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:
the median is $1.60 greater than the mean
Answer:
y = 
Step-by-step explanation:
The equation for a linear graph is usually written in the following format...
y = mx + b
Where m would be the slope, usually referring to rise over run and b would be the y-intercept (where the line crosses the y-axis). From the graph, we can see that the line crosses the y-axis at point 3 so b would be 3. The graph also shows us that for every 1 value that the line rises it moves to the right 2 values. Therefore, the slope would be 1/2. Using these values we can create the following equation...
y = 
Answer:
£4867.2
Step-by-step explanation:
Given data
P= £4500
T=2 years
R= 4%
The compound interest expression
A=P(1+r)^t
substitute
A= 4500(1+0.04)^2
A=4500(1.04)^2
A=4500*1.0816
A=£4867.2
Hence the balance is £4867.2
Answer:
y=1
Step-by-step explanation:
you can use those points to find the slope
use the equation
then plug in the numbers
so (1-1)/(-8-7) = 0/15 so the slope is zero meaning it is a horizontal line which we can tell logically because the y coordinates of both points are 1.
so if you plug those numbers into the formula y=mx+b where m is slope and b is the y intercept then
you get y=0*x+1
then 0*x is just zero and it goes away so the equation for this line is y=1
Hope this helps! :)