Question

Question #1.

The lateral surface area, S, of a cone is given by: ? = ?*SQRT(?^2 + ℎ^2) , where r is the radius of the base and h is the height. Determine the radius of a cone that has a surface area of 1200 m2 and a height of 20 m. Solve by using the bisection iteration method. Start with rl = 15 m, ru = 16 m and calculate the first four(4) iterations.

Question #2.

Determine the fourth (4) root of 200 by finding the numerical solution of the equation x4 - 200 = 0. Use False position method. Start with xl = 3, xu = 4 and carry out the first four(4) iterations.

I need a script using Matlab, Thank You.

Answer 1

Question1

clc;

clear;

f = @(r) pi*r*sqrt(r^2+20^2) -1200;

rl=input('Enter the first value of guess interval:');

ru=input('Enter the end value of guess interval:');

while f(ru)*f(rl)>0

fprintf('%d and %d', f(ru),f(rl))

fprintf('The guess is incorrect! Enter new guesses\n');

rl=input('Enter the first value of guess interval:') ;

ru=input('Enter the end value of guess interval:');

end

for i=1:4

rr=(ru+rl)/2;

if f(ru)*f(rr)<0

rl=rr;

else

ru=rr;

end

fprintf('Root after %i interation is: %ff \n',i,rr);

end

fprintf('The required root of the equation is:%f',rr)

Question1

clc;

clear;

f = @(x) x^4-200;

xl=input('Enter the first value of guess interval:');

xu=input('Enter the end value of guess interval:');

while f(xu)*f(xl)>0

fprintf('The guess is incorrect! Enter new guesses\n');

xl=input('Enter the first value of guess interval:') ;

xu=input('Enter the end value of guess interval:');

end

for i=1:4

xr = xu - f(xu)* (xu-xl)/(f(xu)-f(xl));

if f(xu)*f(xr)<0

xl=xr;

else

xu=xr;

end

fprintf('Root after %i interation is: %d \n',i,xr);

end

fprintf('The required root of the equation is:%d',xr)