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 problem here for finding the average value, baby or for function of x and y Just go to e to poor minus five Ry press three eggs over boundary off 0 to 2 for eggs and zero to do for way. So remember that for the formula for, uh, average over you. Let's not it like a V. This is good toe one over a wear a is air here form over a where they use the area off brown eyes. So the formula is this entry girl, tow the region A Is the area off our This is Baron Artist. If if this function xy why then the eggs and the way. That's good. So the program here first with to find a how do we find this area? So remiss Kitsch the burners first and see her weekend. Finally our area Sorry and tried to make kids Where if we heard of marriage, Anything current. So that's kind of okay. Yeah. Him. Use this. Brinker, This is X axis. Now this is a wise axes. So exes from zero. We have settle here, but I never want to hear. And two the same unit he had have hardly here and to one two then for eggs is from 0 to 2. Is that actual exes From a zero Here it is. The line tow to And then why Horses from 00 Here you want to sore means that our age. Is he This is a a This is our A there. So we found our eh? So instead our aides goto 0 to 2. It's also too is that their area is to minus zero times two minus zero which is it's good to this area is Goto four Hey is good too Our AIDS Goto for good is go to two times two is a total fraud. So for we get what ese? A notation that good What a V average Very you for average very You were vehicle toe one There's a saying then in two eggs is good our wise from 0 to 2 I ran to from zero to to This is for eggs. They're very often f Is it Tober minus five? Why Fredo? Why for us? Three eggs, then the eggs the white This is right. Easy, integral think is easy. It's no confusion. So this is yes this hour is a wonderful. So this is going to weaken Herve. Our average function is good too. Or every fraction is take two one of before then we interest rates. Why? This is right or true. Yes, 0 to 2 devoted to. But okay, we can integrate first treat with respect to two eggs. E my last five. Paul, Why is a constant is that we have orders to integrate e to pour my lands toe poor three x. You remember where the formula? I don't know if I can. I have some space. He it right The formula. You know, when we heard integral off E to Peru you off eggs functional for eggs then in the eggs prayer function affects D eggs. You remember that This is good too. One over you derivative. You know, for eggs derivative for over you off exit, they leave in tears. Primary this then it'll bore you off eggs Ghetto boy, you So with this formula is that for we have one of you derivative? You derivative is they're ready for us to prospective eggs Means that is one of our three. This is goingto one over three because they revert you off this function R pra function exponents function is to go to one of the three. So And we have I will write to you one of minus fighter. Why, Chrissie? Three eggs, then. Very new to this, then here we have the X, and they have the Y. This three picks? Yeah, here. So because I can't even arise this front office for me because we don't need it so that they can have enough space. He made Mr this. Okay, we friend the integral for X has teed off writing D eggs Have to put the browns off eggs. Rondo Frank zero toe two Is Avery off eggs? Then we have the why he you were here. So this sickle to this average, various go to run over four. So here we have 31 wealthy, even we can. It's pride. One of our three things one over four is one of that word. This can save the press one of her toe, then an integral from zero 22 When x is going toe to hear, we're hav e to pour my nurse. Bye. Why? Then we'll put extra here. Would put two. Here is three times two is six Rossi six, then minus When exes go to zero. We ever heard of it, Tober? My nurse 60 y then do you do you want good? Using the same formula. Unfortunate street. I just address it. Did sports can remember it. Remember, that is one provided derivative times here to provide you. Is that here? Were hurt. This is goingto run over it. Where then Time Z he ever have? Because we are going to integrate with respecting toe. Why is that? We have minus one over five. Remember that we divide. Bye. Very beautiful for you. You is good toe minus five year. Why one over fight. I'm number five won over 5 to 4 times the e to pour my last five. Why? Process six. They remind us in trigger off the swan. This is my last five is not minus six. Sorry. That's five. Why? Yes, And that's bravery. So it means that z minus also one over five. That's gonna be press mine us with this. Mind us. It's my for us. One of us. That five e to bore minus five. Why then be put for you to hear and zero this kind of B goes to you. We have one of our 51 of our five year means that we can put it here. So is one of the 12 times five is one over 60 six feet zero on all of us. 60 one of us 60 here we herds. He too poor minus five. If we report to hear is Ito for mine As Tim, I studied with positive. I think there is no confusion. So Ko have minors. This isn't mine issue for put to hear Here we get my last five times two is my last in then press six. Is it to poor minus four? Then? Here we have minus with zero. Here's press Something's that press here because K minus before put Syria is one. So is a press six. You was into you then because this was positive. Didn't remind us This isn't mine. Us Teterboro zero is minus one. So this is their different Ursa at the no. If she If you would like to compute, you can use your cricketer. You can get one of us 60. If you weren't baked, used, partisan or unnecessary, you can keep this answer But in that case, you can have one over 60 times E fucka. Great. This was Kirker. They get 26 0.8. Tour 73 payments, right? Write it here. What? There's no not enough spirits. So the answer is this one to feel dome mind. Let me give you the final answer even if you use your cracker at that and riff right goods. So our average very you is good too Ever into value. We're over 60 then Time Z 26 point A two, seven, three, six. You can compute it. That's great. So this is the answer for

## Recommended Questions