the-cambridge-diet-supplies-8-g-of-calcium-per-day-in-addition-to-the-nutrients-listed-in-table-1-fo

Name: the cambridge diet supplies 8 g of calcium per day in addition to the nutrients listed in table 1 fo
Uploaded: 2020-07-17
Duration: 1 min
Channel: Numerade

Question

The Cambridge Diet supplies .8 g of calcium per day, in addition to the nutrients listed in Table 1 for Example 1. The amounts of calcium per unit (100 g) supplied by the three ingredients in the Cambridge Diet are as follows: 1.26 g from nonfat milk, .19 g from soy flour, and .8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 80 g of protein, 0 g of carbohydrate, 3.4 g of fat, and .18 g of calcium.
a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein necessary to supply the precise amounts of protein, carbohydrate, fat, and calcium in the Cambridge Diet. State what the variables in the equation represent.
b. [M] Solve the equation in (a) and discuss your answer.

Jack Chen · Accepted Answer

Okay, so you use appropriate for your signed the variable in this way, use for wearables to denote the amount off the food. According to the table. In a textbook, we can ride out, assist off Damiri questions in its magics form like this. So if calculator we have love following solutions. But in this solution, you see that X three and X for a negative. Which doesn&#x27;t make sense, because, um, this problem is a re award program. Um, this negative results are not allowed now. Music. It&#x27;s not. It&#x27;s impossible to find out a combination off this food, such that the nutrition satisfy is, um, target.

Ankit Gupta · Answer

let one cause yogurt gun din, ex milligram Hailsham, and one was she&#x27;s contents. Why? Milligram tells him so. Here the question is given. Eight was serving off plane known for yogurt and one one oz. Serving off Swiss cheese content. 6 76 milligram off television. So from here it ticks. Plus why is equal to 6 76? Or we can get fires equal toe 6 76 minus itics We can call. This is the question of but one now. The second information is the yogurt carton. Tens, four milligram, more than twice the calcium in the cheese. So that is X is equal to dries up. The why less four begin applied a value. If I from the question number ones will get here. X is equal toe dries off. 6 76 miners it takes. Let&#x27;s four. The X will be equal toe after my playing. This thing will get here 1352 minors off 16 X plus four. We&#x27;ll get here after stalling for over 70. Next will be equal to 1356 or the value of X will be equal to 79.76 milligram we can find the video off life from the questionable one of Isaac will too. 6 76 minus eight multiplied by 79.76 from your the value of I will be equal toe 37.9. Do milligram. So this is the calcium containing the cheese in 79.76 of the calcium content in the yogurt.

