Reference no: EM131084375
1: Express cos3θ in terms of cos θ.
2: The polynomial f(x) = x4 + ax3 + bx2 + cx + d has real coefficients and f(2i) = f(2 + i) = 0. What is a + b + c + d?
3: Let m and n be integers such that each can be expressed as a sum of 2 squares, say m = a2 + b2 and n = c2 + d2. Using complex numbers, show that mn can also be expressed as the sum of two squares. (For example, 17 = 42 + 1 and 13 = 22 + 32 and sure enough, 17 · 13 = 221 = 142 + 52.)
4: (a) Factor z5 + z + 1 into two polynomials with integer coefficients.
(b) Find all roots of z6 + z4 + z3 + z2 + 1 = 0.
5: A1, ..., An are vertices of a regular polygon inscribed in a circle of radius r and center O. P is a point on OA1, extended beyond A1. Show that:
k=1∏n P Ak = OPn - rn.
6: A pocket calculator has the ability to add, subtract, and take reciprocals, but cannot multiply. One way to perform multiplication is by successive addition but this is tedious and particular difficult with fractions. Show that one can use the operations on the calculator to mulitiply two numbers.
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Discuss one obstacle that teachers may encounter
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Recombinant dna and veterinary medicine
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Do you agree with leiber and weisberg portrayal of america
: Do you agree with Leiber and Weisberg portrayal of American primacy in determining identity on a global scale? How does this relate to our discussion in class in in the Misa chapter?
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What is the keq of this reaction
: At body temperature, If the [F16BP] = 100 mM, [GAP] = 0.10 mM, [DHAP]= 0.10 mM, what is the free energy of the reaction? Is it favorable or unfavorable?
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Find all roots of equation
: Factor z5 + z + 1 into two polynomials with integer coefficients. Find all roots of z6 + z4 + z3 + z2 + 1 = 0
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Problem regarding the communication effectiveness
: Identify two (2) key skills that you learned during the course that you think will add to your communication effectiveness.
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How your program would address the needs of this stage
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What is your definition of research
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Acceptance of dangerous knowledge
: In a post of a minimum of 500 words, discuss modern implications of what could be considered the dangerous knowledge of life and death. As a modern society, have we crossed a line to the acceptance of dangerous knowledge? no plagarising, APA refer..
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