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).
Hello!
First you to do 65 * 0.20
0.20 is 20% as a decimal
65 * 0.20 = 13
$13 is how much John saves.
To find out how much the skateboard cost you subtract how much he saved by the cost of the skateboard
65 - 13 = 52
The skateboard cost $52
Hope this helps!
Ermm, Don't you think it's 60?
Cause in my caculatons it's 60
yes sure, i learned this before so
1. a. make a proportion here, of percentage. 
if you cross multiply and divide you get 90%.
1. b. obviously the empty seats would be 10%.
2. a. proportion again, 
cross multiply then divide you ge 15%
3. 30% in decimal form is 0.3. multiply it then to the total amount, so 0.3 x 15 = 4.5
Answer:
A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral with both pairs of opposite sides parallel and congruent. ... The geometric markings shown on the rectangle below indicate parallel sides with an equal number of arrows and congruent sides indicated with an equal number of hatch (hash) marks.
Step-by-step explanation:
