Answer:
<em>hope</em><em> </em><em>this</em><em> </em><em>helps</em><em> </em><em>you</em><em>.</em><em>.</em><em>.</em><em>!</em>
Express the repeating decimal 0.73 as a geometric series and find its sum
1 answer:
0.737373...=0.73+0.73(0.01)+0.73(0.01)²+0.73(0.01)³...
The sum is 73/99.
We start out with
0.737373... = 0.73 + 0.0073 + 0.000073 + 0.00000073 + ...
This is the same as
0.737373... = 0.73 + 0.73(0.01) + 0.73(0.0001) + 0.73(0.000001) + ...
Which is the same as
0.737373... = 0.73 + 0.73(0.01) + 0.73(0.01)² + 0.73(0.01)³ + ...
The term number, n, relates to the exponent; when n = 2, the exponent is 1; when n = 3, the exponent is 2; etc. This means the exponent is represented by n-1 in our series.
To find the sum, we see first that it is convergent because r = 0.01 < 1. We can find the sum using
a/(1-r), where a is the first term, 0.73:
0.73/(1-0.01) = 0.73/0.99 = 73/99
The sum is 73/99.
We start out with
0.737373... = 0.73 + 0.0073 + 0.000073 + 0.00000073 + ...
This is the same as
0.737373... = 0.73 + 0.73(0.01) + 0.73(0.0001) + 0.73(0.000001) + ...
Which is the same as
0.737373... = 0.73 + 0.73(0.01) + 0.73(0.01)² + 0.73(0.01)³ + ...
The term number, n, relates to the exponent; when n = 2, the exponent is 1; when n = 3, the exponent is 2; etc. This means the exponent is represented by n-1 in our series.
To find the sum, we see first that it is convergent because r = 0.01 < 1. We can find the sum using
a/(1-r), where a is the first term, 0.73:
0.73/(1-0.01) = 0.73/0.99 = 73/99
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Answer:
20 miles.
Step-by-step explanation:
Let m be number of miles.
Laguana's Truck Rentals charges $20 plus $2 per mile.
Total cost of Laguana's Truck = .... (1)
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Total cost of Salvatori's truck = ... (2)
We need to find the number of hours after that the total cost for both companies will be the same.
Therefore, after 20 miles the total cost for both companies will be the same.