A college theater has a seating capacity of 2000. It reserves x tickets for students and y tickets for general admission. For parts (a)-(d) write an inequality to represent the given statement. a. The total number of seats available is at most 2000. b. The college wants to reserve at least 3 times as many student tickets as general admission tickets. c. The number of student tickets cannot be negative. d. The number of general admission tickets cannot be negative. e. Graph the solution set to the system of inequalities from parts (a)-(d).
A college theater has a seating capacity of 2000. It reserves x tickets for students and y tickets for general admission. For parts (a)-(d) write an inequality to represent the given statement. a. The total number of seats available is at most 2000. b. The college wants to reserve at least 3 times as many student tickets as general admission tickets. c. The number of student tickets cannot be negative. d. The number of general admission tickets cannot be negative. e. Graph the solution set to the system of inequalities from parts (a)-(d).
Solution Summary: The author explains that the required inequality is x+yle 2000. The number of student tickets cannot be negative.
A college theater has a seating capacity of
2000.
It reserves
x
tickets for students and
y
tickets for general admission. For parts (a)-(d) write an inequality to represent the given statement.
a. The total number of seats available is at most
2000.
b. The college wants to reserve at least
3
times as many student tickets as general admission tickets.
c. The number of student tickets cannot be negative.
d. The number of general admission tickets cannot be negative.
e. Graph the solution set to the system of inequalities from parts (a)-(d).
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.
Elementary Statistics: Picturing the World (7th Edition)
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