Solve the following nonlinear system using Newton's method 1 f1(x1, x2, x3)=3x₁ = cos(x2x3) - - 2 f2(x1, x2, x3) = x² - 81(x2 +0.1)² + sin x3 + 1.06 f3(x1, x2, x3) = ex1x2 +20x3 + Using x (0) X1 X2 X3 10π-3 3 = 0.1, 0.1, 0.1 as initial conditio

2. (a) State Fermat's principle for the propagation of a light ray from point P at (x1,y1) to Q at (x2, y2), expressing the principle as a problem in Calculus of Variations. (b) Suppose c(y) is the speed of light in a medium, given by c(y) Y where a is a constant. Find the path of a light ray between the points P: (−1,3) and Q (1, 3). Is there more than one possible path? (c) Sketch the path of the light ray, and interpret what an observer at Q would see if there were a light source at P.

On a given day, the sea level pressure is 1013.2 hPA. The temperature at 3,000 ft AMSL is given as minus 4°C. The temperature difference compared with the ISA is: Can you give me a step by step explanation  ISA - 13°C ISA - 4°C (c)ISA - 10°C (d) ISA +10°C ISA is +15 Celsius  Answer is -13Celsius

answer the question attched

Also, construct a know-show table to outline the proof of this proposition.

why the know-show table below is not valid: I know something is wrong in the step p2-p5 but I don't know how to explain it. Can you explain why please.

Consider the following statement: For all integers a and b, if a 0 (mod 6) and b #0 (mod 6), then ab #0 (mod 6). Which of the following statements are true? (select all that apply) Original statement ✓ Contrapositive Converse Negation ☐ None of the statements are true

Proposition: If m is an odd integer, then m + 6 is an odd integer. Proof: For m + 6 to be an odd integer, there must exist an integer n such that m+6=2n+1. Subtracting 6 from both sides, we see that m = 2n+1-6 = = 2n― 6+1 = 2(n − 3) + 1. Since the integers are closed under subtraction, then n-3 € Z. Hence, the last equation implies that m = = 2q+1 where q = n = 3. This proves - that if m is an odd integer, then m + 6 is an odd integer. Based upon the Reading assignment and the Elements of Style >>, which of the following is the most significant error in the proof? The proof does not use complete sentences The proof contains a sentence that begins with a mathematical symbol The proof uses cumbersome notation The proof contains a variable used for more than one object The proof is written backwards The proof uses an example to prove the general case

Determine the force in members HI and FI of the truss shown when P = 100 kips.