Hello, Numerator. Welcome back. Okay, so we're in chapter three, Section nine. Page 2 50 number 39. And so you're a cameraman. Yeah. Yeah. And your camera? I can't get away with this thing. So your camera is your 4000 ft from, say, a space shuttle taking All right, So this All right, So and then it's taking off over here, presumably at right angles from the ground from at least initially. Oh, well, I really hate this graphic editor. Yeah. All right. Yeah. Sorry, guys. This is really dominance, huh? Mhm. Let's pretend Okay, already. So So let's say this is where the camera starts out. There's the takeoff point, and this is where the space shuttle ends up. Okay, so this length here, I'm gonna call it X is a constant 4000 ft. You want to know at the moment that why is 3000 ft and apparently the greatest change of of whitey whitey T for the space shuttle is 600 ft per second, At least at this instant at the instant went wise. 3000. You want to figure out how fast this is changing? Pretended to straight line McGuinness. You don't know how fast called the Z Z is changing. Okay, already. So since it's the right triangle, presumably we have I use this movie. Okay, we have Z squared is 4000 square plus y squared because the X because X is not changing. But why is changing? So if you wanna know how fast disease changing find is e d T. So French it implicitly and you get to Z dizzied ET is equal toe now the river of 4000 square toe. It's a constant zero to get to y do anything. So to figure out these DDT Alright, related rates thes e d. T is based on TV while eating, uh, you need to know why which you have. We need to know why Prime which we have. We need to nosy. So what is the well at the moment there, Why is 3000 Z? He is the square root of 4000 squared plus 3000 square. Okay, uh, what's that? 16 million and nine million is 25 million square Bruce of 25 million. Because 1000 squared is 2000, tens of thousands of million and three squared is 9 to 9 million. 10 things. 60 million family. So that reduces to 5. 5000 doesn't. Oh, yeah, it's a 345 triangle. Done. So these 5000 ft. Okay, so I think we can do part A This part. A. Okay, Yeah. 39. Okay. What is wrong with this thing? Three. M'membe has to do with this angle here. Call it feta. A fest that fate is changing. If you're keeping the camera trained on the space shuttle, that is increasing, right? Defended. He would be positive. But right now we're looking for a disease ET so perfect. We're going to say the twos canceled. Right? So now we have 5000 thes e d t or Z. Private life equals 3000 divided T and D Y T t was given a 600. So divide that by 5000 and you get that easy to use. Your crime is 3/5 3000, 5600. And the fifth of 620 times three is 360 pay per second. Yeah. Yes, the exes and wise. We're in feet and the white t was in feet per second. So this is gonna be 360 people. Second Alright, Support be what we have to do with theater So you could talk about the sign of Fada. Is Thea opposite of the hypotenuse 3000 of Zig eso 3000? It's not a constant. So why over Z or you could talk about the co sign? Being 4000 over Z Z is changing. The 4000 isn't changing. We've been talking about the tangent is why over 4000? Because Y is changing with the X is not changing on differentiate That's any one of those expressions. Skip the fate of the tea or think of prime um tangents. Probably nice. Why not? What's tangent? Okay, let's strike tangents. So the tangent of Fada is Why were 4000 so go to one So 39 b The tangent of Fada Mhm his wife over 8000 is not changing. X is not changing, But why is changing all right eso we differentiate both sides implicitly. We expected to using change role we got C can't squared data through attention seeking squared eso through the tangent of stuff is sick and scared of stuff the stuff through stuff change going and this is just gonna be 1 4/1000 of the white GTO and we have the White ET It's still 600 but we don't have is a seeking Well, think about it if she can is one over the Coast Square Seeking is one of the coast and so she can't squares one over the coastline square. Alright, so we divide both sides by seeking square, really multiplying, whether simple we just close side squared So defeated ET is gonna be the coast sine squared of theta over 4000, uh, times they wanted to now do nt t is apparently 600 ft per second and the co sign Well, let's go back to the original diagram Person is the adjacent over the high patterns. So Cartola so that's 4000 at this moment, over 5000 or four fits. Okay, so that's gonna be 1 4000 of 4/5 squared time 600. So that's 6/40 is 3/20 times 16/25. Mhm is is 48 over. Where does that reduce anymore? It does. It produces 2 8/10 4/5, as you just a little bit reduced by four. You got a four appear. You've got a five, man. Okay, so it's gonna be three times four is 12 in the numerator over 505 125. I don't think that reduces anymore. Uh, and that's defeated the Tisa radiance per second, which is 0.96 radiance for second. Exactly. That rounded off. Just run that by my little graphing calculator there. So the theater DT potato prime is exactly 0096 ratings per second. All right, I'm right. That's it for question 39. Hope that was helpful. Good luck with your homework. See you next time. Bye bye.