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Company sells sets of kitchen knives A Basic Set consists of 2 utility knives and chefs knife A Regular Set consists of utility knives_ chefs knife and slicer: Delu...

Question

Company sells sets of kitchen knives A Basic Set consists of 2 utility knives and chefs knife A Regular Set consists of utility knives_ chefs knife and slicer: Deluxe Set consists of 3 utility knives chefs knife , and slicer: The profit is S30 on Basic Set; S50 on Regular Set, and 570 on Deluxe Set: The factory has on hand 400 utility knives, 200 chefs knives, and 00 slicers_ (a) If all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum pr

company sells sets of kitchen knives A Basic Set consists of 2 utility knives and chefs knife A Regular Set consists of utility knives_ chefs knife and slicer: Deluxe Set consists of 3 utility knives chefs knife , and slicer: The profit is S30 on Basic Set; S50 on Regular Set, and 570 on Deluxe Set: The factory has on hand 400 utility knives, 200 chefs knives, and 00 slicers_ (a) If all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum profit? (b) A consultant for the company notes that more profit is made on Regular Set than on Basic Set, yet the result from part (a_ recommends making up more Basic Sets than Regular Sets She is puzzled how this can be the best solution. How would you respond? (a) Find the objective function to be used to maximize profit: Let X1 be the number of Basic Sets, let *z be the number of Regular Sets and let X3 be the number of Deluxe Sets_ What is the objective function? z-Lx1 Ex+ Dx: (Do not include the symbol in your answers )



Answers

Set up and solve Exercises 23–29 by the simplex method.

The Cut-Right Company sells sets of kitchen knives. The Basic Set consists of 2 utility knives and 1 chef’s knife. The Regular Set consists of 2 utility knives, 1 chef’s knife, and 1 slicer. The Deluxe Set consists of 3 utility knives, 1 chef’s knife, and 1 slicer. Their profit is 30 on a Basic Set, $\$ 40$ on a Regular Set, and $\$ 60$ on a Deluxe Set. The factory has on hand 800 utility knives, 400 chef's knives, and 200 slicers. (See Exercise 30 in Section 4.1 . )
a. Assuming that all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum profit?
b. A consultant for the Cut-Right Company notes that more profit is made on a Regular Set of knives than on a Basic Set, yet the result from part a recommends making up 100 Basic Sets but no Regular Sets. She is puzzled how this can be the best solution. How would you respond?

They can hear you were told to cut right companies selling sets of kitchen. Now the basic set consists of two utility knives and one chef's knife. Regular set consists of two utility knives, once Chef's Knife and one slicer, and the deluxe set consists of three utility knives, one chef's knife and one slicer. We're told the Prophet is $30 in the basic set, $40 in a regular set and $60 in the deluxe set. Or else told the factory has on hand 800 utility knives, 400 chefs, knives and 200 slicers. Now, in part A, we're told, you assume that all sets will be sold and were asked how many of each type should be made up in order to maximize profits and were asked, What is the maximum profit in this case? Well, well, let X one b. The number of basic sets. Yeah, X two will be the number of regular sets. Morning, it's and X three is the number of deluxe sets speaking. Restate the problem as we want to find x one greater than or equal to zero x two greater than or equal to zero x three greater than three quarter zero s one greater than or equal to zero s to greater than equal to zero and s three greater than or equal to zero Mhm such that our objective function Z which is $30 times x one plus $40 times x two, plus $60 times x three This is our total profit is maximized. So this is in fact, a linear programming exercise. Right? Gramps? Messed, yes, but we also we have the constraints. That's two x one plus two x two plus three x three plus s one. The test equals 800. The total number of utility knives, x one plus x two plus x three plus s two equals 400 the total number of chef's knives. And finally, now and then we have x two plus x three plus s three equals the number of slicers, which is 200 and rearranging our objective function we have that mm 30 x one plus 40 x two plus 60 x three minus z equals zero which we can also multiply through by a negative one to get plus z and then negative 60. Negative 40 and negative 30. I just can't. And so we'll set up a table for Excel Table has the columns x one x two x three s, one s, two s three and z. Yeah, And then we have in the last column. It was just straight. 800 450. 200. Well, and finally the bottom right zero below the first column. We have our entries to 10 and then negative 30 below x two. We use our system of equations and we have 211 negative. 