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:
x <= -5
Step-by-step explanation:
4x + 12 <= -8
4x <= -20
x <= -5
Mathematics is the subject that is most popular in the class and is liked by the students.
<u>Explanation:</u>
Among all the subjects that are added in the curriculum of the students in the school, Mathematics is the subject that is mostly liked by the students in the class and in the school.
To find this that mathematics was the favorite subject of the students, a a survey was conducted by the school people in the class of a professor and through that survey it was shown that Mathematics was a subject that was mostly liked by all the students.
The answer to this question would be true.
An odd number wouldn't have any 2 in their factor because it is the definition of odd number, can't be divided by 2. Since they have no probability of having factor 2, then their GCF would not become an even number.
9514 1404 393
Answer:
see the attachment for a graph
Step-by-step explanation:
With the given point and slope, the equation of the line can be written in point-slope form:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y -2 = 1/2(x +1) . . . . line with slope 1/2 through point (-1, 2)
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Slope is the ratio of rise to run, so a slope of 1/2 means the line will rise 1 unit for each 2 units of run (to the right). If you're plotting this by hand, you can identify a second point that is 2 right and 1 up from the given point:
(-1 +2, 2 +1) = (1, 3).
You can draw your line through those two points.
