$1.$ Complete the learner template to compute the power output from a wind turbine with and wind velocity $.($Note that $).$ Assigns the resulting value $($in Watts$)$ to a variable named wind$\_$power.

$2.$ Continue completing the template to use a vector of radius values r$\_$vals $=[1,12,24,40,60,80,100,120,200]$ and calculate the corresponding power output of the turbine $[2]$ with those radii at the same wind velocity as above. Use vector operations in Matlab. See reference $[5].$ In a figure $1,$ plot r$\_$vals versus power$\_$output. Label the xaxis 'Radius $($m$)\text{'}$ and the y$-$axis 'Power $($W$)\text{'}.$ Use a fontsize of $20$ for your axis labels. Use a red line in your plot with a thickness of $3$ units. Indicate every data point with $(*).$ Store the elements of the rendered line in a "graphics handle" called 'graph$\_$properties'. $($Hint : see help for plot, xlabel commands $[3]).$ Note that the tests in this automatically graded script are very strict so your spacing and syntax in the labels has to be exactly as written here.

$3.$ If you have to perform the same mathematical operation on arrays of numbers in MATLAB, you have two approaches you can use. $($This actually also applies to other numerical packagages like numpy and scipy in Python$).$ You can use 'for loops' or vector operations. In MATLAB, vector operations are faster than 'for loops'. You will now test this observation yourself by implementing the calculation in $(2)$ above using the two methods: 'for loops' $[4]$ and vector operations $[5],$ and then measuring the time it takes for the computer to perform the computation. You will need to use MATLAB function 'tic' and 'toc' $[6]$ to calculate elapsed time. You will need to measure the average execution time over $2000$ iterations $($use variable M to denote number of iterations$)$ of each method to get a reliable measure of T$\_$f $("$for$"$ loop execution time$)$ and T$\_$v $("$vector computation" execution time$).$ Use MATLAB help to figure this out as well as $[6].$ Complete the learner template code to perform the following steps.

Use the vector math you used in $(2)$ above to perform the same calculation $2000$ times. Assign the values to power$\_$output$\_$a$.$ This should be the same as power$\_$output you calculated above. Assign the duration to the variable T$\_$v

Use a single "for loop" to calculate the power output in $(2).$ Assign the values to the vector power$\_$output$\_$f $.$ Measure the time it takes to perform this operation $2000$ times. Assign that value to the variable T$\_$f

Calculate the ratio T$\_$f$/$T$\_$v and assign that to the variable ratio.