Answer:
0
Step-by-step explanation:
-7+-3
0
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Answer:
45/126 or 5/14
Step-by-step explanation:
a / b = 5/8
b / c = 9/14
a = 5
b = 8
b = 9
8 * 9 = 72
b = 72
If b was = 8 and now = 72, multiply a by 9.
b = 45
If b was 9 and now is 72, multiply c by 9.
c = 14 * 9 = 140 - 14 = 126
b / c = 45/126 or 5/14
You are welcome!
Kayden Kohl
9th Grade Student
Answer: 5 1/2
Step-by-step explanation:
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).