#help-19

1 messages · Page 4 of 1

delicate rover
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So for the first fraction x 2

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Then add them

manic niche
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oh okay, i get that

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thank you!

delicate rover
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Yw

manic niche
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.close

odd edgeBOT
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Available help channel!

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clear tree
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Can someone explain to me how we got square root of 2

questions.png
odd edgeBOT
quasi sparrow
odd edgeBOT
#

@clear tree Has your question been resolved?

odd edgeBOT
#
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Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

verbal hound
#

Just started learning Matrix but Teacher wont explain things normally
i still cant understand how this

firefox_XQP2JjTaXb.png
odd edgeBOT
verbal hound
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become this

firefox_gF78vO5ZUW.png
wooden python
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factor out 10 from the first row

verbal hound
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i got only that

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what about other stuff?

swift rock
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row operations

verbal hound
swift rock
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teacher didnt teach row operations? they are quite important

verbal hound
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whole class is confused

wooden python
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oh shit i did not notice the other rows

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this sounds like something that should be broken into several steps tbh

swift rock
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yeah , take common and then do row operations instead of in 1 step

verbal hound
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https://www.youtube.com/watch?v=fvQ013dZb9c
this video helped me alot to understand what is matrix and how to find determinant

YouTube
3Blue1Brown Русский
Детерминант | Сущность Линейной Алгебры, глава 5

Детерминант линейной трансформации есть мера того насколько площади/объемы изменяются в этой трансформации.

Оригинал: http://3b1b.co/eola

Подобные видео финансируются сообществом через Patreon.
Там вы сможете получить доступ к новым видео раньше всех.
http://3b1b.co/support

3blue1brown это канал с анимированной математикой...

▶ Play video
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Teacher didnt even mention anything about using matrix in spaces

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From all the classes in the University, math sucks as hell

wooden python
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а, так вы по-русски говорите?

verbal hound
wooden python
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the rule is not strict

verbal hound
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Makes sense

wooden python
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actually is there even a rule about this?

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no i don't see it

verbal hound
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just read them, apparently no

wooden python
# verbal hound become this

так что, между этими двумя определителями что ли никаких промежуточных шагов не было?

verbal hound
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я ни слова не понял

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из того, что тут написано

wooden python
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о так это ж совсем другое дело

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так

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элементарные операции над матрицами бывают трех видов:

  1. перестановка двух строк (меняет знак определителя)
  2. умножение строки на множитель (определитель умножается на тот же множитель)
  3. прибавление отной строки с каким-то коэффициентом в другую (определитель не меняется, каким бы ни был коэффициент)
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вот это вам препод рассказал? или он проспидранил/пропустил/рассказал предельно непонятно (нужное подчеркнуть)?

verbal hound
wooden python
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ы

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понятно

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вообще я бы сделала так

verbal hound
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У нас 2 пары по пятницам, Лекция и Практика, но там все в шоке на протяжении 3х часов

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Я еще умер с того, что если поменять местами строки у матрицы, у которой и так нулевой определитель

wooden python
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сначала выносим 10 из первой строчки, получаем $10\vmqty{3&-1&12&8 \ -5&3&-34&-23 \ 1&1&3&-7 \ -9&2&8&-15}$

clever fjordBOT
verbal hound
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то он будет отрицательным

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само -0 не помещается в голове

wooden python
verbal hound
# wooden python шта?

Я после пары сидел, общался с ней, она мне постоянно про какие то свойства говорит

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тип

wooden python
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не поняла, о чем ты

verbal hound
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если у матрицы, нулевой определитель

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и ты поменяешь местами строки

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то он будет отрицательный по свойству

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ничего не понял

wooden python
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то определитель как был 0, так и останется

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-0 = 0

verbal hound
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я еще не понял

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вот есть допустим

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тройная матрица
и 2 из 3 строк одинаковые

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если их местами поменять, то определитель будет отрицательный

wooden python
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тройная в смысле 3 на 3?

verbal hound
wooden python
verbal hound
wooden python
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ну тк

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пусть D -- определитель исходной матрицы

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после преобразования он станет равен -D, согласно свойству

verbal hound
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это понятно, если бы были разные значения

wooden python
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но получили мы ту же самую матрицу, из чего следует, что D = -D

verbal hound
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но если 2 из 3 строк одинаковые

wooden python
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ты меня хоть дослушай, пожалуйста...

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пусть D -- определитель исходной матрицы
после преобразования он станет равен -D, согласно свойству
но получили мы ту же самую матрицу, из чего следует, что D = -D

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ферштейн?

verbal hound
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фраза D = -D меня убивает, учитывая что я на программиста иду

wooden python
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хоспаде

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ну тогда D == -D

verbal hound
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Прости если доставляю проблемы

wooden python
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если так не нравится привычка математиков не обозначать вещи так, как они пишутся в императивных ЯП типа си или джавы

verbal hound
wooden python
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нихрена оно не выдает false.

verbal hound
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ладно, не будем усложнять

wooden python
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у уравнения D = -D решение есть

verbal hound
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в твоем пониманииD = -D словами как переводится

wooden python
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определитель исходной матрицы (D) равен (=) определителю преобразованной (-D)

verbal hound
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Хорошо, если расматривать, что определитель это площадь/объем фигуры

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то я пойму

wooden python
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да глубоко нам пофиг на объемы и площади

verbal hound
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ибо площадь/объем не могут быть отрицательными (в базовом понимании)

verbal hound
wooden python
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а определитель как объем вообще берется со знаком, означающим ориентацию, так что вот это вот про "площадь/объем не могут быть отрицательными" идет лесом

verbal hound
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ужас

wooden python
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(1) пусть D -- определитель исходной матрицы
(2) после преобразования он станет равен -D, согласно свойству
(3) но получили мы ту же самую матрицу, а значит D = -D

verbal hound
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ладно, если я буду использовать определитель в уравнении или в функциях

wooden python
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скажи пожалуйста, какая из этих строчек вызывает непонимание?

verbal hound
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он будет положительный или отрицательный

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мне его как рассматривать

wooden python
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вопрос поставлен слишком размыто, так что я на него ответить не могу.

verbal hound
wooden python
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так я так и говорю

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определитель до преобразования РАВЕН определителю после

verbal hound
wooden python
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??

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не путай, пожалуйста, понятия "что-то отрицательное" и "что-то, у чего спереди торчит минус".

verbal hound
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не знал, что у минуса есть и такие понятия

wooden python
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-D есть произведение -1 и D

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скажем так

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если у переменной отрицательное значение, то, поставив перед ней минус, ты получишь положительное число

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например, если x = -9, то -x = 9

verbal hound
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так, это понятно

wooden python
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вроде классе в шестом проходят, что минус на минус дает плюс

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то есть -D ни в коем случае не надо воспринимать как что-то точно отрицательное

verbal hound
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тоесть, сам D может быть чем то отрицательным

wooden python
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само D может быть каким угодно вещественным числом -- хоть положительным, хоть отрицательным, хоть нулем

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-D есть произведение -1 и D, ни больше, ни меньше

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безо всяких там додумок

verbal hound
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ладно, по такой логике получается
-9 = -1 * (-9)

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или я путаю что-то снова

wooden python
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опять путаешь

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-9 = -1 * 9 тогда уж

verbal hound
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ну так

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D = -D
и если D = -9
то получается
-9 = -(-9)

wooden python
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правильно, получается ложное утрерждение

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значит, D ≠ -9

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уравнение D = -D можно и нужно решить, причем для этого не требуется знаний больше, чем школьная алгебра класс этак за шестой

verbal hound
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интересно

wooden python
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и тогда ты получишь, чему равен этот несчастный определитель

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алгебру из школы знаешь/помнишь?

verbal hound
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да

wooden python
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ну вот реши мне уравнение x = -x

verbal hound
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погнали.
x - (-x) = 0
x + x = 0
x = 0

wooden python
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браво

verbal hound
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тоесть

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ща

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D = -D Верно только для D = 0?

wooden python
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естественно

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то есть ты только что доказал своими усилиями, что если у матрицы две строчки совпадают, то ее определитель равен нулю

verbal hound
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я в шоке

verbal hound
wooden python
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хороший вопрос

verbal hound
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Ну хотябы слава богу что есть такие люди как ты

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так бы я потерялся

wooden python
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надеюсь, что моими силами у тебя случилось просветление, хоть и на небольшом масштабе

verbal hound
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Ладно, вернемся к первоначальному вопросу.
Операции над строками

wooden python
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таки да

verbal hound
wooden python
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скопирую то, что раньше написала
элементарные операции над матрицами бывают трех видов:

  1. перестановка двух строк (меняет знак определителя. или, что то же самое, определитель умножается на -1)
  2. умножение строки на множитель (определитель умножается на тот же множитель)
  3. прибавление отной строки с каким-то коэффициентом в другую (определитель не меняется, каким бы ни был коэффициент)
verbal hound
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Работает это ли со слобцами

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?

wooden python
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да, и ровно таким же образом.

verbal hound
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понятно

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чтоб не листать

firefox_gNMAfWY1ji.png
wooden python
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в твоем скрине колдуют только со строками

verbal hound
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пишут что сложили строки, но размер матрица не поменялся

wooden python
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он и не должен

verbal hound
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ага

wooden python
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тут как раз удобно в сишной нотации писать

# 
row_i += coeff * row_j;
verbal hound
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я так понимаю, коэффициент в таких вещах, обязательная вещь?

wooden python
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оче удобные операторы присваивания с операцией += и -=, чтобы как раз вот эту операцию объяснять, особенно программистам и иже с ними

verbal hound
wooden python
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все равно определитель от этого не меняется никак, так что пофиг. но и как отдельный вид операции выделять не надо.

verbal hound
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угу

verbal hound
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в матрице оно остается таким же

wooden python
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строка, которую прибавляем, да, остается как есть

verbal hound
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понятно

wooden python
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так вот, как бы написала я: сначала выносим 10 из первой строчки, получаем $\Delta_4 = 10\vmqty{3&-1&12&8 \ -5&3&-34&-23 \ 1&1&3&-7 \ -9&2&8&-15}$

а уже затем колдуем с прибавлением первой строчки ко всем остальным (по-хорошему надо делать поочередно, но в данном случае пофиг в каком порядке)

clever fjordBOT
verbal hound
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тоесть

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мы первую строку

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ко всем остальным прибавляем?

wooden python
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то есть затем делаются вот такие операции (запишу на си-псведокоде):

row_2 += 3 * row_1;
row_3 += row_1;
row_4 += 2 * row_1;
verbal hound
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а умножение

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точнее

wooden python
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и делаем это очень аккуратно, ибо к 24 арифметических действиях, выполняемых в уме, легко по неосторожности ошибиться

verbal hound
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коэффициент вообще обязателен тут?

wooden python
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в смысле?

verbal hound
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ну то что мы умножаем на 3, 1, 2

wooden python
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можно все коэффициенты взять за единицу, и это все равно будет допустимо

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а то, что мы берем их именно такими, как написано, это не из-за того, что ТАК НАДО, а имеет мотивацию

verbal hound
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точнее, удобные

wooden python
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типа того

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немного точнее: наша цель -- очистить один из столбцов (в данном случае второй), т.е. следать так, чтобы в нем был ровно один ненулевой элемент

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затем, когда мы раскроем определитель по Лапласу вдоль очищенного столбца, будет только одно слагаемое

verbal hound
wooden python
#

э

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забыла, как по-русски называется, сек

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по-английски Laplace expansion, сейчас поищу

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https://ru.wikipedia.org/wiki/Теорема_Лапласа

Теорема Лапласа

Теоре́ма Лапла́са — одна из теорем линейной алгебры. Названа в честь французского математика Пьера-Симона Лапласа (1749 — 1827), которому приписывают формулирование этой теоремы в 1772 году, хотя частный случай этой теоремы о разложении определителя по строке (столбцу) был известен ещё Лейбницу.

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вот

verbal hound
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Не, все правильно

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Нам не рассказывали о ней

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видимо еще рано до нее

wooden python
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как так

verbal hound
wooden python
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определители старших порядков без нее считать -- геморрой

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разве что к треугольному виду приводить

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но тогда дофигища циферок за собой приходится тащить

verbal hound
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тут так делали

image.png
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В душе не знаю, кто такой Саррюс

wooden python
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есть удобная ормула для вычисления определителей 3 на 3 (и только 3 на 3), в честь него названная

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можешь показать, что там за равенства (1.6)? мб что-то знакомое

verbal hound
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щас

wooden python
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или вообще скинь-ка сам учебник. он же у тебя скорее всего пдф

verbal hound
verbal hound
wooden python
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а

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ну то есть вы это называете просто разложением (без фамилии)

verbal hound
#

@wooden python Можно попросить об просьбе? У меня математика только первый курс, каждую пятницу. С текущим преподавателем я не думаю что смогу осилить математику. Если ты не против, могу ли я иногда писать тебе и выделять пару минут твоего времени?

wooden python
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да пожалуйста

verbal hound
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Потому что я сам потом ребятам из группы обьясняю щас все что ты пишешь

wooden python
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я по возможности буду отвечать ессно

verbal hound
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все благодарны

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спасибо огромное

wooden python
#

рада была помочь

verbal hound
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что с чем складывали кстати

image.png
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что у нас получилась 3 на 3 матрица

wooden python
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вот тут как раз не складывали, а разложили

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по 2-му столбцу, который мы только что очистили

verbal hound
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а

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тоесть второй столбец

wooden python
verbal hound
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у нас пусткой был

wooden python
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чтобы вот в этой сумме только одно слагаемое было

verbal hound
# wooden python

знаки сигма, я ни разу не использовал, понятия не имею что оно означает

wooden python
#

это сумма

verbal hound
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а

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грубо говоря

wooden python
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в качестве совсем на пальцах объяснения можно ее записать как цикл for

verbal hound
#

опять же через си язык

wooden python
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то есть типа

verbal hound
#

да да

wooden python
# 
double sum = 0;
for (int i = m; i <= n; i++) {
  sum += a[i];
}
#

после выполнения этого кода в переменной \verb|sum| будет храниться значение суммы $\sum_{i=m}^n a_i$

clever fjordBOT
wooden python
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чтобы не писать каждый раз многоточия

verbal hound
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все все, теперь понял

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а куда первая строка делась

firefox_lR7I0q7Syg.png
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вместе со 2 столбцом

wooden python
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их вычеркнули

verbal hound
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так можно?

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ну, какие то условия для этого должны же быть

wooden python
verbal hound
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так, надо обдумать

wooden python
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сейчас проиллюстрирую

verbal hound
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понятно

wooden python
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знаки минус и плюс идут от (-1)^(i+j) в определении алг. дополнения

image.png
verbal hound
#

я заметил

wooden python
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я иногда это представляю себе как шахматную доску, у которой верхний левый угол окрашен в "плюс"

verbal hound
#

это я постараюсь сам сделать

image.png
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ибо концепцию работы с этим понимаю

odd edgeBOT
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@verbal hound Has your question been resolved?

wooden python
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так что в итоге

verbal hound
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я кушал ((

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но получилось

#

сошлось

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спасибо, я если что, буду обращаться @wooden python

#

закрываю вопрос на сегодня

#

.close

odd edgeBOT
#
Channel closed

Closed by @verbal hound

Use .reopen if this was a mistake.

#
Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

autumn bear
#

Completely lost on this problem, I think I could go about this by brute forcing pdf's but that calculation is going to get impossibly hard to do and the hint that the problem gives makes me think that's not the best way to do it anyways

image.png
odd edgeBOT
autumn bear
#

I know we can rewrite P(X2>X1) as P(X2-X1 > 0), but I don't think that actually advances my ability to solve this at all

verbal hound
#

P is the probability, right?

autumn bear
#

yeah

verbal hound
#

and N(0, 1) its any number from 0 to 1 like 0.15123 and so on

autumn bear
#

No, N(0,1) is a Normal distribution 0 mean STD of 1

odd edgeBOT
#

@autumn bear Has your question been resolved?

odd edgeBOT
#

@autumn bear Has your question been resolved?

odd edgeBOT
#

@autumn bear Has your question been resolved?

autumn bear
#

<@&286206848099549185> After stepping away for a couple hours and not hearing back from an email to my professor, I'm still completely lost on this problem, looking for anyone who can nudge me in the right direction

autumn bear
#

.close

odd edgeBOT
#
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mystic saffron
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next sonnet
#

can anyone explain to me how to find the great common denominator? in a problem like this

375757549_1527473731121431_7433544867486476470_n.png
odd edgeBOT
next sonnet
#

it makes sense to me when I'm adding two fractions together but I haven't done it with 3 or when they're on opposite sides

#

kind of confuses me

#

the screenshot I sent is the instructional video I was watching. I'm not sure how they got 6(x+1).

young moss
#

Just find "x" in this?

next sonnet
#

or how I'd do it in another problem

#

right

young moss
#

is that the question

next sonnet
#

yeah

#

my thought process for finding x here is

#

multiplying both sides by x+1

#

or subtracting by 1/2 then multiplying both sides by x+1

#

but it gives me junk when I try that

young moss
#

Ok

#

Soooo

#

On the right hand side we have

#

$/1/(3x+3)$

#

ugh

next sonnet
#

lolol

#

Is it because

young moss
#

$1/(3x+3)$

clever fjordBOT
young moss
#

we have this

next sonnet
#

6x + 6 is the lowest denominator they can all share

young moss
#

do u see anything common in the denominator?

grizzled tide
#

if you care and dont know, you can do $\frac{1}{3x+3}$ for formatted fractions

clever fjordBOT
next sonnet
#

I don't understand

young moss
tepid yacht
young moss
#

@next sonnet I got the LCD as 6(x+1)(3x+3).

next sonnet
#

How do you find it

#

Also what is the (3x+3) doing there

young moss
#
  • Multiply the entire equation by the least common denominator (LCD) of (x+1), 2, and (3x+3).
  • The LCD in this case is 6(x+1)(3x+3).
next sonnet
#

in my head I'm thinking

#

hm

#

weird

#

lcd of allthose

#

wouldn';t that just be

#

6x + 6

#

because they can all multiply into that

#

multiply the 1/2 by 3x+3/3x+3

young moss
#

Simplify the equation:

  • Distribute the LCD to each term in the equation to eliminate the denominators.
  • This will result in a new equation without fractions.
next sonnet
#

I don't get how you get the lced

#

lcd

#

here lemme try again

#

so I look at this and I think

#

ok let me make 3/x+1 have the same denominator has 1/3x+3

young moss
#

Just multiply all the denominators

#

Multiply the entire equation by the least common denominator (LCD) of (x+1), 2, and (3x+3).
The LCD in this case is 6(x+1)(3x+3).

next sonnet
#

oh

#

so

#

to find

#

the

#

LCD

#

multiply all the denominators together

#

that's the lowest possible denominator they can create

#

right

#

then I multiply all th terms by that LCD over 1 to cancel out the denominator?

#

it's weird in the video they say greatest common denominator

#

so whats the difference

young moss
#

Simplify the equation:

  • Distribute the LCD to each term in the equation to eliminate the denominators.
  • This will result in a new equation without fractions.
  1. Solve for x:
  • Simplify and rearrange the equation to isolate the variable x on one side.
  • Combine like terms and move all terms involving x to one side of the equation.
next sonnet
#

makes sense

young moss
next sonnet
#

yes

young moss
#

if u do ill send lvl 4

next sonnet
#

does this always work

#

if there's 3 fractions

#

I can multiply all the denominators together

#

that gives me the LCD

#

multiply all the terms by that to cancel out the denominators

#

gives me a new equation no fractions

#

solve for x

young moss
#

@next sonnet did u get it?

young moss
#

sorry for late response am solving a chem question for myself xD

next sonnet
#

np

#

I got it but I'm nolt confident with it yet

#

but thankls

young moss
#

Ill check

next sonnet
#

ok I'm lost again

#

when I get the LCD

#

should I multiply the numerator by the other denominators as well

#

so the 3 in the first numerator

#

gets multiplied by 2 and 3x+3?

odd edgeBOT
#

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#
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mystic saffron
#

I am having trouble calculating the angular and linear velocity given this information only.

image.png
odd edgeBOT
#

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sharp zephyr
odd edgeBOT
sharp zephyr
#

how is it not .00056

#

lemme get my work

#

20 - .005 = 19.995

#

19.995 = x^2 - x

#

x=5.0005555898

#

5.0005555898 - 5 = 0.0005555898

#

0.00056

odd edgeBOT
#

@sharp zephyr Has your question been resolved?

sharp zephyr
#

<@&286206848099549185>

odd edgeBOT
#

@sharp zephyr Has your question been resolved?

summer river
sharp zephyr
#

wat

exotic lance
#

Hello

#

mmm let's see

#

,calc (1+sqrt(1+4*20.005))/2 - 5

clever fjordBOT
#

Result:

5.5552126623581e-4
exotic lance
#

yeah still your answer looks correct 🤔

#

,calc 5 - (1+sqrt(1+4*19.995))/2

clever fjordBOT
#

Result:

5.5558985334248e-4
exotic lance
#

for this maybe you have to round it down (?, so f(x) doesn't exceed the limit

#

,calc (5+0.00056)^2-(5+0.00056)

clever fjordBOT
#

Result:

20.0050403136
exotic lance
#

,calc (5+0.000559)^2-(5+0.000559)

clever fjordBOT
#

Result:

20.005031312481
exotic lance
#

this value of x is in |x-5| < 0.00056, still the function exceeds 20.005

#

Well that's something to consider, it's a new thing for me with respect to limits 🤔

odd edgeBOT
#

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cursive obsidian
#

how to solve #6

image.png
odd edgeBOT
tardy lagoon
#

!status

odd edgeBOT
# 
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
cursive obsidian
#

1 for me

tardy lagoon
#

what are the properties of tangent lines

cursive obsidian
#

huh

#

it has to touch the function once

tardy lagoon
#

one more

cursive obsidian
#

wait what thats the only one ik 😭

tardy lagoon
#

their slope is the same for a point

cursive obsidian
#

ohh

#

okayy

#

wait then how do i solve this then

rain tundra
#

Find the derivative of f(x) then equate it to the slope of y= -(3/4) x + 3

fallow tapir
#

you can solve this either by derivatives or using the concept of determinants.

