#help-0

1 messages Β· Page 578 of 1

keen python
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how do I create a mapping based on these ?

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smth like

(x,y,z) -> (x +2, y+z)

livid jolt
# keen python
  1. check if the {(1, 0, 0), (2, 1, 0), (0, 0, 3)} make a basis for R3 or not
  2. write down a linear combination of them
  3. compute T(x, y, z) on the linear combination
dawn wraith
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<@&286206848099549185> could you please answer me? I really need this

small stag
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All of them I believe

keen python
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@livid jolt

unknown.png
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the next steps are unclear to me

hardy pewter
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Guys

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What's 2+1

alpine sable
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umm

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idk

hardy pewter
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2+1=??

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Pls help

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Or I will fail exam

shell widget
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5

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i think

candid torrent
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gets muted

hard thorn
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no its 0.5

shell widget
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is it

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hmm

night geyser
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just move on

hard thorn
#

what’s the solutions of sin(x)=-1/2 if x is in [0;2pi]

muted raft
ocean sealBOT
dawn wraith
small stag
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No problem

dawn wraith
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Does the same go for a quadrilateral that’s inscribed in a circle with the perpendicular medians?

keen python
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@muted raft I'm not sure what you are doing
is there another way

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in this video he said that

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A is equal to [ T(e_1), ...., T(e_n) ]

muted raft
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Well, you can always express the standard basis in terms of $\begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix}, \begin{pmatrix} 2 \ 1 \ 0 \end{pmatrix}, \begin{pmatrix} 0 \ 0 \ 3 \end{pmatrix}$ and then just compute $T\qty(\begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix}), T\qty(\begin{pmatrix} 0 \ 1 \ 0 \end{pmatrix}), T\qty(\begin{pmatrix} 0 \ 0 \ 1 \end{pmatrix})$

ocean sealBOT
keen python
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but how do I compute it if I dont have T yet

muted raft
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@keen python Ok, lets make it simple and do it the easy way

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We will apply the definition of linearity to find the standard matrx.

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Do you recall what that means?

keen python
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we didnt talk about that yet

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a mate solved it like this

muted raft
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Shouldn't linearity be the first thing to learn in linear algebra thinkingbread

keen python
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yeah we did that

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but not what a standard matrix is

muted raft
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Standard matrix is just columns that are images of the standard basis. So just T(1, 0, 0) T(0, 1, 0) T(0, 0, 1)

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So we want to find this standard matrix. We already know from our given that T(1, 0, 0) = (1, 0)

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So our first column would be (1, 0)

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Now, our second vector from standard basis we need is (0, 1, 0)

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We need to write (0, 1, 0) as a linear combination of vectors from your basis.

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which was why another person had asked you to check if they form basis in R^3 or not.

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So we need to observe that $\begin{pmatrix} 0 \ 1 \ 0 \end{pmatrix} = \begin{pmatrix} 2 \ 1 \ 0 \end{pmatrix} - 2 \cdot \begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix}$

ocean sealBOT
keen python
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so before you do anything check if we form a basis ?

muted raft
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Yes

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Now,

keen python
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ok thank you

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I understand

muted raft
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ok Can you continue from here then?

keen python
muted raft
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Yup

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that is pretty much it.

keen python
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you want to transorm it to canon basis

muted raft
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Since we already know that they form basis, that means every vector can be written as linear combination from those vectors.

keen python
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and the results form the standard matrix

muted raft
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Yes

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Looks like you are good to go so good luck

keen python
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I see why it works but somehow I dont understand why

muted raft
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What part do you not understand?

keen python
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do you maybe know any good tutorials

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@muted raft like why do we have to do this whole stuff ?

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to express the mappings ins canon basis

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cant we just say that standard matrix is (1,0), (3,2), (3,-3)

muted raft
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No.

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Your basis is B = {(1, 0, 0), (2, 1, 0), (0, 0, 3)}. The matrix you wrote is the matrix associated with basis B.

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You want to change it to standard matrix which is associated with the basis S= {(1, 0, 0), (0, 1, 0), (0, 0, 1)}

keen python
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for example here

muted raft
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$\begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} = \frac{1}{2} \begin{pmatrix} 1 \ 1 \ 0 \end{pmatrix} - \frac{1}{2} \begin{pmatrix} 0 \ 1 \ 1 \end{pmatrix} + \frac{1}{2} \begin{pmatrix} 1 \ 0 \ 1 \end{pmatrix}$

ocean sealBOT
muted raft
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Do you know how I got this solution?

keen python
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not really

muted raft
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$\begin{bmatrix} A | \begin{pmatrix} 1 \ 0 \ 0 \end{pmatrix} \end{bmatrix} = \begin{bmatrix} 1 & 0 & 1 & 1 \ 1 & 1 & 0 & 0 \ 0 & 1 & 1 & 0 \end{bmatrix}$

ocean sealBOT
muted raft
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Write it as an augmented matrix then solve it by converting it into reduced-row echelon form.

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aka apply gauss jordan elimination.

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What was the latex notation for augmented matrix again?

keen python
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oh never heard of augemented matrix before

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is there another way

muted raft
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We are basically just solving system of linear equations.

vale wigeon
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for this problem you can add all three of your things

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to get T(2,2,2) = (1,1)+(2,0)+(1,-3)

keen python
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Ahhhh

vale wigeon
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so (4,-2) i guess

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halve to get T(1,1,1) and it's easy after that

keen python
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Just was confused by the name

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So we are looking for a linear combination to get that vector

vale wigeon
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we are looking for the values of T on (1,0,0), (0,1,0) and (0,0,1)

keen python
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Ye now I understand what she did

vale wigeon
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this may take multiple steps

muted raft
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Ann, do you happen to know latex notation for augmented matrix?

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I don't recall if it exists at all.

vale wigeon
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there is a way to write those but it's hacky

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you basically have to use an array environment enclosed in a \left and \right

muted raft
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ahhh i see

keen python
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And do that for (0,1,0) and (0,0,1)

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?

