Answer:
The series is absolutely convergent.
Step-by-step explanation:
By ratio test, we find the limit as n approaches infinity of
|[a_(n+1)]/a_n|
a_n = (-1)^(n - 1).(3^n)/(2^n.n^3)
a_(n+1) = (-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)
[a_(n+1)]/a_n = [(-1)^n.3^(n+1)/(2^(n+1).(n+1)^3)] × [(2^n.n^3)/(-1)^(n - 1).(3^n)]
= |-3n³/2(n+1)³|
= 3n³/2(n+1)³
= (3/2)[1/(1 + 1/n)³]
Now, we take the limit of (3/2)[1/(1 + 1/n)³] as n approaches infinity
= (3/2)limit of [1/(1 + 1/n)³] as n approaches infinity
= 3/2 × 1
= 3/2
The series is therefore, absolutely convergent, and the limit is 3/2
Milligrams centigrams grams kilograms tonnes ( non American tonnes)
The amount she will have left is $10,500
<h3>How to calculate tax and earning</h3>
Given the foliwng paramters
Total amount earned by the student = $15000
Assume we have the following parameters
Earning paid off in taxes = $1500
Amount spent on living expenses = $3000
Amount she will have left = 15000 - (1500 + 3000)
Amount she will have left = 15,000 - 4500
Amount she will have left = 10,500
Hence the amount she will have left is $10,500
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The function for this problem is:
h(t) = -16(t)^2 + vt + s
h= the height
t= time
v= velocity
s= starting height
With the information given, we know that the starting height is 0, since it was from the ground, and the velocity of the ball is 35 feet per second. Inserting the these information into the equation, we get:
h(t) = -16(t)^2 + 35t
Now the question asks to find the maximum height. It can be done by using a grapher to graph the maximum of the parabola. It could also be done by finding the vertex, which would be the maximum, of the graph by using x= -b/(2a), where b is equal to 35 and a is equal to -16. We get x=35/32, the x-value of where the vertex lies. You can use this value as the t-value in the previous equation to find the h-value of the vertex. When you do, you get h= 19.1 feet, or answer D.
Answer:
7 hours
Step-by-step explanation:
The total amount is the flat fee plus the amount per hour times the number of hours
16 + 8h = 72
Subtract 16 from each side
16+8h-16 = 72 -16
8h = 56
Divide by 8
8h/8 = 56/8
h = 7
7 hours