A man is in a boat 2 miles from the nearest point on the coast. He is to go to point Q, located 3 miles down inland (see figure). 3-x (a) The man rows at 1 mile per hour and walks at 2 miles per hour. Toward what point on the coast to reach point Q in the least time? (Round your answer to two decimal places.) mile(s) down the coast (b) The man rows at v, miles per hour and walks at v2 miles per hour. Let 0, and 0, be the magnitu sin(0,) sin(02) Show that the man will reach point Q in the least time when V1 V2 Write the equation for time in terms of x, v, and v2. t = Write the equation for the derivative of time in terms of x, V1, and v2. dt dx Write the equations for sin(0,) and sin(0,) in terms of x.

A radar gun recorded the speed of an arrow as it was shot off of a cliff.  Here is the information…                                                 time                 speed                                                 0 seconds        200                                                 1                      168                                                 2                      136                                                 3                      104   It was recorded that the speed of the arrow when it hit the ground was -210.88 feet per second.  Use all of this information to determine the initial height that the arrow was shot from

MA.912.F.1.5 Date: Period: Callie and her friend Elena are reading through different novels they checked out from their school library last Tuesday. Callie's progress through her novel can be modeled by the function p(d) = -25d +318, where p(d) represents the number of pages remaining to be read and d is the number of days since receiving the book. Elena's progress through her novel is modeled by the graph below. АУ # Pages Left 400 350 300 250 200 * 150 100 50 (3275) (8,75) 2 3 4 5 6 7 # Days Part A. Which student's novel has more pages to read? 8 9 10 11 Part B. Assuming they both continue to read at a constant rate, which student will complete their novel first?

A paved road runs east through the desert into a town. A dunebuggy is located 5 miles west and 2 miles south of the town, in the desert. (A dunebuggy is sort of a car made to go on dirt.) The buggy can travel 30 mph in the desert, and 50 mph on the road. Find the route that gets it into town the fastest. In particular, in the picture below find the value of x that results in the fastest route for the dunebuggy. 5mi Road Town 2mi Route Buggy