40 being a bloodshot under x three, we have three one. Sorry, Adam. You think he would? 311 Negative 60. Step one under s one. We have 100 as to we have 010 and rest three. We have 001 none. Jersey. We have 0001 We have zeros between these, That's what. So this is really the most crucial part. This is what we set up in Excel. And then we solve using Excel's silver using the silver Oh, right. We find that the maximum profits Z is equal to $15,000 medicine, and this occurs when X one equals 100. Yeah. So we have 100 basic X two equals zero. So no regular was just and x three equals 200 and 200 deluxe sets are made and then presumably sold. I don't know. Leave the okay now in part B. Yeah. Uh huh. Questions one the and the wife. We're told that a consultant for the cut right company well notes that more profit is made on a regular set of knives than on a basic set. Yet our result from part A, if you saw, recommends making up 100 basic sets but no regular sets. She's puzzled how this can be the best solution. How can we can explain this to her? Well, she needs to broaden her scope. The issue is not about basic stuhn and regular sets. Mhm. Well, the issue is about the number hurt you. Your life? Yeah. The issue is that the number of slicers is shared among the number of other sets. Right now, the dialects set generates more profit. Yeah, set up at this. Why are you listening? It suits you important than the other two sets and therefore it should be prioritized and using this resource. What right

So this problem. We're looking at the bureau manufacturing company and trying to decide what allocation of television sets they should make in their plant. No reading all the way through it. You can see that The question is, what should they do to maximize their profit? So that's our end goal. This is a maximization problem. Always good to read the poll problem through. Before you start trying to make sense of the numbers, see what the goal is. So our goal is to maximize profit. Well, first, let's go through and find what the prophet actually is. Well, the profit on a flex can set is $350. So I'm gonna let X up one equal the number of flex scan Ah, sets that they sell. Great idea to mark down what the variables mean. It's very if you don't, it's very easy to get to the end of this problem and then not remember what the variables were that you set up so except one is going to be the number of flex can sets we sell. Now what's the profit for the other one Will. The panoramic one has a $500 profit So this is the panoramic. So there's my profit. If I knew how many of each set was sold, I could tell you what my profit is. And we want to find the maximum profit, which makes sense. That's what most companies do want to dio. Now. There are some things that are going to be constraints, things we have to keep in mind. First, we haven't assembly line. I'm just gonna mark with These are we have an assembly line. Every flex can takes five hours in the assembly line. Each panoramic takes seven hours. So this is how much time I'm going to need in my assembly line. And at most I have 3600 hours available to make thes TV sets. Next, it has to go get a Cabinet. So in the Cabinet Department, the Flex scans take one hour and the panoramic steak two hours each, and at most I can use 900 hours in the Cabinet shop. Now our last thing is our testing and packaging, and there were told that each doesn't matter which one it is. Testing a packaging takes four hours apiece, so that's four hours for the 1st 14 hours for the second one. And at most, I could spend 2600 hours in the testing and packaging area. Now, this last one here, I can make this a little bit simpler to keep our numbers a little smaller. If I divide everything by four, this gives me except one plus. Except to is less than or equal to 650. So I'll probably use that one. It just makes life a little bit easier Having smaller numbers. Okay, so here are my criteria. My, my constraints. And there's my Maximus in my profit equation that I want to maximize. Okay, So what I have done is I've used our desk most graphing calculator here. You can use a graphic calculator, anything that you're comfortable with, and you can see that I have three equations. Okay? And let me just come back out and put these in one of the time. So this is our assembly, our cabinet making and our testing and packaging. And you can see there is an overlap. So those are the corners. Those four here. We also have a corner at 00 But if I make nothing, I have no profit. So that is by far the smallest. I'm not even gonna look at that one. I'm gonna acknowledge that it is a corner point, but it makes no sense to make no TVs in this context. I'm making something. I wanna have a profit. So these are the four points we're looking at. So I'm going to come over here back to our white board. This is not in any particular order. I'm just going to