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For ccrtain ilcm thal currently being sold on the shopping network on national television; the demand cunvc "p= D(q) = 5(9) = 2q" Sq +5 (s pointa) 25 and ...

Question

For ccrtain ilcm thal currently being sold on the shopping network on national television; the demand cunvc "p= D(q) = 5(9) = 2q" Sq +5 (s pointa) 25 and thc cupply curvc I

For ccrtain ilcm thal currently being sold on the shopping network on national television; the demand cunvc "p= D(q) = 5(9) = 2q" Sq +5 (s pointa) 25 and thc cupply curvc I



Answers

A demand equation is given by $p=\sqrt{9-x}$, where $p$ is the price per item when $x$ items are demanded. Find $d R / d x$ when $x=1$.

In this question. Would you calling about the elasticity, E p, I think What you mind? Speed, time secure Plan B even you might kill the pay and you were given the e P zero here. Everything smaller than one. We call the demand be in elastic I and it's credit than one week on the demand will be elastic in this question were given the U P ego to the 700 off the P plus five. Or we can register to the 700 times B plus £5 on this one for the be equal to the 15. Now, let's try to find that arrested stay E p it will equal Adjumani speed. I'm skilled and be I'm gonna kill him the B they will get equal to u minus B here you pray I'm getting equal to the 700 times by the power again. The minus one attempts beepers one power managed to buy the general attempts derivative on the papers five equal to one and they would have divided by 700 B plus £5 on this one. It would seem to find this out Then we have minus with the mind us so we'll have to be and then be plus five by minus tube plus one. So you go to the P over B plus five here and want to find elasticity and the PICO to the 15 you get in Coachella 15/15 plus five. So he could, you know, 15. 20. I will get to go to the three off. A far doesn't smaller than one. Therefore we have the demand. Will be there in elastic. Mhm, yeah.

So the P intercept you have this function here are written in terms off cube, right piece here and there in the function Written terms of Q and A P intercept means that you put Q of course zero. So at p intercept que zero. So p interceptors gonna have have off zero right is cute. Here is gonna be syrup. Uh, that is gonna be 50 minus 0.3 zero square writes API intercept is 50. Right? So 0 50 is an intercept on the P excess is an is an intercept. Okay. On the P axis a que intercept, we do the same. Put P equals zero So p at the Samos half of every cue. Right? So it put this one because zero and then we solve this one. Thanks. So, services 50 equals 0.3 Cues were right from here. I got here. Then I divide boots size by that. What do I get? Get Q squared equals, uh, what is 50 over 500.0 three and that is 1666.67 Right. And soon Q is gonna be ah, plus or a minus square root of that right. And, you know, this is quantity, right? Yeah, cuse quantity. And we don't have negative quantities, So we're gonna think just a positive. So que is square root. Positives were route because it is measured in, uh, quantities and qualities. Supposed Be positive. You can have a negative quantity. So 40.8 to right. So, uh, that is also the, um Okay, uh, if we're gonna use intersects. Yeah. So zero 40.82 is also and intercept on the, uh, que access rate. So, uh, so So that is those are the intercept rate. So the interpretation here is that for this 0 50 means Dad, find a quantity is zero prize is 50 right? And here, when you have a, uh, a quantity to be 40 point 82 surprises zero. Right. So when quantity is 40.82 surprises, you're in here on a quantity. Zero surprises 50 right? That is the interpretation s so good to be parts. And the be part, we're going to do it in on a different page. Finding f of two anyway. So ever every 20 every 20 is gonna be 50. Myers, 2.3 right and 20 squared Soon 20 squares. Let's see. Yep. Is correct. So the same function? 15 minus yet. Correct. Ah, that is 38 right? $38. Remember, this is the same. A surprise, Right? To 38 daughters, right? Yeah. Um, So, in terms of demand, uh, when the demand is 2020 Right, Uh, in terms off, uh, demand when a quantity a quantity demanded is 20. Right, then the price is gonna be $38. So when you're demanding equality off to money, the price is gonna be, uh, $30. So quantity off 20. Being sold is gonna uday price off if a customer and put it this way. If a customer wants to get 20 uh, off the quantities of the products being sold, they're supposed to pay pay up. Uh, $38. Right now. I gotta find f prime of 20. So every problem 20. Gotta find the f prime of Q first. Right, which is negative. A zero point unity times to you is, uh, negative. Do 0.6 Uh, Q. Right. Because this is the equation yet so negative. 0.6 que. That is the derivative. Now, if you do have prime of 20 that is gonna be negative. 1.2. All right, negative 1.2. And that is also so having a negative 1.2 daughters here means that, uh, the demand is 20. And you're trying to decrease the prize by 0.2. Right? So if, uh, you're the differ and you want people, Teoh, increase your demand. Then you have tow degrees, your prize enterprise of the quantity by 1.2. So for one person to increase the demand to even 21 here, this is 20 to 21. Here you have to decrease the price by $1.2 to enable customers to demand one more of the quantity. A that is, that is the interpretation.

