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.
Answer:
mud
Step-by-step explanation:
Answer:
t = 54 seconds
Step-by-step explanation:
The equation that models the path of a rocket into the air is given by :

It is required to find the time after which the rocket will hit the ground. When it hits the ground, the height of the rocket will becomes zero. It means,
h(t) = 0
i.e.

It means after 54 seconds, the rocket will hit the ground.
Answer:
140
Step-by-step explanation:
The arithmetic series is 5, 7, 9, 11, ........., 23.
First u have to determine the no. of terms that can be done by using
Tₙ = [a + (n - 1)d]
Tₙ-------nth term
a---------first term
n---------no.of terms in the series
d---------common difference
here a = 5,d = 2.
let it contain n terms Tₙ= [a + (n-1)d]
Substitute Tₙ, a, and d in the equation
23 = 5 + (n - 1)2
Subtract 5 from each side.
18 = (n-1)2
Divide each side by 2
(n - 1) = 9
Add 1 to each side
n = 9 + 1 = 10
The sum of the arithmetic sequence formula: Sₙ= (n/2)[2a+(n-1)d]
Substitute Sₙ, a, n and d in the equation
Sₙ= (10/2)[2(5) + (10-1)2]
Sₙ= (5)[10 + (9)2]
Sₙ= 5[10 + 18]
Sₙ= 5[28] = 140
Therefore the sum of the arithmetic sequence is 140.
700% increase.
Step-by-step explanation:
The duration was 3 decades, or 30 years. The population starts at 100%, then doubles to 200% (decade 1), then 400% (decade 2), then 800% (decade 3).
800% - 100% = 700%