• 2 months ago
Transcript
00:00:00So, let us recap what we have learnt in the previous class.
00:00:12In the previous class, we have learnt how to joke two vectors.
00:00:24In the previous class, we have learnt how to joke two vectors in the form of i and j.
00:00:38For example, there was a vector a, 5i plus 2j and another vector b, 2i plus 6j.
00:00:45In the previous class, we have learnt how to joke two vectors in the form of i, 5i plus 2j and another vector b, 2i plus 6j.
00:01:09In the previous class, we have learnt how to joke two vectors in the form of i and j.
00:01:22In the previous class, we have learnt how to joke two vectors in the form of i and j.
00:01:36In the previous class, we have learnt how to joke two vectors in the form of i, 5i plus 2j and another vector b, 2i plus 6j.
00:01:43In the previous class, we have learnt how to joke two vectors in the form of i, 5i plus 2j and another vector b, 2i plus 6j.
00:01:53The sum of the equal parts of the two vectors is equal to the sum of the equal parts of the two vectors.
00:02:04The sum of the equal parts of the two vectors is equal to the sum of the equal parts of the two vectors.
00:02:16Do you remember everything up to this point?
00:02:23Wonderful!
00:02:25Thank you very much, Jack.
00:02:29Very good.
00:02:31Brother, give me career advice.
00:02:35Study now.
00:02:37Study now.
00:02:39In the next two years, you will not worry about anything except studying.
00:02:44This is an I.Q. question for you.
00:02:47The concepts that we have learnt in the previous class,
00:02:50how to joke two vectors in the form of i and j,
00:02:55we have to apply those concepts to solve this problem.
00:03:03A, B, C is a vector.
00:03:07A, B, C is a vector.
00:03:12A, B, C is a vector.
00:03:15A, B, C is a vector.
00:03:17A, B, C is a vector.
00:03:20A, B, C is a vector.
00:03:23How much is the value of O C?
00:03:26How much is the value of O C?
00:03:29How much is the value of O C?
00:03:32Show me.
00:03:33Tell me.
00:03:34How much is the value of O C?
00:03:38These are very good questions for the objective.
00:03:41What did you do?
00:03:44Some people did this.
00:03:46Very good.
00:03:47I was trying to make a mistake like this.
00:03:49Unbelievable.
00:03:50See this.
00:03:51What did many people do?
00:03:52Many people did this.
00:03:53A, B is a bash.
00:03:56A, B is a bash.
00:03:57What is A, B?
00:03:58A, B is 2 i cap minus 6 j cap plus 6 k cap.
00:04:03Plus 6 k cap.
00:04:04This is a vector.
00:04:05This is a bash.
00:04:07You want a bash.
00:04:09Let's divide this by 2.
00:04:11If I divide this by 2,
00:04:14If I divide this by 2,
00:04:173 j plus 3 k.
00:04:21Many people gave this answer.
00:04:23First, we want the value of O C vector.
00:04:28We want the value of this vector.
00:04:31Now, many people give this as an answer.
00:04:35They say, is this vector actually an O C vector?
00:04:39They say, is this vector actually an O C vector?
00:04:42No.
00:04:43Why not?
00:04:44Because A, B vector was equal to this.
00:04:47This is A, B vector.
00:04:49If we divide this by 2,
00:04:52we will get a vector like this.
00:04:54We will get a vector like this.
00:04:57So, keep this in mind.
00:04:59It is easy for us to get the value of O C.
00:05:03No problem.
00:05:04But, if we wanted to get the value of O C,
00:05:09we would never get the value of O C
00:05:12if we divide A, B by 2.
00:05:15Because, if we divide A, B by 2,
00:05:19we will get the same value.
00:05:22We will get the value of O A and O C.
00:05:25This is right.
00:05:26No problem.
00:05:27But, many people give this as an answer.
00:05:29This will not be the answer.
00:05:31This will not be the answer.
