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##### Problem 5. Let B consist of all binary sequences {bn}, i.e. infinite sequences of 0's and 1'8 (a) Show that B is uncountable by using the Cantor diagonalization argument or by showing there is a bijection from B to P(N), the power set of the natural numbers_ (b) Let S be the subset of S consisting of sequences which end in all 1' , i.e. there is an integer N with bn = 1 for all n > N_ Show that S is countable by writing S a8 a countable union of finite sets. Hint: for k â‚¬ N l

Problem 5. Let B consist of all binary sequences {bn}, i.e. infinite sequences of 0's and 1'8 (a) Show that B is uncountable by using the Cantor diagonalization argument or by showing there is a bijection from B to P(N), the power set of the natural numbers_ (b) Let S be the subset of S co...

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##### A piece of glass acquires a charge of 1.4x 107 C after being rubbed with a cloth: Which statement is correct? 8.8 x 1011 electrons were removed from the glass 8.8 X 1011 protons were added to the glass. 7.4x 101 electrons were removed from the glass_ 7.4 x 1010 protons were added to the glass. No protons or electrons were moved, the glass acquired a charge because it is in its nature to do so_10. What is the equivalent resistance between points a and b in the picture? 2.00 7.10 9.8 0 13.5 Q 20 Q

A piece of glass acquires a charge of 1.4x 107 C after being rubbed with a cloth: Which statement is correct? 8.8 x 1011 electrons were removed from the glass 8.8 X 1011 protons were added to the glass. 7.4x 101 electrons were removed from the glass_ 7.4 x 1010 protons were added to the glass. No pr...

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##### 25.a) 65 and be able to draw SIO,O00 year from A man retirement wants t0 retire at age retirement benefits. saving?( supplement his Social Security income and employee retirciet he snticiales invesocg his cuvings in goverment Securitibat hed sboeld retum 5%/ that led to equation (2.8), Year compounded continuously: By repeating the arguments show account - satisfies the ODE that after retirement the principal P() in his dP =.OSP-10 (2.14)where we have used units of S1O00. and find formula for

25.a) 65 and be able to draw SIO,O00 year from A man retirement wants t0 retire at age retirement benefits. saving?( supplement his Social Security income and employee retirciet he snticiales invesocg his cuvings in goverment Securitibat hed sboeld retum 5%/ that led to equation (2.8), Year compoun...

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##### Point) Find y as a function of x ify" _ 9y' - y + 9y = 0,J0) = -1, y (0) = -5, y" (0) = 313. yx) =

point) Find y as a function of x if y" _ 9y' - y + 9y = 0, J0) = -1, y (0) = -5, y" (0) = 313. yx) =...

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a) (8 points) Find all local maxima; minima, and saddle points of f(z,y) =1_y +Iy + 3 and evaluate f(z,y) at each point. 2 +4v} + 927 find the gradieot VF; Find tbe Givea F(s,y,2) ptipi9) 6od ponal line t0 the ellipeoid 1? ++4v*+92 = 49 (6 eee pae 6zqukesjom 5 tf thc [bint Ro(8,1,2) 21 #c:...

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##### Have 40 ' (indistinguishable) cherry gumdrops t0 Exercise 5.3.17 Suppose that we Bob; Chad, Diane; Edward and Fran . be distributed among six children: Alice Alice must receive between 5 and 12 gumdrops. Bob must receive between 7 and 11 gundrops Chad must receive between 4 and 16 gumdrops. The number of gumdrops that Diane receives must be & multiple of three. Edward must receive exactly three more gumdrops than Alice. Finally, Fran must receive exactly one less gumdrop than Diane. Fin

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