help-19

[brittle notch]

Hm

How?

[wild spruce]

$(n-1)\sum_{i=0}^{k-1}n^i$

[clever fjord]

Pop

[brittle notch]

That looks more simplified

This looks like a question

[wild spruce]

$\frac{n^k}{\sum_{i=0}^{k-1}n^i}$

[clever fjord]

Pop

[brittle notch]

Yes

[wild spruce]

isnt this just the shit before

💀

[brittle notch]

But this is the previous step

Of what we got earlier

[wild spruce]

its the same

[brittle notch]

I'm satisfied with this being called simplified

[wild spruce]

fr

aight then

[brittle notch]

Yea but u just used sigma

[wild spruce]

fr

thanks mate

[brittle notch]

Lol

[wild spruce]

im closing the section

[brittle notch]

Mhm

[wild spruce]

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[woeful escarp]

.reopen

[cedar geyser]

how do i do this, im not sure how to start

[odd edge]

@cedar geyser Has your question been resolved?

[cedar geyser]

<@&286206848099549185>

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@cedar geyser Has your question been resolved?

[versed bough]

hey wsp!
note that the hydrostatic pressure is P=dgh where P is the pressure, d is the density of the fluid, g is the acceleration, and h is the depth
how can you use this to find the answer?
(apologies if this is incorrect)

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[dusky locust]

Can somebody explain why this is wrong?

[dusky locust]

I used the normal approximation and used 3.5, 6.5 to account for continuity correction

BTW n = 14

p(4<= x<= 6) = p(-0.84 <= Z<= 0.84) = p(z<= 0.84) - p(z<= -0.84). Is this correct?

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[elder vault]

This is a tough one

[elder vault]

Because these related points can not be expressed in integers

It fked me up

Let me know how would you guys solve it

[frigid canopy]

Could you please post a picture of the original question instead? Kind of hard to read it when it is as a video.

[elder vault]

I cannot

I already skip this one in the web

I think you can press the stop button

Then it would looks like a picture of certain frame

[frigid canopy]

I feel like some information is missing.

[slow sphinx]

Look not looks*

[elder vault]

thank you

[elder vault]

that is illusive

[frigid canopy]

I don't follow.

[latent scaffold]

You're wondering about the website's solution?

[odd edge]

@elder vault Has your question been resolved?

[elder vault]

.close

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[pure laurel]

I am confused in how this works anyone pls

[arctic tide]

Easiest way to do this

is to determine which letter is on the opposite side of A

The question gives u three options

for letters

A,E,E,E,M

so try to see if you can eliminate any of these

[pure laurel]

Ok

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[stone swift]

hi imma need some help to get through the steps

[inland rover]

what have you understood till now?

[stone swift]

Tbh not sure what to do after I figured out part a. Idk how to approach part b

I tried out factoring and foiling out the polynomial and got 4x(x-8)(x-4) idk if thats right tho

[inland rover]

find the derivative and make it =0

[stone swift]

Ah ok

Sorry, not that good at this. Is it then 12x^2 - 96x + 128 = 0 ?

[half fulcrum]

,w expand x(16-2x)(8-2x)

[clever fjord]

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[half fulcrum]

yes

that is correct

f' is what you wrote

now find the value of x that gives the max volume

[stone swift]

Would it be abt 6.31? When rounded to 2 decimal places

Uhh hallo?

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@stone swift Has your question been resolved?

[stone swift]

Yep thx

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[tired lintel]

How do you divide polynomials

[tired lintel]

ex 3x²+3x+1/x-1

[swift lake]

long division as like we do normally but using algebra

[tired lintel]

I dont get it

[swift lake]

u know long division for 3505/5

[uneven osprey]

ig you should watch a tutorial for that
here in chat it is difficult to explain and you'll most probably don't even get what we try to explain

[swift lake]

find it on yt

[tired lintel]

Ight 👍

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[solemn knot]

I was curious why this direct substitution for a, b, and c is possible

like what path to go to if it were to prove that this are the only combination that is right

[uneven osprey]

that positive integers made only one combination of a, b and c possible

for example if they just gave integers, there could be a possibility of negative integers, so there could be another combination

but here it is not that case

[sand horizon]

Lambert proved that pi is irrationnal with thoses

[solemn knot]

how come however I wont be able to use this reasoning for other equations? like per se

a+b = 6
a+b = 5+1
therefore a=5 and b=1.. but it could also be a=4 b=2

[solemn knot]

given that a and b are positive integers in here

[uneven osprey]

here the fraction and their numerators being 1 played a huge role
due to them possibility of other combinations could be rejected

[sand horizon]

If multiple answers were possible, they wont ask for the sum and further more they arent multiples, cuz the only way to write 50/7 like b+1/c its 7+1/7, with others numbers theyre wouldnt be a 1 on top.

[sand horizon]

Its just to precise where does they takes values

So its from $\bN^3$

[clever fjord]

YakuBros

[solemn knot]

make sense, I guess I was coming from where its a problem I've encountered myself and not given by a sample paper

so I sort of disregarded the reason 'they wont ask for the sum if there arent precise values'

[sand horizon]

But if it wasnt given, your process is really good

[dapper canyon]

b >= 1 and 1/c > 0 so b+1/c > 1 so 0< 1/(b + 1/c) < 1 so a < 3.14 < a+1 but a is a positive integer so a = 3.