00:05:33Now, what should we do?
00:05:35It is easy.
00:05:37Before everything,
00:05:40we want to get the value of this vector.
00:05:45If we want to get the value of this vector,
00:05:53value is equal to
00:05:55square root of 2 E square plus
00:05:58minus 6 E square plus 6 E square.
00:06:01Then, we will get the value of this vector.
00:06:04We will get the value of this vector.
00:06:07Square root of 4 Jog 36 Jog 36
00:06:09is equal to 8.72.
00:06:118.72.
00:06:13It can be any acre.
00:06:15I have taken acre meter.
00:06:17Then, O C is a vector.
00:06:20O C is a vector.
00:06:22What is the value of this vector?
00:06:24What is the value of the value of this vector?
00:06:27This value is equal to
00:06:29half of this.
00:06:31How much is this?
00:06:328.72.
00:06:33This is equal to 4.35.
00:06:35This is equal to 4.36.
00:06:39This is equal to 4.36.
00:06:41Is it correct?
00:06:43Ok.
00:06:45Then,
00:06:47take care of this.
00:06:49Now, everything is clear.
00:06:51Then, the point I want to emphasize here is
00:06:55that AB vector
00:06:57is equal to
00:06:59O C.
00:07:01In many cases,
00:07:03if you want to divide O C by 2,
00:07:05then you have to divide it by 2.
00:07:08Yes.
00:07:09If you divide it by 2
00:07:11and if you multiply it,
00:07:13then ultimately O C will be multiplied.
00:07:15There is no problem.
00:07:16But, there is a small conceptual barrier.
00:07:20I am saying this to clear it.
00:07:22The AB vector
00:07:24is equal to
00:07:26A to B.
00:07:28This is what I am trying to emphasize.
00:07:30This is what I am trying to emphasize.
00:07:32If you divide it by half,
00:07:34you will get A O vector.
00:07:36You will not get O C vector.
00:07:38Yes.
00:07:39If you divide it by half,
00:07:41you will get A O vector.
00:07:43You will not get O C vector.
00:07:45There is no problem.
00:07:47But, take care of this.
00:07:49If you divide it by half,
00:07:51you will get O A vector.
00:07:53If you divide it by half,
00:07:55you will get O A vector.
00:07:57Very good.
00:08:27Yes.
00:08:28If you divide it by half,
00:08:30you will get O A vector.
00:08:32Yes.
00:08:33If you divide it by half,
00:08:35you will get O A vector.
00:08:37Yes.
00:08:38If you divide it by half,
00:08:40you will get O A vector.
00:08:42Yes.
00:08:43If you divide it by half,
00:08:45you will get O A vector.
00:08:47Yes.
00:08:48If you divide it by half,
00:08:50you will get O A vector.
00:08:52Yes.
00:08:53If you divide it by half,
00:08:55you will get O A vector.
00:08:57Yes.
00:08:58If you divide it by half,
00:09:00you will get O A vector.
00:09:02Yes.
00:09:03If you divide it by half,
00:09:05you will get O A vector.
00:09:07Yes.
00:09:08If you divide it by half,
00:09:10you will get O A vector.
00:09:12Yes.
00:09:13If you divide it by half,
00:09:15you will get O A vector.
00:09:17Yes.
00:09:18If you divide it by half,
00:09:20you will get O A vector.
00:09:22Yes.
00:09:23If you divide it by half,
00:09:25you will get O A vector.
00:09:27Yes.
00:09:28If you divide it by half,
00:09:30you will get O A vector.
00:09:32Yes.
00:09:33If you divide it by half,
00:09:35you will get O A vector.
00:09:37Yes.
00:09:38If you divide it by half,
00:09:40you will get O A vector.
00:09:42Yes.
00:09:43If you divide it by half,
00:09:45you will get O A vector.
00:09:47Yes.
00:09:48If you divide it by half,
00:09:50you will get O A vector.
