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He pages book come from the prnbing press 35 arge, TGtrectangular sheets of paper: Bach shecl Es through senas of rollers and folded in half several times folio: Ha...

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He pages book come from the prnbing press 35 arge, TGtrectangular sheets of paper: Bach shecl Es through senas of rollers and folded in half several times folio: Half of a [olio sheet that hzs been fokled once is called quarto balf of a quarto uciavo Each fold perentliculti previous [old and the first fold pemendicular the longest side.Origin:zl sheetFolioOunnoOcuavoPart0f ?If the original sheet 64 inches Wdth _ud inches high and folded Aabove #hat Jret Fuioir lowetIerma| de eientlor "Jch:

he pages book come from the prnbing press 35 arge, TGtrectangular sheets of paper: Bach shecl Es through senas of rollers and folded in half several times folio: Half of a [olio sheet that hzs been fokled once is called quarto balf of a quarto uciavo Each fold perentliculti previous [old and the first fold pemendicular the longest side. Origin:zl sheet Folio Ounno Ocuavo Part 0f ? If the original sheet 64 inches Wdth _ud inches high and folded Aabove #hat Jret Fuioir lowetIerma| de eientlor "Jch: orginai qanO Ociarot OT"nal: Bolllo : Ouiio (cnien: Tunc here cebicn



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In $1796,$ Gottried Christoph Härtel, a German music publisher, calculated the cost of printing music using an engraved plate technology and used these estimated cost functions to make production decisions. Härtel figured that the fixed cost of printing a musical page-the cost of engraving the plates-was 900 pfennings. The marginal cost of each additional copy of the page was 5 pfennings (Scherer, 2001). a. Graph the total cost, average total cost, average variable cost, and marginal cost functions. b. Is there a cost advantage to having only one music publisher print a given composition? Why? c. Härtel used his data to do the following type of analysis. Suppose he expected to sell exactly 300 copies of a composition at 15 pfennings per page of the composition. What was the greatest amount the publisher would be willing to pay the composer per page of the composition?

In this problem. We have four different songs and were given a set of statements about them to determine the length of each song. So the first statement is that the total playing time off all four songs is 14.3 minutes. So we can write that as w plus X plus y plus z. So the total playing time of each of the four songs is equal to 14.3 minutes are a second statement? Is that, um why song? Why is three minutes shorter than song W So why equals W minus three? Our third statement is that Song Z is 2.7 minutes shorter. Been song X. So soaring Z equals song X minus 2.7 minutes. And then finally, the combined time of Song X and song. Why is five times a song Z? So our fourth statement, the combined Times X Plus y, is equal to five times the length of songs E. And so now we have four equations and we're gonna make it a little simpler by moving all of the unknowns toe one side of the equation. So our first equation remains the same w plus X plus y plus c his 14.3 for a second equation. We're gonna move the w so negative W um, plus y equals negative three for 1/3 equation we're gonna with the X to the other side. So negative x plus Z is equal to negative 2.7. And then for our fourth equation, we're gonna move the sea to the other side. X plus y minus five z is equal to zero. And so now we have it. Now that we have it in this form, we can make it into a matrix. So matrix A is our coefficient matrix. It's gonna be a four by four matrix because we have 1234 equations and w X y and CSR for unknowns in our first equation. All of the coefficients are one for each of the unknowns. In our second equation are coefficient for W is negative. One x There's no X term. So it's zero. Why is one And then there's nosy term, um, for third equation, there's no w or why. But X is negative one and Z is one. And then, for our last equation, there's no w term access. One wise one and these negative five. Then we have our matrix of unknowns, which are W, X, Y and Z, and then finally are matrix of known values on the right side of the equation. So 14.3 negative three negative 2.7 and zero and so to solve for unknowns, we're gonna take her in verse of a and multiply it right B. And so I've already included The Matrix using to a calculator. So we need to do is take the inverse of a and multiply it by B, and we get that song. W is 5.9 minutes. Some X is 4.1, so W's 5.9 x 4.1. Why is 2.9 and see is 1.4. So those are before lengths of thes songs that were unknown.

A ream of £20 of paper. Today's five from sheets and is about two inches high. Suppose we take one sheet important half unfolded half again and just continuing on as long as possible. The first thing we want to do is complete this chart they give us, So let's go ahead and think about this. Let's actually get a piece of paper here and boarded. How so? I cut it here. Then I'm going toe sandwich it over. So this should look something kind of like this. And I'll kind of draw like that to show that there's two being so at this point, there would be two layers now if we were to, let's say, cut it like this that unfold this half over. Well, we have 12 layers here. Well, let's go ahead and draw that. So we still have those two layers and then we have these two laters that we're also going to stack on top of each other, so it looks something kind of like that. Now. So or two folds. We have four layers, and you might guess if we were to cut it in the middle again and then try to hold this. Well, we still have the four layers that we originally had and then 1234 layers I get stucked on top. So that would be eight. And I'm not even going to attempt to do it. Or or but you might notice that each time this goes up by a multiple, too. So then you might say, Oh, well, this is probably 16. This one is 32 and we could actually write. Each of these has so first to to the one shoots in second, two to the third, two to the poor due to the fifth. So then that beams over here we get to to the 10. And then for this last one, we'd get to to the 50 and over here I went ahead and plugged all this in to excel really quickly to help us with the number. So to to the 10 waas 10 24 then two to the 50th Power is that large number there. It's one times 10 to the 15th power. So something absolutely huge

So here we have a question that says that the thickness of a book varies directly with the number of pages that it has. And it tells us that a book that is 3.27 years thick has 750 pages, so we can write the variation equation. Um, because we know it varies directly so we can say that the thickness of the book equals K times the number of pages. And we can use the dad that you give to figure out what K is. So we plug in 3.2 centimeters for T and 750 pages for P. And if you do the math, you get that K equals 0.0 for three centimetres per page, so we can express this as t equals 0.43 set of years for Paige Kind spew. So, no, Aso's. What would the thickness of a book with 957 pages be? So we just need to plug that into P so t equals 0.0 for three centimeters per page times 957 pages, which equals 4.1 centimeters

And this problem. We're talking about three consecutive pages. Um, that would be the first one x, um, the next one bx +11 more and then two more. So those are the three consecutive ones and that the riddle here is basically this that the article is on three consecutive pages. So that 62 lessons so minus 62 off of something, then four times the last page numbers of four times X plus two that's the last one is the same as is equal to the sum of all the patient are so X plus X plus one plus X plus two. All three added together. So let's go and distribute four times access for acts and four times. This, too, is a plus eight minus 2 62. Let's combine the exes altogether to get three X and the one in the two to get plus three. Let's combine the eight minus 62. In this case, it will be negative 54 or minus 54. Let's subtract three X off both sides to get the X has gone here, which have X left and then add 50 for to both sides to get this gone and B equals 57. So the first pages 57 and the next one add one will be 58 the next one add one more is 59.


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