13 Pages

prac_rel

Course: PHYS 2040, Fall 2009
School: Maple Springs
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Word Count: 10837

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Coursehero >> Maryland >> Maple Springs >> PHYS 2040

Course Hero has millions of student submitted documents similar to the one
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Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
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Ff(x)36 b Fg(=)f(200)f(km,)197 1184 y Ff(y)f Fg(=)d(20)g(km,)g Ff(z)35 b Fg(=)30 b(500)g(km,)g(and)g Ff(t)h Fg(=)f(100)f Ff(\026)p Fg(s.)43 b(What)30 b(are)h(the)f(co)s(ordinates)g(of)g(this)g (ev)m(en)m(t)i(in)197 1304 y(the)i Ff(S)432 1268 y Fe(0)489 1304 y Fg(frame)f(whic)m(h)i(mo)m(v)m(es)g(in)e(the)i(direction)d(of)i (increasing)f Ff(x)i Fg(with)e(sp)s(eed)i(0.9)p Ff(c)p Fg(?)48 b(Chec)m(k)197 1425 y(y)m(our)35 b(answ)m(ers)i(b)m(y)f(using)e (the)i(in)m(v)m(erse)g(Loren)m(tz)f(transformation)e(equations)i(to)g (obtain)e(the)197 1545 y(original)c(data.)72 1749 y(4.)81 b([v)-5 b(ariation)31 b(on)h(T)-8 b(ext)34 b(Problem)d(28,)h(page)h (84]\(10)f(marks\))197 1869 y(An)i(exerimen)m(ter)g(in)f(the)h Ff(S)39 b Fg(frames)34 b(arranges)f(to)h(trigger)e(t)m(w)m(o)j(\015ash) m(bulbs)f(sim)m(ultaneously)-8 b(,)197 1989 y(a)31 b(red)i(\015ash)f (lo)s(cated)f(at)h(the)g(origin)e(and)i(a)f(green)i(\015ash)f(at)g Ff(x)p Fg(=10)g(km.)43 b(An)32 b(observ)m(er)h(in)e(the)197 2110 y Ff(S)263 2074 y Fe(0)326 2110 y Fg(frame,)41 b(mo)m(ving)e(at)h (a)g(sp)s(eed)h(of)f(0.75)p Ff(c)f Fg(in)h(the)g(direction)f(of)h (increasing)f Ff(x)p Fg(,)k(also)c(views)197 2230 y(these)34 b(\015ashes.)238 2434 y(\(a\))48 b(What)33 b(time)e(in)m(terv)-5 b(al)32 b(b)s(et)m(w)m(een)i(them)e(do)s(es)i(she)f(\014nd?)233 2595 y(\(b\))48 b(Whic)m(h)33 b(\015ash)g(do)s(es)g(she)h(sa)m(y)g(o)s (ccurs)f(\014rst?)72 2799 y(2.)81 b([v)-5 b(ariation)31 b(on)h(T)-8 b(ext)34 b(Problem)d(24,)h(page)h(84])197 2919 y(The)d(mean)e(lifetime)e(of)i(particles)g(called)f(m)m(uons)i (stopp)s(ed)h(in)e(a)g(lead)g(blo)s(c)m(k)h(in)f(a)h(lab)s(oratory)197 3040 y(is)38 b(measured)g(to)g(b)s(e)g(2.2)g Ff(\026)p Fg(s.)61 b(The)39 b(mean)f(lifetime)d(of)i(high-sp)s(eed)i(m)m(uons)f (observ)m(ed)i(from)197 3160 y(cosmic)29 b(ra)m(ys)i(observ)m(ed)h (from)d(the)h(earth)h(is)e(measured)i(to)e(b)s(e)i(22)e Ff(\026)p Fg(s.)43 b(What)30 b(is)g(the)g(sp)s(eed)h(of)197 3280 y(these)j(cosmic)e(ra)m(y)h(m)m(uons?)72 3484 y(3.)81 b([v)-5 b(ariation)31 b(on)h(T)-8 b(ext)34 b(Problem)d(39,)h(page)h (85]\(6)f(marks\))197 3604 y(Observ)m(er)44 b Ff(S)j Fg(notes)c(that)f(t)m(w)m(o)g(coloured)g(\015ashes)h(of)f(ligh)m(t,)g (separated)h(b)m(y)g(1.5)f(km,)i(o)s(ccur)197 3725 y(along)e(the)j(p)s (ositiv)m(e)e(branc)m(h)i(of)f(the)g Ff(x)g Fg(axis.)78 b(A)44 b(red)g(\015ash)h(o)s(ccurs)g(\014rst,)i(follo)m(w)m(ed)c(after) 197 3845 y(2.5)d Ff(\026)p Fg(s)h(b)m(y)g(a)f(green)h(\015ash,)i(the)e (latter)f(b)s(eing)g(the)h(more)e(distan)m(t)i(from)e(the)i(origin)d (of)i(her)197 3965 y(reference)35 b(frame.)44 b(A)33 b(second)i(observ)m(er,)g Ff(S)1821 3929 y Fe(0)1844 3965 y Fg(,)e(obtains)g(exactly)h(the)f(same)g(n)m(umerical)f(v)-5 b(alues)197 4086 y(for)33 b(the)g(time)f(di\013erence)i(and)f(the)h (absolute)f(spatial)f(separation)h(b)s(et)m(w)m(een)i(the)f(t)m(w)m(o)g (ev)m(en)m(ts)197 4206 y(but)f(declares)g(that)f(the)h(green)g(\015ash) g(o)s(ccurs)h(\014rst.)238 4410 y(\(a\))48 b(What)33 b(is)f(the)h(relativ)m(e)f(sp)s(eed)i(of)e Ff(S)1744 4373 y Fe(0)1800 4410 y Fg(with)g(resp)s(ect)i(to)e Ff(S)6 b Fg(?)233 4571 y(\(b\))48 b(Whic)m(h)33 b(\015ash)g(will)e Ff(S)1199 4535 y Fe(0)1254 4571 y Fg(sa)m(y)j(w)m(as)f(most)f(distan)m (t)h(from)e(the)i(origin)e(of)h(her)h(frame?)72 4775 y(4.)49 b(A)33 b(particle)e(w)m(as)j(observ)m(ed)h(to)e(b)s(e)g (created)g(at)g(t)g(=)f(10)h(ns,)g(tra)m(v)m(el)g(with)g(sp)s(eed)h Ff(u)3243 4790 y Fd(x)3319 4775 y Fg(=)f(-\()p Ff(c)p Fg(/2\),)197 4895 y(and)j(then)g(to)f(deca)m(y)i(at)f(t)f(=)h(30)f(ns.) 54 b(T)-8 b(o)35 b(an)h(observ)m(er)h(who)f(w)m(as)h(mo)m(ving)e(with)g (a)g(sp)s(eed)i(of)197 5016 y(-\(4/5\))p Ff(c)31 b Fg(along)g(the)i (common)e Ff(x)23 b Fc(\000)g Ff(x)1577 4979 y Fe(0)1633 5016 y Fg(axis:)238 5219 y(\(a\))48 b(What)33 b(w)m(as)h(the)f(v)m(elo) s(cit)m(y)f(of)g(the)h(particle)e(during)h(its)g(trip?)233 5381 y(\(b\))48 b(What)39 b(w)m(as)h(the)f(distance)g(b)s(et)m(w)m(een) i(the)e(p)s(osition)e(where)j(the)f(particle)e(w)m(as)j(created)411 5501 y(and)33 b(the)g(p)s(osition)e(at)h(whic)m(h)h(it)f(deca)m(y)m (ed?)243 5663 y(\(c\))49 b(Ho)m(w)33 b(m)m(uc)m(h)g(time)e(elapsed)h(b) s(et)m(w)m(een)i(the)f(instan)m(t)f(it)f(w)m(as)i(created)g(and)f(the)h (instan)m(t)f(it)411 5784 y(deca)m(y)m(ed?)p eop %%Page: 2 2 2 1 bop 233 331 a Fg(\(d\))48 b(Ho)m(w)35 b(can)g(observ)m(ers)i(in)c (t)m(w)m(o)i(frames)f(mo)m(ving)f(with)h(a)g(relativ)m(e)g(v)m(elo)s (cit)m(y)g(observ)m(e)i(the)411 451 y(same)k(v)-5 b(alues)40 b(for)f(the)i(distance)f(co)m(v)m(ered)i(and)e(lifetime)d(for)i(this)h (particle?)64 b(Do)s(esn't)411 572 y(this)33 b(con)m(tradict)f (relativit)m(y)f(\(i.e.,)i(what)g(happ)s(ened)h(to)e(length)g(con)m (traction)g(and)h(time)411 692 y(dilation\)?)72 896 y(5.)49 b(A)43 b(particle)f(is)g(observ)m(ed)j(to)e(ha)m(v)m(e)h(a)f(v)m(elo)s (cit)m(y)e Ff(~)-47 b(u)45 b Fg(=)g(\()p