Ankit Gupta · Answer

Okay. Here in this the skinless chicken breast contain 140 calories. Ok, 27 grams off proteins of just writing those intrusion here. This is for chicken. Okay, so for chicken, this is 114 calories on then 27 grams off protein. So this is for protein. Okay, then. Three grams of fat services free grams off fact, then 13 milligram off calcium. So this is calcium, which is 13 milligram. All right on. Then It say&#x27;s 64 milligrams of sodium. So this is 64 milligrams of sodium. This is for chicken right now. If I just jump for the potato one cup, 1/2 cup of potatoes of this writing for tackles in here. This is what you can. This is what? Potatoes? More potatoes. It has 100 it gallery. So this is 100 and 80 calories okay than four grams of protein. So this is four grams off body, then 11 grounds of fired. So this is 11 grams of facts. This corresponding to it then 662. 24 grams of calcium. So 24 milligrams of calcium and six center and two milligrams of sodium okay for the broccoli. For the broccoli. It convinced 50 calories. Okay, this is 50 calories, right? So just waiting for B on calories, then five grams of protein and one grams of fat. So five grams of protein, one grams of fat, then one gram of fat. After that, 82 milligrams off calcium and 20 milligrams of sodium. So 82 and 20. Right. So this is the question which is given now. The first question says that right. Opened by five automatics for both, for all to see pp and be okay. So if Siri presents for chicken Okay. So because this one by five or Dmytryk So 1st 1 row and five columns Who sees equals to one party? 27 3 30 and 64 for the 2nd 1 which is speak potatoes. This is when it 4 11 24 6 62 on for the broadly. Right, this is B. So for the broccoli, this is simply be five bun. Did he do? And so this is the 1st 1 The 2nd 1 is all about finding this value. So this is just the big question, right? So frustrating being here. It just small town so that I&#x27;ll be using this values as above. So the Beit One, which is just to find the really of C plus two times off people s three times, will be OK so that by loosened comes out to be that is equals to see. This is 100 and 40 nights, 140 less Okay, despite ing hair directly, very did not do this. Remove this thing calculation parts of 1 40 on 22 times off to OK, so 100 times of two is 360 on three times. So leave his under and 50. So it simply comes out to be 6 14 15 right? 2345 and 6 615 Hit. Similarly, this is 27. Four times two is eight and five times trees of being. So this is eared and five inches. Study invite 13 and seven is 20. So this is 50. Similarly, for the tournament, this is three plus 22 less three. So this is 20. Eat a rape. This is 13 bless body ape less 246. So they simply comes out to be six and it is 14 and 3 17 Okay, so for 489 And when then services three or seven right here. And the last entry is 64. Bless. This is 6 62 times of two. Okay, so this is 246 to 12 6 to 12 in one. Tareen on. This is 60 day there of war for less for is eight. Six x 12 and 14. And this is 1444. Okay, so this is that I knew.

Sarah Lewites · Answer

So this problem we&#x27;re going to use the intermission that are given in order to write and fall of a system of equations so that we can find how many milligrams of calcium are in a glass of milk, a serving ice cream and one calcium supplement. So let&#x27;s let X stand for the milligrams of housing in one glass of milk. Why the same for serving ice cream and see the milligrams of calcium in one calcium supplement? So we have our variables, and now we&#x27;ll use those variables along with the information that&#x27;s given to us. Most problem too, right to three equations. So our first equation is based off of the information from the first day. So we know that one class of milk and one serving of ice cream and one calcium supplement is 1180 of milligrams of calcium. Then, on the second day, the calcium from it too. Hands of milk on one tipping of ice cream and one supplement provides 1680 milligrams calcium, and on the third day we have one glass of milk. US. Two servings of ice cream plus one supplement are a total of 1200 and 60 milligrams of calcium back today. So now that we have our three equations, we can take some steps towards solving them. So first, let&#x27;s solve for X using equations one and two. So we&#x27;re going to be adding together equation too less negative one times. Equation one. This will eliminate Y and Z and we will solve for X. So equation, too is to acts us. Why thus the equal 16. 80 and then we&#x27;ll be subtracting X subtracting. Why attracting the subtracting 1100 eating. So we&#x27;re summing these two equations together and we get X on one side and then why? And see it get eliminated, which is really great because now we&#x27;re solving for X. So we get X equals 500. So now we know that there are 500 milligrams in one serving of milk. So this is our first solution. Next, let&#x27;s add together equations three and one in order to solve for why So we&#x27;re going to be doing Equation three plus negative one times equation one and will be eliminating X and Z here to solve for y. So we&#x27;ll write equation three x less to I I seen because 1 2060 and then we&#x27;re adding on this negative question. One said Negative X minus slide. Try to see it was negative. 1180. So when we add these together, our exes will eliminate at his easel a living. So we will be left with why on this side and then on the other side, we get equals beauty. So now we know that there are 80 milligrams in one serving of ice cream. So this is the second part of our solution. So now we need to find Z and so we&#x27;re going to input our values for X And why into equation one. We could do any of the equations. A question one does seem simplest. So let&#x27;s do that. So when we input values for X and y here we have 500 or X plus 80 for why plus Z equals 1100 eating Z plus 5 80 because 11 80. By combining like terms and then subtracting 5 80 we get the equals 600. So there are 600 milligrams of calcium and one calcium supplement. So this is our final solution and we now know all three milligrams. So we are done