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Is there a faster way ?

noble sinew
# muted raft ahhh i see

Write this before \begin{document}:
\makeatletter
\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
\hskip -\arraycolsep
\let@ifnextchar\new@ifnextchar
\array{#1}}
\makeatother

Then you can make an augmented matrix by doing \begin{pmatrix} [ccc|c] ... \end{pmatrix} for example (This gives first 3 columns then a straight line down and then the last column)

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So for example the following command will give you:
$$\begin{pmatrix}[ccc|c] 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 2 \\ 0 & 0 & 1 & 3\end{pmatrix}$$

unknown.png
alpine sable
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\\

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Do three \ to display two

muted raft
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OH i see.

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Thanks a lot.

pale river
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Quick question: does x between 2 and 3 mean 2 < x < 3

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or the same thing, with less than or equal to

shell widget
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2 < x < 3 is correct, include equal sign if it says inclusive

opaque galleon
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I need to calculate an angle between two 3D vectors in which the x,y,z of each vector will mostly, but not always be different than each other. How can I achieve this? (usecase: working on a game where the red dot with the yellow arrow is the gun, while the red dot at the top of the triangle is the target. I need the gun to aim towards this top red dot, which I believe involves finding the angle between these two vectors (or dots).

Screenshot_2673.png
nocturne mirage
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Hi everyone.. could anyone answer me why linear algebra is useful in group theory?

alpine sable
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anyone free?
i got an assignment that i want help solving it, it's a 10 question assignment.
and eh idk what i got but im paying in uc nitro codes lol so yea dm me

muted raft
alpine sable
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it isn't money doe

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● Do not cheat on tests or exams. Do not be academically dishonest. Do not offer money for doing homework assignments, and vice versa.

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it isn't money .-.

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Post assignment

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I dont know what uc nitro codes are

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well they are unchecked nitro codes lol

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I dont know what nitro is, just post assignment

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k

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btw they are 10 questions and 120 mins, when timer ends i fail

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Donate it to charity or something

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Is it a test?

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nop

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its an assignment

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teachers give us shitty assignments every day

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Whats the topic?

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doesn't say in title

1b5a30510381abb321cdf3ac8409baa7.png
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but here they are

alpine sable
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  • 2
    4
    2
  • 4
    (choosing btw)
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well i can donate like $30 to charity only cause im pretty broke

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btw that's a solving with steps kind of potato

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question

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same thing

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choosing:

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1
2
4

  • 4
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steps

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choosing:

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{ 3 , - 4 }
{ 3 , - 1 , 1 }
{ 3 , 1 , - 4 }
{ 3 , - 1 }

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choosing:

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3
2
0
1

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steps

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steps

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steps

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btw (im asking this here because i didn't come in last 2 days cause of some fam probs and the teacher doesn't respond to any of my messages)

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and assignments go to smth called assessments that help in my exam, like if i get 20 from 100 and i did the homework good, i will get like 50-60 grades

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some good/bad system

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bad cause its literally timed

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@alpine sable is that still allowed or no

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cause tbh idk shit and my professor doesn't answer to any of my messages and i only have like 1 hour left on it

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Is what allowed

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like is asking for that allowed

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if i don't know anything? and i have 1 hour left

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I mean, it's a test. People wont give you answers here

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no

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it isn't

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1 se

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sec

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It's timed homework for which you want answers in an hour

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@alpine sable it isn't a test

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lol

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its assignments but for online classes

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we take classes on an app that our school bought sub in

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it's zoom but better lol

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every assignment is like that

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@alpine sable will u please help me?

pale terrace
alpine sable
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.-.

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No clue what S.S. means.
Two numbers, x and y
Three times first plus twice second is 13

pale terrace
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Hi I'm having trouble getting started with this question and I would appreciate if someone taught me how to think about them ^^^

alpine sable
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Write that down

alpine sable
alpine sable
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9

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this?

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Yeah

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ight 1 sec

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Two numbers, give them names. a and b or x and y

alpine sable
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can u tell me the steps

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I wont give you the solution, I can guide yoi

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You*

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.-.

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how will i know the solution in 1 hour

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Two numbers call them x and y

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if i didn't even join session

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ok

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Three times first plus two times second gives you 13

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what's first and second

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x y?

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x and y, we dont know them

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Yes

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ight ok

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So whats the equation when you write it down? In terms of x and y

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im trying but my brain isn't functioning

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i just woke up few mins ago

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ok so now

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3 x X + 2 x Y

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= 13

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Yes

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Thats step 1

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lol this is gonna take so long

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Step 2: first added to three times second is 16

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and i'll not submit the assignment in time

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Then fail

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why .-.

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ok how about this

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can you solve the stuff now, and after the assignment can you stay abit or when you're free and dm me and try to explain until my shitty professor answers?

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cause tbh i need all the assignments i can get cause i got some other fam stuff i need to focus on

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assessments*

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1 sec lemmy show u what they are

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these are assessments

alpine sable
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Focus on family stuff then. I wont give you answers sorry

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ok

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ok can u give me a way i can solve the choosing questions

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like not answers

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Could have finished 1 question by now

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Find help elsewhere

alpine sable
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and 1 question in 1 hour .-.

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You want solutions, not help. Find someone to solve it for you then. Giving out answers is against the rules

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Sorr,

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Sorry

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well i will sit and understand the questions after i solve it

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Ping helpers, maybe someone will. I doubt it though

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<@&286206848099549185>

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well i think its a gonner anyways

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rip

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Guess randomly. Or google it

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if it took 1 hour to do 1 question it would take longer to make them all

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randomly how

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i will write the answers

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and take pic with my phone and answer it

alpine sable
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i tried this:

sage path
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@alpine sable Standing on the top of the sunset cliff in OB, Jack spotted a ship. If the cliff was 20 meters above sea level and the angle of depression of the ship from Jacks's eye was 10 degrees, how far is the ship from the shore <@&286206848099549185>

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πŸ™ PLEASE BRO

alpine sable
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ill try

sage path
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Kk

kindred helm
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isnt it like this..?

alpine sable
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yeah yeah

sage path
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so the answer is 20/x>

kindred helm
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so your answer is 20/cos(10)

alpine sable
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too slow with geogebra xD

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that isnt correct

kindred helm
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it is not?

