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Volumes of solids Choose the general slicing method, the disk/washer method, or the shell method to answer the following questions.
27. The region bounded by the curves
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- Please work out question 44 and show work for explanation of how you came up with your answer.arrow_forwardA 3T MRI scanner used is tuned for proton imaging. For a given imaging sequence applied to image a patient's leg the gradient strength is 1 G/cm, FOV is 25 cm, and matrix is 250x250. The patient has a titanium screw in their leg that causes a magnetic susceptibility change to the main magnetic field of 0.5 Gauss. How much shift is image position ( in pixels) will be seen in this part of the leg?arrow_forwardQ1: Consider a surface of revolution generated by a Bezier curve defined by the four control points P(0,0,0), (2,1,2), P₂ (3,3,0) P, (2,2,3) respectively, rotating about the X-axis. Calculate the point on the surface at u = 0.25, 0= π/2.arrow_forward
- solve usinv pythonarrow_forwardA damper (or dashpot) is connected to the mass M of the previous problem. This could represent air resistance. The entire system could be a simple model of an automobile wheel suspension system (assuming the automobile body immobile in a vertical direction). Then the damper acts as a shock absorber. As before, the system is displaced and released and x(tg) = x, and v(to) = vo - It can be shown that the motion of the system Is described by the following differential equation: Mx + Dx + Kx(t) = 0 where D is the damping factor of the dashpot and x = v(t) = velocity at time t. Model and simulate the motion of the system from timet= to to t= tf, using a digital computer program, FIG. 1 DAMPER 3 SPRING FIG.I M MASSarrow_forwardElectromagnetic Pulse propagating at oblique angle to a dielectric interface Consider a gaussian wave pulse propagating along the z-axis from region 1 with refractive index n1 and onto a dielectric interface y = m z (for all x). To the left of this dielectric interface, the refractive index is n2. Devise an initial value computer algorithm to determine the time evolution of the reflected and transmitted electromagnetic fields for this pulse. e.g., n1 = 1 , n2 = 2 initial profile (t = 0, with z0 < 0) Ex = E0 exp[-a (z-z0)^2] By = n1 * Ex Choose parameters so that the pulse width is at least a fact of 8 less than the z- domain of integration ( -L < z < L). For the slope of the interface, one could choose m = 1.arrow_forward
- The displacement of an oscillating spring can be described by x = A cos(wt) where x = displacement at time t, A = maximum displacement, w = angular frequency, which depends on the spring constant and the mass attached to the spring, and t = time. Find the displacement, x, with maximum displacement A of 4 cm, for times from 0 to 120 seconds with increments of 30 seconds, and angular frequencies from 0.4 to 0.6 radians/sec, with increments of 0.1 radians/sec. The displacement for all combinations of times and angular frequencies needs to be calculated. Use meshgrid. Display your results in a matrix with angular frequencies along the top row and times along the left column like so (you may put zero, 0, or NaN, in the upper left corner:arrow_forwardThe flanged steel cantilever beam with riveted bracket is subjected to the couple and two forces shown, and their effect on the design of the attachment at A must be determined. Replace the two forces and couple by an equivalent couple M and resultant R at A. The couple is positive if counterclockwise, negative if clockwise. 1.92 KN 0.67 m 1.71 m- 68° A 6 Answers: M = i kN.m R=( i i+ i y I L 460 N.m 10.17 m 10.17 m 1.08 KN j) kNarrow_forwardLet S be the set of six points with coordinates A(0, -2), B(4, -2), C(1, 1), D(3, 1), E(5, 2), and F(0, 2). Construct the Voronoi diagram and the Delone tesselation for S.arrow_forward
- has to be answered by v pyhtonarrow_forwardA fixed beam is subjected to a uniformly-distributed load with an intensity of f = 10 N/mm length of L = 200 mm. Now determine the support reaction forces, internal shear forces and moments, then plot its internal shear force and moment diagram. f[N/m] L 1. Define the paramters, use L and f as the variables y Xarrow_forwarduse a CAS to perform the following steps for the given curve over the closed interval. a. Plot the curve together with the polygonal path approximations for n = 2, 4, 8 partition points over the interval. b. Find the corresponding approximation to the length of the curve by summing the lengths of the line segments. c. Evaluate the length of the curve using an integral. Compare your approximations for n = 2, 4, 8 with the actual length given by the integral. How does the actual length compare with the approximations as n increases? Explain your answer. x = 2t^3 - 16t^2 + 25t + 5, y = t^2 + t - 3, 0 … t … 6arrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr