At which three points x1, x2, and x3 closest to x=0 but with x> 0 will the displacement of the string y(x, t) be zero for all times? these are the first three nodal points. express the first three nonzero nodal points as multiples of the wavelength λ, using constants like π. list the factors that multiply λ in increasing order, separated by commas.

The triangles are similar. what is the value of x? x=

Asmall (but heavy) particle placed in a glass of water will follow a zigzag motion because the particle will bounce off of the water molecules it meets. this is called brownian motion. a physicist simulates this on a computer, by varying the distance a particle can travel (called the mean free length), on average, before it collides with a water molecule and assigning the change in motion to be one of 8 directions, each with a similar probability. by running the simulated particle (with the same mean free length) many times she determines that it should take 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. next she lets a real particle fall through a glass of water and finds that it took 18 seconds. what does she conclude, and why?

With finding limits of multi variable !