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ithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water du rd with these tendencies is released from an island that is 3 km from the nearest point B on the shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will rgy expenditure. Points B and D are 10 km apart. (Round your answers to two decimal places.) island (a) In general, if it takes 1.1 times. s much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area? km from B (b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively. Assuming the bird's energy expenditure minimized, determine a function for the ratio W/L in terms of x, the distance from B to C. W (c) What should the value of W/L be in order for the bird to fly directly to its nesting area D? (d) If the ornithologists observe that birds of a certain species reach the shore at a point 3 km from B, how many times more energy does it take a bird to fly over water than land?

ithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water du rd with these tendencies is released from an island that is 3 km from the nearest point B on the shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will rgy expenditure. Points B and D are 10 km apart. (Round your answers to two decimal places.) island (a) In general, if it takes 1.1 times. s much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area? km from B (b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively. Assuming the bird's energy expenditure minimized, determine a function for the ratio W/L in terms of x, the distance from B to C. W (c) What should the value of W/L be in order for the bird to fly directly to its nesting area D? (d) If the ornithologists observe that birds of a certain species reach the shore at a point 3 km from B, how many times more energy does it take a bird to fly over water than land?

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter8: Areas Of Polygons And Circles
Section8.5: More Area Relationships In The Circle
Problem 42E: A goat is tethered to a barn by a 12-ft chain. If the chain is connected to the barn at a point 6 ft...
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4.6 Question 15

Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 3 km from the nearest point B on the shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. Points B and D are 10 km apart. (Round your answers to two decimal places.) island D nest (a) In general, if it takes 1.1 times as much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area? km from B (b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively. Assuming the bird's energy expenditure is minimized, determine a function for the ratio W/L in terms of x, the distance from B to C. W= = (c) What should the value of W/L be in order for the bird to fly directly to its nesting area D? (d) If the ornithologists observe that birds of a certain species reach the shore at a point 3 km from B, how many times more energy does it take a bird to fly over water than land?
Transcribed Image Text:Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 3 km from the nearest point B on the shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. Points B and D are 10 km apart. (Round your answers to two decimal places.) island D nest (a) In general, if it takes 1.1 times as much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area? km from B (b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively. Assuming the bird's energy expenditure is minimized, determine a function for the ratio W/L in terms of x, the distance from B to C. W= = (c) What should the value of W/L be in order for the bird to fly directly to its nesting area D? (d) If the ornithologists observe that birds of a certain species reach the shore at a point 3 km from B, how many times more energy does it take a bird to fly over water than land?
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