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Mat ? mum score (pr Each valbe Un(nu Cuesior z4 Md to lovol dl hctr exporimant #th tAo teet & tector 1ola tno-Incto = Mabu Dreseit teresciE LEMn To idor9 {corlo...

Question

Mat ? mum score (pr Each valbe Un(nu Cuesior z4 Md to lovol dl hctr exporimant #th tAo teet & tector 1ola tno-Incto = Mabu Dreseit teresciE LEMn To idor9 {corlon ire natono oltro Amtah {Eet bertntenFeclo0a44 mod shok NO mmeredto mttuot mkonan t0 Winali vala thoud Qau tot NO Mdedaeton} Mtrred @ te 007u 444 Haua

Mat ? mum score (pr Each valbe Un(nu Cuesior z4 Md to lovol dl hctr exporimant #th tAo teet & tector 1ola tno-Incto = Mabu Dreseit teresciE LEMn To idor9 {corlon ire natono oltro Amtah {Eet bertnten Feclo 0a44 mod shok NO mmeredto mttuot mkonan t0 Winali vala thoud Qau tot NO Mdedaeton} Mtrred @ te 007u 444 Haua



Answers

Exactly how were the MPC and MPS in Table $21-4$ computed? Illustrate by calculating $M P C$ and $M P S$ between points $A$ and $B$. Explain why it must always be true that $M P \bar{C}+M P S=1$.

On a given question. We have two equations, right for P S and P P. So we'll be represents. The points is called by each player later had actually represents the number of games player. So P s is a close to 24 minus two s and PP's well plus two weeks. So the first part is where to write a table, right? With the help of laughing Utility, for the point is caught by each player for the 1st 12 games. Like so we can substitute one by one for X equals 1234 right upto 12. And we can get the value of P S and P p. Okay, so I'll make a table for X Bs and BP like quite extensive gusto. One toe play for five, six, 789 10, 11, 12 for years. And you feel like so for X equals the one where you substitute here x one. We get PSS 22 here 14 like for exports of similarly 12, 18, 18, 16, 20 14 22 Well 24 Mexico So 7 10 26 8 28 6 30 4 30 to 8 34 0 and 36. Right? So this is the result, which we get. So this is a solution for first. But now, in the second part, we have to find the solution off system of equations. So from in this table, we can observe that forex sequester. Today we have equal number off his school, uh, made by the two place. Right. So here, the solution off the equation system off equation should be expressed. The tree. Thanks. Now, in the next part, we have to find the solution with the help off algae epically matter so we can create water questions like so we get four legs is a question 12. Well, that's a question T. Right. So this is the solution off. Systematic question with the help of graphical. So the algae bickley matter now, the next parties were to compare. We can see that in part B way got X across the tree and in part c, we got Texaco. Three writes about The results are the same. Now, the next parties way have to find were the internal deserts in the context off the situation. Right. So here we can see that the solution is a tude when you and I scored. When the number When the number of points they scored by both players. Awesome. Yes, right. So this is the interpretation interpretation that we get the sister translucent like

In a 2008 football game, the Patriots scored three fewer points than the Giants. 31 points total were scored in the game. How many points were scored by each team? Now that we've read our problem, we need to decide on a variable to use to write up our equation. And since we're talking about things in terms of the Giants were going to go ahead and use a Capital G, and that's going to be the Giants points now. Our next step is to write our problem out in words. And so we know that for this football game, the Giants points scored, plus the Patriots coins. We're equal to the total points of the game. Now we need to write out a mathematically equation using our variable. So we know the Giants scored G points, and we know the Patriots scored three fewer points than the Giants, so that would be the Giants score minus three and that there were 31 points total in the game. Now we're going to solve our equation, so we're going to combine like terms and we get to G minus three equals 31. We're going to add three to both sides to G is now equal to 34 and we're going to divide both sides by two and we find out that G is equal to 17. Now we have an answer. We know that G is equal to 17 but we need to interpret that in words. And since we said that G stood for Giants points, we're going to say that the Giants scored 17 points and we need to tell how many points each team scored. So we also need to tell that the Patriots scored three fewer points, which would be 14 points.

In this problem, we are given the coordinates of two points and we need to determine certain victims and their magnitudes. Now, in the first question we need to determine the magnitude of the victor. E. Now the vector oa in component form will be the same as the coordinates of the point. E. So this vector in component form will be minus two minus 63 And does the magnitude of oh a will be equal to the square root of the sum of the squares of the components. So this will be the square root of minus two square plus minus six square plus three square. Now this will be equal to square root over 49 and the value of that is equal to seven. So the magnitude of the vector U. A. is equal to seven. The next problem we have been asked to determine the magnitude of the vector U. B. Now the vector will be in component form will be the same as the coordinates of P. So that will be three minus 4 12. And does the magnitude of the vector ruby will be Square root of three square plus -4 square last 12 square. That is equal to the square root of 169 and the value of that is equal to 13, so the magnitude of obi is 13. And the next problem we have been asked to determine the victor A B. Now that will be obi minus O. A. The position vector of b minus the position vector of a. So that will be three minus for 12 minus minus two minus 63 So we subtract the corresponding components, we have three minus of minus two. So that's three plus two minus four minus minus six. So that's minus four plus six. This will be 12 minus three. So this vector will be 5 to 9 in the next part, we need to determine the magnitude of this victor, Evie. That'll be square root over five square plus two square plus nine square. This is equal to square root over 100 and 10 and the value of that is approximately equal To 10.49. Next we need to determine the victor E. Now this will be minus of the victor A B. So this will be equal to minus of the Victor E. B., which we obtained as 5-9. So this will be -5 -2 -9. And last of all, we need to determine the magnitude of the vector B. A. So that will be the magnitude of minus of a B. Which will be equal to the magnitude of a B. So the magnitude of be, it will be the same as the magnitude of a B. Which we already obtained over here in part B. So the value of this Is approximately equal to 10.49

We're going to find the component forms um going from .12.2. So each time we'll be taking our second point and subtracting the corresponding component from the first. So for our first factor we would consider that we do negative four minus negative six and a negative one minus negative. To notice those minus negatives end up being adding. So we get 2 to 1. So it can either be written with the brackets or we can write it in R I. J form which would be to I plus one J. And I don't have to write the one. If you just see the J. You know that there's a one there Kate. Now our next vector notice every single time we're going to be doing negative 1 0. Well this is already in kind of its component form because its origination is at zero. So we can really write our vector as just the negative 161 And if we write an I. J and k notation we could have a negative I plus six, J plus K. Now our third we'll have to a nine minus four A one minus one and a negative three minus negative three. So in the end I have no J and K. So in the notation that I've already written with brackets you would actually place in a zero where there are, you know, um no components of that form. But when you go to write it in I. J and K, you just write that as five A. If you don't write the J and K component, then it's known that those are zero.


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