Christine Anacker · Answer

it was holding. The fishing problems are equation, so we know we need or we know that we&#x27;ve got 23 grams of protein report grams of corn, nine grams protein milk. I need 47 grams protein total. He&#x27;s got two grams of carbs in the court grounds, of course. Corn, grams of carbs. A little less when we have nine grams. That&#x27;s right. We&#x27;ve got 10 milligrams of calcium in the port and middle ground Worry and 10 300 milligram. Um, we need a total of six. Now. The other one&#x27;s Aaron grounds one milligram, if you want to. Doesn&#x27;t matter. I go there all this immunity. All right? Let&#x27;s Yeah. Oh, have there. All right, I&#x27;m gonna my third row. She&#x27;s gonna change it in grams in weight. You 11 30. Awesome. I take my my first real time. What? You know, when you No, my When, what? Seven minus one. Oh, 11 Um um Well, it&#x27;s not great. No waas over 20 one. Well, something. My 13 waas over one one. What? Look, you What do you A day of work or 100? You? I want one. All right, so we&#x27;re going wound about it by one? No. Well, but when it&#x27;s getting one, you know about about All right. Oh, we&#x27;re gonna do a double step here. Just waiting those numbers below. Well, would work. All right, little one, over. Warren, I would like one. What? No, you really? If you want. Or just remember that are, for one. What? It was not one for.

