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: y = 1/2x + 3
Step-by-step explanation:
Use the equation y=mx +b
Find the slope (m) of the line by finding the difference in y over the difference in x. Or "rise over run".
The y-intercept (b) is 3 (when x is zero, it is y).
12 because six people came to the party and you shake their hand
Answer:
if i'm not wrong it should be 2.8
Step-by-step explanation:
I'm realy not sure
Sorry if i'm wrong
Answer: n = -2
Step-by-step explanation:
3n +2(n + 2) = 9n + 12
(simplify 2(n + 2)) =
3n + 2n + 4 = 9n + 12
(subtract 9n from both sides)
3n + 2n - 9n + 4 = 12
-4n + 4 = 12
(subtract 4 from both sides)
-4n = 8
(divide -4 from both sides)
n = -2
