All three series converge, so the answer is D.
The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.
Consider a geometric sequence with the first term a and common ratio |r| < 1. Then the n-th partial sum (the sum of the first n terms) of the sequence is
Multiply both sides by r :
Subtract the latter sum from the first, which eliminates all but the first and last terms:
Solve for :
Then as gets arbitrarily large, the term will converge to 0, leaving us with
So the given series converge to
(I) -243/(1 + 1/9) = -2187/10
(II) -1.1/(1 + 1/10) = -1
(III) 27/(1 + 1/3) = 18
Refer to the diagram shown below.
w = 6 7/8 in = 6.875 in, the width of each device.
d = 3 1/2 in = 3.50 in, the space between teo devices.
The total space needed is
D = 4(w+d) + w
= 5w + 4d
= 5*6875 + 4*3.5
D = 48.375 in or 48 3/8 in
Answer: 48 3/8 inches or 48.375 inches
Answer:
31 degrees
Step-by-step explanation:
Measure angles 1 and 3 are vertical angles, meaning they are equal which means 3 = 149 degrees
Angles 2 and 3 are adjacent and supplementary, meaning that their angles add up to 180.
1<u>8</u>0 - 149 = 31 degrees
Answer:
t = 42857.14 h
Step-by-step explanation:
Given that,
The speed of space shuttle, v = 28000 km/h
We know that, the distance between the Saturn and the Earth is 1,200,000,000 km.
Let t be the time.
As we know, speed = distance/time
So,

So, the required time is equal to 42857.14 hours.