Then (1/b + c) = 50/7 and you proceed similarly

[uneven osprey]

even if there's a case where they want you to get just one combination but you get any other combinations, the question setters will give some other condition that may help to reject the other ones and to consider only one of them correct

[swift lake]

$3.14 = \frac{314}{100}$

[clever fjord]

Newt

[swift lake]

easy a = 3

[solemn knot]

kinda got lost with 0<1/(1/b+c)<1 implying a<3.14<a+1

and where 1/(1/b+c) came from

[dapper canyon]

add a to all sides

[solemn knot]

just to clarify, its 1/b+c not 1/[b+(1/c)]?

[dapper canyon]

oh yeah

[solemn knot]

ohh okay

that made alot of sense now

alright, thanks everyone!

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[restive night]

Pre-calc Conic Sections : Circles

[lethal spoke]

Read on it

Or watch a YouTube video

[restive night]

How does the $r^2$ work here?

[clever fjord]

Beersathought

[restive night]

I mean, I know that in a circle all points are equidistant to the center, but like what is the r^2 here exactly?

[hushed dock]

r is the radius, since the radius is 4, itll be 4^2=16

[restive night]

for the $(x-h)^2 + (y-k)^2 = r^2$

[clever fjord]

Beersathought

[restive night]

yeah

Is it because adding them all up = 16 or whatever?

[glad thunder]

Isn't r^2 = 4 here?

[hushed dock]

wouldnt that mean the radius is 2 then?

[hushed dock]

um im not sure

[glad thunder]

yeah

[hushed dock]

in the diagram it has a radius of 4, not 2

[restive night]

but counting the radius its 4

[glad thunder]

when you're writing the equation of a circle with centre (a, b), the equation will be like (x-a)^2 + (y-b)^2 = r^2 where r is the radius of the circle

[hushed dock]

using this formula, you have found your points and found out the radius is 4 by counting the length, thus your answer is (x-3)^2 + (y+5)^2 =4^2, since you know r=4, thus giving (x-3)^2 + (y+5)^2 =16

[hushed dock]

yuh and the questions tells us r=4, so after subbing in r=4 into r^2, it gives 4^2 = 16

[restive night]

yeah, but in this case, I'm wondering how the (x-h)^2 + (y-k)^2 = r^2 works, like the equation in general

Cause I don't really know where r^2 comes from if that makes sense

[glad thunder]

(x-3)^2 + (y+5)^2 = 4
(x-a)^2 + (y-b)^2 = r^2
4 is in place of r^2 here though?

[hushed dock]

ahhh um sorry i cant help with that as im not too sure myself, i was learnt on how to use that equation but ig this equation tells us the centre point of the circle and the length of its radius

[glad thunder]

the reason for that is because a circle is basically all the points that are a certain distance from a specific point (the centre), we calculate the distance of 2 points with a formula

[restive night]

I see

[hushed dock]

4 isnt in the place of r^2

if you look beersathought got did 4 = r^2 and got marked wrong

[restive night]

What's the reason for them being squared?

[restive night]

yeah

[glad thunder]

oh mb didn't see that it's marked wrong

[glad thunder]

let's use your question as an example

we already know where the centre is (3, -5)

[restive night]

yea

[glad thunder]

so we want to find the equation for all the points that are 4 units apart from (3, -5)

[hushed dock]

https://www.youtube.com/watch?v=orrMC3uNU3U

[restive night]

oh

[restive night]

Alrighty, I'll check this out afterwards

[glad thunder]

if we represent those points with (x, y), when using the distance formula we'll get to sqrt((x-3)^2 + (y+5)^2) = 4

[hushed dock]

i believe this is the formal proof, and explains where your squares and radius comes from, if it doesnt help you could try googling proof for the equation of a circle

[glad thunder]

all we're doing is raising both sides to power 2, I'm assuming just to make it easier to write

[restive night]

Alright, thanks a lot

[restive night]

if thats the case then it will be

$\sqrt{(x^2 - 6x + 9) + (y^2 + 10x + 25)}$

[clever fjord]

Beersathought

[restive night]

?

or the square root will just get cancelled out by the square

[glad thunder]

that's what happens lol

so in the end we'll have $(x-3)^2 + (y+5)^2 = 16$

[clever fjord]

nima

[restive night]

I see

[glad thunder]

notice how the radius also gets squared in the process of removing the square root, that's why it's r^2

[restive night]

Ahh I get it now

alrighty, thanks a lot 🙂

[glad thunder]

cheers!

[restive night]

.close

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[junior mango]

Bob?

[vernal yacht]

do you have an actual question?

[odd edge]

@junior mango Has your question been resolved?

[proper solstice]

!original

[odd edge]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[proper solstice]

!da2a

[odd edge]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[proper solstice]

.close

$sudo force close - Terminate

[shell haven]

Bro tried to use root privileges 💀

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[junior mango]

Ohhh sorry

[junior mango]

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[trail grotto]

Is the question wrong here? I think it should be (x+y+z)³ = 3(x³+y³+z³) in the second part.

[trail grotto]

Question 15.

When I solved the question provided here the answer appears to be (x+y+z)³ = 27xyz. Is it correct?

[lusty helm]

suppose y+z, z+x, x+y as some variable

[trail grotto]

Is a³ + b³ + c³ = 3abc?