Ff(c=)p Fg(4)p Ff(;)17 b(c=)p Fg(2)p Ff(;)g Fg(0\))41 b(in)i(the)g Ff(S)49 b Fg(frame.)74 b(The)197 1016 y Ff(S)263 980 y Fe(0)321 1016 y Fg(frame)35 b(is)g(mo)m(ving)g(at)g(a)h(sp)s(eed)g(of)g(\(4/5\)) p Ff(c)e Fg(in)h(the)h(direction)f(of)g Fb(de)-5 b(cr)g(e)g(asing)34 b Ff(x)i Fg(along)e(the)197 1136 y(common)d Ff(x)23 b Fc(\000)f Ff(x)819 1100 y Fe(0)875 1136 y Fg(axis.)246 1340 y(\(a\))64 b(What)33 b(is)f Ff(u)863 1304 y Fe(0)863 1364 y Fd(x)906 1340 y Fg(?)44 b(\(Y)-8 b(ou)32 b(can)h(giv)m(e)g(it)e (in)h(terms)g(of)h(a)f(fraction)f(of)h Ff(c)p Fg(\))246 1502 y(\(b\))65 b(What)32 b(is)g Ff(u)868 1465 y Fe(0)868 1526 y Fd(y)909 1502 y Fg(?)44 b(\(Y)-8 b(ou)32 b(can)h(giv)m(e)g(it)e (in)h(terms)g(of)h(a)f(fraction)f(of)h Ff(c)p Fg(\))246 1663 y(\(c\))56 b(What)28 b(is)g Fc(j)n Ff(~)-47 b(u)868 1627 y Fe(0)890 1663 y Fc(j)28 b Fg(\(i.e.,)h(the)f(magnitude)f(of)f Ff(~)-47 b(u)1969 1627 y Fe(0)1992 1663 y Fg(\)?)42 b(\(Y)-8 b(ou)28 b(can)g(giv)m(e)g(it)f(in)g(terms)i(of)e(a)h(fraction)411 1784 y(of)33 b Ff(c)p Fg(\))246 1946 y(\(d\))25 b(An)i(observ)m(er)g (in)e(the)i Ff(S)1268 1910 y Fe(0)1316 1946 y Fg(frame)e(measures)i (the)f Ff(y)2208 1910 y Fe(0)2257 1946 y Fg(comp)s(onen)m(t)g(of)f(the) h Fb(momentum)f Fg(\(i.e.,)411 2066 y Ff(p)460 2030 y Fe(0)460 2091 y Fd(y)502 2066 y Fg(\))32 b(of)g(the)h(particle)f(to)g (b)s(e)h(0.6)f(MeV/)p Ff(c)p Fg(.)44 b(What)33 b(is)f(the)h(rest)g (mass)f(of)g(the)h(particle?)72 2270 y(6.)49 b(An)30 b(an)m(tiproton)f(is)h(a)g(particle)e(iden)m(tical)h(to)h(the)g(proton) g(in)f(all)f(resp)s(ects)k(except)g(that)d(it)g(has)197 2390 y(the)39 b(opp)s(osite)f(c)m(harge)h(\(i.e.,)h(it)e(has)h(the)g (same)f(c)m(harge)h(as)g(the)g(electron\).)62 b(An)39 b(an)m(tiproton)197 2510 y(ha)m(ving)32 b(a)g(kinetic)g(energy)h(equal) f(to)g(\(2/3\)M)1908 2525 y Fd(p)1947 2510 y Ff(c)1989 2474 y Fa(2)2061 2510 y Fg(strik)m(es)h(a)f(proton)g(whic)m(h)h(is)e (at)h(rest.)44 b(They)197 2631 y(annihilate)35 b(yielding)i(t)m(w)m(o)h (photons.)60 b(That)38 b(is,)h(the)g(initial)34 b(state)k(con)m(tains)g (only)f(a)h(proton)197 2751 y(and)31 b(an)g(an)m(tiproton)e(and)i(the)h (\014nal)e(state)h(con)m(tains)g(only)f(t)m(w)m(o)i(photons.)43 b(The)32 b(t)m(w)m(o)f(photons)197 2871 y(emerge)38 b(from)f(the)h (reaction)f(tra)m(v)m(elling)g(forw)m(ard)h(or)f(bac)m(kw)m(ard)j(on)e (the)g(line)f(along)f(whic)m(h)197 2992 y(the)d(an)m(tiproton)e(tra)m (v)m(elled.)238 3195 y(\(a\))48 b(What)d(energies)h(do)e(the)i(photons) f(ha)m(v)m(e)h(and)f(in)f(whic)m(h)h(direction)f(is)g(eac)m(h)i(photon) 411 3316 y(heading)33 b(\(i.e.,)f(either)g(along)f(or)h(against)g(the)h (original)c(an)m(tiproton)j(direction\)?)233 3478 