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Unformatted text preview: MATH 160(001)
Midterm 1. Practice Exam 2 1. Determine the center and the radius of the following sphere.
3.7:2 + 33/2 + 322 — 611: + 12y — 242 = ——51 2. The diameter of asphere has endpoints (0, 0, 0) and (1, *4, 2). Determine
the radius and the center of the sphere. 3. Consider the equation Zn: 3;2 ~ + 1. a) Neatly sketch the level curves for the folowing values of z: 2. —1, 0 , 1. 2.
Include apprOpriate labeling. b) Identify the surface. 4. Show all necessary steps in solving the following differential equations. ylzi
a) y y+1
b)ey3/=:L'ln;t' 1 I ,2 _ ,2 1"
c) + a, y — .1 e 5. A solution of suger and water containig 3 ponds of sugar per gallon be—
gins ﬁowing into a tank containing 50 gallons of pure water at the rate of
7 gal. / min. The well—stirred mixture ﬂows out of the tank at the rate of
5 gal. / min. Let S represent the pounds of the sugar in the tank at time t
minutes. a) Set up a differential equation which describes the rate at which the amount
of sugar in the tank chnges with respect to time. b) Solve the differential equation in part a) Determine all unknown constants
ans solve explicitly for S. 6. Assume that the amount (pounds) of salt in a tank at time t ( miutes) is
given by S’ = 100+3t — (0.01)eft S'or t 2 0. Determine the maximum amount
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