Category
📚
LearningTranscript
00:00:30กานประยุก กานประยุกเป็นโจทย์ปัญหา ซึ่งจะออกข้อเดียวแล้วก็ออกข้อเขียนด้วยนะครับ 15 แตมนั่นเอง
00:00:39เป็นการนำประยุกเอาอันดุพันธ์ที่เราเรียนนะครับมาใช้กับอัตราการเปลี่ยนแปลงต่างๆตามสถานการณ์ต่างๆ
00:00:49นะครับ
00:00:52อัตราต่างๆจะดิบเทียบกับเวลาหมดเลยนะครับ ดิบเทียบกับเวลาทั้งหมดก็คือเทียบที่
00:01:01นะครับ พี่โอกตัวอย่างความสัมพันธ์แบบง่ายๆให้ก็คืออย่างเช่น
00:01:07สมมุติว่า
00:01:09สมมุติ
00:01:11สมมุติว่าเรามีกล้วยอยู่อันหนึ่งนะครับแล้วพี่ปล่อยน้ำออกมันหมายความว่าปริมาทลดลงไหม
00:01:20แล้วอัตราของปริมาทลดลงนี่ตรงผลนำให้ h นี่ลดด้วยไหมแล้ว r นี่ลดตามไหม
00:01:30r ก็ต้องลดดีเนี่ยวงเล็กลงไหมเพราะฉะนั้นเนี่ยมันจะเป็นความสัมพันธ์ระหว่างอัตราต่างๆนั่นเองเป็นความสัมพันธ์ระหว่าง dv by dt dr by dtแล้วก็ dh by dtถูกปะ
00:01:44ซึ่งโจทย์เนี่ยเขาก็จะให้มาซักตัวนึงเช่นให้ dv by dt มาแล้วก็ไปให้เราไปหาเองอีกสองตัวอย่างเนี้ยเป็นต้นหรืออีกตัวนึงก็แล้วแต่นะครับเป็นความสัมพันธ์ระหว่างอัตราต่างๆ
00:01:58ซึ่งมันจะต้องเป็นทิศทางเดียวกันด้วยเช่นปริมาทลด r ต้องลด h ต้องลดอย่างเนี้ยเหมือนกันนะครับ
00:02:07ทีนี้การทำเนี่ย
00:02:10ขั้นต่อในการทำโจทย์เนี่ยหนึ่งเราต้องวาดรูป
00:02:15เหมือนภิษฐิกอะ
00:02:17แต่ประเด็นคือในภิษฐิกจะมีสูตรใช่ป่ะแต่ในแคลวต้องสร้างสูตรเอง
00:02:22นะครับ
00:02:23ทีนี้สร้างสูตรเองเนี่ยสร้างจากความรู้รอบตัว
00:02:26ความรู้รอบตัวเรามีไหม
00:02:29มี
00:02:30อันแรก
00:02:32อันแรก
00:02:33อันแรก
00:02:34อันแรก
00:02:35อันแรก
00:02:36อันแรก
00:02:37อันแรก
00:02:38อันแรก
00:02:39อันแรก
00:02:40อันแรก
00:02:41อันแรก
00:02:42อันแรก
00:02:43อันแรก
00:02:44อันแรก
00:02:45อันแรก
00:02:46อันแรก
00:02:47อันแรก
00:02:48อันแรก
00:02:49อันแรก
00:02:50อันแรก
00:02:51อันแรก
00:02:52อันแรก
00:02:53อันแรก
00:02:54อันแรก
00:02:55อันแรก
00:02:56อันแรก
00:02:57อันแรก
00:02:58อันแรก
00:02:59อันแรก
00:03:00อันแรก
00:03:01อันแรก
00:03:02อันแรก
00:03:03อันแรก
00:03:04อันแรก
00:03:05อันแรก
00:03:06อันแรก
00:03:07อันแรก
00:03:08อันแรก
00:03:09อันแรก
00:03:10อันแรก
00:03:11อันแรก
00:03:12อันแรก
00:03:13อันแรก
00:03:14อันแรก
00:03:15อันแรก
00:03:16อันแรก
00:03:17อันแรก
00:03:18อันแรก
00:03:19อันแรก
00:03:20อันแรก
00:03:21อันแรก
00:03:22อันแรก
00:03:23อันแรก
00:03:24อันแรก
00:03:25อันแรก
00:03:26อันแรก
00:03:27อันแรก
00:03:28อันแรก
00:03:29อันแรก
00:03:30อันแรก
00:03:31อันแรก
00:03:32อันแรก
00:03:33อันแรก
00:03:34อันแรก
00:03:35อันแรก
00:03:36อันแรก
00:03:37อันแรก
00:03:38อันแรก
00:03:39อันแรก
00:03:40อันแรก
00:03:41อันแรก
00:03:42อันแรก
00:03:43อันแรก
00:03:44อันแรก
00:03:45อันแรก
00:03:46อันแรก
00:03:47อันแรก
00:03:48อันแรก
00:03:49อันแรก
00:03:50อันแรก
00:03:51อันแรก
00:03:52อันแรก
00:03:53อันแรก
00:03:54อันแรก
00:03:55อันแรก
00:03:56อันแรก
00:03:57อันแรก
00:03:58อันแรก
00:03:59อันแรก
00:04:00อันแรก
00:04:01อันแรก
00:04:02อันแรก
00:04:03อันแรก
00:04:04อันแรก
00:04:05อันแรก
00:04:06อันแรก
00:04:07อันแรก
00:04:08อันแรก
00:04:09อันแรก
00:04:10อันแรก
00:04:11อันแรก
00:04:12อันแรก
00:04:13อันแรก
00:04:14อันแรก
00:04:15อันแรก
00:04:16อันแรก
00:04:17อันแรก
00:04:18อันแรก
00:04:19อันแรก
00:04:20อันแรก
00:04:21อันแรก
00:04:22อันแรก
00:04:23อันแรก
00:04:24อันแรก
00:04:25อันแรก
00:04:26อันแรก
00:04:27อันแรก
00:04:28อันแรก
00:04:29อันแรก
00:04:30อันแรก
00:04:32อันแรก
00:04:33อันแรก
00:04:34อันแรก
00:04:35อันแรก
00:04:36อันแรก
00:04:37อันแรก
00:04:38อันแรก
00:04:39อันแรก
00:04:40อันแรก
00:04:41อันแรก
00:04:42อันแรก
00:04:43อันแรก
00:04:44อันแรก
00:04:45อันแรก
00:04:46อันแรก
00:04:47อันแรก
00:04:48อันแรก
00:04:49อันแรก
00:04:50อันแรก
00:04:51อันแรก
00:04:52อันแรก
00:04:53อันแรก
00:04:54อันแรก
00:04:55อันแรก
00:04:57โอเค
00:04:58พอเราตั้งสมการได้แล้ว
00:05:00ขึ้นอยู่กับปฏิบัติของโจทย์
00:05:02เราจะดิบอันธุภัณฑ์ทั้งสองข้าง
00:05:04เทียบกับเวลา
00:05:08และก็แก้
00:05:10หา
00:05:12อัตราส่วนของการเปลี่ยนแปลงตัวที่ต้องการ
00:05:16หาอัตราส่วนการเปลี่ยนแปลงตัวที่ต้องการ
00:05:20เดี๋ยวเรามาดูกันว่าในหนึ่งโจทย์
00:05:22ทำอะไรบ้างทั้งหมด
00:05:26แม้ว่ามันไม่มีสูตร
00:05:28มีแต่สูตรพื้นฐาน
00:05:30ม.ต.
