Reference no: EM13859409
. Let the pressure P and temperature T at a point (x, y, z) be P(x, y, z) =( x^2+2y^2) /( 1 + z^2), T(x, y, z) = 5 + xy z^2
,a. If the position of an airplane at time t is(x(t), y(t), z(t)) = (2t, t^2 1, cost),find d/dt(P T)^2 at time t = 0 as observed from the airplane.
The shape of a hill is given by z = 1000 - 0.02x^2 - 0.01y^2. Assume that the x-axis ispointing East, and the y-axis is pointing North, and all distances are in metres.3 marks (a) What is the direction of the steepest ascent at the point (0, 100, 900)? (The answershould be in terms of directions of the compass).
(b) What is the slope of the hill at the point (0, 100, 900) in the direction from (a)?
(c) If you ride a bicycle on this hill in the direction of the steepest descent at 5 m/s,what is the rate of change of your altitude (with respect to time) as you pass throughthe point (0, 100, 900)?
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What is the direction of the steepest ascent at the point
: The shape of a hill is given by z = 1000 - 0.02x^2 - 0.01y^2. Assume that the x-axis ispointing East, and the y-axis is pointing North, and all distances are in metres.3 marks (a) What is the direction of the steepest ascent at the point (0, 100, 900..
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Find the equation involving t whose solution tells
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