8. You are out for a day of sailing and plan on coming back to shore for lunch. The boat is currently anchored 2 miles from shore and 6 miles down shore from the 2 mi restaurant. a. If you can sail at a speed of 4mph and walk along the shore at a speed of 3 mph, at what point along the shore should you dock and start walking in order to reach the restaurant in the minimum time? How long will it take you to reach the restaurant? b. If you are able to walk at the same speed, but the wind has picked up and you can sail at a faster speed compared to the problem above, would the optimal place to start walking be closer to or farther from the restaurant compared to your answer on part a? Explain your answer and reasoning using complete sentences and correct grammar.
8. You are out for a day of sailing and plan on coming back to shore for lunch. The boat is currently anchored 2 miles from shore and 6 miles down shore from the 2 mi restaurant. a. If you can sail at a speed of 4mph and walk along the shore at a speed of 3 mph, at what point along the shore should you dock and start walking in order to reach the restaurant in the minimum time? How long will it take you to reach the restaurant? b. If you are able to walk at the same speed, but the wind has picked up and you can sail at a faster speed compared to the problem above, would the optimal place to start walking be closer to or farther from the restaurant compared to your answer on part a? Explain your answer and reasoning using complete sentences and correct grammar.
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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#8 second photo is for refrence if you need one
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t'w- 18-3X + 16-42
12
12
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12
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Transcribed Image Text:8. You are out for a day of sailing and plan on coming back
to shore for lunch. The boat is currently anchored 2
miles from shore and 6 miles down shore from the
2 mi
restaurant.
a. If you can sail at a speed of 4mph and walk
along the shore at a speed of 3 mph, at what
point along the shore should you dock and start
walking in order to reach the restaurant in the minimum time? How long will it take
you to reach the restaurant?
b. If you are able to walk at the same speed, but the wind has picked up and you can sail
at a faster speed compared to the problem above, would the optimal place to start
walking be closer to or farther from the restaurant compared to your answer on part
a? Explain your answer and reasoning using complete sentences and correct grammar.
9. Find the radius (to the nearest tenth) of a cylindrical soda can with a volume of 354 cm³ that
minimizes the surface area of the can. Use the Second Derivative Test to verify the minimum.
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Given that a boat is anchored 2 miles from shore and 6 miles from the restaurant.
VIEWLet x be the point along the shore to dock and start walking to the restaurant.
VIEWThe speed of the boat is 4mph. Therefore, the time required to sail is
VIEWThe total time T(x) will be,
VIEWNote: We use the second derivative test to get the minimum value,
VIEWPart b:
VIEWAnswer:
VIEW
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