factorize the integer 2896753 by using the Quadratic Sieve method

describe your feelings toward math and list at least one positive and one negative experience you have had with a math course or mathematics you use in your daily life?

10.

You are valuing Soda City Inc. It has $150 million of debt, $70 million of cash, and 200 million shares outstanding. You estimate its cost of capital is 8.0%. You forecast that it will generate revenues of $740 million and $760 million over the next two years, after which it will grow at a stable rate in perpetuity. Projected operating profit margin is 40%, tax rate is 20%, reinvestment rate is 60%, and terminal EV/FCFF exit multiple at the end of year 2 is 8. What is your estimate of its share price? Round to one decimal place.

solve the inital value problem ?′′ + 6?′ + 9? = 2?^(-t) ; ?(0) =4, ?’(0) = −6

Consider the equivalence relation on Z defined by the prescription that all positive numbers are equivalent, all negative numbers are equivalent, and 0 is only equivalent to itself. Let f ∶ Z → {a, b} be the function that maps all negative numbers to a and all non-negative numbers to b. Does there exist a function F ∶ X/∼→ {a, b} such that f = F ○ π? If so, describe it

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3. Show that the Galois group of (x² − 3)(x² + 3) over Q is isomorphic to Z₂ × Z₂.

4. Let p(x) be an irreducible polynomial of degree n over a finite field K. Show that its Galois group over K is cyclic of order n.

Discrete Math: Give examples of relations on the set of humans that are:

a) asymmetric and transitive

b) symmetric and antisymmetric

c) reflexive and irreflexive.

Let F be a field and R = Mn(F) the ring of n×n matrices with entires in F. Prove that R has no two sided ideals except (0) and (1).

Give an example of a function whose Taylor polynomial of degree 1 about x = 0 is closer to the values of the function for some values of x than its Taylor polynomial of degree 2 about that point.

Sometimes a constant equilibrium solution has the property that solutions lying on one side of the equilibrium solution tend to approach it, whereas solutions lying on the other side depart from it. In this case the equilibrium solution is said to be semistable. Consider the equation dy/dt = y^2(4 − y 2 ) = f(y), where y(0) = y0 and −∞ < y0 < ∞.

(i) Sketch the graph of f(y) versus y.

(ii) Determine the critical points. (iii) Classify each one as asymptotically stable, unstable, or semistable. (iv) Illustrate several solutions in the ty-plane that illustrate how the different solutions depend upon y0.

1. For each of these relations on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive.

1. {(2, 4), (4, 2)}
2. {(1, 2), (2, 3), (3, 4)}
3. {(1, 1), (2, 2), (3, 3), (4, 4)}
4. {(1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)}

For a) and b) please use the graph representation to determine their properties

For c) and d) please use matrix representation to determine their properties.

1) Define the sets X ={ 1, 2, 3} and Y = {4, 5, 6}. Now, define the relation R from X to Y by xRy if and only if x − y is even. Find all of the elements in R.

2) Define the relation R on ℤ by mRn if and only if 2|(m − n). Show that R is an equivalence relation.