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pex1sol

# pex1sol - Math 16C Practice Exam 1 Problem 1(10 points each...

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Unformatted text preview: Math 16C Practice Exam 1 Problem 1 (10 points each) Find a general solution for the following differential equations. (a3g+y—7=0 golujh‘on l M \ ‘7‘ 37‘ * éu 7) SW” W" 7‘57??? A ” ' 1 y \ A 8‘ AK La 11m): 53"sz 3" 9.“ h— : .a __ 1 S 7-7 7 '3’ y,e\/;x + YCEEWX) , \$6 “ﬁx? '7): J§X+ C\ ( ,1 \éxy‘ lei/3K ? ’- “(3X’c\ Lé/zx ye " -§ ‘7 a e ' ng ﬁx Vx (c) 3331/ + 23/ = 61/12 5mg rd gar, 1 , ii 94% (A M 7/ JV X37 :5 —;’<‘-§ a *7- Lér 100 7 Cg XMQX :‘ ﬁx .x‘ - '1 7’6 + y(;1x’3<") 3 ":23 «(I x ,L (73 ) .. X3 90W! #4 QOM‘ ' A“ " at r 7 J: ><-\ -KH _\__ ’ - L415: 190: as A“ 3 CW 0 “ (e)y’=1+y-3a32(1+y) sax/km 1 _/M y’: \w 4,» -917, g‘mAw’a‘ Ram“ 7’Jth1-O7 '3 \ “3X1 3 \Kx‘anlx "A x2 Lc’c 3. L54) 2 E. i Q 3 y I ((53... K) 4 7((3’112 \) {K‘S’K> 3 Q ’3X\\ {K “K (75”‘5/ “=- (\«szk’é‘x \$2 ‘ xx ye X: Sa(_\$,<1'“ex KJKC‘QX -\-(’ So\v’\'\0 A l 7/ : (Hyﬂl'gxl) 8%;‘5’ : S(\*?x1)a(x ﬁUW) 3 )(“XKJrC Problem 2 (10 points) Determine an equation for a sphere which has a diameter with endpoints (0,0,0) and (4,2, —2). T.\Iv< C(A’KC/ 0% "VQ gghw iii “/1 MsAYaA/QV A +11 i\mb’§€/l c 0*% 0+1 -1 (>0 w W w 7)?)01):(&)r\) m mm a M? me View 5% m A4 mew page 03 «u Aim/«1W W'V go W1! (1 a make/g wi"t\.\ (QA’R/ (Zlﬁﬂ) 0me (7:1ka We am W ”M Wm bemﬁcwxf -\ an)“: 1% Problem 3 (10 points) Verify that y = 06—2z is a solution of the differential equation 3/ + 12y = O for any number C. Then ﬁnd the particular solution speciﬁed by the initial condition y = 5 when 7’-¥9\71‘ 'lCejoJr QCQZK : O / yrs M K30 qivgf {/5 S : (go : C \$0 7: 561% {5 '\\/\.Q Qarjilﬂ/Ka/ <0\l7k:(v\ Problem 4 (10 points) (a) (7 points) Let f(x, y) 2: V5102 + y2 — 3. Sketch the level curves of f for the values 1, V6, and m. (b) (3 points) What is the domain of f? LILVQ/l a/rx/t £°/ QLX,7)‘:1 '. '1: m j H: X1+~7L (la) M AOMAA OX g {S ’Vke S{‘\ 6% QOwAYS (>97) ‘Yof erudA {x1 scyl :13 wk“ §<ASC “ll/(d Maker «ASK jtor )C'wlylr-S'ZO le7123 6 “\Llr (I JVVQ gi‘l 0g ?a\/\7lj DJRH‘t “ll/ﬂ (M'Ole 0% (BULK/f ﬁ/ azimreal (15: (0)0) Problem 5 (10 points) A bacteria culture starts with 500 bacte— ria. After 2 hours, the population size is 1500. Assuming that the culture grows at a rate proportional to its size, ﬁnd the population after 7 hours. Lair we: :6! A mm a we {- (u (my) \/ I 2'5 K7 (Ti/‘4 wk 6‘ (km{ (f {raprarllovxdl +0 V 2 7(0) 3 500 (We «4 Mg 500 widen.) 7/(9\) : ‘500 (M‘kf R \mvrS/ ”tin—UL out \SOO bno‘kQ/I‘A) W M 01‘3Vi-1 \$19017 :: Kn :KthC\ 547/ 1 g Ktl C\ # K£¥Cy3C€K’( if lkﬁﬂﬂ‘iﬂli 50M?“ 74: \/s< yobsooﬂmmsoo in; M3 (ml K ﬂabsoo @ goo :Qef’: Q Q 90 70:} 3 SOUQK’t 7m : \300 22> 60;):6330 e7" 3 Kiﬂgi S2» yUclrswek‘f'J‘ 7 A??? Mia 3; WW) mm m 7L?):Sooe WM” 1° yuan] 0‘? Problem 6 (10 points) A tank contains a solution which is 80% water and 20% alcohol. A second solution which is 40% water and 60% alcohol is added to the tank at a rate of 2 gallons/ minute. At the same time, the tank is drained at a rate of 2 gallons/ minute. Assuming the solution is constantly stirred, how much alcohol will be in the tank after 10 minutes? Lek» yi’c) : drum/(ml 0% AM :A m A an 1: (2A Mmq/ M “Mt {:0 10% al “A 90653qu l/ 4mm! )50 7(0/:/.RO)')\O:Lf . A (a z y’: ('éol'a'(1)'°L : EAGV’ toUlW) '20 Solvﬁ ‘l<\«~€ Xx“ <1, Sal-Enty : g ﬂax \$0 700 : \QU \$67“ l Mia \O (Wm/*6 “‘ﬁmﬂrﬂ \Ml \ac. yélOlfKQ’Xél 0)“!wa 0% a\(ﬂl/\/Ol ’IA “\l/‘Q *aL/xk ...
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