13. (a) Suppose that u is a number with minimal polynomial over Q. Let v u2. What is the minimal polynomial of v over Q? (b) Is 0(u) equal to 0(v)? Explain.
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13. Let A be a 3 x 2 matrix, B be a 4 x 2 matrix, and C be a 4 x 3 matrix. Which of the following matrix products is defined? a) B^TA b) CB c) CAB *d) BA^T
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18.
Is the relation {(3, 5), (4, 5), (5, 0), (1, 1), (4, 0)} a function? Explain. Type your answer below.
19.
Verify that the matrix has no inverse. Type your answer below.
1.
14 A geometric series G has positive first term a, common ratio r and sum to infinity S. The sum to infinity of the even-numbered terms of G (the second, fourth, sixth, ... terms) is -1/2 S. Find the value of r. (a) Given that the third term of G.
14- The best implementation of a heap is a linked based:
true or false
15- the worst Big O is
a.O(2^n)
b. O(n Log2 n)
c. O(n)
d. No answer is correct
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12.) consider the equation 2x^2-11-25x. find the complex solutions (real and non real) of the equation, and simplify as much as possible. show all work.
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15. Compute the following for the given Zn. Write your answer in the form [a] where 0 <= a <= n-1.
a) [21] + [19] in Z12
b) [37][27] in Z45
c) [33] ([83] - [67]) in Z100
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12 When a table -tennis ball is dropped vertically on to a table, the time interval between any particular bounce and the next bounce is 90% of the time interval between that particular bounce and the preceding bounce. The interval between the first and second bounces is 2 seconds. Given.
16. Finda, b,ande such thathag(t)dt and/t)dt are aslar 16, Find a, b, and c such that / g(t) dt and / g(t) dt are as lar 16,Finda,b.andcsuch that..ag(t)dt andrg(t)dt are asl as possible. y = g(t) FIGURE 15 y11+1111+111+11 11 +- 21 12
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14.
Solve the problem.
A coin jar contains nickels, dimes, and quarters. There are 47 coins in all.
There are 12 more nickels than quarters.
The value of the dimes is $3.70 less than the value of the.
11.Solve the linear programming problem by the simplex method.
Maximize p=3x+4y
Subject to x+y <_4
2x+y<_6
x>_0, y>_0
A) x=4 y=0 u=0 v=1 p=16
B) x=4 y=0 u=1 v=0 p=16
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18. Suppose that there are 8 ping pong balls in a bucket. Three of the ping pong balls are white, and 5 of the ping pong balls are red. The experiment is set up where you select one ball, record its color and set it aside. You then select a.
17. Suppose a and b are elements in a group such that lal 4. lbl 2, and a b ba. Find labl. (l order of a a 18. The logical equivalent statement for (p v q) 19. At a conference, 12 members shook hands with each other before and after.
13. Let vi 4 7 and let W (a) Find a nontrivial linear dependence relation, if possible, among vi, vi, US. If not possible, explain why (b) Find a basis for W. (c) What is dim(W)?.
13. Let X12 = {1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12} and let R be the equivalence relation on X12 given by aRb . a and b have the same set of prime divisors The number of distinct equivalence classes is
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