A store manager is accepting applications for part-time workers. he can hire no more than 14 people. so far,he has hired 9 peopl
1 answer:
The manager already hired 9 people. Let be the number of people he still can hire. Since these people will add to the 9 he already hired, when the hiring campaign will be over he will have hired
people. We know that he can't hire more than 14 people, so the number of people hired must be less than or equal to 14:
If we subtract 9 from both sides, we have
so, the manager can hire at most 5 other people
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Answer:
Part A) The distance between Whitney's house and Anh's house is 6.5 miles.
Part B) The total distance traveled by Whitney during the trip was 9.5 miles.
Step-by-step explanation:
Part A)
Notice that during Whitney's journey to Anh's house, her velocity was negative for some time. So, Whitney was travelling backwards. Hence, the total distance Whitney traveled will be greater than the actual distance from Whitney's house to Anh's.
So, instead, we can calculate Whitney's total displacement. Total displacement is given by:
Where <em>v(t)</em> is the velocity function.
So, the displacement of Whitney when she traveled from her house to Anh's house will be:
To calculate the integral, we can split it off at <em>t</em> = 11, <em>t</em> = 16, and <em>t</em> = 24.
The three regions represent three geometric figures, which we can use to calculate the area and then find the integral. Rewriting:
Now, we can calculate the area of each figure.
The first figure is a trapezoid with a height of 0.8 and two bases of 11 and 3. So, its area is:
The second figure is a triangle with a height of 0.6 and a base of 5. So, its area is:
Lastly, the third figure is another triangle will a height of 0.6 and a base of 8. So, its area is:
However, notice that the second figure is below the <em>x</em>-axis. During that interval, Whitney was traveling backwards. Hence, we will subtract the second area from the rest of the areas.
Then the displacement will be:
So, the distance between Whitney's house and Anh's house is 6.5 miles.
Part B)
The total distance differs from displacement in that it includes all the distances in both directions. It is given by:
In other words, all of our values are now positive. We will utilize the same strategy:
Substitute. The only difference is that we will add 1.5 instead of subtracting it. So:
Therefore, in this instance, Whitney traveled a total of 9.5 miles to get to Anh's house.