[lusty helm]

no

it is only for some ques

[trail grotto]

For this one? Wait let me attach my answer.

[lusty helm]

yup that would be better (abt attaching ur ans)

[trail grotto]

Here.

[lusty helm]

how have you taken this?

[trail grotto]

I don't exactly remember. But I think I took this from some other equation's answer.

[lusty helm]

uhm

[trail grotto]

Well, something clicked in my brain and now I solved it. Thank your for your help though.

.close

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[tacit haven]

ive tried using the factorizations of 2554 and doesnt seem to get me anywhere

i translated the question so it looks kinda weird

[frigid canopy]

is that supposed to be the floor function

[tacit haven]

yes

[frigid canopy]

hmm

I think this is beyond me, sorry.

[tacit haven]

its alright

[proper solstice]

,w arccos x = 2pi

[clever fjord]

Results provided by WolframAlpha

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Requested by anshulyolo121

[tacit haven]

...?

i'm starting to think maybe its just the difference of squares of 2555 and 2554

<@&286206848099549185>

[fossil oracle]

is this the question copter ?

[tacit haven]

yes

[lusty helm]

can you explain how you thought that

[tacit haven]

well i realised that if you let n be 2554, after the 1227th term its all just the first term since it has the floor function

maybe im just overcomplicating it

[fossil oracle]

can you explain

what's actually written under a

[tacit haven]

its the floor function

[fossil oracle]

oh ohk

[tacit haven]

i dont really know where to start though

[lusty helm]

uhm

gimme a sec

to see

[fossil oracle]

sorry am pretty busy now i think it might took some time

[lusty helm]

i am getting deja vu feeling rn

[fossil oracle]

maybe later

[lusty helm]

wouldn't terms will start cancelling out

for eg.

a sec

[tacit haven]

this is an old question from an 8th grade competition im going to so im just kinda confused on where to even begin

[lusty helm]

for example

[tacit haven]

i thought of that too

[tacit haven]

alright thanks

[lusty helm]

2555/2 = 1277.5 = 1277

its floor function

and

2444/2 = 1277

and i think it will repeat

[tacit haven]

yeah so the first terms cancel

but im not sure about the others

[fossil oracle]

no worries copter

[lusty helm]

yea it repeats

[tacit haven]

im gonna put other questions from the test here later

[lusty helm]

it would be this

[tacit haven]

oh okay so its just a difference of squares then?

[lusty helm]

yea

[tacit haven]

oh wow

thanks

[lusty helm]

np

[tacit haven]

.close

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[lusty helm]

,w 2555^2 - 2554^2

[clever fjord]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by cool_vansh

[lusty helm]

wait can you reopen?

[tacit haven]

.reopen

[odd edge]

✅

[tacit haven]

?

[lusty helm]

wouldnt there be 2 A1 terms left

of

2555/2554 and 2555/2555

[tacit haven]

yeah but wouldnt there be two a1 terms on both?

[tacit haven]

ohh

[lusty helm]

2554 will have 1 term less

[tacit haven]

so its 5110 then?

[lusty helm]

is A0=0?

yea A0=1

[tacit haven]

the questions didnt say

[lusty helm]

just keep n=0

[tacit haven]

A1 = 1 though

[lusty helm]

a1 =1

yea

so should 5110

i think

[tacit haven]

no wait

5108

[lusty helm]

or 5108

yes

correct

[tacit haven]

aight thanks

i might put up some other questions

[lusty helm]

if you put it rn then you can keep channel open

or else close it

[tacit haven]

didnt it say to open another channel for more questions?

.close

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[lusty helm]

nop

btw,

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[thin palm]

I don’t understand this

what’s on the RHS

coz basically

as cos gets smaller, why does the length increase?

[urban rose]

so you have a doubt in the concept?

[thin palm]

I just want to understand it

[mystic jetty]

cos is base/hypotenuse in triangle
cos is directly proportional base length (and hence inversely to length)

[tacit haven]

from the pythagoreom theorum, a^2 + b^2 = 1, so if a decreases b increases

[thin palm]

okay thanks guys

[urban rose]

analyse it on some basis and you can get it on your own too

geometry helps a lot in the analysis

[lethal spoke]

Focus on the ratios not the length

[urban rose]

yup

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[wary helm]

Can anyone help me please #help-21｜아리스킨충1

[odd edge]

Please don't occupy multiple help channels.

[pastel orbit]

don't open a help channel to ask for help in another help channel

be patient

[wary helm]

I just see people who are just opening tickets getting help for for mine its been over an hour

I wont do it in the future though mb

[odd edge]

@wary helm Has your question been resolved?

[sand horizon]

.close

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[silent jay]

Is this correct?

