The function F of v if the actual frequency of sound emitted by the ambulance is 560 H z when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by F v = f a s 0 s 0 − v , where f a is the actual frequency of the sound at the source, s 0 is the speed of the sound in air 772.4 mph , and v is the speed at which the source of sound is moving toward the observer.
The function F of v if the actual frequency of sound emitted by the ambulance is 560 H z when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by F v = f a s 0 s 0 − v , where f a is the actual frequency of the sound at the source, s 0 is the speed of the sound in air 772.4 mph , and v is the speed at which the source of sound is moving toward the observer.
Solution Summary: The author explains the cost function F of v if the actual frequency of sound emitted by the ambulance is 560Hz.
The function F of v if the actual frequency of sound emitted by the ambulance is 560Hz when an ambulance is moving toward an observer and the frequency of a sound relative to an observer is given by Fv=fas0s0−v , where fa is the actual frequency of the sound at the source, s0 is the speed of the sound in air 772.4mph , and v is the speed at which the source of sound is moving toward the observer.
(b)
To determine
To graph: The sketch of a function given by Fv=560772.4772.4−v on the window 0,1000,100by0,5000,1000 .
(c)
To determine
The effect of the frequency of sound when the speed of the ambulance increases.
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
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