Please write the solution process in detail, thank you!

(a) A rover on Mars has just collected a very interesting soil sample. It will launch a two stage rocket to send the sample to an orbiting satellite for further analysis. The distance above the surface of Mars that the rocket carrying the sample is, after t hours, is given by t) 2 t3 9t2 + 24: kilometers. The rst stage of the rocket. has enough fuel to burn for exactly 6 hours. The rocket's second stage should be red during this 6 hour window when the rocket's height is maximized. 'When shOuld the sec0nd stage he red? (b) A 1 [I1 length of wire is to be cut into two pieces. The rst piece will be bent to form a circle, while the second piece will be bent to form an equilateral triangle. Maximize the total area enclosed by these two shapes