What is a?O input powertemperaturetolerance in the temperaturetarget input powertarget temperatureWhat is L?O input powertemperaturetolerance in the temperaturetarget input powerO target temperatureWhat value of ε is given?°℃What is the corresponding value of 8? (Round your answer to two decimal places.)watts 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 + 2.153w + 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 200°C? (Round your answer to two decimal places.)33.00watts(b) If the temperature is allowed to vary from 200°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→aO input powertemperaturetolerance in the temperaturetarget input powertarget temperatureWhat is f(x)?O input powertemperaturetolerance in the temperatureO target input powertarget temperature

Given, T(w)=0.1w2+2.153w+20 where T is the temperature in degrees Celsius and w is the power input…

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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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
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
2. On a certain day, the depth off a pier at high tide was 6m. After 6h, the depth of the water was 3m. Assume a 12h cycle a. Find the equation of the depth of water, with respect to its average depth, in terms of the time, t hours since high tide. b. Find the depth of water at t=8h

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