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

When turned about its axis of rotation, which shape could have created this three-dimensional object?

You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. the sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. think about how each function is related to its reciprocal function.how are the graphs of the reciprocal functions related to their corresponding original functions? what happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions

What happens to the area as the sliders are adjusted? what do you think the formula for the area of a triangle is divided by 2?