Two spacecraft are following paths in space given by r 1 (sin t, t, t 2 ) and r 2 (cos t, 1 t, t 3 ) If the temperature for points in space is given by T(x, y, z) x 2 y(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

Question: Two spacecraft are following paths in space given by r 1 = (sin t, t, t 2 ) and r 2 = (cos t, 1

Two spacecraft are following paths in space given by r₁ = (sin t, t, t²) and r₂ = (cos t, 1 − t, t³). If the temperature for points in space is given by T(x, y, z) = x²y(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 = π.

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