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2To keep his baseball team hydrated,Daniel mixes powdered sports drink with cold 74ze For best taste , the mix should [ be 9690 water__If Daniel has used 16 scoops ...

Question

2To keep his baseball team hydrated,Daniel mixes powdered sports drink with cold 74ze For best taste , the mix should [ be 9690 water__If Daniel has used 16 scoops of powder and added quarts Of water= ow many gallons _ of wated should he add . given that each soop Caleeie U= @p* aUL 64 7f2 _ cup? Ule LnSUc1 12+U quart= 0.15 Galion qallong 6C yja'er 50 Terefoxe, Jquark=6 Naoy Deniel rus llx V4=4 cups 06 Powuder Shouo Ioe aloele Cor Iest kaste O neans Alolo aied la Jev lunion 490 0 audev Tle4

2To keep his baseball team hydrated,Daniel mixes powdered sports drink with cold 74ze For best taste , the mix should [ be 9690 water__If Daniel has used 16 scoops of powder and added quarts Of water= ow many gallons _ of wated should he add . given that each soop Caleeie U= @p* aUL 64 7f2 _ cup? Ule LnSUc1 12+U quart= 0.15 Galion qallong 6C yja'er 50 Terefoxe, Jquark=6 Naoy Deniel rus llx V4=4 cups 06 Powuder Shouo Ioe aloele Cor Iest kaste O neans Alolo aied la Jev lunion 490 0 audev Tle4 1€ La LeY ied Io sinuyld Ie Qowuerc 0c 24" for ~We 1BRt tas8, aho cost !.2 million dollars. community center that is proieetede are 225 fewer residents than village wants t0 build 53 as it is discovered that there [ Sito tha_folcton per = resident is increased by What iS the revised cost per resident? tp* Cost henc planning began years ags€ ag0_ when pey Yes de p=prewo ixpekon Let n tiaiiy resi dent oc o0o+37 Z00 joo anu nurber izooooo 200,9 10 ( P-225 6,2 x X 266665)X Nev ee 8 ana 80 ++ Cose eed dens Kjar5 esi Ke 312 T} Io € < (` - 2 2 ( ,| 1 2 UC( Ou 67S (? C0 175 /



Answers

Your next-door neighbor, Josephine Rackstraw, surprised her husband last January by having a hot tub installed in their back yard while he was away on an ice-fishing trip. It surprised him, all right, but instead of being pleased he was horrified. "Have you lost your mind, Josephine?" he sputtered. "It will cost a fortune to keep this thing hot, and you know what the President said about conserving energy." "Don't be silly, Ralph," she replied. "It can't cost more than a few pennies a day, even in the dead of winter." "No way -just because you have a PhD, you think you're an expert on everything!" They argued for a while, bringing up several issues that each had been storing for just such an occasion. After calming down and using the tub for a week, they remembered their neighbor (i.e., you) had a chemical engineering education and came to ask if you could settle their argument. You asked a few questions, made several observations, converted everything to metric units, and arrived at the following data, all corresponding to an average outside temperature of $5^{\circ} \mathrm{C}$. - The tub holds 1230 liters of water. - Ralph normally keeps the tub temperature at $29^{\circ} \mathrm{C}$, raises it to $40^{\circ} \mathrm{C}$ when he plans to use it, keeps it at $40^{\circ} \mathrm{C}$ for about one hour, and drops it back to $29^{\circ} \mathrm{C}$ when he is finished. - During heating, it takes about three hours for the water temperature to rise from $29^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. When the heat is shut off, it takes eight hours for the water temperature to drop back to $29^{\circ} \mathrm{C}$. - Electricity costs 10 cents per kilowatt-hour. Taking the heat capacity of the tub contents to be that of pure liquid water and neglecting evaporation, answer the following questions. (a) What is the average rate of heat loss ( $k W$ ) from the tub to the outside air? (Hint: Consider the period when the tub temperature is dropping from $40^{\circ} \mathrm{C}$ to $29^{\circ} \mathrm{C}$.) (b) At what average rate ( $\mathrm{kW}$ ) does the tub heater deliver energy to the water when raising the water temperature? What is the total quantity of electricity (kW\cdoth) that the heater must deliver during this period? [Consider the result of Part (a) when performing the calculation.] (c) (These answers should settle the argument.) Consider a day in which the tub is used once. Use the results of Parts (a) and (b) to estimate the cost (S) of heating the tub from $29^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ and the cost $(\mathrm{S})$ of keeping the tub at a constant temperature. (There is no cost for the period in which $T$ is dropping.) What is the total daily cost of running the tub? Assume the rate of heat loss is independent of the tub temperature. (d) The tub lid, which is an insulator, is removed when the tub is in use. Explain how this fact would probably affect your cost estimates in Part (c).