write down those four points. So 0 450 303 100 475 175 and 650 zero. Those there are four points. So what we need to dio is put those points back into our profit equation. Plug them in, see what profit we get with this allocation of our resource is so for the first one. If I make no flex scans and 450 panoramic six, my profit is going to be 225,000 for my 2nd 0.300 of each. I'll have a profit of 255,000 for my third point. The prophet is 253,750. And for my last point, the prophet is 227,500. Okay, looking at these profits, if I want to make the maximum amount, my maximum is right here. 300 flex scans and 300 panoramic six. Okay, so that's the best way to use my time. And my resource is to get a maximum profit. But what if we make a change? What if we say the flex scan is gonna give us Ah, higher profit? We found a way to get a higher profit from that. So I'm going to remove the 350 and instead we're going to get 450 for each of these. Well, how does that change what I want to dio? Well, it doesn't change our criteria. The time it takes hasn't changed. So this picture hasn't changed. These points haven't changed. All that's changed is my Z. So I'm gonna have a newsy based on this $450 profit for the flex scan. What is my new Z when I look at these exact same points? Well, the first point doesn't have any flex scans in it, so it actually doesn't change. You get the same profit for it. What about the 300? 300? Well, I should get more profit because I am making some flex scans, and in fact, it goes up to 285,000. My third point goes up to 301,250 and my last point goes up to 292,500. So now my new maximum profit is here. I would need to have 475 flex scans and 175 panoramic six. Okay, Now, if you take a look at these in both cases, there is some unused time in my factory. Let's take a look at our first case. Um, and I'm going to just put a little red star here. Okay? 300 of each. Well, if you look at our graph 300 of each, I'm going to remove these other points. No, remove. Remove. Okay. So 300 of each is right here. That's where my red and blue lines intersect. That's our assembly and our cabinet. But as you can see, the the third line, the green, that's our testing and pack and packaging. It's less than what that could be. And if you come back here to see how much we actually used in testing and packaging at 300 a piece, I actually have 200 unused hours in the Cabinet department. Okay? And again, the graph shows that you can see that I'm not on that maximum line. I've got some extra wiggle room there. What about our other point? Well, the other point happened at 475. No scared at that point there, 475 175. In that case, that's where our green and blue and red lines intersect. But not the blue blue is our second one. That was our Cabinet department. And you can see I'm not fully utilizing the Cabinet Department If I come here and look at the Cabinet department for this number here, 475 175. I actually have 75 unused hours, but I wrote the wrong one before I apologize. It's looking ahead. This one has 75 amusing cabinet. The first one was in testing and packaging. Okay, Thea, other two, I'm maxing out by the time, but each case has some unused time, and that's going to be the case no matter what I pick. Because if you look here, if you look on the on our graph, we're maxing out our hours. If we have a point that's actually right on that line, for example, 303 100 is right on the line for red. That's our assembly. I'm using all my assembly time. If I If I do 300 of each, I'm using 3600 hours. I'm using all of my time in cabinetry, but not assembly. Alright, not testing. And you can see that because they don't all meat. If there was a point that all three lines met and converged, that would mean I had a solution where I had no downtime in any department. And that's not the case here. There is no single point where all three of these lines meet. So no matter what solution I use, even if it's not, you know whether it's a maximize solution or not, there is no solution where I use all of my available time with nothing left over

For this problem. We're being asked to maximize the profit for the mural manufacturing company, which is making plasma screen television sets. So let's see what our equation is for the profit that this company is going to make. Well, there are two types of television sets that it makes. One is a flex scan, which makes $350 of profit. So I'm just gonna mark here that my ex up one is going to be my flex scan model. And the second kind that it makes is the panoramic. And there's $500 of profit for that one. That's my panoramic in the ceramic. Okay, so this is my profit equation. $350 of profit for each flex scan. $500 of profit for each panoramic. Now, what are my constraints? Well, one constraint we have is the assembly line. Okay. Now, on the assembly line, we're told that the Flex scan requires