5 Use a spreadsheet to numerically verify the result of Exercises 1-55. For Exercises 23-28 find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit, Assume that revenue, R ( x ) , a n d cos t , C ( x ) , a r e i n d o l l a r s f o r Exercises 23-26 Maximizing parking tickets. Oak Glen currently employs 8 patrol officers who each write an average of 24 parking tickets per day For every additional officer placed on patrol, the average number of parking tickets per day written by each officer decreases by 4 How many additional officers should be placed on patrol in order to maximize the number of parking tickets written per day?
5 Use a spreadsheet to numerically verify the result of Exercises 1-55. For Exercises 23-28 find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit, Assume that revenue, R ( x ) , a n d cos t , C ( x ) , a r e i n d o l l a r s f o r Exercises 23-26 Maximizing parking tickets. Oak Glen currently employs 8 patrol officers who each write an average of 24 parking tickets per day For every additional officer placed on patrol, the average number of parking tickets per day written by each officer decreases by 4 How many additional officers should be placed on patrol in order to maximize the number of parking tickets written per day?
5 Use a spreadsheet to numerically verify the result of Exercises 1-55.
For Exercises 23-28 find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit, Assume that revenue,
R
(
x
)
,
a
n
d
cos
t
,
C
(
x
)
,
a
r
e
i
n
d
o
l
l
a
r
s
f
o
r
Exercises 23-26
Maximizing parking tickets. Oak Glen currently employs 8 patrol officers who each write an average of 24 parking tickets per day For every additional officer placed on patrol, the average number of parking tickets per day written by each officer decreases by 4 How many additional officers should be placed on patrol in order to maximize the number of parking tickets written per day?
Question 3 (5pt): A chemical reaction. In an elementary chemical reaction,
single molecules of two reactants A and B form a molecule of the product C :
ABC. The law of mass action states that the rate of reaction is proportional
to the product of the concentrations of A and B:
d[C]
dt
= k[A][B]
(where k is a constant positive number). Thus, if the initial concentrations are
[A] =
= a moles/L and [B] = b moles/L we write x = [C], then we have
(E):
dx
dt
=
k(ax)(b-x)
1
(a) Write the differential equation (E) with separate variables, i.e. of the form
f(x)dx = g(t)dt.
(b) Assume first that a b. Show that
1
1
1
1
=
(a - x) (b - x)
-
a) a - x
b - x
b)
(c) Find an antiderivative for the function f(x) = (a-x) (b-x) using the previous
question.
(d) Solve the differentiel equation (E), i.e. find x as a function of t. Use the fact
that the initial concentration of C is 0.
(e) Now assume that a = b. Find x(t) assuming that a = b. How does this
expression for x(t) simplify if it is known that [C] =…
3) Find the volume of the solid that lies inside both the sphere x² + y² + z²
cylinder x²+y² = 1.
= 4 and the
1) Compute the following limit.
lim
x-0
2 cos(x) 2x²
-
x4
Chapter 2 Solutions
Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
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