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:
el acento es donde está las tildes
E. 72
6 feet long cast shadow = 24 feet pole
18 feet long cast shadow = 72 feet pole
18/6=3
24x3=72
Answer:
B. 5x + 25 > 75
Step-by-step explanation:
Points available = 25
Additional points earned per puzzle =5
He will advance to the next round if his score is over 75 points.
This means, he will move unto the next stage of his points exceeds 75 or greater than 75
The inequality is:
25 + 5x > 75
It can also be written as
5x + 25 > 75
The correct answer is B. 5x + 25 > 75
5x + 25 > 75
5x > 75 - 25
5x > 50
x > 50 / 5
x > 10
A. 5x + 25 < 75
B. 5x + 25 > 75
C. 25x + 5 > 75
D. 5x + 75 < 25
