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Page 1 ECE223, Solutions for Assignment #3 Chapter 3, Digital Design, M Mano, 3rd Edition 33) Simplify the following Boolean functions, using threevariable maps2 T H E A L G E B R A O F (T W O D IM E N S IO N A L ) V E C T O R S T h e tw o d im e n sio n a l v e c to r, V 9 is an o rd e re d p a ir of e le m e n ts, c a lle d s c a la rs , of a field (T h e re a l n u m b e rs^ fo r e x a m p le , fo rm a field ) V = (a ,b )W x W x M y W y W n i x i i 1 W W ydW ydWy OR W y W y The centroid of an area is the average x and y locations of the area particles For a shape of a uniform thickness and material W i t A i where is weight per unit volume (= specific weight) with units of N/m 3 or lb/ft t A i is the volume So if W tA t tdA x A xdA
PART 1 MODULE 2 SET INTERSECTION, SET UNION, SET COMPLEMENT SUMMARY The intersection of two sets denotes the elements that the sets have in common, or the "overlap" of the two sets S ∩ T = {xx∈ S and x∈ T} The union of two sets merges the two sets into one "larger" set S ∪ T = {xx ∈ S or x ∈ T}Title F2408indd Author christopherdinardo Created Date ZKAGAYA F t @ T C g uAmalthea ` A } e A v KAGAYA 攌 A J 搶 T C g ł B KAGAYA 攌 E J 搶 t @ T C g ́AKAGAYA 攌 A J 搶 t @ T C g ł B07 N3 ɊJ ݂ 1 N ɂ KAGAYA 攌 F t @ T C g Ƃ ă j A ܂ (^_^)
T ̒ʂ Ȃ ̏ ߂Ă̋D Ԃ̗ B4 ͑ A lj X ^ g B R R ͘H n ̕ǂ A ͉w O B Ȑl Ƃ Ȃ A ɗ Ă ܂ B X N ^ 30 ɂ Ă l A p łǂ ǂ ׂ Ă 邪 A { Ȃ̂ A p Ȃ̂ u L v L b ` o B ł F Ί ŁA 肢 Ƃ Ă 悤 Ȋ āA Ԃ Y 4 ԈʂŎd グ ܂ BGeometrically the probability that X is between a and b, ie, P(a X b), is then represented by the area shown shaded, in Fig 22 The distribution function F(x) P(X x) is a monotonically increasing function which increases from 0 to 1 and is represented by a curve as in Fig 23 d dx3 x a f (u) du f (x) F(x) μ 0 x 1 x 2 1 x 2 1 x 2 dF(x) dxX 2 b 300x = 0 V = {300 2x} kip c©F y = 0;
Example 5 X and Y are jointly continuous with joint pdf f(x,y) = (e−(xy) if 0 ≤ x, 0 ≤ y 0, otherwise Let Z = X/Y Find the pdf of Z The first thing we do is draw a picture of the support set (which in this case is the firstFeep feep feep feep Bluegrass Community & Technical Co l eg VA Hospital KET Funkhouser Memorial Coliseum White Hall Kentucky P roud a k KY Clinic Seaton Ctr K rog eFi ld ChemPhys
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In December of 16, Winchester began offering special 30 WCF "Short Range" ammunition to be used for "small game where the more powerful cartridge is not necessary" as it was described in that catalogThe cartridge illustration was shown as the since cartridges contained a 100 gr lead bullet and 6 grains of powderOverdetermined System for a Line Fit (2) Writing out the αx β = y equation for all of the known points (x i,y i), i =1,,mgives the overdetermined system 2 6 6 4 x1 1 x2 1 x m 1 3 7 7 5 » α β – = 2 6 6 4 y1 y2 y m 3 7 7 5 or Ac = y where A = 2 6 6 4 x1 1 x2 1 x m 1 3 7 7 5 c = α β – y = 2 6 6 4 y1 y2 y m 3 7 7 5 Note We cannot solve Ac = y with Gaussian elimination Unless theThe CX was the most important shortrange reconnaissance aircraft and dive bomber of the Finnish Air Force at the outbreak of the Winter War There were 29 of them in combat units, the "FransKalle" was slow but possessed a robust airframe, making it a useful asset
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And xc(t) is the general solution to the associate homogeneous system, x(t) = B(t)x(t) then x(t) = xc(t)xp(t) is the general solution Example 12 Let x0(t) = 4 ¡3 6 ¡7 x(t) ¡4t2 5t ¡6t2 7t1 x(t), x1(t) = 3e2t 2e2t and x2(t) = e¡5t> c c c !` A ̐V w { D x ͓ ̐ y w g T x Ɉ ڂڂꂵ Ă ̂ A ̐g ̂̔閧 ̂ Ō o Ȃ ł B D ɂ͒j ǂ ̃ m Ă c c ܂ t ^ i ̂ I v ͕ D ͏ \ 킸 Ԃ߂Ă ܂ B ŁA g C Łc c D ̍s ׂ͖\ Ă A Ă ɐ y Ɂc c B
Aya Ohzeki ス ス ス ス スハ販サ スC スg ( スX スV) TV TBS スn ス スw スヘゑソス` ス ス ス ス スI スx スナゑソス スミ介頂 ス ス スワゑソス ス ス スI スG ス ス スw スT ス ス ス スO ス ス スB ス スi スX スx スナゑソス スミ介頂 ス ス スワX a f(t)dt This value is f(x) (b) d dx Z b a f(t)dt This value is zero (it's the derivative of a constant) (c) Z b a d dx f(x)dx This value is f(b)−f(a) (d) Z b a f(x)dt This is a little tricky since the integral is in terms of t, but f is an expression in x, it will be constant with respect to t The answer f(x)(b# * ' $ 1 '
6 ft 4 ft 300 2x V = 0 0 x 6 6 ft 6–18 Draw the shear and moment diagrams for the beam, and determine the shear and moment throughout the beam as functions of x 2 kip/ft 8 kip x 10 kip 40 kip ft A 30 kip ft B 5 ft 5 ft 2 kip/ft 5 ft 6–194 1 SYSTEM OF FIRST ORDER DIFFERENTIAL EQUATIONS If xp(t) is a particular solution of the nonhomogeneous system, x(t) = B(t)x(t)b(t);1, if x ≤ a A simple computation yields E(X) = ab 2 Var(X) = (b−a)2 12 M(s) = esb −esa s(b−a) When a = 0 and b = 1, this is known as the uniform distribution over the unit interval, f(x) = 1 1
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SOLUTIONS 1 a F (A,B,C) = A' B' C' A' B' C A B' C' A B' C A B C' A B C Distributive = A'B' (C' C) AB' (C' C) AB (CЂe a r ͂n ` t A ̊i ̔ A r N ^ JVC C J @WTT500 V Y A C X A v A K z A w b h Z b g ̌ ̔ s Ă ܂ m 点 ̃y W ͍ŐV ł y N N n c Ɠ ̂ m 点 z12/29( ) `1/4( ) ܂ŋx Ƃ Ē ܂
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