y(\(b\))48 b(As)35 b(measured)g(in)f(a)g(rest)h(frame)f(of)g(the)h(an)m(tiproton,) f(what)h(energy)g(do)s(es)g(eac)m(h)g(of)f(the)411 3598 y(photons)f(ha)m(v)m(e?)72 3801 y(7.)49 b(A)29 b(particle)f(whic)m(h)i (is)f(a)h(b)s(ound)f(state)h(of)f(a)g(quark)h(and)g(an)f(an)m(tiquark)h (is)f(called)f(a)h(meson.)43 b(A)197 3922 y(meson)37 b(has)g(a)f(particular)f(mass)i(v)-5 b(alue)36 b(whic)m(h)h(is)f (ultimately)e(dep)s(enden)m(t)39 b(on)d(the)h(t)m(yp)s(es)h(of)197 4042 y(constituen)m(t)31 b(quarks)h(and)e(the)h(strength)g(of)f(the)h (in)m(teraction)e(b)s(et)m(w)m(een)j(them)f(\(the)f(so-called)197 4162 y(colour)g(force\).)43 b(An)31 b(analogous)e(system)j(is)e(the)h (h)m(ydrogen)h(atom)e(whic)m(h)h(is)f(the)h(b)s(ound)g(state)197 4283 y(of)c(a)h(proton)f(and)h(an)g(electron.)42 b(The)29 b(h)m(ydrogen)g(atom)d(has)j(a)e(particular)f(mass)i(whic)m(h)h(is)e (not)197 4403 y(just)35 b(the)f(sum)h(of)f(the)h(proton)f(and)g (electron)h(masses.)50 b(A)34 b Ff(D)2487 4367 y Fa(0)2561 4403 y Fg(meson)g(\(whic)m(h)h(consists)g(of)f(a)197 4524 y Fb(charm)c Fg(quark)j(and)e(an)h Fb(up)f Fg(an)m(tiquark\))h(is) e(tra)m(v)m(elling)g(through)i(the)f(lab)s(oratory)f(and)i(breaks)197 4644 y(up)40 b(in)m(to)f(\(i.e.,)i(deca)m(ys)h(in)m(to\))d(a)g Ff(K)1519 4608 y Fe(\000)1618 4644 y Fg(meson)h(and)g(a)g Ff(K)2300 4608 y Fa(+)2399 4644 y Fg(meson.)65 b(The)41 b Ff(K)3055 4608 y Fa(+)3154 4644 y Fg(meson)e(is)h(left)197 4764 y(at)e(rest)h(in)f(the)h(lab)s(oratory)e(frame.)60 b(The)40 b(rest)f(mass)f(of)g(the)h Ff(D)2647 4728 y Fa(0)2725 4764 y Fg(meson)f(is)g(1864)g(MeV/)p Ff(c)3663 4728 y Fa(2)197 4885 y Fg(while)29 b(the)h Ff(K)704 4849 y Fe(\000)793 4885 y Fg(and)g Ff(K)1070 4849 y Fa(+)1159 4885 y Fg(mesons)g(ha)m(v)m(e)h(the)f(same)g(rest)g(mass)g(v)-5 b(alue)29 b(of)g(493.7)g(MeV/)p Ff(c)3451 4849 y Fa(2)3491 4885 y Fg(.)43 b(F)-8 b(or)197 5005 y(comparison,)31 b(the)i(proton)g(rest)g(mass)f(is)g(938.272)g(MeV/)p Ff(c)2398 4969 y Fa(2)2438 5005 y Fg(.)238 5209 y(\(a\))48 b(What)33 b(are)g(the)g(rest)g(masses)g(of)f(the)h Ff(D)1890 5172 y Fa(0)1962 5209 y Fg(and)g Ff(K)2242 5172 y Fe(\000)2333 5209 y Fg(mesons)g(in)f(kilograms?)233 5370 y(\(b\))48 b(What)33 b(is)f(the)h(kinetic)f(energy)i(of)e(the)h Ff(K)1949 5334 y Fe(\000)2041 5370 y Fg(meson?)243 5532 y(\(c\))49 b(What)33 b(w)m(as)h(the)f(total)e(energy)i(of)f(the)h Ff(D)1948 5496 y Fa(0)2020 5532 y Fg(meson?)233 5694 y(\(d\))48 b(What)d(w)m(ould)f(b)s(e)g(the)h(magnitude)e(of)g(the)i (momen)m(tum)d(of)i(the)h Ff(K)3029 5658 y Fa(+)3132 5694 y Fg(meson)f(in)f(the)411 5815 y(frame)h(where)h(the)f Ff(D)1253 5778 y Fa(0)1336 5815 y Fg(meson)g(w)m(ould)g(ha)m(v)m(e)i(b) s(een)e(at)g(rest?)78 b(\(Hin)m(t:)66 b(T)-8 b(ak)m(e)45 b(the)g Ff(D)3664 5778 y Fa(0)411 5935 y Fg(meson)33 b(\015igh)m(t)f(direction)f(to)i(b)s(e)f(along)g(the)h Ff(x)g Fg(axis.\))p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF
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Washington - MATH - 425
Maple Springs - PHYS - 2040
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Maple Springs - PHYS - 2040
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Maple Springs - PHYS - 2040
%!PS-Adobe-2.0 %Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %Title: qprac.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 596 842 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -f qprac %DVIPSParameters: d
Maple Springs - PHYS - 2040
%!PS-Adobe-2.0 %Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %Title: sqprac.dvi %Pages: 4 %PageOrder: Ascend %BoundingBox: 0 0 596 842 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -f sqprac %DVIPSParameters:
Maple Springs - PHYS - 2040
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Washington - MATH - 583
Math 583GEOMETRIC MEASURE THEORY IN EUCLIDEAN SPACE AND TOPICS IN ERGODIC THEORY Spring 2008Instructors: Boris Solomyak Oce: Padelford C-328, Oce Phone 685-1307 E-mail: solomyak[at]math.washington.edu Oce hours: Monday 45, Tuesday 1112, or by
Washington - MATH - 480
Washington - MATH - 480
Washington - MATH - 480
Washington - MATH - 480
Washington - MATH - 480
Washington - MATH - 480
Washington - MATH - 480
Washington - MATH - 480
Washington - MATH - 536
Math 536HOMEWORK 1 (due Wednesday, April 9)Spring 2008Do the following problems from Gamelin (point distribution is indicated in parentheses): 13.1: 2, 6, 10 (3 + 3 + 3) 13.2: 3, 6, 7, 9 (2 + 3 + 3 + 3)1
Washington - MATH - 536
Math 536HOMEWORK 5 (due Wednesday, May 14)Spring 2008Do the following problems from Gamelin (point distribution is indicated in parentheses): 15.2: 3, 8 (3 + 3) 15.4: 3 (3) 15.5: 1, 2 (3 + 3) 15.6: 3, 7 (2 + 3)1
Washington - MATH - 534
Math 534HOMEWORK 1 (due Wednesday, Oct. 3)Autumn 20071. (a) Let |a| 1 and |b| &lt; 1. Show a-b 1. 1 - ab When does equality occur? (b) Calculate ( 1i 2 3 6) for all combinations of signs.2. Let a = e2i with Q. Prove that the sequence {an
Washington - MATH - 535
Math 535HOMEWORK 1 (due Wednesday, Jan 16)Winter 2008Do the following problems from Gamelin (point distribution is indicated in parentheses): 8.1: 3, 4, 8 (2 + 3 + 3) 8.2: 2, 6, 8 (2 + 3 + 2) 8.3: 1, 2 (3 + 2)1
Washington - MATH - 535
Math 535HOMEWORK 2 (due Wednesday, Jan 23)Winter 2008Do the following problems from Gamelin (point distribution is indicated in parentheses): 8.4: 4, 6 (2+3) 8.5: 2, 4 (2 + 3) 8.6: 6, 7, 9, 10 (2 + 2 + 3 + 3) You are welcome to use the hints at
