5. Amy the ant is walking along a path r(t) formed by the intersection of two rock surfaces. One surface, a curved vertical wall, is described by y = x² and the other surface is a plane described by z = x + y. (Ground level would be the ry-plane). Amy is walking on r(t) in such a way that her x-coordinate is given by x(t) = t. At some time, t*, Amy is at the point P(1,1,2). The temperature outside that morning is given by T(x, y, z) = xyz + 20. (a) Determine b Determine the umt tangent. T on Amy's path, at time meterization of Amy's path, r(t) O As Amy passes over the point P, calculate the value (d) As Amy passes over the point P, calculate the value of , where s is arc length along the path. (e) As Amy passes over the point P, calculate the value of dh, where h is Amy's height above ground level. ds

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 13AEXP
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5. Amy the ant is walking along a path r(t) formed by the intersection of two rock surfaces. One surface, a curved vertical wall, is
described by y = x² and the other surface is a plane described by z = x + y. (Ground level would be the ry-plane). Amy is
walking on r(t) in such a way that her x-coordinate is given by x(t) = t. At some time, t*, Amy is at the point P(1,1,2). The
temperature outside that morning is given by T(x, y, z) = xyz + 20.
(a) Determine
b Determine the umt tangent. T on Amy's path, at time
meterization of Amy's path, r(t)
O As Amy passes over the point P, calculate the value
(d) As Amy passes over the point P, calculate the value of , where s is arc length along the path.
(e) As Amy passes over the point P, calculate the value of dh, where h is Amy's height above ground level.
ds
Transcribed Image Text:5. Amy the ant is walking along a path r(t) formed by the intersection of two rock surfaces. One surface, a curved vertical wall, is described by y = x² and the other surface is a plane described by z = x + y. (Ground level would be the ry-plane). Amy is walking on r(t) in such a way that her x-coordinate is given by x(t) = t. At some time, t*, Amy is at the point P(1,1,2). The temperature outside that morning is given by T(x, y, z) = xyz + 20. (a) Determine b Determine the umt tangent. T on Amy's path, at time meterization of Amy's path, r(t) O As Amy passes over the point P, calculate the value (d) As Amy passes over the point P, calculate the value of , where s is arc length along the path. (e) As Amy passes over the point P, calculate the value of dh, where h is Amy's height above ground level. ds
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