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1. Show how to construct a triangle given the length of one side, the distance from an adjacent vertex to the incenter and the radius of the incircle.
2. Show how to construct a triangle ABC given the length of side BC and the altitudes from B and C
Compute the integral of 4y^3 dx -2x^2 dy around the square bounded by the lines y=+/- 1 and x=+/-1. Directly by performing the line integration.
The credit remaining on a phone card is a linear function of the total calling time. The function gives a line with a slope of -.32, when graphed.
A basket contains 6 red apples and 9 green apples . A sample of 5 apples is drawn. Find the probability that the sample contains
Let G be an abelian group such that the operation on G is denoted additively. Show that {a is an element of G| 2a = 0} is a subgroup of G.
Group Homomorphism and Abelian Groups, Let phi: G ---> H be a group homomorphism. Show that phi[G] is abelian if and only if for all x, y in G, we have xyx^(-1)y^(-1) in ker(phi).
Show that if n is odd then the set of all n-cycles consists of two conjugacy classes of equal size in An. Let G be a transitive permutation group on the finite set A with |A|>1. Show that there is some g in G such that g(a) is not equal to a for al..
Determine whether the following are equal. If not, which is smaller, and why?
You select a random sample of n=14 families in your neighborhood and find the following family size (number of people in the family).
Suppose that a store offers gift certificates in denominations of25 dollars and 40 dollars. Determine the possible total amounts you can form using these gift certificates.
A rectangular gate ABCD of mass 120kg where AB=1m and AD=3m is supported at A & B by pins where B is vertically above A. The reaction force at B is always horizontal.
If H and K are subgroup of G, with K a normal subgroup of G, K intersect H=1 and KH=G, then G is called a semidirect product (or split extention) of K by H.
For solving a system of equations, is there a difference between using an algebraic method and using the graphical method? Explain why or why not
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