Washington - MATH - 535
Math 535HOMEWORK 7 (due Wednesday, March 5)Winter 2008Do the following problems from Gamelin (point distribution is indicated in parentheses): 11.3: 6, 8 (3 + 4) 11.6: 1, 2, 3, 4, 5 (2 + 2 + 1 + 4 + 4)1
Washington - MATH - 535
Math 535HOMEWORK 8 (due Wednesday, March 12)Winter 2008Do the following problems from Gamelin (point distribution is indicated in parentheses): 11.5: 1, 3, 4 (2 + 3 + 3) 12.1: 4, 5 (2 + 3) 12.2: 4, 6 (3 + 4)1
Washington - MATH - 480
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Washington - MATH - 480
B. SolomyakHOMEWORK 8 (due Wednesday, June 3)Math 480, Spring 2009READ 7.57.7. Do the following exercises: T7.14 (p.307) (3 pts), T7.15 (p.308) (2 pts), T7.16 (p.308) (5 pts), 7.8, 7.9 (p.322) (5 pts each). Attention: the hints for some of the
Washington - MATH - 480
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Washington - MATH - 526
B. SolomyakMath 526Spring 2003Assignment 4Due Wednedsday, April 30Reading: 7.1, 7.2 from Folland. Problems from Folland: 2, 3 from 7.1; 7, 8, 9 from 7.2
Washington - MATH - 526
B. SolomyakMath 526Spring 2003Assignment 5Due Wednedsday, May 7Reading: 7.3, 3.3, 7.4 from Folland. Problems from Folland: 12, 13 from 7.2; 17, 22, 24 from 7.3
Washington - MATH - 526
B. SolomyakMath 526Spring 2003Assignment 6Due Wednedsday, May 14Reading: 8.1, 8.2 from Folland. Problems from Folland: 1, 3, 4 from 8.1; 8, 9 from 8.2
Washington - MATH - 526
B. SolomyakMath 526Spring 2003Assignment 7Due Wednedsday, May 21Reading: 8.3 from Folland. Problems from Folland: 13, 14, 18, 20 from 8.3 NOTE: there is a typo in 18(b): the integral in LHS should be squared.
Washington - MATH - 526
B. SolomyakMath 526Spring 2003Assignment 8Due Wednedsday, May 28Reading: 8.3 and 8.6 from Folland. Problems from Folland: 15, 16 from 8.3 (note that there are several little typos in these problems) 40, 41 from 8.6
Washington - MATH - 526
B. SolomyakMath 526Spring 2003Assignment 9Due Wednedsday, June 4Reading: 10.1-10.3 from Folland. Problems from Folland: 10.2(a), 10.9 from 10.1 10.13, 10.14, 10.15 from 10.2
Washington - MATH - 309
Math 309 A HOMEWORK #4Spring 2009READ Sections 9.1-9.4 (skim); make sure you understand Table 9.1.1, Figure 9.1.9, Theorem 9.3.2 (statement) and Table 9.3.1. Turn in the following problems at the beginning of the class on WEDNESDAY, May 6: 9.3: 1
Washington - MATH - 309
Math 309 A HOMEWORK #5 READ Sections 10.1 and 10.2.Spring 2009Turn in the following problems at the beginning of the class on WEDNESDAY, May 13: 10.1: 5, 9, 16, 17; 10.2: 14, 16, 17.
