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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‘
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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
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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
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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
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