Project description Only Octave is allowed. programming files

Objective: find dimensions of a door that fits inside the arcade $($touches the

arcade at too points, as in the figure$)$ with the door covering a maximum

surface.

Assume that the floor is the $x-$axis and the $y-$axis is at the centre of the door

$($see figure above$).$

The arcade is given by the polynomial function.

arc$(x)=-a_0{x}^8-a_1{x}^6-a_2{x}^4-a_3{x}^2+a_0+a_1+a_2+a_3$

where the coefficients, $a_0,a_1,$dots are the digits of your student ID in a reverse

order. $($exp: ID $=153310,$ then $p(x)=0+x+3x^2+3x^3+5x^4+x^5)$

Required work:

You need to find the coordinate of the contact Arcade$-$Door points, such

that the door is the largest possible $($in term of surface, the maximum

surface$).$ Note that the problem is symmetric, you need to find only one

contact point $($between $0$ and $1)$ and to other one is simply the negative

value.

You need to consider $4$ cases: $2$ rectangle doors and two square shaped

doors.

For each case you change the arcade equation by considering the ID

digits of each group member. If you are less then $4$ students in the

group just permute the digits.

You need to plot in your OCTAVE$/$MATLAB code the arcade and the

door $($use the plotting command for the doors: Rectangle $($position$\text{'},$

$[$x$\_$pos, y$\_$pos, door$\_$width, door$\_$hight$],$ linewidth', value$)$

x$\_$pos, y$\_$pos: are the left$-$bottom position of the door.