anonymous
  • anonymous
Can anyone help me parametrize sin(x)*e^y=0?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
The solution is Pi
anonymous
  • anonymous
i want to find a parametrization though. You know, x^2+y^2=1, the parametrization is x=cos(t) y=sin(t)
anonymous
  • anonymous
Check this out. http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx

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anonymous
  • anonymous
You mean, you want the parametric equations?
anonymous
  • anonymous
so you mean parametrize z= e^(y)sin(x)
anonymous
  • anonymous
yes chaguanas, i just cant seem to find a relation between x and y, or such. and im checking the link now, murph. thx
anonymous
  • anonymous
the thing is, the link tells you more about how to reverse a parametric eqn than how to make one. Right now, I can't find a relation; i.e. I can't parametrize in polar coordinates nor in spherical coordinates.
anonymous
  • anonymous
ok, the whole question is: find parametric eqns for the three level curves of the function W(x,y)=sin(x)e^y which pass throught the points... well, I found one level curve z at z=0 to be sin(x)e^y=0, so I need to parametrize it.
anonymous
  • anonymous
You need to post the whole question. Because you are not giving us enough info, and even misinterpreting the question.
anonymous
  • anonymous
ok, "find parametric eqns for the three level curves of the function W(x,y)=sin(x)e^y which pass throught the points P=(0,1), Q=(pi/2,0) and R=(pi/6,3). Also compute the vectors of the gradient vector field W at the points P, Q, and R."
anonymous
  • anonymous
I know how to find the gradients, so im more concerned with the first part.
anonymous
  • anonymous
I think you find the dell or gradient, which is a vector, and use that vector in conjunction with the points to find parametric eq
anonymous
  • anonymous
but the gradient only shows change, how can it help me parametrize?
anonymous
  • anonymous
I dont think you can parametrise, end of story
anonymous
  • anonymous
well, it is a homework question. i don't think the books wrote all that for nothing
anonymous
  • anonymous
i do
anonymous
  • anonymous
Be careful with the word parametrise, that was your previous lesson. The gradient are normal to the level curve. You want to find the parametric eq.
anonymous
  • anonymous
i still don't understand, how is the gradient going to help me?
anonymous
  • anonymous
It is going to give you a vector. The vector is used in conjunction with the points to find the parametric eq.
anonymous
  • anonymous
can you tell me how?
anonymous
  • anonymous
Partial derivative in relation to x, partial in relation to y
anonymous
  • anonymous
yes i know, what do you do with the gradient after that?
anonymous
  • anonymous
let's say the vector is <1,2> and point P (0,1). Parametric eq is x=0 + 1t, or x=t y=1+2t
anonymous
  • anonymous
ok, so the vector at (0,1) comes out to . so parametric is x=e*t, y=1? That doesn't come out right.
anonymous
  • anonymous
Don't solve for the vector at (0,!). Just get the vector from the partial fractions. You are anticipating and reading too much into the question.
anonymous
  • anonymous
wait so what is the vector?
anonymous
  • anonymous
Just find the partial derivative in relation to x, partial in relation to y. You already said you know how to do it. In fact, you have already done it. But apparently you made an extra step and put in (0,1).
anonymous
  • anonymous
yeah, but im supposed to somehow use that to parametrize? ok, so i got the gradient and it's
anonymous
  • anonymous
For the rest of your life, don't use the word parametrize. You are not parametrizing. You are finding the parametric equations.
anonymous
  • anonymous
sorry. ok, so how do you use to find the parametric equations?
anonymous
  • anonymous
\[x =t e ^{y} \cos x\]\[y =1+te ^{y}\sin \]
anonymous
  • anonymous
and that's for a general level curve?
anonymous
  • anonymous
so what is the parametric eqn for z=0?
anonymous
  • anonymous
Post your question again, as a new post, this time the whole question; so you can get a fresh perspective from some other guys.
anonymous
  • anonymous
yeah, thx for your help!
