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1. A spherical balloon is inflated so that its volume is increasing at the rate of 7 How fast is the diameter ft² min of the balloon increasing when min the radius is 3 ft? NOTE: Enter the exact answer Rate of change of the diameter = min

1. A spherical balloon is inflated so that its volume is increasing at the rate of 7 How fast is the diameter ft² min of the balloon increasing when min the radius is 3 ft? NOTE: Enter the exact answer Rate of change of the diameter = min

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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9. A rectangular page is to contain 84 square inches of printable area. The margins at the top and bottom of the page are each 1 inch, one side margin is 1 inch, and the other side margin is 2 inches. What should the dimensions of the page be so that the least amount of paper is used? NOTE: Enter the exact answers. width of page = inches height of page= _inches 10. A rectangle has its two lower corners on the x-axis and its two upper corners on the curve y = 64 - x². For all such rectangles, what are the dimensions of the one with largest area? NOTE: Enter the exact answers. width of rectangle = height of rectangle =
Transcribed Image Text:9. A rectangular page is to contain 84 square inches of printable area. The margins at the top and bottom of the page are each 1 inch, one side margin is 1 inch, and the other side margin is 2 inches. What should the dimensions of the page be so that the least amount of paper is used? NOTE: Enter the exact answers. width of page = inches height of page= _inches 10. A rectangle has its two lower corners on the x-axis and its two upper corners on the curve y = 64 - x². For all such rectangles, what are the dimensions of the one with largest area? NOTE: Enter the exact answers. width of rectangle = height of rectangle =
1. A spherical balloon is inflated so that its volume is increasing at the rate of 7 How fast is the diameter of the balloon increasing when min the radius is 3 ft? min NOTE: Enter the exact answer. Rate of change of the diameter = min 2. A conical water tower with vertex down has a radius of 14 ft at the top and is 18 ft high. If water flows into the tank at a rate of 28 ft/min, how fast is the depth of the water increasing when the water is 17 ft deep? Round your answer to two decimal places. The depth of water is increasing at a rate of ft/min. 3. An aircraft is flying horizontally at a constant height of 5000 ft above a fixed observation point (see the figure below). At a certa instant the angle of elevation is 30 and decreasing, and the speed of the aircraft is 240 mi/h. Use 1 mi=5280 ft. a) How fast is decreasing at this instant? Express the result in units of deg/s. Round your answer to one decimal place. 0 is decreasing at a rate of deg/s. b) How fast is the distance between the aircraft and the observation point changing at this instant? Express the result in units of ft/s. Round your answer to the nearest integer fis ft/s Find dy dt x² + y² = 2x + 4y, x = 3 y = 1, and dy dt || 5000 ft given that h= r= inches inches BE 5. Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 How fast is the radius of the spill increasing when the area is 16 mi²? NOTE: Enter the exact answer. mi Rate of change of the radius= 6. A closed rectangular container with a square base is to have a volume of 3456 in³. The material for the top and bottom of the container will cost $4 per in², and the material for the sides will cost $2 per in². Find the dimensions of the container of least cost. Let x be the length of each edge of the base and y be the height. Enter the exact answers, inches x = cm dx dt || y= 7. A cone-shaped paper drinking cup is to hold 40 cm³ of water. Find the height and radius of the cup that will require the least amount of paper. NOTE: Enter the exact answers. Radius= cm Height= cm 8. A cylindrical can, open at the top, is to hold 700 cm³ of liquid. Find the height, h, and the radius, r, that minimize the amount of material needed to manufacture the can. NOTE: Enter the exact answers. cm
Transcribed Image Text:1. A spherical balloon is inflated so that its volume is increasing at the rate of 7 How fast is the diameter of the balloon increasing when min the radius is 3 ft? min NOTE: Enter the exact answer. Rate of change of the diameter = min 2. A conical water tower with vertex down has a radius of 14 ft at the top and is 18 ft high. If water flows into the tank at a rate of 28 ft/min, how fast is the depth of the water increasing when the water is 17 ft deep? Round your answer to two decimal places. The depth of water is increasing at a rate of ft/min. 3. An aircraft is flying horizontally at a constant height of 5000 ft above a fixed observation point (see the figure below). At a certa instant the angle of elevation is 30 and decreasing, and the speed of the aircraft is 240 mi/h. Use 1 mi=5280 ft. a) How fast is decreasing at this instant? Express the result in units of deg/s. Round your answer to one decimal place. 0 is decreasing at a rate of deg/s. b) How fast is the distance between the aircraft and the observation point changing at this instant? Express the result in units of ft/s. Round your answer to the nearest integer fis ft/s Find dy dt x² + y² = 2x + 4y, x = 3 y = 1, and dy dt || 5000 ft given that h= r= inches inches BE 5. Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 6 How fast is the radius of the spill increasing when the area is 16 mi²? NOTE: Enter the exact answer. mi Rate of change of the radius= 6. A closed rectangular container with a square base is to have a volume of 3456 in³. The material for the top and bottom of the container will cost $4 per in², and the material for the sides will cost $2 per in². Find the dimensions of the container of least cost. Let x be the length of each edge of the base and y be the height. Enter the exact answers, inches x = cm dx dt || y= 7. A cone-shaped paper drinking cup is to hold 40 cm³ of water. Find the height and radius of the cup that will require the least amount of paper. NOTE: Enter the exact answers. Radius= cm Height= cm 8. A cylindrical can, open at the top, is to hold 700 cm³ of liquid. Find the height, h, and the radius, r, that minimize the amount of material needed to manufacture the can. NOTE: Enter the exact answers. cm
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