The temperature at a point (x, y,z) is given by T(x, y,z)=200e^-x^2-3y^-9z^2, where T measured in degrees Celsius and x, y,z in meters. Find the rate of change of temperature at the point P(2, -1, 2) in the direction toward the point (3, -3, 3)

Therefore the rate change of temperature at the point P(2,-1,2) in the direction toward the point (3,-3,3) is  °C/m.

Step-by-step explanation:

Given that, the temperature at a point (x,y,z) is

.

Rate change of temperature at the point P(2,-1,2) in the direction toward the point Q (3,-3,3) is

The gradient of the temperature

V==(3,-3,3)-(2,-1,2)=(1,-2,1)

The unit vector of V is

Therefore,

                        °C/m

Therefore the rate change of temperature at the point P(2,-1,2) in the direction toward the point (3,-3,3) is  °C/m.

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.