Big question play. Uh, first of all, we have to troll this and supply and demand curves on this graph. So we first rolled a demand occur. We know that for one extra one borrow off this drink, people are willing to pay five dollars. And for the second bottle, people are willing to pay four dollars. So it's like, four. And then and then the third bottle. And then for and then five for six bottles and above. People are willing to pay zero. So we know that we have to connect this dot in a one five this dot Okay, So, to draw the demand curve, we now have this towers over the maker so we can start from mainstream Question eight Mr A saying that the cost of producing this ring is one point five and so no supply curve this horror santo of it. The wind, which is true, is the maker of. So now we draw this, um, one point flight like around here, when the price is one point five, the firm is going to supply even in a number of this drink. So we can So the supply curve is hold for results. for the answer, questioning how many bottles were each village residents consume? But we can see that when the script is a little bit. So at this point, this intersection is actually four point five. Now, we can just observe from the table, because when the prize is one point five, the quantity is four point. So the equilibrium quantity is four point five, while the equilibrium prize this one point. Right? Okay, So what is the person's comes from our surplus. We know not what we think of consumer surplus. It is the whole triangle right here between the supply and demand curves before the person that paid this amount of money, which is one point five dollars and buy four point five bottles of wine off this drink. At this point, this person's consumer surpluses zero. But as the social or social consumer surface, we should calculate this triangle. All right, question. Be pursuit. Producing this drink creates pollution. So each bottle has an external costs off one, which means that actually, that social supply curve is shitting upward. This s print is the social supply curves. So the optimal price of this drink should be two point five Because we with the black curve, we are ignoring the external cost when producing this kind of trick. So the rial supply curve should be the one. Uh, so if we take this cost into your account So if we look at this blue light, what is the total surplus per person in the allocation? So we just say that the consumer surfaces the big area right here. But now with the rial supply curve, which is the blue line, the consumer surpluses. Actually, I'm smaller. So the difference is this trying go here. I was just like you. Screen color. So the welfare lost this. Actually, this small green triangle here. Okay, Constancy. If there is a girl name Cindy, she decides on Rome to reduce her own consumption. So what does it mean? It means that the demand curves. He's going to shit, laughed a little bit screen. Yeah, why is that? It's because Cindy herself a drinks less off white off this drink so that the men cripple. She left. But the original supply curve, which is the one point five hours from Tome I hear does not change. So, like the equilibrium quality is going to decrease a little like, less wealthy lesson for five. But the price does not change. So how you didn't see these decisions affect little toe surplus? So we can see that. Ussing, this decision is going to make the total surplus smaller because we used to have a beer trying. Go here. Right. But now, with this demand occur of being green, the total surpluses going to decrease, there's a question he now the mayor of this village village imposed on one dollar tax on the this drink. Then let me just delete the Cindy demon. Curt. First of it. So when the government decides to impose this one dollars tax, what is consumption per person now? So when the government imposed a tax demand curve is going to shit over, So we are assuming that they imposed this tax on the consumer. So consumer is not going to buy that much off the drink, so they are going to decrease. There are the man because now it is more expensive to get a drink, right? So since the taxes one dollars, so this statement Ultraman curve ship's power to the new women curve by one dollars. So the difference here is one the other unit. Okay, I'm calculating the customer surplus, the cost and the government remini revenue. So if we look at the new demand curve, let's call the prime with the ship like the original. Yeah, with the original supply curve. Ah, the consumer surplus is now this triangle and the text revenue is going to be the difference between the old demand occur and the new deep man crew. So government revenue is the color in green here. So the original supply curve is ray here, and the original demand curves right here, all in black. But now, actually, this portion ofthe revenue is going to the government. So the area red is the consumer service sown? So we can say that based on this analysis, we would support the make the mayor's policy. Because with this tax, we can end up having the efficient amount off quantity, which is this point


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