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.