00:09:52Yes.
00:09:53If you divide it by half,
00:09:55you will get O A vector.
00:09:57Yes.
00:09:58If you divide it by half,
00:10:00you will get O A vector.
00:10:02Yes.
00:10:03If you divide it by half,
00:10:05you will get O A vector.
00:10:07Yes.
00:10:08If you divide it by half,
00:10:10you will get O A vector.
00:10:12Yes.
00:10:13If you divide it by half,
00:10:15you will get O A vector.
00:10:17Yes.
00:10:18If you divide it by half,
00:10:20you will get O A vector.
00:10:22Yes.
00:10:23If you divide it by half,
00:10:25you will get O A vector.
00:10:27Yes.
00:10:28If you divide it by half,
00:10:30you will get O A vector.
00:10:32Yes.
00:10:33If you divide it by half,
00:10:35you will get O A vector.
00:10:37Yes.
00:10:38If you divide it by half,
00:10:40you will get O A vector.
00:10:42Yes.
00:10:43If you divide it by half,
00:10:45you will get O A vector.
00:10:47Yes.
00:10:48If you divide it by half,
00:10:50you will get O A vector.
00:10:52Yes.
00:10:53If you divide it by half,
00:10:55you will get O A vector.
00:10:57Yes.
00:10:58If you divide it by half,
00:11:00you will get O A vector.
00:11:02Yes.
00:11:03If you divide it by half,
00:11:05you will get O A vector.
00:11:07Yes.
00:11:08If you divide it by half,
00:11:10you will get O A vector.
00:11:12Yes.
00:11:13If you divide it by half,
00:11:15you will get O A vector.
00:11:17Yes.
00:11:18If you divide it by half,
00:11:20you will get O A vector.
00:11:22Yes.
00:11:23If you divide it by half,
00:11:25you will get O A vector.
00:11:27Yes.
00:11:28If you divide it by half,
00:11:30you will get O A vector.
00:11:32Yes.
00:11:33If you divide it by half,
00:11:35you will get O A vector.
00:11:37Yes.
00:11:38If you divide it by half,
00:11:40you will get O A vector.
00:11:42Yes.
00:11:43If you divide it by half,
00:11:45you will get O A vector.
00:11:47Yes.
00:11:48If you divide it by half,
00:11:50you will get O A vector.
00:11:52Yes.
00:11:53If you divide it by half,
00:11:55you will get O A vector.
00:11:57Yes.
00:11:58If you divide it by half,
00:12:00you will get O A vector.
00:12:02Yes.
00:12:03If you divide it by half,
00:12:05you will get O A vector.
00:12:07Yes.
00:12:08If you divide it by half,
00:12:10you will get O A vector.
00:12:12Yes.
00:12:14This is a very difficult question.
00:12:16You must be thinking,
00:12:18why did you eat 10 seconds?
00:12:20This is a very difficult question.
00:12:22This vector,
00:12:23how many points does it have with Y?
00:12:25This is a very difficult question.
00:12:27Y means,
00:12:28how many points does it have with Y?
00:12:30This is a very difficult question.
00:12:32This is a very difficult question.
00:12:34What happens after minus 3?
00:12:36What happens after minus 3?
00:12:38What happens after minus 3?
00:12:40Do you understand the question?
00:12:42Do you understand the question?
00:12:44We were told,
00:12:45we were told,
00:12:46two vectors,
00:12:47one vector is A,
00:12:49this is A,
00:12:50this is A,
00:12:51the vector in pink color,
00:12:52this is A,
00:12:53there are two derivatives of A vector.
00:12:55One is,
00:12:56X is equal to 5,
00:12:57X is equal to 5,
00:12:59and Y is equal to minus 3.
00:13:01Y is equal to minus 3,
00:13:02plus 3 is minus 3.
00:13:03plus 3 is minus 3.
