Answer:
f) a[n] = -(-2)^n +2^n
g) a[n] = (1/2)((-2)^-n +2^-n)
Step-by-step explanation:
Both of these problems are solved in the same way. The characteristic equation comes from ...
a[n] -k²·a[n-2] = 0
Using a[n] = r^n, we have ...
r^n -k²r^(n-2) = 0
r^(n-2)(r² -k²) = 0
r² -k² = 0
r = ±k
a[n] = p·(-k)^n +q·k^n . . . . . . for some constants p and q
We find p and q from the initial conditions.
__
f) k² = 4, so k = 2.
a[0] = 0 = p + q
a[1] = 4 = -2p +2q
Dividing the second equation by 2 and adding the first, we have ...
2 = 2q
q = 1
p = -1
The solution is a[n] = -(-2)^n +2^n.
__
g) k² = 1/4, so k = 1/2.
a[0] = 1 = p + q
a[1] = 0 = -p/2 +q/2
Multiplying the first equation by 1/2 and adding the second, we get ...
1/2 = q
p = 1 -q = 1/2
Using k = 2^-1, we can write the solution as follows.
The solution is a[n] = (1/2)((-2)^-n +2^-n).
Answer:
Zero is an integer which is indicated by the symbol 0 in numbers and it is used to indicate that the count of an item when there are non of the item present which is one of the reasons zero along with the fact that it is the number between positive and negative numbers, why it is not associated with a positive or negative sign.
Step-by-step explanation:
A number which is not zero is said to be a non-zero number and the roots of a function is known as the zeros of the function.
Answer:
I think it's maybe $55.00
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Although you didn't give me any answers to go with your problem, I am assuming that since 15-7 is 8, and 3 + 1 = 4, the answer should be 4. Now regarding if it is times, it would be x2. Because for times 2 would be 8. Overall the answer should be 4.
A rotation 270° counterclockwise about the origin is the same as rotation 90° clockwise about the origin and has a rule:
(x,y)→(y,-x).
Then:
- D(−2,4)→D'(4,2)
- E(4,7)→E'(7,-4)
- F(10,3)→F'(3,-10)
- G(8,0)→G'(0,-8)
Answer: the coordinates of vertices of quadrilateral D′E′F′G′ are D'(4,2), E'(7,-4), F'(3,-10), G'(0,-8).
