You can factor the 32 out of the sum:
We can also change the index as follows
Now, we have a theorem that states that the series
converges if and only if , and in this case we have
This is your case, because you have
which implies that your series converges, and the value is
Answer:
Step-by-step explanation:
Given you will receive a penny today and the amount is tripled each day
so if we write down each day payment we get a geometric progression.
Day 1=1
Day 2=3
Day 3=9
..
the series is 1,3,9,...
it is a geometric progression with a=1 r=3
we know that the general form of nth term in a GP is t(n)=a
t(n)=1*
now we need to find the amount on 12th day by substituting n=12
we get
t(12)=
He will pay on the 12th day .
Correct question is;
Caitlin purchased a prepaid phone card for $20. Long distance calls cost 7 cents a minute using this card. Catin used her card only once to make a long distance all the remaining credit on her card is $16.8. how many minutes did her call last?
Answer:
45 minutes 43 seconds
Step-by-step explanation:
We are told that she purchase the prepaid phone card for $20.
Now she has $16.8 after making the call.
Therefore;
Amount spent on the call = 20 - 16.8 = $3.2
We are told that the long distance call costs 7 cents per minute. Which is $0.07 per minutes
Thus, time spent = $3.2/$0.07 = 45.714 minutes or 45 minutes 43 seconds
Answer:
<h2>
sin2P ≈ 1</h2>
Step-by-step explanation:
Given SinP + SinQ = 7/5...1 and
∠P + ∠Q = 90°... 2
From compound angle; SinP +SinQ = ... 3
Substituting equation 2 into 3 we will have;
SinP +SinQ = = 7/5
since P = 90-Q from equation 1, then;
To get sin2P; Accoding to the trig identity;
Sin2P = 2SinPCosP
Sin2P = 2Sin53.15cos53.15
sin2P = 0.9598
sin2P ≈ 1
Answer:
Relationship between distance and time in simplified form as a unit rate is;
Step-by-step explanation:
Unit rate defined as the rates are expressed as a quantity of 1, such as 5 feet per second or 3 miles per hour, they are called unit rates.
Unit rate =
From the given table:
Take any
time = 4 hours and distance= 188 miles
then, by definition of unit rate;
Unit rate =
Since, this is the constant rate.
Therefore, the relationship between distance and time in simplified form as a unit rate is;