[shell haven]

Yesh

Oh wait nvm I didn't read the left picture

Nah this is totally wrong

They're asking you to write an expression

[uneven osprey]

☠️ why this is giving me GPT vibes?☠️

[shell haven]

Not solve for anything

[silent jay]

my friend give me this he say its correct 😭

[shell haven]

So uh the two cars head in directions perpendicular to each other correct

So that's your pythagorean theorum

[uneven osprey]

it is the most stupidest thing to trust on it in terms of maths

[shell haven]

sqrt(9850)*t would be the expression

[silent jay]

yea i got Distance = 10 x sqrt(98.5) x t

[silent jay]

would it be better to just put what u got

[shell haven]

Idk do you need as simplified as possible

[silent jay]

ima just put yours seems more logical

or idk

thanks

.close

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[tacit haven]

Translationm: Find the lowest point of:

[tacit haven]

i got 16sqrt(11) but idk if its right or not

[tacit haven]

at x = sqrt 11

[fluid tundra]

not correct unfortunately

[tacit haven]

why? could you help?

first i simplified x - a/x into (x^2 - a)/x

this is probably where im wrong

i factored |(x^2 -a)/x| into |x^2 - a| 1/|x|

[south plume]

no that's not wrong

[leaden karma]

,w minimum value of (sum from r=1 to 20 of |x - r/x |)

[clever fjord]

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[leaden karma]

bro

ok wolframalpha

[tacit haven]

what is wolfram on

[south plume]

lmao

it tried

[leaden karma]

what did you do after this

[fluid tundra]

first does it make sense that the minimum occurs at some sqrt(n) where n is an integer

[leaden karma]

you can assume x is positive without loss of generality

[lusty helm]

t we can apply AM GM and get the max and min value of each function

aha it's minus

[leaden karma]

nope because equality doesn't hold for each term at the same point

[leaden karma]

and that

[lusty helm]

yes realised lately

[tacit haven]

well it simplifies to (x^2 - a)/x so i assumed so

[tacit haven]

turned it into [|x^2 - 1| + | x^2 -2| + ... |x^2 - 20|] 1/|x|

[tacit haven]

then using the formula to find the median of the roots you get 10 <= x^2 <= 11

[leaden karma]

what formula?

[uneven osprey]

that works for |x+/-a| things only

[tacit haven]

ohh

thought it worked for x^2 too

then what do i do then?

[fluid tundra]

from here you can get away with doing this problem just by plugging in values of sqrt(n) and finding the smallest

though there may be a better solution

[tacit haven]

"if f(x) = |x - a1| + |x - a2| +... |x - an| and n is even the lowest point of f(x) is in the range median <= x <= next value" here i assumed f(x^2) worked

[tacit haven]

oh okay

[fluid tundra]

(btw you evaluated the expression at sqrt(11) incorrectly)

[uneven osprey]

it might work but a 1/|x| is also in multiplication with it

[leaden karma]

well this would have worked if there wasn't that |x| factor in the denominator

[tacit haven]

ohh😭

[leaden karma]

first, can you justify why the minima/maxima MUST be at one of the values sqrt(n)?

[tacit haven]

well not really

tried using desmos but it gave a confusing answer

[leaden karma]

hmm yeah this doesn't look too easy unfortunately

maybe try using the triangle inequality

[tacit haven]

desmos says 29.399

[fluid tundra]

by the time you find a solution to algebraically "prove" the minimum this approach would already give you the answer

[leaden karma]

i think if you use the triangle inequality on the first and last terms and going in from there you'll get a factor of 19

[leaden karma]

why do you think the minimum will be necessarily at a sqrt(n)?

i don't really see why this is so obvious

[fluid tundra]

summation of cusped functions typically have a minimum at one of the cusps

[leaden karma]

i mean, yes

but still, brute forcing which sqrt(n) it is also seems kind of bad

[tacit haven]

and also time consuming

[fluid tundra]

if this appeared on a test that's exactly what i would do

[tacit haven]

ngl same but id get lazy after 4 tries

[leaden karma]

by checking on geogebra it seems to be that the minimum is at x=sqrt13

[fluid tundra]

that does happen to be correct

but does it matter? no

[late dust]

You only need 4 or 5 tries, you can binary search it

[leaden karma]

indeed

[leaden karma]

binary search?

[fluid tundra]

this isn't even necessary

intuitively, the minimum should be close to n = 11

[late dust]

Well sure

[tacit haven]

desmos says the same

[leaden karma]

i really do not like this logic though

every step is riddled with non-motivated assumptions

if it works for you i guess it works

[late dust]

I mean there is a final step you should do, but I don't see a faster way

[tacit haven]

ive put like 4 of the questions from this test on here and all of them everyone brute forced or guessed😭

[fluid tundra]

welcome to computational-style competition level math

though yes i agree this problem is not really that good

[tacit haven]

there must be a more elementary way to solve this

[leaden karma]

if you check the sequence of minimas

it does seem to follow kind of a random pattern

[tacit haven]

since this test is for 7th - 9th graders

[leaden karma]

no fucking way what

[fluid tundra]

the solution probably involves finding a general form for f(n)

[uneven osprey]

bro's a Thai genius

[fluid tundra]

but even this takes longer than just plugging in values

[leaden karma]

i highly doubt there is one

[fluid tundra]

oh there definitely isn't

[tacit haven]

judging from the other questions they all have reasonable ways to the solution

[fluid tundra]

but once you correctly evaluate f at any value of sqrt(n) then doing more will be easy

[red surge]

you can probs justify this with concavity/convexity

[tacit haven]

its from like 12 years ago though

[leaden karma]

i mean, did you try the triangle inequality at all?

im sure that has atleast some use here

[leaden karma]

yeah that makes sense now that I think about it

sqrt(n) are the only critical points of the graph and the graph is also continuous except at x=0

you could try differentiating that ungodly mess

[late dust]

It's not guaranteed, which is why I said there is a final step

Look at the same sum but with 10 as upper bound

[royal crag]

This could be how a solver/CAS does it, apart from just graphing it somehow and searching minima from there

It would likely be a waste of computational power since you can't do (d/dx)=0, you need subgradients and check for wherever it goes from negative to positive

[odd edge]

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[lusty helm]

what is LHD and RHD coming here

[lusty helm]

for x=2

[frigid canopy]

Left hand derivative.

