= 0.25t3 1.5t2 + 3t + 0.25 for times in the interval (1 point) A person walking

Question

= 0.25t3 1.5t2 + 3t + 0.25 for times in the interval (1 point) A person walking along a straight path has her velocity in miles per hour at time t given by the function v t 0 St3 2. The graph of this function is also given in each of the three diagrams below mph mph mph 3 3 3 y = v(t) y= v(t) 2 2 2 B4 B3 A2 B2 C2 hrs hrs hrs 2 2 Note that in each diagram, we use four rectangles to estimate the area under y = v(t) on the interval [0, 2], but the method by which the four rectangles, respective heights are decided varies among the three individual graphs. Think about how the heights of the rectangles in the left-most diagram are being chosen. Determine the value of S = A1 + A2 + A3 + A4 by evaluating the function y-v(t) at appropriately-chosen values and observing the width of each rectangle. Note, for example, that A3 = v(1)· 2-3 = 1 Use the rectangles in the middle diagram to find the value of T- B B2 +B3+ B Use the rectangles in the right-most diagram to find the value of U C1 + C2 +C3 + C4 Which estimate do you think is the best approximation of D, the total distance the person traveled on [0, 2]? Why?

Explanation / Answer

S :
Hts are clearly 0.25 , 1.4 , 2 and 2.25

Adding them up :
0.25 + 1.4 + 2 + 2.25
5.9

And multiply delta(t) = 1/2
5.9 * 1/2

2.95 ---> ANS

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T :
Hts are
1.4 + 2 + 2.25 + 2.25
7.9

7.9 * 1/2

3.95 --> ANS

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U :
0.9 + 1.75 + 2.15 + 2.25
7.05

7.05 * 1/2

3.525 ---> ANS

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Best estimate:
Would be the U because midpoint sum is always gonna be much more accurate compared to the left/right end sums

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