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Derive the Euler-Lagrange Differential Equation (rigorously). Explain any theorems or results that you use in the derivation (e.g. don't just say "by the fundamental theorem of the calculus of variations" without telling what the fundamental theorem of the calculus of variations is and what it means). Also explain in words and/or pictures why the Euler-Lagrange Differential Equation is believable (intuitively).
A plane is heading due south with an airspeed of 227 mph. A wind from a direction of 60 degrees blowing at 16 mph. Find the bearing of the plane.
A major league pitcher can throw a baseball in excess of 48.8 m/s. if a ball is thrown horizontally at this speed, how much will it drop by the time it reaches the catcher who is 15.7 m away from the point of release?
One tire manufacturer found that after 5,000 miles, y=32 of n = 200 steel-belted tires selected at random were defective. Find an approximate 99 percent confidence interval for p, the proportion of defective tires in the total production.
The three methods of solving linear systems covered are substitution, elimination, and graphing. There are examples posted on the solution field and in the attachment.
Retailers will buy 45 cordless phones from a wholesaler if the price is $10 each but only 20 if the price is $60. The wholesaler will supply 35 phones at $30 each and 49 at $38 each. Assuming the supply and demand functions are linear, find the ma..
Use implicit differentiation to find an equation of the line tangent to the curve x^2 + y^2 at the point (3,-1). Use implicit differentiation to find an equation of the line tangent to xy=12 at the point (4,3)
Probability of Picking Groups of Cards, Find the probability that a hand of 13 cards dealt from a well shuffled pack of 52 contains
Farmer Brown, distant mathematical cousin of Mr. Brown, wants to enclose a grazing area along a river bank and build an opera hall. He has 500m of fencing available and none can be used along the riverbank. What are the dimensions that give the la..
The manufacturer can produce the lamps at a cost of $4 per lamp. At what price should the manufacturer sell the lamp to generate the greatest possible profit?
How many six-digit even numbers less than 200,000 can be formed using all the digits 1, 1, 2, 2, 3 and 5? How many permutations of the letters in the name ABBA are there?
Formulate a linear programming model for the problem.
Correctly match each of the following descriptions to a graph below by inserting the letter of the description that correctly describes the graph in the open box under the graph. The graph has both an Euler circuit and a Hamilton circuit.
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