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Eliminate the Parameter, (x,y), t^2+1, t^2-1, 0

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Hello, Tom from everystepcalculus.com and everystepphysics.com. Eliminating the parameter. This is an rt equations involving t and so let’s do it index 8 get to my menu. We’re already at eliminating the parameters we scroll down to that if you scroll down with the cursor here. rt equation. This came from a Yahoo problem, a kid couldn’t do it. And of course, the people that answered the question didn’t do it very clear and of course the only thing we’re interested in is passing a test and passing Calculus and getting out of there. We have no interest in calculus beyond that. Calculus is the Sodoku math, should be taught only to math majors. It’s like it’s like being required to do crossword puzzles in if you’re an English major or trying to learn the English language to work day after day and crossword puzzles. You’ll end up with nothing. But anyways we’re going to enter the function. The function is, you have to press alpha before you enter anything in these entry lines. Alpha T squared plus one and in this for the y t, function of t. Alpha t squared minus one. Notice that these are all contrived functions. For z, we’re going to have a alpha 0. Put 0 if they don’t give you z. Nothing happens like this in real life. Calculus solves nothing I say but it does solve completely nonsense nobody ever uses it nobody ever did use it. I say it’s okay. I always give you a chance to change functions if you made a mistake but you it’s a good and we’re going to choose number five. We can do all these things to, acceleration, angle, length of an arc
etc. Right now we’re going to choose number five. Press the number or you can scroll down there press a number and try to do this without a program be my guest. Solve for t It seems simple. Y equals t squared minus one. Answer is square root of y plus 1. We substitute for t into x and z equations. There was no z equation, it was zero. And so x equals y plus 2. Notice we we put in here, you should put parentheses around this for your professor but then x is equal y plus 2. and then this equation, you want to put y equals x minus 2. and z of course is 0. You can go back for more calculations or you can go back to the main menu. Pretty neat, huh? everystepcalclus.com Go to that come to my site, buy my programs, pass calculus, keep your head on straight. Don’t let these doing that these professors scam you too much however they do all the time so have a good one.

Eliminate the parameter, t+1, 0, t^2 1

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Transcript

Hello everyone. Tom from everystepcalculus.com and everystepphysics.com. Again we’re going to eliminate the parameter. More nonsense in calculus stuff that never happens. Calculus is Sodoku of math. Let’s do it. But we have to pass calculus, we have to get these tests passed etcetera etcetera so that’s the reason I just say my programs. Index 8 to get to my menu. I’m already at eliminate the parameter, you can scroll down to it when you get your menu. Also you can use second and the cursor here to go you know page by page down to the menu and we’re going to enter our r t functions. You have to press alpha before you enter anything in these entry lines here so the first one is alpha t plus 1. And of course alpha for y is zero and alpha for z is T squared minus one. All contrived variables, of course. Here they are you can check and see if it’s correct. If it’s not, you can change them. I say it’s ok. and we’re going to choose eliminating the perimeter, number five. Again, I show you what you’ve entered here. We’re not changing we’ve already checked in already. And we’re going to solve for t in the x equation, okay. So we take x and we solve for t and t equals x minus 1. pretty simple try solving harder questions even like this one. So we put this back into x X and we get x equals x. ok no big deal there. Z is t squared minus one. So you gonna put X minus one squared minus one. Now you doing the calculations yourself you you square this and subtract 1 to get this. Let me see you do that. I can’t do it wouldn’t do it without my program why would you do I would you waste your time on this nonsense. And the answer is x equals x, y equals 0, z equals x squared minus 2x. We’ve eliminated the parameter. Okay, great. everystepcalclus.com. Go to my site buy my programs, pass your calculus test. Tell your friends about this program. Have a good one.

Graphing a parametric equation

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Raw Transcript

Hello everyone, this is Tom from everystepcalculus.com, everystepphysics.com. We’re gonna do a sketch by hand concerning parametric equations. A position formula for position vectors, and then eliminate the parameter. The parameter is T. So let’s do it. Index 8 to get to my menu. I’m already at sketch graph. Here’s the position in vector format. And you have to press alpha before you enter anything into these entry lines here. Alpha T squared minus 4, and alpha t divided by 2. If z is not given, enter 0. Alpha 0. I always show you what you’ve entered, you can change it if you want in my programs. And we’re gonna scroll down here to sketch by hand. I put in the arbitrary numbers for you that you’re gonna then work in the formula. Here’s the answer, you put these on a graph paper and you sketch the graph of this function. We’re gonna go back now and eliminate the parameter.
Of course you know how to do that, don’t you. It’s all nonsense if you ask me, calculus is nonsense. Eliminating parameter. Solve for t in the y equation, which we did here. t equals 2y, and then you put that in the x equations, into the x equation here. And here’s the answer: 4y squared minus 4. Sometimes your professor might want you to put it into a 0 format or an equal 0 format. You change, transpose, the x to the other side minus x, and then change the sign, x minus 4y squared plus 4 equals 0. Alright, pretty neat, huh? Everystepcalculus.com, go to my site, buy my program if you wanna pass calculus, and subscribe if you wanna see more videos that I might make. And don’t forget physics, either, okay? Have a good one.

