Mathematics: The temperature at a point (x, y, z) is given by t(x, y, z) = 200e−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(4, −1, 4) in the direction towards the point (5, −5, 6).

The temperature at a point (x, y, z) is given by

Ответ:

prettyswagg63oz3tyz

10.01.2022

Mathematics

Looks like the temperature is given by

$t(x,y,z)=200e^{-x^2-3y^2-7z^2}$

We have gradient at any point (x,y,z)

$\nabla t(x,y,z)=200e^{-x^2-3y^2-7z^2}(-2x,-6y,-14z)$

Then the rate of change of at in the direction of (5, -5, 6) is given by

$\nabla t(4,-1,4)\cdot\dfrac{(5,-5,6)}{\|(5,-5,6)\|}=\left(-\dfrac{400}{e^{131}}(4,-3,28)\right)\cdot\dfrac{(5,-5,6)}{\sqrt{86}}=-\dfrac{40600}{e^{131}}\sqrt{\dfrac2{43}}$

which is very nearly 0.

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Ответ:

ashtynbursiaga

12.02.2022

Mathematics

(from top row to bottom row, left to right) 4, 32, 128, 12, 24, 96

Step-by-step explanation:

So, the first pair in the table would be 2/3 (club soda to grape juice). You can use that pair, or in other mathematical terms fraction, to generate other fractions equivalent to it, such as 4/6, 8/12, and 16/24 (those are some of the fractions in the table btw :D).

Hope this helped :D

(and have a great day/afternoon/night!!)

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The temperature at a point (x, y, z) is given by t(x, y, z) = 200e−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(4, −1, 4) in the direction towards the point (5, −5, 6).

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