Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 71, Problem 17A
To determine
To sketch:
A right triangle for the given angle and the sides of the triangle are to be labelled as positive or negative.
Label the sides of the triangle as positive or negative.
To find: The reference angles and functions of the angles.
The value of sine, cosine, tangent, cotangent, cosecant, secant for a given angle, up to 4 decimals.
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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 71 Solutions
Mathematics For Machine Technology
Ch. 71 - Prob. 1ACh. 71 - Find the distance y to the nearest hundredth of an...Ch. 71 - Prob. 3ACh. 71 - If A = 3650', determine sin A, cos A, tan A, cot...Ch. 71 - Prob. 5ACh. 71 - Find x.Ch. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 9ACh. 71 - For each angle, sketch a right triangle. Label the...
Ch. 71 - Prob. 11ACh. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 13ACh. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 15ACh. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 17ACh. 71 - For each angle, sketch a right triangle. Label the...
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