So Q represents this demand function here. So three times five minus p over the square with P squared plus one and were asked defying how cute changes with respect to Pete or essentially, what they really just want to know is what is D Q by DP or the derivative of Hewlett Respect. So let's go ahead and start. So oh, uh, d too. Bye. So remember this thirty. Here's a constant, so I can really just pull it out when I'm taking the derivative. So be thirty, and then I can just place the derivative on the inside here across the negative sign. So the over times by minus the derivative with respect P of p times so we could use the product rule to try to take the derivative of the over the square root of B squared plus one. But I just prefer to use the power of the product rule anytime. I assumed she just have a power in the denominator. So what we're going to do is rewrite that first as a power. So peace where plus one so the square root is the one half power, and then, since its end, the denominator I They're on a negative sign on to it so you can go ahead and drop for thirty down that it's here. So the derivative of a constant is zero to the drone of the five zero. This negative sign here, I'm just gonna go ahead and pull all the way out And then I'll just be left with the derivative of P times P squared plus one to the negative one half power. So just there's here. And to do this I'm going to use product Cool. So remember what product will says is I'll have a pee times the derivative Oh, peace where plus one to the negative one half power Plus where I have the places switch So p square plus one to the negative one half hour times the derivative oh so negative thirty times he need So the derivative of P squared plus one to the night of one half is the generalized product Cool So it's negative one half i'LL move out front Subtract one off So negative one half times p squared plus one and I subtract one from that power So negative three ums And then I have to take the ribbon on the inside, which will be to he. Okay, then I, uh he squared plus one to the negative one half power and then the derivative of P Whose What? So now what I'm going to do is rewrite this a little bit, get rid of the negative exponents and mighty Zoe's fractions. So I'll have so in this first denominator there'LL be peace where plus one to that we have power in the numerator So I also need to remember this too. And they're actually so not the two because here this too and this too will cancel out And then in the numerator, these peas can multiply together. So when the numerator all in double it negative p square since I have the negative with this one half right here and then I'll add this too one over p squared plus one to the one half power And if I want to go ahead and combine these all need to get a common denominator So I just need to multiply the right one by peace where'd plus one over peace where plus one and doing their owned up with negative thirty. So you'll notice that the negative p squared in Peace Square Cam's Slow and I'll just have one in the numerator and this will be over peace where plus one to the three power or just moving the negative thirty into the numerator Negative thirty over he squared plus one to the three hops and we'LL go ahead and stop there.

Okay, so we're giving Q and were asked to find e que over dp What that's equal to Let's see, let's multiply out are dirty. So that's 30 times fine, which is 1 50 minus 30 p over the square root, which is P squared plus one to the power of 1/2. No, let's stick our derivative. So, um, we're gonna need to use the question rule here. That's what the falling. But you let's let this PV So we have the derivative of our constant. Is this still? And then we have you prime. That's negative. 30 times view minus me prime. That's 1/2 p squared plus one depart native would have times did derivative over inside. That's two p and in times you all over b squared. That's 1/2 to the power of to which is this one


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