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Problem 7 (3+3 points, without calculator) The concentration change of two specific chemical rengents is described...
Problem 4: SpaceTime diagrams (25 points) Consider the two points labeled 1 and 2 in this...
Problem 4: SpaceTime diagrams (25 points) Consider the two points labeled 1 and 2 in this spacetime diagram. Notice that in the Lorentz frame represented by this diagram, both events are in the future: ti > 0 and t2 > 0. (The diagonal lines with 45° slope represent the light cone.) ct (a) Prove that, regardless of the value of ß-u/c, when you boost to a different Lorentz frame, the event 1 remains in the future, that is, 0 always....
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n...
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n and 0 <p<1. (1) Show that **- 1 = 2* for any 1 Sxsn. (2) Show that when 0 < x < (n + 1)p, P(X = x) is an increasing function x and for (n + 1)p <x Sn, P(X = x) is a decreasing function x. (3) A certain basketball player makes a foul shot with probability 0.80. Determine for whal value...
Problem 4: (20 Points) X is a uniform random variable with parameters -5 and 5. Given...
Problem 4: (20 Points) X is a uniform random variable with parameters -5 and 5. Given the event B-VI > 3) 1. (5 points) What is the probability of the event B, P(B)? 2. (5 points) What is the conditional PDF, fxB()7 3. (5 points) Find the conditional expected value, E[X |B]. 4. (5 points) Find the conditional variance, var[X]B].
Week 1 Assignment: Chemical Kinetics Introduction to Integrated Rate Laws 7 of 28> solve for concentration....
Week 1 Assignment: Chemical Kinetics Introduction to Integrated Rate Laws 7 of 28> solve for concentration. The rate constant for a certain reaction is k = 9.00x10-3 s-1 、 If the initial reactant concentration was 0.200 M, what will the concentration be after 19.0 minutes? A car starts at mile marker 145 on a highway and drives at 55 mi/hr in the direction of decreasing marker numbers. What mile marker will the car reach after 2 hours? Express your answer...
Problem 7 (20 Points Fully developed flow between two, flate, infinite, parallel plates can be described...
Problem 7 (20 Points Fully developed flow between two, flate, infinite, parallel plates can be described using the boundary layer equation in nondimensional terms where Note that D is the separation distance between the plates and V is the velocity of the upper plate. There are two very important simplifications that can be made to this equation in fully developed internal flow. Make these simplifications and solve for u* as a function of y* (get me the equation of u'...
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by Gaus...
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by Gaussian elimination and express the general solution in vector form. (b) (5 points) Write down the corresponding homogenous system Ax-0 explicitly and determine all non-trivial solutions from (a) without resolving the system
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by...
Problem 3. Consider the following system of two equations, in terms of the parameter 7, which...
Problem 3. Consider the following system of two equations, in terms of the parameter 7, which describes the respective populations of two species: 1 = *(- zv- ) yz ( +x). y' 2 (a.) List all critical points and discuss the stability at the points in relation to the parameter 7. (b.) What values of the parameter y will allow a stable solution in which both species have positive populations.
Reinforcement Problem # 4 (20 pts.) A) Given A state-space system is described: (39)+(7 933) (195)...
Reinforcement Problem # 4 (20 pts.) A) Given A state-space system is described: (39)+(7 933) (195) y = (0 - 1)(**) +(1) B) Determine Step 1: The block diagram representation with x1(0) = x2(0) = 0. Step 2: The transfer function Y(S)/F(s) through block diagram reduction. Step 3: The output value of y(t) due to input f(t) = u(t). Evaluation Criteria Rubric for Reinforcement Problem # 4 Gained Activities Step 1. Step 2. Step 3 Describe the techniques and procedures...
Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5)...
Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5) Write an expression for the frequency response of the system, H(e/). b. (5) Sketch the magnitude response of the system as a function of frequency over Nyquist interval. (5) Determine the output when the input is xln] 5+2cos(0.5 sequence e. (5) Determine the output when the input is the unit-step sequence uln.
Problem 3. (15 points) Consider the feedback system in Figure 3, where G(s)1 (s -1)3 Ge(s)...
