A chain of resistors we discussed in class (assuming R = 1 Ohm) has its effective...
1. In class, we have discussed the following theorem: "When the domains of r and y are not dependent, then X and Y are independent if and only if fx,y(x, y) -g(x)h(y) for all r, y for some functions g and h." In this exercise, we will explore what happens if the domains of r and y are dependent Let fxy(x, y) = 6x for 0 < x < y < 1. (a) Sketch the region 0 < x <...
3. In class we discussed the heat conduction problem with the boundary conditions a(0, t) 0, t4(1,t)-0, t > 0 and the initial condition u(r,0) f(a) We found the solution to be of the form where (2n-1)n 1,2,3,. TL 20 Now consider the heat conduction problem with the boundary conditions u(0, t) 1,u(T, t)0, t>0 and the initial condition ur,0) 0. Find u(r,t). Hint: First you must find the steady state. 3. In class we discussed the heat conduction problem...
In class, we analyzed Buffon's needle experiment. We showed that if a large sheet of paper has parallel lines that are 1 inch apart, and we throw a needle of length 1/2 inch at it, the probability that the needle hits a line is l/r. We can estimate π by throwing many needles and seeing how many throws hit a line. Suppose we throw a needle n times, and each throw is independent. Let X be the number of throws...
1. Consider the pendulum model that we discussed in class. It's also on page 71 of the lecture notes 4. Again, for simplicity, we assume m-1-1-1 Suppose in addition we consider a damping force of this model as follows. The magnitude of the damping force is proptional to angular velocity while its direction is opposite to the one of the angular velocity. For simplicity, we may assume the damping force to be -' Then the net external torque become τ...
1. In class we derived how a transformer can up or downregulate the voltage in an electrical circuit with an alternating current. (a) Use the conservation of energy to deduce how the currents I1 and I2 must be related if you know the ratio of ε1/ε2 (for the purpose of calculating the power delivered by a circuit ignore any complications due to the fact that I(t) and ε(t) are time-varying). (b) In class I argued that power transmission is more...
4. In class, we analyzed Buffon's needle experiment. We showed that if a large sheet of paper has parallel lines that are 1 inch apart, and we throw a needle of length 1/2 inch at it, the probability that the needle hits a line is 1/ . We can estimate by throwing many needles and seeing how many throws hit a ine. Suppose we throw a needle n times, and each throw is independent. Let X be the number of...
In class, we analyzed Buffon's needle experiment. We showed that if a large sheet of paper has parallel lines that are 1 inch apart, and we throw a needle of length 1/2 inch at it, the probability that the needle hits a line is l/r. We can estimate π by throwing many needles and seeing how many throws hit a line. Suppose we throw a needle n times, and each throw is independent. Let X be the number of throws...
QUESTION 18 According to class materials, the program is allowed to overload operators only if at least one incoming parameter received by the operator has a class type. 1. (a) True 2. (b) False QUESTION 19 According to the course materials, a function can take value parameters and reference parameters. A value parameter is a separate variable from the one in main() or another calling function only if the function value parameter has a different name than the one in...
9? how do l do it? thank you we in uredu Post Class R 1 50 2011 helps in urb e con Question 9) (4 points] According to the Center for Paranormal Activity and Defense (a secret division of the FBI), 10% of people have come in contact with an extraterrestrial being. Suppose 10 people are randomly selected and the numbers who have come in contact with extraterrestrial beings is recorded. • Why could this be modeled as a binomial...
1 Tasks In the class, we showed that a magnet free falling inside a copper tube experiences a braking force that slows down its fall. You are to re-explain this phenomenon using approximate yet sufficient detail math description and validate the explanation using simulation to validate the experimental observation. The tasks are: 1) Refer to the diagram on Appendix A, sketch clearly in your own interpretation of the Faraday's and Lorentz's law in the dash magenta oval in the diagram...