[ T ] In cartography, Earth is approximated by all oblate spheroid rather than a sphere. The radii at the equator and poles are approximately 3963 mi and 3950 mi, respectively. a. Write the equation in standard form of the ellipsoid that represents the shape of Earth. Assume the center of Earth is at the origin and that the trace formed by plane z = 0 corresponds to the equator. b. Sketch the graph. c. Find the equation of the intersection curve of the surface with plane z = 1000 that is parallel to the x y -plane. The intersection curve is called a parallel. d. Find the equation of the intersection curve of the surface with plane x + y = 0 that passes through the z -axis . The intersection curve is called a meridian.
[ T ] In cartography, Earth is approximated by all oblate spheroid rather than a sphere. The radii at the equator and poles are approximately 3963 mi and 3950 mi, respectively. a. Write the equation in standard form of the ellipsoid that represents the shape of Earth. Assume the center of Earth is at the origin and that the trace formed by plane z = 0 corresponds to the equator. b. Sketch the graph. c. Find the equation of the intersection curve of the surface with plane z = 1000 that is parallel to the x y -plane. The intersection curve is called a parallel. d. Find the equation of the intersection curve of the surface with plane x + y = 0 that passes through the z -axis . The intersection curve is called a meridian.
[
T
]
In cartography, Earth is approximated by all oblate spheroid rather than a sphere. The radii at the equator and poles are approximately
3963
mi and
3950
mi, respectively.
a. Write the equation in standard form of the ellipsoid that represents the shape of Earth. Assume the center of Earth is at the origin and that the trace formed by plane
z
=
0
corresponds to the equator.
b. Sketch the graph.
c. Find the equation of the intersection curve of the surface with plane
z
=
1000
that is parallel to the
x
y
-plane. The intersection curve is called a parallel.
d. Find the equation of the intersection curve of the surface with plane
x
+
y
=
0
that passes through the
z
-axis
.
The intersection curve is called a meridian.
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9. (a) Use pseudocode to describe an algo-
rithm for determining the value of a
game tree when both players follow a
minmax strategy.
(b) Suppose that T₁ and T2 are spanning
trees of a simple graph G. Moreover,
suppose that ₁ is an edge in T₁ that is
not in T2. Show that there is an edge
2 in T2 that is not in T₁ such that
T₁ remains a spanning tree if ₁ is
removed from it and 2 is added to it,
and T2 remains a spanning tree if 2 is
removed from it and e₁ is added to it.
(c) Show that a
degree-constrained
spanning tree of a simple graph in
which each vertex has degree not
exceeding 2 2 consists of a single
Hamiltonian path in the graph.
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