Mathematics for the Trades: A Guided Approach, Books a la Carte edition (11th Edition)
11th Edition
ISBN: 9780134765785
Author: Hal Saunders
Publisher: PEARSON
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Chapter 9, Problem 7BPS
Practical Applications
Manufacturing How many cubic feet of propane will the tank in the figure contain? (1 ft3 = 1728 in.3) (Round to the nearest tenth of a cubic foot.)
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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
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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 9 Solutions
Mathematics for the Trades: A Guided Approach, Books a la Carte edition (11th Edition)
Ch. 9.1 - What is the perimeter of a regular hexagon with...Ch. 9.1 - Find the area:Ch. 9.1 - Find the volume of each of the following right...Ch. 9.1 - Find the volume of each of the following right...Ch. 9.1 - Find the volume of each of the following right...Ch. 9.1 - Find the volume of each of the following right...Ch. 9.1 - Prob. 5AECh. 9.1 - Find the volume of each of the following right...Ch. 9.1 - Find the volume of each of the following right...Ch. 9.1 - Find the volume of each of the following right...
Ch. 9.1 - Find the lateral surface area and the volume of...Ch. 9.1 - Find the lateral surface area and the volume of...Ch. 9.1 - Find the lateral surface area and the volume of...Ch. 9.1 - Find the lateral surface area and the volume of...Ch. 9.1 - Find the lateral surface area and the volume of...Ch. 9.1 - Find the lateral surface area and the volume of...Ch. 9.1 - C. Find the total outside surface area and the...Ch. 9.1 - C. Find the total outside surface area and the...Ch. 9.1 - C. Find the total outside surface area and the...Ch. 9.1 - C. Find the total outside surface area and the...Ch. 9.1 - C. Find the total outside surface area and the...Ch. 9.1 - C. Find the total outside surface area and the...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.1 - Practical Applications. Round to the nearest tenth...Ch. 9.2 - What type of triangle has two equal sides?Ch. 9.2 - What is the formula for the area of an equilateral...Ch. 9.2 - Prob. 1AECh. 9.2 - Prob. 2AECh. 9.2 - Prob. 3AECh. 9.2 - Prob. 4AECh. 9.2 - Prob. 5AECh. 9.2 - Prob. 6AECh. 9.2 - Prob. 7AECh. 9.2 - Prob. 8AECh. 9.2 - Find the total outside surface area and volume of...Ch. 9.2 - Find the total outside surface area and volume of...Ch. 9.2 - Find the total outside surface area and volume of...Ch. 9.2 - Find the total outside surface area and volume of...Ch. 9.2 - Find the total outside surface area and volume of...Ch. 9.2 - Find the total outside surface area and volume of...Ch. 9.2 - Find the total outside surface area and volume of...Ch. 9.2 - B. Find the total outside surface area and volume...Ch. 9.2 - Prob. 1CECh. 9.2 - C. Practical Applications Metalworking A...Ch. 9.2 - Prob. 3CECh. 9.2 - C. Practical Applications Agriculture How many...Ch. 9.2 - C. Practical Applications Sheet Metal Trades How...Ch. 9.2 - C. Practical Applications Construction How many...Ch. 9.3 - What is the formula for the circumference of a...Ch. 9.3 - Find the area of a circle with diameter 10 cm....Ch. 9.3 - Find the lateral surface area and volume of each...Ch. 9.3 - Find the lateral surface area and volume of each...Ch. 9.3 - Find the lateral surface area and volume of each...Ch. 9.3 - Find the lateral surface area and volume of each...Ch. 9.3 - Find the lateral surface area and volume of each...Ch. 9.3 - Find the lateral surface area and volume of each...Ch. 9.3 - Find the total surface area and volume of each of...Ch. 9.3 - Find the total surface area and volume of each of...Ch. 9.3 - Find the total surface area and volume of each of...Ch. 9.3 - Find the total surface area and volume of each of...Ch. 9.3 - Find the total surface area and volume of each of...Ch. 9.3 - Find the total surface area and volume of each of...Ch. 9.3 - Practical Applications. (Round to the nearest...Ch. 9.3 - Practical Applications. (Round to the nearest...Ch. 9.3 - Practical Applications. (Round to the nearest...Ch. 9.3 - Practical Applications. (Round to the nearest...Ch. 9.3 - Practical Applications. (Round to the nearest...Ch. 9.3 - Practical Applications. (Round to the nearest...Ch. 9.3 - Practical Applications. (Round to the nearest...Ch. 9.3 - Industrial Technology How high should a 50-gal...Ch. 9.3 - Plumbing A marble-top bathroom sink has the shape...Ch. 9.3 - Sheet Metal Trades How many square inches of sheet...Ch. 9.3 - Machine Trades What is the weight of the bushing...Ch. 9.3 - Manufacturing Find the capacity in gallons of the...Ch. 9.3 - Plumbing A septic tank has the shape shown in the...Ch. 9.3 - Construction How many cubic yards of concrete are...Ch. 9.3 - Machine Trades At a density of 0.0925 lb/in.3,...Ch. 9.3 - Painting A spherical tank has a diameter of 16.5...Ch. 9.3 - Industrial Technology A cylindrical tank 72 cm in...Ch. 9.3 - Agriculture The water tower shown in the figure...Ch. 9.3 - Automotive Trades In an automobile engine, the...Ch. 9.3 - Automotive Trades A cylindrical hose 24 in. long...Ch. 9.3 - Agriculture The water trough shown in the figure...Ch. 9.3 - Painting The metal silo shown in the figure has a...Ch. 9.3 - Construction An outdoor cylindrical fire pit has...Ch. 9.3 - Water/Wastewater Treatment Due to a rupture in a...Ch. 9.3 - Manufacturing If a particular