help-17

[past sail]

you can optimize it considering 1 - tan(x) and 1-cot(x) as fractions

that0s the same who i did

your work is well

but you can optimize it

[vocal sleet]

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[balmy garnet]

Can someone help

[hexed needle]

is f'' positive or negative at that point

[vocal sleet]

@balmy garnet Has your question been resolved?

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[rotund crest]

Can anyone explain this to me? In ex.1 why is the second limit has the same equation as the first one and in ex.2 why is the second step (b) has the same equation as the first one but not the first step (a)?

[paper depot]

is there an image that didn't get through

[rotund crest]

Oh wait sorry

[rotund crest]

Here

[paper depot]

not clear what the goal is here

what exactly are you trying to do w/ these functions

[rotund crest]

Test if each of these equations are continuous or not

Wait it didn't get much clearer

[paper depot]

In ex.1 why is the second limit has the same equation as the first one
im having trouble understanding what you mean here

[paper depot]

well ok you are testing these for continuity

uhhh

[rotund crest]

This is what i meant

[exotic surge]

Step a and b both have the same equations from what I see

“why is the second step (b) has the same equation as the first one but not the first step (a)?” I don’t get what you mean here

[rotund crest]

This is example 1

[rotund crest]

This is example 2

[paper depot]

this work seems to be testing the function for continuity only at the endpoints of the interval

and it's just silent about what happens on all other points of the interval

[rotund crest]

I'm just confused shouldn't f(b) be the same as the second equation?

[exotic surge]

Try to be specific about which equations, I don’t know what is the “second equation”

[rotund crest]

first equation x^2 - 9 domain is 1/ second equation x + 3 domain is 4

I was reviewing for exam so I need to understand it

[exotic surge]

[1, 4] is the range in which we have to check if the function f is continuous. The start of a range is denoted by “a” and the end is denoted by “b”

So a = 1, b = 4

We need to find if the function is continuous at both points a and b (1 and 4) so we do the three tests for both a and b

f(a)
Lim x->a f(x)

f(b)
Lim x->a f(b)

[vocal sleet]

@rotund crest Has your question been resolved?

[rotund crest]

can someone brifely explain this?

[dire torrent]

What specifically?

[rotund crest]

explain why in the first example the f(b) is the same as the first one and in the second example why the first step (a) in f(b) is the second equation while the second step (b) is the same as the first one

[dire torrent]

I assume a is -3 and b is 1?

[rotund crest]

in the first example yes

[dire torrent]

And you want to know why you take the same piece of the function for both a and b, right?

[rotund crest]

well in ex.1 the two equations are x - 6 and x-1/x+1so i want to know why x-6 is the equation used in f(a) and f(b) instead of x-1/x+1

[dire torrent]

Ok

Well, first notice that the function f(α) they give you is defined in two pieces

One for each equation they give you

And after each equation they give you an inequality, for α-6 for example the inequality is α<2

Essentially, given a real number α, the function will give you an image defined by an equation depending on which inequality it satisfies

Both -3 and 1 satisfy α<2, so they're both given by the same equation

[rotund crest]

but what about example 2 why in f(b) the first step (a) used the first equation which is x^2-9 while the second step (b) uses the second equation which is x+5

[dire torrent]

Same thing, your a there is 1 and your b is 4

The inequality for one equation is α<4, which 1 satisfies

And for the other equation it's α≤4, which 4 satisfies

[rotund crest]

ohhhh now i get it thanks

[vocal sleet]

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[tacit creek]

Is this right reasoning to solve this exercise? The result is right but I am not sure about how I've found it, I think it might be too dismissive

[pseudo finch]

I think this is not the right reasoning.

This limit is of the (→1)^(→infinity) form

My bad, i typed 0 instead of infinity at first

[tacit creek]

No worries, where do you find 1^inf tho? Like I am missing the one? I thought maybe I should've used exponents rule (bringing the 1+3x/1+2x to an exponent) but it wouldn't become 1^->inf?

[serene needle]

If you take x into the brackets
It becomes 0^infinite
That is not any undermined form

[pseudo finch]

$$The {\frac{1+3x}{1+2x}}^{1/x} is of the (→1)^(→infinity) form$$

[twin meteor]

PRAKHAR

[tacit creek]

So I should take x into brackets as in x^x?

Given that it is root x

[serene needle]

Yes

It be comes
$(\frac{x^x + 3^{x+1}}{1+2x})^{1/x}$

[twin meteor]

Cняıƨ

[serene needle]

It's clearly 0^\infinity

[visual marsh]

isnt it 0 ( 1^inf) = 0?

like we get the 1^inf part as e

[pseudo finch]

@tacit creek

[visual marsh]

am i correct?

prakhar and chriz

[pseudo finch]

Yes

[visual marsh]

u shudnt be giving answers directly

[pseudo finch]

But it would help them learn better.

I've explained the (→1)^(→infinity) part

Sometimes, illustrations can help better than solving something by oneself.

[tacit creek]

Are you using the asymptotes rule for the first part? The f(x) and g(x) I mean. Like is that why you are doing 1+f(x)? To find the g(x) so that f(x) - g(x) = g(x)*(f(x)/g(x) -1) ->0 is true?

Or is it another rule?

[pseudo finch]

We are not finding g(x).

