,
V = 4/3 × π × (12.05)³
V = 7,329.084 cm³ ≈ 7,329 cm³
Hence, the volume of a standard NBA basketball is 7,329 cm³.
Learn more about Volume of a sphere here:
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Bluegrass was develope from tradition
Simple / repetitive cuord proggression the
,
the country Acoustic instrumen
7. What wast the social significance of cover songs in early
What was the significance of cover songs in early rock music
Ronald's bill at the end of his lunch was $20.00. Using a proportion, determine the amount of his bill that he must leave for a 19% tip.
Answer:
23.80$
Step-by-step explanation:
[tex]\frac{20}{x} =\frac{100percent}{19percent}[/tex]
X = (20 × 19) ÷ 100
X =380 ÷ 100
X = 3.8$
20.00+ 3.8=
23.80
.
Which line is parallel to the line that passes through the points of (2,-5) and (-4,1)
Answer:
y= -x-5
Step-by-step explanation:
m=1-(-5)/-4-2
m=-1
-1= -x
y=-x-5
claire is considering in a new business
Diagonal of a square is 4 root 2. Find the length of a side of a square
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{4\sqrt{2}}\\ a=\stackrel{adjacent}{s}\\ b=\stackrel{opposite}{s}\\ \end{cases}\implies (4\sqrt{2})^2~~ = ~~s^2~~ + ~~s^2 \\\\\\ 4^2\sqrt{2^2}~~ = ~~2s^2\implies 16(2)=2s^2\implies 32=2s^2\implies \cfrac{32}{2}=s^2 \\\\\\ 16=s^2\implies \sqrt{16}=s\implies \boxed{4=s}[/tex]
What is the solution of the system of equations shown in the following graph? Please help
Answer:
aedi on
Step-by-step explanation:
A bag contains 2 gold marbles, 8 silver marbles, and 20 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $5, if it is silver, you win $2. If it costs $1 to play, what is your expected profit or loss if you play this game?
Answer:
expected loss of 4/30 ≈ 0.13 dollars
Step-by-step explanation:
profit = revenue - expenses
expected profit= expected revenue - expected expenses
how i solve this is by multiplying each revenue and expense by its probability and solving from there
revenue of gold = 5
revenue of silver = 2
revenue of black = 0
this exhausts all of our revenue options
total marbles = 2+8+20 = 30
# of gold marbles = 2
probability of gold = 2/30
# of silver marbles = 8
probability of silver = 8/30
# of black marbles = 20
probability of black = 20/30
expected revenue = sum of possible revenues multiplied by their probability
= 5 * 2/30 + 2 * 8/30 + 0 * 20/30 = 10/30 + 16/30 = 26/30
cost = 1 no matter what
expected profit = expected revenue - expected expenses
= 26/30 - 1
= -4/30
= an expected loss of 4/30
4/30 ≈ 0.13
What are the values of mode and median in the following set of numbers? 1,3,3,6,6,5,4,3,1,1,2 Mode: 1, 2, Median: 2 Mode: 1,3, Median: 3 Mode: 2,3, Median: 2 Mode: 1,3, Median: 2.5
[tex]1 \: 3 \: 3 \: 6 \: 6 \: 5 \: 4 \: 3 \: 1 \: 1 \: 2[/tex]
to find:the mode and median of the given numbers set.
solution:mode:the most frequently occurred number.
[tex]mode = 1 \: and \: 3[/tex]
median:first arrange all the numbers in either decending or ascending order, then find the number in the middle.
[tex]1 \: 1 \: 1 \: 2 \: 3 \: 3 \: 3 \: 4 \: 5 \: 6 \: 6[/tex]
[tex]median = 3[/tex]
hence, the median of the following data set is 3 and the mode is 1 and 3
PLEASE HELP ILL GIVE BRAINLIESTTTTTT
Step-by-step explanation:
Explaination: So first of all um what I am going to do is I need to find the area of this semicircle. So the area of the semicircle, I'm going to use pi times the radius squared and then divided by two. So I'm using the formula of the area of a circle and then I'm dividing it by two because it's half of a circle. And then I'm going to add that to the area of a triangle which is base times height divided by two.
Hope it helps you