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1. Let S be the set of all nonzero real numbers. That is, S = R - {0}. Consider the relation R on S given by xRy iff xy > 0.
(a) Prove that R is an equivalence relation on S, and describe the distinct equivalence classes of R.
(b) Why is the relation R2 on S given by xR2y iff xy < 0 NOT an equivalence relation?
P and Q are the points (12,0) and (0,-5) respectively,find the length of the median through the origin O of the triangle OPQ
Let 0 ! V1 ! ! Vk ! 0 be a long exact sequence of vector spaces with linear maps. Show that P (??1)i dim Vi = 0.
with t =[a b c] construct a matrix A = 1 1 1 a b c a^2 b^2 c^2 a^3 b^3 c^3 using vector operations
ho we can find the area of diffrent types of polygon
The measures of the angles of a triangle are in the ratio of 3:4:5. Evaluate of the largest angle. a. 75° b. 37.5° c. 45° d. 60° a. The addition of the measures of t
Factor Expressions Involving Large Powers, Radicals, and Trig Functions You can use substitution to factor expressions involving large powers, radicals, and trig functions
Given f (x) = - x 2 + 6 x -11 determine each of the following. (a) f ( 2) (b) f ( -10) (c) f (t ) Solution (a) f ( 2) = - ( 2) 2 + 6(2) -11 = -3 (
what are the factors af 34?
Question: The following payoff table shows profit for a decision analysis problem with two decision alternatives and three states of nature. (a) Construct a decision tr
Raul has 56 bouncy balls. He puts three times as many balls into red gift bags as he puts into green gift bags. If he puts the same number of balls in each bag, how many balls does
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