The function in the exponent is g(x)

[visual marsh]

u cant derive it using log

1^inf limits

[pseudo finch]

I wrote $\frac{1+3x}{1+2x}$ in the form of 1+f(x)

[twin meteor]

PRAKHAR

[pseudo finch]

To be able to use that formula for (→1)^(→infinity) form of a limit.

@tacit creek do you understand it now?

[tacit creek]

A bit better, I think I am gonna reverse solve it to understand it better tho

Thanks for the help :)

[pseudo finch]

What do you mean by reverse solve ?

[tacit creek]

Like solve every passage but in reverse so I can see better the reasoning, like from the xe^(1/1+2x) I am going back to xe^(x/1+2x*1/x) to the first one

Usually it helps me out to understand better

[pseudo finch]

Like, reading and comprehending up from the final result?

[tacit creek]

Yep

And redoing some of the passages

[pseudo finch]

If you want, you can search up the proof of the formula of (→1)^(→infinity) form of limit.

[tacit creek]

Will do. I am closing the thread now. Thanks again :)

.close

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[twilit magnet]

Determine all integers 𝑛 ≥ 2 that have a representation 𝑛 = 𝑎^2+ 𝑏^2 , where 𝑎 is the smallest positive divisor of 𝑛 different from 1 and 𝑏 is an arbitrary divisor of 𝑛.

[twilit magnet]

This so far

[copper crypt]

I think you're right about b being even

Also I think it needs to be a multiple of a

So I guess you can write that n is a^2(1+x^2)

[twilit magnet]

What’s the x?

Just an integer?

[copper crypt]

where b=ax

[twilit magnet]

But how can we conclude that b is a multiple of a

[copper crypt]

Because if it wasn't, then a^2+b^2 wouldn't be a multiple of a

It's like the even thing generalized

Though b has to be even regardless of what a is I think

[twilit magnet]

Okay how can I continue with b = ax

[copper crypt]

I mean I'm not really sure lol

[copper crypt]

But you can write this

And maybe use the fact that n is a multiple of b

[vocal sleet]

@twilit magnet Has your question been resolved?

[dense eagle]

now notice that k | n/2

so we have 1+k^2 = n/4 so you can eliminate a lot of cases

& then you should be able to do something similar for the other values of a

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[uneven mango]

How to determine if a parabola is horizontal or vertical y²=16x

[alpine kestrel]

which one is squared determines it

[uneven mango]

Ok thanks

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[alpine kestrel]

x being squared means vertical… it’s kinda flipflopped

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[pearl gale]

can anybody help me with this? like how i would get this answer? im using distance formula

[alpine kestrel]

u just use distance formula 4 times and add them

[pearl gale]

wdym, my bad im slow

[alpine kestrel]

like calculate each line

[pearl gale]

ohhh alright thanks that makes more sense

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[dire fog]

Hey I'm rlly lost on how to find the angle measurements, can someone tell me what they are and how to get them

[paper depot]

we arent just gonna give you answers if thats what you were trying to ask for

[dire fog]

No no sorry

[paper depot]

also is this a test or sth

[dire fog]

No

It's just an assistant I procrastinated

[paper depot]

this is the one angle you're given

you should know that:

• the diagonals of a rhombus intersect at right angles
• and in so doing, the rhombus is broken up into 4 right triangles that are all congruent to one another

[dire fog]

Ohh

[paper depot]

this lets you fill out the entire diagram with angle measures

[dire fog]

So would dae be 27?

[paper depot]

no

triangle DAB is isosceles beacuse DA=AB (as a rhombus' sides are all equal by defn)

and AE is its altitude from the apex, thus also its bisector at the same time

[dire fog]

mmm okay

I think I get it ty

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[onyx spade]

how should i find the intervals

[onyx spade]

i did (0, 3.1) and apprently its not right

[vocal sleet]

Show your work, and if possible, explain where you are stuck.

[flat whale]

the dot at 0 has an r value of ?

[onyx spade]

2.8?

bc theta is 0 and a is 2.8

@flat whale

[flat whale]

no

r = distance from origin

what's the distance from (0, 0) to (0, 0)

[vocal sleet]

@onyx spade Has your question been resolved?

[onyx spade]

0

[vocal sleet]

@onyx spade Has your question been resolved?

[flat whale]

yea so you should know 2.8 is incorrect

[onyx spade]

How should i do this then

[flat whale]

what's the answer to this

plug that into the equation for r

[onyx spade]

0

[flat whale]

yes r = 0

[flat whale]

solve for theta

[flat whale]

yes

[onyx spade]

So 0 to 2.8?

[flat whale]

try it yes

[onyx spade]

it worked
thNK

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[dreamy fractal]

How would I find these two do i take the derivative first im confused

[paper bridge]

by the fundamental theorem of calculus $F'(x)=\dv{x}[F(x)-F(4)]=f(x)$

[twin meteor]

vengeance

[dreamy fractal]

so i just plug in the x for a 2

to get F(2)-F(4)

and thats my answer?

[paper bridge]

no bruh

F'(x)=f(x)

F'(2)=f(2)

[dreamy fractal]

.close

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[ebon light]

What does it mean when it asks for the equation of the tangent line?

<@&286206848099549185>

[restive tundra]

Do you know what a tangent line is?

[vocal sleet]

@ebon light Has your question been resolved?

[ebon light]

Yes I do know

This is what I tried to do

Using 2 points from the graph to try to find a slope

And then plugging it in to y=mx+b

[restive tundra]

Okay nice

[ebon light]

Does that work????

