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The demand for a bookisgen by&:-Ump 250000 copies per vear Where p is the price per book In dlars; The supplyis gwen byp=20p + Wuwope per Vear Fid Ie price at w...

Question

The demand for a bookisgen by&:-Ump 250000 copies per vear Where p is the price per book In dlars; The supplyis gwen byp=20p + Wuwope per Vear Fid Ie price at which supplyand demand balanceFind all solutions of the given system of equations and check your answer graphically; HINT [First eliminate all fractions and decimals; see Example 3,] (IF there is no soluton; enter NO SOLUTION, IF the system is dependent; express your answer in terms 0f x, Where y = Vx): ) 02x + OAy = 07 0Jk = OJy 0.9(w

The demand for a bookisgen by&:-Ump 250000 copies per vear Where p is the price per book In dlars; The supplyis gwen byp=20p + Wuwope per Vear Fid Ie price at which supplyand demand balance Find all solutions of the given system of equations and check your answer graphically; HINT [First eliminate all fractions and decimals; see Example 3,] (IF there is no soluton; enter NO SOLUTION, IF the system is dependent; express your answer in terms 0f x, Where y = Vx): ) 02x + OAy = 07 0Jk = OJy 0.9 (wle(l338 4



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Equilibrium Price The demand and supply functions for your college newspaper are $q=-10,000 p+2,000$ and $q=4,000 p+600,$ respectively, where $p$ is the price in dollars. At what price should the newspapers be sold so that there is neither a surplus nor a shortage of papers? [HINT: See Example $8 .$

This video is going to give a very um detailed but general overview of linear functions. So we know that a linear functions of the form Y equals mx plus B. Where B is going to be the Y intercept. So that's oftentimes our starting point and then m is our slope. But the way that we get this is oftentimes mixed up. It's not necessarily given to us in this nice way. Oftentimes were given to Different values, for example, X one, Y 1. So we're given a point and it may not be a point given specifically to us, but we're told that at this time or at this price we have this amount or this number of items sold, something like that. And then we have X2, Y two as another point. Well, with these points we can find the slope which is as we know why two minus Y. One divided by mhm X 2-. Excellent. So with that in mind we know that that is going to become our slope. Now that we have our slope. We want to find the Y intercept. To do that. We plug in a point for our wine X values. It could be any point, this one or this one or any other one that we have and that will allow us to find the B value. So once we do that, we're allowed to use linear interpolation, we have a new function and we can determine based on this function what value are different X values will determine our function to be. That's how we use it. And there are many applications for it, as we will soon see. Um And these applications well, they might sound complicated really. It all boils down to this. White goes on explicit B and finding the different values given two points or given a set of data points.

Look at this particular question belongs to supply and divide, in which there are two questions given by is equals to do For people less 40 x on by is equals to 500 minus 25 x. Okay, look, we revolt, but it's X and y bias prize and dollars and X is the number of units produced. So what I'm doing Just subtracting this two equations directly. So this is zero in here by zero, and that is equal store 2 40 minus 500. So this is to 40 minus 500 plus four p x on bless 25 X. Right. So what? It will be it really simply 260. But what? This is 25 40 which simply comes out with 65 that is equals two X. Okay, so this can sense on how many times the simply cancels on 14. So we have excuse equals to four. So let's just try to find out the value if I so also, why is equals to if I just put an equation and bullets it too. So this is 500 minus 25 games off four. So this is 105 100 minus 100. Assembly comes up with 400. Okay, so at this point of time again, clearly said, therefore, therefore, four on $400 will be the final answer. All right, this is dollars, Mrs Straight, darling. Clear. Okay.

Okay, in this situation, we have a supply equation, and we have a demand equation in the supply equation X represents the supply and in the demand equation X represents the demand, and P represents the price. And we're looking for the point where the supply is equal to the demand for the same price. So we're looking for the point of intersection of these two equations, so let's go ahead and do a substitution. Let's take the first equation and isolate WPI by dividing both sides by X. And then let's substitute that into the other equation for Pete. So we have 16 over X equals 10 X plus 12. We'll solve that equation for X. Let's multiply both sides by X, and we get 16 equals 10 X squared plus 12 x moving all the terms over to one side. We have zero equals 10 X squared plus 12 x minus 16 and we can divide that equation by two. So zero equals five X squared plus six x minus eight. And let's see if we can find a way to factor that. How about if we try five x times X to give us five X squared and then four times to to give us eight. And if we have plus on the two and minus on the four, the insides and outsides, we're going to add up to six X, so that's good. And now we're going to set each of these factors equal to zero, and we'll solve for X. So with the 1st 1 we get X equals 4/5 and with the 2nd 1 we get X equals negative, too. But it doesn't make sense in this context for this supply or the demand to be negative. So let's eliminate the negative answer. So what we're saying is that X is 4/5 and X represents the supply 4/5 of 1000 so 4/5 of 1000 calculators, which we could just call 800 calculators. We also need to know the price. So let's go back to one of our original equations. The price is 16 divided by X, so the price is 16 divided by 4/5. Dividing by 4/5 is the same as multiplying by 5/4. Think of your fractions, and that gives us 20 so $20 per calculator for 800 calculators at the equilibrium point

So we have P equals 5000 times the quantity one minus four divided by four plus E. Raised to the negative 0.0 two X. Yeah. And they want to select p equal 300. So we're like P equal 300 equals 5000 1 -4/4 plus E. to the negative zero two X. Bye Bye. Okay So 2 to 3/50 equals one minus four over four plus E. To the negative zero two X. Subtract one. So three divided by 50 minus one. Now I am going to yeah I'm gonna change the negative .94 to a fraction. So I have negative 47/50 equals negative poor Over four plus E. Raised to the negative 0.2 X. I'm gonna cross multiply. So I am negative 200 which is negative four times 50 Equals -47 times four plus E. To the negative .002 x. and four times 47 is 188, -188 plus knots in my missed minus 47 E. To the negative 470.2 X. So now I'm going to add 1 88 And I get a negative 12 Equals -47. He Raised to the negative .002 x divide by -47. Yeah -12 divided by negative 47 Is simply 12/47. Doesn't reduce he to the negative 0.2 X. So now my variable is as isolated as I'm going to get it. I'm gonna take the natural log of both sides. Natural log of 12/47 equals negative 0.2 X. Natural Law of E. Which is one, Divide by 0.-202. Yeah. Yeah. And I have X equals natural log 12 divided by 47 and parentheses E divided. But we do that any steps Divided by negative .002 and I get 600 82. And that would be whatever units we're talking about.


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