Answered: 2- An insulated rod of length 30 cm has… | bartleby

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 18EQ

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2- An insulated rod of length 30 cm has its ends A and B kept at 20•C and
80•C respectively until steady state conditions prevail. The temperature at
each end is then suddenly reduced to 0 •C and kept so. Find the resulting
temperature distribution u(x, t) taking origin at A
tho tomperatures at 30°C

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Consider the cross section of a long rectangular metallic plate where the boundaries are subject to three different temperatures in degree Celsius, as shown in figure below. Engineers are interested in knowing the temperature distribution inside the plate in a specific period of time so they can determine the internal thermal stress. Assuming the boundary temperatures are held constant during that specific period of time, the temperature inside the plate will reach certain equilibrium after some time has passed. Finding this equilibrium temperature distribution at different points on the plate is desirable, but extremely difficult. However, one can consider a few points on the plate and approximate the temperature of these points. This approximation can be done using the mean value approach (the temperature will be approximated by averaging the 4 adjacent temperature, as we have done in class). a) b) 20 20 32 Metal Plate 24 32 24 24 24 What are the temperatures at x1 = °C, x2 = °C, X3…
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A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with = 2.1. (Round your answers to two decimal places.) (a) Compute a 95% CI for μ when n = 25 and x = 56.0. watts (b) Compute a 95% CI for μ when n = 100 and x = 56.0. watts (c) Compute a 99% CI for μ when n = 100 and x = 56.0. watts (d) Compute an 82% CI for μ when n = 100 and x = 56.0. watts (e) How large must n be if the width of the 99% interval for u is to be 1.0? (Round your answer up to the nearest whole number.) n =
A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with = 2.1. (Round your answers to two decimal places.) (a) Compute a 95% CI for μ when n = 25 and x = 55.6. watts (b) Compute a 95% CI for μ when n = 100 and x = 55.6. watts (c) Compute a 99% CI for μ when n = 100 and x = 55.6. watts (d) Compute an 82% CI for μ when n = 100 and X = 55.6. watts (e) How large must n be if the width of the 99% interval for u is to be 1.0? (Round your answer up to the nearest whole number.) n = You may need to use the appropriate table in the Appendix of Tables to answer this question.
A computer algebra system is recommended. Consider a rod of length 28 for which a? = 1. Suppose the initial temperature distribution is given by u(x, 0) = x20-X and that the boundary conditions are u(0, t) = 28 and u(28, t) = 0. 28 (a) Find the temperature in the rod as a function of position and time. 28 - x +
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A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray- load loss is normally distributed with = 2.8. (Round your answers to two decimal places.) (a) Compute a 95% CI for μ when n = 25 and X = 58.3. watts (b) Compute a 95% CI for μ when n = 100 and X = 58.3. watts (c) Compute a 99% CI for μ when n = 100 and x = 58.3. watts (d) Compute an 82% CI for μ when n = 100 and x = 58.3. watts (e) How large must n be if the width of the 99% interval for u is to be 1.0? (Round your answer up to the nearest whole number.) n =
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