I’m not sure

If I will get it right

[restive tundra]

I can't really see what the graph looks like at point B so I can't tell you if you're correct or not

But so long as you pick two points that are both on the tangent line then you can do it like that

(they have to be points on the tangent line, so not necessarily on the actual graph)

I would also say though that at point B, the tangent line is supposed to have slope 0, so you might wanna have another look at that

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[ebon light]

Kk thank you bro

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[austere jolt]

Anybody an expert in OriginLab graphing software by a chance?

[vocal sleet]

@austere jolt Has your question been resolved?

[flat whale]

Probably not

#computing-software is better suited. And just ask your question

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@austere jolt Has your question been resolved?

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[soft plume]

2 log (x+11) = (1/2)^x

[vocal sleet]

@soft plume Has your question been resolved?

[soft plume]

@reef grove

<@&286206848099549185>

@everyone

[flat whale]

,w solve 2 log (x+11) = (1/2)^x

[twin meteor]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[flat whale]

doesn't look solvable

[spiral turtle]

There might be something stupid you can do with the Lambert W function, but it looks pretty bleak, and generally if there's a way to use the W function WA will find it

[soft walrus]

,w 2log_10(x+11)=(1/2)^x integer solution

[twin meteor]

Results provided by WolframAlpha

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[spiral turtle]

Ohhhhh

Lol, log_10

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[trim valley]

I know it uses the two definitions I wrote for rank(A) and rank(B), but i'm stuck on where the application of the definitions can give us the arguments for the proof that rank A + rank B ⩽ n, given AB = 0

[surreal basin]

you here?

[trim valley]

yes

[surreal basin]

you should try focusing on proving that null(A) + null(B) ≥ p first

if you have null(A) + null(B) ≥ p then you can use rank-nullity to turn that into rank(A) + rank(B) ≤ n

[surreal basin]

you can start here because its easier to intuit

each time you use a matrix, you "lose" a certain number of directions

null(B) and null(A) are how many

youll notice null(AB) is the nullity of an mxp matrix of 0s and so is p

so you have to lose a total of at least p directions when you use B and then A

[trim valley]

nullity and rank always add up to the number of columns, so converting that nullity inequality to ranks would show something like rank(A)+rank(B)≤nrank(A)+rank(B)≤n? wouldn't each time we'd be subtracting from total columns n? @surreal basin

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[vital ginkgo]

simplify 5th dimension

[tired whale]

watch the video on youtube

the popular one

a teen explains 5th dimension

[vital ginkgo]

i did like years ago

gotta watch again

[bronze osprey]

great you should go watch the YT video

you can come back if you have any more question but for now you should close this channel

[vital ginkgo]

btw i am only in 8th grade

[bronze osprey]

ok good to know

[vital ginkgo]

the video is about 4th dimension

though it is not possible for us to percieve 4th dimension i have basic understanding about 4th dimension

i want to learn 5th dimension

[bronze osprey]

https://www.youtube.com/watch?v=zwAD6dRSVyI

in fact you can learn about n dimensions in general

the trick is to think about 5 dimensions as lists of 5 numbers

so for example, spheres have the same distance from any point of their surfaces to the origin

in 3 dimensions that just becomes $\sqrt{(\sqrt{x^2 + y^2})^2 + z^2} = r$

[twin meteor]

south

[vital ginkgo]

i appreciate all your efforts

[bronze osprey]

or $\sqrt{x^2 + y^2 + z^2} = r \implies x^2 + y^2 + z^2 = r^2$

[twin meteor]

south

[vital ginkgo]

this is more understandable for me

[bronze osprey]

yes but the derivation is really important

then in 4 dimensions it actually becomes $x^2 + y^2 + z^2 + w^2 = r^2$

[twin meteor]

south

[vital ginkgo]

what is "r"

[bronze osprey]

r is the radius!

the radius of the (hyper)sphere

[vital ginkgo]

ok now i am understanding

[bronze osprey]

really try to take your time on understanding this example with 12, 9, 8

then replace 12, 9, 8 with x, y, z

[vital ginkgo]

can you simplify this for me

you are the best person in the world

[tired whale]

fr

[bronze osprey]

simplify what?

[tired whale]

South the goat

[vital ginkgo]

i can imagiine the 4th dimension using a teseract can u refer any visual for 5th dimension?

[bronze osprey]

human minds weren't meant to visualise the 5th dimension

[tired whale]

it's just the shadow of the 4d cube you are imagining

[bronze osprey]

what I am saying is that you scrap that visualisation idea entirely

[tired whale]

you can't visualise the 4th dimension

[bronze osprey]

it's so much easier to think about lists of 5 numbers

[tired whale]

yes

[vital ginkgo]

ok done

[vital ginkgo]

ik that we are meant to be 3rd dimensional and it is physically impossible for us to percieve 5th dimension

[tired whale]

right

[vital ginkgo]

ok i am understanding it now

[tired whale]

the tesseract you are visualising is just the shadow

[bronze osprey]

so yeah the interesting thing is not boxes (cuboids) in higher dimensions

it's actually spheres

[tired whale]

tell me more

[bronze osprey]

watch the video to find out

[vital ginkgo]

the 4th dimension explained by high schooler used cubes so the idea of cubes was fixed into my mind

[tired whale]

i have watched all 3b1b videos but a while ago, i don't think i remember so yes I will watch it again

[bronze osprey]

well it fails beyond the 4th dimensions as expected

that video is pretty cool, it's from more than 10 years ago

[tired whale]

3b1b the goat

[bronze osprey]

not the 3b1b video actually

there's another video about the tessaract

https://www.youtube.com/watch?v=eGguwYPC32I

this one

[tired whale]

yeah I recommended this earlier

it's oversimplied though

good for beginners

[vital ginkgo]

are u both postgraduates?

