Answer:
The value of f(z) is not constant in any neighbourhood of D. The proof is as explained in the explaination.
Step-by-step explanation:
Given
For any given function f(z), it is analytic and not constant throughout a domain D
To Prove
The function f(z) is non-constant constant in the neighbourhood lying in D.
Proof
1-Assume that the value of f(z) is analytic and has a constant throughout some neighbourhood in D which is ω₀
2-Now consider another function F₁(z) where
F₁(z)=f(z)-ω₀
3-As f(z) is analytic throughout D and F₁(z) is a difference of an analytic function and a constant so it is also an analytic function.
4-Assume that the value of F₁(z) is 0 throughout the domain D thus F₁(z)≡0 in domain D.
5-Replacing value of F₁(z) in the above gives:
F₁(z)≡0 in domain D
f(z)-ω₀≡0 in domain D
f(z)≡0+ω₀ in domain D
f(z)≡ω₀ in domain D
So this indicates that the value of f(z) for all values in domain D is a constant ω₀.
This contradicts with the initial given statement, where the value of f(z) is not constant thus the assumption is wrong and the value of f(z) is not constant in any neighbourhood of D.
A rectangular pool is being constructed with a length that is four times the width. There will be a walkway constructed around the pool that is 6 feet wide all around. Write a factored expression for the area in square feet of the pool and the walkway combined.
Answer:
(4x²+36) feet²
Step-by-step explanation:
Area of the pool = L × W
Take width as x and Length as 4x
4x × x = (4x²)feet² {area of pool}
Area of walkway = L × W
6 × 6 = 36feet²
Total area = 4x² + 36 feet²
Can someone help me with this problem please. ( I need it as fast as possible).
Answer:
D-B-A-C
Step-by-step explanation:
40 POINTS!!!
Two construction companies are building homes in a new neighborhood. Company A has built 18 homes and plans to build an additional 6 homes each month. Company B has built 41 homes and plans to build an additional 4 homes each month. if building goes according to their plans, in how many months will the total number of homes built by the companies be equal to each other?
Answer:
14 months until there equal
Answer:
14 months
Step-by-step explanation:
Mario traced this trapezoid.
Answer:
84sq. in
Step-by-step explanation:
Area of the rectangle = length * width
Given
Length = 7in
Width = 12in
Area of the rectangle = 7in * 12in
Area of the rectangle = 84sq. in
Hence the area of the rectangle is 84sq. in
A 1/17th scale model of a new hybrid car is tested in a wind tunnel at the same Reynolds number as that of the full-scale prototype. The drag coefficient of the model is the same as that of the prototype. Assuming the model and prototype are both tested in air, find the ratio of the drag on the scale model (Fm) to the drag on the prototype (Fp), i.e., Fm/Fp. Since the size of the model is 1/17th of the size of the prototype, the projected area of the model is (1/17)2 of the projected area of the prototype. Round your answer to the nearest tenth.
Answer:
The ratio of the drag coefficients [tex]\dfrac{F_m}{F_p}[/tex] is approximately 0.0002
Step-by-step explanation:
The given Reynolds number of the model = The Reynolds number of the prototype
The drag coefficient of the model, [tex]c_{m}[/tex] = The drag coefficient of the prototype, [tex]c_{p}[/tex]
The medium of the test for the model, [tex]\rho_m[/tex] = The medium of the test for the prototype, [tex]\rho_p[/tex]
The drag force is given as follows;
[tex]F_D = C_D \times A \times \dfrac{\rho \cdot V^2}{2}[/tex]
We have;
[tex]L_p = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2 \times L_m[/tex]
Therefore;
[tex]\dfrac{L_p}{L_m} = \dfrac{\rho _p}{\rho _m} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_m} \right)^2[/tex]
[tex]\dfrac{L_p}{L_m} =\dfrac{17}{1}[/tex]
[tex]\therefore \dfrac{L_p}{L_m} = \dfrac{17}{1} =\dfrac{\rho _p}{\rho _p} \times \left(\dfrac{V_p}{V_m} \right)^2 \times \left(\dfrac{c_p}{c_p} \right)^2 = \left(\dfrac{V_p}{V_m} \right)^2[/tex]
[tex]\dfrac{17}{1} = \left(\dfrac{V_p}{V_m} \right)^2[/tex]
[tex]\dfrac{F_p}{F_m} = \dfrac{c_p \times A_p \times \dfrac{\rho_p \cdot V_p^2}{2}}{c_m \times A_m \times \dfrac{\rho_m \cdot V_m^2}{2}} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}[/tex]
[tex]\dfrac{A_m}{A_p} = \left( \dfrac{1}{17} \right)^2[/tex]
[tex]\dfrac{F_p}{F_m} = \dfrac{A_p}{A_m} \times \dfrac{V_p^2}{V_m^2}= \left (\dfrac{17}{1} \right)^2 \times \left( \left\dfrac{17}{1} \right) = 17^3[/tex]
[tex]\dfrac{F_m}{F_p} = \left( \left\dfrac{1}{17} \right)^3[/tex]= (1/17)^3 ≈ 0.0002
The ratio of the drag coefficients [tex]\dfrac{F_m}{F_p}[/tex] ≈ 0.0002.
