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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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#8 second photo is for refrence if you need one
Sail 4mph
walh 3mph
d=rt t-d
tx)= ७-x.
4mph
2-XZ
3mph
walh
(2m
le miles 0-X
413
314
3.052mi =minimum?
t'w- 18-3X + 16-42
12
12
-4x²-3x+34
12
8x
f 8X-3
12
O X=-3
2.
f"x)=
of
Transcribed Image Text:Sail 4mph walh 3mph d=rt t-d tx)= ७-x. 4mph 2-XZ 3mph walh (2m le miles 0-X 413 314 3.052mi =minimum? t'w- 18-3X + 16-42 12 12 -4x²-3x+34 12 8x f 8X-3 12 O X=-3 2. f"x)= of
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.
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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