Numerade

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The efficiency of an Otto cycle is increased by increasing ________.(a) Compression ratio and/or increasing the ratio of specific heats(b) Compression ratio and/or decreasing the ratio of specific heats(c) Pressure ratio and/or decreasing the ratio of specific heats(d) Temperature ratio and/or decreasing the ratio of specific heats

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Locate and classify all extrema in the graph. (By classifying the extrema, we mean listing whether each extremum is a relative or absolute maximum or minimum.) Also, locate any stationary points or singular points that are not relative extrema. (Order your answers from smallest to largest x.) f has ---Select--- ?at (x, y) = f has ---Select--- at (x, y) = f has ---Select--- ?at (x, y) =

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4. Which of the following is least true of the urinary bladder? a. It contains the detrusor muscle. b. It receives urine from two ureters. c. The bladder wall is responsive to the effects of ADH. d. Micturition occurs when the detrusor muscle contracts and the sphincters relax.

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For the next two problems, find the particular solution that satisfies the initial conditions. f'(x) = 10x - 12x^3 (2 points) f(3) = 2 f''(\theta) = \sin \theta (4 points) f'(0) = 1 f(0) = 6

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4. Consider the following matrix game \begin{equation*} A = \begin{bmatrix} 1 & 0 & -1 \\ 0 & 0 & 0 \\ -1 & 0 & 1 \end{bmatrix} . \end{equation*} a) Verify that A can not be reduced by using domination rules. b) Find the von Neumann value and the optimal strategies for both players by using the general method you have learned in the class: \begin{itemize} \item Write the initial game tableau (dual non-canonical). \item Find a MBFT by using just two pivot transformations---use the algorithm to find appropriate pivots. \item Apply SA to find the optimal solutions. \item Report the optimal strategies and the von Neumann value of the game. \end{itemize} c) Matrix A has a saddle point---find it. Can you directly report the von Neumann value and the optimal strategies for the game? Compare with (b).

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1. State a Knight's Tour for the figure below. Your tour must start and end in square 2. The blank squares are used for counting the Knight's movements (one over and two down or two down and one over). 1 2 3 4 5 6 2. Next, draw a graph that matches your tour in #1. 3. Draw an adjacency matrix for this graph. 4. Find, Extra credit; Write pseudocode for implementing this recursive function in a computer program. 5. Does the set of positive integers have the same cardinality as the positive odd integers? Prove that your answer is correct.

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The figure below shows two blocks connected by a string of negligible mass passing over a frictionless pulley. $m_1 = 3.8$ kg and $\theta = 12.0^\circ$. Assume that the incline is smooth. (a) For what value of $m_2$ (in kg) will the system be in equilibrium? $m_2 = 0.79$ Did you draw two free-body diagrams, one for each mass and identify the forces acting on each of them? For $m_2$ take the $+x$-axis to be down the incline and the $y$-axis to be perpendicular to the incline. kg (b) If the block has to slide down the incline with an acceleration of 0.6 m/s$^2$, what should be the value of $m_2$ (in kg)? $m_2 = 0.557$ Check for consistency in the sign of each force. kg

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3.20. Compute the Fourier transform of the signals in Figure P3.20. Plot the magnitude and phase of the Fourier transform. Use the symbolic manipulator to perform the integrations or to check the answers.

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QUESTION 5 Suppose that G is a plane graph that has 15 edges in the boundary of its exterior region and all the other regions of G contain 4, 6, or 8 regions in their boundary. Use Grinberg's Theorem to show that G cannot contain a Hamilton circuit.

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kevin d.