For Exercises 47-50, find the bearing to the nearest tenth of a degree. A boat leaves Matheson Hammock Marina at a constant speed of 3.5 mph . The boat travels south for 36 min and then east for 24 min to a favorite fishing spot. After a day of fishing, find the bearing that the captain should use to travel back to the marina.
For Exercises 47-50, find the bearing to the nearest tenth of a degree. A boat leaves Matheson Hammock Marina at a constant speed of 3.5 mph . The boat travels south for 36 min and then east for 24 min to a favorite fishing spot. After a day of fishing, find the bearing that the captain should use to travel back to the marina.
For Exercises 47-50, find the bearing to the nearest tenth of a degree.
A boat leaves Matheson Hammock Marina at a constant speed of
3.5
mph
. The boat travels south for
36
min
and then east for
24
min
to a favorite fishing spot. After a day of fishing, find the bearing that the captain should use to travel back to the marina.
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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