In Problems 53 - 56 , (A) Graph f and g in the same coordinate system . (B) Solve f x = g x algebraically to two decimal places. (C) Solve f x > g x using parts A and B (D) Solve f x < g x using parts A and B f x = − 0.9 x 2 + 7.2 x g x = 1.2 x + 5.5 0 ≤ x ≤ 8
In Problems 53 - 56 , (A) Graph f and g in the same coordinate system . (B) Solve f x = g x algebraically to two decimal places. (C) Solve f x > g x using parts A and B (D) Solve f x < g x using parts A and B f x = − 0.9 x 2 + 7.2 x g x = 1.2 x + 5.5 0 ≤ x ≤ 8
Solution Summary: The author compares the functions f(x)=-0.9x 2+7.2x and
(B) Solve
f
x
=
g
x
algebraically to two decimal places.
(C) Solve
f
x
>
g
x
using parts
A
and
B
(D) Solve
f
x
<
g
x
using parts
A
and
B
f
x
=
−
0.9
x
2
+
7.2
x
g
x
=
1.2
x
+
5.5
0
≤
x
≤
8
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
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Assume that a company is considering purchasing a machine for $50,000 that will have a five-year useful life and a $5,000 salvage value. The
machine will lower operating costs by $17,000 per year. The company's required rate of return is 15%. The net present value of this investment
is closest to:
Click here to view Exhibit 12B-1 and Exhibit 12B-2, to determine the appropriate discount factor(s) using the tables provided.
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
Chapter 2 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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