Parametric Equations-Find Speed

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Find Speed

x=t^3-4*t

y=t^2+1

z=0

Raw Transcript

Hello everyone, Tom from everystepcalculus.com, everystepphysics.com, a problem dealing with parametric equations and the item of speed. So let’s do it! Index 8 to get to my menu, go to speed. Speed is a scaler, it has no direction, no angle, unless you add time to it, which I’ll show you in my program here. There’s speed, and write all this on your paper here, the r(t) formula is x(t)i, j, and k, and x, y, and z. And we have our functions for x and y. You have to press alpha before you enter anything into these entry lines here. Alpha… the problem is T cubed minus 4 times T. And Alpha T squared plus one. Looks like the “t” is missing. Here we go, put the “t” in. Here we go, and alpha 0 for the z component, or the K component if it’s not given. These are all set up problems, they don’t happen in real life,
which is nonsense for calculus. A lot of it is like that in calculus. So, I always show you what you’ve entered, you can change it if you want. Say it’s okay. And we’re gonna scroll down here to the calculation– you have different things on the menu that you can do with this entry of “t” variables. Speed, there it is there, and of course you write the derivative of the magnitude of it, which is actually the square of the derivatives. Calculus, the sudoku of math. X prime, here’s the derivatives of that and the magnitude is then the derivative squared. I’m going to say that the time was not given in this problem at first, so to do it we’re gonna go back, we’re gonna press number 2. And so speed is the square root of 3t squared plus 2t minus 4. We’re gonna go back and do it again. Add some time component. Press yes for time… add– yes, let’s put 7 seconds. And so, it’s t equals 7, you’re entering it into the variable of the function. You’re gonna put parenthesis around this “7” on your paper but I have to use quotation marks. Turns out to be that. Turns out to be 12.5 units per second. But, because “t” is given… “t” is given, so we do have an answer, it’s 1.4732, arc tangent of the rise over run.  Have a good one, everystepcalculus.com, go to my site, buy my program if you want to pass calculus easy, or subscribe and see other videos I might make. And don’t forget about physics either. Thanks so much. Have a good one.

 

What is Parametric Equation?-Video

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Transcript
This video is on parametric equations. A parametric equation is, you’re adding a parameter of t time to every x y and z function, and that’s where we add the parameter and that’s the reason we call them parametric equations. And let’s do it. Turn the calculator on here. We’re going to get back to the home screen here. Clear the calculator we can go F1 eight and it clears that screen here. You press second alpha and put in the letters i n d e x, and then you push alpha and get into the number 8 and closed parenthesis to add this and get my formula for my menu. Press enter and we’re into my menu. And you can see all the things available in my menu for you to pass calculus and do your homework. Position vectors, product rule, projection of a and b, all those kinds of things you will be involved with in calculus one two or three. We’re going to do parametric equations now. That’s concerned with position vectors. If z is not given you enter zero in for z, then you can do the other two, x and y. So there’s the vector r t is generally an r t, is equal to this vector here, x t, y t and z t. So you have to press alpha to enter the functions in the entry lines here, so let’s do it, three times t let’s say plus four for x t, here’s y t, let’s enter have to push alpha, five times t and let’s do the z one, or let’s put alpha just for to make it simple and put z you can see that the z one is zero. Gives you a chance to change it if you’ve made a mistake, and we have all these things that we can do with this formula now with these functions in there. We can eliminate the parameter. Which eliminates the t and changes it back to an x function. Let’s do that quick, I’ll go through these quick so you can see. You solve for t, here’s the solution for t, and then you substitute t into every other x y and z, but ah here’s one point six seven times x minus three point nine and that eliminated the t parameter. Let’s go length of arc, you want to do that, fine, let’s go press four, notice it’s an integral over a and b, with the derivative of the r t formula. And rt we’re going to put in what we entered, I’ll go through it quick, put this all on your paper, write it down exactly as you see it, and we’re doing the square of each one, over the time of let’s say, you have to push alpha, let’s say from two to alpha six, shows you from two to six, here we’re doing this, write this on your paper and each individual one is gone, there it is, and here we substitute etcetera in there, and here we have approximately twenty three point four units. We can do speed, do you wanna do speed, let’s push number seven here and do speed, unit vectors or speed is the square root of these squared. Square root of nine, twenty five zero. 5.8 meters per second. Ah pretty neat huh? everystepcalculus.com, check it out. Go to my site and you’ll love these programs.