sage path
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?

alpine sable
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isnt it the one thats along the water

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instead of the hypothenuse

sage path
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😰 pls i only got 1:24 min left

kindred helm
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that wouldnt make any sense delta

alpine sable
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why wouldnt it

kindred helm
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for the ship to be the base?

alpine sable
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the shore starts from the bottom

kindred helm
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how far is ship from the shore. if jack spots the ship from the cliff

alpine sable
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yeah assuming the cliff is straight

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its tangent that u use

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to solve for the base of the triangle

kindred helm
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im not a native speaker but i got a strong feeling im right here. could be wrong though lol

alpine sable
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me neither and same

kindred helm
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yeah the shore starts from the bottom

sage path
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ty guys!

alpine sable
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πŸ˜„

kindred helm
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but how far away is it from the shore

sage path
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i got no idea

alpine sable
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and it makes no sense for a to be 10 degrees there

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its 80

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cus 90-10

kindred helm
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true

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i just rereadi t

sage path
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30 seconds left

kindred helm
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so cos 20/cos(80) and it comes out

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to 115.175

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115.175 meters

alpine sable
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thats the hypothenuse

kindred helm
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yea

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it is

alpine sable
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not the distance to the shore

kindred helm
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bruh youre right

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haha

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dude im stupid now i understand what ur saying

alpine sable
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can u help me with my problem tho?

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no idea how to solve this

sage path
kindred helm
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hmm

alpine sable
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it's just school bro

kindred helm
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delta u in uni?

sage path
# alpine sable please?

lol don't beg em, suddenly they start to feel like they better than you and act all holy. just ask someone else

alpine sable
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i told him to ask someone else

kindred helm
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i have never integrated a function like that

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that has x on the top

alpine sable
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yeah me neither

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i tried

kindred helm
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i dont know of a single formula

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i think thats uni stuff

alpine sable
#

$\int_{ }^{ }\frac{x}{x+3}dx=\int_{ }^{ }x\left(x+3\right)^{-1}$

ocean sealBOT
alpine sable
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do x+3-3 and split into two fractions

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but have no idea how to go past this

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bruh forgot the dx there

muted raft
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Couldn't you just u sub this?

manic quail
kindred helm
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how does the sub thing work?

manic quail
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let u=x+3

alpine sable
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i guess u do x(u)^-1 du*1?

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in the integral of cpurse

manic quail
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Have you never done substitution?

alpine sable
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we havent had those yet

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im just bored and learnin ahead of time

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i did quite a lot of those yesterday but cant say i got them to the heart

manic quail
alpine sable
#

that integral at the start looks like pure suffering

dawn robin
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$\int{ }^{ }\frac{x}{x+3}dx=\int{ }^{ }x\frac{x+3-3}{x+3}$

ocean sealBOT
#

HyperBolt

482698680885837844.png
alpine sable
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that's what i suggested, then split the fractions

dawn robin
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Sorry im new here

alpine sable
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into 1 and -3/(x+3)

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why the x at front tho

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where did it come from

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all good

dawn robin
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That is gonna be way easier

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As @alpine sable said

alpine sable
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the x shouldn't be there, typo

dawn robin
#

Just a sec

alpine sable
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yeah thought so

dawn robin
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$\int{ }^{ }\frac{x}{x+3}dx=\int{ }^{ }\frac{x+3-3}{x+3}$

ocean sealBOT
#

HyperBolt

482698680885837844.png
alpine sable
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add dx at the end and it's perfect

dawn robin
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Then you just can split x+3 and -3

alpine sable
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ahh

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hard on a phone πŸ˜„

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atleast on a phone u can use the technique of pen and paper

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and picture

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not if you're on a bus

dawn robin
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$\int{ }^{ }\frac{x}{x+3}dx=\int{ }^{ }\frac{x+3-3}{x+3}dx=\int{ }^{ }\frac{x+3}{x+3}-\frac{3}{x+3}dx$

ocean sealBOT
#

HyperBolt

482698680885837844.png
alpine sable
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not keeping a notebook on u at all times to do some quick maths

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the first part simplifies to 1 right

dawn robin
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Clear from here @alpine sable ?

alpine sable
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yeah

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first part is 1 yep

dawn robin
kindred helm
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show how its done after uve done it

alpine sable
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done these with a number on top

dawn robin
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then you got there ?

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Great

alpine sable
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ill solve and post my solution

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a bit

kindred helm
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is it x - 1/3 * ln(x+3) + C

dawn robin
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Then you got the exact solution

kindred helm
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i dont know what u mean

alpine sable
#

1-3(ln(|x+3|))

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+c

kindred helm
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true abs value

dawn robin
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no abs value

kindred helm
#

u meant 1/3 instead of 1-3?

dawn robin
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No

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Just sec

alpine sable
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i meant 1-3

kindred helm
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true no abs value x is x > -3

alpine sable
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forgot about that part, it was stated yeah

dawn robin
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x - 3 * ln (x+3) + C

kindred helm
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ahhhhhh im stupid i forgot

dawn robin
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no abs cause x>-3

kindred helm
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obv you can take the constant out

alpine sable
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$\int_{ }^{ }\frac{x}{x+3}dx=\int_{ }^{ }\frac{x+3}{x+3}-\frac{3}{x+3}=\int_{ }^{ }1-\frac{1}{3}\cdot\frac{1}{x+3}=x-\frac{1}{3}\ln\left(x+3\right)+c$

ocean sealBOT
twin raft
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that symbol gives me the scary

alpine sable
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forgot the dxs

dawn robin
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It is 3 not 1/3 @alpine sable

kindred helm
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yeah it is 3

dawn robin
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3 ln

alpine sable
#

dude cmon how the hell did i miss that

kindred helm
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i did too lol..

