The temperature at a point

(x, y, z)

is given by

T(x, y, z) = 300e−x2 − 3y2 − 7z2

where T is measured in °C and

x, y, z

in meters.

(a) Find the rate of change of temperature at the point

P(2, −1, 3)

in the direction towards the point

(5, −3, 4).

°C/m

(b) In which direction does the temperature increase fastest at P?

(c) Find the maximum rate of increase at P.

Expert Answer

3

step-by-step explanation:

because where the point where the 2 lines intersect is (3,-1) the x value is 3

answer: 5

step-by-step explanation:

since, the range is the difference between the lowest and highest values of the given sample space.

and, here the sample space = { 3, 1, 0, 4, 1, 4, 2, 3, 0, 5, 0, 1, 1, 2, 0, 4, 1,4, 4 ,2 ,3 ,2 ,0 ,1 ,4 }

here, the highest value of the given sample = 5

and, the lowest value = 0

therefore, the range of the sample space = 5 - 0 = 5