[tired whale]

nah

still in school

High school

[vital ginkgo]

its good for me

[vital ginkgo]

noice

[tired whale]

it's good to start from there

[vital ginkgo]

still older and more intelligent than me

[tired whale]

and eventually use numbers instead of physical structures

[tired whale]

you good bruh

[vital ginkgo]

i dunno

school teaches all the bullshit

i do not want to learn bullshit from school

instead i wanna learn more about physics and mathematics

[tired whale]

correct

[tired whale]

good thinking buddy

[vital ginkgo]

thanks man

my parents obviously do not support me

but i think you do

thank you brother

[tired whale]

i do

!stop

[vital ginkgo]

in my dreams i am a menace which makes me wonder, if i a menace in a naive's dream or a naive in a menace's dream which makes me question my own existence

[tired whale]

bro is onto nothing 🙏

please ask your question or .close, you always can dm me

[vital ginkgo]

ok mate

.close

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[kind hemlock]

can a 3 dimensional statistics table display more complex datasets?

[sweet birch]

I mean, "maybe"

it's sure as hell not better for displaying things

[true cliff]

be my tutor

im doing linear calc 1a

wait ive never seen opal nitro

holy moly

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[kind hemlock]

yes

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[spare wigeon]

Have i done part (d) correctly ?

[vocal sleet]

@spare wigeon Has your question been resolved?

[spare wigeon]

<@&286206848099549185>

[vocal sleet]

@spare wigeon Has your question been resolved?

[dawn grail]

What is the problem?

WAIT MY BAD

I think the answer would be Ax instead x (made this mistake in my recent Linear Algebra midterm)

[vocal sleet]

@spare wigeon Has your question been resolved?

[spare wigeon]

why Ax?

i moved the A^T A in the line above

[dawn grail]

I think that is the actual approximate vector iirc

[spare wigeon]

uh i dont think i understand by what you mean

someone previously told me i messed up at the A^TAx = A^TB part but im not sure why

[dawn grail]

No I believe that's how you set up the normal equation

[vocal sleet]

@spare wigeon Has your question been resolved?

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[warped creek]

hello

[fervent wasp]

Wsp

[warped creek]

who needs help

[fervent wasp]

Any questions today?

[warped creek]

oh wait

i wanted to help

not to be helped

[fervent wasp]

That’s not how it works lol, you claim the channel to ask questions here

[warped creek]

but how can i help people

[fervent wasp]

If you’re trying to help, just check out others’ channel

[flat python]

Someone will post a quesiton in one of these channels, and then you help them

[warped creek]

ok but how do I get helpful role

im still 14, but im pretty advanced

[fervent wasp]

You have to constantly engage in helping others in a period of time

[warped creek]

ohh

ok

thanks

[fervent wasp]

It’s not hard to claim one, it took me 2 weeks to reach this

[odd helm]

don't know where my helpful role is 😦

[flat python]

how is that done actually

I've been here longer and I still don't have it

is it just, "they're here a lot, I'll give em the role"

[paper bridge]

its called speedrunning and being consistent

[paper bridge]

a bot runs the system lmao

[flat python]

Lmao

[paper bridge]

a bot determines whether you get the role

[flat python]

Yeah with amount of messages right?

[fervent wasp]

No, there is a hidden criteria

[paper bridge]

yes

contribution to threads iirc

[flat python]

Yeah so pretty much worse explenations give you the role quicker, because people don't understand you lmao

[odd helm]

what sorta threads

[paper bridge]

(i.e., msgs per total messages per thread iirc)

[flat python]

that's pretty funny

[paper bridge]

eh

i speedran it

2 weeks

it takes a hellish time

[flat python]

I don't really care about the role

it's just funny honestly

[paper bridge]

just gonna not lie here

helpful role alts are more likely to get helpful

than real people 💀

[fervent wasp]

It makes you lose the role faster as well 😭

Alr, enough jokes here

[paper bridge]

@warped creek aight if you dont have a real qn you can close post

[fervent wasp]

@warped creek enjoy your stay

[outer warren]

nothing meaningful here,
gonna close it

.close

[vocal sleet]

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[fervent wasp]

.clpse

[paper bridge]

no way bro

the curse of permutations is wild

[vocal sleet]

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[vital scroll]

Help please

[vocal sleet]

@vital scroll Has your question been resolved?

[vital scroll]

<@&286206848099549185>

[sacred hinge]

Okay so the period

First question

What is the period?

[silk osprey]

draw the graph of d vs t on the axes

[radiant canyon]

yeah draw the function and find the trows or smth

[vital scroll]

Period? Like 0>_ t _<?

[radiant canyon]

should i get a sinosudal function label model ?

[sacred hinge]

In this example would you need to do 2pi/b=30…? I’m just trying to remember

[radiant canyon]

i think that should help

we're trying to find the lowest part,

[vital scroll]

Ohhh

Wait so

If I remember the form y=mx+c

Is d like y

And t like x?