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well its late and i thought about it for 5 seconds thats my excuse

dawn robin
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I think it is a little attention error

alpine sable
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$\int_{ }^{ }\frac{x}{x+3}dx=\int_{ }^{ }\frac{x+3}{x+3}-\frac{3}{x+3}dx=\int_{ }^{ }1-3\cdot\frac{1}{x+3}dx=x-3\ln\left(x+3\right)+c$

ocean sealBOT
alpine sable
#

now it should be correct

twin raft
#

can i get some help laters

dawn robin
#

Happens to even the great mathematicans

alpine sable
twin raft
#

i dont get it i keep getting wrong answer
finite difference
200x / ((x^2) + 1)
f'(4)
i get f(4.01) being smaller than f(3.99)
so it gives me negative number
h=0.001

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so

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doing it the f(4.01)-f(3.99)/2h

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sec ill screenshot

fluid valley
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hello everyone !

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how can i generate this sequence ?

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1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8,…

alpine sable
#

odd numbers once, evens twice?

twin raft
muted raft
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floor(2n/3)

dawn robin
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So every difference should be negative

twin raft
#

πŸ€”

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so why am i getting wrong answer

fluid valley
alpine sable
#

ty

gusty pawn
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how do I make Kc the subject

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my last two braincells are giving up on me

elfin hamlet
#

I need help

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A to the 2 power Γ— c to the 2 power

surreal lantern
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Could someone help me out? I did this word problem but I don’t think I did it correctly.

image0.jpg
alpine sable
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@surreal lantern, I just joined this server, but trig questions are up my ally. I’ll answer this, just give me a few minutes.

surreal lantern
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Thanks so much!

alpine sable
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Btw, bearing is the clock rotation from north

surreal lantern
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Yup this is how my teacher described it.

image0.jpg
alpine sable
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When sixty consecutive odd integers are added together, their sum is 4800. Determine the largest of the sixty integers.

daring chasm
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obligatory question if this is a test or not

alpine sable
#

I would start by doing that an odd number is 2n+1, the next consecutive odd is 2n+3, and maybe try work out the sum from there? I’m not sure how you’d do it without noting all 60 numbers tho πŸ˜‚πŸ˜‚

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I did that

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And got this

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I know I went wrong some where

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But I do not understand where

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I’d try approach it with a series, calculate sum of 60 numbers with progression: 1,3,5,7,9 etc. Then take that away from 4800 and you’d be left with 120n=4800-sum of integers, find value for n and then use arithmetic sequence formula to find 60th number and substitute if you have to

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Thats what I did

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The sum of the integers is 900

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I’ll give it a try, two mins :))

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kk

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I got 139 as the final answer, I’m unsure if it’s right but I did it via the method I suggested,

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Hmmm

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I got 133

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I used the arithmetic series and arithmetic sequences to work it out, are you aware of those formula?

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Yes

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What did you get as the value of n

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I got n as 10

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I got n as 7.5

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Would you like me to send my working?

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Yes

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Please

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I got the sum of the odd integers as 900

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I’m not sure where you got that from

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2+4+6+8+10 = 30 and 12+14+16+18+20= 80, therefore I said that they increase my a common difference of 50. So, 30+80+130+180+230+280. Adding them all up I got: 930

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That’s even numbers?

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I know, allow me to further explain my thinking

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The sum of the sixty of the consecutive integers would then be: 1830. Using the formula: n(n+1)/2

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1830-930= 900

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There are 5 integers that make up 30 and 80 respectively i only count 30 total integers in your calculation to 930. You’d need to keep adding 6 more :))

tight basin
#

can someone check if i have done it right?

unknown.png
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so far,,

alpine sable
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If you add the remaining 6 digits you get 3660 which is a total of 60 integers

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For even numbers*

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Ohhhh

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I see

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Try it now, hopefully it’ll work out 😁

#

@tight basin I’m stuck on this too funnily enough, what I think you could do is differentiate first which removes b as it’s an integer, then substitute x=1/6 which means gradient function is 0 (I think), then rearrange for a. Then you may be able to work out b? I’m not too sure how just yet

#

@surreal lantern, I feel like such an idiot, i certainly did something wrong

#

Lemme show you what I did

#

It’s been a few months since I’ve done this, and this is old for me

tight basin
#

just doesnt say how it got -2 so kinda annoying

alpine sable
#

Sorry if I wasn’t much help

#

@tight basin same here I got -13, not sure how she got -2

#

Here is a similar question from one of my online classes

image0.jpg
tight basin
#

stupid

alpine sable
#

I think your teacher is wrong 😬, subbing a=-2 in the differential doesn’t equal 0

#

What negative two?

#

Yeah apparently

#

Wdym?

#

His teacher got a =-2 but we both got it as -13

#

I think we are doing different questions

tight basin
#

@alpine sable

#

idk how they got a+4b=10

#

lolwtf

alpine sable
#

I’m really confused how they got that result tf

#

I mean I get how to obtain the second derivative but and all that but it seems strange that you have to use the second derivative

#

A point of inflection is just where the gradient is 0 so surely the first derivative would work too

tight basin
#

first deriative is for stationary point

#

they got a+4b= 10 by multiplying everything by four after u sub in g(-1/2)

alpine sable
#

I have literally no idea where they got a+4b=10 either because I can only make it as a+b=10

#

Unless I’m missing something

tight basin
#

sub in -1/2 into g(x)

#

tell me what u get

#

dont simplify anything

alpine sable
#

Yeah I got -1/2 +1/4(a) -2 +b =0

#

Wait nvm I did a stupid, I now have a + 4b=10

tight basin
#

ye just a shitty question

alpine sable
#

Yup

#

They got the answer wrong though for sure because second derivative is only used to determine the nature of the stationary point right?

#

Though saying that a point of inflection still has a second derivative of 0

daring chasm
#

so starting from 1, it'd be n^2, where n is the number of terms

#

now ofc you don't want to start from 1, and you can subtract the point where you want to start out

#

in this case 60 earlier, since you want to add up 60 numbers

#

so you'd end up with n^2-(n-60)^2 - then you could factor it out by the difference of the squares as 60(2n-60)

#

and n is the nth odd number starting at 1

alpine sable
#

I got the answer, it was the guy I was helping out who needed help. 139 was indeed the answer 😊

daring chasm
#

yeah then solve 60(2n-60)=4800, resulting in 70

#

that's the 70th odd number, with the 1st being 1, so you multiply by 2, subtract 1, yep 139

steel scaffold
#

i dont even understand the question

oak chasm
#

@steel scaffold What's the height of the bottom triangle if the base is 1?

steel scaffold
oak chasm
#

Right, so you can get the area of the bottom triangle from base and height.

