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 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 towards the origin.
Solutions
milcah answered 2 years agoRelated 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 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...
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?
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What is the relationship (directly proportional, inversely
proportional, or no relationship) between dose, clearance,
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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).
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