Consider a point moving on the xy plane. For all the trajectories listed below, derive the ex- pressions for f(t), ö(t), F(t), T(t), ā(t) in terms of î and 6: (a) r(t) = 8, ø(t) = 4 (b) r(t) = 8, ¢(t) = 4 + 17t (c) r(t) = 8t, $(t) = -4+17t

Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .

In a study conducted at Dartmouth College, mice with a particular type of cancerous tumor were treated with a chemotherapy drug called Cisplatin. If the volume of one of these tumors at the time of treatment is Vo, then the volume of the tumor t days after treatment is modeled by the function V(t) = = Vo(0.99e- + 0.01e0.239t). -0.1216t 1. Set Vo = 3 and plot V(t) over the interval 0 ≤ t ≤ 16. Appropriately adjust the viewing window to see the behavior of V(t) and sketch the graph below. 2. From the graph, estimate the time at which the volume of the tumor decreased to half its original amount. There are two such times, record each to the nearest whole number. 3. With Vo = 3, write down the equation whose solution gives the time at which the tumor is half its original volume. (Re)write the equation with zero in the right-hand side. 4. Using one of your answers from 2. as to and your equation from 3., apply two steps of Newton's method to better approximate this time. (Round to 3 decimal…