00:05:32ประยุคแค่ม.ต.กับดิบ
00:05:34ข้อหนึ่งทำจริงๆ
00:05:36ไม่ถึง 5 นาที
00:05:38จะเสร็จแล้ว
00:05:40เพราะนั้นเข้าห้องสอบเจออัตราต่อมพัฒน์
00:05:42ใช้เวลาไม่น่าเกิน 5-10 นาที
00:05:44และเอาเวลาที่เหลือ
00:05:46ไปทำกับข้อเขียนข้ออื่น
00:05:48ถ้าทำเป็น
00:05:50มุ่งเล็บถ้าทำเป็น
00:05:52จะไม่เกิน 5-10 นาที
00:05:54ต่อข้อ
00:05:56สมมุติว่าลูกบอลลูน
00:05:58ถูกป้องให้พองด้วยอัตรา
00:06:00เวลาเราทำ เราทำเหมือนพิธิก
00:06:02คือจับหน่วย
00:06:04ป้องให้พอง
00:06:06ด้วยอัตรา นี่คือหน่วยของอะไร
00:06:10พ.ม.กล.3
00:06:12นี่คือ dv
00:06:14เทียบกับเวลาคือ dv by dt
00:06:16เทียบกับบวก10
00:06:18ลูกบากเซนติเมตต่อนาที
00:06:22ทำไมต้องเป็นบวก
00:06:24มันป้องให้พองปริมาทเพิ่มขึ้น
00:06:26ถ้าปล่อยลม.อ.คือติกลบ
00:06:30ป้องเข้าไปเป็นบวก
00:06:36ลูกบากเซนติเมตต่อนาที
00:06:38อันนี้คือข้อที่ง่าย
00:06:40เนี่ยสุดเลย
00:06:42จงหาอัตราการเปลี่ยนแปลงของลัสมี
00:06:44ตามเซ็นต์ถ้าปริมาทเพิ่มขึ้น
00:06:46ลัสมีก็ต้องเป็นไงด้วย
00:06:48ก็ต้องเพิ่มขึ้นด้วย
00:06:50พระนะนั้นอัตราที่เราสะคิดได้
00:06:52มันต้องเป็นฮ่าบวก
00:06:54เหมือนกันค่า W
00:07:00ดีอาร์บายดีทีว่าเท่ากันเท่าไหร่
00:07:04อย่างนี้รูปนักขนาด
00:07:05This is a simple way to compute the value of r, which is 5.
00:07:12This is a simple way to compute the value of r, which is 5.
00:07:18After we have calculated the value of r,
00:07:24Calculus says that each pair is a pair that we have created.
00:07:29Calculus says that each pair is a pair that we have created.
00:07:34Calculus says that each pair is a pair that we have created.
00:07:40Sometimes, there are 8 pairs in one equation.
00:07:46We have to set all of the pairs to the teacher every time.
00:07:51We have to set all of the pairs to the teacher every time.
00:07:56We have to set all of the pairs to the teacher every time.
00:08:01Let's calculate the first parameter, value for centimeters
00:08:09Let's calculate the first parameter, value for centimeters
00:08:12Let's calculate the first parameter, value for centimeters
00:08:14Oh, I forgot to write the value of D shall be not missing the new factors.
00:08:46After we define the object, we will start to set the relationship.
00:08:50The relationship equation is still easy, but when we go deeper, it will be more difficult.
00:08:57For example, we notice that it gives the value of what?
00:09:01Volume, right?
00:09:03It gives the value of volume, but we need the value of r.
00:09:08So we have to find the relationship between v and r.
00:09:12What is the relationship between v and r in the circle?
00:09:17v is equal to 4 divided by 3, r is equal to 3.
00:09:26This is the relationship between v and r, which is the volume equation, right?
00:09:31The volume of the circle.
00:09:35Now we will notice that there are only two variables.
00:09:39If we divide v by 1, this side will also be divided, right?
00:09:49This side will also be divided, but 4 divided by 3 is a number, so we don't have to divide.
00:09:54How much can we divide r to the power of 3?
00:10:00Does it have an integer?
00:10:03Because it's different, right?
00:10:06Because it's different, it will have an integer.
00:10:12It's an integer, right? But this is r.
00:10:16Then we will know that if we know the value of v, it will also affect the value of r.
00:10:22This is the relationship between dv divided by dt and dr divided by dt.
00:10:26Now, how much is the value of v?
00:10:3010 plus 10.
00:10:34Therefore, I will get dr divided by dt equal to 10.
00:10:435 divided by 2, right?
00:10:465 divided by 2, r is equal to 2, right?
00:10:52Notice that I haven't added the value of r yet.
00:10:57Why? Because this is the value of r.
00:11:04If the value of v changes, the value of r will also change.
00:11:10Now, how much r do we need?