#

(quadratic equations)

cursive obsidian
fallow tapir
#

which one?

cursive obsidian
#

wait how do i find the derivative of k

cursive obsidian
tardy lagoon
#

k is just a constant

rain tundra
#

It's a constant

cursive obsidian
#

so it stays k after being differentiated?

fallow tapir
#

ig quadratic equations are taught before differentiation but alr

cursive obsidian
#

😭

fallow tapir
#

np

#

do it by derivatives

cursive obsidian
#

okok

#

wait so does k change to anything??

fallow tapir
#

k is a constant.

cursive obsidian
#

oh so it becomes 0

clever fjordBOT
#

Dyssrupt

799148360539308073.png
cursive obsidian
#

ohhh okayyy thanksks

#

and d/dx 1/x is equal to 0/1 after being differentiated right?

mystic saffron
#

no

cursive obsidian
#

oh huh

mystic saffron
#

1/x = x^ -1

#

now apply the power rule

cursive obsidian
#

oh wait yeah

#

-x^-2

mystic saffron
#

yes

cursive obsidian
#

-1/x^2

mystic saffron
#

yup

#

now what.

cursive obsidian
#

uh i have no idea 😃

mystic saffron
#

why did you diff the function?

cursive obsidian
#

im just following what they told me above 😭

mystic saffron
#

...

cursive obsidian
#

i dont know why we have to differentiate it to get k

mystic saffron
#

you could have asked why tf am i diff?

#

do you want the concept or the answer?

cursive obsidian
#

i would but its like 1 am and im just tryna finish this so i can sleep. ill like figure out whats going on tmrw morning ykykyk

cursive obsidian
#

cause i have more of these to do so might as well learn it nvm

mystic saffron
#

they two sentences you just said contradict each other LMAO

cursive obsidian
#

💀 yeah ik

mystic saffron
cursive obsidian
#

ima take the first one back

#

okok tyty

mystic saffron
#

so diff'in gives you the slope of the tangent

cursive obsidian
#

ohh

mystic saffron
#

at "x" point

cursive obsidian
#

so the slope is -1?

mystic saffron
#

so you diff it and got -k/x^2

mystic saffron
cursive obsidian
#

yeah

#

oh no

mystic saffron
#

after diffing it?

cursive obsidian
#

-k/x^2

mystic saffron
#

yea so thats the slope of the tangent at x point

#

but the question isnt that

cursive obsidian
#

oh so thats the whole slope okay okay

#

yeah

mystic saffron
#

the question is asking for a line to be the tangent at some point

cursive obsidian
#

yeah

mystic saffron
#

so if we just equate the slope of the line to be the slope of the "tangent" we just got by diff'ing

#

we might get our answer

cursive obsidian
#

what

mystic saffron
#

💀

#

whats the slope of the line?

cursive obsidian
#

😭 wait what do u mean by equate

cursive obsidian
mystic saffron
#

=

cursive obsidian
#

oh

#

whoopsies

mystic saffron
cursive obsidian
#

😅

mystic saffron
#

not the eqn

cursive obsidian
#

OH HELP -k/x^2

mystic saffron
#

thats the slope of the second function

cursive obsidian
#

oh

mystic saffron
#

im asking the slope of the line

cursive obsidian
#

OHH

#

MB

#

-3/4

mystic saffron
#

yes.

cursive obsidian
#

yaaa

mystic saffron
#

equate em

#

you ll get k = 3 and point x = 2

cursive obsidian
#

-3/4 = -k/x^2

#

so k = 3

#

and x = 2

#

yeah

mystic saffron
cursive obsidian
#

wait what do i do next

#

oh

mystic saffron
#

idk

cursive obsidian
#

LMAOO

#

so k = 3

mystic saffron
#

if you got you answer type .close

#

yup!

cursive obsidian
#

oKAY OKAY THANKS 🙏

#

.close

odd edgeBOT
#
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cursive obsidian
#

hello one more problem im so confused on

Screenshot_2023-09-15_at_1.32.23_AM.png
odd edgeBOT
mystic saffron
#

probably not

cursive obsidian
#

oh wha 😭

desert marlin
cursive obsidian
#

also hii again

cursive obsidian
#

lemme check

#

set x = 3? or like the equation i get after differentiating equal to 3??

desert marlin
#

set the equation equal to 3

cursive obsidian
#

oh okok

#

i get x = 3/2

#

which isnt 3

desert marlin
#

x does not have to equal 3

cursive obsidian
#

so therefore it doesnt have a tan line with slope m =3??

#

oh

desert marlin
#

if f'(x) represents the slope of the tangent line at point x

#

set f'(x)=3

#

if there is a solution

#

then at this x-value

#

the slope of the tangent line is 3

cursive obsidian
#

oh wait what

#

okk one sec

#

i just checked on a graph it doesnt work

#

oh

#

yeah it doesnt give me any real number solution

#

OKOK TYY 🙏

#

.close

odd edgeBOT
#
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acoustic atlas
#

hello

odd edgeBOT
acoustic atlas
#

what is biomial theroem guys

#

the junk part is confusing to me

summer cradle
#

do you know the binomial theorem? it says (x + deltax)^n = x^n + nx^(n-1)*deltax + other stuff

#

he is just calling the other stuff “junk” and not writing it out

acoustic atlas
#

ok

#

yeah i don't know i didn't like math that much as a kid now I love it so yeah

#

thanks btw

#

.close

odd edgeBOT
#
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clever pecan
odd edgeBOT
clever pecan
#

The length contraction equation does show that the distance gets shortened

#

however, the first statement is confusing me

#

I was thinking that time dilation affects the time taken

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#

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dire jolt
odd edgeBOT
dire jolt
#

in the case i want to calculate the force of 2Q and Q on q, i will calculate the force of both charges on q and add?

crisp wadi
#

Subtract rather since the forces have opposite directions

zenith jasper
#

add them as vectors

odd edgeBOT
#

@dire jolt Has your question been resolved?

dire jolt
crisp wadi
#

Clearly, the 2Q and Q charges are located on different sides of the diagram

#

With q being in the middle

dire jolt
#

i am stupid

#

n the figure, if Q = 30 C, q = 5.0 C, and d = 30 cm, what is the magnitude of the
electrostatic force on q?

dire jolt
#

.close

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#
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twilit spoke
#

Show or disprove the logical equivalence:
a -> (b -> c) <-> a ^ b -> c

odd edgeBOT
twilit spoke
#

How do I solve this?

