Question

Two spacecraft are following paths in space given by r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for the points is given by T(x,y,z)=x^2y(1−z), use the Chain Rule to determine the rate of change of the difference D in the temperatures the two spacecraft experience at time t=3.

(Use decimal notation. Give your answer to two decimal places.)

Answer #1

Two spacecraft are following paths in space given by
r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for
the points is given by T(x,y,z)=x^2y(8−z), use the Chain Rule to
determine the rate of change of the difference D in the
temperatures the two spacecraft experience at time t=1.
(Use decimal notation. Give your answer to two decimal
places.)

Two spacecraft are following paths in space given by
r1=〈sin(t),t,t^2〉r1=〈sin(t),t,t^2〉 and
r2=〈cos(t),1−t,t^3〉.r2=〈cos(t),1−t,t^3〉. If the temperature for
the points is given by T(x,y,z)=x^2y(5−z),T(x,y,z)=x^2y(5−z), use
the Chain Rule to determine the rate of change of the difference D
in the temperatures the two spacecraft experience at time t=2.
(Use decimal notation. Give your answer to two decimal
places.)

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