[sacred hinge]

Um

[silk osprey]

not quite

[radiant canyon]

yeah... but don't use the slope formula

[sacred hinge]

It’s better to just think of it as an input and output

[silk osprey]

y = asin(bx) + c

[radiant canyon]

yes

[vital scroll]

Ohh

I meant like

For t

[sacred hinge]

Output=b, input is like t

[vital scroll]

I substitute in the values

[radiant canyon]

yeah x and y input and output

[silk osprey]

t is the independent variable here

[sacred hinge]

Just a one to one injection

[silk osprey]

d

brother just said one to one injection

[sacred hinge]

Wait it might be a bijection

[vital scroll]

Ohh

[sacred hinge]

No no, it’s a surjection

[silk osprey]

bro

what are we talking about 😭

[sacred hinge]

Idk trying to explain it

Okay so d=output t=input

[radiant canyon]

@vital scroll do you know how to graph the function?

[silk osprey]

what does this have to do with surjections and injections

[vital scroll]

Yes

[radiant canyon]

oh than try that then

[vital scroll]

I can plot coordinates for a sine graph

[sacred hinge]

Nothing

[radiant canyon]

sounds good!

[vital scroll]

Okay thakk you

[radiant canyon]

no problem

[silk osprey]

you're welcome

[vital scroll]

<33

.close

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[cunning token]

Help

[cunning token]

I dont understant second rectangle and third rectangle

How I get?

How i can find base?

[ornate seal]

Well.. base for second triangle is pi/4 - pi/6

Based on the graph

Hence pi/12

[cunning token]

Thx

.close

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[graceful barn]

can some one please help me with this?

[green crow]

How much did u do?

Where r u stuck?

[atomic jasper]

make a drawing

[brazen condor]

Draw a quick sketch

[graceful barn]

ok

i dont get the second part

[atomic jasper]

just focus on the first part for now

did you make the drawing?

the 3 lines?

[graceful barn]

yes

[atomic jasper]

can you show?

[graceful barn]

im on my laptop no

[atomic jasper]

okay sure

[brazen condor]

should've got smth like this right?

[graceful barn]

yeah

[atomic jasper]

what is the sidelength you alreayd see here?

[graceful barn]

8

[brazen condor]

and one length is twice the size of another length

so the width must be half or double of the sidelength we found

do you get where I'm coming from?

if not then ask

[graceful barn]

i dont get it

[brazen condor]

so it says in the question

one length is twice the size of another length

but we don't know what length they're talking about

[graceful barn]

it could be any of the four length?

[brazen condor]

this is about the side length you found

the 8

[graceful barn]

ohh

[brazen condor]

from -2 to 6

[graceful barn]

yeah

[brazen condor]

we don't whether 8 is the smaller length or the bigger length

so we do both cases in this question, one case being that 8 is the bigger length (hence double it) or 8 is the smaller length (hence halve it)

[graceful barn]

so 16 and 4?

[brazen condor]

16 OR 4

[graceful barn]

right

[brazen condor]

you're on the right track

you know one of the vertical lines is set at x=3 right?

[graceful barn]

yes

[brazen condor]

well we don't know whether it's above or under x=3

so again we do both cases for above and under

+/- 4

+/- 16

you get me?

[graceful barn]

yeah

[brazen condor]

so doing that you should've got 4 equations

for the line

you got that?

[graceful barn]

so how do i get the equations

[brazen condor]

you add and subtract 4 from x=3

and do the same for the 16 case

do you get why we do that?

[graceful barn]

no

[brazen condor]

well this line could either be to the right or left of x=3

[graceful barn]

ohhh

[brazen condor]

you don't know whether it's to the right or left so you do both cases

[graceful barn]

get it

[brazen condor]

so get your 4 equations and tell me them

[graceful barn]

im getting 19 and -13

[brazen condor]

right that's for the 16 case

now repeat that for the 4 case

[graceful barn]

what do i add to 4?

or subtract

[brazen condor]

no no, you're not adding or subtracting to 4

you're doing that to x=3 still

but remember the halving or doubling of the 8 earlier

we doubled it to get the 16 case but also halved it to get the 4 case

[graceful barn]

yes

[brazen condor]

so what you did right now was for the 16 case

I'm saying do what you did

but instead of adding and subtracting 16, add and subtract 4

you get me?

[graceful barn]

to -2 and 6?

[brazen condor]

no to the x=3

cuz x=3 is one of the vertical lines

[graceful barn]

so -1 and 7?

[brazen condor]

there you go

[graceful barn]

ahh ok

[brazen condor]

so x=-1, x=7, x=19, x=-13

[graceful barn]

yes i get it now

[brazen condor]

that's with the assumption that our 4th line is vertical

you may think that it could be horizontal but the width is already fixed from x=3 to some other x so the 4th line could only be vertical

[brazen condor]

this is just deeper understanding, dw too much about this

[brazen condor]

but yes there are your equations

[graceful barn]

ok tysm

[brazen condor]

np, as long as you understand it for the future then that's what's important

[graceful barn]

.close.

[brazen condor]

no fullstop at the end

[graceful barn]

.close

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[onyx spade]

is this not right

[paper depot]

might they be looking for you to evaluate cos(45°)

[onyx spade]

unit circle?

[paper depot]

if that makes it easier for you, yes.

[vocal sleet]

@onyx spade Has your question been resolved?