five hours and the panoramic takes seven hours and at most I've got 3600 hours available on the assembly line. Our second constraint comes at the cabinet shop and there were told that the flex can only takes one hour in the cabinet shop, the panoramic takes too. Okay. And adding all of those up, I have 900 hours total available in the cabinet shop. My third constraint happens in testing and packing like that red. So in the testing and packing area, there were told that the flex scan takes four hours, as does the panoramic. So each one of those takes four hours altogether as 2600 hours. Now, I'm going to simplify this one slightly. I'm going to just divide everything by four just to keep my number's a little smaller. And this becomes 650. I do need to remember, though, that if something comes back with the slack variable for that equation, I need to remember that I made an adjustment. Will have toe, um, work on that at the end if something comes back for that one. Okay, Let's look at how I can add my slack variables so I could enter these into my grid. My first equation, my assembly. I'm just gonna write these in blue, so they kind of stand out a little bit. Five x up one plus seven x up to plus my first slack variable is going to equal 3600. My second equation. I'm going to add my second slack variable, and that will equal 900. And then for my third equation, I have my third slack variable. And that equals 650. Okay, Knowing all of those, I can now put together my grid. I have two X variables. I have three slack variables and I have ze. So let's enter our blue constraint equations in here. If I pull out all of my coefficients, I have 57 and one I don't have any of those variables and it equals 3600. My second equation is 12 It has the second slack variable in that equals 900. And my third one is one and one, and it has my third slack variable equaling 6 50 and my indicator row at the bottom I'm going to take and I'm gonna market with a blue arrow appear at the top, my equation for Z and I'm going to set everything equal to zero. So when I pull all of the terms over to the left hand side, I have negative 350 x of one minus 500 except to no slack variables and dizzy. Hey, so here's my grid. Okay, Now, I know that I'm going to be redoing my grid down here, So I'm going to going to set this up really quick. All of my same variables. Now let's take a look at where our pivot point's going to be. If I look at my indicator row, negative 500 is the biggest negative number I have. So we'll be looking at the ratio of my Constance to the X Up two column. And when I do that, 3 36 100 divided by seven is about 514. Yes, that's got it. With a decimal 900 divided by two is 450 and 6 50 divided by one is obviously 6 50. So the smallest one is the two. There's my pivot point. So the row with the pivot point my second row is not going to change. That stays the same to get rid of my other rose. Well, to get rid of the top row, I've kind of don't have a whole lot of room right there, so I'm just gonna put this off to the side. I'm going to take negative seven times the second row, plus twice the first row. And I'm going to put that back into the first row all the way across in my new grid. And when I do that, I end up with three 02 negative. 700 900. Remember, the goal was to make every number in the same row or same column with the pivot number all equal to zero. Okay, well, what about my third row? Well, in order to get that one that I'm circling here to get that to become a zero, what I'm gonna do is take negative the opposite of the second row, plus twice the third row, and that will go into the third row position. Doing that across the row gives me 100 negative. 1 to 0 and 400. Okay, finally, we need to dio are indicator row at the bottom. To get rid of that, I'll take 500 times the second row plus twice, the fourth wrote. And that's what I'll put in the fourth row all the way across. And when I dio, my output is negative. 200 00 500 02 and then 450,000. Hey, we are not done. We still have a negative in our indicator, wrote negative 200. So to find our pivot point, we're gonna look at the values in the x of one column or Exubera column and compare them to our constants. So no. 1 900 divided by three is 300 900 divided by one is 904 100 divided by one is 400. So this three right here gives me my smallest ratio. That's my new pivot point so and bring that down a bit. So I've got some room toe work and we make our next grid. So the road with the pivot point does not change. So I'm just going to copy Row one all the way across, as is. Hey, I want to get rid of every other number in that except one collar. I want them all to equal zero, so let's look at the second row to get rid of that. I will take the opposite of the first row, plus three times the second row, and that will go into the second row space across the board. When I do that, I end up with 06 Negative to 10. 