00:13:04When we know the derivatives of a vector,
00:13:06when we know the derivatives of a vector,
00:13:08can't we find the original vector?
00:13:10Yes, we can.
00:13:12When we know the derivatives of a vector,
00:13:14can't we find the original vector?
00:13:16Can't we find the original vector?
00:13:18You have understood it.
00:13:20Very good.
00:13:21So,
00:13:22So,
00:13:23see,
00:13:24so,
00:13:25see,
00:13:26see,
00:13:27see,
00:13:28see,
00:13:29so,
00:13:30so,
00:13:31see,
00:13:32see,
00:13:33see,
00:13:34see,
00:13:35see,
00:13:36see,
00:13:37see,
00:13:38see,
00:13:39see,
00:13:40I am just thinking of it like this, two arms of a tribune, one arm is 5 acres and the other arm is 3 acres.
00:13:46What? One arm is 5 acres and the other arm is 3 acres.
00:13:49So, look, at the time of tan theta, is it long by earth?
00:13:52Long by earth. So, 3 by 5.
00:13:54So, how much is theta?
00:13:56Theta will be tan inverse 3 by 5.
00:13:59Tan inverse 3 by 5.
00:14:01Let's see how much it is.
00:14:02Tan inverse 3 by 5.
00:14:04How much is this?
00:14:0530 decimal 9 6.
00:14:0730 decimal 9 6 has come, little friends.
00:14:0930 decimal 9 6.
00:14:11Do 9 6 with me.
00:14:13Theta is 30 decimal 9 6.
00:14:15Now, do we want this angle?
00:14:17Do we want this angle?
00:14:18No, we want the angle.
00:14:19We want the angle with this y-axis.
00:14:21The angle with y-axis.
00:14:22So, how much will be the angle with y-axis?
00:14:25Plus the angle with y-axis.
00:14:28Plus the angle with y-axis.
00:14:33Equal.
00:14:3430 decimal 9 6 will be there.
00:14:3630 decimal 9 6 will be there.
00:14:37We have to add 90 degree with it.
00:14:3990 degree with it.
00:14:41So, 120 decimal 9 6.
00:14:43120 decimal 9 6 degree.
00:14:45Very good.
00:14:47You have got it.
00:14:49Yes.
00:14:51Good.
00:14:52120 decimal 9 6.
00:14:53Why don't you give minus 3?
00:14:57I don't understand.
00:14:58Minus 3.
00:14:59Why don't you give minus?
00:15:00Okay.
00:15:01Because, see.
00:15:02What did the minus understand?
00:15:03The minus understood that the angle with y-axis is equal to 3.
00:15:08Now, what did we do?
00:15:11We have this triangle.
00:15:14Do I know the angle with this y-axis?
00:15:18I know the angle with this y-axis.
00:15:20So, when I can find the angle with both the y-axis,
00:15:23then it is easy for me to find this angle.
00:15:26Here, by giving minus, we are giving minus for the negative angle.
00:15:31We are giving minus for the negative angle.
00:15:34Okay?
00:15:35So, if we have a triangle.
00:15:37If we have a triangle,
00:15:38if we say that this side is 5 acres and this side is 3 acres,
00:15:42then how much will be the value of theta?
00:15:44So, what did we do?
00:15:45Couldn't we get 10 theta?
00:15:47So, in the same way,
00:15:48it understood that minus 3 is the angle with minus.
00:15:51Then, we understood that the vector is in this angle.
00:15:56Then, what is the value of the angle?
00:16:00Then, 10 theta is equal to 3 by 5.
00:16:05Now, did you understand?
00:16:07Now, did you understand?
00:16:10Why is it 10?
00:16:12This is a very difficult question.
00:16:14Why is it 10?
00:16:15If you have a class 9-10 student around you,
00:16:18then you can ask him.
00:16:20Brother, when there is a length here,
00:16:23when there is a length,
00:16:25then which trigonometric function do we use?
