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e-lub [12.9K]
3 years ago
7

The sum of the first k terms in the sequence is 118096, find the value of k. The first term is 78732 the common ratio is 1/3.

Mathematics
1 answer:
FrozenT [24]3 years ago
8 0

Answer:

k = 10

Step-by-step explanation:

The sum of k terms of a geometric sequence with first term a1 and common ratio r is given by ...

... Sk = a1·(1 -r^k)/(1 -r)

For the given numbers, this is ...

... 118096 = 78732·(1 -(1/3)^k)/(1 -1/3)

Manipulating this to get the term containing k, we have

... 1 -(2/3)(118096/78732) = (1/3)^k

... 1/59049 = (1/3)^k

Taking logarithms, we get

... -log(59049) = -k·log(3)

... log(59049)/log(3) = k = 10

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3 years ago
A rhino can run 28 miles per hour. What is that speed in feet per second, to the nearest whole number?
Mrrafil [7]

Answer:

A rhino runs at a speed of about 28 miles per hour.

We need to determine the speed in feet per second.

Converting miles to feet:

The miles can be converted to feet by multiplying 5280 with 28 miles per hour.

Thus, we have;

28 x 5280 = 14784028 × 5280 = 147840

Thus, the speed of the rhino in feet per hour is 147840

Converting hours to seconds:

The hours can be converted into seconds by dividing 147840 by 3600 (Because an hour has 60 seconds in a minute and 60 minutes in an hour)

Thus, we get;

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Rounding off to the nearest whole number, we get;

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6 0
3 years ago
The speed of an object can be found by taking the distance it travels and dividing it by the time it takes to travel that distan
Alexus [3.1K]

Answer:

<h2>True the speed S in in Feet/second</h2>

Step-by-step explanation:

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Answer:

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Hope it helps!

7 0
3 years ago
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