00 1800 Right. Third row. Well, again, I have the same number in the second row and the third row. So my equation is gonna look the same. Negative are sub one plus three times the third row, and that will go into the third row position. Doing that gives me 00 negative. 2460 and 300. Now we just have to get rid of that negative 200 in the bottom row. To do that, I'm going to take 500 times the first row. I'm sorry. Timmy did write 500. I met, right, 200. Try that again. So 200 times the first row, plus three times the fourth row. And I'm going to put that into the fourth row position. Doing that all the way across that row gives me 00 401 100 06 and one million, 530,000. There are no more negatives in my indicator row, so we are complete so I can start reading the answer off of this grid. Uh huh. Except one just has one non zero. So I could say that three X up one equals 900 or X up one equals 300 except to also has only one non zero. So six X up to equals 1800 or accept to also equals 300. So without looking at any of the other variables, I know that the optimal number of units to make our 300 of each type of television set Now, I can also see that from my slack variables. S sub one and s up to are both going to be zero but s up. Three is not s up. Three. I could say six s up. Three equals 300 or as sub three equals 50. Now, I'm just gonna come back up to the top and remind you s up. Three. If you remember, I made those numbers a little bit smaller. I divided it by four. Everything in my first one divided by four. My second one. So I really need to multiply this by four to go back to the original equation. So s up three for my original equation is 200. So what does that mean? Well, that means that in that third constraint, which was my testing and packing facility, I have 200 unused hours. So I've got some, You know, everything else. I maxed out to capacity, but I still had room available here in that particular department. And what is? We come back so you can see this little bit better. What is my maximum profit? Well, six z equals 1,530,000 or Z equals 200 55,000. That is the maximum profit for selling 300 of each type of television set.

So for a problem? A. They're telling us that the total monthly profit for the rear projection television is going to be $125. For this reason, you would have $125 multiplied by X because that would equal the total profit for all of the rear projection televisions for the plasma televisions were going to write 200. Why? Because it take to you get a profit of $200 for each plasma television and then we're going to multiply 200 by wives. You get the total profit for all of them in a month now, adding, those two values together will get us our total profit, which is the which will cause Z equals 125 x plus 200. Why? To be our total. Our objective function for the told prophet the factory can have in one month now for part B, they give us some constraints. They tell us that for the for a rear projection televisions, they cannot be more than 450 of them. And then for the plot televisions, there cannot be more than 200 of them. For this. We're going to have X is less than or equal to 450 because we know that it can equal 450 but it just can't exceed it. And then why is less than or equal to 200? For the same reason we know it can equal 200. We can make up to 200 but we cannot exceed 200 plasma televisions being made no for they also tell you about the amount of the costs that it takes to make these televisions each plasma television. It costs $900 to make them. Then for each rear projection television, it costs $600 to make them. So now, to get the total monthly cost, they you have to multiply the 600 by the number of re projection television, which is why I put 600 X and then the 900 by the number of plasma televisions. We just why put 900 X and then they tell you that three that $360,000 is a total amount of money that they can spend in a month. No more digging knocks it. Spend any more than that, so to mont to model. This I put a less than or equals to sign in between them because we know that if we have this whole total here, it's not going to exceed the $360,000 No moving on to part C. They tell us to graft this. You could see my graph here that I created. And this graph is going to model all three inequalities that we have so far for the X is less than were equal to 450. You could see here that 450 is where you have the purple line that marks that Marcia Inequality. And then the Purple Line is going to be bold ID because X can equal 450. And then here you see the black line, which marks that X can be. I mean, why can be equal to or less than 200? And then for this, equate for this red line here you're going this red line models 600 X plus 900. Why is less than or equal to 360,000? And basically what you're seeing here is that this whole