Taylor Shimono · Answer

in this problem. We know that we have a nutritionist who is studying different types of food that he can feed. Or she can feed two rats to give them a different amounts of some nutrients in their diets. So essentially, we&#x27;re given a table where each a row over table is going to correspond to the different amounts of each nutrient provided, uh, and it&#x27;s sorted bright type of food that the A nutritionist can feed to the rats. So essentially, we can see that this is going to be just a system of equations problem, and we&#x27;re going to be able to solve it using matrix equations. So for part of the problem, we want to find the inverse of our three by three matrix, which is essentially just our co efficient matrix directly from our table. So we know that in order to find the inverse of the Matrix three by three matrix, we&#x27;re going to essentially replace that right bracket with a dash line, um and then right up, uh, and identity matrix on the right hand side and we&#x27;re going to row reduce so that the left hand side of our matrix is going to become the three by three identity matrix. And whenever we&#x27;re left with only right hand side will be our or our inverse matrix. I&#x27;m so we could go ahead and start, um, by subtracting a road to minus roll one. And then I&#x27;m also going to subtract row three minus row one to get rid of the three in our first position here, I&#x27;m so once I do that row one is going to stay the same. So that&#x27;ll be 313 100 off road to minus. Row one is going to give us four minus three, which is one two minus one, which is one four minus three negative 110 and row three minus. Row one will give us zero one one negative. 101 I&#x27;m so from here, I&#x27;m going to go ahead and do two steps at once, which is a little bit risky because it makes it a lot easier to mess up. But I&#x27;m going to replace a Row two and row one, so I&#x27;m going to switch these two and then I&#x27;m going to perform our original row one minus our original row two. So we&#x27;ll see if I can squeeze my matrix in right here. Um, our new row one is the same as our original row two. Our new road too. Oh, is our original row one minus. They should have been three times our road to. So we have Roe one, which is three minus three times. One will be zero, and we have one. Minus three will give us negative too. Three minus three will again give us zero. And then we have one plus three will be four zero minus three will give us negative three and zero minus zero. And our row three stayed the same here. I&#x27;m so from here, I can see that I&#x27;m going to go ahead and swap a row three and wrote to Oh, I&#x27;m so my matrix is going to have the same row One row two is not going to be 011 Negative. One is your one. And row three will be zero negative to zero four negative. 30 I&#x27;m so we can go ahead and, uh, continue on by subtracting a row three. We&#x27;re actually going to add row three plus two times wrote to, in order to get rid of this negative too. Right here. I&#x27;m so gonna do that. Row one will stay the same. 111 negative. 110 Row two is going to stay the same. 011 Negative 101 And Row three is not going to be zero a negative. Two plus two will be zero zero plus one is two works to be zero plus two is two now. Then we have negative for minus two would give us too negative. Three minus zero and zero plus two. I&#x27;m so from here, our next up is going to be dividing. Ah, Ro three by two I&#x27;m so we&#x27;re going to do is divide straight across each of our terms there. 011 negative 101 And then we have 001 one negative three halves. One I mean then So going backwards. We&#x27;re now going to you perform row to minus row three. We can also do row one minus row three of the same time. Ah, and we&#x27;re going to transform this into one minus zero is one one minus zero is 11 minus one is zero. And then we have negative one minus one one plus three halves. So five halves, I&#x27;m and then zero minus one in row two, We have 010 a negative one three halves. Positive. Three house here. Zero and then finally wrote three is still going to be 001 one negative. Three halves one. And our last up is going to be computing row one minus row two. And so once we do that, we&#x27;re going to have found our finished inverted matrix. So we get 100 on the negative. Two plus one will give us negative one five. House minus three halves is one, and then we have negative 110 Uh, our second row is 010 negative. One, three halves, zero. And finally, we have 001 one negative. Three halves, one So we can see that are inverse matrix is going to be this three by three matrix right here. Um, and so we could go ahead and, uh, create a new page here. Two saves in space. I&#x27;m looked. So are inverse matrix from apart, eh? Was this three by three matrix given by negative 11 Negative. One negative. One three halves zero one negative. Three halves and one and so part beaver problem. Um is going to give us some values that the nutritionist wants the daily diet of the rights to contain. And so, essentially, what we&#x27;re going to do since we said this was a matrix equation is multiply our inverse matrix. So negative 11 negative one negative 13 house zero one negative. Three halves, one. Bye. The three by one matrix of each of the amount that we want this to be equal to. So we have 10 milligrams of folic acid of 14 milligrams of coleene and 13 milligrams of in hospital. I&#x27;m so from here, essentially, we&#x27;re just going to multiply straight across, um, and then combine all of our terms. Well, um, and I made a small mistake in my matrix right here. Thief. First position should have actually been a zero. And in the first column and second row, it should have been a negative to rather than negative one s. Oh, that was just during one of my additions. Um, but anyway, when we will buy this out, we&#x27;re going to end up finding that we should use, uh, one one ounce of type a one ounce of type B and two ounces of type C. I&#x27;m so far apart. See the problem? We&#x27;re essentially going to do the same thing. We&#x27;re going to go ahead and multiply and s so we want this time. 01 negative one negative 23 halves, zero one negative three halves, one a times are desired values of a nine milligrams 12 milligrams and 10 milligrams. And so when you multiply it out this time, we&#x27;re going to find that we want two ounces of typing, zero ounces of type B and one ounce of type C. And then so for party were problem overhead and start a new screen here. I&#x27;m so again our initial matrix that we had, uh, was this three by three matrix 01 negative one a negative, too. Three house zero in one negative three halves, one in, uh, in this case, we want Thio. Find some combination that&#x27;s going to give us two milligrams of full of acid, four milligrams of coleene in one milligram or 11 milligrams of in hospital. I&#x27;m somebody will buy these out in our first rope. We&#x27;re going to get two times zero plus four, minus 11. Our second roll. Give us negative for plus six minus zero. And finally we have to a minus six plus 11 so we can see that we&#x27;re going to have a negative seven positive, too, Um, and then positive seven. But since our first term is a negative number, we can&#x27;t give the rats in negative amount of food. So that tells us that no, it&#x27;s not going to be possible to have a combination that&#x27;s going to give us these exact values.

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

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Absolute Value - Example 1

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Linear Algebra and Its Applications

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Absolute Value - Example 1

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David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Heather Z.

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications