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The table shows a speedometer readings at 10-second intervals during a 1-minute period for a car racing at the Daytona International Speedway in Florida.

(a) Estimate the distance the race car traveled during this time period using the velocities at the beginning of the time intervals.

(b) Give another estimate using the velocities at the end of the time periods.

(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.

a. $10[182.9+168.0+106.6+99.8+124.5+176.1]$$\frac{\text { miles }}{3600}$

b. $10[168.0+106.6+99.8+124.5+176.1+ 175.6]$$\frac{\text { miles }}{3600}$

c. neither

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Campbell University

Oregon State University

University of Nottingham

Idaho State University

So in this problem were given The speedometer readings at 10 2nd intervals during a one minute period for a racing car. And so we have that table of those. Okay. Were used to estimate the distance the car traveled. Using the velocities at the beginning of intervals that has to do it again using the loss at the end of the intervals. And then we are asked uh our estimates in estimates in parts A and B. Upper and lower estimates. Well let's think about this for a minute. If this is our graph of our data, think of something like this. Okay. And we draw in these rectangles that are going to use the left side of the curve like so okay, be like this right all the time. That means that the laughter of the beginning. Okay, the beginning are going to be the lower sums and the ending ones then are going to be the upper sums our estimates. Okay, so that's how that's going to work for us. So let's look at the data now. So we are given this set of data right here. I just piped it into a little spreadsheet real quick right here, Time from 0 to 60 seconds and our velocity of the speedometer and miles per second. His shows are 18, 168 and so on. Okay, So I know each of these intervals is 10 seconds. So whatever delta T is 10. So then taking the 10 times the beginning. So I mean is this first one b 10 times the 1 82.9. Is this the 1829? And so the next 10 it becomes the 168 would be that one? Okay. That gives us the lower sums of 87, 79. Course, this is in miles. And then the upper sums, yeah. Would be the ones on the ending right over here. Okay. And that 10 miles. Okay? We can see the difference between the two and we see which ones are the lower and which ones are the upper sums.

Oklahoma State University