#

The ^ should be a V upside down

proud ibex
#

The biconditonal <-> is another way to denote logical equivalence

#

So we can take the two sides and show they're logically equivalent using truth tables

twilit spoke
#

Yeah I was just about to ask

#

I asked gpt and it gave me one but one of them was T and one was F

#

Specifically when a is T and b, c is F

proud ibex
#

Is the second statement (a ^ b) -> c or a ^ (b -> c)?

twilit spoke
#

Neither

#

a ^ b -> c

#

But the “^” is a large one

#

Representing “and”

proud ibex
#

There is no order of operations defined for logical operations, so a ^ b -> c doesn't make sense. It's possible that (a ^ b) -> c and a ^ (b -> c) are logically equivalent and the statement is being renamed a ^ b -> c, but we can't take that for granted

twilit spoke
#

The last one is T F

#

So it shouldn’t be right

stark heart
#

@twilit spoke
Don't forget to close the channel using
.close

odd edgeBOT
#

@twilit spoke Has your question been resolved?

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wary fern
#

can anyone give me a hint? im so stuck with this

image.png
odd edgeBOT
wary fern
#

i tried v = 4pi/3 r^3 and calculating dv/dr but no help

tardy lagoon
#

umm

#

you want to find dV/dt

viscid flint
#

and you need a more complicated eqn than that because the water isn't in the shape of a sphere

odd edgeBOT
#

@wary fern Has your question been resolved?

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#
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sleek falcon
#

how do you show that something is a basis for r^3

odd edgeBOT
wooden python
#

you mean R^3?

#

not to be That Person

sleek falcon
#

Yes sorry

wooden python
#

but to show that something is a duck you show that it satisfies the definition of a duck

sleek falcon
#

trying to do this

Screenshot_2023-09-15_at_10.12.14_AM.png
wooden python
#

do you have a definition of basis on hand

#

or was your teacher cruel and incompetent to you by withholding it from you

sleek falcon
#

i have my other friends notes from another school

#

i feel like my teachers notes are not amazing and we really only briefly touched this

mystic saffron
#

verify the linear independence of all the vectors v1-v3

wooden python
#

let V be a vector space

sleek falcon
#

linear independence means that all the coefficiences are equal to 0 rigt

wooden python
#

in order for a subset B ⊆ V to be a basis for V, two things must happen:

  • B must be linearly independent
  • B must be a spanning set for V, i.e. every vector in V must be expressible as a linear combination of B
wooden python
sleek falcon
mystic saffron
#

linearly independent means that only the trivial solution is a valid solution to that equation

sleek falcon
#

so like one point of intersection?

wooden python
# sleek falcon

you must digest the definition of linear independence as a whole.

#

if you try to regurgitate only bits and pieces of it, you will choke.

#

and it will be unpleasant for everybody involved.

sleek falcon
#

so i need to find the basis?

wooden python
#

no

sleek falcon
#

why not

wooden python
#

you're not "finding" a basis

#

that isn't your goal

#

your goal is to prove that {v1, v2, v3} is a basis

#

this consists of two big steps, each of which can be broken into some sub-steps, as follows:

#

in what follows, S := {v_1, v_2, v_3}, the set you are looking at.

  1. verify that S is linearly independent:
    a. write down the equation x_1 v_1 + x_2 v_2 + x_3 v_3 = 0, where x_i are real-number variables.
    b. rewrite the vector equation as a system of three linear equations in three variables, and solve it
    c. verify that the ONLY solution of this system is the trivial one, i.e. x_1=0, x_2=0, x_3=0.
  2. verify that S spans R^3:
    a. take an arbitrary vector u = (u_1, u_2, u_3) ∈ R^3.
    b. write down the equation x_1 v_1 + x_2 v_2 + x_3 v_3 = u.
    c. solve the system for x_1, x_2 and x_3.
    d. verify that your solution exists no matter what u is.
sleek falcon
#

thank you sm

odd edgeBOT
#

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desert stump
#

If a fair coin is tossed 50 times it gives 50 heads

odd edgeBOT
desert stump
#

Are next 50 tosses as likely to be heads as the first 50

mystic saffron
odd edgeBOT
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desert stump
#

.reopen

odd edgeBOT
#

✅

rigid vapor
#

hey

desert stump
#

I just realised that Probability of getting X heads after getting X heads is dependent on X

rigid vapor
#

;-;

desert stump
#

So a longer sequence of heads is less likely to repeat after occurring than a shorter sequence of heads

#

However a sequence HHH is less frequent than a HHT

#

Expected number of tosses before one gets 3 heads is 14

#

Expected number of tosses before one gets 2 heads and a tail is 10

#

Sorry but anyone can help me?

#

I then understood that two sequences can be equiprobable but different in terms of their rarity or surprise or entropy

#

So a Head Head Head is more surprising than Head Head Tail even though both are equally likely to occur

odd edgeBOT
#

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odd edgeBOT
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gray lodge
odd edgeBOT
gray lodge
#

I don’t know how to do this

mystic saffron
#

do a substitution (should be obvious what it is) and then perform integration by psrts

gray lodge
#

Like this?

errant bone
#

looks great so far!

gray lodge
#

I think I got it, I appreciate the help

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oblique token
#

is my answer correct?

odd edgeBOT
oblique token
#

or does it need to be brackets

#

or is it (-inf, inf)

tawdry cave
#

What do the black dots represent?