00:16:29This is what is around class 9-10.
00:16:31You can ask him.
00:16:33Is it clear?
00:16:34Okay.
00:16:35This is a tera-long object.
00:16:38What is 10 theta?
00:16:39It is not length by area.
00:16:41Is 10 theta equal to length by area?
00:16:43What is length?
00:16:44The opposite of theta is length.
00:16:46So, the opposite of theta is length and this is area.
00:16:49It is easy.
00:16:5010 theta is equal to length by area.
00:16:51That's it.
00:16:52So, we did length by area.
00:16:54Now, theta is equal to tan inverse 3 by 5.
00:16:58How can we do it?
00:16:59Tan inverse 3 by 5.
00:17:00Let me show you a calculator.
00:17:02Okay.
00:17:03So, tan inverse 3 by 5.
00:17:05Do you have a calculator?
00:17:07Do you have a calculator?
00:17:09Do you understand?
00:17:11No.
00:17:12To say y-axis,
00:17:13positive and negative of y should be 2.
00:17:15But if you mention the answer with positive y-axis,
00:17:18then you don't have to say 2 answers.
00:17:20Do you understand?
00:17:21Yes.
00:17:22See.
00:17:23How can we do tan inverse?
00:17:25Shift and then tan.
00:17:27See, it is written tan inverse in turquoise color.
00:17:30See, it is written tan inverse in turquoise color.
00:17:32So, shift and then tan.
00:17:34What is the answer?
00:17:35Tan inverse.
00:17:36Then, 3 divided by 5.
00:17:38Close the bracket.
00:17:40What is the answer?
00:17:4130.963.
00:17:4330.963.
00:17:45Do you understand?
00:17:47Yes.
00:17:48Okay.
00:17:49This calculator is a bit small.
00:17:51So, it is the same thing.
00:17:53See, it is written tan inverse and then 3 divided by 5.
00:17:56We will see a few more things in the calculator.
00:17:58So, I have kept the calculator open.
00:18:00So, it is easy.
00:18:02Good.
00:18:03Now, let's move to the next problem.
00:18:05This is a very basic question.
00:18:07Tell me.
00:18:09What is this?
00:18:11In ABC tribhuj,
00:18:14the middle points of AB and AC are E and F.
00:18:18What did I say?
00:18:19ABC is a tribhuj.
00:18:21Can you see?
00:18:22ABC is a tribhuj.
00:18:23In ABC tribhuj,
00:18:24E is the middle point of AB
00:18:27and F is the middle point of AC.
00:18:30So,
00:18:31how many vectors are there in E and F?
00:18:34We are told
00:18:35how many vectors are there in B and C?
00:18:37How many vectors are there in B and C?
00:18:39For this,
00:18:40you have to get a formula.
00:18:42I remember that there was a formula like this.
00:18:45If the middle point of a tribhuj is
00:18:47the simple line connecting the two middle points,
00:18:50that is,
00:18:51the upper half of the tribhuj.
00:18:53Right?
00:18:54Yes.
00:18:55Good.
00:18:56So, what do we have to do here?
00:18:57We have to find the value of E and F.
00:18:59How much is the value of E and F?
00:19:02We have to find the value of E and F.
00:19:03Root of r
00:19:044 e square
00:19:06plus
00:19:07minus 2 e square
00:19:08plus
00:19:09It is not necessary to add minus 2 here.
00:19:11Plus 5 e square.
00:19:12So, how much is this?
00:19:13How much is the value of E and F?
00:19:154, 4, 16, 2, 2, 4, 25
00:19:18Root of r
00:19:196.70
00:19:216.71
00:19:23So, how much is the value of E and F?
00:19:24How much is the value of B and C?
00:19:26B and C are equal to
00:19:282 into E F
00:19:302 into
00:19:326.71
00:19:34So, how much is the value of this?
