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Consider a Lagrangian system, with configuration space R^n, given by (x^1, ... x^n); and Lagrangian L(x', ..., x^n; v^1, ... v^n). Now consider a new system of coordinates, (y^1,... ^n), for this same system, so the y's are functions of the x's; and, inverting, the x's are also functions of the y's. Find the Lagrangian in the y-coordinate system, and show that it produces the same physical equations of motion for the system as does the Lagrangian in the x-coordinate system.
How do you interpret the solution of a system of equations by the corresponding graph? Please provide example. What is the situation when two linear inequalities have no solution?
Prove the Second Isomorphism Theorem: If A is an ideal of R and S is a subring of R, then S+A is a subring, A, and (S intersecting A) are ideals of S+A and S, respectively, and (S+A)/A isomorphic to A/(S intersecting A).
Why is it true that any two points satisfying a linear equation will give you the same graph for the line represented by the equation?
Explain in simple terms how solving linear equations is similar and different than solving linear inequalities. Cite and explain three examples.
Explain how you would conduct the survey. What are the ethical implications if the manufacturer of Brand A toothpaste asked you to survey only its employees?
Solve the system using elementary row operations on the equations of the augmented matrix. Follow the systematic elimination proceedure.
What score does a patient at the 75th percentile receive? d. What percentage of patients score between 185 and 199?
What similarities and differences do you see between functions and linear equations that you studied in Chapter 3? Are all linear equations functions?
Evaluate the nearest distance between two tunnels using cosine rule. In a mine, two tunnels are dug starting at the same point.
What is the probability of rolling a total of 7 in two rolls of a standard dice if you get an even number on the first roll?
Probability of Drawing Two Red and Two Blue Marbles, A bag contains 4 red, 3 white and 5 blue marbles, What is the probability that in a sample of 4 marbles that are drawn
Determine the equation of the Straight line from the given data - Find the equation of the indicated curve, subject to the given conditions, Sketch the curve
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