Answer:
The given series converges and 
Step-by-step explanation:
Given is 108, -18, 3,...
It is an alternate series. An alternate series is convergent if:
1. The series is decreasing.
2. If the last term (n-th term) of series converges to 0.
<u>Since each next term is less than its preceding term, so it is decreasing.</u>
First term, a = 108
Second term = -18
Common ratio, r = -18/108 = -1/6
General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ
<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>
Hence, the given series converges.
Now limit will be: 
Hence,
Answer:
Step-by-step explanation:
<u>The data given:</u>
- 93, 81, 94, 71, 89, 92, 94, 99
<u>Put the data in the ascending order:</u>
- 71, 81, 89, 92, 93, 94, 94, 99
<u>Since the data size is even, the median is the average of middle two:</u>
- median = (92 + 93)/2 = 92.5
Answer:
A simplified method for dividing a polynomial by another polynomial of the first degree is synthetic division.
Answer:
Approximately 42 times larger
Step-by-step explanation:
The diameter of a sphere is 2,160 mm.
The diameter of a second sphere is 7,520 mm.
To see how many times larger is the diameter of second sphere is than the diameter of the second sphere, we divide to get:
To see how many times larger the volume is, we cube both sides
This implies that
Therefore the volume of the second sphere is approximately 42 times larger
Answer:
3
Step-by-step explanation:
