Okay, We'll come back. New raid. Here we go. Alright. We're in Chapter five. Section one of Thomas's captains. 14 Tradition. We're on page 2. 58 number 19. Now, we're not giving a function or a graph this time to estimated area were given a table of values. F zero is 55. 1 is 70. It increases our way to FF 87 26 An increasing function. So right. Three months, some would be an underestimate and a love three months, um, would be an underestimate. They're asking us to give over a number under estimates for five hours worth. Let's see. What is this? This is, um this table has given its time and ours, and the function value is leakage of oil tanker leaking oil in gallons per hour. Okay, so I'm going to say that the total amount of oil lost is now, let's make this easy. They want five rectangles. They went from the first five hours. Right. So I'm gonna say Delta X of one, and then f of one, which is 70 was up to which is 97 plus f of three, which is 1 36 less effort forward just 1 90. Is that not? This will be my underestimate. And F five was 2 to 65 and I punches up in my calculator already. I got 758 gallons of oil leaked in the first five hours of the leak. All right, because, uh, taxes in hours and the white values in gallons per hours of the units were getting here in gallons. Alright, what's my overestimate? That would be my left. Some, which is gonna be dealt X is one times f of zero, which is 50. So we're just shifting to the left f of one percent of to puts up of three plus f of my rights. My rights, um, isn't over. So this is my underestimate, okay? And f of four, we just 1 90. So we're using a lot of the same membership were dropping off, dropping the 2 56 and adding the fifties were using a zero none of five Here. We're using f of 12 ff 50 f before, and that's some I got e got 543 gallons. Alright, so that's over. The first five hours with the dubbed X of one. They didn't give us a dubbed X eso. I just made that up. Okay. Now, for not part, that's part of the part B is Can you do this with for eight hours? Okay. So stood up for eight hours. So my overestimate Marie, three months. Um, you give me the same thing. Really? Don't. Tax of one times f of one concept of two. What's up for three plus four? I'm just reading off the table. That's given a page to 38. Number 19 after five. We gotta go away to a debate, which is a whole table rates of close to 56 30 65 plus it for six because for seven. Sorry, plus up of eight. So this uses that won't separate from may. Overestimate. Alright. Already punched this up. I got about what I get. This works out to 23 2363 counts and my underestimate using my left sums So we're starting with f of zero the approximate it has detected just one times. The first time, which is f of zero, is 50. What's up? One is 70% to 97 except for three is one and 1 36. So we're going from F zero f of seven instead of it for one that made so 1 36 plus 1. 90 after four is 1. 90 of course, of five was stupid to 65. You keep on doing that. What? Sets of sixes. 3. 96 3 69. And then the eighth height is every 75 16, And one times that is that. And add it all up. And I got what I get 1600 93 girls they actually answers. Suck somewhere between sandwich. Their, um, stuff hasn't goes to infinity. Let someone write some shit boat approached. The correct answer is somewhere around traps. Um, all right, now, the tanker leaks 720 gallons per hour after the eighth hour, so it stays at 7. 20. If the tanker originally had 25,000 gallons of oil, Approximately how many more hours will collapse in the worst case? And in the best case, All right, well, let's see. Let's say we lost 2363 gallons. So let's say I have so time right. How much longer it takes for the spill toe stop. I guess so. My time estimate after the eighth hour is, um I'm using approximations. Right. So let's say we lost 23 63. All right, So I'll be 25,000 minus 23 63 over 720. So there was this. A number of gallons divided by gallons per hour will give you ours. Mhm. Right. There's gonna be gallons divided by gallons per hour. Remember he divided by a fraction you don't You multiplied by the reciprocal, so multiplying by hours per gallon, gallon canceling to get ours. Yeah, and I didn't punch the stuff on the Calculate. Let's do that. All right, so it's quantity or parentheses. 25,000 minus our overestimate 23. So this will be an understand how long it takes to finish leaking because they've lost a lot of ready quantity. Divided by 7. 20. This about 31.440 if you run with the nearest 1000. So what do we got here? 31 point or 40 hours. Okay. And that would be Let's see, that would be my underestimate has already lost a lot of stuff. Okay, so my overestimate, the time it's gonna take to finish leaking. Let's say, is 25,000 how much I started with minus 1693. Underestimate that. We had over 7. 20 and that's gonna work out Toe wash. All right, look, it's my calculator. I'm just gonna type over the 23 63 with the 16 93. And if you're under this afternoon's thousands of an hour, it's 32.371 So there's my overestimate. There's my unrest mint of the amount of time it will take to finish the leak. All right, there you go. So there's five our estimates over over and under estimates. There's the eight hour estimates over and under estimates. And then let's see estimate of how much time is gonna take the leak beyond the first eight hours. And there you go. So that was helpful, right? Have a nice day. Because look what your homework. See you next time. Bye bye.