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Unformatted text preview: Or.) if ”'3’ 4&6 Version 002 /AAAAC w DGQOGC — Gilbert  (78759)  1 This printout should have 3 questions.
Multiplechoice questions may continue on
the next column or page W find all choices
before answering. 001 10.0 points Determine which one of the following equa—
tions has graph 1 y2 =zw~1
2 m~y2m1
3 10—22 =1
4 22 zyml
5. 2:21—2 m1
6. (9—532 2 lcorrect
Explanation: The graph is a cylinder with axis parallel
to the z»axis. In addition its trace on the
my—plane is a parabola opening in the positive
y—direction and having positive y—intercept.
Consequently, the graph is that of the equa—
tion keywords: quadric surface, graph of equation,
cylinder, 3D graph, paraboiic cylinder, 002 10.0 points Find a parameterization of the horizontal
circie of radius 4 having center (2, 5, m1). 1. r(t) = (2m4sint)i~(5+4cost)j—k
2. r(t) 2 (2+4sint)i+(5m4cost)j+k 3. r(t) m (2— 4sint)i+ (5+4cost)j w k
correct 4. r(t) w (2+4cost)i~i~5j+(l~4sént)k
5. r(t) = ((2w4cost)i~5j+(l+4sint)k 6. r(t) = (2+4cost)i+5jw(lm4sint)k Explanation:
if the vector function r(t) m 33(t) i ~+~ y(t)j + z(t) k traces out a horizontal circle having center
(2, 5, —1), then z(t) 2 —1 for all t because
the circle must lie in the horizontal plane
z(t) : m1. On the other hand, the projection red) = $(t)i+y(t)j
of this circle on the mywplane is a circie of radius 4 having center at (2, 5, 0). Thus, as
as circle in the my—plane it has the equation (m——2)2+(y—5)2 m is.
Consequentiy,
(2305) W 2)2 + (W)  5V = 16, andso
r(z';) = (2m4sint)i+(5+4cost)j—— k is one parametrization of the horizontal circle of radius 4 and center (2, 5, , ~1). keywords: vector function, space curve, circle,
plane, radius, center circle, 003 10.0 points Version 002/AAAAC ~— DGQOGC — Gilbert W (78759) ' Find an equation for the plane passing
through the point P(5, 3, 6) and perpendicu—
lar to the z—axis. 1. y :2 ~3 2. a: = m5 3. z 7—— ﬁcorrect
4. y = 3. 5. :1: = 5 6. z x —6
Explanation: If the plane is perpendicular to the z—axis,
then it is of the form 2: 2 d. But if this
plane also passes through P(5, 3, 6), then it
has equation ...
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 Fall '09
 Gilbert

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