[vocal sleet]

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[low minnow]

hey yall i have my midterm tomorrow how do i factor these 💔💔 (ill be asking a lot of questions tonight i missed a lot of classes 😭)

[oak magnet]

you must use foil method

[outer warren]

would you be able to factorise something like
pq - pr

[low minnow]

p(q-r)

[low minnow]

what is that

[outer warren]

try applying that here

[low minnow]

oh yes i know that ok

[outer warren]

note that (5-4a) = -(4a - 5)

[low minnow]

okay let me try

[oak magnet]

well ramonov method is cooler, mine is a little heavy

[low minnow]

wait no i dont get it

how do i distribute it and what do i distribute

i think im doing the wrong thing

[oak magnet]

you can take -2 out from 4-2b

[low minnow]

...how

im so confused rn

[oak magnet]

the same way you did there

[outer warren]

first do

note that (5-4a) = -(4a - 5)

[low minnow]

so like 2(2-b)?

[low minnow]

noted

[oak magnet]

nvm follow ramonov

[low minnow]

whats ramonov 💔

[oak magnet]

the blue guy

[low minnow]

ah ok

[outer warren]

$$\red{(4a-5)}(b-2) - \red{(4a-5)}(4-2b)$$
try applying $$\red{p}q - \red{p}r = \red{p}(q-r)$$ to that

[twin meteor]

ℝαμOmeganato5

[low minnow]

so 4a-5(b-2-4-2b)?

4a-5(-b-6) right am i doing smt wrong

oh

[oak magnet]

thats the idea but be careful to sign

[low minnow]

+2b?

3b-6?

SO RHATS

3(b-2)

WOA

THANK YOU

🙏🙏🫶🫶🫶💔💔

❤️❤️*

.close

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[fossil drift]

hello help me find x i would appreciate it

[fossil drift]

this is what I found yet but i cant elaborate further

[spiral turtle]

You may need to break out the law of sines, using the fact that ABE (in your lower image) is isoceles.

[lone linden]

oh this question

https://mindyourdecisions.com/blog/2020/05/22/insanely-hard-geometry-problem-solve-for-the-angle/

[fossil drift]

thx very much

[vocal sleet]

@fossil drift Has your question been resolved?

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[ashen warren]

i’m stuck on question 15, i am not not too sure what the next step is

[regal bane]

<@&268886789983436800>

[oak magnet]

<@&268886789983436800>

[regal bane]

Namington you're so fast

[paper depot]

quickest draw in the wild west?

[oak magnet]

Not even a draw fr

[ashen warren]

what the

[oak magnet]

Not for you dw

[autumn trail]

They knew you'd ping before you even thought to pung!

[regal bane]

You've got two vectors, they're drawn correctly. What do you get when you add them?

[ashen warren]

like add the -3 and 2?

[paper depot]

no, add these as vectors

maybe it will help to write the "2 km southwest" in component form

oh 2 miles nevermind not kilometers

yurop moment

[ashen warren]

so <0, 2> for the second vector?.. then add them...?

[young mica]

Distance from home: 4.4 approx
Direction to walk home: 197.7d

[young mica]

if it is right i can give more explation

[ashen warren]

please go away im trying to learn

[young mica]

okkay okaay going gooingg

[regal bane]

That would be 2 miles north.
You actually want 2 miles southwest.
You'll need trig to get this answer

[ashen warren]

does it matter which one? or could be either sin or cos

[young mica]

define the displacement vectors
Compute Final Position
Distance from Home
Direction to Walk Home divide question in steps

[ashen warren]

.close

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[tulip cobalt]

I'm not sure how to prove this

[safe pilot]

.

[hidden gyro]

what do you know about dimater?

do you know the 90 degree angle theorem?

[tulip cobalt]

yeah

but what from that?

do i use pythagoras?

[hidden gyro]

so PQ is perpendicular to QR

[hidden gyro]

there is a simpler way

[tulip cobalt]

Aaaaaaaaaaaaaaaaaaaaaaaaaa

bruhhhhhhhhhhhhh

I didn't think about that

ty

[hidden gyro]

welcome

[tulip cobalt]

.close

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[whole bronze]

how would I evaluate logbase8(32) without a calculator easily?

[whole bronze]

this was a question on a quiz and i resorted to just plugging in random fractions to exponentiate 8 by to find something that worked

ultimately didnt even get it right

the opposite of exponentiating right

as in how subtracting is the opposite of adding

[peak axle]

The operational inverse of exp would be radicals not logarithms, but it's a similar idea

[marsh charm]

you can express 8 and 32 as powers of 2

than with some log rules c/b is your answe

oh

well thats really all u do

[whole bronze]

really? as in logbase2^3(2^5)? or am i misunderstanding you because i didnt know that was possible

[marsh charm]

nope

ur correct

thats it

[whole bronze]

the exponent a base is raised to to get the logbase right?

[rough hound]

Just use change of base formhla

[whole bronze]

the exponent 32 must be raised to to get 8

[whole bronze]

oh thats true, log(32)/log(8), but how would i evaluate this withoutt a calculator?

[rough hound]

If u use 2 as the new base then its obvious its 5/3 but yea need to know what log means.

[whole bronze]

really? but doesnt the logbase, 8 in this case, have to be equal to 32 rasied to something?

[rough hound]

Log y to the base x is just what x needs to be raised to get y.

So, log 32 to the base 2 is what 2 needs to be raised to get 32 and that's 5. For 8, it's 3.

[whole bronze]

why is it to the base of 2? in the question it says logbase8(32)

cant type it out how it looks on the paper but yea

[rough hound]

In case u use change of base...

