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3 years ago

Find the sum of the following infinite geometric series, if it exists.

Mathematics

2 answers:

zvonat [6]3 years ago

7 0

Answer: Does not exist

Step-by-step explanation:

The given geometric series : $60 + 84 + 117.6 + 164.64 +…$

Here the first term : $a=60$

The second term : $ar=84$

Now, the common ratio in this series will be :_

$r=\dfrac{ar}{a}=\dfrac{84}{60}=1.4>1$

We know that if the common ratio in infinite geometric series does not lies between (-1,1) , then the series is diverging. And the sum of the infinite geometric series will not exists.

Hence, the sum of the given infinite geometric series does not exist.

Rasek [7]3 years ago

4 0

$q=\dfrac{84}{60}=1.4 > 1\ \text{ therefore you answer: Does not exist}$

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2 years ago

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Answer:

2. The y-intercept is 33 ft. The ball is 33 feet away from the wall.

3. It will take the ball 11 seconds to touch the wall.

4. The slope is -3 ft. The ball is rolling toward the wall at 3 ft per second

Step-by-step explanation:

Let x be the number of seconds.

We are told that a ball is rolling at a rate of 3 ft per second toward a wall that is 33 feet away.

Since the ball is rolling towards wall at a rate of 3 ft per second. This means that remaining distance between wall and ball is decreasing 3 ft with each passing second. Hence, the slope of our line will be negative 3 ft.

As initially ball was 33 feet away from wall, so our y-intercept will be 33.

Upon substituting our values in slope-intercept form of equation we will get equation of our line representing remaining distance between ball and wall after x seconds as:

$y=-3x+33$

Let us find the number of seconds that ball will take to touch the wall by finding the x-intercept of our line. Since x-intercept is the point when line crosses x-axis and at this point y equals 0. The x-Intercept of a line is obtained by putting the value of y as zero in the equation of a line.

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Therefore, after 11 seconds ball will touch the wall.

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