Suppose f(x,y,z) = Ax2 + Bxy + Cxyz2. What is ▽f? Near the surface of Earth Fdirection (up)We can also write this as F- (mgy)• = "Del" = â+ŷ³y + 2 ºz = a measure of how something changes in space.дz●gravəду●●- (mgy) =-ŷ (mgy) = -mgŷWhat is the meaning of f(x,y,z)??grav●=: -mgŷ where ŷ is unit vector that points in the y-is called "Del" or "Gradient"is an operator that converts a scalar function into a vector.If f(x,y,z) is some general function of position, f(x,y,z) is a vector that points in thedirection that the function f(x,y,z) increases the fastest.Conservative forces are related to changes in potential energy:• In general, Fcons = −(PE)A conservative force points in the direction that the associated potential energydecreases the fastest.Golden Rule: Nature runs downhill! Left on her own, Nature tries to minimize thepotential energy.Problem : Suppose f(x,y,z) = Ax² + Bxy + Cxyz². What is f?

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Suppose f(x,y,z) = Ax2 + Bxy + Cxyz2. What is ▽f?

Horizons: Exploring the Universe (MindTap Course List)

14th Edition

ISBN:9781305960961

Author:Michael A. Seeds, Dana Backman

Publisher:Michael A. Seeds, Dana Backman

Chapter20: Astrobiology: Life On Other Worlds

Section: Chapter Questions

Problem 6P

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According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

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Suppose f(x,y,z) = Ax² + Bxy + Cxyz². What is ▽f?

Near the surface of Earth F
direction (up)
We can also write this as F
- (mgy)
• = "Del" = â+ŷ³y + 2 ºz = a measure of how something changes in space.
дz
●
grav
ə
ду
●
●
- (mgy) =-ŷ (mgy) = -mgŷ
What is the meaning of f(x,y,z)??
grav
●
=
: -mgŷ where ŷ is unit vector that points in the y-
is called "Del" or "Gradient"
is an operator that converts a scalar function into a vector.
If f(x,y,z) is some general function of position, f(x,y,z) is a vector that points in the
direction that the function f(x,y,z) increases the fastest.
Conservative forces are related to changes in potential energy:
• In general, Fcons = −(PE)
A conservative force points in the direction that the associated potential energy
decreases the fastest.
Golden Rule: Nature runs downhill! Left on her own, Nature tries to minimize the
potential energy.
Problem : Suppose f(x,y,z) = Ax² + Bxy + Cxyz². What is f?

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