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- Calculus volume 3
- Vectors in space
- Quadric surfaces
[T] The intersection between cylinder
and sphere
is called a
Viviani curve .
- Solve the system consisting of the equations of the surfaces to find the equation of the intersection curve. (
Hint: Find
and
in terms of
- Use a computer algebra system (CAS) to visualize the intersection curve on sphere
a.
where
b.
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Hyperboloid of one sheet
and elliptic cone
are represented in the following figure along with their intersection curves. Identify the intersection curves and find their equations (
Hint: Find
y from the system consisting of the equations of the surfaces.)
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[T] Use a CAS to create the intersection between cylinder
and ellipsoid
and find the equations of the intersection curves.
two ellipses of equations
in planes
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[T] A spheroid is an ellipsoid with two equal semiaxes. For instance, the equation of a spheroid with the
z -axis as its axis of symmetry is given by
where
and
are positive real numbers. The spheroid is called
oblate if
and
prolate for
- The eye cornea is approximated as a prolate spheroid with an axis that is the eye, where
Write the equation of the spheroid that models the cornea and sketch the surface.
- Give two examples of objects with prolate spheroid shapes.
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[T] In cartography, Earth is approximated by an oblate spheroid rather than a sphere. The radii at the equator and poles are approximately
mi and
mi, respectively.
- 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
corresponds to the equator.
- Sketch the graph.
- Find the equation of the intersection curve of the surface with plane
that is parallel to the
xy -plane. The intersection curve is called a
parallel .
- Find the equation of the intersection curve of the surface with plane
that passes through the
z -axis. The intersection curve is called a
meridian .
a.
b.
;
c. The intersection curve is the ellipse of equation
and the intersection is an ellipse.; d. The intersection curve is the ellipse of equation
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[T] A set of buzzing stunt magnets (or “rattlesnake eggs”) includes two sparkling, polished, superstrong spheroid-shaped magnets well-known for children’s entertainment. Each magnet is
in. long and
in. wide at the middle. While tossing them into the air, they create a buzzing sound as they attract each other.
- Write the equation of the prolate spheroid centered at the origin that describes the shape of one of the magnets.
- Write the equations of the prolate spheroids that model the shape of the buzzing stunt magnets. Use a CAS to create the graphs.
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[T] A heart-shaped surface is given by equation
- Use a CAS to graph the surface that models this shape.
- Determine and sketch the trace of the heart-shaped surface on the
xz -plane.
a.
b. The intersection curve is
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[T] The ring torus symmetric about the
z -axis is a special type of surface in topology and its equation is given by
where
The numbers
and
are called are the major and minor radii, respectively, of the surface. The following figure shows a ring torus for which
- Write the equation of the ring torus with
and use a CAS to graph the surface. Compare the graph with the figure given.
- Determine the equation and sketch the trace of the ring torus from a. on the
xy -plane.
- Give two examples of objects with ring torus shapes.
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Questions & Answers
how did the oxygen help a human being
how did the nutrition help the plants
Biology is a branch of Natural science which deals/About living Organism.
evolutionary history and relationship of an organism or group of organisms
AI-Robot
cell is the smallest unit of the humanity biologically
Abraham
HOW CAN MAN ORGAN FUNCTION
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
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Source:
OpenStax, Calculus volume 3. OpenStax CNX. Feb 05, 2016 Download for free at http://legacy.cnx.org/content/col11966/1.2
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