And right hand derivative.

[lusty helm]

yes

nvm

there was a silly mistake

.close

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[tiny sigil]

I need help what steps do I take in order to find the value of a baseball card

Please @ me when you see this I may be off discord

[cold sage]

what was your process in getting these inputs you have

[tiny sigil]

4K I divided 493/363=e13k 13 representing the years between 1977 1990

Then I inputed the answer and got 263e^0.048t

[cold sage]

263 but yeah that checks out, what are you struggling with then?

[tiny sigil]

And then I subtract 2015 and 1977 and got 38 and then put it for the equation

Part D what is doubling time for the value of the baseball cards the nearest tenth of a year

[cold sage]

you seem to have a good grasp

[cold sage]

ah

it means how long does it take the value of the card to double

solving 2(263)=263e^(0.048t) would be enough

[tiny sigil]

Okay I will try that

See I got confused on which values to input

14.44056626?)

And just rounded up right

I think I tried 14.44 and it said it was the wrong answer

[cold sage]

,w ln(2)/0.048

[clever fjord]

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[cold sage]

ah

'nearest 10th'

youre doing hundreth

[tiny sigil]

14.4?

[cold sage]

si

[tiny sigil]

Ah gracias ^^

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[tiny sigil]

.reopen

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✅

[tiny sigil]

Wait one more question how do I do the last part section e

I need help with the last part section e

[cold sage]

throw an idea at me

[tiny sigil]

Haha

Uhh 🤔 hmm

263 e^0.048(2260)?

Or ln 2/2260 maybe

[cold sage]

not quite

remember what the equation you found actually means

A=263e^(0.048t)
t is the years after 1977
A is the value at time t

[cold sage]

i dont believe so

2260 is the value we want right?

[tiny sigil]

Si

[cold sage]

so A=2260

then we find t to know when that value is achieved

[tiny sigil]

2260=263e^(0.048)t

Sorry I'm a little slow

2260=263e^(0.048)1977?

[odd edge]

@tiny sigil Has your question been resolved?

[tiny sigil]

@cold sage

[cold sage]

This is alright, but you need to solve for t

Like how we found the doubling time

[tiny sigil]

So solve the equation to find t or substitute t with a value

@cold sage sorry I know you're probably busy ^^'

[cold sage]

Its alright, yeah you need to solve for t, very similar to the way you solved for d

[tiny sigil]

(2)2260=263e^(0.048)t or ln 2/2260

Sorry I'm just confused

t= 44.81179291?

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[tiny sigil]

2260=263e^(0.048)(14.4)?

.reopen

[odd edge]

✅

[tiny sigil]

I figured it out thank you for your help

.close

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[dapper nymph]

I dont get how they get a^22 as the derivative. Why is it not product rule of a^22 and x so 22a^21(x) - a^22 ?

[slim kettle]

What is the derivative of f(x) = ax where 'a' is a constant?

[dapper nymph]

a?

[slim kettle]

Yeah

If 'a' is constant, then a^22 is also a constant

Right?

[dapper nymph]

oh i see

I didnt know a was a constant

[slim kettle]

Haha

np

You got it now

[dapper nymph]

Why would they not say that lol

[slim kettle]

Becuz it's already given

[dapper nymph]

oh wait they did lol

assume a is a constant

[slim kettle]

Cuz the function is in terms of x

f(x)

So any other variable gotta be constant

[dapper nymph]

gotcha, thanks!

[slim kettle]

Haha, never mention brudder

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[clever fjord]

clikz

[wanton bison]

looks well done

[void spire]

Btw you couldve found a function of the side bisector of those 2 points then just plug x = 0

[clever fjord]

clikz
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[silent jay]

@void spire like this?

[void spire]

Yes

[silent jay]

oh ok I understand

[void spire]

Idk if its easier. But i think it could be

I mean geting the slope and midpoint is easy. Then basically just plug it in y = ax + b to get b and that is your answer

[silent jay]

yea I think that way is better

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[fallow adder]

Why did we put n * s instead of n * p? doesnt the full p (everything that is in the second screenshot) represent the vector of the line?

[wanton bison]

looks like pi is a plane, not a vector

you can tell by this that if r and n are orthogonal that the plane pi and line p are parallel

[fallow adder]

yes but n is the normal vector of pi

[wanton bison]

yea

[fallow adder]

so we put the vector of n * the vector of the line p

[wanton bison]

if you were to move the vector r onto the plane pi

wouldnt they be parallel to p?

thats the equivalent to seeing if n and r are orthogonal

[fallow adder]

and I dont understand why we dont use this form of the vector and only use the direction vector s of it

[wanton bison]

you can take in fact any vector that points in the same direction as p

the direction vector is just the most convenient one

you can also take this one

as long as it's in p or at least parallel to p

[fallow adder]

what about the size of n and r, dont they have to be the same size to be = 0 aka on a 90 degree angle?

