The temperature at a point (x,y,z) is given by T(x,y,z)=200ex2(y2)/4(z2)/9, wher
ID: 2850124 • Letter: T
Question
The temperature at a point (x,y,z) is given by T(x,y,z)=200ex2(y2)/4(z2)/9, where T is measured in degrees Celsius and x, y, and zin meters. There are lots of places to make silly errors in this problem; just try to keep track of what needs to be a unit vector.
Find the rate of change of the temperature at the point (-1, 1, -2) in the direction toward the point (3, -1, -3).
the answer I got that is incorrect: 480t^14
In which direction (unit vector) does the temperature increase the fastest at (-1, 1, -2)?
the answer I got that is incorrect: 36/sqrt469,-18/sqrt469 ,1/sqrt469
What is the maximum rate of increase of T at (-1, 1, -2)?
the answer I got that is incorrect: 400e^(-61/36)sqrt496
Please help, will rate highly if answer is correct!!
Explanation / Answer
T(x,y,z)=200ex2(y2)/4(z2)/9
T=<-2x,-y/2,-2z/9>
at the point (-1, 1, -2)=>T=<2,-1/2,4/9>
vectorat the point (-1, 1, -2) in the direction toward the point (3, -1, -3). =(3, -1, -3)-(-1, 1, -2)=<4, -2, -1>
rate of change of the temperature at the point (-1, 1, -2) in the direction toward the point (3, -1, -3).
=<2,-1/2,4/9><4, -2, -1>/|<4, -2, -1>|
=(2+1-(4/9)/[(4)2+(-2)2+(-1)2]
=23/(921)
=0.558
direction (unit vector) does the temperature increase the fastest at (-1, 1, -2)
T/|T|=<2,-1/2,4/9>/[(2)2+(-1/2)2+(4/9)2]
T/|T|=<2,-1/2,4/9>/[1441/324]
T/|T|=<2/[1441/324],(-1/2)/[1441/324],(4/9)/[1441/324]>
T/|T|=<0.948,-0.237,0.2107>
maximum rate of increase of T at (-1, 1, -2)=|T|=2.11
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.