00:11:16While r is 5 cm, we substitute the value of r.
00:11:245 divided by 2, r is equal to 25.
00:11:291 divided by 10, r is equal to 1 cm per minute.
00:11:37Now, we don't have to calculate the value of r.
00:11:43We can leave the value of r in the answer.
00:11:49But the important thing in the next lesson is to summarize the answer.
00:11:53Because by saying this, they don't know about us.
00:11:55We have to summarize that the value of r increases.
00:12:04Why do I use the word increase?
00:12:07Because it is a positive value.
00:12:09The value of r increases, right?
00:12:11The value of r increases by 1 over 10π cm per minute.
00:12:20Who wrote only this is not full.
00:12:23Because there is a reason.
00:12:27Writing only this looks easy, right?
00:12:29But it's not full.
00:12:30Because it's not full, it's not always like this.
00:12:33It's not constant.
00:12:34It depends on the value of r, right?
00:12:35Therefore, we have to say that the value of r is 5 cm.
00:12:43This is the correct thing.
00:12:45If anyone is lazy to write, please write the value of r.
00:12:51Increasing late and decreasing late.
00:13:22Floridians have an increasing late at this moment.
00:13:34Is it confusing?
00:13:51I'm not confused.
00:13:52This is the easiest question.
00:13:54Next, question 2.
00:13:56Where are you going?
00:14:09Really
00:14:10Why do you need 10 flowers?
00:14:17Because it will come out on Monday.
00:14:20If the reservoir is a circle, which has a height of 10 feet,
00:14:32do you believe that it will come out?
00:14:35I didn't say 3 million percent.
00:14:38I said 10 flowers.
00:14:49I will analyze this question for you.
00:14:52This question has been answered since 2005, right?
00:14:55All 12 years that have passed, it has never come out.
00:14:59Next year
00:15:04The reservoir is a circle, which has a height of 10 feet.
00:15:11The top radius is 5 feet.
00:15:13I will tell you that the real thing in the test will not have this picture.
00:15:17You have to draw the picture yourself.
00:15:18Understand?
00:15:19I wrote all the dimensions myself.
00:15:21I'll draw it for you now.
00:15:24The height is 10 feet.
00:15:27The top radius is 5 feet.
00:15:30Add water to the tank.
00:15:34Does it mean that the water level is positive or negative?
00:15:37Add water must be positive.
00:15:39What if you let it out?
00:15:41Negative.
00:15:42Be careful about the machine.
00:15:43Adding water will be positive.
00:15:45If you let it out, it will be negative.
00:15:47Be careful.
00:15:50Add water with 9 feet.
00:15:53It's dv by dt.
00:15:54Find the change in water level.
00:15:58The water level is y.
00:16:01The water level is x.
00:16:04The water level in the tank is 6 feet.
00:16:08The water level in the tank is 6 feet.
00:16:10The water level from the bottom to the top is 6 feet.
00:16:13If you change the word a little bit, it's deep.
00:16:16What is it?
00:16:17Depth.
00:16:18If it's depth, you have to count from top to bottom.
00:16:21If it's 6 feet deep, you have to answer that y is 4 instead.
00:16:25Do you understand?
00:16:27If the tank is 10 feet deep, and the water level is 6 feet, there will be only 4 left.
00:16:31If you use the word deep, you have to minus it.
00:16:34If it's high, you have to count from bottom to top.
00:16:37If it's deep, you have to count from top to bottom.
00:16:39You have to look at the text.
00:16:41Whether they use the word deep or high.
00:16:45Understand?
00:16:46If you use the word high, you count from bottom to top.
00:16:48If you use the word deep, you count from top to bottom.
00:16:51Like how much deep the water level is.
00:16:53Can you figure it out?
00:16:55I made a mistake here.
00:17:03Let's set the value first.
00:17:05v is equal to volume.
00:17:10The volume of water in the tank.
00:17:15The unit is...
00:17:16Why is it so quiet?
00:17:20That's good.
00:17:22That's very good.
00:17:24That's very good.
00:17:26It's good that they don't know.
00:17:28It's a big problem.
00:17:30That was a big problem.
00:17:36y is the height of the water.
00:17:38The height of the water in the tank.
00:17:40I use the unit as foot.
00:17:42x is the volume of water.
00:17:45The unit is foot.
00:17:51That's all for the translation.
00:17:55The rest is fixed.
00:17:57There's no translation.
00:17:59If you want to translate,
00:18:01you have to set it up again.
00:18:03But that's enough.
00:18:05Okay.
00:18:07Now, I want to know
00:18:09the relationship between
00:18:11the volume of water in the tank
00:18:14and the height
00:18:16and the unit.
00:18:18v
00:18:20What's the formula for the volume of water in the tank?
00:18:25It's not right.
00:18:39Why is it not right?
00:18:41Because we don't use r and h.
00:18:43We use x and y.
00:18:45So if you write pi r equals 2h
00:18:47and you don't use the unit above
00:18:49according to the unit,
00:18:51do you get it?
00:18:53No, you don't.
00:18:55You have to write it down.
00:18:57Except that
00:18:59if you don't want to confuse,
00:19:01you can use r and h.
00:19:03Do you get it?
00:19:05The point is
00:19:07if you dip it,
00:19:09does it have the value of v?
00:19:11It has dv by dt.
00:19:13If you dip it,
00:19:15does it have the value of x?
00:19:17And it's different from t, right?
00:19:19So what will happen is
00:19:21it has dy by dt
00:19:23and dx by dt.
00:19:25Right?
00:19:27The point is
00:19:29it doesn't have the value of dx by dt, right?
00:19:31It has the value of y
00:19:33and the value of y.
00:19:35But it doesn't have the value of x.
00:19:37Right?
00:19:39So what we have to do is
00:19:41get rid of the x
00:19:43and leave only the y.
00:19:45Right?
00:19:47How to get rid of it?
00:19:49For a banana,
00:19:51it has a triangle here.
00:19:53It's a small triangle
00:19:55of water and a big triangle
00:19:57of a banana.
00:19:59This is a similar triangle.
00:20:07And a similar triangle
00:20:13has a small triangle
00:20:15and a big triangle.
00:20:17Right?