[wanton bison]

no

the angle doesnt change

just because you change size

take triangles for example

[fallow adder]

I dont get it

[wanton bison]

no matter how much you scale the vector

the angle remains

because the direction doesnt change

[fallow adder]

oh ok true

[wanton bison]

and i took triangle as an example

cause you scale its lengths (but proportionally cause it's closed) the angles still remain

[fallow adder]

so because s and n are on a 90 degree angle then no matter what they should be = 0

[wanton bison]

yea

[fallow adder]

could we take anything other to figure out that n * that something else = 0 when a normal vector and a line in this form is given?

I'm guessing not, right?

[wanton bison]

any multiple of the direction vector can be taken

[fallow adder]

multiple as in s * a scalar?

[wanton bison]

yea exactly

[fallow adder]

wait so K here is a scalar or a point on the line?

[wanton bison]

k is a scalar

it's defined as an element of R

[fallow adder]

oh yea true

[fallow adder]

wait so with this we actually get the point vector of r no?

[odd edge]

@fallow adder Has your question been resolved?

[fallow adder]

<@&286206848099549185>

[wanton bison]

I dont understand this

[fallow adder]

with this function we are calculating the point vector of r right (what is inside the red box of the second screenshot)?,

[wanton bison]

the point of vector?

[wanton bison]

why is r twice appearing?

,,\vec{r} = \vec{r}_r + k \cdot \vec{s}

[clever fjord]

𝔸dωn𝓲²s

[wanton bison]

You are basically at r_r and from there you are going into the direction of the vector s

[fallow adder]

point vector, as in a point in space that has a vector from 0 to it

oh sorry it may be some other name in English

our teacher usually uses r to annotate that we are we can insert a point at r to get the point vector

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[fallow adder]

.close

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[neon oak]

I’m pretty confused on this topic in general but to be more specific I’m confused how to find the vertical and horizontal displacement. Im
Not sure how to decide which coordinates to subtract from the other

[shell chasm]

do you know how to calculate the hypotenuse of a right triangle?

[neon oak]

Yea, a^2+b^2=c^2

I’m sure I can just find the lengths of the base and height and find the 2/5 of each but that’s not the way khan academy wants me to solve it

[shell chasm]

now, find a hypotenuse of the line such that it has the value $\frac{2}{5}\cdot AC$

[clever fjord]

boss

[shell chasm]

then obtain the needed value for y

[neon oak]

Alright hold on

[shell chasm]

$\frac{2}{5}\cdot AC = \frac{2}{5} \cdot \sqrt{101}$ if i read everything correctly

[clever fjord]

boss

[neon oak]

Then what?

This is getting more confusing if anything since all the answer choices are whole/mixed numbers coordinates

[shell chasm]

then you know how much you need to go right from point B such that $AB = \frac{2}{5}\cdot AC$

[clever fjord]

boss

[shell chasm]

from this you can calculate the y value using the linear function that goes thru A and C

$f(-8+dx) = y_B$

[clever fjord]

boss

[shell chasm]

where $dx = |-8-x_B|$

[clever fjord]

boss

[neon oak]

What does the d stand for?

[shell chasm]

"how much do i need to go right from point A to reach B on the linear function AC"

thats the meaning behind dx

[wanton bison]

interesting notation

[shell chasm]

idk better xD

[neon oak]

I really appreciate the help but this made it more confusing+i didn’t get my question answered on how to find the vertical/horizontal displacement of 2 coordinates😭

[wanton bison]

relax

[shell chasm]

we dont wanna present the solution instantly

we want you to learn

[wanton bison]

well do i

[shell chasm]

can you please be more precise on what you do not understand?

[neon oak]

Alright hold up let me try to comprehend it step by step

[shell chasm]

take your time

[wanton bison]

If we know the coordinates of A

and AB is just 2/5 of AC

wouldn't that be applicable on the coordinates as well?

[neon oak]

Yes

That’s how khan academy is showing it

[shell chasm]

remember: many ways lead to paris (rome)

do it how you understand it the easiest

[wanton bison]

some boss shit

[shell chasm]

hihi

[neon oak]

But in order to do that, you need to find the vertical/horizontal distance, where from you add to to the coordinates of A since it is asking for the line of AB

[shell chasm]

what you need to find is:
A step dx such that the red line has the lenght of $\frac{2}{5}\cdot AC$ from A

[clever fjord]

boss

[shell chasm]

maybe start by defining the linear function that goes thru A and C

do you know how to do this?

linear functions are fully defined by 2 points, so there exists a concrete formula to calculate the needed coefficients

[shell chasm]

$f_{AC}(x) = m\cdot x + b$ you need to find m and b

[clever fjord]

boss

[neon oak]

This is how I understand it and that’s the answer, and i got the vertical/horizontal displacements by looking at the graph, but I’m confused on how to find it when I’m just given coordinates and i can’t see a graph

[shell chasm]

but there is clearly a graph thru A and C, its blue. maybe i dont understand

[neon oak]

I’m asking cuz these type of questions pop up

[shell chasm]

thats a similar question

[neon oak]

Sorry i should’ve showed that type of question first lol

[shell chasm]

its the same

just with 2/3 instead of 2/5

otherwise exactly the same

[neon oak]

What does the X stand for?

I’m trying to use your method for this problem

[shell chasm]

the $x_B$?

[clever fjord]

boss

[neon oak]

Nah the x in the dx

[shell chasm]

you mean the $dx$?

