Two spacecraft are following paths in space given by r1=〈sin(t),t,t2〉r1=〈sin⁡(t),t,t2〉 and r2=〈cos(t),1−t,t3〉.r2=〈cos⁡(t),1−t,t3〉. If the temperature for...

Two spacecraft are following paths in space given by r1=〈sin(t),t,t2〉r1=〈sin⁡(t),t,t2〉 and r2=〈cos(t),1−t,t3〉.r2=〈cos⁡(t),1−t,t3〉. If the temperature for the points is given by T(x,y,z)=x2y(6−z),T(x,y,z)=x2y(6−z), use the Chain Rule to determine the rate of change of the difference DD in the temperatures the two spacecraft experience at time t=2.t=2.

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

dDdt=dDdt=

Solutions

Expert Solution

The rate of change in the temperature is given by the difference in the rate of change in the temperature with respect to the first aircraft and the rate of change in the temperature with respect to the second aircraft and then evaluated at t=4.

milcah answered 1 year ago

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