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Problera # 3' Wna+ +k2 en1le (A) an4 distance () Lrom +62 16 pts oritin Peia+ if # 0 + 9 X,11 (9Afaatrs 24 ('6.2 ; 50.7')...

Question

Problera # 3' Wna+ +k2 en1le (A) an4 distance () Lrom +62 16 pts oritin Peia+ if # 0 + 9 X,11 (9Afaatrs 24 ('6.2 ; 50.7')

Problera # 3' Wna+ +k2 en1le (A) an4 distance () Lrom +62 16 pts oritin Peia+ if # 0 + 9 X,11 (9Afaatrs 24 ('6.2 ; 50.7')



Answers

In Problems $29-34$, find the distance between each pair of points. $$ (1.0,3.2,4.5) \text { and }(1.4,1.0,6.5) $$

All right. We need to find the distance between these two points. And the way we're gonna do that is by subtracting our exes 2.3 minus and negative, 4.5 and then squaring that we're gonna add that to whatever happens, it was tracked our wise negative 1.2 minus 3.7. Also going to square that and find the square root of that big sum. So let's do a couple steps in the middle here. 2.3 minus a negative. 4.5 is like saying 2.3 plus 4.5. That ends up being 6 28 We're gonna square 6.8 negative. 1.2 minus 3.7. That ends up being a negative 4.9, which I put in parentheses. We're also going to square deftly. Don't know either these off the top of my head. So I put him in my calculator, get the square of 6.8 is 46.24 All right. Now, 4.9 times 4.9. That ends up being 24.1 And these are the two things that we're going to add before we find it's very and so if we do that, we get that we're finding the square root that some of these two numbers is 70 0.25 And if we're looking for the square root of that, that ends up being 8.19 rounds in your 1000 38 too, if I'm rounding there, so that's the distance between these two points.

Were given two points and the Cartesian plane and were asked to find the distance between these points. So our points are 9.5 negative 2.6 and negative 3.982 To find the distance between these two points will apply the formula for the distance between any two points in the Cartesian plane. This formula says that the distance between two points se x one, y one and x two y two is equal to the square root of X one minus x two squared plus why one minus y two squared and therefore the distance between two points. 9.5 negative 2.6 and negative 3.98 point two This is going to be thes square root of 9.5 minus negative 3.9 were 9.5 plus 3.9. I want to make things neater plus negative 2.6 minus 8.2 squared and this is the same as the square root of 9.5 plus 3.9. This is 13.4 squared plus negative to six minus 82 This is negative 10.8 squared and you can either do this by hand or use a calculator to calculate these squares of 13.4 and negative 10.8. In a way, you should get square root of 179.56 plus 116.64 and adding these together you get 296.2. So the square root of 296 0.2 and he plugged this into a calculator. This is approximately 17.2, so our answer is the square root of 296.2. Now let's check our answer to see if it's reasonable. Well, first of all, one of the properties of the distance function is that for any two points in the X Y plane, the distance between these points is always greater than or equal to zero, and moreover, the distance is equal to zero Yes, and only if the two points are the same. Now we see that are two points are not the same, and the distance between them is positive. So, so far are answer makes sense. Now let's draw are two points to see if we can sort of eyeball the distance. And there we can check to make sure that our distance function matches our intuition. So again are two points are 9.5 and negative, 2.6 as well as negative 3.9 and 8.2. So I'll draw my X Y plane here, the X Axis Marange from negative 10 to Positive 10. And the Y axis will range from negative 10 deposit of 10 as well. So our 1st 0.95 negative 2.6 is located about here, and their second point negative 3.98 point two is located around here. Yeah, and our distance function is supposed to be a measurement of the length of the line segment between two points. So looking at this line segment, yeah, we see that 17.2 is probably a good approximation after all, we could see that the length is going toe lie between 20 and 10

It's over this problem. We want to find the distance between our two points to negative 40 and 06 negative three. And we know that to find the distance between the 23 dimensional points, we are going to some into our distance formula in space, which is given to us right here so we can go ahead and call the point to negative 40.1. And so we will call a 06 negative 3.2. And when we plug in these points to our formula, we get the distance between our two points is equal to our x zero minus X one is two squared plus R Y +26 minus Why one will be negative for so, uh, minus negatives going to end up being plus four and finally plus C two is negative three minus C +10 squared and we can go ahead and simplify all of these terms to get our distance is equal to negative. Two squared plus 10 squared plus negative three squared. And when we square each of these numbers, we are going to get this is equal to negative. Two squared is four last chance court is 100 plus three squared is nine. So our distance between these two points is equal to the square root of 113. And if we put this in her calculator to give us around 10.63

So this time they want Thio compute the distance between we're in it. What? Well, let's call these points and okay, So distance between A and B, we're going to use their formula kind to be equal to the square root. Uh, the sums of the squares of the differences of each quarter. Well, it's pretty hard. Take the X coordinates subtracting from each other. Where for the exporting it different. I'll take the difference of the white co ordinates and wear them. And I'll take the difference of the Zeke ordinance. We can't forget about them. Remember to square that in the end, see what we get. We're gonna get the square root one seven before zero is just for you. Square that and that's extinct. What are the negatives? Cancel out. You'll end up with positive seven. That looks like it's another 49 onstage fifties near one away from Wolf. So it's two. Less than 100. So that 98 Plus I think this is the square. Yeah, 98 plus Extend. Well, it's 114. Okay, so this is your final answer. It's an irrational number. This very 114. If you wanted to arrange. Well, that's a buck. 10 in less than 11. Maybe closer to 11. If you get an answer somewhere in that range. Look, you are correct. Uh


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