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).
1. 4 times 6
2. 8 divided by 2
3. 4 squared 2
Answer:∠1 and ∠5
Step-by-step explanation:
(A) ∠3 and ∠6 forms the interior angles on the same side of the transversal. Thus, this option is incorrect.
(B) ∠1 and ∠4 forms the linear pair on the straight line a, thus this option is incorrect.
(C) ∠1 and ∠5 forms the corresponding angle pair, thus this option is correct.
(D) ∠6 and ∠7 forms the linear pair on the straight line a, thus this option is incorrect.
Answer: 20 oranges and 5 mangoes
Step-by-step explanation:
Define the following:
x = number of oranges
y = number of mangoes
Make the following system of equations:
x + y = 25
0.35x + 1.00y = 12.00
Solve for x:
y = 25 - x
⇒ 0.35x + 1.00(25 - x) = 12.00
⇒ 0.35x + 25 - x = 12.00
⇒ -0.65x = -13.00
⇒ x = 20
Solve for y:
20 + y = 25
y = 5
∴ 20 oranges and 5 mangoes were purchased.
Answer:
13 units^2
Step-by-step explanation:
one side of the square =
So area of square = Length * Length
= 
*
= 13
