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205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:40:02 | Recall that we are dealing with magnitudes | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:40:09 | So it will definitely be positive | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:40:12 | So m^2 | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:40:14 | m^3 | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:40:14 | etc | 0 | 1 | 644,866,111,505,956,900 | BLACK1 | 3122 | BLACK1 | false | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:40:19 | all positive | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:40:29 | why not just do the normal expansion for each | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:40:31 | The reason I didn't differentiate M | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:40:39 | is because it was hard to simplify that | 0 | 1 | 706,934,233,012,371,600 | Ansh_ | 3502 | Arya | false | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:40:40 | look | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:41:10 | don't you have to do implicit differentatino now | 1 | 0 | 644,866,111,505,956,900 | BLACK1 | 3122 | BLACK1 | false | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:42:38 | No | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:42:44 | Implicit differentiate not necessary | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:42:57 | or are we going to move the square roto to the other side | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:43:03 | wouldn't that still be alot harder? | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:44:10 | Chain rule | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:44:28 | $$f(g(x)) = f'(g(x))g'(x)$$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 18:44:31 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:44:59 | so how are we going to deal with the M^2 ? | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:45:15 | What do you mean? | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:45:20 | Ohh | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:45:39 | Find $\frac{dM^2}{d\theta}$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 18:45:43 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:46:09 | Because $M >0$, if you square all values the maximum will still occur at the same $\theta$ point! | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:46:55 | I frogot how can we check wther something is max and min | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 18:47:02 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:47:12 | You don't need to in this example | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:47:32 | Just plug in the $\theta$ values which make $\frac{dM^2}{d\theta}=0$ into $|e^{i\theta} -2| + |e^{i\theta} + 2|$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 18:48:02 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:48:22 | The one which gives you the largest value is the maximum | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:49:07 | image.png | 1 | 0 | 734,628,928,420,839,600 | Anticipation | 0902 | Anticipation | false | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:49:31 | you differentiated wrong | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:50:15 | What is $\frac{d}{d\theta}25 - 16\cos^2(\theta)$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 18:50:17 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:52:03 | isn't that 32sin(theta) | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:52:14 | Nope | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:52:18 | i mean 32sincs(theta) | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:52:22 | 32sincos(theta) | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:52:47 | yes $32\sin(\theta)\cos(\theta)$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 18:52:49 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:53:39 | image.png | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:54:07 | 🤔 | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:54:24 | what did i do wrong? | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:54:40 | What values of $\theta$ make $\sin(2\theta) = 0$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 18:54:42 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:54:45 | from 0 to 2pi | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:55:54 | pi/2, 2pi + pi/2 | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:56:02 | 3pi/2 | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 536,452,419,219,882,000 | DontalRulz | 01/29/2022 18:56:06 | Double derivative I’m pretty sure | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:56:07 | and then divide by 2 | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:56:27 | what about 0? | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:56:42 | yeah | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:56:46 | theta = 0 | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:56:48 | pi | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:56:49 | 2pi | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:56:50 | 3pi | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:58:09 | So you should have $\theta = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 18:58:12 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:58:22 | yeah | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:58:25 | but which one should we use? | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:58:31 | Plug them all in | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:58:34 | to | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:59:00 | $M(\theta)= |e^{i\theta} -2| + |e^{i\theta} + 2|$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 18:59:10 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 18:59:48 | and see which gives you the largest number on this list | unknown.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:59:53 | wouldn't that just be 1 + 3 | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 18:59:54 | so 4 | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:00:21 | You've subbed in theta = 0 | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 19:00:21 | but what about the other values of theta? | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:00:22 | i presume | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:00:25 | try the others | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:00:40 | $M(0) = 4$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 19:00:50 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:01:12 | What is $M(\frac{\pi}{2})$? | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 19:01:22 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 19:01:25 | that's 10 | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:01:46 | 🤔 | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 19:02:05 | 2root(5) | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:02:19 | :catthumbsup: | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:02:21 | you've got it | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 19:02:28 | thanks that helped alot | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:02:31 | Now do you understand how we got the answer | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:02:41 | do you understand all the workings | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:02:43 | The M^2 | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:02:44 | etc | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 19:02:45 | yeah | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 19:02:52 | so can we graph it? | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:03:09 | Graph it? | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 19:04:04 | okay thanks i get it | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:04:57 | Notice that if $M$ had values that were $<0$. We would have to be careful with $M^2$ because squaring the largest negative will make it larger the largest positive | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 19:05:00 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:05:01 | if that makes sense | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 872,024,354,572,103,700 | <><><> | 01/29/2022 19:05:45 | But since $ |e^{i\theta} -2| + |e^{i\theta} + 2$ are magnitudes. We don't have to worry about this problem. Because it will always be $>0$ | 0 | 1 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 510,789,298,321,096,700 | TeXit | 01/29/2022 19:05:48 | **azeem321** | 872024354572103731.png | 0 | 1 | null | null | null | null | null | ||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 19:17:08 | okay thanks | 1 | 0 | null | null | null | null | null | |||||
205,745 | help-1 | 7b52abb03fb7407db36920ea05f5564f | 475,966,350,322,303,000 | Brightness | 01/29/2022 19:17:09 | .close | 1 | 0 | null | null | null | null | null | |||||
205,746 | help-1 | 3055db4fe95b4eed8fdd35e11f8e5b75 | 217,248,583,227,801,600 | itsalivenger | 01/29/2022 19:40:38 | hiii i just don't understand the definition of a limit can someone explain it i mean with example | 1 | 0 | null | null | null | null | null | |||||
205,746 | help-1 | 3055db4fe95b4eed8fdd35e11f8e5b75 | 217,248,583,227,801,600 | itsalivenger | 01/29/2022 19:40:55 | am talking about limit for sequences | 1 | 0 | 161,888,429,980,778,500 | Simon Petrikov | 9097 | Simon Petrikov | false | |||||
205,746 | help-1 | 3055db4fe95b4eed8fdd35e11f8e5b75 | 217,248,583,227,801,600 | itsalivenger | 01/29/2022 19:40:59 | AND functions | 1 | 0 | null | null | null | null | null | |||||
205,746 | help-1 | 3055db4fe95b4eed8fdd35e11f8e5b75 | 521,445,300,989,198,340 | WHAT? | 01/29/2022 19:41:03 | Have you seen a picture? | 0 | 1 | null | null | null | null | null |
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