5 Use a spreadsheet to numerically verify the result of Exercises 1-55. Maximizing area. Grayson Farms plans to enclose three parallel rectangular livestock pens within one large rectangular area using 600 ft of fencing One side of the enclosure is a pre-existing stone wall. a. If the three rectangular pens have their longer sides parallel to the stone wall, find the largest possible total area that can be enclosed b. If the three rectangular pens have their shorter sides perpendicular to the stone wall, find the largest possible total area that can be enclosed
5 Use a spreadsheet to numerically verify the result of Exercises 1-55. Maximizing area. Grayson Farms plans to enclose three parallel rectangular livestock pens within one large rectangular area using 600 ft of fencing One side of the enclosure is a pre-existing stone wall. a. If the three rectangular pens have their longer sides parallel to the stone wall, find the largest possible total area that can be enclosed b. If the three rectangular pens have their shorter sides perpendicular to the stone wall, find the largest possible total area that can be enclosed
Solution Summary: The author calculates the largest possible area that can be enclosed by three parallel livestock pens with in one large rectangular area by 600 ft of fencing.
5 Use a spreadsheet to numerically verify the result of Exercises 1-55.
Maximizing area. Grayson Farms plans to enclose three parallel rectangular livestock pens within one large rectangular area using 600 ft of fencing One side of the enclosure is a pre-existing stone wall.
a. If the three rectangular pens have their longer sides parallel to the stone wall, find the largest possible total area that can be enclosed
b. If the three rectangular pens have their shorter sides perpendicular to the stone wall, find the largest possible total area that can be enclosed
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
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)
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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