Part $1)[7$ marks$]$

An airplane that is flying horizontally passes over an air station at an altitude of $21000$ meters at a speed of $310$ meters per second. At what rate is the distance of the airplane from the station increasing when the distance between the airplane and the station is $32500$ meters? Provide all the details of your solution.

Write the solution to this question on the exam booklet provided by your instructor.

Part $2)[7$ marks$]$

A gutter is to be made out of a strip of metal $30$ cm wide, with the cross section having the form shown. What depth $\backslash (\backslash$boldsymbol$\{$x$\}\backslash )$ gives the maximum cross sectional area?

$($The area of a trapezoid is given by the equation $\backslash ($ A$=($a$+$b$)($h $/2)\backslash ),$ where $\backslash ($ a $\backslash )$ and $\backslash ($ b $\backslash )$ are the fength of the two parallel sides $($bases$)$ and $\backslash ($ h $\backslash )$ is the height.$)$ Provide all the details of your answer.