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:
To find this out, we first need to see the change, is it a positive change or a negative change? Well in this case, as the temperature is increasing, we find that the change is positive. The next step we need to do, id that, how much was the change by, we can find this out by finding the absolute value of the difference of -16°F and 7°F
The absolute value means, the operations answer has to be positive, if not then it will become positive.
|-16°F -7°F|
=> |-23°F|
=> 23°F
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Thank You!!
We are given
P = <span>$1,945.61
r = 11.2%
Amin = $156
A = $300
First, we convert the interest to effective monthly terms
i = 11.2%/12 = 0.933%
After one month, the interest saved by paying more than the minimum is
</span>(0.00933) (300 - 156) = $1.35
X + 3y = 14
x + 3(3x - 14) = 14
x + 9x - 42 = 14
10x - 42 = 14
<u> + 42 + 42</u>
<u>10x</u> = <u>56</u>
10 10
x = 5.6
5.6 + 3y = 14
<u>- 5.6 - 5.6</u>
<u>3y</u> = <u>8.4</u>
3 3
y = 2.7
(x, y) = (2.7, 5.6)
Answer:
false
Step-by-step explanation:
i dont understand kinda
but if you add it,
88<106
so false
