Question For the circuit shown below, E = 24 V, L 8 mH, and R=322. After steady state is reached with S, closed and S, open, at t 0, S, is closed and is opened. Determine (a) the current through L at t = 0. (b) the current through L at t - 3.5 x 10 $, (c) the voltage across R on the right at t = 3.5 x 10 s, and (d) the rate at which current through L changes at t = 3.5 x 10 4 4 S. R 0000 s Hint A. Additional Hints for (a) A. Additional Hints for 4 a. The current through L att 0 b. The current through L att 3.5 x 10 sis (b) c. The voltage across Ratt 3,5 x 10 4 15 d. The rate at which current through changes att A/s. Additional Hints for.(a) V. Additional Hints for (c) 3.5 x 10 sis

Your mobile phone contains a micro-electronic mechanical system (MEMS) gyroscope integrated circuit to sense physical rotation. The details are complicated (and irrelevant to the q!), but it can be approximated as a mass oscillating horizontally on a spring. For the design shown, the mass is 220 ng (2.2 x 107 kg) and it oscillates at 7.0 kHz. (a) What is the Your mobile phone contains a micro-electronic mechanical system (MEMS) gyroscope integrated circuit to sense physical rotation. The details are complicated (and irrelevant to the q!), but it can be approximated as a mass oscillating horizontally on a spring. For the design shown, the mass is 220 ng (2.2 x 107 kg) and it oscillates at 7.0 kHz. (a) What is the overall spring constant of the spring used in the design? [2 marks] To make the gyroscope work, the mass must be made to oscillate at its natural spring-mass frequency. This is achieved using electrostatic forces (attraction of opposite charges) between the mass and the body of the device. To accelerate the mass to make it oscillate, the electrostatic force must be applied in a way that reinforces the motion. This is done by measuring the position of the mass electronically and then applying the correct force based on this. (b) Using labelled diagrams and text explain how the position, velocity, and acceleration of the mass varies with time, including the phase relationship between them. [4 marks] (c) Thinking back to your mechanics study, explain how the applied force should vary with time in order to increase the amplitude of the oscillation. [hint: what variable are you trying to affect?] [2 marks] (d) If the amplitude of the oscillation is 0.20 μm (2.0 x 107 m), then calculate and explain how much mechanical and potential energy is present in the oscillator. [2 marks]

(1 point) Determine the average rate of change of the following function between the given values of the variable: f(x) = x4 - - X; x = -2, x = 3 Average rate of change = .

Question Suppose three point masses are placed in the xy-plane as follows (assume coordinates are given in meters): mi = 5 kg, placed at (-2, -3) m2 = 3 kg, placed at (2,3) 'm3 = 2 kg, placed at (-3, -2) Find the center of mass of the system. Write your answer as an ordered pair Provide your answer below:

let f(x)= x^2-5, g(x)= 2x^3+x and p(x)= f(x)g(x). a) computedp/dx b) compute f'(x)g'(x)

10. A box is lying on top of a trailer, which is parked on the road. According to Newton's third law, what is the reaction force to the gravitational pull of the box on the trailer? The normal force of the trailer on the box The gravitational pull of the trailer on the box The gravitational pull of the trailer on Earth The normal force of the road on the trailer The weight of the trailer The normal force of the trailer on the road The gravitational pull of the box on Earth The weight of the box

Suppose that a company is developing a new touch-screen cell phone. Historically, 70% of their new phones have resulted in high consumer demand, whereas 30% have resulted in low consumer demand. The company has the decision of choosing between two models with different features that require different amount of investment and have different sales potential. Estimated profit/loss are shown in the payoff table below. State of Nature High demand, ($) Low demand, ($) Model 1 300,000 -40,000 Model 2 275,000 -15000 Now suppose the firm conducts a market research study to obtain sample information and better understand the nature of consumer demand. The market research cost $10,000 Analysis of past market research studies, conducted prior to introducing similar products, has found that the survey response will be either high or low. There is a 69% chance that the survey will return a high survey response (results) and there is a 31% chance that the survey will result in lo-demand response (results). The relevant conditional probabilities are as follows: P (high consumer demand, high survey response = 0.913) P (low consumer demand, low survey response = 0.087) P (high consumer demand, high survey response = 0.226) P (low consumer demand, low survey response = 0.774) Calculate the expected value of sample information (EVSI). Develop a decision tree and analyze using QM for Windows. Determine the optimal solution.