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![You are designing a spherical tank (see figure below) of radius R-3m, to hold water for a small village in a developing country. The volume of liquid it can hold can be computed as 3R- h Where h is the depth of the water and Vis the volume of water. Write a function that uses the Newton-Raphson method to calculate the root and number of iterations to obtain the root. Your function should accept the function f, derivative function df, initial guess xi, and the precision as inputs. A. function [root, iter] = newraph(f,df,x, precision) Write an m-file that uses the function from part A to determine the depth that the tank must be filled to so that it holds 30m3 of water. Prompt the user for the initial guess of xi. Use a precision of 1e-4. Your m-file should plot the function f and derivative function df. Also, mark the roots with a blue upward triangle. B.](https://d2vlcm61l7u1fs.cloudfront.net/media%2F0b3%2F0b3086ae-5069-4c67-bbbc-386cb7003f1a%2Fphp8CXfo7.png)
MATLAB question
You are designing a spherical tank (see figure below) of radius R = 3m, to hold water for a small village in a developing country. The volume of liquid it can hold can be computed as V = pi h^2 3R – h/3 Where h is the depth of the water and V is the volume of water. A. Write a function that uses the Newton-Raphson method to calculate the root and number of iterations to obtain the root. Your function should accept the function f, derivative function df, initial guess x_i, and the precision as inputs. function [root, iter] = newraph(f, df, x, precision) B. Write an m-file that uses the function from part A to determine the depth that the tank must be filled to so that it holds 30m^3 of water. Prompt the user for the initial guess of xi. Use a precision of 1e – 4. Your m-file should plot the function f and derivative function df. Also, mark the roots with a blue upward triangle.
Expert Answer
A)
%—————-newraph.m————————–
function [root, iter]= newraph(f,df,xi,precision)
iter=0; % to count the iteration
er=999;% intial error should be very high
x=xi;
while er>precision
x1=xi-(f(x)/df(x));
er=xi-x1
x=xi;
iter=iter+1;
end
root=xi;
To call the above function do following
% define the function f as :
R=value of R here
v=@(h) pi*h^2((3*R-h)/3)
%this is the derivative of the above function
dv=@(h) 2*pi*h*R-pi*h^2
%
vi=initial guess;
precision=put yor value here
Now call the functioin as
>>[root, iter]=newraph(v,dv,vi,precision);
B)
