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Choose ten of your friends, and make a graph where the edges represent two friends being Facebook friends. (Do not include yourself in the graph). Order your friends alphabetically, and label the vertices v1, v2, ..., v10 respectively.
This will be most interesting if all of your friends know each other. Now, answer the following questions about the graph that you drew.
(a) Find the shortest and longest paths from v1 to v10.(b) Which vertex has the highest degree? (c) Find minimum spanning tree, and draw that tree.
Let R be a ring with the property that every element is either nilpotent or invertible. If a, b, c are in R with a and b nilpotent, show that ac, ca, and a + b are nilpotent.
Let f be a function given by-Is there a function g: R ---> R such that g'=f? Be careful applying definition of the derivative
A beacon on a lighthouse 2000m away from the nearest point P on a straight shoreline revolves at the rate of 10 pi radians per minute. How fast is the beam of the light moving along the shoreline when it is 500m from P?
Showing all working, solve the following pair of simultaneous equations for i1 and i2, expressing the answers to exact whole numbers:
To start a business, Tom borrowed $20,000, part at 16% annual interest rate and part at 15%. If the total amount of interest on both loans is $3120, how much did he borrow at 16%?
The width of a rectangle is 1 foot less than the length. The area is 20 feet squared. Find the length and width.
How many weighings of a balance scale are needed to find a lighter counterfeit coin among four coins? Describe an algorithm to describe the lighter coin using this number of weighings.
Compactness and find the Area of region using definite integrals
With a yearly inflation rate of 7%, prices are given by P=p(1.05)^t, where p is the price in dollars when t=0 and t is the time in years. Suppose p=1. How fast (in cents/ year) are prices rising when t=12?
Compare the advantages and disadvantages of substitution and elimination methods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.
Using law of cosines for solving the problem.
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Round you answer to four decimal places. Enter your answers as a comma-separated list.)
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