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1. Find the slope of the curve x²+ y² -6x - 4y - 21 = 0 at (0,7). Compute also the tangent line and normal line at (0,7)

1. Find the slope of the curve x²+ y² -6x - 4y - 21 = 0 at (0,7). Compute also the tangent line and normal line at (0,7)

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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Application Problems 5. A statue 3m high is standing on a base 4m high. If an observer's eye is 1.5m above the ground, how far should he stand from the base in order that the angle subtended is a maximum? 6. A Norman window is in the shape or a rectangle surmounted by a semi-circle. What is the ratio of the. width of the rectangle to the total height so that it will yield a window admitting the most light for a given perimeter? 7. The volume or the closed cylindrical tank is 11.3 cubic meter. If the total surface area is a minimum, what 1s its base radius, in m? 8. The distance a body travels is a function of time and is given by x(t) = 16t+8t². Find its velocity at t = 3.
Transcribed Image Text:Application Problems 5. A statue 3m high is standing on a base 4m high. If an observer's eye is 1.5m above the ground, how far should he stand from the base in order that the angle subtended is a maximum? 6. A Norman window is in the shape or a rectangle surmounted by a semi-circle. What is the ratio of the. width of the rectangle to the total height so that it will yield a window admitting the most light for a given perimeter? 7. The volume or the closed cylindrical tank is 11.3 cubic meter. If the total surface area is a minimum, what 1s its base radius, in m? 8. The distance a body travels is a function of time and is given by x(t) = 16t+8t². Find its velocity at t = 3.
Application Problems 1. Find the slope of the curve x²+ y² -6x - 4y - 21 = 0 at (0,7). Compute also the tangent line and normal line at (0,7) 2. Determine the radius of curvature at (1,2) of the curve y² - 4x = 0. 3. The number of newspaper copies distributed is given by C = 50t² - 200t + 10000, where t is in years. Find the minimum number of copies distributed from 2016 to 2021. 4. A boatman is at A, which is 4.5km from the nearest point B on a straight shore BM. He wishes to reach, in minimum time, a point C situated on the shore 9km from B, how far should he land if he can row at the rate of 6kph and walk at the rate of 7.5 kph.
Transcribed Image Text:Application Problems 1. Find the slope of the curve x²+ y² -6x - 4y - 21 = 0 at (0,7). Compute also the tangent line and normal line at (0,7) 2. Determine the radius of curvature at (1,2) of the curve y² - 4x = 0. 3. The number of newspaper copies distributed is given by C = 50t² - 200t + 10000, where t is in years. Find the minimum number of copies distributed from 2016 to 2021. 4. A boatman is at A, which is 4.5km from the nearest point B on a straight shore BM. He wishes to reach, in minimum time, a point C situated on the shore 9km from B, how far should he land if he can row at the rate of 6kph and walk at the rate of 7.5 kph.
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