[neon oak]

Yes

[clever fjord]

boss

[shell chasm]

try to see it from the perspective of being at point A:
"how much do i need to go right from point A to reach B on the linear function AC" = dx

[neon oak]

Yea but how would I get a coordinate from that

[shell chasm]

$x_B = -8 + dx$

[clever fjord]

boss

[shell chasm]

and you know that $2/5 \cdot \sqrt{101} = \sqrt{(dx)^2 + (f(dx))^2}$

now solve for dx

[clever fjord]

boss

[shell chasm]

as i already mentioned you first need to calculate $f(x)$ but this is trivial since you have the coordinates of 2 points lying on $f(x)$

[clever fjord]

boss

[neon oak]

I tried using your method for the most recent problem i showed you

Did I miss out on anything?

Cuz the answer is crazy😭

[shell chasm]

yes you did

you cannot just add the lenght $10.7703$ to both your x and y value

[clever fjord]

boss

[shell chasm]

because that means that you have moved more than you want since: $10.7703 < \sqrt{10.7703^2 + 10.7703^2} = \sqrt{2} \cdot 10.7703$

[clever fjord]

boss

[neon oak]

What is the point in finding the amount of space that is 2/3 of line AC?

[shell chasm]

well you want to solve the problem dont you?

what do you mean by "space" ? and "2/3 of line AC" ?

[wanton bison]

have you solved this?

[shell chasm]

maybe you are better in explaining?

[neon oak]

From my perspective, 10.7703 is the distance from A to B(the space) which is 2/3’s of A to C

[wanton bison]

idk if it's right

[neon oak]

Sorry if I’m being difficult😭

[neon oak]

@wanton bison

It was right

[wanton bison]

I just noticed both triangles are similar

Since we know the green

if we get the angle at C for example

and we know the hypotenuse (length of AB) then we can get the other red sides

and thus the coordinate change from A to B

[shell chasm]

very intelligent aswell!

a more geometric approach

like it.

my approach is maybe too deep into analysis..

[wanton bison]

i tried it but it seems kinda too off

2/5

[neon oak]

Isn’t that like trigonometry since we have to find the angle?

[wanton bison]

ok it's identical to mine :D

[wanton bison]

yea

i hate trigonemtry but in this case

turns out it's easy if you use it

haha

[tacit haven]

what is the question?

[wanton bison]

well done guys

[neon oak]

💀💀💀💀

I forgot all abt trigonometry 😭 ah well I will come by it soon for the SAT

[wanton bison]

yea true (wtf is SAT)

[shell chasm]

wtf is a kilometer?

[neon oak]

Well using my method/khan academy’s, I was confused on how to find the vertical and horizontal displacement of 2 coordinates

Which i know is x2-x1, and y2-y1

[tacit haven]

dont you use the formula (nx1 + mx2)/m + n?

[neon oak]

But I’m confused if it matters which coordinate we use for x1,y1, and x2,y2

[tacit haven]

where the line is split into m:n

[neon oak]

Hold up doing it rn

[tacit haven]

you get B(5.6, ) and smth else

[neon oak]

I’m doing it for this problem

Like this?

@tacit haven

W equation if it works for problem like these

[shell chasm]

you need to understand the formula

not just use something

that wont carry you thru university

[neon oak]

It didn’t give me the right answer so it isn’t right but i might be doing it wrong, but if it gave me the right answer i think I would understand it

I realized I learn best when I learn in reverse and analyze why that got that

[tacit haven]

m = 2, n = 3

[tacit haven]

i would show him the proof but i forgot how to do it

[neon oak]

How come M is the numerator and N is the denominator?

[tacit haven]

the formula is used for when line A is split into m:n

[neon oak]

Do you mean N=all the pieces and M=the amount of piecies its asking

[tacit haven]

since AC is split into 2:3, you can substitute

[neon oak]

I’m thinking visually btw

[tacit haven]

m + n is the whole line

[neon oak]

Ohhh we looking at different problems

I think

[neon oak]

This is what I’m talking abt

[tacit haven]

yeah if AB: BC is 2:3, m is 2 and n is 3

[neon oak]

Where did the 2:3 come from, in the equation it says 2:1

[tacit haven]

mbmb

yeah m = 2, n = 1 if you are referencing it from point A

so for this question if you let point A be (x1,y1) you get the x coordinate to be (2 - 8)/3

which is -2

[neon oak]

Does it matter what point we use as (x1,y1)?

@tacit haven

[odd edge]

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[odd edge]

@shell chasm Has your question been resolved?

[odd edge]

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[golden silo]

yo for this do i convert the amounts into decimals

[golden silo]

so instead of 4 ft 2 inches i should make it as the proper decimal which is 4.167

?

[nimble blaze]

better to work with improper fractions

[golden silo]

hmm

[golden silo]

so in this case i got my answer thru decimal and fraction form as 25 feet

would that be correct or incorrect

i get a bit shaky with fractions sometimes

but then iagain i js use a calculator

[nimble blaze]

yes, 25 is correct

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[golden silo]

yo i also forgot

[golden silo]

i have another question

i spent a lot of time

on this proof

and im lost

[tacit haven]

?

[golden silo]

its a proof i have to fill out

and i have to use those things wiht dropdowns as reasons

but im so lost

because its saying XY but thats not shown in the model

please

im desperate!!!

