A geometric series is written as 
, where 
is the first term of the series and 
is the common ratio.
In other words, to compute the next term in the series you have to multiply the previous one by .
Since we know that the first time is 6 (but we don't know the common ratio), the first terms are
.
Let's use the other information, since the last term is 
, we know that 
, otherwise the terms would be bigger and bigger.
The information about the sum tells us that
We have a formula to compute the sum of the powers of a certain variable, namely
So, the equation becomes
The only integer solution to this expression is 
.
If you want to check the result, we have
and the last term is
To solve this problem, all we have to do is to thoroughly
analyze the situation step by step.
First let us work on the remaining 10 gallons of water in
the tank. We are given that 2 / 3 of the water initially in the tank leaked
out. Therefore this means that we are left with 1 / 3 the original amount of
water which is 10 gallons, hence:
(1 / 3) Vi = 10 gallons
where Vi is the initial volume of water inside the tank,
calculating for Vi:
Vi = 3 (10 gallons)
Vi = 30 gallons
We are also given that this initial volume of water is
just 3 / 4 of the total capacity of the tank, therefore:
(3 / 4) Vc = Vi
where Vc is the volume capacity of the tank, calculating
for Vc:
Vc = 4 Vi / 3
Vc = 4 (30 gallons) / 3
Vc = 40 gallons
Answer:
<span>Capacity of the fish tank is 40 gallons</span>
Angle of fire in degrees = 90 + 30 =120 degrees
Angle of fire radians =180 degrees = π
120* π/180=120π /180 OR 4π/6 OR 2π/3
Answer:
Calculated weight of water = 10.01 g
percentage error = 0.1%
Step-by-step explanation:
Given:
Weight of graduate = 35.825 g
Weight of graduate + Water = 45.835 g
Now,
The weight of water = ( Weight of graduate + Water ) - Weight of graduate
or
The weight of water = 45.835 - 35.825
or
The weight of water = 10.01 g
Now,
The percentage of error = 
or
The percentage error = 
or
The percentage error = 0.1%
Answer:
$7.94
Step-by-step explanation:
We have been given that on January 4, Janelle Ruskinoff deposited $2192.06 in a savings account that pays 5.5 percent interest compounded daily. We are asked to find the amount of interest earned in 24 days.
We will use compound interest formula to solve our given problem.
, where,
A = Final amount after t years,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = time in years.
24 days in years would be 
.
Upon substituting our given values in above formula, we will get:
To find amount of interest earned, we will subtract principal amount from final amount as:
Therefore, her money will earn approximately $7.94 in 24 days.
