1. The fuel efficiency of vehicles depends on engine revolutions per minute(rpm = x)) and usually is 70% at 4,000 rpm. The rate of change of the fuelefficiency, with respect to the rpm, is proportional to the fuel efficiencyE(x). Assume that the proportionality constant is equal to 0.0003.infoa) Find the differential equation that represent the fuel efficiency with arespect to rpm.b) Find the fuel efficiency E(x) in terms of rpm.c) What is the fuel efficiency at 2000 rpm?dedEda9377

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Answered: 1. The fuel efficiency of vehicles…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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"Newton’s cooling law, states that an object cools or heats at a rate that is proportional to the difference between the temperature of the surroundings and the object’s temperature. At time t = 0, the temperature in a room is 0°C. The room is heated at a steady rate of 3°C per hour. Let T(t) be the temperature of an object in the room after t hours. (a) Briefly explain why T’(t) + kT(t) = 3kt (b) Assume that T(0) = 0. Find the temperature of the object T(t), expressed by k. This can be solved without having succeeded in (a), by using the information in (a)."
Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation = k(T – A), where T is the temperature of the object after t units of time dt dT have passed, A is the ambient temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 188 degrees and, after sitting in room temperature of 68 degrees for 18 minutes, the coffee reaches 178 degrees. How long will it take before the coffee reaches 166 degrees? Include at least 2 decimal places in your answer. minutes
find the second derivative
Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation =k(TA), where T is the temperature of the object after t units of time have passed, A is dT dt the ambient temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 62 degrees for 14 minutes, the coffee reaches 170 degrees. How long will it take before the coffee reaches 160 degrees? Include at least 2 decimal places in your answer. minutes
please show work
The quantity of oxygen that can dissolve in water depends on the temperature of the water. (So thermal pollution influences the oxygen content of water.) The graph shows how oxygen solubility S varies as a function of the water temperature T. SA (mg/L) 16+ 12- 8 4 0 8 16 24 32 40 T(°C) (a) What is the meaning of the derivative S '(T)? OS (T) is the rate at which oxygen solubility changes with respect to the water temperature. OS '(T) is the rate at which temperature changes with respect to the oxygen solubility. OS '(T) is the rate at which temperature changes with respect to the temperature. OS '(T) is the rate at which oxygen solubility changes with respect to the oxygen solubility. OS (T) is the current level of oxygen solubility for a given temperature. (b) Estimate the value of S '(8). (Round your answer to three decimal places.) S '(8) = (mg/L)/°C
Researchers have found a correlation between respiratory rate and body mass in the first three years of life. This correlation can be expressed by the function log R(w) = 1.85-0.48 log (w), where w is the body weight (in kilograms) and R(w) is the respiratory rate (in breaths per minute). a. Find R'(w) using implicit differentiation. b. Find R'(w) by first solving the equation for R(w). c. Discuss the two procedures. Is there a situation when you would want to use lone method over another? a. R'(w) =[| (Simplify your answer. Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.)

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