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18. Find the point on the plane 2x + 5y +z= 10 that is nearest to (2,0,1). What are the values of x, y, and z for the point? y= (Type integers or simplified fractions.)

18. Find the point on the plane 2x + 5y +z= 10 that is nearest to (2,0,1). What are the values of x, y, and z for the point? y= (Type integers or simplified fractions.)

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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18. Find the point on the plane 2x + 5y +z= 10 that is nearest to (2,0,1). What are the values of x, y, and z for the point? y = z= (Type integers or simplified fractions.) 19. Find the unit tangent vector T and the curvature K for the following parameterized curve. r(t) = (17 cos t,3 cos t,4 sin t) The unit tangent vector is T= ( (Type exact answers, using radicals as needed.) The curvature is K= 20. A box is to be made where the material for the sides and the lid cost $0.20 per square foot and the cost for the bottom is $0.50 per square foot. Find the dimensions of a box with volume 5 cubic feet that has minimum cost. The box with volume 5 cubic feet that has minimum cost has length ft, width ft, and height ft. (Round to four decimal places as needed.)
Transcribed Image Text:18. Find the point on the plane 2x + 5y +z= 10 that is nearest to (2,0,1). What are the values of x, y, and z for the point? y = z= (Type integers or simplified fractions.) 19. Find the unit tangent vector T and the curvature K for the following parameterized curve. r(t) = (17 cos t,3 cos t,4 sin t) The unit tangent vector is T= ( (Type exact answers, using radicals as needed.) The curvature is K= 20. A box is to be made where the material for the sides and the lid cost $0.20 per square foot and the cost for the bottom is $0.50 per square foot. Find the dimensions of a box with volume 5 cubic feet that has minimum cost. The box with volume 5 cubic feet that has minimum cost has length ft, width ft, and height ft. (Round to four decimal places as needed.)
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