Mainly e and d

Q.2.8 The temperature on a square plate is given by the following two-dimensional function T(x,y)=80e(x1)2e3(y1)2 where x[0,1] and y[0,1]. The temperature of the plate is 80C at the corner x=y= 1. (a) Write a MATLAB code to plot contours where T(x,y)=70,60,50,40,30,27,20,10,5. Note the contour line for T=27C. (b) Calculate the partial derivatives xT and yT. (c) You have spotted a spider on the x=0 edge of this plate. You know that spider likes to be in an area where the temperature T=27C. Any cooler or hotter, it will not be good for the spider. You are required to find the y location where you will tell the spider (for this exercise, you have the special ability to talk to the spiders!) to go in order to feel the temperature of T=27C. You might like to follow the steps below to answer this question. i. Explain why you will need to solve f(y)=80e(01)2e3(y1)227=0 in order to get the initial y location for the spider. ii. Plot the function f(y)=80e(01)2e3(y1)227 iii. Guess what the y value should be such that f(y)=0. iv. Use this guess value of y and the Newton-Raphson method to find a more accurate ii. Plot the function f(y)=80e(01)2e3(y1)227 iii. Guess what the y value should be such that f(y)=0. iv. Use this guess value of y and the Newton-Raphson method to find a more accurate value of y such that f(y)=0. In implementing the Newton-Raphson method, use your answer in 2.8b. (d) Now that you have told the spider where the y value is such that T=27C at x=0, the spider now tells you that she/he would like to walk to the right edge of the plate, x=1 but only along the path where T=27C. Modify your code in (c) to such that you can find this path. Check your answer with the contour of T(x,y)=27C in part (a)