4a. 99m + 81 = 130m. 4b. 40 + 30z = 70z
5a. 24v + 18 = 41v. 5b. 12c + 16 = 28c
6c. 44 + 48v= 92v. 6b. 40 + 12s = 52s.
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:
The set of natural numbers is the set of all positive integers, then this set is:
{1, 2, 3, ...}
and the 24th letter of the alphabet is x
Now we want to write the expression given in the sentence "It is one more than the sum of the first three natural numbers, followed by the 24th letter of the alphabet"
We can "break" this in parts, so it is easier to understand.
Then:
"...the sum of the first 3 natural numbers..."
is:
1 + 2 + 3
Then:
"...the sum of the first 3 natural numbers, followed by the 24th letter of the alphabet"
This can be written as:
(1 + 2 + 3) + x
Now we can analyze the complete sentence:
"It is one more than the sum of the first three natural numbers, followed by the 24th letter of the alphabet"
This is equal to the expression we found above plus one, then we can write this as:
[(1 + 2 + 3) + x] + 1
[6 + x] + 1
6 + x + 1
7 + x
Answer:
B) $697.87
Step-by-step explanation:
