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- Further applications of
- Parametric equations
Section exercises
Verbal
What is a system of parametric equations?
A pair of functions that is dependent on an external factor. The two functions are written in terms of the same parameter. For example,
and
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Explain how to eliminate a parameter given a set of parametric equations.
Choose one equation to solve for
substitute into the other equation and simplify.
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What is a benefit of using parametric equations?
Some equations cannot be written as functions, like a circle. However, when written as two parametric equations, separately the equations are functions.
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Algebraic
For the following exercises, eliminate the parameter
to rewrite the parametric equation as a Cartesian equation.
For the following exercises, rewrite the parametric equation as a Cartesian equation by building an
table.
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by setting
or by setting
For the following exercises, parameterize (write parametric equations for) each Cartesian equation by using
and
Identify the curve.
Parameterize the line from
to
so that the line is at
at
and at
at
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Parameterize the line from
to
so that the line is at
at
and at
at
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Technology
For the following exercises, use the table feature in the graphing calculator to determine whether the graphs intersect.
For the following exercises, use a graphing calculator to complete the table of values for each set of parametric equations.
Extensions
Find two different sets of parametric equations for
answers may vary:
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Find two different sets of parametric equations for
answers may vary: ,
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Questions & Answers
how does the planets on our solar system orbit
how many Messier objects are there in space
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
Roaul
I want to be an astronomer. That's my dream
Astrit
Who named the the whole galaxy?
what is the dark matter
Richard
what are the factors upon which the atmosphere is stratified
bigbang is the beginning of the universe
Sokak
but thats just a theory
Sokak
nothing will happen, don't worry brother.
Vansh
these are Rocky substances between mars and jupiter
GANGAIN
Comets are cosmic snowballs of frozen gases , rock and dust that orbit the sun. They are mostly found between the orbits of Venus and Mercury.
Aarya
hey can anyone guide me abt international astronomy olympiad
sahil
how can we learn right and true ?
why the moon is always appear in an elliptical shape
Because when astroid hit the Earth then a piece of elliptical shape of the earth was separated which is now called moon.
Hemen
Did you mean eye sight or sea level
Minal
oh sorry it's sea level
lidiya
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
w astronomy and cosmology!
Michele
another theory of universe except big ban
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
I think it couldn't possible on earth
Nagalakshmi
in this time i don't Know
Michele
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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Source:
OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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