Part $1$: Use one Excel file to submit your solutions; one worksheet per question; total number of worksheets in the Excel file should be $2.$ Data should be well organized and center$-$aligned vertically and horizontally. Independent variables should be programmed. Constants should not be embedded in the formulas.

$1$a$.$ In an Excel spreadsheet, create a table of the function, f$($x$)=3$x$2-12\mathrm{.}4$x $+3$

for $0<=$ x $<=4,$ step $0\mathrm{.}1.$ Results should be in two decimal places.

$1$b$.$ Using linear interpolation, determine the two points where f$($x$)$ crosses the x$-$axis.

$1$c$.$ Write a VLOOKUP program to determine f$($x$)$ at any arbitrary point in the Table.

$2.$ Using the equations for the canon ball problem shown here:

$($a$)$ Obtain a solution in an Excel spreadsheet for h$($t$)$ and x$($t$)$

for $0<=$ t $<=1\mathrm{.}2$ s$,$ step $0\mathrm{.}01$ s$.$ Initial speed, v $=10$ m$/$s$.$

Launch angle, $\backslash$theta $=35$o$.$ Gravity, g $=9\mathrm{.}81$ m$/$s$2.$

$($b$)$ On the table generated, use the cell fill command to color code the cells containing the maximum height reached, the total flight time, and the total distance traveled at ground level.

Results should be in two decimal places. Your solution should look like the sample shown here.

Part $2$: Name your M$-$files according to the question number and submit in the Dropbox:

$3($a$)$ Write a simple MATLAB script $($M$-$file$)$ to calculate the inverse of the following trigonometric functions; sine$,$ cosine, and tangent of any angle.

$3($b$)$ For the right$-$angle triangle shown here, write a simple MATLAB script $($M$-$file$)$ to calculate h and $$ given any input values of x and y$.$

$4.$ Consider the analytic solution of the projectile problem described in Section $1\mathrm{.}1\mathrm{.}2.$ Write a MATLAB script that will prompt the user to enter the launch speed and angle, and will compute the peak height, flight time, and horizontal distance travelled using the analytic equations.

$5.$ Write a MATLAB function that will take a $(4\backslash$times $4)$ matrix as an input argument and will return a $(4\backslash$times $1)$ array containing the averages of each of the four rows of the input matrix.