009A Sample Final 2, Problem 9 - Revision history

Kayla Murray at 17:25, 1 December 2017

2017-12-01T17:25:14Z

2017-03-08T03:35:26Z

2017-03-08T03:35:07Z

2017-03-08T03:30:08Z

2017-03-06T21:55:29Z

2017-02-19T01:56:43Z

2017-02-18T02:30:22Z

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 <span class="exam">A plane begins its takeoff at 2:00pm on a 2500-mile flight. After 5.5 hours, the plane arrives at its destination. Give a precise mathematical reason using the mean value theorem to explain why there are at least two times during the flight when the speed of the plane is 400 miles per hour.
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+<hr>
-!Foundations: &nbsp;
+[[009A Sample Final 2, Problem 9 Solution|'''<u>Solution</u>''']]
-'''Solution:'''
+[[009A Sample Final 2, Problem 9 Detailed Solution|'''<u>Detailed Solution</u>''']]
 [[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

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 !Final Answer: &nbsp;
 |-
-|See solution above.
+|&nbsp; &nbsp; &nbsp; &nbsp;See above.
 |}
 [[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

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 |&nbsp; &nbsp; &nbsp; &nbsp;<math>\frac{2500 \text{ miles}}{5.5 \text{ hrs}}\approx 454.5 \text{ miles/hr}.</math>
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 !Step 2: &nbsp;
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+|In order to average this speed, the plane had to go from 0mph, up to full speed, past 454.5mph, and then it had to go back down to 0mph to land.
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+|This means that there will be at least two times where the plane of the speed is 400mph.
 |}
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 !Final Answer: &nbsp;
 |-
+|See solution above.
 |}
 [[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

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 '''Solution:'''
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-!Step 1: &nbsp;
+!Final Answer: &nbsp;
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+|
 |}
 [[009A_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

← Older revision		Revision as of 02:30, 18 February 2017
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−	<span class="exam">~~Compute~~	+	<span class="exam">A plane begins its takeoff at 2:00pm on a 2500-mile flight. After 5.5 hours, the plane arrives at its destination. Give a precise mathematical reason using the mean value theorem to explain why there are at least two times during the flight when the speed of the plane is 400 miles per hour.
−
−	:~~:<span class="exam">~~a~~) <math style="vertical~~-~~align: -14px">\lim_{x\rightarrow 4} \frac{\sqrt{x+~~5~~}-3}{x-4}</math>~~
−
−	~~::<span class="exam">b) <math style="vertical-align: -14px">\lim_{x\rightarrow 0} \frac{\sin^2x}{3x}</math>~~
−
−	~~::<span class="exam">c) <math style="vertical-align: -14px">\lim_{x\rightarrow -\infty} \frac{\sqrt{x^2+2}}{2x-1}</math>~~

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 !Foundations: &nbsp;
 |-
+|'''Mean Value Theorem'''
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+|
 |-
+|
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+|
 |}
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 !Step 1: &nbsp;
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+|On average the plane flew
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+|&nbsp; &nbsp; &nbsp; &nbsp;<math>\frac{2500 \text{ miles}}{5.5 \text{ hrs}}\approx 454.5 \text{ miles/hr}.</math>
 |-
+|