132-5 Problem 5 (Proposition)Translate the given statement into propositional logic using the propositions provided: On certain highwaysin the Washington, DC metro area you are allowed to travel on high occupancy lanes during rush hour onlyif there are at least three passengers in the vehicle. Express your answer in terms of r:"You are travelingduring rush hour." t"You are riding in a car with at least three passengers." and h:“You can travel on a highoccupancy lane."

Given, r : you are traveling during rush hour. t : you are riding in a car with at least three…

Answered: Translate the given statement into…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter11: Nonlinear Programming

Section11.8: Lagrange Multipliers

Problem 8P

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3. Show that the premises "It is not Sunny this afternoon and it is colder than yesterday." "We will go swimming only if it is Sunny," "If we do not go swimming then we will take a Canoe trip." and "If we take canoe trip then we will be home by sunset" lead to the conclusion "We will be home by sunset."
PROBLEM 4 Translate each of the following English statements into logical expressions. The domain of discourse is the set of all real mumbers. (a) The reciprocal of every positive mumber less than one is greater than one. (b) There is no smallest mumber. (c) Every number other than 0 has a multiplicative inverse.
Problem 4 Discrete Mathematics.Combinations and Permutations. (5,10,10): Soccer A local high school soccer team has 20 players. However, only 11 players play at any given time during a game. In how many ways can the coach choose 11 players To be more realistic, the 11 players playing a game normally consist of 4 midfielders, 3 defend ers, 3 attackers and 1 goalkeeper. Assume that there are 7 midfielders, 6 defenders, 5 attackers and 2 goalkeepers on the team 2. In how many ways can the coach choose a group of 4 midfielders, 3 defenders, 3 attackers and 1 goalkeeper? 3. Assume that one of the defenders can also play attacker. Now in how many ways can the coach choose a group of 4 midfielders, 3 defenders, 3 attackers and 1 goalkeeper?
I A bob attached to a cord is moved to the right where its vertical position is 1.05 cm above the equilibrium position and is then given an initial speed of 0.6 m/s. What are the values of the maximum speed and maximum height reached by the bob? (Take g = 9.8 m/s') (a) hmax (b)hmax =D1.87 cm; tnax 3.44 m/s (c) hmax (d) hmax 2.89 cm; Vnax = 0.75 m/s 1.87 cm; max 0.75 m/s 2.89 cm; 1,ax 3.44 m/s or frequency to 2/:
With this exercise, we shall develop a solution to the following riddle. Two adults, their three children, and their dog are on a walk when they come upon a river. They have a boat, but it can only hold a maximum of one adult with either one child or the dog; or three chidren; or two children and the dog. Anyone (other than the dog) can row the boat; but it would be too much work for one child to row across by themself. How can they all get across the river? You are required to solve this riddle by modelling it using a labelled transition system (LTS). 1. What are the states of your LTS consist of? Make sure you consider all the aspects of the riddle. Justify your notion of state. 2. What are the actions of your LTS? List all the actions. Justify your choice of actions. 3. Drawing out the entire LTS may be a time consuming task as there could be very many states and transitions. However, drawing out only part of the LTS is doable. Draw part of the LTS, anywhere between 7 and 12…
2. The flight of a model rocket can be modeled as follows. During the first 0.15 s the rocket is propelled upward by the rocket engine with a force of 16 N. The rocket then flies up while slowing down under the force of gravity. After it reaches the apex, the rocket starts to fall back down. When its downward velocity reaches 20 m/s, a parachute opens (assumed to open instantly), and the rocket continues to drop at a constant speed of 20 m/s until it hits the ground. Write a program that calculates and plots the speed and altitude of the rocket as a function of time during the flight.
PROBLEM 14. [TIME ALLOWED = 5 MINUTES] Let p and q be the propositions: p : I bought a lottery ticket this week. q : I won the million dollar jackpot on Friday. The proposition (p  q) as an English sentence is: (a) I did not buy a lottery ticket this week, and I did not win the million dollar jackpot on Friday. (b) Either I bought a lottery ticket this week or I won the million dollar jackpot on Friday. (c) Not better than good beer. (d) None of the above.
a. b. The following is an utterance from the Oracle at Delphi: More than one of the triumvirate will be assassinated. Crassus will be assassinated and either Caesar will not be assassinated or Pompey will be assassinated, if and only if, Pompey will not be assassinated and either Crassus or Caesar will be assassinated. Assume these constituent propositions: Ca : Caesar will be assassinated Cr: Crasus wil be assassinated P: Pompey will be assassinated the second sentence can be formalized thus: Provide a formalization of the first sentence, "More than one of the triumvirate will be assassinated," using the propositional constituents identified. Construct a truth table to determine who will be assassinated. Be sure to explain how the truth table helps you answer this question.
a)A thief robbing a store finds 5 items; the items are worth 8,10,7,20 and 11 dollars and weights 2,3,2,7 and 7 pounds. He wants to take as valuable a load as possible, but he can carry at most 9 pounds in his knapsack. What is the maximum worth of items that he can take? b) What if the thief somehow managed to increase the capacity of his knapsack by 2 pounds? What will be the maximum worth of items that he can take then?
The Green Monster, as shown below, is a wall 37 feet high in left field at Fenway Park in Boston. The wall is 310 feet from home plate down the third base line. If the batter hits the ball 4 feet above the ground, neglecting air resistance, determine the minimum speed that the bat must impart to the ball that is hit over the Green Monster. height above home plate [ft] 200 The equations of motions for the baseball are x(t) = (u cos 0)t and y(t) = y + (u sin 0)t-t² as depicted in the diagram below. The ball's initial speed is u. The gravitational constant g is 9.8 m/sec². The height at which the ball is struck is yo. 180 The coordinates depict the geometry with the origin at the home plate. The ball is struck at y = 4 ft. The top of the Green Monster, which is 310 feet from home plate, is noted as (310,37). 160 140 120 100 80 60 (0,4) 40 (0,0) Gulf у In a well-documented MATLAB script hmwk8Q3.m, using vectorizing methods, plot the five baseball trajectories for the speeds u = 70, 80, 90,…
Please help step by step with Program R (CS) with a final code for understanding thank you.
Please work out question 30 and show work for explanation of how you came up with your answer.

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