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PantAt the Par P-Vamue Determine 2 1 3 0.0032 Whetner [C 2 1 Round the 1Part 4 Pan: ~ D 341 State of 4 0,05 centage concivs 1 aqec 84 ; ACnocse 8 ; 1 il1eci 12 11...

Question

PantAt the Par P-Vamue Determine 2 1 3 0.0032 Whetner [C 2 1 Round the 1Part 4 Pan: ~ D 341 State of 4 0,05 centage concivs 1 aqec 84 ; ACnocse 8 ; 1 il1eci 12 11

Pant At the Par P-Vamue Determine 2 1 3 0.0032 Whetner [C 2 1 Round the 1 Part 4 Pan: ~ D 341 State of 4 0,05 centage concivs 1 aqec 84 ; ACnocse 8 ; 1 il 1 eci 1 2 1 1



Answers

Exer $1-8:$ Find, if possible, $A+B, A-B, 2 A,$ and $-3 B$ $$A=\left[\begin{array}{rrr} 3 & -2 & 2 \\ 0 & 1 & -4 \\ -3 & 2 & -1 \end{array}\right], \quad B=\left[\begin{array}{rr} 4 & 0 \\ 2 & -1 \\ -1 & 3 \end{array}\right]$$

Well, everyone, this is Ricky and they were working on a problem. Five from a model test number six. And so this is a question asking us about sphere that's inscribed in a cube. And what the ratio of the falling sphere to the booth. All right, So to start this question, let's write down the formulas for both of our severe and for acute first fear, 4/3 choir cute. And for the volume of the Cube, a heart issues this will rather Cuba's the length aside. Yes, threes as cute. And then, if we translate this where the length of side ISS equal to the radius spear, get or rather the diameter of the spear, get what you are. That's a cute Wallace to paint way Now if we look at the ratio votes spear. Q. Start with Why are huge? Huge. You see that? Ready? I drop out. And for my what a fine two. Everything's fine Pi over 63.14 over six, which is about 0.52 I hope this video is helpful. Seeing that

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.

The problem we're told that A. Is the matrix 210 -3 negative seven. Yeah 0 -24. And matrix B. This 4 -20 1 1 -2. Mhm. 005 Now you have 3 -10. And we want to find the product of A times B. Now to find a times b. Let's write these out next to each other. So we have 210 -3. Then you have 70 -24 times for negative to zero 1 1 -2 005 They have three. They have 10 animals. My major is we multiply roads by columns. Mm. We have two times 4 Plus one times 1. 10 times zero plus negative three times negative three. Eight plus one plus nine gives us 18. Now moving over we have two times now you have to Plus one times 1. 10 times zero. What's negative three times negative one adding those together gives us zero. Okay and lastly here We have two times zero. What's one times now you have to 10 times five. Last Day of three times 0. And that gives us negative too. What? Now? We're gonna move down to the second row and do the same thing there. Yeah. Okay. Take the second round where we take NATO seven times four. Well zero Times 1. Its name two times 0 Plus four times -3. And that's -40. Move forward. We have negative seven times. Now you have to 10 times one Bosnia of two times 0 Plus four times negative one. And that gives us 10 and then last three times that last room we have negative seven times zero zero times. Then you have to What's the name of two times 5 was four times 0. And that gives us -10. And so here we have that product.

So one important skill is our ability to be able to read tables and understand the value of a function based on the table. So we're given a table with X and Y values. If we're asked to identify what f. Of, let's say some random value. three. If we want to find F. Of three, then we know that the X value is equal to three. So we want to look on our table where X is equal to three and then we go down at what the ffx value is and whatever that F. Of X value is in the same column as the three value, that will be our F. Of X value. So we can practice this further if we want, it's important that we understand the concept behind it. So if we're given something like um what we have in problem um problem one, We see in problem one were given Um if it were given f. of three, We see that F of X is equal to 0.25. would be our answer there and that's how he would solve it.


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