What is it's origin?
State the problem with picture.
Explain how the cycloid relates to the solution.

Solution Preview

Please see the attached file for the complete solution.

Brachistrochrome Problem

1)What is it's origin?
2)State the problem with picture
3)Explain how the cycloid relates to the solution.

Answers:

1)
A Brachistochrone curve, or curve of fastest descent, is the curve between two points that is covered in the least time by a body that starts at the first point with zero speed and passes down along the curve to the second point, under the action of constant gravity and ignoring friction.

Galileo incorrectly stated in 1638 in his Discourse on two new sciences that this curve was an arc of a circle. Johann Bernoulli solved the problem (by reference to the previously analysed tautochrone curve) before posing it to readers of Acta Eruditorum in June 1696. Five mathematicians responded with solutions: Isaac Newton, Jakob Bernoulli (Johann's brother), Gottfried Leibniz and Guillaume François Antoine de l'Hôpital. Four of the solutions (excluding l'Hôpital's) were published in the May 1697 ...

Solution Summary

Brachistochrone curves are discussed in detail. The solution is detailed and well presented.

Graphically, competitive market supply is measured by the
vertical difference of competitor demand curves.
vertical sum of competitor demand curves.
horizontal difference of competitor MC curves
horizontal sum of competitor MC curves.

I need to find the orthogonal trajectories of the family of curves, y = 1/(x+c) where k is an arbitrary constant.
So far, I had figured on c = (1/y) - x
m1 = -1/(x^2 + (1/y) - x)
m2 = x^2 + (1/y) - x
I don't know how to figure beyond that. Probably because those were calculated wrong. Please show me how it's done. Tha

Cost Data
Consider the following cost functions:
TC = 20 + 4Q
TC = 20 + 2Q + 0.5Q2
TC = 20 + 4Q - 0.1Q2
Using Excel, calculate all cost curves using a range of quantity from 0 to 15.
Total cost
Total fixed Cost
Total variable cost
Average total cost
Average fixed cost
Average variable cost
Marginal cost

Suppose the demand and supply curves for eggs for the United States are given by the following equations:
Qd= 100 - 20P
Qs= 10 + 40P
Where Qd = millions of dozens of eggs Americans would like to buy each year; Qs = millions of dozen of eggs U.S. fa

How many curves does t have and what are they related to about the t-distribution?
Is there a restriction on the sample size when s can be used instead of sigma in the statement below?
The standard deviations s1 and s2 can be used when Ó1 and Ó2 are unknown and you believe that the underlying distribution is normal. Th

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The file with the problem is attached.
Graph the AFC, ATC, AVC, and MC curves for the given fixed and variable costs.
Explain the relationship between the MC curve and the two average cost curves.