Hello, i need help on my assignment. I have just started to learn MTHLAB and nee

Question

Hello, i need help on my assignment. I have just started to learn MTHLAB and need some help with these problems. Thank You

4. Derivatives dy dt2 v. Assume y(t)A cos(w t) B sin(w t). Use Matlab and the diff function to find the expressiony Simplify the expression using the simplify function. Use the collect function to get a result with the cos (wt) and sin (wt) terms grouped together. Show each of these results at the console. Experiment with pretty and latex (and an online LaTex renderer) to see the output in neater forms 5. Basic integration t/2 Show that tan-11 = 0 sin2x dx 6. Integration with simple probability application The results of a certain biological test are found to be normally distributed, with an average value H of 1000 and a standard deviation ? of 150, we can define zo-(x-?)/? as a measure of the number of standard deviations from the mean that a number x is. It can be shown that the probability that a test score will be above a certain value x s eiven by pluan) - j e.ind the robbiliy hat will be 1300 Use boththe int value xo is given by p(x2 xoe dz. Find the probability that x will be 2 1300. Use both the int 2Tt Zo function (and vpa) and the integral function.

Explanation / Answer

4.)

MATLAB CODE:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

syms A B w t
y=A*cos(w*t)+B*sin(w*t);
sol=diff(y,t,2)+y;
simplify(sol)%%%%using simplify
collect(sol)%%%%using simplify

%%%%%%%%%%%%%%%%%%%%%%%%%

OUTPUT:

Untitled

ans =

-(A*cos(t*w) + B*sin(t*w))*(w^2 - 1)


ans =

(- A*cos(t*w) - B*sin(t*w))*w^2 + A*cos(t*w) + B*sin(t*w)

5.

MATLAB CODE:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

syms x
sol1=atan(1)%%%calculating taninv(1)
f=(sin(x))^2;
sol2=vpa(int(f,[0,pi/2]))%%%using int to get integration value AND vpa

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

SOLUTION:

>> Untitled2

sol1 =

0.7854

sol2 =

0.78539816339744830961566084581988

6.

MATLAB CODE:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

syms z
x=1300;
sigma=150;
mu=1000;
zo=(x-mu)/sigma;
f=exp(-z^2/2);
p=(1/sqrt(2*pi))*int(f,[zo,inf]);
vpa(p)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

SOLUTION:

ans =

0.022750131948179208621560237846009

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