Question

APPLIED PROJECT CAS WHERE TO SIT AT THE MOVIES A movie theater has a screen that is positioned 10 ft off the floor and is 25 ft high. The first row of seats is placed 9 ft from the screen and the rows are set 3 ft apart. The floor of the seating area is inclined at an incline that you sit is x. The theater has 21 rows of seats, so 0x 60. Suppose you decide that the best place to sit is in the row where the angle 0 subtended by the screen at your eyes is a maximum. Let's also suppose that your eyes are 4 ft above the floor, as shown in the figure. (In Exercise 4.7.78 we looked at a horizontal, but this project involves a more complicated situation and requires technology.) angle of a-20° above the horizontal and the distance up the simpler version of this problem, where the floor is 1. Show that 25 ft a+ b 625 arccoS 2ab 14 f sin a) a-(9+x cos a) +(31-x where 10 ft b-(9+x cos a) +(x sin a 6) and 9 ft 2. Use a graph of 0 as a function of x to estimate the value of x that maximizes 0. In which row should you sit? What is the viewing angle 0 in this row? 3. Use your computer algebra system to differentiate 0 and find a numerical value for the root of the equation de/dx 0. Does this value confirm your result in Problem 2? 4. Use the graph of 0 to estimate the average value of 0 on the interval 0 x60. Then use your CAS to compute the average value. Compare with the maximum and minimum values of 0.

Answer 1

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