A cleaning company charges $ 100 for each office it cleans. The fixed monthly cost of $ 480 for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is $ 52 per office and includes labor, gasoline, and cleaning supplies. (See Example 9) a. Write a linear cost function representing the cost C x in $ to the company to clean x offices per month. b. Write a linear revenue function representing the revenue R x in $ for cleaning x offices per month. c. Determine the number of offices to be cleaned per month for the company to break even. d. If 28 offices are cleaned, will the company make money or lose money?
A cleaning company charges $ 100 for each office it cleans. The fixed monthly cost of $ 480 for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is $ 52 per office and includes labor, gasoline, and cleaning supplies. (See Example 9) a. Write a linear cost function representing the cost C x in $ to the company to clean x offices per month. b. Write a linear revenue function representing the revenue R x in $ for cleaning x offices per month. c. Determine the number of offices to be cleaned per month for the company to break even. d. If 28 offices are cleaned, will the company make money or lose money?
A cleaning company charges
$
100
for each office it cleans. The fixed monthly cost of
$
480
for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is
$
52
per office and includes labor, gasoline, and cleaning supplies. (See Example 9)
a. Write a linear cost function representing the cost
C
x
in $
to the company to clean
x
offices per month.
b. Write a linear revenue function representing the revenue
R
x
in $
for cleaning
x
offices per month.
c. Determine the number of offices to be cleaned per month for the company to break even.
d. If 28 offices are cleaned, will the company make money or lose money?
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.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.