#

Now, what's the base of the second triangle? It's the hypotenuse of the bottom triangle. What's that length?

steel scaffold
#

sqrt(4/3)?

oak chasm
#

Yep.

#

So, what's the other nonhypotenuse side (the "height") of the second triangle?

steel scaffold
#

sqrt(4)/3

oak chasm
#

Yep, which can be simplified a bit.

#

So, you have the base and height of the second triangle, so you can find its area.

#

What's the base of the top triangle, which is also the hypotenuse of the second triangle?

steel scaffold
#

0.7698003589

oak chasm
#

No, it should be 4/3.

#

$\cos(30^{\circ}) = \frac{\frac{2}{\sqrt{3}}}{x}$

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
oak chasm
#

The base of the middle triangle was sqrt(4/3), which is 2/sqrt(3). That's the adjacent side, which is the numerator on cosine. The hypotenuse is the denominator of cosine.

#

So, $x = \frac{2}{\sqrt{3} \cos(30^{\circ})}$

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
steel scaffold
#

hmm ok i see

oak chasm
#

So, $x = \frac{2 \times 2}{\sqrt{3} \times \sqrt{3}} = \frac{4}{3}$

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
oak chasm
#

Now we know the base of the top triangle, what's its height side?

steel scaffold
#

4/3 tan30

oak chasm
#

Yep, and what's $\tan(30^{\circ})$?

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
steel scaffold
#

1/sqrt3

oak chasm
#

OK, so you have the base and height of the top triangle.

#

Find the area of all three triangles, add it together.

steel scaffold
#

1.186775553

oak chasm
#

No, it's 2.37 something, but what's the exact answer?

steel scaffold
oak chasm
#

Oh, I see. I think I made a mistake. One moment.

#

Yes, you were right.

#

,w (1 1/sqrt(3) + 2/sqrt(3) 2/3 + 4/3 4/(3 sqrt(3)))/2

ocean sealBOT
oak chasm
#

So it has $\sqrt{3}$ in the exact answer.

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
oak chasm
#

So, it'll be one of the answers with .5 in the power of three.

steel scaffold
#

wdym

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
steel scaffold
#

yea

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
steel scaffold
#

yea

oak chasm
#

So, the .5 has to show up in the answer.

#

It can't be answer C.

steel scaffold
#

there are 12 triangles not 3

oak chasm
#

Oh!

#

Missed that.

steel scaffold
#

and there are different angles for some

#

not all have 30 degrees

#

i assume 4 4 4

#

wait no

oak chasm
#

It says they're similar triangles, which means the angles are the same in all of them.

steel scaffold
#

oh yea

oak chasm
#

But basically, let's make it easier for ourselves.

#

The area of the bottom triangle is $\frac{1}{2 \sqrt{3}}$.

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
#

Chai T. Rex

537482727557955597.png
#

Chai T. Rex

537482727557955597.png
#

Chai T. Rex

537482727557955597.png
oak chasm
#

So, the total area is $\frac{1}{\sqrt{3}} \sum\limits_{i = 0}^{11} \left(\frac{4}{3}\right)^i$

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
steel scaffold
oak chasm
#

Let me recheck.

steel scaffold
#

each base is sqrt(4/3) times the previous base

#

i think

#

yea

oak chasm
#

Sorry, computer crash.

#

@steel scaffold Yeah, good catch.

#

So, the area is $\left(\frac{2}{\sqrt{3}}\right)^2 = \frac{4}{3}$ times as much.

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
oak chasm
#

So, it comes out to the same thing, but I made a typo.

#

No, wait, another typo.

#

So, the total area is $\frac{1}{2 \sqrt{3}} \sum\limits_{i = 0}^{11} \left(\frac{4}{3}\right)^i$

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
#

Chai T. Rex

537482727557955597.png
oak chasm
#

@steel scaffold I think that's correct.

steel scaffold
#

yea i think

oak chasm
#

,w 1/(2 Sqrt[3]) Sum[(4/3)^i, {i, 0, 11}]

ocean sealBOT
oak chasm
#

So, that should be the total area of all 12.

steel scaffold
#

hmm i see

#

is there another way that I could calculate the area of all 12 without having to use sigma?

oak chasm
#

Well, you could do sigma by hand.

#

,w 1/(2 Sqrt[3]) (1 + 4/3 + (4/3)^2 + (4/3)^3 + (4/3)^4 + (4/3)^5 + (4/3)^6 + (4/3)^7 + (4/3)^8 + (4/3)^9 + (4/3)^10 + (4/3)^11)

ocean sealBOT
oak chasm
#

The trick to save a lot of work is to notice that the sides of each successive triangle are 2/sqrt(3) times as large, so the area must be 4/3 as large as the previous.

#

So, you have the first area plus 4/3 of the first area plus 4/3 times 4/3 = 4/3 squared of the first area, etc.

#

This allows you to find the area of just the first triangle and multiply it by that.

steel scaffold
#

oh ok i see

#

thanks for the help really appreciate it

oak chasm
#

You're welcome.

unreal herald
#

am having math problem on scaling image from all sides and keeping the corner position

unknown.png
#

this piece of code work only before rotation

snow tundra
#

Determine the excise tax to be paid on a house that sells for $268,210 if the buyer makes a $25,000 down payment and the seller takes back a second mortgage for $50,000?
[7:56 PM]
A)$536 .42 B)$537 C)$533 D)$538
[7:57 PM]
so the answer is B but can anyone explain how you get the answer please?

amp12128 β€” Today at 8:34 PM
$268,500/500 = $537
this is all it says soo idk where they got 500 from

twilit sierra
#

my exam got cancelled

night geyser
#

πŸ‘

sly mantle
#

πŸ‘’

night geyser
#

(deleted message with mod ping to remove venmo info)

manic glade
#

CβŠ†A, f:A->B

#

need to prove that CβŠ†f^-1(f(C))

#

so i suppose my task here is to show that for every x in c that x is also in f^-1(f(C))

#

and im having trouble formulating that into something more explicit than a vague gesture at the page and saying "well of course it is, look at it"

#

any tips?

