If we try x equals one and we will get y equals plus or -1.
So now for instance if we try applauding X equals zero equals 0. And so each value of X is going to give us two different values of why on the right hand side. Because when we take the square root from the denominator that will give us a plus or minus and then when you cube that plus or minus, that uh positive or negative sign will be retained when you cubit. We should also make sure that we write plus or minus, X equals or plus or minus X to the three halves. And so when we substitute in X equals C squared, we get y equals X to the three halves, notably. And you can see you get that by writing Y equals t cubed which is T to the three halves or rather t squared to the three halves. And from this we can just plug in Y equals X two the three halves. So we can write out the equations X equals t squared from the X component.Īnd why equals T. All right, so we need to make some substitution to express this vector valued function as a function of X and Y. Okay, so let's go ahead and sketch that here. Here we are asked to sketch the plane curve for the vector valued function R f t equals t squared comets. And so we will draw that here and that is all that the question is asking for. So we are told that it is one common negative too. And then This our prime of negative one here is telling us what the rate of change is at that point. This first one are of negative one is giving us the vector too the point on the curve. We can go ahead and sketch this on the graph here. So when t equals negative one are negative, one is going to be negative three comma the one squared plus one is two. And then finally part C asks us to sketch the position vector R. Component here is just one meaty derivative of the Y component is to t. Heart be is asking us to find the derivative of this vector valued function which is as simple as taking the derivative of each component one at a time. Then we go up by one on each side and continue curving up like that. Okay because there's a plus two inside the parentheses we shift left to negative two and because there's a plus one we shift up to one so the apex of the problem is right there. And so we can go ahead and just write down what that curve looks like. And this gives us a relationship between X&Y for this parametric curve. So we have Y equals X plus two squared Plus one.
So we can change this, X equals two plus two to be T equals X plus two. And from here we're going to solve the system of equations. X equals to my t minus two from the X.Ĭomponent and why equals t squared plus one from the Y component. We can do this by writing out two equations. First we are asked to sketchy playing curb with the given vector equation. So here we are asked to find a few things related to the specter valued function harv t equals t minus two squared plus one. The Adelie Amigos, despite being wacky, aren't gay you see them hitting on the ladies quite a few times. Mumble isn't gay - he actively tells Gloria he'd like to have an egg with her sometime.Astrakhan, Mumble's mom says, "So he's a little different-I've always kinda liked different." Humans with Asperger's are called "A little different." The penguins make a big deal about how he hatched. This explanation makes the most sense.It also may be a metaphor for going out of the closet. Following on that statement, this statement made the most 'exact' sense to me (sabrinadiamond).Eventually, he learns to bond with others by having their different skills work together.
His father is also 'a little bit weird' (autistic-spectrum disorders are believed to be partially hereditary). Mumbles seems to be wired differently from the other emperor penguins, and he excels at a skill that they find strange.
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