00:20:19The small triangle is x'y
00:20:21is equal to 5'10.
00:20:23So x is equal to
00:20:251 over 2 y.
00:20:27Right?
00:20:31So I can replace x
00:20:33to get rid of x.
00:20:41Oh, what should I feed it?
00:20:43I don't want to eat it.
00:20:47Shabu?
00:20:51A cup of milk tea is enough.
00:20:53Right?
00:20:59I want to tell you this.
00:21:01Have you ever done an algorithm
00:21:03in LVB-II?
00:21:07Do you know that
00:21:09in LVB-II there are
00:21:11more than 30 questions
00:21:13of math that have just been published.
00:21:15Not just now.
00:21:17Just a few days ago.
00:21:21No.
00:21:27No.
00:21:29No.
00:21:31I want to tell you that
00:21:33in LVB-II,
00:21:35there is this question.
00:21:37But it's about water.
00:21:39How do people in the university
00:21:41know about water?
00:21:43If you do LVB-II,
00:21:45I'll give you more water
00:21:47because it won't be like homework.
00:21:49And most of the time,
00:21:51homework doesn't come out
00:21:53in the correct answer.
00:21:55For example,
00:21:57in homework,
00:21:59it doesn't come out
00:22:01in the correct answer.
00:22:05This is how to solve the question.
00:22:07Sometimes it doesn't come out
00:22:09because it's a trick.
00:22:11But if it comes out,
00:22:13it's like that.
00:22:17It's in LVB-II.
00:22:19But it's okay.
00:22:21Tomorrow, I'll cut some sentences
00:22:23to teach you.
00:22:25About 70% of that.
00:22:31Few people know that there is.
00:22:37But if you're free,
00:22:39you can do it.
00:22:41There will be questions and answers.
00:22:43But there are also wrong answers.
00:22:45So you have to have a little bit of theory.
00:22:55Okay, it's done.
00:22:57Dip y equal to 3,
00:22:59get 3y equal to 2,
00:23:01add dy by dt.
00:23:03Now I don't add dx by dt anymore.
00:23:05So we can substitute.
00:23:07dy by dt is plus 9
00:23:09because we add water.
00:23:11If we add water, it will be minus 9.
00:23:13We have to be careful.
00:23:17Part 4,
00:23:19y equal to 2,
00:23:21dy by dt.
00:23:23Notice that I don't substitute y yet.
00:23:25I'll substitute at the last term
00:23:27to add y first.
00:23:31We'll get 36.
00:23:33Part y equal to 2,
00:23:35I'll substitute at the last term
00:23:37to add y.
00:23:39y equal to
00:23:416.
00:23:43After dip,
00:23:45add term y,
00:23:47substitute y equal to 6 at the end.
00:23:51We'll get 1.
00:23:53The unit is
00:23:55foot per
00:23:57minute.
00:23:59foot per minute.
00:24:01Notice that we get
00:24:03positive value, right?
00:24:05In Internet,
00:24:07we have it in LVV2,
00:24:09but we use Google Translate.
00:24:11I don't know.
00:24:15We use Google Translate.
00:24:17For example,
00:24:19we use the word
00:24:21differentiable, right?
00:24:23We use can find,
00:24:25something like that.
00:24:27I'm not a translator.
00:24:29I'm just a TA.
00:24:33I don't know.
00:24:35I think it's used
00:24:37to translate students.
00:24:41I'm lazy, so I use
00:24:43TPT to translate.
00:24:45I have to answer the conclusion.
00:24:47The conclusion is
00:24:49the height of water
00:24:51increases or decreases?
00:24:53The height of water
00:24:55increases or decreases?
00:25:011 part
00:25:03I
00:25:05foot
00:25:07per minute
00:25:09at
00:25:11y equal to
00:25:136 feet.
00:25:23.
00:25:25.
00:25:27.
00:25:29.
00:25:31.
00:25:33.
00:25:35.
00:25:37.
00:25:39.
00:25:41.
00:25:43.
00:25:45.
00:25:47.
00:25:49.
00:25:51.
00:25:53.
00:25:55.
00:25:57.
00:25:59.
00:26:01.
00:26:03.
00:26:07.
00:26:09.
00:26:11.
00:26:13.
00:26:15.
00:26:19.
00:26:21.
00:26:23.
00:26:25.
00:26:27.
00:26:29.
00:26:31.
00:26:33.
00:26:35.
00:26:37.
00:26:39.
00:26:41.
00:26:43.
00:26:47.
00:26:49.
00:26:51.
00:26:53.
00:26:55.
00:26:57.
00:26:59.
00:27:01.
00:27:03.
00:27:05.
00:27:07.
00:27:09.
00:27:11.
00:27:13.
00:27:17.
00:27:19.
00:27:21.
00:27:23.
00:27:25.
00:27:27.
00:27:29.
00:27:31.
00:27:33.
00:27:35.
00:27:37.
00:27:39.
00:27:43.
00:27:45.
00:27:47.
00:27:49.
00:27:51.
00:27:53.
00:27:55.
00:27:57.
00:27:59.
00:28:01.
00:28:03.
00:28:05.
00:28:07.
00:28:09.
00:28:13.
00:28:15.
00:28:17.
00:28:19.
00:28:21.
00:28:23.
00:28:25.
00:28:27.
00:28:29.
00:28:31.
00:28:33.
00:28:35.
00:28:37.
00:28:41.
00:28:43.
00:28:45.
00:28:47.
00:28:49.
00:28:51.
00:28:53.
00:28:55.
00:28:57.
00:28:59.
00:29:01.
00:29:03.
00:29:07.
00:29:09.
00:29:11.
00:29:13.
00:29:15.
00:29:17.
00:29:19.
00:29:21.
00:29:23.
00:29:25.
00:29:27.
00:29:29.
00:29:31.
00:29:35.
00:29:37.
00:29:39.
00:29:41.
00:29:43.
00:29:45.
00:29:47.
00:29:49.
00:29:51.
00:29:53.
00:29:55.
00:29:57.
00:29:59.
00:30:03.
00:30:05.
00:30:07.
00:30:09.
00:30:11.
00:30:13.
00:30:15.
00:30:17.
00:30:19.
00:30:21.
00:30:23.
00:30:25.
00:30:27.
00:30:31.
00:30:33.
00:30:35.
00:30:37.
00:30:39.
00:30:41.
00:30:43.
00:30:45.
00:30:47.
00:30:49.
00:30:51.
00:30:53.
00:30:55.
00:30:59.
00:31:01.
00:31:03.
00:31:05.
00:31:07.
00:31:09.
00:31:11.
00:31:13.
00:31:15.
00:31:17.
00:31:19.
00:31:21.
00:31:23.
00:31:25.
00:31:27.
00:31:29.
00:31:31.
00:31:33.
00:31:35.
00:31:37.
00:31:39.
00:31:41.
00:31:43.
00:31:47.
00:31:49.
00:31:51.
00:31:55.
00:31:57.
00:31:59.
00:32:01.
00:32:03.
00:32:05.
00:32:07.
00:32:09.
00:32:11.
00:32:13.
00:32:15.
00:32:17.
00:32:19.
00:32:23.
00:32:25.
00:32:27.
00:32:29.
00:32:31.
00:32:33.
00:32:35.
00:32:37.
00:32:39.
00:32:41.
00:32:43.
00:32:45.
00:32:47.
00:32:51.
00:32:53.
00:32:55.
00:32:57.
00:32:59.
00:33:01.
00:33:03.
00:33:05.
00:33:07.
00:33:09.
00:33:11.
00:33:13.
00:33:15.
00:33:17.
00:33:23.
00:33:25.
00:33:27.
00:33:29.
00:33:31.
00:33:33.
00:33:35.
00:33:37.
00:33:39.
00:33:41.
00:33:43.
00:33:47.
00:33:49.
00:33:51.
00:33:53.
00:33:55.
00:33:57.
00:33:59.
00:34:01.
00:34:03.
00:34:05.
00:34:07.
00:34:09.
00:34:11.
00:34:15.
00:34:17.
00:34:19.
00:34:21.
00:34:23.
00:34:25.
00:34:27.
00:34:29.
00:34:31.
00:34:33.
00:34:35.
00:34:37.
00:34:39.
00:34:41.
00:34:43.
00:34:45.
00:34:47.
00:34:49.
00:34:51.
00:34:53.
00:34:55.
00:34:57.
00:34:59.
00:35:01.
00:35:03.
00:35:05.
00:35:07.
00:35:11.
00:35:13.
00:35:15.
00:35:17.
00:35:19.
00:35:21.
00:35:23.
00:35:25.
00:35:27.
00:35:29.
00:35:31.
00:35:33.
00:35:35.
00:35:39.
00:35:41.
00:35:43.
00:35:45.
00:35:47.
00:35:49.
00:35:51.
00:35:53.
00:35:55.
00:35:57.
00:35:59.
00:36:01.
00:36:03.
00:36:07.
00:36:09.
00:36:11.
00:36:13.
00:36:15.
00:36:17.
00:36:19.
00:36:21.
00:36:23.
00:36:25.
00:36:27.
00:36:29.
00:36:31.
00:36:35.
00:36:37.
00:36:39.
00:36:41.
00:36:43.
00:36:45.
00:36:47.
00:36:49.
00:36:51.
00:36:53.
00:36:55.
00:36:57.
00:36:59.
00:37:01.
00:37:03.
00:37:05.
00:37:07.
00:37:09.
00:37:11.
00:37:13.
00:37:15.
00:37:17.
00:37:19.
00:37:21.
00:37:23.
00:37:25.
00:37:27.
00:37:29.
00:37:31.
00:37:33.
00:37:35.
00:37:37.
00:37:39.
00:37:41.
00:37:43.
00:37:45.
00:37:47.
00:37:49.
00:37:51.
00:37:53.
00:37:57.
00:37:59.
00:38:01.
00:38:03.
00:38:05.
00:38:07.
00:38:09.
00:38:11.
00:38:13.
00:38:15.
00:38:17.
00:38:19.
00:38:21.
00:38:25.
00:38:27.
00:38:29.
00:38:31.
00:38:33.
00:38:35.
00:38:37.
00:38:39.
00:38:41.
00:38:43.
00:38:45.
00:38:47.
00:38:49.
00:38:53.
00:38:55.
00:38:57.
00:38:59.
00:39:01.
00:39:03.
00:39:05.
00:39:07.
00:39:09.
00:39:11.
00:39:13.
00:39:15.
00:39:17.
00:39:21.
00:39:23.
00:39:25.
00:39:27.
00:39:29.
00:39:31.
00:39:33.
00:39:35.
00:39:37.
00:39:39.
00:39:41.
00:39:43.
00:39:45.
00:39:47.
00:39:51.
00:39:53.
00:39:55.
00:39:57.
00:39:59.
00:40:01.
00:40:03.
00:40:05.
00:40:07.
00:40:09.
00:40:11.
00:40:13.
00:40:15.
00:40:17.
00:40:19.
00:40:21.
00:40:23.
00:40:25.
00:40:27.
00:40:29.
00:40:31.
00:40:33.
00:40:37.
00:40:39.
00:40:41.
00:40:45.
00:40:47.
00:40:49.
00:40:51.
00:40:53.
00:40:55.
00:40:57.
00:40:59.
00:41:01.
00:41:03.
00:41:05.
00:41:07.
00:41:09.
00:41:13.
00:41:15.
00:41:17.
00:41:19.
00:41:21.
00:41:23.
00:41:25.
00:41:27.
00:41:29.
00:41:31.
00:41:33.
00:41:35.
00:41:37.
00:41:41.
00:41:43.
00:41:45.
00:41:47.
00:41:49.
00:41:51.
00:41:53.
00:41:55.
00:41:57.
00:41:59.
00:42:01.
00:42:03.
00:42:05.
00:42:09.
00:42:11.
00:42:13.
00:42:15.
00:42:17.
00:42:19.
00:42:21.
00:42:23.
00:42:25.
00:42:27.
00:42:29.
00:42:31.
00:42:33.
00:42:35.
00:42:37.
00:42:39.
00:42:41.
00:42:43.
00:42:45.
00:42:47.
00:42:49.
00:42:51.
00:42:53.
00:42:55.
00:42:57.
00:42:59.
00:43:01.
00:43:03.
00:43:05.
00:43:07.
00:43:09.
00:43:11.
00:43:13.
00:43:15.
00:43:17.
00:43:19.
00:43:21.
00:43:23.
00:43:25.
00:43:27.
00:43:29.
00:43:31.
00:43:33.
00:43:35.
00:43:37.
00:43:39.
00:43:41.
00:43:43.
00:43:45.
00:43:47.
00:43:49.
00:43:51.
00:43:53.
00:43:57.
00:43:59.
00:44:01.
00:44:03.
00:44:05.
00:44:07.
00:44:09.
00:44:11.
00:44:13.
00:44:15.
00:44:17.
00:44:19.
00:44:21.
00:44:25.
00:44:27.
00:44:29.
00:44:31.
00:44:33.
00:44:35.
00:44:37.
00:44:39.
00:44:41.
00:44:43.
00:44:45.
00:44:47.
00:44:49.
00:44:51.
00:44:55.
00:44:57.
00:44:59.
00:45:01.
00:45:03.
00:45:05.
00:45:07.
00:45:09.
00:45:11.
00:45:13.
00:45:15.
00:45:17.
00:45:21.
00:45:23.
00:45:25.
00:45:27.
00:45:29.
00:45:31.
00:45:33.
00:45:35.
00:45:37.
00:45:39.
00:45:41.
00:45:43.
00:45:45.
00:45:49.
00:45:51.
00:45:53.
00:45:55.
00:45:57.
00:45:59.
00:46:01.
00:46:03.
00:46:05.
00:46:07.
00:46:09.
00:46:11.
00:46:13.
00:46:15.
00:46:17.
00:46:19.
00:46:21.
00:46:23.
00:46:25.
00:46:27.
00:46:29.
00:46:31.
00:46:33.
00:46:35.
00:46:37.
00:46:39.
00:46:41.
00:46:45.
00:46:47.
00:46:49.
00:46:51.
00:46:53.
00:46:55.
00:46:57.
00:46:59.
00:47:01.
00:47:03.
00:47:05.
00:47:07.
00:47:09.
00:47:13.
00:47:15.
00:47:17.
00:47:19.
00:47:21.
00:47:23.
00:47:25.
00:47:27.
00:47:29.
00:47:31.
00:47:33.
00:47:35.
00:47:37.
00:47:41.
00:47:43.
00:47:45.
00:47:47.
00:47:49.
00:47:51.
00:47:53.
00:47:55.
00:47:57.
00:47:59.
00:48:01.
00:48:03.
00:48:05.
00:48:09.
00:48:11.
00:48:13.
00:48:15.
00:48:17.
00:48:19.
00:48:21.
00:48:23.
00:48:25.
00:48:27.
00:48:29.
00:48:31.
00:48:33.
00:48:37.
00:48:39.
00:48:41.
00:48:43.
00:48:45.
00:48:47.
00:48:49.
00:48:51.
00:48:53.
00:48:55.
00:48:57.
00:48:59.
00:49:01.
00:49:05.
00:49:07.
00:49:09.
00:49:11.
00:49:13.
00:49:15.
00:49:17.
00:49:19.
00:49:21.
00:49:23.
00:49:25.
00:49:27.
00:49:29.
00:49:33.
00:49:35.
00:49:37.
00:49:39.
00:49:41.
00:49:43.
00:49:45.
00:49:47.
00:49:49.
00:49:51.
00:49:53.
00:49:55.
00:49:57.
00:49:59.
00:50:01.
00:50:03.
00:50:05.
00:50:07.
00:50:09.
00:50:11.
00:50:13.
00:50:15.
00:50:17.
00:50:21.
00:50:23.
00:50:25.
00:50:29.
00:50:31.
00:50:33.
00:50:35.
00:50:37.
00:50:39.
00:50:41.
00:50:43.
00:50:45.
00:50:47.
00:50:49.
00:50:51.
00:50:53.
00:50:55.
00:50:59.
00:51:01.
00:51:03.
00:51:05.
00:51:07.
00:51:09.
00:51:11.
00:51:13.
00:51:15.
00:51:17.
00:51:19.
00:51:21.
00:51:23.
00:51:29.
00:51:31.
00:51:33.
00:51:35.
00:51:37.
00:51:39.
00:51:41.
00:51:43.
00:51:45.
00:51:47.
00:51:49.
00:51:53.
00:51:55.
00:51:57.
00:51:59.
00:52:01.
00:52:03.
00:52:05.
00:52:07.
00:52:09.
00:52:11.
00:52:13.
00:52:15.
00:52:17.
00:52:21.
00:52:23.
00:52:25.
00:52:27.
00:52:29.
00:52:31.
00:52:33.
00:52:35.
00:52:37.
00:52:39.
00:52:41.
00:52:43.
00:52:45.
00:52:49.
00:52:51.
00:52:53.
00:52:55.
00:52:57.
00:52:59.
00:53:01.
00:53:03.
00:53:05.
00:53:07.
00:53:09.
00:53:11.
00:53:13.
00:53:17.
00:53:19.
00:53:21.
00:53:23.
00:53:25.
00:53:27.
00:53:29.
00:53:31.
00:53:33.
00:53:35.
00:53:37.
00:53:39.
00:53:41.
00:53:43.
00:53:47.
00:53:49.
00:53:51.
00:53:53.
00:53:55.
00:53:57.
00:53:59.
00:54:01.
00:54:03.
00:54:05.
00:54:07.
00:54:09.
00:54:13.
00:54:15.
00:54:17.
00:54:19.
00:54:21.
00:54:23.
00:54:25.
00:54:27.
00:54:29.
00:54:31.
00:54:33.
00:54:35.
00:54:37.
00:54:39.
00:54:43.
00:54:45.
00:54:47.
00:54:49.
00:54:51.
00:54:53.
00:54:55.
00:54:57.
00:54:59.
00:55:01.
00:55:03.
00:55:05.
00:55:09.
00:55:11.
00:55:13.
00:55:15.
00:55:17.
00:55:19.
00:55:21.
00:55:23.
00:55:25.
00:55:27.
00:55:29.
00:55:31.
00:55:33.
00:55:37.
00:55:39.
00:55:41.
00:55:43.
00:55:45.
00:55:47.
00:55:49.
00:55:51.
00:55:53.
00:55:55.
00:55:57.
00:55:59.
00:56:01.
00:56:05.
00:56:07.
00:56:09.
00:56:11.
00:56:13.
00:56:15.
00:56:17.
00:56:19.
00:56:21.
00:56:23.
00:56:25.
00:56:27.
00:56:29.
00:56:33.
00:56:35.
00:56:37.
00:56:39.
00:56:41.
00:56:43.
00:56:45.
00:56:47.
00:56:49.
00:56:51.
00:56:53.
00:56:55.
00:56:57.
00:56:59.
00:57:01.
00:57:03.
00:57:05.
00:57:07.
00:57:09.
00:57:11.
00:57:13.
00:57:15.
00:57:17.
00:57:19.
00:57:21.
00:57:23.
00:57:25.
00:57:29.
00:57:31.
00:57:33.
00:57:35.
00:57:37.
00:57:39.
00:57:41.
00:57:43.
00:57:45.
00:57:47.
00:57:49.
00:57:51.
00:57:53.
00:57:57.
00:57:59.
00:58:01.
00:58:03.
00:58:05.
00:58:07.
00:58:09.
00:58:11.
00:58:13.
00:58:15.
00:58:17.
00:58:19.
00:58:21.
00:58:23.
00:58:27.
00:58:29.
00:58:31.
00:58:33.
00:58:35.
00:58:37.
00:58:39.
00:58:41.
00:58:43.
00:58:45.
00:58:47.
00:58:49.
00:58:51.
00:58:53.
00:58:55.
00:58:57.
00:58:59.
00:59:01.
00:59:03.
00:59:05.
00:59:07.
00:59:09.
00:59:11.
00:59:13.
00:59:15.
00:59:17.
00:59:21.
00:59:23.
00:59:25.
00:59:27.
00:59:29.
00:59:31.
00:59:33.
00:59:35.
00:59:37.
00:59:39.
00:59:41.
00:59:43.
00:59:45.
00:59:49.
00:59:51.
00:59:53.
00:59:55.
00:59:57.
00:59:59.
01:00:01.
01:00:03.
01:00:05.
01:00:07.
01:00:09.
01:00:11.
01:00:13.
01:00:15.
01:00:17.
01:00:19.
01:00:21.
01:00:23.
01:00:25.
01:00:27.
01:00:29.
01:00:31.
01:00:33.
01:00:35.
01:00:37.
01:00:39.
01:00:41.
01:00:45.
01:00:47.
01:00:49.
01:00:51.
01:00:53.
01:00:55.
01:00:57.
01:00:59.
01:01:01.
01:01:03.
01:01:05.
01:01:07.
01:01:09.
01:01:11.
01:01:13.
01:01:15.
01:01:17.
01:01:19.
01:01:21.
01:01:23.
01:01:25.
01:01:27.
01:01:29.
01:01:31.
01:01:33.
01:01:35.
01:01:37.
01:01:39.
01:01:41.
01:01:43.
01:01:45.
01:01:47.
01:01:49.
01:01:51.
01:01:55.
01:01:57.
01:01:59.
01:02:01.
01:02:03.
01:02:07.
01:02:09.
01:02:11.
01:02:13.
01:02:15.
01:02:17.
01:02:19.
01:02:21.
01:02:23.
01:02:25.
01:02:27.
01:02:29.
01:02:31.
01:02:35.
01:02:37.
01:02:39.
01:02:41.
01:02:43.
01:02:45.
01:02:47.
01:02:49.
01:02:51.
01:02:53.
01:02:55.
01:02:57.
01:02:59.
01:03:03.
01:03:05.
01:03:07.
01:03:09.
01:03:11.
01:03:13.
01:03:15.
01:03:17.
01:03:19.
01:03:21.
01:03:23.
01:03:25.
01:03:27.
01:03:29.
01:03:33.
01:03:35.
01:03:37.
01:03:39.
01:03:41.
01:03:43.
01:03:45.
01:03:47.
01:03:49.
01:03:51.
01:03:53.
01:03:55.
01:03:59.
01:04:01.
01:04:03.
01:04:05.
01:04:07.
01:04:09.
01:04:11.
01:04:13.
01:04:15.
01:04:17.
01:04:19.
01:04:21.
01:04:23.
01:04:27.
01:04:29.
01:04:31.
01:04:33.
01:04:35.
01:04:37.
01:04:39.
01:04:41.
01:04:43.
01:04:45.
01:04:47.
01:04:49.
01:04:51.
01:04:55.
01:04:57.
01:04:59.
01:05:01.
01:05:03.
01:05:05.
01:05:07.
01:05:09.
01:05:11.
01:05:13.
01:05:15.
01:05:17.
01:05:19.
01:05:23.
01:05:25.
01:05:27.
01:05:29.
01:05:31.
01:05:33.
01:05:35.
01:05:37.
01:05:39.
01:05:41.
01:05:43.
01:05:45.
01:05:47.
01:05:49.
01:05:53.
01:05:55.
01:05:57.
01:05:59.
01:06:01.
01:06:03.
01:06:05.
01:06:07.
01:06:09.
01:06:11.
01:06:13.
01:06:15.
01:06:17.
01:06:21.
01:06:23.
01:06:25.
01:06:27.
01:06:29.
01:06:31.
01:06:33.
01:06:35.
01:06:37.
01:06:39.
01:06:41.
01:06:43.
01:06:45.
01:06:47.
01:06:49.
01:06:51.
01:06:53.
01:06:55.
01:06:57.
01:07:01.
01:07:03.
01:07:05.
01:07:07.
01:07:09.
01:07:11.
01:07:15.
01:07:17.
01:07:19.
01:07:21.
01:07:23.
01:07:25.
01:07:27.
01:07:29.
01:07:31.
01:07:33.
01:07:35.
01:07:37.
01:07:39.
01:07:43.
01:07:45.
01:07:47.
01:07:49.
01:07:51.
01:07:53.
01:07:55.
01:07:57.
01:07:59.
01:08:01.
01:08:03.
01:08:05.
01:08:07.