[whole bronze]

ohhh so to get rid of the log on the side you exponentiate both sides by b

but why do you do that?

[whole bronze]

and what is a in this case

8^x = 32

where do i go from there though?

[vocal sleet]

@whole bronze Has your question been resolved?

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[livid void]

$V_1 - IR_3 - IR_2 +V2= 0$

[twin meteor]

Ousel

[livid void]

Am I setting this up correctly for Loop 1?

$V_1 +V2= + IR_3 + IR_2$

[twin meteor]

Ousel

[livid void]

$\frac{V_1 +V2}{R_2}= + IR_3 + I_2$

[twin meteor]

Ousel

[livid void]

$\frac{1.39}{R_3}= + I_3 + I_2$

[twin meteor]

Ousel

[marsh charm]

wut are those loops

[livid void]

what my teach provided us 🙃

[marsh charm]

isnt it always bottom left to right

but like

in a circle

[livid void]

depends on current flow

[marsh charm]

nvm ur arrows still work they just wack

[livid void]

Is it correct though? >_>

[marsh charm]

V1 would be negative no? its a voltage drop

[livid void]

Well so thats the thing

my teach keeps saying to follow the signs

[marsh charm]

what

what signs

[livid void]

V_1 is positive cuz it goes through positive

[marsh charm]

v1 is definitely negative

ill double check tho

i could just be crazy

i literally took a test on this shit 2 hours ago

[livid void]

Ok so how the heck do you know which is positive and negative, cuz that whats i keep getting lost on

[marsh charm]

so

[livid void]

and ive been told multiple things which is probably worst

[marsh charm]

tell me what u know about this

[livid void]

Im pretty sure everything except the signs lmao

[marsh charm]

like is that all ur confused about?

[livid void]

cuz ive been working on this stuff for like 2 weeks now

[marsh charm]

the signs of everything?

or just the batteries

[livid void]

Well I did an example but I think I messed the loops up

[marsh charm]

so when i do these the loop always goes like a parabola kinda

from the bottom left to the bottom right

[marsh charm]

at the very least the signs are wrong

so

uh

wanna just pull up

a new circut

and ill do it on my ipad

and show u

[livid void]

so is it just the voltage you start with that is opposite?

gotcha

[marsh charm]

do u want me to explain or do a problem

i can do either

[livid void]

So this is the same as the one on top, but what we did in class, just for context

Which ever is easiest for you

just wanna finally understand this lol

[marsh charm]

so

when ur going from

a low potential to a high potential on batteries

its always a voltage jump

so V is positive

when your going from a high potential to a low potential its a voltage drop

so V is negative

On resistors if your going from a low potential to a high potential with a current the current is added instead of subtracted

and the opposite for high to low they would be subtracted

does that make sense?

[livid void]

I think so

[marsh charm]

if you redo the original problem i can tell u if u did it right

[livid void]

im pulling it up on my tablet to draw, one sec

[drifting jackal]

So you contradicted yourself here for this image. If going ccw, you're going low potential to high potential for V1 which is a voltage jump like you said but you said it's -V1

[marsh charm]

i ment for my loop

idk what that is

ive never seen it like that

[drifting jackal]

That's a loop

[marsh charm]

but like

my loop starts

at the bottom left

[drifting jackal]

Okay and?

[marsh charm]

so i went from + to -

meaning its a voltage drop

i very well could be wrong somewhere

[drifting jackal]

You can start wherever you want, just as long as you keep the same convention

[marsh charm]

gotcha

[drifting jackal]

That's going cw

OP went ccw

[marsh charm]

im still learning circuts litterally rn

yea

i didnt know u could go either direction

[livid void]

Um so laptop went into airplane mode cuz charger wasnt plugged in

so I was afk technically 😅

[livid void]

This is what I originally wrote for the loop provided

[drifting jackal]

You just need to be consistent. If loop 1 is going ccw, then ideally loop 2 should be ccw too and not cw

[drifting jackal]

Yeah that looks fine

[marsh charm]

looks correct to me

[livid void]

so I_3 + I_2 =0.046

guess ill go from there then

[marsh charm]

did you make the other equation?

you need to do a system of equations to solve it

[marsh charm]

im lokey not sure whats going on here but its possible we learned to do them in different ways

[livid void]

My teacher just does crazy loops

And im not sure if its my learning style or how he teaches but im not understanding a decent bit of it

[marsh charm]

organic tutor has a really good video

on how to do them

if you want i could link it

[livid void]

sure, I need good resources outside of school at this point

[marsh charm]

https://www.youtube.com/watch?v=6F_rmZ1nXFQ&t

https://www.youtube.com/watch?v=2Zu3ppq3n8I&

this ones a lot longer

if u wanted more examples

[livid void]

😮‍💨

Hopefully get it figured out, so far behind trying to understand this section

[marsh charm]

i read what u wrote

ur equations are fine

but im not sure where u solved them

yea i genuinely got no idea whats going on in the center

[livid void]

not done yet

just what I had

I got the 3 equations now

[drifting jackal]

One key thing that you are lacking from this, is the resistor in the middle, R2. So following your work, loop 1 has a voltage drop through it but notice how loop 2 affects R2 as well, so you actually have R2(-I1 + I2)

[livid void]

I feel like I should be doing the outside loop first

like starting at junction a ccw

[marsh charm]

they used i1 i2 and i3 here

im p sure what he wrote was right unless im blind

[livid void]

I think I need to erase the 2 equations on the bottom left

or the signs are wrong...huh let me rewrite this

[drifting jackal]

Also the way you are doing the work isn't conventional either. You don't label currents for each component, the current is based on the loops

[livid void]

Im doing it the way ive been taught i guess, which based on 5 other people have mentioned in this server, doesn ot seem correct

[drifting jackal]

That image is just funky

The way you were taught is not conventional

[livid void]

Physics 2 is giving hurting my mental health (/s...halfway)

one sec

[marsh charm]

have you done inductors yet

[livid void]

gonna upload my pdf notes

[marsh charm]

prob not ig if they arent on these already

[livid void]

Lecture 7 is kirchoffs loops

If yall wanna just try and explain it to me how yall do it though id be willing to learn.

