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Mandarinka [93]
4 years ago
15

Find the sum of 3+9+27...+6561

Mathematics
1 answer:
Nikolay [14]4 years ago
7 0
The sum of the first n terms of a geometric series with first term a₁ and common ratio r is given by the formula
S_{n}=a_{1}\cdot\dfrac{r^{n}-1}{r-1}

Then your sum is
\sum\limits_{n=1}^{8}3^{n}=3\cdot\dfrac{3^{8}-1}{3-1}=9840

The sum of this geometric series with first term 3 and common ratio 3 is ...
   J  9840
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Jane spent 3 hours exploring a mountain with a dirt bike. First, she rode 55 miles uphill. After she reached the peak she rode f
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Answer:

Her speed on the summit was 35 mph.

Step-by-step explanation:

Her speed on the summit was "x" mph while her speed while climbing was "x - 10" mph. The distance she rode uphill was 55 miles and on the summit it was 28 miles. The total time she explored the mountain was 3 hours. Therefore:

time uphill = distance uphill / speed uphill = 55 / (x - 10)

time summit = distance summit / speed summit = 28 / x

total time = time uphill + time summit

3 = [55 / (x - 10)] + 28 / x

3 = [55*x + 28*(x - 10)]/[x*(x - 10)]

3*x*(x - 10) = 55*x + 28*x - 280

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x1 = {-(-113) + sqrt[(-113)² - 4*(3)*(280)]}/(2*3) = 35 mph

x2 = {-(-113) - sqrt[(-113)² - 4*(3)*(280)]}/(2*3) = 2.67 mph

Since her speed on the uphill couldn't be negative the speed on the summit can only be 35 mph.

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