#

verbally i can say that its true because that set contains all elements in A that "point" to the elements in B and that that set contains C

#

might as well mention the other part while im at it, need to also prove that if f is bijective then c=f^-1(f(C))

sly mantle
#

it's no more than using definitions of image set & preimage

manic glade
#

just feels like that falls short of the task to "prove" it

sly mantle
#

i meant most of the proof involves using those definitions

manic glade
#

for every x∊C f(x)∊f(C) β‡’ x∊f^-1(f(C)) β‡’ CβŠ†f^-1(f(C)) does this look right?

sly mantle
#

yes

manic glade
pale cargo
#

Hi

#

what should i do first

#

this is out of context, but after I have a complex number in polar form, it's equal to z

winged plank
#

What is the question?

pale cargo
winged plank
#

Oh

#

I would start off by putting z in it's normal form

#

a+bi

pale cargo
#

then

#

i know those lol

#

im asking if i should find z first then multiply, THEN take the conjucate

#

or

#

find the conjucte then multiply

winged plank
#

Well if you have it in a+bi form I would just multiply them together and then take the conjugate

#

you've already done the heavy lifting

pale cargo
#

are both ways correct?

winged plank
#

I don't really know

#

I don't think so

#

but I may be wrong try it out

#

The question is (a-bi)^2 = Conj((a+bi)^2)

pale cargo
#

bro

#

i need it in polar form

winged plank
#

Yeah you can convert from a+bi to polar form

pale cargo
#

k

winged plank
#

the radius is just the magnitude of a+bi and the angle is just arctan(b/a) I believe

pale cargo
#

i think maybe do z*z first

#

then take their conjucate

winged plank
#

That's what I would do 😎

pale cargo
small stag
#

Multiply first because it asks for the conjugate of the product

#

,w conj(z) * conj(z) = conj(z*z)

ocean sealBOT
small stag
#

Oh nvm then

winged plank
#

Oh hey that other way does work

pale cargo
#

so both...

winged plank
#

man I forget how conjugates work some times damn

small stag
#

Indeed it does sorry not too well versed with complex

pale cargo
#

lol

winged plank
#

Tell me what you get

pale cargo
#

well after simplification of the algibric form

#

i got "i"

#

which is [0,90] i guess?

small stag
#

What is z*

pale cargo
#

idk

#

is the polar form of "i" [0,90]?

winged plank
#

Polar form is r * e^ix

#

What is r?

pale cargo
#

r is zero

winged plank
#

No, what is the magnitude of z?

#

Oh wait nvm

#

Hey just do -e^0

pale cargo
#

1

#

1

winged plank
#

right?

pale cargo
#

1

small stag
pale cargo
#

i simplified the big fraction

small stag
#

Nvm continue

winged plank
#

Okay cool so the magnitude is 1

#

So our polar form looks like this e^ix right?

#

but recall that e^ix=cos(x)+i*sin(x)

#

What value of x does cos(x)+i*sin(x) = -1?

ocean sealBOT
#

Chai T. Rex

537482727557955597.png
winged plank
#

Yeah exactly and cos(x)=-1 when x= pi so that means (z * z)^*=e^(i * pi)

#

@small stag

wicked frost
#

Every value of (2n+1)$pie

winged plank
#

Well that's only if you're a math major

wicked frost
#

Well range is not defined so we have to assume (-infi,+infi)

winged plank
#

Around these parts we only care about first order terms and finite solution sets

vale wigeon
#

consider: in how many numbers does the digit 1 appear in the hundreds place?

#

repeat for the other digits and the tens and units places.

#

come to a conclusion about how one might calculate the sum.

elfin matrix
#

So i was doing this problem then i forgot what to do after

vale wigeon
#

well you made it so that the x only appears on the left

#

why not add or subtract something else to both sides to get rid of that +10

elfin matrix
#

Its asking for solution set

#

And all the answers on the multiple choice are not decimals and i keep on getting decimals and i check it online and it says decimals too

vale wigeon
#

are fractions a no-go?

#

also it feels as if you ignored my suggestion

elfin matrix
#

Im sorry i guess i took it the wrong way

#

I tried adding 4x instead and then 10 and then 5 to try out different ones like you said

#

I just ended up putting this cause it made the most sense with what i got

vale wigeon
#

thonk what the fuck?

#

none of these are correct.

#

the correct answer is x <= 5/9

#

,w -4x + 10 >= 5x + 5

ocean sealBOT
elfin matrix
#

Thats exactly what ive been getting

#

And i even started doing it different ways to get different answers to just get one from the choices

#

But i couldnt find any so i just put the one with 5 cause 5/9

vale wigeon
#

well the thing is

#

all the answer options are wrong

#

so the correct course of action is to talk to your teacher and hope they don't double down

alpine sable
#

is 2log|x-2| = log(x-2)Β² ?

vale wigeon
#

2 log|x-2| = log( (x-2)^2 ) yes

serene hearth
#

Can someone guide me as to how I can solve a simple question like this on matlab?

unknown.png
# 
syms y(x)
ode = diff(y,x) == -0.0004332 .* y;
cond = y(1) == 0.005;
ySol(x) = dsolve(ode,cond);
disp (ySol(-0.002));```
#

This is my code so far, however it doesn't work as intended, the value it returns looks too random.

alpine sable
#

can this be simplified any further

IMG_20210425_135650.jpg
serene hearth
woeful pulsar
#

please don't crosspost

inner zinc
#

Ok

#

Sorry

woeful pulsar
inner zinc
#

I m new here

sly mantle
#

@inner zinc please familiarize yourself with the rules in #❓how-to-get-help; in particular don't multipost

inner zinc
#

Ok

elfin wasp
#

any help on this physics question

unknown.png
raw badge
#

Physics server, link for which you'll find in #old-network, is more suited for this

elfin wasp
#

alright, I thought this was more maths based question with mechanics

kindred helm
#

is it asking for mu? i dont understand the question because of my bad english

alpine sable
#

If x=1/6 at the point of inflection on f(x)=4x^3 +ax^2, how do you work out a? If you take the first derivative you get f’(x) 12x^2 +2ax=0, the second derivative f’’(x)=24x +2a. Sub in the x=1/6 and for f’(x) you get a=-1, sub in x=1/3 for f’’(x) and you get a=-2. That shouldn’t happen right? What have I missed?