#

Are those holes?

oblique token
#

no, just to help you visualize the image and demonstrate piecewise functions

tawdry cave
oblique token
#

idk, i thought it was like extrema where you don't include them

#

.close

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cold mesa
#

Im confused as to how answer for this question is positive infinity

odd edgeBOT
cold mesa
tawdry cave
#

What do you think it should be?

cold mesa
#

Wait sorry let me explain

#

If i find the limit from the right side it makes sense that its positive infinity

#

but when i calculate limit from the left side

desert marlin
#

!noclopen

odd edgeBOT
#

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem, and is confusing for helpers, making it more difficult for them to answer your question. We ask you to please be patient, even if your channel has not received much attention. If you are having a problem with a helper, please report it to <@&833154869451292722> rather than closing the channel and attempting to seek out another helper.

cold mesa
#

the denomitor would be negative when foiled

tawdry cave
cold mesa
#

Well i solved for it through this way

reef sandal
# cold mesa

The (x+7) factor is what's making it go to positive infinity. Think about the value of x+7 for values of x close to 0, from both sides

reef sandal
cold mesa
#

oooh

#

yes forgot to square .99

reef sandal
#

Also -.99 is close to -1

cold mesa
#

yea I was just using it to calculate the left side of 0

#

but now the squared make sense as to why its positvie

tawdry cave
#

You should choose a point closer to zero. -0.01 woule be a better candidate.

reef sandal
#

You can do it analytically. For any value of x in a close neighbourhood of x = 0, x + 7 and x^2 are both gonna be positive

cold mesa
#

thank you guys

#

.close

odd edgeBOT
#
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odd edgeBOT
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proud schooner
#

1 more attempt at getting help. Is this graph correct? here is the instruction

Domain: [-3,5]
x-intercepts: (–3, 0), (5, 0)
f(1) = –3
f(x) has a relative min of –3 at x = –2 and a relative min of –5 at x = 3
f(x) has a relative max of –2 occurring at x = 0
f(x) is increasing on the interval (-2,0)∪(3,5)
f(x) is decreasing on the intervals (-3,-2)∪(0,3)

IMG_20230915_182800.jpg
odd edgeBOT
lean willow
#

(1,-3) isn't on the graph

proud schooner
#

should it be?

odd edgeBOT
#

@proud schooner Has your question been resolved?

odd edgeBOT
#

@proud schooner Has your question been resolved?

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hearty socket
odd edgeBOT
hearty socket
#

i want help with questions b-d

#

i am not totally sure on my answers

warped grove
hearty socket
#

okay

#

for B, my answer is 2^5

brisk sage
#

A is 2^8 right?

hearty socket
warped grove
#

That's not quite correct

hearty socket
warped grove
#

Ah okay I see your confusion

hearty socket
#

so the variability is in the 5 coins

warped grove
#

It says "exactly three heads" so if 3 coins are heads, then the rest HAVE to be tails

#

But the trick is that it might not always be the same 3 flips which are heads

#

So for example maybe flips 1, 2, 3 are heads and 4 through 8 are tails

#

Or maybe 1, 5, 7 are heads and the rest are tails

#

Do you see what I'm saying?

hearty socket
#

8P3

warped grove
#

yup, almost!

#

why 8P3 and not 8C3?

young moss
brisk sage
#

Isn’t it just 8 choose 3?

warped grove
#

Let them figure it out

hearty socket
#

order doesn't amtter

warped grove
#

Yup, so b will be 8C3

hearty socket
#

C is a bit harder

warped grove
#

Yeah it is haha

hearty socket
#

8C3+8C4...8C8

#

that's my guess

warped grove
#

yup that's correct!

#

there's a trick you can do which makes it so you don't have to calculate 6 different 8Ck terms though

#

do you want to hear it?

hearty socket
#

ofcourse

warped grove
#

okay so how many possible outcomes do not contain at least three heads?

hearty socket
#

8C1+8C2

warped grove
#

Don't forget 8C0 :)

#

but yup!

#

So the possible outcomes that DON'T contain at least three heads is 8C0 + 8C1 + 8C2

#

the total number of outcomes is 2^8 like you said before

hearty socket
#

subtract them from the total number of outcomes

warped grove
#

So 2^8 - (8C0 + 8C1 + 8C2) is another way to calculate the same thing :)

#

exactly!

hearty socket
#

D is pretty hard

#

i couldn't figure it out

warped grove
#

hmmm so if there's the same number of heads and tails

#

how many heads are there?

hearty socket
#

actually

#

it's easy

#

if you do 8C4

warped grove
#

yup!

#

perfect

hearty socket
#

there is symmetry

young moss
#

i know this isnt my question but Im so confused 💀

hearty socket
#

so you can WLOG

hearty socket
#

this is basic combinatorics

#

it's still a bit hard

young moss
#

which grade is that 😭

warped grove
hearty socket
hearty socket
#

i am actually mixing up different concepts

#

so forget about it

warped grove
#

Yeah there's no need to invoke that here

hearty socket
#

you are going to have to take discrete math if you do compsci

young moss
hearty socket
#

you have a degree ?

warped grove
#

I think I learned this in Algebra 2 class in the US

#

But yeah it's totally reasonable for a question like this to show up in a computer science class (probably a class named Discrete Math or something) in college

hearty socket
brisk sage
#

As someone who took discrete math, why the hell is it needed for Computer Science?

warped grove
#

this sort of stuff is a basic tool you need if you're trying to calculate stuff like runtime

#

also it's good to know various tricks to simplify stuff mathematically

hearty socket
#

it has applications in encryptions for example

#

number theory is important for that

brisk sage
#

Interesting

#

And I’m just tryna learn more statistics (someone please help me with my problem)

warped grove
#

btw @hearty socket has your question been resolved?

