lume; U Book & Closed Notes Manical Engine Problem #1 (50 point): Find the centroid of...
both questions Use a computer algebra system and the fact that the centroid of the region having area A bounded by the simple closed path C is xd to find the centroid of the region. R: region bounded by the graphs of y -x and y 3 sin θ and outside the circle x-2 cos θ, y-2 sin θ, Evaluate the line integral Let R be the region inside the ellipse x-4 cos θ, y (3x2y + 7) dx +...
General Notes 1) This is a closed book and closed notes test. No discussion. No cellphone, tablets or laptops. Only regular calculator allowed. 2) Please read the problems carefully and always calculate with units. 3) Start with those you feel more comfortable with; don't get stuck on one problem. 4) Show the logic flow of your solution when running out of time. Write on the back when running out of space 5) During the test, any activities such as copying...
webwork math233 17742 huang s19 16.4 parametrized surfaces /1 16.4 Parametrized surfaces: Problem 1 Problem List Next Problem Previóus Problem (1 point) Show that Ф (u, u)-- (9u t-3, u-u, 17u t u) parametrizes the plane 2x-y-z--6. Then (a) Calculate Tu. T. and n(u, v) (b) Find the area of S-D(D), where D = (mu) : 0 < u < 6,0 < u < 7 (c) Express f(x, y, 2 yz in terms of u and v and evaluate JTs...
1. Centroids: Determine the area and location of the centroid X and Y of the following shape using double integrals and polar coordinates. Use the angles in radians. Use b=4 inches 300 450 A x area = ſſ dxdy 1. Centroids: Determine the area and location of the centroid X and Y of the following shape using double integrals and polar coordinates. Use the angles in radians. Use b=4 inches 300 450 A x area = ſſ dxdy 2. Parameterization...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds- 1 point)...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
Sec7.1: Problem 8 Previous Problem List Next (1 point) Book Problem 21 0 to 3 sin() and y = 4 cos(x) from Sketch the region that lies between the curves y 0.9. Notice that this region consists of two separate parts. Using a graphing calculator, the x-coordinate c of the point of intersection is approximately equal to 927 dx+ Se 0,9 dr The area A of this region is Jc After integrating, A = Note: You an earn partial credit...
(1 point) Book Problem 24 * F(z) = *5(e)dt , where f(t) = 51 9+u? du, find u F"(x) = and F"(3)
Take that a (Figure 1) 50 mm Part A Determine the distance to the centroid of the beam's cross-sectional area Express your answer to three significant figures and include the appropriate units z= | Value | Units | Submit Request Answer Part B Find the moment of inertia about the y axis. Express your answer to three significant figures and include the appropriate units LA IValue Units Figure 1 of 1 Submit Request Answer < Return to Assignment Provide Feedback
u Review Part B - Calculate the moment of inertia Learning Goal: To find the centroid and moment of inertia of an I-beam's cross section, and to use the flexure formula to find the stress at a point on the cross section due to an internal bending moment. Once the position of the centroid is known, the moment of inertia can be calculated. What is the moment of inertia of the section for bending around the z-axis? Express your answer...