Question

In: Math

The temperature T in a metal ball is inversely proportional to the distance from the center...

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 120 degrees F .

a) Find the rate of change of T at (1, 1,2) in the direction towards the point (2, 1,3).

b) Show that at any point in the ball the direction of greatest increase in the temperature is given by a vector that points toward the origin.

Solutions

Expert Solution

milcah answered 2 years ago
Next > < Previous

Related Solutions

The temperature T in a metal ball is inversely proportional to the distance from the center...
The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 120°. (a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (3, 3, 4).
The temperature T in a metal ball is inversely proportional to the distance from the center...
The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 160°. (a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (3, 1, 4). (b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points...
The temperature T at a point (x,y,z) in space is inversely proportional to the square of...
The temperature T at a point (x,y,z) in space is inversely proportional to the square of the distance from (x,y,z) to the origin. It is known that T(0,0,1) = 500. a. [2] Compute T(2,0,0). b. [3] Find the rate of change of T at the point (2,3,3) in the direction of the point (3,1,1). c. [3] What is the maximal rate of change of T at the point (2,3,3)?
The diffusion rate of a gas is directly proportional to what variables and inversely proportional to...
The diffusion rate of a gas is directly proportional to what variables and inversely proportional to what variables?
What is the relationship (directly proportional, inversely proportional, or no relationship) between dose, clearance, bioavailability, and...
What is the relationship (directly proportional, inversely proportional, or no relationship) between dose, clearance, bioavailability, and steady state plasma concentration?
Which of the following is true of variance? a. Its value is inversely proportional to the...
Which of the following is true of variance? a. Its value is inversely proportional to the degree to which the data is spread from the mean. b. The formula to calculate variance of a population is not the same as the formula to calculate variance of a sample. c. It is the square root of standard deviation. d. It only requires the middle 50% of data to be calculated
Imagine a ball heated to a temperature T. This Ball emits thermions with a current density...
Imagine a ball heated to a temperature T. This Ball emits thermions with a current density at the surface given by C , which is proportional to AG(Richardson's constant) and proportional to W(Work function) . a) Using charge conservation,find the current density at any distance 'r' from center. b) Using continuity equation, find the charge density p(r,t) at time 't' ; t > 0 and it is given that p(r,t=0) = 0. c) By solving Maxwell's equations, also find the...
Dependency is inversely proportional to the alternative sources of supply. If something is plentiful, possession of...
Dependency is inversely proportional to the alternative sources of supply. If something is plentiful, possession of it will not increase your power. What 3 factors create Dependence?
(a) Show that for logarithmic oxidation, the rate of oxide growth dy/dt is inversely proportional to...
(a) Show that for logarithmic oxidation, the rate of oxide growth dy/dt is inversely proportional to the time for large reaction times. (b) Then show that the oxidation rate approaches 0 for a large reaction time.
According to Boyle’s law, for a certain gas, pressure an volume are inversely proportional: P =...
According to Boyle’s law, for a certain gas, pressure an volume are inversely proportional: P = 800/V where V is measured in and pressure P in pounds per square inch. a) Find the rate of change of P when V=20 , and interpret its meaning (carefully state the units). b) Find the average rate of change of P when V changes from 20 to 25 . Compare your result with a).
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT