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(8 points) Suppose the terrain of a hillside is represented as the graph z = f(x). Suppose f(a) = c and Vf(a) = = -5 4 3 Give a vector in R³ tangent to the curve through [a] along which the elevation stays constant. (Be prepared to explain your answer to the class.) 間 Give a vector in R3 pointing in the direction tangent at a that goes uphill as steeply as possible. (Be prepared to explain your answer to the class.) 111 Consider a typical map, in which east is depicted in the e₁ direction and north is depicted in the e2 direction. If you walk along a path at [a] heading due south, at what angle (in radians) are you walking uphill at that instant? (Be prepared to explain your answer to the class.) You may give your answer in terms of an inverse trigonometric function. a If you now walk along a path at heading southeast, at what angle (in radians) are you walking uphill at that instant? (Be prepared to explain your answer to the class.) You may give your answer in terms of an inverse trigonometric function.

(8 points) Suppose the terrain of a hillside is represented as the graph z = f(x). Suppose f(a) = c and Vf(a) = = -5 4 3 Give a vector in R³ tangent to the curve through [a] along which the elevation stays constant. (Be prepared to explain your answer to the class.) 間 Give a vector in R3 pointing in the direction tangent at a that goes uphill as steeply as possible. (Be prepared to explain your answer to the class.) 111 Consider a typical map, in which east is depicted in the e₁ direction and north is depicted in the e2 direction. If you walk along a path at [a] heading due south, at what angle (in radians) are you walking uphill at that instant? (Be prepared to explain your answer to the class.) You may give your answer in terms of an inverse trigonometric function. a If you now walk along a path at heading southeast, at what angle (in radians) are you walking uphill at that instant? (Be prepared to explain your answer to the class.) You may give your answer in terms of an inverse trigonometric function.

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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(8 points) Suppose the terrain of a hillside is represented as the graph z = f(x). Suppose f(a) = c and Vf(a) = = -5 4 3 Give a vector in R³ tangent to the curve through [a] along which the elevation stays constant. (Be prepared to explain your answer to the class.) 間 Give a vector in R3 pointing in the direction tangent at a that goes uphill as steeply as possible. (Be prepared to explain your answer to the class.) 111 Consider a typical map, in which east is depicted in the e₁ direction and north is depicted in the e2 direction. If you walk along a path at [a] heading due south, at what angle (in radians) are you walking uphill at that instant? (Be prepared to explain your answer to the class.) You may give your answer in terms of an inverse trigonometric function. a If you now walk along a path at heading southeast, at what angle (in radians) are you walking uphill at that instant? (Be prepared to explain your answer to the class.) You may give your answer in terms of an inverse trigonometric function.
Transcribed Image Text:(8 points) Suppose the terrain of a hillside is represented as the graph z = f(x). Suppose f(a) = c and Vf(a) = = -5 4 3 Give a vector in R³ tangent to the curve through [a] along which the elevation stays constant. (Be prepared to explain your answer to the class.) 間 Give a vector in R3 pointing in the direction tangent at a that goes uphill as steeply as possible. (Be prepared to explain your answer to the class.) 111 Consider a typical map, in which east is depicted in the e₁ direction and north is depicted in the e2 direction. If you walk along a path at [a] heading due south, at what angle (in radians) are you walking uphill at that instant? (Be prepared to explain your answer to the class.) You may give your answer in terms of an inverse trigonometric function. a If you now walk along a path at heading southeast, at what angle (in radians) are you walking uphill at that instant? (Be prepared to explain your answer to the class.) You may give your answer in terms of an inverse trigonometric function.
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