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
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
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)?
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The diffusion rate of a gas is directly proportional to what
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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
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c.
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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
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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
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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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