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Concept explainers
Sports and Leisure In the 1936 Summer Olympic Games, Jesse Owens won the 100-meter dash in a time of 10.3 seconds. If he could have raced at that speed against Usain Bolt in the 2016 Olympic Games, how far behind, to the nearest tenth of a meter, would Owens have been when Bolt finished the race? (See Example 3 on page 429.)
EXAMPLE 3 Sports and Leisure In the 2016 Summer Olympic Games, Usain Bolt of Jamaica won the men’s 100-meter dash in a time of 9.81 seconds. In the 1964 Games, Bob Hayes of the United States won the same event in a time of 10.0 seconds. Suppose these two champions could have run against each other at those same speeds. How far behind, in meters, would Hayes be as Bolt crossed the finish line?
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Chapter 7 Solutions
Mathematics for the Trades: A Guided Approach, Books a la Carte edition (11th Edition)
- 2. Find each derivative. Write answers with positive exponents. a) Dx 9x -3 [97] b) f'(3) if f(x) = x²-5x² 8arrow_forwardT3.2: Prove that if the Graceful Tree Conjecture (every tree has a graceful labeling) is true and T' is a tree with m edges, then K2, decomposes into 2m - 1 copies of T. Hint - Delete a leaf to get 7" and apply the decomposition of K2(m-1)+1 = K2m-1 into T'. Then explain how the decomposition allows the pendant edge to be added to a new vertex to obtain a decomposition of K2m into copies of T.arrow_forwardUse the matrix tree theorem to determine the number of spanning trees of the graphs Kr∨sK1.These are the graphs formed by by adding all edges between a complete graph on r vertices and atrivial graph (no edges) on s vertices.arrow_forward
- The maximum capacity spanning tree problem is as follows for a given graph G = (V, E) withcapacities c(uv) on the edges. The capacity of a tree T is defined as the minimum capacity of anedge in T. The maximum capacity spanning tree problem is to determine the maximum capacity ofa spanning tree.(i) Describe how to modify the input graph to find a maximum weight spanning tree making use ofa minimum weight spanning tree algorithm.(ii) Show that a maximum (weight) spanning tree is also a maximum capacity spanning tree.(iii) Is the converse of part (ii) true? That is, is it true that a maximum capacity spanning tree is alsoa maximum spanning tree? Either give counterexamples (of all sizes) or a proof.(iv) Prove the following max-min result. The maximum capacity of a spanning tree is equal to theminimum bottleneck value of a cut. For a subset U ⊆ V , the cut [U, V − U] is the set of edgesbetween U and V − U. The bottleneck value of a cut [U, V − U] is the largest capacity among theedges of…arrow_forward1) Find The inverse The domain of m(x) = tion and of the function The inverse function 3- √x-aarrow_forwardProve that the following version of a greedy algorithm produces a minimum spanning tree in aweighted graph. Start with a vertex v as the initial tree and at each stage add an edge with minimumweight having exactly one end in the current tree. Stop when all vertices have been addedarrow_forward
- b. According to the analyst, what is the probability that the confidence score is not 1? 11. Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.10 B 3 0.30 C 2 0.40 D 1 0.10 F O 0.10 a. Depict the probability distribution graphically. Comment on whether or not the probability distribution is symmetric. b. Convert the probability distribution to a cumulative probability distribution. C. What is the probability of earning at least a B in Professor Sanchez's course? d. What is the probability of passing Professor Sanchez's course? 2. Professor Khurana expects to be able to use her grant money to fund up to two students for research assistance. While she realizes that there is a 5% chance that she may not be able to fund any student, there is an 80% chance that she will be able to fund two students. a. What hat is the proarrow_forwardGraph the following function. Please also graph the asymptote. Thank you.arrow_forwardA ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related rates questions below. (Hint: Use two carefully labeled similar right triangles.) (a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt= feet/sec. (b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt= feet/sec.arrow_forward
- Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z² = x²+ +12 x Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. 2z dz dt dx 2x. +2y dt dx dy dz x +y dt dt dt 2z dy dt × dx (x+y dt dy dtarrow_forwardAn elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 ground level Assume that x is increasing at a rate of 3 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ Noarrow_forwardAt a local college, for sections of economics are taught during the day and two sections are taught at night. 70 percent of the day sections are taught by full time faculty. 20 percent of the evening sections are taught by full time faculty. If Jane has a part time teacher for her economics course, what is the probability that she is taking a night class?arrow_forward
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