Parametric Equations Video

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Raw Transcript

This video is on parametric equations. A parametric equation is, you’re adding a parameter of t time to every x y and z function, and that’s where we add the parameter and that’s the reason we call them parametric equations. And let’s do it. Turn the calculator on here. We’re going to get back to the home screen here. Clear the calculator we can go F1 eight and it clears that screen here. You press second alpha and put in the letters i n d e x, and then you push alpha and get into the number 8 and closed parenthesis to add this and get my formula for my menu. Press enter and we’re into my menu. And you can see all the things available in my menu for you to pass calculus and do your homework. Position vectors, product rule, projection of a and b, all those kinds of things you will be involved with in calculus one two or three. We’re going to do parametric equations now. That’s concerned with position vectors. If z is not given you enter zero in for z, then you can do the other two, x and y. So there’s the vector r t is generally an r t, is equal to this vector here, x t, y t and z t. So you have to press alpha to enter the functions in the entry lines here, so let’s do it, three times t let’s say plus four for x t, here’s y t, let’s enter have to push alpha, five times t and let’s do the z one, or let’s put alpha just for to make it simple and put z you can see that the z one is zero. Gives you a chance to change it if you’ve made a mistake, and we have all these things that we can do with this formula now with these functions in there. We can eliminate the parameter. Which eliminates the t and changes it back to an x function. Let’s do that quick, I’ll go through these quick so you can see. You solve for t, here’s the solution for t, and then you substitute t into every other x y and z, but ah here’s one point six seven times x minus three point nine and that eliminated the t parameter. Let’s go length of arc, you want to do that, fine, let’s go press four, notice it’s an integral over a and b, with the derivative of the r t formula. And rt we’re going to put in what we entered, I’ll go through it quick, put this all on your paper, write it down exactly as you see it, and we’re doing the square of each one, over the time of let’s say, you have to push alpha, let’s say from two to alpha six, shows you from two to six, here we’re doing this, write this on your paper and each individual one is gone, there it is, and here we substitute etcetera in there, and here we have approximately twenty three point four units. We can do speed, do you wanna do speed, let’s push number seven here and do speed, unit vectors or speed is the square root of these squared. Square root of nine, twenty five zero. 5.8 meters per second. Ah pretty neat huh? Everystepcalculus.com, check it out. Go to my site and you’ll love these programs.

Parametric Equations, Calculus Program, App, TI 89 Titanium

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Raw Transcript

This video is on parametric equations. A parametric equation is, you’re adding a
parameter of t time to every x y and z function, and that’s where we add the
parameter and that’s the reason we call them parametric equations. And let’s do
it. Turn the calculator on here. We’re going to get back to the home screen here.
Clear the calculator we can go F1 eight and it clears that screen here. You press
second alpha and put in the letters i n d e x, and then you push alpha and get
into the number 8 and closed parenthesis to add this and get my formula for my
menu. Press enter and we’re into my menu. And you can see all the things
available in my menu for you to pass calculus and do your homework. Position
vectors, product rule, projection of a and b, all those kinds of things you will be
involved with in calculus one two or three. We’re going to do parametric
equations now. That’s concerned with position vectors. If z is not given you
enter zero in for z, then you can do the other two, x and y. So there’s the vector
r t is generally an r t, is equal to this vector here, x t, y t and z t. So you have to
press alpha to enter the functions in the entry lines here, so let’s do it, three
times t let’s say plus four for x t, here’s y t, let’s enter have to push alpha, five
times t and let’s do the z one, or let’s put alpha just for to make it simple and put
z you can see that the z one is zero. Gives you a chance to change it if you’ve
made a mistake, and we have all these things that we can do with this formula
now with these functions in there. We can eliminate the parameter. Which
eliminates the t and changes it back to an x function. Let’s do that quick, I’ll go
through these quick so you can see. You solve for t, here’s the solution for t, and
then you substitute t into every other x y and z, but ah here’s one point six seven
times x minus three point nine and that eliminated the t parameter. Let’s go
length of arc, you want to do that, fine, let’s go press four, notice it’s an integral
over a and b, with the derivative of the r t formula. And rt we’re going to put in
what we entered, I’ll go through it quick, put this all on your paper, write it down
exactly as you see it, and we’re doing the square of each one, over the time of
let’s say, you have to push alpha, let’s say from two to alpha six, shows you from
two to six, here we’re doing this, write this on your paper and each individual one
is gone, there it is, and here we substitute etcetera in there, and here we have
approximately twenty three point four units. We can do speed, do you wanna do
speed, let’s push number seven here and do speed, unit vectors or speed is the
square root of these squared. Square root of nine, twenty five zero. 5.8 meters
per second. Ah pretty neat huh? Everystepcalculus dot com, check it out. Go to
my site and you’ll love these programs.