Question
Solve the following nonlinear root finding problem with three unknowns using the Newton-Raphson method. Iterate three times starting from initial point (I =1, 52 =1, T3 = 1).371 COS (T2T3- 2 4x} _ 625.2 +253 =1 20T3` texp(~ T1T2_ =-9
Solve the following nonlinear root finding problem with three unknowns using the Newton-Raphson method. Iterate three times starting from initial point (I =1, 52 =1, T3 = 1). 371 COS (T2T3- 2 4x} _ 625.2 +253 =1 20T3` texp(~ T1T2_ =-9
Answers
Find all degree solutions to the following equations. $$\cos \left(A-50^{\circ}\right)=\frac{\sqrt{3}}{2}$$
We are given the function asking X cubed plus three X squared plus three X equals zero. First thing we do is take out three Xs Coleman on we get the core traffic function X squared plus X plus one, and we'll use the quadratic formula to find the root that's equal. Do minus one plus minus under your friend, minus four upon Duke. So these are going to be imaginary news. We write them in the same sort that minus one place through three I hold on to, and I don't the set form on. Now. We'll find a real solution, that 84 calculator and see it on the craft visually for us. We set up the window as they have masters, too, for the craft that X from minus 5 to 5. Advice from my despite 25 Aun said the appropriate skills as well, Once that enter the function. That's three X Cube plus three X Square plus three X When they don't now adopted Zito for the X axis and refined the intersection point. As we see, there's only one point. We still use the calculator for that. Although we're show what it's gonna be we selected Intersect option. Find the point. As you know, reasons are only the solution
So we need to find all degree solutions and we have the function or the equation. Co sign of a plus 30 degrees is equal to one half, so this means that Fada is equal toe. A plus 30 and co sign of data is equal toe one half when we have the reference angle of 60 degrees. We know that Kassian is positive and quadrant one and quadrant four. So theta in quadrant one is 60 degrees and fada in quadrant four is 360 minus 60 degrees just 300 degrees. So that means a plus 30 degrees is equal to 60 degrees or a plus. 30 degrees is equal to 300 degrees. Okay, so this means that a is equal to 30 degrees or a is equal to 270 degrees. So to find all degree solutions, we add 360 degrees K. Because the period of cosign is 360 degrees, so a is equal to 30 degrees plus 360 degrees K, and A is also equal to 270 degrees plus 360 degrees K.
Okay, so we are going to find all the zeros for effort back. Zeke with the coast on a two x minus, X squared, plus two acts. So first, let's get the graph on the board like this. We could see that one of them is around 0.5 ish and one of them is around 1.5 ish so we can ask for our estimates down as X zero is able to make it a 0.5 and the other as X of zero, is equal to 1.5. And of course, our after thanks is equal Teoh co sign of two X minus X squared, plus two acts. It means that the derivative of F of X is going to be equal to negative to sign of two X minus two X plus two. We're going to plug these in, starting with negative 0.5, and there is equal to co sign of two Times City to minus C two Squared was two times he to. And then there's this gonna be rated to con sign of two times C two honest to come see two plus two we want to do is equal to X minus Ethel Banks, divided by Fama, backs them one got it as a new that's of one. And as usual, we just carried these down over and the weekend yet that the answer is about he lives your 0.33541 You're saying for 1.5 again, over have to do is replace the X of zero as 1.5 from negative 0.5 and then we get 1.33306 So those are gonna be our answers. Regular 0.335 for one and 1.33306 is it?
According to question, Horse six is given us root tree according to and you have to find the general solution off process. Now we know that course sixes in Khost, Cordant and poor quadrant. So when Cossacks is present in her court First Squadron and values on you, the next will be simply equals pi upon sick. But when Koszics is present in the port quarter and then develop off X will be simply equal school fight minus of fire. Ponsi, that is 11 fight upon seeks now, since the coup period off the coastline function is to fight. Therefore, general solution is given as X equals 5.6 plus who in fight and X IQ was 11 5.6? Let's win fight That in is any easier. So this will be the final answer, okay?