Washington - MATH - 309
Math 309 A HOMEWORK #6 READ Sections 10.3 and 10.4.Spring 2009Turn in the following problems at the beginning of the class on WEDNESDAY, May 20: 10.3: 5, 6; 10.4: 8, 11, 12, 16, 17, 19.Note that 10.4 #8, 11, 12 don't require any computations (j
Washington - MATH - 309
Math 309 A HOMEWORK #7 READ Sections 10.5 and 10.6.Spring 2009Turn in the following problems at the beginning of the class on FRIDAY, May 29: 10.5: 2, 6, 7, 18, 19; 10.6: 2, 4, 6, 11(a), 13(a),(d).
Washington - MATH - 309
Math 309 APreparation for MIDTERM 2Spring 2009The test will be on Friday, May 29. It will cover 9.3, 10.110.6. You can bring one standard 8 11 sheet of handwritten notes (no printed materials), 2-sided is OK. No calculators or other electronic
Washington - MATH - 309
MATHEMATICS 308COMPLEX NUMBERSThe introduction of complex numbers in the 16th century made it possible to solve the equation x2 + 1 = 0. These notes present one way of dening complex numbers. The Complex Plane. A complex number z is given by a pa
NYU - SB - 513
Phonetics and Phonology of Transparent Vowels in HungarianSTEFAN BENUS, ADAMANTIOS GAFOS, LOUIS GOLDSTEIN New York University, Haskins Laboratories, Yale University1. Introduction Vowel harmony is a requirement by which vowels in a certain dom
NYU - SB - 513
Gestural coordination and the distribution of English &quot;geminates&quot; Stefan Benus, Iris Smorodinsky, and Adamantios Gafos 1. IntroductionRecent work has argued that phonology includes grammatical principles and representations that refer to the tempora
NYU - SB - 513
The role of prosody in the pragmatic meaning of `whatever'Stefan Benus, New York University January, 2001 In this paper, I investigate the role of prosody in cueing negative pragmatic meaning associated with the use of `whatever'. I suggest that the
NYU - SB - 513
Deriving Consonant Cluster Phonotactics: Evidence from Singapore English Arto Anttila, Vivienne Fong, Stefan Benus, Jennifer NyczNew York University National University of Singapore and New York University1.OverviewConsonant clusters are o
Washington - MATH - 324
Math 324 B EXTRA CREDIT ASSIGNMENT #1 Turn in on Monday, October 14, at the beginning of the class. (This is OPTIONAL; you wont be penalized for not doing this assignment.) 1 (up to 5 points of extra credit) Show that arctan(x) arctan(x) dx = ln x
Washington - MATH - 324
Math 324 B EXTRA CREDIT ASSIGNMENT #3Fall 2002Turn in on Monday, November 25, at the beginning of the class. (This is OPTIONAL; you won't be penalized for not doing this assignment.) Do problem 2 from &quot;Problems Plus&quot; at the end of Chapter 16 (17)
Washington - MATH - 324
Math 324 BQUIZ 1 SAMPLE PROBLEMSFall 20021. Find the volume of the solid bounded by the surface z = 4 - 4xy and the planes z = 0, x = 0, y = 1, and y = x. 2. Set up (but do not evaluate) the triple integrals needed to find the center of mass of
Washington - MATH - 309
Math 309 AANSWERS TO PRACTICE PROBLEMSSpring 20091. For each of the following, (a) determine the order of the ODE, (b) state whether the equation is linear or nonlinear, (c) find constant solutions, if any. (i) t2 y + ty + 2y = sin t; (ii) (1 +
Washington - MATH - 425
Math 425/575HOMEWORK 1 ANSWERS/SOLUTIONSWinter 20074.58. (b) x = 0 is a discontinuity; f (0-) = f (0) = 0, f (0+) = +. (c) x = 0 is a discontinuity; f (0-) does not exist; f (0+) = +. (d) f (0-) = 1, f (0+) = 0, so x = 0 is a jump discontinuity
