50"-+ Hole R:10 in I Ts" *27"4 + x 50"—* Problem 4. Find for the trapezoidal...
Let x In I dx. a) Find the exact value of 1 b) Use composite trapezoidal rule with n = 4 subintervals to approximatel. Calculate the exact error c) Use composite simpson's rule with n = 4 subintervals to approximatel. Calculate the d) Use composite simpson's rule with n = 6 subintervals to approximate I. Calculate the exact error exact error
4. For: 1 + x3 dx a) Evaluate I using the trapezoidal rule with n= 4. (15 pts) b) Evaluate I using the 1/3 Simpson's rule with n=2. (10 pts) Trapezoidal Rule Single Application 1 = (6-a) f(b) + f(a) Composite (b-a) 2n I= i=1 Simpson's 1/3 Rule Single Application Composite b) Evaluate I using the 1/3 Simpson's rule with n=2. (10 pts) Trapezoidal Rule Single Application f(b) + f(a) I = (b-a) 2 Composite I = (b − a)...
10 points a. 5 points Sam is pouring concrte into a hole in the shape of a triangular prism. The hole is 4 meters wide, 4 meters long, and 6 meters deep at its deepest point A partially filled hole with the correct dimensions is shown to the right Sam is looking dowa into the hole and obaserves that 6 the rectangular top surface of the concrete is growing at a rate of 0.8 meters squared per minute. Find the...
Problem 1. The relative probability of r is given by: x < 0 1 cos( n(r) 0 <x< 10 10 x. a) Sketch n(x) on the domain 0 <I<10. b) Find a probability density function for r (p(r)) by normalizing n(x). c) What is the average value of r? Problem 1. The relative probability of r is given by: x
Question 8: 10 Marks The area of the surface described by zf(x,y) for (r,)e R is given by Find an approximation to the area of the surface on the hemisphere r2 + y2 + z2-9,2 the region in the plane described by R-((r, yjo-r 1,0 y I) using: 0 that lies above 8.1 Trapezoidal rule in both directions 8.2 Simpson rule in both directions 8.3 Three-term Gaussian quadrature formulas in both directions 131 131 Question 8: 10 Marks The area...
The mass of a proton is 1.67x 10-27 kg (10%) Problem 10: A 50% Part (a) Find the rest energy in joules. 0
0 Figure 2: The potential barrier setup for Problem 4 4. (10 points) "Burrowing a hole in the wall" Some particles of mass m and energy E move from the left to the potential barrier shown in Figure 2 below 0 <0 Uo 20 U(x) where Uo is some positive value (a) (5 points) Write the Time-Independent Schrödinger equations and the physically acceptable general solutions for the wave function (x) in regions I and II as labeled in Figure 2...
Problem 1. For the trapezoidal channel cross section shown below, find the following geometric quantities in terms of bottom width b, flow depth y, and side slope m. Provide the appropriate dimensions for each tem using the L-T-F (Length-Time-Force) system. For example, [b] L (a) Flow area, A (b) Wetted perimeter, P (c) Hydraulic radius, R (d) Top water surface width, T A (e) Hydraulic depth, D= T Problem 2. Write a function in Matlab that calculates each of the...
1. (20 pts.). In the circuit shown in the diagram R 10 m,Ra 0.02 , R 01 , Rs -30 mt Rs 40 min. Rs 50 min. R7 60 min, and ε 100 V. A) (10 pts.) find the equivalent resistance for this circuit; B) (5 pts.) find the voltage and the current for the resistor R C) (5 pts.) find the electric power in the resistor Rr. 2. (20 pts.). In the cir rcuit shown in the diagram, find...
Problem B-4-1 Find the transfer function X (s)/X/(s) of the mechanical system shown in Figure 4-50. The displacements x; and X, are measured from their respective equilibrium positions. Obtain the displacement xo(t) when the input x;(t) is a step displacement of magnitude X; occurring at t = 0. Assume that x.(0-) = 0. T Figure 4-50 Mechanical system.