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Question: Rewrite Euclid's division theorem, using the notation above for statements about variables. Leave out the references to universes so that you can see clearly the order in which the quantifiers occur. The form of Euclid's division theorem is ∀m(∀n(∃q(∃r(p(m, n, q, r))))).
A telephone company charges customers a certain amount for the first minute of a long distance call and another amount for each additional minute. A customer makes two calls to the same city-a 38-minute call for $1.99 and a 14-minute call for $0.7..
Prove that if p ∈ N is a prime number, then there exist a real number x, such that x2 = p. Moreover, x ∉ Q.
Let A and B be the endpoints of diameter of a circle of radius a and let P be any other point on circle. Determine the vectors u→ = AP and v→ = BP (in terms of a and θ) and show that u→ and v→ are orthogonal.
He takes twice as long at full speed to get back to the dock going against the current. How fast will his fishing boat go?
Write down the equation of motion for the point particle of mass m moving in the Kepler potential U (x) = -A /x + B /x2 and find extrema of the potential function and their position on the exis ξ. In which cases are the extrema stable and unstable?
A nickel, two dimes, and three quarters are in a cup. We draw three coins, one at a time without replacement. What is the probability that the first coin is a nickel? What is the probability that the second coin is a nickel? What is the probabilit..
If you start with an initial surplus of 1, what is the probability that you will be ruined by time 2 or before? Given ψ (6) = a, ψ (5) = b, ψ (4) = c, express ψ (7) in terms of a, b, c.
A house sits on a rectangular piece of land. Two of the sides measure 104 ft each. If all four sides measure 576 ft, how long is each of the other two sides?
What is the distance between the observer and Q? 2) how much elevation did the plane gain between P and Q?
a person who can row 2.6 mph in still water wants to row due east across a river. the river is flowing from the north at a rate of .8 mph. determine the heading of the boat that will be required for it to travel due east.
Find the area bounded by the graphs- f(x) = x2 and g(x) = x3
Now, for the same J-shaped member, determine MAx, MAy, and MAz, the couple moments at the support about the x, y, and z axes, respectively, required to keep the system in equilibrium. The cylinder weighs WB = 5.40lb ; a vertical force F = 1.70lb a..
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