A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60 for each private lesson, but has a variable cost for each lesson of $35 to pay the instructor. a. Write a linear cost function representing the cost to the studio C x to hold x private lessons for a given month. b. Write a linear revenue function representing the revenue R x for holding x private lessons for the month. c. Write a linear profit function representing the profit P x for holding x private lessons for the month. d. Determine the number of private lessons that must be held for the studio to make a profit. e. If 82 private lessons are held during a given month, how much money will the studio make or lose?
A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60 for each private lesson, but has a variable cost for each lesson of $35 to pay the instructor. a. Write a linear cost function representing the cost to the studio C x to hold x private lessons for a given month. b. Write a linear revenue function representing the revenue R x for holding x private lessons for the month. c. Write a linear profit function representing the profit P x for holding x private lessons for the month. d. Determine the number of private lessons that must be held for the studio to make a profit. e. If 82 private lessons are held during a given month, how much money will the studio make or lose?
A dance studio has fixed monthly costs of
$1500
that include rent, utilities, insurance, and advertising. The studio charges
$60
for each private lesson, but has a variable cost for each lesson of
$35
to pay the instructor.
a. Write a linear cost function representing the cost to the studio
C
x
to hold
x
private lessons for a given month.
b. Write a linear revenue function representing the revenue
R
x
for holding
x
private lessons for the month.
c. Write a linear profit function representing the profit
P
x
for holding
x
private lessons for the month.
d. Determine the number of private lessons that must be held for the studio to make a profit.
e. If 82 private lessons are held during a given month, how much money will the studio make or lose?
Can you help explain what I did based on partial fractions decomposition?
Suppose that a particle moves along a straight line with velocity v (t) = 62t, where 0 < t <3 (v(t)
in meters per second, t in seconds). Find the displacement d (t) at time t and the displacement up to
t = 3.
d(t)
ds
= ["v (s) da = {
The displacement up to t = 3 is
d(3)-
meters.
Let f (x) = x², a 3, and b
=
=
4.
Answer exactly.
a. Find the average value fave of f between a and b.
fave
b. Find a point c where f (c) = fave. Enter only one of the possible values for c.
c=
College Algebra with Modeling & Visualization (5th Edition)
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