versed osprey
#

why is minus sqaure root of 7 an irrational number

gray isle
#

@alpine sable you're not using your x=1/6 properly

lyric lynx
gray isle
#

when consider inflection, you're only really interested in the second deriviative

versed osprey
gray isle
#

i.e. solve f''(1/6) = 0

lyric lynx
#

Actually, it would be better to say the square root of any prime number is irrational, and 7 is prime.

versed osprey
lyric lynx
#

I'm pretty sure the former statement is still correct though.

versed osprey
lyric lynx
#

Not necessarily. In fact, I can't think of a single case where that is true.

livid path
#

Hi

#

I am new here

#

If I ever need help

#

Would u guys and girls help

versed osprey
jagged imp
versed osprey
#

ok ill note it down

sullen juniper
#

not sure where to begin doing this, idek what the question means lol

unknown.png
raw badge
gray isle
#

it's asking you to find the size of angle C

sullen juniper
#

thank you

gray isle
#

note that the given 103Β° is for angle A and is rounded.

#

you could apply the sine rule (which may be what they want)

#

since you are given all 3 sides, you can instead apply the cosine rule to get a more accurate result

sullen juniper
#

thanks

opaque cape
#

why is there only one possible value of x and how, i feel like im missing smthn i didnt realize

unknown.png
lyric lynx
#

context?

jagged imp
#

show the whole question, there's probably something earlier in the question that doesnt permit negative numbers or smthn

lyric lynx
jagged imp
#

in isolation, whats written is fine

opaque cape
#

oh right

lyric lynx
#

boom

#

a length cannot be negative

opaque cape
#

oh why not

lyric lynx
#

convention

#

also because in the context of this question, a negative length makes no sense.

opaque cape
#

ohhh i get it

#

thanks

serene hearth
#

It returns a value like this

#

which imo looks too absurd? xD

lyric lynx
#

Gotta love computers

#

The equation solution will be an exponential, so that seems correct...

#

But you're going to want to simplify it to a decimal

#

$\frac{1}{200}e^{0.004315}$

ocean sealBOT
#

John_Cavanaugh

747488113542299768.png
lyric lynx
#

Check my work

acoustic crater
# 
A number is selected at random from the set {1,2,3,4,...,20}. Find the probability of the following events

1. drawing an odd number
2. drawing an event number
3. drawing a prime number
4. drawing a composite number
5. drawing a number divisible by 3 or 5
6. drawing a number divisible by 4 or a factor of 20
7. drawing an odd number or a factor of 18
8. drawing an even number or a factor of 11

i need to finish my homework because my mom is gonna kill me again, so I need help in someone.

lyric lynx
nimble wyvern
#

@acoustic crater what you need help with? which number

faint trench
#

need a bit of help with finding the domain over which a function has an inverse, but not sure if im doing it right. The function is f(x) = (x^2)/(x^2 - 9), and i need to find the domain where it has an inverse. any help is appreciated, thanks.

leaden hill
#

guys

#

I know its so easy

#

ise means if

#

how we were doing these :/

vague coral
#

well (2sqrt(3))^(1/3) = (3sqrt(x))^(1/6)
(2sqrt(3))Β² = 3sqrt(x)
12 = 3sqrt(x)
sqrt(x) = 4
x = 16

#

If I'm not wrong

leaden hill
#

u sure?

vague coral
#

you can verify

leaden hill
#

i forgot

#

do these type of quesitons so

#

I cant πŸ˜„

vague coral
#

I mean you plug 16 in the equation and see if it's correct '-'

copper silo
#

im stuck on this

glass lichen
copper silo
#

nothing

glass lichen
#

Have you tried googling stuff about kites?

#

specifically about their diagonals

copper silo
#

could you just tell me how to do it?

glass lichen
#

diagonals of kites are perpendicular.

#

a quick google would do that as well

copper silo
#

yeah so i gotta find the perpindicular gradient how do i do that?

glass lichen
#

use the definition of perpendicular slope

copper silo
#

which is?

glass lichen
#

look at your notes or google yourself. I'm not gonna spoonfeed all the things you can easily google

copper silo
#

why not?

glass lichen
#

Cause you should be able to type on google. .

copper silo
#

i prefer human interaction

coral pagoda
#

I think the problem moshill is currently dealing with is that you are not showing much attempt on trying to solve the problem on your own.
They gave you guidance, but note they will not just give the answer to you. That's not how it works here.

chrome steppe
#

becuase kites are (hopefully) perpendicular, i think it should be the reciprocal of AC's equation + or - an offset

chrome steppe
# copper silo

there's not enough evidence if the angles arent 90 degrees

glass lichen
#

kites arent perpendicular

#

their diagonals are

chrome steppe
#

yes

#

thats what i meant

#

(y=-\frac{1}{3}x+\frac{4}{3})

ocean sealBOT
#

bow wow

809561937636753418.png
chrome steppe
#

i put it on a graphing calculator and it worked

copper silo
#

so how i do it?

chrome steppe
#

(x=\frac{1}{3}y-\frac{2}{3}) is the reciprocal to AC's equation

ocean sealBOT
#

bow wow

809561937636753418.png
chrome steppe
#

welp

#

this equation makes the same line as AC

copper silo
#

you gotta find the perpendicular gradient first

chrome steppe
#

if you swap x and y back it will rotate 90 degrees

#

and then (i think) you square the 2 in 2/3

#

i'll check

#

no

#

the offset is different

copper silo
#

welp the answers tell me to find the perpendicualr gradient

chrome steppe
#

google that

ocean sealBOT
half pasture
#

Sorry I meant $C_2[a,\infty)$

ocean sealBOT
chrome steppe
#

is this group theory?

#

im not at that level yet

half pasture
#

No, this is calculus

chrome steppe
#

oh

glass lichen
#

by parts..?