[tacit haven]

i know which are true, but i dunno the names of why they're true

[golden silo]

damn

im kinda cooked rn

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[odd edge]

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[odd edge]

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[gloomy mason]

What am I supposed to do ?

[devout dove]

What do you already know from the equation?

[cursive field]

is this a test by any chance

[gloomy mason]

That it is in a slope intercept form

[gloomy mason]

no

[cursive field]

good

okay what can you infer from the equation itself

and also

[odd edge]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[devout dove]

^^

[cursive field]

okay

like i said, what can you infer from the equation itself

[gloomy mason]

i studied this chapter 2 months back but now i dont remember a thing

[devout dove]

y = mx + b

[gloomy mason]

the slope should be negative ?

[cursive field]

good

[devout dove]

What do the parts of this equation represent?

[cursive field]

so which options does that eliminate

[gloomy mason]

c and d

[cursive field]

no...

try again

you said that the line formed by the equation has negative slope

so, which options would that eliminate?

[gloomy mason]

oh

a and b

[uneven osprey]

😭 no

[gloomy mason]

im cooked

[cursive field]

...

okay

[cinder elk]

Negative slope means that starting from the left moving to the right it is going downwards

[cursive field]

i'll explain slope

positive slope means it goes upwards from left to right

[gloomy mason]

a and d ?

[cursive field]

yes

a and d have negative slope

that is correct

[gloomy mason]

oh

[cursive field]

do you understand slope now?

[gloomy mason]

yeah

totally

[cursive field]

you sure?

[gloomy mason]

yeah.. but i still dont know how to identify a graph just from the given slope

[cursive field]

why not

oh i see what you mean

[gloomy mason]

i think

c is the answer

[cursive field]

but you understand why b and c have been eliminated right

correct

how'd you get there?

wait what

no not c

[cinder elk]

slope can also be explained as rise over run

[cursive field]

did you mistype

[cinder elk]

$\frac{rise}{run}$ or $\frac{how_far_up}{how_far_over}$

[gloomy mason]

because 3 is y the line is intersecting it in graph c

i think so

[cursive field]

wha...?

that's fine

but

c has positive slope

[gloomy mason]

yeah ik this

[gloomy mason]

ohh

so its b ?

[cursive field]

$\frac{\text{rise}}{\text{run}}$ or $\frac{\text{how far up}}{\text{how far over}}$

[gloomy mason]

with the same logic applied

[clever fjord]

ren

[cursive field]

no?????

dude

[cinder elk]

thank you

[cursive field]

are you just guessing

[cursive field]

np

[gloomy mason]

yeah

[cursive field]

okay listen to me

we are trying to help you learn

and are also giving you clues

but if you disregard all of that

and just guess

[cinder elk]

y = mx + b
m = slope
b = y-intercept (where the line crosses the up and down axis)

[cursive field]

there's no point to all of this

[gloomy mason]

okay

i got it

i think

b and c got eliminated

[gloomy mason]

im sorry

[gloomy mason]

alright

[gloomy mason]

how do i apply this to my equation

[cinder elk]

Well, what is the b in the equation you have?

[devout dove]

Choose two points on the line and find the difference in height and length

[gloomy mason]

3

[gloomy mason]

but i am i supposed to know which lines to choose

[cinder elk]

Which of the graphs that you have left, show to intersect at the 3 on the y axis

[gloomy mason]

a has -3 and d +3

[cinder elk]

The perfectly up and down line that is thick is the y-axis
The perfectly left and right line that is thick is the x-axis
The third thick line is the line of the equation

[cinder elk]

So, is your b positive or negative?

[gloomy mason]

pos

so d is the ans ?

thats it ?

[cinder elk]

yep!

For your slope

[gloomy mason]

this looks easy

now

i have another ques though

[gloomy mason]

there are so many points intersecting which ones should i use to identify the slope

[cinder elk]

See how those two lines cross at "perfect spots" they cross at intersections of the y and x axes

Well I would choose points you can perfectly describe

[gloomy mason]

ohh

[cinder elk]

see how the graph passes directly over a whole number on the x axis?

[gloomy mason]

yeah

[cinder elk]

I would use that as one of your points as you can perfectly describe it

Where else does it perfectly cross at a point like that (Doesn't have to be across the x-axis)

[gloomy mason]

im getting 1/4

i choose (2,0) and (6,1) as my points

i think they perfectly intersect

[cinder elk]

Yep!

[gloomy mason]

but i also see (-1,-2) as another perfect spot

is it wrong ?

[cinder elk]

not (-1, -2), you seem to have (y, x) it's typically written as (x, y)

[gloomy mason]

oh my bad

[cinder elk]

But no, you can use any two points that they intersect

you will get the same answer

[gloomy mason]

ohh

this is crazy

like i can use (-2,-1) and (6,1) instead of using (2,0)

[cinder elk]

yeah, you will get an equivalent answer that when simplified will give you 1/4, as you solved for here

[gloomy mason]

oh

thanks a lot man

this chapter is way easier now

[cinder elk]

No problem

[gloomy mason]

hey

another doubt

how do i find the y intercept

with a graph given

[cinder elk]

just look at where the graph passes over the y-axis

[gloomy mason]

easy

i completed my entire exercise

thanks a lot man

the explaination given there sucks so i didnt understand a thing

this one got me

[cinder elk]

Do you know how to solve for y?

Fundamentally the y-intercept is the remainder when you plug in x = 0