A man launches his boat from point A on a bank of a straight river, 4 km wide, and wants to reach point B, 4 km downstream on the opposite bank, as quickly as possible (see the figure below). Hecould row his boat directly across the river to point C and then run to B, or he could row directly to B, or he could row to some point D between C and B and then run to B. If he can row 6 km/h andrun 8 km/h, how far (in km) downstream from C should he land to reach B as soon as possible? (We assume that the speed of the water is negligible compared to the speed at which the man rows.Hint: This question is based on EXAMPLE 4 in Section 4.7 of the textbook. However, for this question, the textbook has added a challenge which may require an unexpected solution. Look for itl)Akm from C

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Answered: A man launches his boat from point A on…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose a farmer wants to fence off a rectangular field alongside a river with a total area of 15, 000 m?. The three sides that do not border the river will cost $10 per meter while the side that borders the river will cost $20 per meter since it must be taller. What should the dimensions of the field be so as to minimize the total cost?
It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that…
It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that…
The United States Postal Service ships a package under large-package rates if the sum of the Tength and the girth of the package is greater than 84 inches and less than or equal to 108 inches. The "length" of the package is considered to be the length of its longest side, and the "girth" of the package is the distance around the package perpendicular to its length. Fran wants to ship packages under the USPS large-package rates. Her package is a rectangular solid (see picture) whose length is 40 inches. What is the largest volume that her package can have?
A hiker is returning to a campsite that is 5 miles east and 2 miles south fromtheir current position. The hiker is currently walking east along a path at a pace of 4 milesper hour. The hiker plans to leave the path and walk in a straight line diagonally towardsthe cabin through the woods. The hiker can only walk at a pace of 3 miles per hour throughthe woods. Where should the hiker leave the path and turn into the woods if they want toget to the campsite as quickly as possible?
It's true — sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the "escaping" dunes. Roads, parking lots, campgrounds, small buildings, trees, and other vegetation are destroyed when a sand dune moves in and takes over. Such dunes are called "escape dunes" in the sense that they move out of the main body of sand dunes and, by the force of nature (prevailing winds), take over whatever space they choose to occupy. In most cases, dune movement does not occur quickly. An escape dune can take years to relocate itself. Just how fast does an escape dune move? Let x be a random variable representing movement (in feet per year) of such sand dunes (measured from the crest of the dune). Let us assume that…
live 9 (rectangular) blocks from Tech, and I walk each morning. The trip is 3 blocks north and 6 blocks west; and I have to follow the streets, so I cannot cut diagonally. At each intersection, I must choose whether to walk north or walk west. Thus, I must make 9 choices of which to take, but of course must go north 3 times and west 6 times. How many possible complete trips to Tech are there?
Farmer Brown wants to upgrade the fencing around his rectanger pasture. He would like to put a stone fence along one(1) side and a wooden fence along the other three (3) sides. The cost of the stone fence is $100 per linear foot, and the cost of the wooden fence is $20 per linear foot. a. If the pasture must have an area of 7,500 square feet, what are the dimensions of the field which will minimize the cost of the fencing? What will the cost of the fencing be at the dimensions that you found?
Suppose it takes 10 hours to fill a rectangular swimming pool of uniform depth. How long will it take to fill a similarly shaped swimming pool if all of the dimensions are doubled?

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