$1.$ How fast is the shadow cast by a $300$ ft tall building decreasing, when the angle of elevation of the sun is $\backslash (\backslash$frac$\{\backslash$pi$\}\{3\}\backslash ),$ given that the angle is increasing by $\backslash (\backslash$frac$\{1\}\{3\}\backslash$mathrm$\{$rad$\}/\backslash$mathrm$\{$s$\}\backslash )?$ Use the Find, Given, When, Solve format. Use exact values.

$2.$ Henry's, a camera store, sells Canon cameras for $\backslash (\backslash$$ $650\backslash )$ each, and typically sells $6000$ cameras each month. For each increase in price of $\backslash (\backslash$$ $10\backslash ),$ they expect that the sales will fall by $100$ each month.

a$.$ Find the demand function, $\backslash (\backslash$mathrm$\{$p$\}(\backslash$mathrm$\{$x$\})\backslash ),$ where x is the number of cameras sold.

b$.$ Find the price that will maximize the revenue.