00:19:36If we multiply by 2,
00:19:37we get
00:19:3813, 10, 11, 4, 1
00:19:4013, 10, 11, 4, 2
00:19:42It is like this.
00:19:444, 1, 6
00:19:454, 1, 6, 4, 2
00:19:464, 1, 6, 4, 2
00:19:48It is very easy.
00:19:50It is very easy.
00:19:52Is there anything written on Facebook?
00:19:54Is there anything written on Facebook?
00:19:56Yes, there is. I can see.
00:19:58Ok.
00:20:00Now, let's come to
00:20:02the next
00:20:04very important problem.
00:20:06It is a very conceptual problem.
00:20:08Before seeing this,
00:20:10let's see a small theory.
00:20:12Let's see.
00:20:14What we have studied so far is
00:20:16that if
00:20:18we have two vectors like this,
00:20:20then the topics and
00:20:22problems will be very fun.
00:20:24It will be very enjoyable.
00:20:26You will see that after studying this,
00:20:28you will not want to eat biryani.
00:20:30It will be like, if someone asks you
00:20:32if you want to eat biryani,
00:20:34then you will say no.
00:20:36Let me do some vector math.
00:20:38Do you understand? It is so much fun.
00:20:40If we have
00:20:42two vectors like this,
00:20:442i plus 3j
00:20:46and 4i
00:20:48plus 9j.
00:20:50If we have two vectors like this,
00:20:52then
00:20:54what did we do?
00:20:56For a plus b,
00:20:58we added i's,
00:21:006i cap,
00:21:02and j's, 12j cap.
00:21:04This is what we did.
00:21:06Now,
00:21:08the point is
00:21:10that
00:21:12we will not be happy
00:21:14all the time.
00:21:16Will we be happy all the time?
00:21:18Will you be able to
00:21:20light this vector beautifully
00:21:22in ij format?
00:21:24Will you be able to light a vector
00:21:26with the help of another vector?
00:21:28Will you be happy all the time?
00:21:30No, you will not.
00:21:32You will have problems,
00:21:34you will have sorrows.
00:21:36You will be told that
00:21:38x-axis is 30 degrees to the east,
00:21:4010 meters.
00:21:42From there,
00:21:443 kilometers to the south,
00:21:4630 degrees to the west.
00:21:48In this way,
00:21:50you will be told
00:21:52about the vectors.
00:21:54For example,
00:21:56you will be told
00:21:58that a vector,
00:22:00suppose,
00:22:02y-axis is 30 degrees to the east,
00:22:04which is 10 newtons.
00:22:06For example,
00:22:08you will be told about a force.
00:22:10How is the force applied?
00:22:12It is applied to both the sides.
00:22:14Suppose,
00:22:16the value of a vector is 10 newtons.
00:22:18Suppose,
00:22:20the value of a ball is 10 newtons.
00:22:22It is 30 degrees to the east.
00:22:24How is it?
00:22:26It is 30 degrees to the east.
00:22:28Now,
00:22:30this vector
00:22:32is written in ij format.
00:22:34Is this vector
00:22:36written in ij format?
00:22:38Both the sides are given.
00:22:40Both the sides are given.
00:22:42But, we are not given
00:22:44such a beautiful formula.
00:22:46We are given a vector
00:22:48which is 10 newtons
00:22:50and it is 30 degrees to the east.
00:22:52This is how it is given.
00:22:54In this way,
00:22:56suppose,
00:22:58we have one vector.
00:23:00Suppose,
00:23:02we have another vector.
00:23:04Suppose,
00:23:06we have another force
00:23:08which is 20 newtons.
00:23:10Suppose,
00:23:12its angle is 6 degrees.
00:23:14Now, you decide to apply
00:23:16both the vectors.
00:23:18Now, you decide to apply
00:23:20both the vectors.
00:23:22It is not so easy to apply
00:23:24both the vectors.
00:23:26But, since we have two vectors,
00:23:28we can easily apply the equation.
