A teacher hands out the following graph to four students who are asked to describe a real world situation that could be modeled
by the graph. We may assume the graph runs from (0,10) to (9,0) and the graph is a curve and not a straight line. Chose the description below that least fits what is modeled by the graph
A) the weight of ten pounds of melting over time in a yard and taking nine hours to completely change into water and seep into the ground.
B) time in hours elapsed is on the x axis and temperature in degrees above room temperature is the y axis and the graph measures something cooling down over time
C) the volume of helium filled balloon that is slowly leaking air
D) the height of a rocket on the ground that first goes up and then comes down
A) the weight of ten pounds of melting over time in a yard and taking nine hours to completely change into water and seep into the ground.
B) time in hours elapsed is on the x axis and temperature in degrees above room temperature is the y axis and the graph measures something cooling down over time
C) the volume of helium filled balloon that is slowly leaking air
D) the height of a rocket on the ground that first goes up and then comes down
2 answers:
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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.