[ 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
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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.
The diagram shows a cone and its axis of rotation. Which type of cross section is formed when the cone is intersected by a plane containing
the axis of rotation?
Wendy is skiing along a circular ski trail that has a radius of 2.8 km. She starts at the 3-o'clock position and travels in the CCW direction. Wendy stops skiing when she is 0.883 km to the right and 2.657 km above the center of the ski trail. Imagine an angle with its vertex at the center of the circular ski trail that subtends Wendy's path.
TIP: Draw a picture! Include in your picture of Wendy's path: the trail, the coordinates where Wendy starts and stops, the angle that Wendy traverses, and the distance s that Wendy travels.
a. How many radians is the angle, 0, swept out since Wendy started skiing? __radians
Preview Hint: You might use one of the following functions: cos -1, sin , or tan
b. How many kilometers, s, has Wendy skied since she started skiing?
___km
Hint: Recall that = (or s = r. theta)if an angle has a measure of radians and subtends an arc s units long along a circle with a radius r units long.
Finite Mathematics & Its Applications (12th Edition)
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