A crystal growth furnace is used in research to determine how best to manufacture crystals used in electric components for the space shuttle. For proper growth of the crystal, the temperature must becontrolled accurately by adjusting the input power. Suppose the relationship is given byT(w) = 0.1w² + 2.157w + 20where T is the temperature in degrees Celsius and w is the power input in watts.(a) How much power is needed to maintain the temperature at 199°C? (Round your answer to two decimal places.)watts(b) If the temperature is allowed to vary from 199°C by up to ±1°C, what range of wattage is allowed for the input power? (Round your answers to two decimal places.)watts < W<watts(c) In terms of the &, & definition of lim f(x) = L, what is x?x→ainput powertemperaturetolerance in the temperaturetarget input powertarget temperatureWhat is f(x)?input powertemperaturetolerance in the temperaturetarget input powerO target temperature What is a?input powertemperaturetolerance in the temperaturetarget input powertarget temperatureWhat is L?input powertemperaturetolerance in the temperaturetarget input powertarget temperatureWhat value of & is given?°CWhat is the corresponding value of 8? (Round your answer to two decimal places.)watts

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Answered: A crystal growth furnace is used in…

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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An RLC circuit, as shown in the figure, withresistance R=10 ohms, capacitance C=0.01 farads and an inductor L=0.5 H, it also has a voltage source E(t) = 12 volts. Assuming that at time t=0 there is no charge on the capacitor and no current in the circuit, determine the charge on the capacitor and the current in the circuit from the moment the switch is closed. In solving this exercise you must calculate and present the following: c) Determine the particular solution of the non-homogeneous differential equation qp, posing the simultaneous equations and their corresponding solution to establish the value of the indeterminate coefficients. d) Determine the general solution for the charge on the capacitor, that is, q(t) = qh + qp
3. A simple pendulum is a weight on the end of a string or rod, which when given an initial push, swings back and forth under the influence of gravity. The period T of a pendulum is the time taken for two swings (left to right and back again). The formula for the period is T = 27 dT (a) Find d 9 where is the length of the pendulum (in meters) and g is the acceleration due to gravity (in m/sec2). Note that g is a positive constant. lo zulev lie (x)) (8) (b) When the length of the pendulum increases, does the period increase or decrease? Justify your answer. (0) al bar nob
4
Question 1 A tank initially holds 200 gal of brine solution containing 3 lb of salt. At t=0, another brine solution containing 3 lb of salt per gallon is poured into the tank at the rate of 6 gal / min, while the well stirred mixture leaves the tank at the same rate. Find the time at which the mixture in the tank contains 6 lb of salt. (A) 0.216 min B) 0.168 min 2.13 min D) 0.02 min
A tank contains 1,000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. Let y(t) be the amount of salt (in kg) in the tank after t minutes. (a) Find the rate of change of amount of salt in the tank after t minutes. dy dt kg min How much salt is in the tank when t = 0? y(0) How much salt (in kg) is in the tank after t minutes? y = = kg (b) How much salt (in kg) is in the tank after 50 minutes? (Round the answer to one decimal place.) y(50) = kg
Suppose the number of bacteria in a culture increases by 50% every hour if left on its own. Assuming that biologists decide to remove approximately one thousand bacteria from the culture every 10 minutes, which of the following equations best models the population P = P(t) of the bacteria culture, where t' is in hours? A. dP = 5P-1000 dt dP B. at dP C. dt dP D. dt E. dP at = 5P-6000 1.5P-6000 = 1.5P-1000 = -5P-1000
Suppose an RL circuit with a 11 resistor and a 6H inductor is driven by the voltage E(t) est V. If the initial resistor current is I(0) OA, find the current I, the voltages across the inductor E₁ and the resistor ER in terms of time t. A I(t) = = ER(t) EL(t) = = = V V
An RLC circuit, as shown in the figure, withresistance R=10 ohms, capacitance C=0.01 farads and an inductor L=0.5 H, it also has a voltage source E(t) = 12 volts. Assuming that at time t=0 there is no charge on the capacitor and no current in the circuit, determine the charge on the capacitor and the current in the circuit from the moment the switch is closed. In solving this exercise you must calculate and present the following: e) Determine the particular solution of q(t) by establishing the values of the constants C1 & C2, through the application of the initial values. f) Draw the graph of the final solution q(t) obtained (you can use an application and paste the graph).

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