00:23:30Suppose,
00:23:32we have to apply the equation.
00:23:34Suppose,
00:23:36we have to find the angle
00:23:38between the two vectors.
00:23:40Suppose, the angle is 90 degrees.
00:23:42Suppose, the angle is 90 degrees.
00:23:44We can apply the equation.
00:23:46We can easily find the angle
00:23:48between the two vectors.
00:23:50We can also find the angle
00:23:52between the two sides.
00:23:54But,
00:23:56if I can find the formula
00:23:58which is 2pi plus 9j.
00:24:00If I can find the formula
00:24:02which is 2pi plus 9j.
00:24:04If I can find the formula
00:24:06which is 2pi plus 9j.
00:24:08If I can find the formula
00:24:10which is 2pi plus 9j.
00:24:12If I can find the formula
00:24:14which is 2pi plus 9j.
00:24:16If I can find the formula
00:24:18which is 2pi plus 9j.
00:24:20If I can find the formula
00:24:22which is 2pi plus 9j.
00:24:24If I can find the formula
00:24:26which is 2pi plus 9j.
00:24:28If I can find the formula
00:24:30which is 2pi plus 9j.
00:24:32If I can find the formula
00:24:34which is 2pi plus 9j.
00:24:36If I can find the formula
00:24:38which is 2pi plus 9j.
00:24:40If I can find the formula
00:24:42which is 2pi plus 9j.
00:24:44If I can find the formula
00:24:46which is 2pi plus 9j.
00:24:48If I can find the formula
00:24:50which is 2pi plus 9j.
00:24:52If I can find the formula
00:24:54which is 2pi plus 9j.
00:24:56If I can find the formula
00:24:58which is 2pi plus 9j.
00:25:00If I can find the formula
00:25:02which is 2pi plus 9j.
00:25:04If I can find the formula
00:25:06which is 2pi plus 9j.
00:25:08If I can find the formula
00:25:10which is 2pi plus 9j.
00:25:12If I can find the formula
00:25:14which is 2pi plus 9j.
00:25:16If I can find the formula
00:25:18which is 2pi plus 9j.
00:25:20If I can find the formula
00:25:22which is 2pi plus 9j.
00:25:24If I can find the formula
00:25:26which is 2pi plus 9j.
00:25:28If I can find the formula
00:25:30which is 2pi plus 9j.
00:25:32If I can find the formula
00:25:34which is 2pi plus 9j.
00:25:36If I can find the formula
00:25:38which is 2pi plus 9j.
00:25:40If I can find the formula
00:25:42which is 2pi plus 9j.
00:25:44If I can find the formula
00:25:46which is 2pi plus 9j.
00:25:48If I can find the formula
00:25:50which is 2pi plus 9j.
00:25:52If I can find the formula
00:25:54which is 2pi plus 9j.
00:25:56If I can find the formula
00:25:58which is 2pi plus 9j.
00:26:00If I can find the formula
00:26:02which is 2pi plus 9j.
00:26:04If I can find the formula
00:26:06which is 2pi plus 9j.
00:26:08If I can find the formula
00:26:10which is 2pi plus 9j.
00:26:12If I can find the formula
00:26:14which is 2pi plus 9j.
00:26:16If I can find the formula
00:26:18which is 2pi plus 9j.
00:26:20If I can find the formula
00:26:22which is 2pi plus 9j.
00:26:24If I can find the formula
00:26:26which is 2pi plus 9j.
00:26:28If I can find the formula
00:26:30which is 2pi plus 9j.
00:26:32If I can find the formula
00:26:34which is 2pi plus 9j.
00:26:36If I can find the formula
00:26:38which is 2pi plus 9j.
00:26:40If I can find the formula
00:26:42which is 2pi plus 9j.
00:26:44If I can find the formula
00:26:46which is 2pi plus 9j.
00:27:16.
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