In each case, calculate the circumference and the area.
The radius is 22 cm.
Your answer
Answer:
Circumference of circle = 138.28 cm (Approx.)
Area of circle = 1,521.11 cm² (Approx.)
Step-by-step explanation:
Given:
Radius of circle = 22 cm
Find:
Circumference of circle
Area of circle
Computation:
Circumference of circle = 2πr
Circumference of circle = 2(22/7)(22)
Circumference of circle = 2(3.1428)(22)
Circumference of circle = 138.2832
Circumference of circle = 138.28 cm (Approx.)
Area of circle = πr²
Area of circle = (22/7)(22)²
Area of circle = (3.1428)(22)(22)
Area of circle = 1,521.1152
Area of circle = 1,521.11 cm² (Approx.)
Help please I’ll give extra points and brainlist
Answer:
Step-by-step explanation:
Probably D, he's measuring voltage across the wire.. and then across the light bulb, there would be very little across the wire and a lot across the light bulb
At 3:30 p.m., you have 15 megabytes of a movie. At 3:45 p.m., you have 75 megabytes. What is the download rate in megabytes per minute?
Will give the brainliest answer and 20 points to anyone who can give a complete answer and not a scam link or a joke answer or begging for points (those 3 types of answers will be reported)
Courtney and Christy both leave the coffee shop at the same time, but in opposite directions. If Christy travels 9 mph faster than Courtney and after 7 hours they are 189 miles apart, how fast is each traveling?
Courtney is traveling ___________ mph.
Christy is traveling _____________ mph.
Answer:
Courtney is travelling at 9mph
Christy is travelling at 18mph
Step-by-step explanation:
Courtney's speed = x
Christy's speed = y
Christy travels 9 mph faster than Courtney: x+9=y
Distance = speed * time
Courtney's distance after 7 hours = 7x
Christy's distance after 7 hours = 7y
After 7 hours, they're 189 miles apart:
7x+7y=189
x+y=27
x+y=27
x+x+9=27
2x=18
x=9
y=x+9
y=9+9
y=18
Find mean & margin of error if 28.4 < µ < 38.8
Answer:
The mean is of 33.6
The margin of error is of 5.2.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this question:
Lower bound: 28.4
Upper bound: 38.8
Mean
(28.4+38.8)/2 = 33.6.
The mean is of 33.6
Margin of error:
(38.8 - 28.4)/2 = 5.2
The margin of error is of 5.2.
simplify 3 times x² times y times 4z times x times 2y times z
Answer:
3(x^2 x Y)(4z x X)(2y x Z)
Step-by-step explanation:
Answer:
[tex]3(x^{3} * 2y^2*4z^2)[/tex]
Step-by-step explanation:
x^2(x) = x^3
2y(y) = 2y^2
4z(z) = 4z^3
Multiple it all by 3
Evaluate the piecewise function when x = -1.
Step-by-step explanation:
-2<-1<1, so f(-1)=-1-2=-3
A quarter has a diameter of 24 mm.
Which measurement is closest to the
circumference of the quarter in
millimeters?
