PLEASE HELP, MAJOR, brainest if correct

The a992 steel rod bc has a diameter of 50 mm and is used as a strut to support the beam. determine the maximum intensity w of the uniform distributed load that can be applied to the beam without risk of causing the strut to buckle. take f. s. = 2 against bucklin

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

Select light for the type of wave, adjust the wavelength so that the light is red, and increase the amplitude of the light to the max. then, select the start button at the source location to begin producing the waves. light is a form of electromagnetic wave, containing oscillating electric and magnetic fields. the wave amplitude detector mentioned above shows how the electric field oscillates in time at the location of the probe. the amplitude of the wave at the location of the probe is equal to the maximum electric field measured. how does the amplitude of the wave depend on the distance from the source?