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.
__
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.
__
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:
A car dealership needs $13050 to sell the car to earn the 45% profit if a car dealership buys a car for $9000.
Step-by-step explanation:
Car cost = $9000
Profit percentage = 45% profit
Thus,
Profit amount = 45% of 9000
= 45/100 × 9000
= 0.45 × 9000
= $4050
In order to determine how much a car dealership needs to sell the car to earn the 45% profit, all we need is to add the profit amount i.e. $4050, and the car cost i.e. $9000.
i.e.
Car cost + Profit amount = $9000 + $4050
= $13050
Therefore, a car dealership needs $13050 to sell the car to earn the 45% profit if a car dealership buys s car for $9000.
Answer:
the x² test statistic 13.71
Option a) 13.71 is the correct answer.
Step-by-step explanation:
Given the data in the question;
Feeder 1 2 3 4
Observed visits; 60 90 92 58
data sample = 300
Expected = 300 / 4 = 75
the x² test statistic = ?
= ∑[ ( - )²/]
= [ (60 - 75)² / 75 ] + [ (90 - 75)² / 75 ] + [ (92 - 75)² / 75 ] + [ (58 - 75)² / 75 ]
= [ 3 ] + [ 3 ] + [ 3.8533 ] + [ 3.8533 ]
= 13.7066 ≈ 13.71
Therefore, the x² test statistic 13.71
Option a) 13.71 is the correct answer.
Hello there!
The statement that would NOT be true would be option A. All isosceles triangles are also equilateral triangles. The rest of the statements would be TRUE.
Hope this helps and have a great day! :)
Answer:
1092
Step-by-step explanation:
We have been given that the number of bacteria in the colony t minutes after the initial count modeled by the function . We are asked to find the average rate of change in the number of bacteria over the first 6 minutes of the experiment.
We will use average rate of change formula to solve our given problem.
Upon substituting our given values, we will get:
Therefore, the average rate of change in the number of bacteria is 1092 bacteria per minute.