A. 452.39 mm
B. 37.7 mm
C. 75.4 mm
D. 150.8 mm
Answer:
C or D
Step-by-step explanation:
ted is twice his sister's age and three years younger than joe. ted's sister is half of a century plus ten. how old is ted how old is ted's sister
Answer:
120, 60
Step-by-step explanation:
half a century = 60 + 10 x 2 = ted.
she is 60.
Please help me 7th grade math math
Answer: 1/8
Step-by-step explanation: hoped this helped:))
Answer:
i think its 1/3
Step-by-step explanation:
Please explain step by step I dont get it.
Answer: B
Step-by-step explanation:
108 divide by 54 = 2
That equation means she paid 2 dollars per ticket, not 1 dollar for 2 tickets
(There is no 1 in the equation also)
Find the value of y. geometry!!
Answer:
y = 54
Step-by-step explanation:
Once again we are going to use the inscribed angle and intercepted arc relationship where the inscribed angle is equal to half of the measure of the intercepted arc.
Angle "y" is the inscribed angle and its intercepted arc has a measure of 108°
So y = one half of 108
[tex]\frac{108}{2} =54[/tex]
So we can conclude that y = 54
The length of a rectangle is 2 meters longer than the width. If the area is 30 square meters, find the rectangle's dimensions.
What is the equation of the following line?
Answer:
Answer is F. y = 6x
Step-by-step explanation:
Helppppp plzzzzzzz!!!!! 15+PTS and brainliest!!!!!!!!! ASAP plzzz!!!!!!!!
Answer:
75 FT
Step-by-step explanation:
Multiple 5 by 4 for each of the three squares, then multiply 5 by 3 for each triangle and divide it by 2. Add them all together and you get 75.
Answer:
75 Ft
Step-by-step explanation:
I told you im surewhwhwhhwhshsbsbwbsbsbsbs
Find the Perimeter of this figure. I do y get it
Answer:
56m
Step-by-step explanation:
5+7+5+11+7+16+5
= 56
Will give brainliest
Answer: Because the question uses the word “distinct” meaning obvious, and clear, I would select AB, AC, CB. (If it’s asking for all the possible line segments, I would select AB, AC, CB, BA, CA, BC).
4. Let's say we do an opinion poll and find that 56% of the people say the Green Bay Packers
are their favorite team, while 22% choose the Chicago bears, and 10% choose the Dallas
Cowboys. What percent of people must have a favorite team other than these three teams?
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest inch, how many inches are in 8 meters?
Answer:
314.96in
Step-by-step explanation:
The groundhog population of Punxsutawny, Pennsylvania is closely monitored each year. Two years ago the population decreased by 12%. Last year the number of groundhogs increased by 6%. This year the population also increased by 9%. What was the percentage increase/decrease of groundhogs over these three years? Round your answer to the nearest tenth of a percentage poin
Answer:
There was a increase of 1.7% over these three years
Step-by-step explanation:
Multipliers:
For a decrease of a%, we multiply by: [tex]\frac{100-a}{100}[/tex]
For a increase of a%, we multiply by: [tex]\frac{100+a}{100}[/tex]
What was the percentage increase/decrease of groundhogs over these three years?
Decrease of 12%(multiplication by 0.88).
Increase of 6%(multiplication by 1.06).
Increase of 9%(multiplication by 1.09).
After these three years:
0.88*1.06*1.09 = 1.017
1.017 - 1 = 0.017
0.017*100% = 1.7%
There was a increase of 1.7% over these three years
The net of a triangular prism is shown
below.
8.5 cm
10 cm
10 cm
10 cm
What is the total surface area of the prism?
A 470 cm?
C 390.5 cm?
B 385 cm
D 342.5 cm
Answer:
i think a.... sorry if im wrong
Step-by-step explanation:
Find the volume of the pyramid.
Please Help!
Answer:
144cm
Step-by-step explanation:
Just search it up lol
What do those emojis mean in words?
Which function is continuous at x = –4?
Answer:
The correct answer is C. I tried B and got it wrong
Step-by-step explanation:
If a•b=b, what must the value of a be?
A.1
B.0
C.2
D.b
Answer:
a
Step-by-step explanation:
an example
1x2=2
1 is a, 2 is b, see they equal the same 2 and 2.
Answer:
B. 0
Step-by-step explanation:
Any number multiplied by 0 equals zero.