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ComnIne populdllon mhumuredy Inungt the Callfornia Gold Rush oon Ino rnciion a Chera trnveat hncu 1850 graph ol I(l) -Iny tlg Ihc InllatingUnel aeae nopunuon lnan ancn taroi b) FInd Ewo dllutont elta} itatyuk lo #ech Vo eudu (utu cnge ol P wilh tuepucloThecartha Canulilon olne Ioun (eached zoroUtrg Ihacalnt ndlcalerIne qudon 0ilnlininrhechotu Itatanlin whule ta 040(0a4mangu M4e 450oamleeaes D yer0 spanc/[] vearsUsinqDorl: indcmedIhe graph of f4 tha inkerval wch Ihe bolzut Ena span whora %he avar

comn Ine populdllon mhumuredy Inungt the Callfornia Gold Rush oon Ino rnciion a Chera trnveat hncu 1850 graph ol I(l) -Iny tlg Ihc Inllating Unel aeae nopunuon lnan ancn taroi b) FInd Ewo dllutont elta} itatyuk lo #ech Vo eudu (utu cnge ol P wilh tuepuclo Thecartha Canulilon olne Ioun (eached zoro Utrg Ihacalnt ndlcaler Ine qudon 0il nlinin rhechotu Itatanlin whule ta 040(0a4 mangu M4e 450 oamleeae s D yer0 spanc/[] vears Usinq Dorl: indcmed Ihe graph of f4 tha inkerval wch Ihe bolzut Ena span whora %he avarage rata charge wa Tzera



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Solve each problem. An accountant determines the charge for filing a tax return by using the function $C=50+40[t]$ for $t>0,$ where $C$ is in dollars and $t$ is in hours. Sketch the graph of this function. For what values of $\ell$ is the charge over $5235 ?$

Problem. 95. Um, we're filing, ah, tax return. And the charge for filing that tax return is C equals 50 plus 40 t where C is the charge in dollars and t is the time and ours all right. And we have the greatest integer function in T. Okay, So if that's ah desk, more fraction, it gets rounded down to the nearest integer. And they want to know what values of T is the charge over to 35. Okay, so we want see greater than 2. 35. This is our function right here. Dysfunction right here. See? Okay. So I am gonna substitute that function in place of C. All right. So in place of, say, 50 plus 40 t is greater than 2. 35 minus 50 on both sides. Fifties cancel 40 t is greater than 1 85 and dividing both sides by 40. We have tea is greater than 4.6 to 5. Now, remember, for tea, we have the greatest integer function. Okay, so this decimal is always going to get cut off because it rounds it down to the nearest integer. All right. So because the decimal is always rounded down. We need to round tee up because he has to be greater than this decimal. But if it even if see this is greater than 4.625 let's say it's 4.9. It's still going to get rounded down to four. So that's not gonna work. So we need to round it up. So we get rid of that decimal, and we say T is greater than five. Okay, and that makes perfect sense. If you plug in five for tea, you'll get 40 times five, which is 200 plus 50 is 2 50. Okay, but if T is less than five, it will get rounded down to four. You know that four times 40 is 1 60 plus 50. That's to 10. That's no good. That's not greater than 2 35. So it has to be five or more so, really, I should have said greater than or equal to five. Okay? And they also wanted us to sketch the graph. So I just counted by ones for the X axis that's ours, and I counted by forties for the Y axis. That's cost. It's because it goes up $40 every hour. Okay, so up to one hour T is gonna be zero, and it's just $50 upto one hour. So we start. We start right here upto one hour. Okay, That's gonna be $50 all right? And it goes up by 40 each time. And you know what? I sink. I think it will be better if I rewrite this y axis and start with a 50. So let's do that. I'm gonna start with 50 on the white axis. That will make things easier. All right. So this will be 50 then we'll count by 40 each time. 90 1 30 1 70 to 10 2. 50 and so on. And we'll pretend Will say it started at 10. All right. The X axis started at zero. Okay, let's try this again. And I think I'll make it in red so you could see it better. Okay, so for the first hour, it's $50 for the first hour. All right? And if x 50 equals one all the way up to 1.999 it's gonna be $90. Okay, So I'm gonna make a open, open circle here, and it jumps up to $90 at one all right, and then make an open circle at two, and it jumps upto 1 $30. I make an open circle at three, and it jumps upto 1 $70. Open circle at four. It jumps up 2 to 10 and so on. It keeps going. Keeps going up and up like steps. All right, so that's this. That's the sketch of the graph. Each time it goes up to the next hole, our it jumps up by $40. Okay, but any fraction of an hour gets rounded down because this is the greatest integer function, which means it's rounded down.

Hi in the given problem, there are the two charged particles, this is plus Q and here this is minus cute. Suppose this plus Q is put at a point A And -6 is put at another point b. And there is a point P Midway between these two charged particles. So the distance of this observation point P is same from both of these two charged particles. No, it is given that initially there was only one charge particle plus Q present here. In that case electrical acting at point P will be going away from this positive charge and this electric field which we can represent by E. That is given to be E hail. So the magnitude of this electric field, as per expression will be key into Q by our square, which has given us E. Here. No, if we put another charge minus you here, we know electric field always direct towards the negative charge. So due to this negative charge put at B the direction of electric field due to this negative charge means we can represent it by E B. That will also be towards this point B. And the magnitude of this electric field, E B will be given by K into Q by our square as the distance will be seen. That is also equal to art. Hence now net electric field acting at the same point B is given as E is equal to, or we can say let it be E dash. So this E dash is equal to E Bless E B. This E A was E. And the E B is also equal to the value E. So we can write it like E also here. So the net electrical at point P now comes out to be twice of E means twice of the original electric field. Hence here we can say corruption. B is correct. Thank you.

In this problem were given it agency, which represents tickles a za function of a number of units. And we're also giving another function, which is the function for number iss as a functional, uh, T. Which is so what's right? The house function in the park for some time s. So they're 60 times. Thanks. A 1.60. You plus 19. He spurred Waas, um, minus T Bone's one plus 13. 30. And from this we find because six you close 11 40 Sprayed minus 30 of laws 1200 Name. Um, first, we need to find the topic of assumption. This bunch. No, they were killed while construction with respect. Piece of these your D t s. This is Victor 96 of three. T squared, plus lemon 42 tea. When 30 um, in party, we're gonna really did their dysfunction. But for that one buddy plan for T you find difficult to be or 400 donated to hear when you play. Uh, Ryan, but this is a question. You find the change of changing complexion. Um, be great teeth under is to and from this we can see that after four hours because this breaking greater changing coasts is breaking the record trading post import Beware Just to show why the red, as you can see from here, not from here Coast function this proportional to the time. Cute, right? A fungus and everything is proportion. Pretty, uh, great. Since C is not in for tea and see firm, that is warm or Colston, This is a no no, that's why you're right. Is not We can see. Isn't your formal tea to the end? Wire end is different one.

E x for lift off exit was be He's negative. Which means charge at X equals B is negative. Similar? The we would have charged for exit was a to be glass of juice. Now way with have que a over he'll be the absolute value equals one R manager off Q A equals. Manage it off. You be on the potential years as a function of X will be given something like he had, you have the negative charge and here you have. The positive charge at this is X equals B and this is X acquis a on the potential will be like it will be on symmetric about X equals AMX.


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