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Let A be the adjacency matrix of an undirected network and 1 be the column vector whose elements are all 1. In terms of these quantities, write expressions for:
a) the vector k whose elements are the degrees ki of the vertices;
b) the number m of edges in the network;
c) the matrix N whose element Nij is equal to the number of common neighbors of vertices i and j;
d) the total number of triangles in the network, where a triangle means three vertices, each connected by edges to both of the others
suppose cotx -6.5 and sinxlt0. find the following quantities you can use .5 instead of a square root in a numerical
Find the dimensions of a rectangular fence that encloses an area of 81 feet that uses a minimum amount of material.
James borrows $12,000 for equipment so that he could do some of his personal training work in his garage. He agreed to repay $13,200 after 300 days. Find the amount of interest and the interest rate.
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.)
If the fund earns interest at the rate of 10% year compounded quarterly, determine the size of each (equal) quarterly installment that should be deposited in the fund.
The number of parks, y, being built in a city is a linear function of time, x, and is graphed on a rectangular coordinate system. Write a paragraph describing your interpretation when the slope is positive
an art dealer has a client who will buy the masterpiece rain delay for 50000.the dealer can buy the painting now for
a ranger in tower b, located 60 miles at a direction of 46 degress drom tower a, spots the fire at a direction of 283 degrees. how far from tower a is the fire? how far from tower b
Transform each equation to standard form. Then find the center, foci, major and minor axes, and ends of each latus rectum. Draw the curve
worth, missouri is 25 miles more north of independence, missouri than it is west of putnam, missouri. The distance between independence and putnam is approximately 120 miles. Find the distance between putnam and worth and the distance between wort..
If A is nonsingular, show that the characteristic values of A^(-1) are the reciprocals of A, and that A and A^(-1) have the same characteristic vectors.
Let n >= 2 be a number. Define the graph L2(n) as follows: Vertices are ordered pairs from the set {1, ..., n}. Two vertices are adjacent if they have the same first coordinate, or the same second coordinate (but not both).
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