#

if so type .close

odd edgeBOT
#

@hearty socket Has your question been resolved?

brisk sage
odd edgeBOT
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haughty tendon
odd edgeBOT
haughty tendon
#

new to this so bare with me

#

I understand to set it up into 2 cases and solve

#

I got x<2 and x>2 but I dont understand why my final answer would be x<2, x>4. the book says why but im just not getting it

#

I don't understand how this can be shown on a number line as well

odd edgeBOT
#

@haughty tendon Has your question been resolved?

nocturne belfry
#

we can split to two cases

#

x-4 > 0 and x-4 < 0, right?

haughty tendon
#

wait figured it out

#

i think

#

can i send u a pic of my number line

#

2 sec

#

this is for seperate question

nocturne belfry
#

if you just want your answer checked you should use desmos

haughty tendon
#

no no its just that im using a number line to find which x's satisfy

#

i wanted to know if the method im using is valid or im just making stuff up in my head

nocturne belfry
#

any method is valid if it leads to the right answer

haughty tendon
#

so the way i visualized the number line would work

#

?

nocturne belfry
#

i dont understand what youre doing

haughty tendon
#

yes neither do i actually

#

okay just help me out

#

so yes

#

we can split into two cases

#

pls and thank u

nocturne belfry
#

you must split

#

step #1 is multiply by a quantity you dont know is positive or negative

haughty tendon
#

so x-4

nocturne belfry
#

hrm?

haughty tendon
#

.closd

#

.close

odd edgeBOT
#
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royal herald
#

Yea why not

#

(a+b)^4

#

Now just expand

#

Oh

viscid flint
#

thé 4th term in what ordering

ruby pagoda
#

you can

#

do it with a and b

#

yes

#

did you expand the whole thing

#

like this

image.png
#

that's what it means to expand

#

ok what exactly is your original question

#

gotta expand the whole thing ig

#

doesn't matter

#

isn't it symmetrical

#

yes it is

#

you have n

#

so you can write it as an equation

#

right?

#

now you subtitue in a and b

#

you have a=(w+x) right

#

and b=(y+z)

#

you did your substitution up there

#

so what were you trying to do

#

that looks exactly like brute force

odd edgeBOT
#

@open crescent Has your question been resolved?

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@open crescent Has your question been resolved?

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royal sphinx
odd edgeBOT
royal sphinx
#

how do you do this integral

#

im kinda lost

ruby pagoda
#

try u-substitution

#

try u=sqrt(x)

odd edgeBOT
#

@royal sphinx Has your question been resolved?

rugged whale
#

try u = sqrt(1-x)

odd edgeBOT
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echo patio
#

in general this entire part

image.png
odd edgeBOT
tardy lagoon
#

m

#

@echo patio maybe write x bar as $\frac{1}{N}\sum_{m=1}^N(x_m)$

clever fjordBOT
#

WhereWolf(ping if needed)

681490543494430807.png
odd edgeBOT
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@echo patio Has your question been resolved?

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hollow spade
#

how to do this

image.png
odd edgeBOT
noble gorge
#

make denominator the same

#

add them up

#

oh right

#

u need to find the denominator

#

wait

hollow spade
#

this is the answer . I dont know about the third line

image.png
noble gorge
#

oh

#

they separate it

#

from 1/1 - 1/2

hollow spade
#

why and how does this work

tall veldt
#

You can check yourself that $\frac{1}{n(n+1)} = \frac1n - \frac{1}{n+1}$

clever fjordBOT
#

ΣΑCu

182179228840755200.png
mystic saffron
#

by means of partial fractions decomposition

hollow spade
mystic saffron
#

it's partial fractions decomposition

#

don't memorise it

smoky crystal
#

what level of math are you at?

tall veldt
#

Its just something you can sometimes do to fractions with a product in the denominator

sterile blaze
#

you can write it as
3 - [1+
(- 1/2 + 1/2)+
(-1/3+1/3)+
...
(-1/7+1/7)
-1/8]

#

by regrouping, and all those middle terms =0 so they disappear.

hollow spade
zenith jasper
sterile blaze
#

oh, oops.

mystic saffron
clever fjordBOT
smoky crystal
#

i think

hollow spade
smoky crystal
#

year 7 is perhaps early for partial fraction decomposition

#

because I was taught it as part of calc 2

mystic saffron
#

it's all algebraic manipulations though

#

not something they cannot understand

smoky crystal
#

yeah but let's not jump the gun here

#

$\frac{1}{n(n+1)} = \frac{1+0}{n(n+1)} = \frac{1 + (n - n)}{n(n+1)} = \frac{1 + n}{n(n+1)} + \frac{-n}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1}$

clever fjordBOT
#

accialto

421086209431961600.png
hollow spade
#

why does this thing equal to 1/n - 1/ n+1

image.png
smoky crystal
#

$\frac{1 + n}{n(n+1)} = \frac{1(n+1)}{n(n+1)} = \frac{1}{n}$

clever fjordBOT
#

accialto

421086209431961600.png
zenith jasper
#

$\frac{\cancel{1 + n}}{n\cancel{(n+1)}} + \frac{-\cancel{n}}{\cancel{n}(n+1)} = \frac{1}{n} - \frac{1}{n+1}$

clever fjordBOT
#

tushar

176048095543558147.png
smoky crystal
#

this

#

^

hollow spade
zenith jasper
#

yes, a -1

#

that’s why the second term is subtracted

smoky crystal
#

$\frac{1}{n} + \frac{-1}{n+1} = \frac{1}{n} - \frac{1}{n+1}$

clever fjordBOT
#

accialto

421086209431961600.png
hollow spade
#

oh !! omg

#

thank !

#

.close

odd edgeBOT
#
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odd edgeBOT
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plain sun
#

Can someone help me with a?

IMG_3622.jpg
odd edgeBOT
plain sun
#

wait

#

ok yeah i have no idea'

#

nvm

#

.close

odd edgeBOT
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plain sun
#

Can someone help me with question 1a?

IMG_3623.jpg
odd edgeBOT
#

@plain sun Has your question been resolved?

plain sun
#

<@&286206848099549185>

plain sun
#

.close

odd edgeBOT
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bright iris
#

so my teacher said that Fcostheeta won't produce any torque but i want to know why it does it not don't mind my drawing btw i was just trying to draw a wrench thingy not math related i know but i would appreciate if someone would help

image.png