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Point) Let A =Determine the values of x and Y for which A? = A. -3...

Question

Point) Let A =Determine the values of x and Y for which A? = A. -3

point) Let A = Determine the values of x and Y for which A? = A. -3



Answers

If $ x^2 + xy + y^3 = 1, $ find the value of $ y" $ at the point where $ x = 1. $

Yeah, for this problem our goal is to show that with the given function Y equals execute that are sub tangent. No matter what the points exit was a will always be equal to a over three. So that means that for execute whatever point you plug in so you plug in X equals five. Sub tangent will be five thirds. If you plug in X equals seven September will be seven things. So the main thing we want to do calculate our sub tangent has come up with our slope of the tangent line, which again is going to be that y is equal to the derivative of the function at a multiplied by x minus a plus the function itself at the point A. So that's a relative of X cubes. Using the power role is going to be three expert. And so when we plug in a for both of these were going to get three a square and a cute respectively. And that once we sub in it's going to give y is equal to three A squared, multiplied by x minus a plus a cute. And so when we simplify this and we're going to get that Y is equal to three a squared times X minus three X cubed. And then we encounter in our plus a cube that's going to give minus to a cube. So now you want to find out when the sub tangent or the tangent itself intersects the X axis. And that is going to happen when our y intercept zero. Because when we are at y equals zero. We were on the X axis. So to do that, we're going to plug in zero for why that's gonna give us that zero is equal to three A squared x minus two A. Cute. Or the three a squared X is equal to two. A cute. Yeah. And so then when we factor out the three X squared from our Ekstrom, We are going to get that X is equal to two a over three. Mhm. So now to calculate the length of the sub tangent, we're going to take the point we plugged in. So in this case a and some track from its when we intercept the X axis so to 8/3 and so we can rewrite this. Um has three A over three minus two A over three, which is equal to one A over three Or a over three. And that would prove our original problem.

In this occasion given order pair eggs upon three plus one cuomo. Why native To a .3 equal to 5.3 cuomo one about three. So here you can see that as the other pair are equal, the corresponding elements should also be equal. Therefore eggs upon three Plus one equal to 5.3. And why negative two upon three Equal to one upon 3. So now we simplify this. So here we get eggs Plus three equal to five. So X. Equal do we get to? And here three Y. Negative two equal to one. So here we get. Why could one those X equal to two? And Why couldn't do 1? It is over final answer.

With this question, we can start up with y minus 81 cube is equal to three times a day once where multiplied by x minus 81 So we can rearrange this to end up with X divided by to a one divided by three minus. Why? Divided by two A one square is equal to one. So the X intercept is, um you know that the X, sir, the X intercept zero off to anyone but but three public zero. That's Oh, by the way, its label that Oh, on r o a. One comma zero. So the cell tension is Q R, which is equal to the absolute value of to a one divided by three minus a one, which is equal to a sub one divided by

So we want to determine the location of the point X. Y. Z. That satisfies the given condition. So in this case It's gonna be x equals a negative three. So this is going to look like is Um the 0.-3 here. And then let's choose a couple other points. And in all these cases we're gonna let X equal major three, change the Y value. But how we can change this value right here. So it doesn't look like these points of anything in calling, they just kind of like jumbled up. But when we center this graph right here, notice what happens this right here is the X. Axis. And we see that all these points are perfectly aligned up along the X axis. We can even look at it like this and see if that's the case. So because of that we see that that is a similarity to have now, it's not gonna be a perfect line unfortunately because we can't perfectly center this. But if we could we would see that they'd be in a perfect line. So that's the relationship that we have


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