Business and Economics

Packaging The manufacturer of a fruit juice drink has decided to try innovative packaging in order to revitalize sagging sales. The fruit juice drink is to be packaged in containers in the shapeof tetrahedra in which three edges are perpendicular, as shown in the figure below. Two of the perpendicular edges will be 3 in. long, and the third edge will be 6 in. long. Find the volume of the container. (Hint: The equation of the plane shown in the figure is $z=f(x, y)=6-2 x-2 y$ .

## Discussion

## Video Transcript

We have a question here to find the average value off function River Its function for Frank's wife, which go to eggs six x times Why two eggs over the bra under one less dinner. Go to three tow place Done. Roberto Extras than go to three means that the brown dwarf eggs It's good too is from 2 to 5. And why is the defendant from 1 to 3? So how to find the average? Very a fraction. So we you know, if you will remember the formula, this is the formula. I'm trying to find the grounders Did average of function is starting Couldn't this one So it doesn't mind the formula for brown for average friend average of function Actually we found first the average the area for brown ours this one off, eh? Where a is burnt his area for Browner's or function doing teams in the group because we have that warranty grew to the defiant the legend This is tape where a is the area off brown earth then therefore accept the over exit deal for so then how can we find them the area A. How can we find the value of a So I even do some sketch here, for example, we have eggs from 2 to 5 and have one unit here. So three fool five, five. This is the one. This is too and they're for wash. That's why this is the thanks and what is defined from 1 to 3. This is a but however one here have to hear it helped three here remember that the units must be equal. So the finding the way sort for X is defend from. And yes, the Skinner is defining the from two that we heard. I don't have this from two and five twin 25. Then why it's defend from one. So city sword means that we we need this area here. This is a This region is a This is or we need So you see there where that's his five over too is for decide And this side you see where where is three minus 13 miners, one five miners. Toe sort means that is good too. This shows that our age this impressed that from this figure we can see that Hey is good too. Three minus one. Let's go toe to toe battalion Mazzy five miners. Cool disco two or three things. Three, which is good toe six. This is a way. So then, so far, so good, we we can easily find our Harvard of function. Is that well, we have this impressed that we can have one. You are or ever is gonna be good to win over which is going to war over six. Integrating this one with respect to why, I mean, that is into girl from 123 then into from total five. If our function for Frakes is goingto 60 eggs, why plus tow X, then de exit do away. This is easy there. Brought in several Thinks he knows complicated. So this kind of beaker to warn of a six and to grow from 1 to 3. Remember that the single off 60 eggs thing was Why is 60? Why is constant means that this is going to If you're interested, this one with respect to X, this goto excess square over Joe means that is three. Why exist, squared member that you have extra or Virgil Time of 60 y So six over to its go to three. Excuse me, Just keep this there so That's it, Gunny. Quick cares. We can. So for the Bruins and trigger of two eggs, you know where where this is? Definitely Your stable is goingto excess grey it, then report their value. They're burned off X is too toe five, I mean five minimum two rights in five. I'm sorry. The off away And after this one. This is good too. If we pull X here we have one of the six, then integral 1 to 6. So what is the very this Valium Frank's here is five is that we have 25. 25 times six is 100. It's 25. 25 times three is 75 stories. No Hollywood 25 75. Why? Because you have 25. We have 25 25 times three is 75. Then before you pull five here we have plus 25 then minus people to hear. We have fruit four times three is minus twere is why then? Minus four, then the y. This is good too. Or wanted by six. And a group from 1 to 3. Excuse me. He is a known six is three. So is 1230 for three This 0.6 75. Right now it's worth is 63 62 three Why? Why so 25 minus four is 21 pressed twinning one feel for it. Deal for it Actually this culture one of our six it's one of our six. He and we are going to integrate this worm. Or if respect to write that this is photos This is a constant. This is why What country quarrel for Why is the wife's gray overto is that we have 63 over a tune Time Z y squared then impress twin Towe one What? Because he I would have constant And this work However we have very from 123 This is the one. This is three Nice. So we kind of substitute thievery or I hear and then find our solution. So maybe it was this this space I think this is enough for us to finish this program. So war is the average or average Where are you recorded? You ve our average Very you is good too. One of us six burn dividing by six on dividing by six on DDE Sorry. This is all right. Save it one by six dimes when executed. Three. We have nine because three square its name. So it hurts 62 3 Her too. Then if we bought three here is night. This square is nine minus. If we put wanna hear? No, it's my last one. Good. Then press twin to earn times. If we pull three here without three minus one then our forward is over. This is good too. One of us six here nine minus 7 19 minus one is 88 over to is full. So four times 64 is 252 52 then impress. Uh, this is tool because it is three minus one times two remain as one is 22 times 21 is 42 for you too, then finery. This is good too. One of us six time Z 294 toe under 94 294. Dividing by six. When you gonna use your Uncle Gary curator. But it's easy is good to 49. If anyone does, he articulated that can divide by six. You see is 40 nine Sure. Our average value off function I read your photo for our function is Goto 40 nine. This is the end of the program

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