Problem 3. (15 points) Consider the feedback system in Figure 3, where G(s)1 (s -1)3 Ge(s) G(s) Figure 3: Problem 3 1. Let the compensator be given by a pure gain, ie, Ge(s)-K, K 0 (a) Draw the root locus of the compensated system (b) Is it possible to stabilize the systems by selecting K appropriately? If so, find the range for K such that the closed-loop system is BIBO stable. If not, explain. 2. This time, let the compensator...
Problem 4: SpaceTime diagrams (25 points) Consider the two points labeled 1 and 2 in this spacetime diagram. Notice that in the Lorentz frame represented by this diagram, both events are in the future: ti > 0 and t2 > 0. (The diagonal lines with 45° slope represent the light cone.) ct (a) Prove that, regardless of the value of ß-u/c, when you boost to a different Lorentz frame, the event 1 remains in the future, that is, 0 always....
Problem 7 (15 points). Let X be random variable with the binomial distribution with parameters n and 0 <p<1. (1) Show that **- 1 = 2* for any 1 Sxsn. (2) Show that when 0 < x < (n + 1)p, P(X = x) is an increasing function x and for (n + 1)p <x Sn, P(X = x) is a decreasing function x. (3) A certain basketball player makes a foul shot with probability 0.80. Determine for whal value...
Problem 4: (20 Points) X is a uniform random variable with parameters -5 and 5. Given the event B-VI > 3) 1. (5 points) What is the probability of the event B, P(B)? 2. (5 points) What is the conditional PDF, fxB()7 3. (5 points) Find the conditional expected value, E[X |B]. 4. (5 points) Find the conditional variance, var[X]B].
Week 1 Assignment: Chemical Kinetics Introduction to Integrated Rate Laws 7 of 28> solve for concentration. The rate constant for a certain reaction is k = 9.00x10-3 s-1 、 If the initial reactant concentration was 0.200 M, what will the concentration be after 19.0 minutes? A car starts at mile marker 145 on a highway and drives at 55 mi/hr in the direction of decreasing marker numbers. What mile marker will the car reach after 2 hours? Express your answer...
Problem 7 (20 Points Fully developed flow between two, flate, infinite, parallel plates can be described using the boundary layer equation in nondimensional terms where Note that D is the separation distance between the plates and V is the velocity of the upper plate. There are two very important simplifications that can be made to this equation in fully developed internal flow. Make these simplifications and solve for u* as a function of y* (get me the equation of u'...
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by Gaussian elimination and express the general solution in vector form. (b) (5 points) Write down the corresponding homogenous system Ax-0 explicitly and determine all non-trivial solutions from (a) without resolving the system
7. (20 points) Let 0-1 5 3 A -2 34 2 -3-5 (a) ( 15 points) Solve the linear system Ax = b by...
Problem 3. Consider the following system of two equations, in terms of the parameter 7, which describes the respective populations of two species: 1 = *(- zv- ) yz ( +x). y' 2 (a.) List all critical points and discuss the stability at the points in relation to the parameter 7. (b.) What values of the parameter y will allow a stable solution in which both species have positive populations.
Reinforcement Problem # 4 (20 pts.) A) Given A state-space system is described: (39)+(7 933) (195) y = (0 - 1)(**) +(1) B) Determine Step 1: The block diagram representation with x1(0) = x2(0) = 0. Step 2: The transfer function Y(S)/F(s) through block diagram reduction. Step 3: The output value of y(t) due to input f(t) = u(t). Evaluation Criteria Rubric for Reinforcement Problem # 4 Gained Activities Step 1. Step 2. Step 3 Describe the techniques and procedures...
Problem 3 (25 points A linear time-invariant filter is described by the difference equation a. (5) Write an expression for the frequency response of the system, H(e/). b. (5) Sketch the magnitude response of the system as a function of frequency over Nyquist interval. (5) Determine the output when the input is xln] 5+2cos(0.5 sequence e. (5) Determine the output when the input is the unit-step sequence uln.
Problem 3. (15 points) Consider the feedback system in Figure 3, where G(s)1 (s -1)3 Ge(s) G(s) Figure 3: Problem 3 1. Let the compensator be given by a pure gain, ie, Ge(s)-K, K 0 (a) Draw the root locus of the compensated system (b) Is it possible to stabilize the systems by selecting K appropriately? If so, find the range for K such that the closed-loop system is BIBO stable. If not, explain. 2. This time, let the compensator...
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