Avehicle of ‘dry’ mass m0, with no propulsion, is moving without friction on hor- izontal ground. rain is falling vertically. while the rain is falling, for each time interval ∆t, an amount of rain ∆mr = b∆t hits the vehicle, sticks to it, and then moves along with zero relative velocity with respect to the vehicle. the vehicle is observed to be slowing down. in a reference system fixed to the ground, at time t = 0, the cart is initially moving with speed v0. (a) at time t, the vehicle is traveling with speed v(t). for the time interval [t, t+∆t], while the rain is falling, determine a differential relation for the change in speed of the vehicle ∆v. write your answer using some or all of the following: t, ∆t, m0 and b. (b) integrate your result from part (a) to find the speed v(t) of the cart at time t. write your answer using some or all of the following: v0, b, m0 and t.

where is the circuit diagram ?

bacteria that live on the ocean floor are sustained by phytoplankton. phytoplankton, microscopic marine photosynthetic organisms, have a vastly significant role to play not only in the marine food web of which they’re part of, but also on a more global scale. despite their infinitely small size in comparison to other marine organisms, these tiny creatures occupy an immensely important ecological niche: they are the foundation of the marine food web, and as primary producers, play key roles in supporting all other organisms in the marine environment, as well as in the regulation of the earth’s climate through the sequestration of carbon, oxygen production, and other related processes. phytoplankton account for roughly half of all global primary productivity; therefore, their significance extends far beyond the marine environment alone. there is an intriguing sense of irony in the realization that these tiny living beings that often live out their existence unnoticed and undetected by the rest of the world, have such a far-reaching impact on the lives of virtually all other living organisms on the planet, particularly on those in the marine environment. the world that we have become accustomed to has been and is continuously shaped by the workings of these miniscule yet vital “plants of the sea”.

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