Portland - PH - 223
Including relativistic effects into the Doppler Effect Observer: stationary Source: in motionAuBu TBTB is the period of the wave (measured by the observer B)c TB After one pulse is emitted, the second pulse is not emitted but after TB se
Oakland University - CSE - 598
Lance Gallop Protein-Protein Interactions: Predictions and Web Portal Computational Biology For the duration of this project I was the technical half of a two person team: my responsibilities were to analyze, upgrade, and ultimately re-code an existi
Washington - MATH - 425
Math 425/575HOMEWORK 2 ANSWERS/SOLUTIONSWinter 20075.10 We argue by contradiction. Suppose that f (x) A R (not infinity) as x b-. By the definition of the limit, there exists c (a, b) such that |f (x)| |A| + 1 for all x (c, b). By the Mea
Washington - MATH - 425
Math 425/575 5.31. Since f (t)2HOMEWORK 3 ANSWERS/SOLUTIONS = f (t) f (t) = const, we haved [f (t) dtWinter 2007 f (t)] = 2f (t) f (t) = 0.5.33. It is clear that D1 f (x, y) and D2 f (x, y) exist for (x, y) = (0, 0). Since f (x, 0) = f (0
Portland - PH - 223
KEY SOLUTION05/07/01PHYSICS 223 Exam #1NAME_Use g= 10 m/s2 in your calculations. Wherever appropriate answers must include units.1. Fig. 1a shows a spring, 20 cm long. The spring gets compressed 2 cm when a block of mass M1 = 0.2 Kg. is att
Portland - PH - 223
05/07/03PHYSICS 223 Exam #1NAME_Feynman_Please write your name also on the back side of this examUse g = 10 m/s2 in your calculations. 1. 1A A uniform thin stick of mass M = 0.2 Kg and length L = 60 cm is pivoted at one end. The period of oscil
Portland - PH - 223
Including relativistic effects into the Doppler Effect Observer: stationary Source: in motionAuBu TB c TBTB is the period of the wave (measured by the observer B)After one pulse is emitted, the second pulse is not emitted but after TB seco
Washington - MATH - 426
B. SolomyakMath 426/576 REVISED syllabus FUNDAMENTAL CONCEPTS OF ANALYSIS IIISpring 2004 Instructor: Boris Solomyak, Room C-328 Padelford, Oce Phone 685-1307. Email: solomyak@math.washington.edu Oce Hours: Mondays 5:00-5:45, Thursdays 1-2, or
Portland - PH - 223
Laser Telecommunication ExperimentLASERModulator Photo-detectorA diagram of our laser telecommunication kit.Electric signalLaser beamModulatedelectric signaltimeLaserModulatorThis picture represents how human voice (sound signals)
Portland - PH - 223
KEY SOLUTION05/07/01PHYSICS 223 Exam #1NAME_Use g= 10 m/s2 in your calculations. Wherever appropriate answers must include units.1. Fig. 1a shows a spring, 20 cm long. The spring gets compressed 2 cm when a block of mass M1 = 0.2 Kg. is att
Portland - PH - 223
Physics 223M ay 7th, 2001M idterm Exam12Number of students10 8 6 4 2 0 60 65 70 75 80 85 90 95 100G r a d e
Berkeley - IB - 168
IB 168: Systematics of Vascular PlantsSpring 2009Key concepts - Lecture 3 (1/28/09; end of Phylogenetics/Tracheophyte introduction) Not all shared characteristics are informative about phylogenetic relationships Hennig (1966): Shared, derived cha
Berkeley - IB - 168
Lecture 8: Key Concepts (Conifers)IB 168 Spring 2009As noted last time, seeds arose during the upper Devonian (~350 million years ago), a time of wet climate during the Paleozoic; based on that climatic setting, evolution of the seed was probably