The temperature at a point (x, y, z) is given by400ex-3y2- 9z2--_(x, y, z)where T is measured in °C and x, y, z in meters(a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (5, -5, 6)oc/m(b) In which direction does the temperature increase fastest at P?(c) Find the maximum rate of increase at P.

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Asked Dec 3, 2019
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The temperature at a point

(x, y, z)

is given by

T(x, y, z) = 400e−x2 − 3y2 − 9z2

where T is measured in °C and

x, y, z

in meters.

The temperature at a point (x, y, z) is given by
400ex-3y2- 9z2
--_
(x, y, z)
where T is measured in °C and x, y, z in meters
(a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (5, -5, 6)
oc/m
(b) In which direction does the temperature increase fastest at P?
(c) Find the maximum rate of increase at P.
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The temperature at a point (x, y, z) is given by 400ex-3y2- 9z2 --_ (x, y, z) where T is measured in °C and x, y, z in meters (a) Find the rate of change of temperature at the point P(4, -1, 2) in the direction towards the point (5, -5, 6) oc/m (b) In which direction does the temperature increase fastest at P? (c) Find the maximum rate of increase at P.

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Expert Answer

Step 1

As the question doesnt specifies the part to be answered so answering the part 'a' of the question here.

The...

T(x,y,z)= 400e-3y2-9;
T=-800xe-3y2-92
T, =-2400ye-3y2-92?
T. =-7200zer-3y2-922
(x,y,z) = 400e*-3y2_9x?
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T(x,y,z)= 400e-3y2-9; T=-800xe-3y2-92 T, =-2400ye-3y2-92? T. =-7200zer-3y2-922 (x,y,z) = 400e*-3y2_9x?

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