[marsh charm]

am i gonna get malware if i open these pdfs

[drifting jackal]

My suggestion, since kcl/kvl is a tough topic in general for people, look up videos and watch them. Go to your prof for help. Ask the TA, etc

[marsh charm]

that wouldnt be nice

[drifting jackal]

Your school might have a tutoring center that you can go to

[marsh charm]

u really only need like a single organic tutor video to understand it

not to gas him up or anything

[livid void]

Ill go through those videos then and come back if I need to ig

[drifting jackal]

You're missing the point. I'm saying there are tons of resources out there that can be utilized

[livid void]

thing is ive been using them 😅

Just not clicking for some reason I guess

First time really having to combine equations though

usually a single loop gives enough info to finish the rest

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[rocky knot]

can someone help me do the algebra on the last part

[rocky knot]

ik how to do the qeustion i just cant seem to do the algebra

[barren ether]

so u got 0.8 = (1-a)e^-k(1) + a
and 0.72 = (1-a)e^-k(2) + a

u can isolate e^-k by subtracting a, dividing by (1-a) and taking natural log of both sides and solve for k, then plug in original solve for a by expanding then plug that back into k, then just solve for y(13) which should be trivial from there

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[rocky knot]

ok ty that works

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[bronze osprey]

<@&268886789983436800>

[vocal sleet]

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[tidal solar]

need help pls:

From a window, W, 20 metres above ground level, the angle of depression of the the bottom, B, of a tower is 15 degrees 26 minutes and the angle of elevation of the top, T, is 28 degrees 47 minutes.

Complete the diagram clearly, showing all the angles of the triabgles

[outer warren]

draw a horizontal line through W

angles of elevation and depression are angles made with the horizontal

[tidal solar]

so i make it a right angle

and solve from there?

??

could someone help me

i have no idea how to solve it

or well put in the values

[outer warren]

did you draw a horizontal line through W?

[tidal solar]

yes sir

[outer warren]

the angle of depression of the the bottom, B, of a tower is 15 degrees 26 minutes
the grammar is a bit of but from context, that means that the angle between WB and that line you just drew is ^ that angle

[tidal solar]

ohh ok

tyt

ty*

[outer warren]

same idea of the eelvation

[tidal solar]

thanks so much

i get it now

.close

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[polar vine]

Yo

[polar vine]

Do you have any idea abt the general process of thinking for these questions?

I said that FD3 is b,c-->e

In FD1 we have a,b,c-->d, e,f,g

a,b,c-->e
Since we have b and c determines e then there's a proper susbet there thus it's partial

But turns out I am wrong

[edgy gulch]

databases yikes

[edgy gulch]

which one is wrong

[polar vine]

What I wrote is wrong ..

The solution in the pic

[edgy gulch]

yeah which one

fd1 fd2 fd3 fd4

[polar vine]

I don't get fd3

If a,b,c determines d c f g then we can say that a b c are determining either d c f or g alone right??

[spiral turtle]

You have to take all of the FDs together.

FD3 is an FD that mentions e as an output. FD1 does as well. Even though FD3 has two inputs, this is the smallest set of inputs that outputs e.

[spiral turtle]

Let's do a little mathier. Let's say we have a vector valued function.

f(a,b,c) = [2g(a,b,c), b+c, g(a,b,c), 3a]

Do you see how this satisfies your FD list?

Note to specify the output variable f (as opposed to the function f) I defined a function g (as opposed to the output variable g).

[polar vine]

Ommmm....

[spiral turtle]

This is because how f (variable) is defined was not specified.

So I just said, "it is some combination"

[polar vine]

So f(a,b,c) can't be just equal to one parameter

So as in FD1

[spiral turtle]

So you can think of FD1 as the full function, and then FD2-4 as slices of this function

[polar vine]

I mean if we think abt that way....

We'll have proper susbet of each attribute..?

[spiral turtle]

Subset?

[polar vine]

Cuz we can cut it into small parts

[spiral turtle]

Well, sure I suppose

[polar vine]

Yeah

Then

[spiral turtle]

Probably not a formal subset

But you seem to have the correct idea

Using functional dependencies is important to reduce memory contention. It allows you to reorder operations so that they wait on each other less.

[polar vine]

So to label fds we just look closely into smaller pieces and see if one of the determinants express one of the dependencies by themselves in thus case we'll have a proper subset which is partial

[spiral turtle]

I don't think you're using "determinants" here correctly

Oh my bad

It's a database thing

Sure sure

[polar vine]

Don't remind me of linear algebra now haha

[spiral turtle]

This sort of data dependency tracking I've only ever used in the context of reordering microops in a pipelined CPU before.

So we didn't use the same terminology

[polar vine]

I see..

Thanks alot for helping out