shaded area is old is where you're going to be seeing the prophet happen. You can't have anything outside of here. We're not gonna be working here. We're only working within these parameters inside this shaded region. No. For the red line to model to be able to graft 600 X plus 900 wise less than or equal to 360,000. Why? We're going to need to isolate this. Why that I circled and bring it over here in nicely by himself and then sulfur. Why? So we can be able to grab it here, just as I did. So to do that, we start with our original inequality and then looking here, we're going to subtract 900. Why? From both sides and subtract $360,000 from both sides. And now, from there we get 600 extra minus 360,000 is less than or equal to not minus 900. Why so for here from here, we know that to get the wide by itself, you're going to need to divide by minus 900 by both sides. The rule here when doing this is that when you divide by negative in inequality, you have to switch the signs tow opposite. So minus 900 why becomes why? While minus 300 360,000 becomes plus $360,000 divided by 900? Because the minus here and the minus here would combine to make a plus. So whenever you have two negatives divided by each other, that makes a positive. And then, for the 600 for the 600 x will be 600 divided by a negative 900 X. And then, since you have a positive being divided by negative, you would that would end up being in negative, which is why I have a negative sign here. Moving on. We can just simply cross out the zeros that we see to make math easier. So we crossed out. The 20 is here and we get 6/9, and then the six negative 6/9 here can be simplified into negative 2/3. So we have negative 2/3 Times X and then the 360,000 becomes 3609 100 becomes a nine. And from here we can just we know that through 36 divided by nine is four that we bring the two zeros down and I will get US 400. So our final equation that we used to graft this red line is going to be negative. 2/3 X plus 400. Why is less than or equal to why? Or negative 2/3 X plus 400 is less is going to be greater than or equal to? Why moving on to the next portion they give us, they tell us I mean to do to evaluate the objective function for the total monthly profit each of the five Burgess ease up the graft region. So I went ahead and wrote down all the points where the birds he's occur. If you go back up here, you can see them also. And now basically, what they're telling us is to use the equation from before that tells us to total monthly profit and basically solved for each one of these. So for the first bird, ISI 00 we're going to do Z equals 125 times zero plus 200 times zero. So we know zero time zero zero times Anything equals zero so wanted 25 times 00 then 200 times 00 than adding those together You get zero. So we know our total monthly profit would be zero if we had zero plasma televisions and zero, um zero. We're project volatile televisions. Now, for the next one, we have 0 200 soc schools 125 times zero close. 200 times. 200. No, if we multiply 1 to 25 times zero, you get zero here. Plus and 200 times 200 now be 40 12 for 40,000. So now 40,000 with equal Z. For the next problem, we have 300 or the next point. We have 302 100. So the equals 125 times 300 plus 200 times 200 suddenly no, 200 times to hundreds. Going to beat you cool, too. 40,000 from our previous problem and then 125 times three. If you just do the math, you did these other particles 15 and then three times to go. Six plus one people seven and three times one equals three. You know, it could bring the zeros at the end giving us 37,000 500. And now we add those two together and we get Yeah. Seven, the 7000 500 equals Z for the next point, 451 100 z. He was 125 times or 100 50 plus 200 Carnes. One of your now 200 times. 100 that is going Teoh have a sequel. 20,000. And for 125 times 450. If I just get my calculator, we could do the math. Yeah, 56,250 equals E. Then you add those two together and you get 76,000 250 equals Z Not for the last 0.450 0 we have does e equals 125 times 450 plus 200 times zero, 200 times zero equals zero close. And then we know that 125 times 40 50 is 56,250 from our previous point that we plotted or that we saw for So we get Z equals 56,000 250 Now for a problem e they give you a phrase and they want you to fill in the blank and they essentially ask you where how, wearing how you get the greatest prophet. So you go back up here. We look for where he had the greatest prophet, and we see that we have the greatest prophet at 72 $7500 where we made 300 rear projections and each month and 20 plasma televisions each month. So therefore the television manufacturer make the greatest problem by manufacturing 300 rear projection television each month and 20 plasma television each month. The maximum monthly profit is $77,500. Oh, sorry. I meant 200. Don't make the greatest prophet.


