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Question: (a) Consider the problem of minimizing x2 +y2 subject to x +2y = a (where a is a constant). Solve the problem by transforming it into an unconstrained optimization problem with one variable.
(b) Show that the Lagrange method leads to the same solution. Verify (2) in this case.
(c) Explain the solution by studying the level curves of f (x, y) = x2 +y2 and the graph of the straight line x + 2y = a. Can you give a geometric interpretation of the problem? Does the corresponding maximization problem have a solution?
Find the length of an arc intercepted by an a central angle of .769 radian on a circle with radius 11.4cm.
Assume that 25 cars of that year and type are randomly selected. In this binomial distribution application, which Excel statement will find the probability of 7 or fewer white luxury cars?
Determine the highest real root of: f(x) = 2x3 - 11.7x2 + 17.7x - 5 iteration using the secant method. Use x-i 3 and x0 = 4. Secant algorithm: xi+1 = xi - {f(xi) (xi-1 - xi)} / {f(xi-1) - f(xi).
How many different bit strings can be transmitted if the string must begin with a 1 bit, must include three additional 1 bits (so that a total of four 1 bits is sent), must include a total of 12 0 bits, and must have at least two 0 bits following ..
A spring has a natural length of 26 cm. If a 25 N force is required to keep it stretched to a length of 39 cm, how much work W is required to stretch it from 26 cm to 28 cm? (Round your answer to the nearest hundredth.)
Consider the allegations by Peter Navarro that China is responsible for the economic problems that currently challenge the United States. In your opinion, is he on the right track?
Describe the major phases of statistics. Formulate a business problem and analyse it by applying these phases?
A ball re-bounds one-half the height from which it is dropped. The ball is dropped from a height of 160 feet and keeps bouncing. What is the total vertical distance the ball will travel from the moment it is dropped until it hits the floor for the..
Probability: Problems and Solutions, How many ways are there of drawing a red, a black, and a green ball from a bucket with 2-Red, 2-Black, and 5-Green balls?
At the end of t years, the future value of an investment of $9000 in an account that pays 9% APR compounded monthly is 9000(1+.09/12)12t dollars. Assuming no withdrawals or additional deposits,
At time t, the displacement of a point on a vibrating guitar string stretched between x = 0and x = p is given by the function.
If it costs 1.9 times as much money to lay pipe in the water as it does on land, how far down the shoreline from should the pipe from the island reach land in order to minimize the total construction costs?
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