A ship leaves port at 8 knots heading N 27 ° W . After 2 hr it makes a 90 ° clockwise turn to a new bearing of N 63 ° E and travels for 1.4 hr . (See Example 7) a. Find the ship's distance from port to the nearest tenth of a nautical mile. b. Find the bearing required for the ship to return to port. Round to the nearest degree.
A ship leaves port at 8 knots heading N 27 ° W . After 2 hr it makes a 90 ° clockwise turn to a new bearing of N 63 ° E and travels for 1.4 hr . (See Example 7) a. Find the ship's distance from port to the nearest tenth of a nautical mile. b. Find the bearing required for the ship to return to port. Round to the nearest degree.
A ship leaves port at
8
knots heading
N
27
°
W
. After
2
hr
it makes a
90
°
clockwise turn to a new bearing of
N
63
°
E
and travels for
1.4
hr
. (See Example 7)
a. Find the ship's distance from port to the nearest tenth of a nautical mile.
b. Find the bearing required for the ship to return to port. Round to the nearest degree.
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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How to apply the law of sines to find the remaining parts of a triangle; Author: Brian McLogan;https://www.youtube.com/watch?v=NdRF18HWkmE;License: Standard YouTube License, CC-BY