Invasive species often display a wave of advance as they colonize new areas. mathematical models based on random dispersal and reproduction have demonstrated that the speed with which such waves move is given by the expression 2 dr , where r is the reproductive rate of individuals and d is a parameter quantifying dispersal. calculate v'(r), the derivative of the wave speed with respect to the reproductive rate r.

Glass is transparent to visibile light under normal conditions; however, at extremely high intensities, glass will absorb most of the light incident upon it. this works through a process known as multiphoton absorption. in this process, several photons are absorbed at the same time. if very intense light whose photons carry 2ev of energy is shined onto a material with a band gap of 4ev, that light can be absorbed through two-photon absorption, because two photons have the right amount of energy to bridge the band gap. what is the minimum number of photons of 800-nm light that are needed to equal or exceed the band gap of fused silica glass

An object has a weight of 500 on earth what is the mass of this object

Gas cloud 1 is likely to form a star. gas cloud 2 is not. based on this information, match the given conditions with each cloud