$\"\"$

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The ball is dropped from the height of $\"\"$ feet.

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Every time it strikes the ground, it bounces up to $\"\"$ of the previous height.

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The first term of the geometric sequence is $\"\"$ .

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The common ratio is $\"\"$ .

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(a)

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Find the height for which the ball will bounce after it strikes the ground third time.

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Every time it strikes the ground, it bounces up to $\"\"$ of the previous height.

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Observe the figure:

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The height of the ball bounced for second strike is $\"\"$ feet.

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$\"\"$

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$\"\"$ .

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Height for the ball after striking the ground for third time is $\"\"$ feet.

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$\"\"$

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(b)

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Formula for $\"\"$ term in geometric sequence is $\"\"$ .

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Here if the ball strikes the ground $\"\"$ times then the ball is bounced by $\"\"$ times.

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Substitute $\"\"$ and $\"\"$ .

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After $\"\"$ strikes, the height of the ball bounced is $\"\"$ .

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$\"\"$

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(c)

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Find for strike, the height of the ball less than $\"\"$ inches.

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Height of the ball is $\"\"$ inches $\"\"$ foot.

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$\"\"$

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$\"\"$

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Take logarithm of each side.

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$\"\"$

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The height of the ball less than $\"\"$ inches for $\"\"$ strike.

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$\"\"$

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(d)

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Find the total distance does the ball travel before it stops bouncing.

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If $\"\"$ , the infinite series conveges and its sum is $\"\"$ .

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Where $\"\"$ is the first term and $\"\"$ is the common ratio.

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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The total distance travelled by the ball before it stops bouncing is $\"\"$ feet.

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$\"\"$

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(a) Height for the ball after striking the ground for third time is $\"\"$ feet.

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(b) After $\"\"$ strikes, the height of the ball bounced is $\"\"$ .

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(c) The height of the ball less than $\"\"$ inches for $\"\"$ strike.

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(d) The total distance travelled by the ball before it stops bouncing is $\"\"$ feet.