01:08:11.
01:08:13.
01:08:15.
01:08:17.
01:08:19.
01:08:21.
01:08:23.
01:08:25.
01:08:27.
01:08:29.
01:08:31.
01:08:33.
01:08:35.
01:08:39.
01:08:41.
01:08:43.
01:08:45.
01:08:47.
01:08:49.
01:08:51.
01:08:53.
01:08:55.
01:08:57.
01:08:59.
01:09:01.
01:09:03.
01:09:05.
01:09:09.
01:09:11.
01:09:13.
01:09:15.
01:09:17.
01:09:19.
01:09:21.
01:09:23.
01:09:25.
01:09:27.
01:09:29.
01:09:31.
01:09:35.
01:09:37.
01:09:39.
01:09:41.
01:09:43.
01:09:45.
01:09:47.
01:09:49.
01:09:51.
01:09:53.
01:09:55.
01:09:57.
01:09:59.
01:10:03.
01:10:05.
01:10:07.
01:10:09.
01:10:11.
01:10:13.
01:10:15.
01:10:17.
01:10:19.
01:10:21.
01:10:23.
01:10:25.
01:10:27.
01:10:31.
01:10:33.
01:10:35.
01:10:37.
01:10:39.
01:10:41.
01:10:43.
01:10:45.
01:10:47.
01:10:49.
01:10:51.
01:10:53.
01:10:55.
01:10:59.
01:11:01.
01:11:03.
01:11:05.
01:11:07.
01:11:09.
01:11:11.
01:11:13.
01:11:15.
01:11:17.
01:11:19.
01:11:21.
01:11:23.
01:11:27.
01:11:29.
01:11:31.
01:11:33.
01:11:35.
01:11:37.
01:11:39.
01:11:41.
01:11:43.
01:11:45.
01:11:47.
01:11:49.
01:11:51.
01:11:53.
01:11:57.
01:11:59.
01:12:01.
01:12:03.
01:12:05.
01:12:07.
01:12:09.
01:12:11.
01:12:13.
01:12:15.
01:12:17.
01:12:19.
01:12:23.
01:12:25.
01:12:27.
01:12:29.
01:12:31.
01:12:33.
01:12:35.
01:12:37.
01:12:39.
01:12:41.
01:12:43.
01:12:45.
01:12:47.
01:12:53.
01:12:55.
01:12:57.
01:12:59.
01:13:01.
01:13:03.
01:13:05.
01:13:07.
01:13:09.
01:13:11.
01:13:13.
01:13:15.
01:13:17.
01:13:19.
01:13:21.
01:13:23.
01:13:25.
01:13:27.
01:13:29.
01:13:31.
01:13:33.
01:13:35.
01:13:37.
01:13:39.
01:13:41.
01:13:43.
01:13:45.
01:13:47.
01:13:49.
01:13:51.
01:13:53.
01:13:55.
01:13:57.
01:13:59.
01:14:01.
01:14:03.
01:14:05.
01:14:07.
01:14:09.
01:14:13.
01:14:15.
01:14:17.
01:14:19.
01:14:21.
01:14:23.
01:14:25.
01:14:27.
01:14:29.
01:14:31.
01:14:33.
01:14:35.
01:14:37.
01:14:39.
01:14:41.
01:14:43.
01:14:45.
01:14:47.
01:14:49.
01:14:51.
01:14:53.
01:14:55.
01:14:57.
01:14:59.
01:15:01.
01:15:03.
01:15:05.
01:15:09.
01:15:11.
01:15:13.
01:15:15.
01:15:17.
01:15:19.
01:15:21.
01:15:23.
01:15:25.
01:15:27.
01:15:29.
01:15:31.
01:15:33.
01:15:35.
01:15:37.
01:15:39.
01:15:41.
01:15:43.
01:15:45.
01:15:47.
01:15:49.
01:15:51.
01:15:53.
01:15:55.
01:15:57.
01:15:59.
01:16:01.
01:16:05.
01:16:07.
01:16:09.
01:16:11.
01:16:13.
01:16:15.
01:16:17.
01:16:19.
01:16:21.
01:16:23.
01:16:25.
01:16:27.
01:16:29.
01:16:33.
01:16:35.
01:16:37.
01:16:39.
01:16:41.
01:16:43.
01:16:45.
01:16:47.
01:16:49.
01:16:51.
01:16:53.
01:16:55.
01:16:57.
01:17:01.
01:17:03.
01:17:05.
01:17:07.
01:17:09.
01:17:11.
01:17:13.
01:17:15.
01:17:17.
01:17:19.
01:17:21.
01:17:23.
01:17:25.
01:17:29.
01:17:31.
01:17:33.
01:17:35.
01:17:37.
01:17:39.
01:17:41.
01:17:43.
01:17:45.
01:17:47.
01:17:49.
01:17:51.
01:17:53.
01:17:55.
01:17:59.
01:18:01.
01:18:03.
01:18:05.
01:18:07.
01:18:09.
01:18:11.
01:18:13.
01:18:15.
01:18:17.
01:18:19.
01:18:21.
01:18:25.
01:18:27.
01:18:29.
01:18:31.
01:18:33.
01:18:35.
01:18:37.
01:18:39.
01:18:41.
01:18:43.
01:18:45.
01:18:47.
01:18:49.
01:18:53.
01:18:55.
01:18:57.
01:18:59.
01:19:01.
01:19:03.
01:19:05.
01:19:07.
01:19:09.
01:19:11.
01:19:13.
01:19:15.
01:19:17.
01:19:19.
01:19:21.
01:19:23.
01:19:25.
01:19:27.
01:19:29.
01:19:31.
01:19:33.
01:19:35.
01:19:37.
01:19:39.
01:19:41.
01:19:43.
01:19:45.
01:19:49.
01:19:51.
01:19:53.
01:19:55.
01:19:57.
01:19:59.
01:20:01.
01:20:03.
01:20:05.
01:20:07.
01:20:09.
01:20:11.
01:20:13.
01:20:17.
01:20:19.
01:20:21.
01:20:23.
01:20:25.
01:20:27.
01:20:29.
01:20:31.
01:20:33.
01:20:35.
01:20:37.
01:20:39.