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Question: Consider the problem max xy subject to x + y = 2. Show that (x, y) = (1, 1), with λ = 1, is the only solution of the first-order conditions. (That this is indeed the solution of the problem is easily seen by reducing it to the one-variable problem of maximizing xy = x(2 - x).) But (1, 1) does not maximize the Lagrangian L(x, y) = xy - 1 · (x + y - 2). Why not?
Objective questions based on regression
A multiple choice test consists of six questions, each of which has five choices. Each question has exactly one correct answer. William guesses randomly at each answer. What is the probability that he gets four or fewer questions correct? (Round yo..
How much gravitational potential energy does a 70 kg high-diver have on the 10 meter platform? Note: g = 9.8 m/s2and the unit for energy is a joule, which is equal to a Newton times meters (J = N*m).
Consider the real number iteration scheme x_n+1 = f(x_n) for n = 1, 2, ... with x_1 given. In addition, suppose there is a number 0
What was the maximum instantaneous rate of descent during the flight? At what time did it happen?
Consider the farmer in Exercise 7 whose field borders the river. Assume he wants the area of the plot to be 800 square feet. What should its dimensions be if he wants to use the least amount of fencing?
q1in the second order differential equation we described the motion of the pendulum. unfortunately the differential
Hyperbolic functions are similar to trigonometric functions. Define hyperbolic cosine, denoted cosh(x) as cosh(x) = (ex + e-x) / 2, and define hyperbolic sine, denoted sinh(x), as sinh(x) = (ex + e-x) / 2.
Estimate the relative error in the calculated surface area.
The Wyden Company paid a dividend of $1.28 per share last year. If the current selling price of the stock is $37.63, what is the current yield on the stock? Round your answer to the nearest tenth percent, and show all work.
A cash register contains only five dollar and ten dollar bills. It contains twice as many five's as ten's and the total amount of money in the cash register is 640 dollars. How many ten's are in the cash register?
The solution set of Ax = b is the set of all vectors of the form w = p + vh, where vh is any solution of the equation Ax =
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