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In Problems $15-42,$ solve each system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. $$\left\{\begin{array}{l} 2 x-4 y=-2 \\ 3 x+2 y=3 \end{array}\right.$$
In Problems $15-42,$ solve each system of equations using Cramer's Rule if it is applicable. If Cramer's Rule is not applicable, say so. $$\left\{\begin{array}{l} 2 x-4 y=-2 \\ 3 x+2 y=3 \end{array}\right.$$...
5 answers
You randomly select one card from a 52-card deck. Find the probability of selecting:a red 2 or a black 3
You randomly select one card from a 52-card deck. Find the probability of selecting: a red 2 or a black 3...
5 answers
Question 24 (3 points) ANSWER ON A SEPARATE PEICE OF PAPER: During a chemical reaction In the lab, element X is formed which consists of four isotopes. Their relative abundance are as follows,X-280 (95.0%), X-281 (0.85%), X-282 (4.13%), and X-286 (0.014%). Calculate the average atomic mass of this element:
Question 24 (3 points) ANSWER ON A SEPARATE PEICE OF PAPER: During a chemical reaction In the lab, element X is formed which consists of four isotopes. Their relative abundance are as follows,X-280 (95.0%), X-281 (0.85%), X-282 (4.13%), and X-286 (0.014%). Calculate the average atomic mass of this e...
5 answers
For the diprotic weak acidH2A, 𝐾a1=2.4×10−6Ka1=2.4×10−6 and 𝐾a2=6.5×10−9Ka2=6.5×10−9.What is the pH of a 0.07000.0700 M solutionof H2AH2A?pH=pH=What are the equilibrium concentrationsof H2AH2A and A2−A2− in this solution?[H2A]=[H2A]=MM[A2−]=[A2−]=
For the diprotic weak acid H2A, 𝐾a1=2.4×10−6Ka1=2.4×10−6 and 𝐾a2=6.5×10−9Ka2=6.5×10−9. What is the pH of a 0.07000.0700 M solution of H2AH2A? pH=pH= What are the equilibrium concentrations of H2AH2A and A2−A2− in this solution? [H2A]=...
5 answers
Determine whether each of the following series converge O1 diverge and state the test(s) used to obtain the result. cos(nw) 1) n3/4 n=L2)2 (2n + 1)32 nl 3) en? n=l
Determine whether each of the following series converge O1 diverge and state the test(s) used to obtain the result. cos(nw) 1) n3/4 n=L 2) 2 (2n + 1)3 2 nl 3) en? n=l...
5 answers
Obincehached coiled spring amjima Mhfiou 5 S#Crnd?Dhadpullad dowm (naqabye direclion trom Iha r854 positon) canimaiarsthan raleased Wce enialion lorIe oislznce d Dlhe DodromTA5knosinon aner seronis Ilne amolihidaCpnimaiarsTha equalion Ihe dishange ol the object Irom d5 rest postion i5 (Typo = Utac anshu UIA &5 (udcti Uso Inluours Hrareecc ANY nurniayrTu tqualon |
obinc ehached coiled spring amjima Mhfiou 5 S#Crnd? Dhad pullad dowm (naqabye direclion trom Iha r854 positon) canimaiars than raleased Wce enialion lorIe oislznce d Dlhe Dodrom TA5knosinon aner seronis Ilne amolihida Cpnimaiars Tha equalion Ihe dishange ol the object Irom d5 rest postion i5 (Typo =...

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