If c is the curve given by r(t)=(1+2sint)i+(1+3sin2t)j+(1+1sin 3t)k, 0≤t≤π2 and f is the radial vector field f(x, y,z)=xi+yj+zk, compute the work done by f on a particle moving along c.

Awave is produced in a rope. the wave has a speed of 33 m/s and a frequency of 22 hz. what wavelength is produced?

A3.9 g aluminum foil ball with a charge of +4.1×10−9 c is suspended on a string in a uniform horizontal e⃗ field. the string deviates to the right and makes an angle of 30∘ with the vertical. part a part complete what information about the e⃗ field can you determine for this situation? what information about the field can you determine for this situation? only the magnitude of e⃗ only the direction of e⃗ both the magnitude and the direction of e⃗ none of the above previous answers correct part b determine the magnitude of the electric field. express your answer with the appropriate units. e e = nothing nothing request answer part c determine the direction of the electric field. determine the direction of the electric field. to the right to the left away from you toward you

Part 1: a magnetic levitation or maglev train rides rails without touching them. explain how this works using your data. include the appropriate magnet drawing in your answer. part 2: two objects are near a bar magnet. one is about 1 cm away, while the other is 6 cm away. compare and contrast the magnetic force that affects each object. use your data to answer the question