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. Find the rate of change of temperature at the point P(2, −1, 3) in the direction towards the point (6, −4, 6).

Rate of change C per meter.

Step-by-step explanation:

Given,

Then,

Change of temperature at the point say, along the direction say, is,

=

Hence the rate of change  of temperature is C per meter.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

1 mph

step-by-step explanation:

if the question is asking how much does she drive per mile then,

13 / 13 = 1 mph