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(AAA) Corresponding angles are congruent.
Therefore, the sides of the triangles are proportional:
cross multiply
use distributive property
subtract 100 from both sides
divide both sides by 100
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(SAS)
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
Therefore we have the equation:
The perimeter of △PQR:
Substitute the value of y to the expression:
First part of question:
Find the general term that represents the situation in terms of k.
The general term for geometric series is:
= the first term of the series
= the geometric ratio
would represent the height at which the ball is first dropped. Therefore:
We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:
Our general term would be:
Second part of question:
If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.
represents the initial height:
represents the number of times the ball bounces:
Plugging this back into our general term of the geometric series:
represents the highest height of the ball after 6 bounces.
Third part of question:
If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time.
This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:
We already know these variables:
Therefore: