Lab $7$: User$-$defined function $($week $8)$

Question $1$

The relationship between the traffic flow $(q)$ in vehicle per hour $($vph$)$ and the density $(k)$ in vehicle per mile $($ vpm $)$ is as following:

$q=ak-b{k}^2$

Where; $a=45\mathrm{.}5$ and $b=-0\mathrm{.}24$

$($a$)$ Write a MATLAB function to calculate the traffic flow as a function of the density

$($b$)$ Plot the flow for the density from $0$ until $189$ vpm and determine maximum of the flow and also the density at maximum flow. Add axis labels $(k,$ Density $($vpm$))$ and $(q,$ Flow $($vph$))$ in addition to the title $($Flow vs$.$ Density$).$

Question $2$

$(1)$ define $x$

$(2)$ call a function called "main" that takes the vector $x$ input, and produce the following outputs:

Vector $W$ defined by $W(x)=-0\mathrm{.}2x^5+e^{-0\mathrm{.}5x}$

Vector $Z$ defined by $Z(x)=x^3+5x^2$

$(3)$ plot Z vs W using red dotted line. Add appropriate $x$ and $y$ labels.

Question $3$

The range of an object shot at an angle $$ with respect to the x $-$axis and an initial velocity $v_o$ is given by: $,$ range $=\frac{v_0^2}{(g)}sin(2)$

Where; $v_o=100\frac{m}{s}$;$g=9\mathrm{.}81\frac{m}{s^2},$ and $$ varies from $0$ to $\frac{}{2}$ with $100$ elements.

Create a MATLAB function $(1$ input$)$ that returns:

$($a$)$ A Plot of the range distance vs$.$ angle $.$

$($b$)$ The maximum range and the corresponding $$ value.

Question $4$

Create an anonymous function for $10e^{-2x}$ and use it to plot the function over the range $0x2$