Homework # 7

7.17

First I solved it graphically and I can approximate the root to 2.55

Matlab:

x = (-8:0.0001:6);

f_x = @(x) x.^3 + 3.5*x.^2 -40;

plot(x,f_x(x));

Then I solved it using the function fzero in Matlab with the result of 2.5676

Matlab:

x = fzero(inline('x.^3 + 3.5*x.^2 -40'),3)

 7.19

I used Wolfram Alpha to calculate the roots for the first part of the equation:

Then I plugged the roots in and got this equation:

8.9

The First thing I did was rearrange the equation to this:

Then I used the zero function in Matlab to solve the equation and I got: 2.9449

Matlab:

x = fzero(inline('(pi*h.^3)/3 - pi*(h.^2)*(1) + (0.5)'),3)

8.14

Matlab:

%Modified Secant Method

P = (0:0.1:20000);

l_k = 50;

Delta = 250;

eck = 0.4;

E = 200000;

lk = 50;

f_x = @(P) (Delta)./(1+((eck)*sec(0.5*sqrt(P/(E))*l_k)));

plot(P,f_x(P));

for iter = 1:3

    

    sol(iter) = P-(Delta*P*f_x(P))/(f_x(P+Delta*P)-f_x(P));

    Delta = P;

    P = sol(iter);

    

end

sol()

8.17

 8.30

8.46