Examples of using Squared plus y squared in English and their translations into Polish
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So you get x squared plus y squared is equal to 4y.
Well, you should already see we have an x squared plus y squared.
What if I had x squared plus y squared is equal to 100?
The sum of their squares is going to be equal to x squared plus y squared.
We know that x squared plus y squared is equal to r squared. .
It tells us right there.r squared is equal to x squared plus y squared.
So minus x squared plus y squared plus z squared, with respect to x.
Remember the original formula I just showed you. x squared plus y squared is equal to r squared. .
It's x squared plus y squared, so you get x squared plus y squared is equal to a to the fourth.
So times 10 e to the minus x squared plus y squared plus z squared.
So it's x squared plus y squared, right? That's r squared is equal to x-- sorry, is equal to y plus x.
Pythagorean Theorem, you get x squared plus y squared is equal to r squared. .
I explained it in the unit circle video, andthat's because the equation for the unit circle is x squared plus y squared is equal to 1.
And we already say,well x squared plus y squared is equal to r squared. .
So the radius away from the center, that's just going to be r squared is just x squared plus y squared plus z squared.
Because it's always X squared plus Y squared equals R squared. .
So the derivative of the outside expression, the way I imagine it, is equal to 10 e to the minus x squared plus y squared plus z squared.
We had figured out that x squared plus y squared is equal to r squared. .
So if we were to divide both sides of this by r squared, we would get-- and this is just little algebraic manipulation-- x squared over r squared plus y squared over r squared is equal to 1.
The next one they give us is x squared plus y squared is equal to 9 times y/x squared. .
An ellipse was pretty much this, but these two numbers could be different. Because your distance from the center could change.So it's x squared over a squared plus y squared over b squared is equal to 1.
The first one, they want us to convert this, x squared plus y squared is equal to 4, to polar coordinates.
Instead of x squared plus y squared plus z squared, I wrote r squared, just to kind of give you the intuition that this expression is just saying the square of the distance as we get away from the center of our room, or from the coordinate 0, 0, 0.
And that's just minus 2z times 10 e to the minus x squared plus y squared plus z squared.
So when x andy is equal to 0, x squared plus y squared is 0, you're exactly 0 away from the center, or we're at the center.
If we want to put all of the variable terms on left hand side,we could say that this is equal to x squared plus y squared minus cx to the third is equal to 0.
So the unshifted circle was x squared plus y squared is equal to-- let me write it this way-- is equal to 3 squared, that's the same thing as 9, and let's say that the new circle, the shifted circle, is x minus 1 squared plus y plus 2 squared is equal to 3 squared.
So we multiply both sides times x squared, you get x squared plus y squared is equal to cx to the third.
If we do some pattern matching, well x squared plus y squared we know that's equal to r squared. .
So the general orthe standard form for an ellipse centered at the origin is x squared over a squared plus y squared over b squared is equal to 1.