Construction. A construction company has 840 feet of chain-link fence that is used to enclose storage areas for equipment and materials at construction sites. The supervisor wants to set up two identical rectangular storage areas sharing a common fence (see the figure). Assuming that all fencing is used, (A) Express the total area A x enclosed by both pens as a function of x . (B) From physical considerations, what is the domain of the function A ? (C) Graph function A in a rectangular coordinate system . (D) Use the graph to discuss the number and approximate locations of values of x that would produce storage areas with a combined area of 25 , 000 square feet. (E) Approximate graphically (to the nearest foot) the values of x that would produce storage areas with a combined area of 25 , 000 square feet. (F) Determine algebraically the dimensions of the storage areas that have the maximum total combined area. What is the maximum area?
Construction. A construction company has 840 feet of chain-link fence that is used to enclose storage areas for equipment and materials at construction sites. The supervisor wants to set up two identical rectangular storage areas sharing a common fence (see the figure). Assuming that all fencing is used, (A) Express the total area A x enclosed by both pens as a function of x . (B) From physical considerations, what is the domain of the function A ? (C) Graph function A in a rectangular coordinate system . (D) Use the graph to discuss the number and approximate locations of values of x that would produce storage areas with a combined area of 25 , 000 square feet. (E) Approximate graphically (to the nearest foot) the values of x that would produce storage areas with a combined area of 25 , 000 square feet. (F) Determine algebraically the dimensions of the storage areas that have the maximum total combined area. What is the maximum area?
Construction. A construction company has
840
feet of chain-link fence that is used to enclose storage areas for equipment and materials at construction sites. The supervisor wants to set up two identical rectangular storage areas sharing a common fence (see the figure).
Assuming that all fencing is used,
(A) Express the total area
A
x
enclosed by both pens as a function of
x
.
(B) From physical considerations, what is the domain of the function
A
?
(C) Graph function A in a rectangular coordinate system.
(D) Use the graph to discuss the number and approximate locations of values of
x
that would produce storage areas with a combined area of
25
,
000
square feet.
(E) Approximate graphically (to the nearest foot) the values of
x
that would produce storage areas with a combined area of
25
,
000
square feet.
(F) Determine algebraically the dimensions of the storage areas that have the maximum total combined area. What is the maximum area?
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Q2: Using the Laplace transform, find the solution for the following equation
y"" +y" = 6et + 6t + 6. Suppose zero initial conditions (y"" (0) = y"(0) = y'(0) = y(0) = 0).
1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
3. Let
f(z) =
sin (22) + cos (T2)
2(22+1)(z+1)
Compute f(z)dz over each of the contours/closed curves C1, C2, C3 and C4 shown
below.
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Chapter 2 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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