6-18 Determine the force in each member of the truss and state if the members are in tension or compression. Set P₁ = 10 kN, P₂ = 8 kN. G E 2 m A B P₁ D 1 m -2 m P2

A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i+ 3xyj + 3y2k. Use Stokes' Theorem to find the work done.

ind a salutien co the Inear equation 14x-y=-14

The two-dimensional wave equation describing the vibrations of an infi- nite string is Θη Ot2 2021 მ2 where n = n(x,t), — -x 0 is a constant. Its general solution can be written as n(x,t) = F(x-ct) + G(x + ct), with F and G arbitrary smooth functions. If at time t = 0 the shape of the string is n(x, t = 0) at 9 = 5+x4 and the string is released with velocity (x, t = 0) = 0, determine n(x,t) for t > 0.

3 Charged Closed Wire Consider a thin closed wire with the radius R localized at the origin on the xy-plane, which is charged uniformly with the total charge Q. (i) What is the charge density p in this problem? (ii) Calculate the electric field along the z axis? (Hint: First, consider an infinitessimal piece of the charge.)

Please show all work ง 5. Evaluate the vector surface integral JJ (+2², x + 2y + 32², 5x − 2y + 2³) . Ndo. S Here, S is the sphere Sy²+2 1. = Since S is a closed surface, the outside of S is considered as the positive side on S. Hint: use the divergence theorem.

Consider the radiation with the following wavelengths: 1. 600 nm II. 200 nm III. 1200 nm Arrange by: LOWEST energy LOWEST frequency HIGHEST energy_ ergy_||| A. I, I, III B. II, II, I C. III, III, I D. III, II, II E. II, II, III 20

Problem 4. (20 points) Consider a LTV system (t) = A(t)x(t) where x(t) = R² and === 3 A(t) == -2-6t 4+8t] -1-2t 2+2t -2 4 = +2t. -1 2 A1 A2 Vt ≥ 0. ' Note that A₁ is the exact same state dynamics matrix in Problem 3 (hence A² = 0) and A₂ = A₁-I. Find the fundamental matrix (t), namely, the state transition matrix (t,0), of the system.

Sketch the region bounded by the curves x=y34,x=2, and y=0 then find the volume of the solid generated by revolving this region about the y-axis. I need answer typing clear urjent no chatgpt used i will give upvotes

D nctions Question 10 Use the diagram below to find each of the following: sine of point a • cose of point b • tane of point c d e