Osakai.rutgers.edu : MULI ×/14.5 The Gracient and D cowww.webassi x.e35. 5uopose

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Osakai.rutgers.edu : MULI ×/14.5 The Gracient and D cowww.webassi x.e35. 5uopose You Are Hik > 9. 0.91/1 points | Previous Anawons RogaCalcET3 14535 My Notes Ask Your Assume that the positive x-axis points East and the positive y-axis points North. Suppose you are hiking on a terrain modeled by z = xy + y3-x2. You are at the point (5, 1,-19). (a) Determine the slope you would encounter if you headed due West from your position. What angle of inclination docs that correspond to7 (Round your answer to three decimal placcs.) 1.480 radians (b Deter 17 the slope you would encounter if yuu eaded due North-West from your position. What angle of inclination does that correspond to? (Round your answer to three decimal places.) 4B8 radians (c) Determine the slope you would encounter If you headed due South East from your positlon. What angle of Inclinatlon does that correspond to (Round your answer to three decimal places.) 1 48 radians (d)Delermine the sleeesl slope yuu ould encouiler Iyour posiliun. 115 Determine the compass dirertinn measured wise in degrees from st that you would head to realize this steepest slope. (Round your answer to three decimal places.) 138.3x eBook 247 PM O Type here to search 217/2018

Explanation / Answer

9)

z=xy +y3-x2

gradient,f= y-2x,x+3y2

at point (5,1,-19)

gradient,f= 1-2*5,5+3*12

f= -9,8

(a)

unit direction vector = -1,0

slope =-9,8.-1,0

slope =(-9*-1)+(8*0)

slope =9

inclination =tan-1(9)

inclination =1.460 radians

(b)

unit direction vector = -1/2,1/2

slope =-9,8.-1/2,1/2

slope =(-9*-1/2)+(8*1/2)

slope =17/2

inclination =tan-1(17/2)

inclination =1.488 radians

(c)

unit direction vector = 1/2,-1/2

slope =-9,8.1/2,-1/2

slope =(-9*1/2)+(8*-1/2)

slope =-17/2

inclination =-tan-1(17/2)

inclination =-1.488 radians

(d)

f= -9,8

steepest slope =|f|

steepest slope =[(-9)2+82]

steepest slope =145

=180o-tan-1(8/9)

=180o-41.633539336570198878182940192603o

=138.3664606634298011218170598074o

=138.366o

compass direction =N (138.366o-90o )W

compass direction =N 48.366o W

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