anonymous
  • anonymous
most ppl here dont know multivariable calc though
anonymous
  • anonymous
One or two of them do. There is someone named Lokisan who comes on at odd hours and goes through all pass questions and sends a response.
anonymous
  • anonymous
I think I got it. plug in values for P in your original eq. I think it gives your 0. So one of your level curve is sinxe^y=0. Do it for the other two points. Then find parametric eq of each.
anonymous
  • anonymous
yes, that was exactly my original question, which was "find the parametric equation of sin(x)e^y=0", but I just couldn't find a parameter that satisfies the equation
anonymous
  • anonymous
*parametric equations
anonymous
  • anonymous
Finding parametric equations is a very simple process. Use partial fractions to get a vector, and with that vector and the point find values of x and y, (the answers include t)
anonymous
  • anonymous
you did that for me before, but so what is the vector? I got the gradient, so what do you want me to do with it?
anonymous
  • anonymous
where did you go?
anonymous
  • anonymous
i lost the post, this is moving so fast
anonymous
  • anonymous
hahaha, scroll down a bit more
anonymous
  • anonymous
computer wont let me
anonymous
  • anonymous
listen, im not trying to take sides because I don't even worship a god. However, i'm just saying that everything happens for a reason. If something happens, don't look to god. look to another reason. That's why they got meterology and all that what not, right?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
whats this about worshipping the laws of nature. we dont even know the laws of nature are permanent
anonymous
  • anonymous
physics? yes, it is. are you saying that gravity is not permanent, that it does not equal 9.8m/s^2 when close to Earth's surface?
anonymous
  • anonymous
right, we dont know what will happen in the future
anonymous
  • anonymous
there is no reason to prevent gravity from ceasing, mass will cease, etc , in the next instant
anonymous
  • anonymous
just because our "laws" have described nature in the past, who is to say what will happen in the future
anonymous
  • anonymous
science works until it stops working, so to speak. and then we try something else
anonymous
  • anonymous
but there arent any real laws. or permanent
anonymous
  • anonymous
everything changes
anonymous
  • anonymous
yes, i suppose that if god decides to change the laws of physics, then he will. however, for now, earthquakes will always occur when a tectonic plate happens to accidentally brush up against another one, and fires will keep on reacting as long as there is oxygen to fuel it, and babies cannot be magically lifted into the air without any physics behind it
anonymous
  • anonymous
nothing can be done, nor should be done, to change that. or else there will be devastating consequences
anonymous
  • anonymous
no i mean, aside from god
anonymous
  • anonymous
even if god doesnt exist, the laws of nature can spontaneously change. what is there to provent that?
anonymous
  • anonymous
actually, god's existence could be arguably a reason that gravity will not cease. he is there to prevent it. but i dont see any evidence for god. so we are truly floating blindly in space , and our laws have no permanence
anonymous
  • anonymous
that's philosophy. out of my range, out of the range of mathematics too, within which we are posting =D but, science has worked for hundreds of thousands of years, and it doesn't seem to be changing now, so why should it?
anonymous
  • anonymous
why should it not . actually there is a reason why it should. empirically everything changes
anonymous
  • anonymous
oh i hope i didnt contradict myself
anonymous
  • anonymous
if you can find one, (outside of quantum mechanics, and any other science that is still developing) I should like to know it
anonymous
  • anonymous
can find what? an example of a law changing, oh
anonymous
  • anonymous
well then science will just have to modify things a bit
anonymous
  • anonymous
the only reason why science works in the first place is because there is consistency in the universe, regularity, repeatability. if we lose this regularity (doesnt matter what it is), then science wont work . you cant frame a law of nature if there is nothing for it to express , if nothing is predictable
anonymous
  • anonymous
youre right though, this is outside the scope of math problems
anonymous
  • anonymous
if we lose a regularity, then we search further, because we can always assume there is a regularity in the universe. Even "regularity" cannot be strictly defined. what occurs often is regularity, sometimes things that are irregular in the beginning become regular as we understand it more
anonymous
  • anonymous
hence, quantum mechanics and the such

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