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Question: Use Exercise I to construct an algorithm for determining whether a directed graph contains a circuit.
Exercise I: Show that if G is a directed graph and T is a spanning tree constructed using depth-first search, then G contains a circuit if and only if G contains a back edge (see Exercise II) relative to the spanning tree T .
Exercise II; Show that if G is a directed graph and T is a spanning tree constructed using depth-first search, then every edge not in the spanning tree is a forward edge connecting an ancestor to a descendant, a back edge connecting a descendant to an ancestor, or a cross edge connecting a vertex to a vertex in a previously visited sub tree.
Use your calculator to evaluate the following expression if x = 9.69, and y = –8.02. Round your answer to the nearest tenth.
a certain type of light bulb has a life time can be represented by a normal distribution with a mean of 500 hours and a standard deviation of 100 hours
Prove that a polynomial function y = P(x) is continuous at every number x.
A specialty-freezer company has determined that the operating costs at one of its plants can be approximated by the function:
If the total cost of producing x gimcracks is C(x) = 144 + 40x + x2 how many gimcracks should you make in order to minimize the average cost of a gimcrack? What is the minimum possible average cost?
The message is meant to be an array of length n, in which a symbol may be used more than once. Find the density of X and the CDF of X.
a rectangular table is six times as long as it is wide. If the area is 96ft2 , find the length and the width of the table?
how many samples of 3 apples can be drawn from the crate? how many samples of 3 could be drawn in which all 3 are rotten?
Evaluate f(x)=(2x^4-(3^x/100)) for at least five values of x between 0 and 1. Use this and possible a graphical calculator to evaluate limx->0 (2x^4-(3^x/100))
1. How might a particular actual or hypothetical argument that a worthwhile goal (end) justifies use of unethical persuasive techniques (means) be viewed as an example of Situational Perspective?
Find the derivative of y with respect to x. y = sec ^ -1 (x^2 + 1), x > 0
The relative number N of gas molecules in a container that are moving at a velocity v can be shown to be N = av2e-bv2, where a and b are constants.
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