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The percent change in the number of people who went to the pool
between the first and last week is 10% less
Step-by-step explanation:
The given is:
- In the first week of July, a record 1,060 people went to the local swimming pool
- In the second week, 105 fewer people went to the pool
- In the third week, 135 more people went to the pool than in the second week
- In the fourth week, 136 fewer people went to the pool than in the third week
We need to find the percent change in the number of people who
went to the pool between the first and last weeks
∵ There were 1060 people in the 1st week
∵ There were 105 fewer people in the 2nd week
∴ The number of people in the 2nd week = 1060 - 105 = 955
∴ There were 955 people in the 2nd week
∵ There were 135 more people in the 3rd week than the 2nd week
∵ There were 955 people in the 2nd week
∴ The number of people in the 3rd week = 955 + 135 = 1090
∴ There were 1090 people in the 3rd week
∵ There were 136 fewer people in the 4th week than in the 3rd week
∵ There were 1090 people in the 3rd week
∴ The number of people in the 4th week = 1090 - 136 = 954
∴ There were 954 people in the 4th week
Let us find the change from 1st week to last week
∵ There were 1060 people in the 1 st week
∵ There were 954 people in the last week
∴ The change = 1060 - 954 = 106
∵ Percent change = × 100%
∴ Percent change = × 100%
∴ Percent change = 10%
The percent change in the number of people who went to the pool
between the first and last week is 10% less
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Since S is a point on the segment QR, then:
Use the diagram and trigonometric relationships to find the value of QS and QR. Then, use the above equation to solve for SR.
In the right triangle PQS, the side QS is opposite to the angle of 32º, and the side PQ is adjacent to the angle of 32º. Then, use the tangent trigonometric function to relate PQ to QS:
Isolate QS and replace PQ=14:
On the other hand, notice that the side QR in the right triangle PQR is opposite to the angle QPR, which has a measure of 32º+24º=56º.
Then, by a similar reasoning, we can use again the tangent function to find QR:
We have found expressions for QS and QR in terms of trigonometric relationships. Then, we can find an expression for SR:
Replace the expressions for QR and QS:
Use a calculator to find decimal expressions for tan(56º) and tan(32º). Then, find SR:
Therefore, to the nearest tenth, the length of the side SR (or RS, which is the same) is 12.0.