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.
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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.
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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: 84.09%
Step-by-step explanation:
1. 220-30=? ?=185
2. Divide 185 by 220 (as a fraction, 185 out of 220 is 185/220 which also means divide) 185 divided by 220 is about 0.8409
3. Multiply 0.8409 by 100 (since there is two zeros in 100 we can move the decimal to the right twice which gets you 84.09
Answer:
Huh
Step-by-step explanation:
Our answer is
Our greatest common factor, or GCF, is
, so when we factor is out, our divide each term by
, we get our answer. To check this, we can multiply the
back across the parenthesis and see if we get the same result as our initial question.
Hope this helped! :))