extrusion process is...Ch. 9.4 - Find c:Ch. 9.4 - Prob. 2LCCh. 9.4 - Find the lateral surface area and volume of each...Ch. 9.4 - Find the lateral surface area and volume of each...Ch. 9.4 - Find the lateral surface area and volume of each...Ch. 9.4 - Find the lateral surface area and volume of each...Ch. 9.4 - Prob. 1BECh. 9.4 - Prob. 2BECh. 9.4 - Find the lateral surface area and volume of each...Ch. 9.4 - Find the lateral surface area and volume of each...Ch. 9.4 - Prob. 1CECh. 9.4 - Find the volume of each figure. (Use 3.14 and...Ch. 9.4 - Find the volume of each figure. (Use 3.14 and...Ch. 9.4 - Find the volume of each figure. (Use 3.14 and...Ch. 9.4 - Prob. 1DECh. 9.4 - Prob. 2DECh. 9.4 - Prob. 3DECh. 9.4 - Practical Applications. (Round to the nearest...Ch. 9.4 - Prob. 5DECh. 9.4 - Practical Applications. (Round to the nearest...Ch. 9.4 - Practical Applications. (Round to the nearest...Ch. 9.4 - Practical Applications. (Round to the nearest...Ch. 9.4 - Prob. 9DECh. 9.4 - Welding A cone-shaped hopper is constructed by...Ch. 9.4 - Prob. 11DECh. 9.4 - Practical Applications. (Round to the nearest...Ch. 9.4 - Practical Applications. (Round to the nearest...Ch. 9 - Identify solid figures, including prisms, cubes,...Ch. 9 - Find the surface area and volume of solid objects....Ch. 9 - Solve practical problems involving solid figures....Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Prob. 12APSCh. 9 - Prob. 13APSCh. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Prob. 17APSCh. 9 - Solve the following problems involving solid...Ch. 9 - Solve the following problems involving solid...Ch. 9 - Prob. 20APSCh. 9 - Prob. 21APSCh. 9 - Practical Applications Manufacturing How many...Ch. 9 - Practical Applications Construction How many cubic...Ch. 9 - Practical Applications Metalworking What is the...Ch. 9 - Practical Applications Plumbing What is the...Ch. 9 - Practical Applications Painting How many quarts of...Ch. 9 - Practical Applications Construction A hole must be...Ch. 9 - Practical Applications Manufacturing How many...Ch. 9 - Practical Applications Industrial Technology What...Ch. 9 - Practical Applications Automotive Trades At a...Ch. 9 - Practical Applications Masonry A slim jumbo...Ch. 9 - Practical Applications Construction A foundation...Ch. 9 - Practical Applications Manufacturing How many...Ch. 9 - Practical Applications Construction How many cubic...Ch. 9 - Practical Applications Sheet Metal Trades How many...Ch. 9 - Practical Applications Industrial Technology Find...Ch. 9 - Prob. 16BPSCh. 9 - Prob. 17BPSCh. 9 - Practical Applications Welding A rectangular tank...Ch. 9 - Practical Applications Automotive Trades An oil...Ch. 9 - Practical Applications Welding Calculate the...Ch. 9 - Prob. 21BPSCh. 9 - Practical Applications Welding Calculate the...Ch. 9 - Masonry A square pillar is built using 1558...Ch. 9 - Landscaping In the figure shown below, the solid...Ch. 9 - Carpentry A granite kitchen countertop is 1516 in....Ch. 9 - Prob. 26BPSCh. 9 - Prob. 27BPSCh. 9 - Prob. 28BPSCh. 9 - Prob. 29BPSCh. 9 - Prob. 30BPSCh. 9 - Landscaping A landscape contractor needs to fill...
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- 6. [10 marks] Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of T. (a) How many vertices does BL(T) have? (b) How many edges does BL(T) have? Prove that your answers are correct.arrow_forward4. [10 marks] Find both a matching of maximum size and a vertex cover of minimum size in the following bipartite graph. Prove that your answer is correct. ย ພarrow_forward5. [10 marks] Let G = (V,E) be a graph, and let X C V be a set of vertices. Prove that if |S||N(S)\X for every SCX, then G contains a matching M that matches every vertex of X (i.e., such that every x X is an end of an edge in M).arrow_forward
- Q/show that 2" +4 has a removable discontinuity at Z=2i Z(≥2-21)arrow_forwardRefer to page 100 for problems on graph theory and linear algebra. Instructions: • Analyze the adjacency matrix of a given graph to find its eigenvalues and eigenvectors. • Interpret the eigenvalues in the context of graph properties like connectivity or clustering. Discuss applications of spectral graph theory in network analysis. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]arrow_forwardRefer to page 110 for problems on optimization. Instructions: Given a loss function, analyze its critical points to identify minima and maxima. • Discuss the role of gradient descent in finding the optimal solution. . Compare convex and non-convex functions and their implications for optimization. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]arrow_forward
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- Only 100% sure experts solve it correct complete solutions okarrow_forwardGive an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.arrow_forward3. [10 marks] Let Go (Vo, Eo) and G₁ = (V1, E1) be two graphs that ⚫ have at least 2 vertices each, ⚫are disjoint (i.e., Von V₁ = 0), ⚫ and are both Eulerian. Consider connecting Go and G₁ by adding a set of new edges F, where each new edge has one end in Vo and the other end in V₁. (a) Is it possible to add a set of edges F of the form (x, y) with x € Vo and y = V₁ so that the resulting graph (VUV₁, Eo UE₁ UF) is Eulerian? (b) If so, what is the size of the smallest possible F? Prove that your answers are correct.arrow_forward
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