#

that's what im drawn to at first

half pasture
#

the hint is "integration by parts"

glass lichen
#

right

half pasture
#

but how?

glass lichen
#

so pick one of the f'(x) to be u and the other to be dv

half pasture
#

I tried that.... I didn't get anywhere

#

You get $f(x)f'(x)-\int_a^\infty f''(x)f(x)dx$

ocean sealBOT
glass lichen
#

right yeah

half pasture
#

but both terms might not converge

chrome steppe
# copper silo

if you remove the offset from the other eq i sent, then y=2 will have x=-6, so the offset must be -(-((6-2))/3, so 4/3

glass lichen
#

well you know for the integral to converge $\lim_{x\to\infty}f''(x)=\lim_{x\to\infty}f(x)=0$

ocean sealBOT
#

moshill1

186109587366215691.png
half pasture
#

Thats simpy false

#

simply

#

There are positive functions that don't have a limit at infinity, but their integral converges

vagrant rover
#

Is this question solvable? I don't necessarily want an answer, I just want to know if the question is written wrong. I have been having a problem with questions not having a correct answer.

5f04bd05d1072b14f6e60c95112f4c90.png
chrome steppe
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if you do an expaned version of the quadratic formula, (so ax^3 + bx^2 +cx + d)

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you can make any wave like that

glass lichen
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that's not a wave

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that's a cubic

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so there's no such thing as expanded version of the quadratic formula

vagrant rover
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Are yo uguys talking to me?

glass lichen
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I was talking to bow

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but you know the roots so you can write the factored form of the cubic.

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then use the y-int to find the a value

vagrant rover
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Thanks

half pasture
candid sluice
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This seems like a pretty hard problem

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Well doesnt seem like it

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It is

nimble wyvern
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umm

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when x is 0. you get y=160

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you can eliminate 2 answers

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just from that

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B

subtle mantle
# ocean seal **Omri**

What if you integrate by parts again to get something $-\int_{a}^{\infty} (f’(x))^2 dx$

ocean sealBOT
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Wew Lads Tbh

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half pasture
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You just get 0=0...

subtle mantle
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I think it would be $f(x)f’(x)- f’’(x)f’(x)+\int (f’(x))^2 dx$

nimble wyvern
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@half pasture where you get 0=0?

ocean sealBOT
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Wew Lads Tbh
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half pasture
ocean sealBOT
subtle mantle
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Yeah that seems more correct

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Still though maybe the idea leads somewhere?

half pasture
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And you just get a trivial identity

subtle mantle
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Only other thing I can think of is maybe try integration by parts on $\int (f’’(x))^2 dx$ but I’ll need to actually write it all out to see if it leads anywhere

ocean sealBOT
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Wew Lads Tbh
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(You may edit your message to recompile.)

233993116418441216.png
half pasture
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How? $f$ is not three times differentiable

ocean sealBOT
subtle mantle
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Yeah that’s the problem

gritty pine
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do i need geometry to learn trigonometry? sorry for the stupid question

gray isle
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yes

gritty pine
hollow cypress
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what's the construct called if equivalences between a and b are themselves all equivalent?

analog locust
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hi

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how does this work?

vale wigeon
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product rule in reverse

analog locust
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umm.... im bad at calculus

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more explanation?

vale wigeon
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2t is the derivative of 4+t^2

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...are you at least familiar with the product rule?

analog locust
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umm.... not really

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can you explain it to me please?

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or is there some sort of step-by-step explanation for it?

vale wigeon
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look up "calculus product rule derivation" if you want a proof

analog locust
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im just plunging into ODE without knowing this stuff and it felt a bit hard 😦

vale wigeon
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wait what

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you're plunging into ODE without a solid grasp of calculus?

analog locust
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yes, im planning to speed-through it πŸ™‚

vale wigeon
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ew no

analog locust
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any advice where I can learn calculus?

vale wigeon
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math is not meant to be speedran

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there are plenty of places

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such as khan academy

analog locust
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I don't have the luxury... my exam is in 3 months 😦

vale wigeon
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bruh

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i mean like ok just to put this into perspective
this is like if you tried to start solving quadratic equations while barely knowing how to multiply.

analog locust
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is there like a table of content/recommended book or something similar to have an overview of what I need to know to do ODE?

vale wigeon
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paul's online math notes

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should be a decent-ish resource

analog locust
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hmm....

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would around 9 hours a week be enough to get to ODE in 3 months?

vale wigeon
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i have no idea

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maybe?

analog locust
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@vale wigeon do I need to do Calculus 1-3 before ODE?

vale wigeon
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1 and 2 definitely, 3 maybe

analog locust
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and what happens if the independent variable was also a part of the derrivative?

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I noticed that t was there too

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y*

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the dependent variable*

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ok... im a bit confused

vale wigeon
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of course youre confused

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this is like trying to explain a particular instance of factorization to someone who struggles with multiplying numbers ;p

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like

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no really, i could try and state the product rule time and time again

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it would be no use because it will not stick

analog locust
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I just skimmed it

vale wigeon
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like ok for reference here is the rule itself: $$\dv{x} [f(x) g(x)] = f(x) g'(x) + f'(x) g(x)$$

ocean sealBOT
analog locust
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its like taking a derivative of 4+t^2 times y, right?

vale wigeon
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yes thats exactly what is on the right-hand side

analog locust
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lets say 4+y^2 is f(x) and y is g(x)

vale wigeon
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(4+t^2)y, differentiated

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4+t^2 itself differentiates to 2t

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y differentiates to dy/dt, almost tautologically

analog locust
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I just need to do f'(x)(g(x) + f(x)g'(x)?

vale wigeon
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"need to do" is one way of putting it Β―_(ツ)_/Β―

analog locust
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I can't do that since I am not enrolled in calculus 😦

analog locust
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how does it differentiates to dy/dt?

vale wigeon
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what do you think dy/dt even is

subtle mantle
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the derivative of y is dy/dt by definition

vale wigeon
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if not the derivative of y

analog locust
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oh my goodness, I never thought of that

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thanks!!!

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nope, what's canvas page?

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umm...

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what is the derivatives of some number y? @vale wigeon