help-13

[austere ember]

so 3 - 5 * 7 + 64

now what

[frozen hornet]

so 14 + 64?

so 78?

[austere ember]

where did 14 come from

3 - 5 * 7 + 64

multiplication next

[frozen hornet]

5 * 7 = 35

then we subtract?

[austere ember]

right

so 3 - 35 + 64

[frozen hornet]

so 32

• 64 = 96?

[austere ember]

3 - 35 is not 32

a small positive number minus a big positive number? you'd expect that to be negative

you're at 3 on the number line and then moving 35 units to the left

[frozen hornet]

-38

[austere ember]

that would be -3 - 35

if it helps

3 - 35 is the same thing as - (35 - 3)

[frozen hornet]

-32?

[austere ember]

a - b is the same thing as -(b-a)

yes

-32

[frozen hornet]

ahhhhhhhhhhhhhhhhhhhhhhhhhhH

okay

so -32

[austere ember]

so -32 + 64

and of course you can rearrange these terms

[frozen hornet]

positive 32

[austere ember]

that's the same as 64 - 32

yes

32

[frozen hornet]

lo hicimossssssssssssssss

yay

all done

[austere ember]

hablas?

[frozen hornet]

un poco

you?

[austere ember]

mismo

estudie en escuela por cuatro anos

[frozen hornet]

lindo asf

my family is from puerto rico so theyre bilingual

[austere ember]

this isn't even spanglish atm it's some combination of text slang and spanish and english

"lindo asf" would send my spanish teacher to the hospital

[frozen hornet]

LOL goals

[cedar kiln]

@frozen hornet Has your question been resolved?

[cedar kiln]

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[carmine spire]

Quick question, what does doe 0 mean in the top question

[crimson sedge]

it means

g(h(x))

[carmine spire]

no like, I know that

but what does 0 mean in that equation

I don't get it

[blazing zephyr]

theres none

[crimson sedge]

i think its called

"of"

[mighty shuttle]

composition symbol

[crimson sedge]

so g of h x

[mighty shuttle]

(gof)(x)= g(f(x))

[crimson sedge]

yea this ^

[carmine spire]

I see, would you guys prefer using the first way to write it, or with the 0

[crimson sedge]

the one without O

for me

[mighty shuttle]

$g(f(x)$ easier to format in TeX

wait

[wraith dagger]

ƒ(Why am. I here)=I don't Know

[mighty shuttle]

this

[carmine spire]

Also, is there a reason for the the second question to be f evaluated first, all I remember is that the first one inside has to be evaluated first

[crimson sedge]

yea there is a reason

if g(h(x)) has to be defined, f(x) should lie in the domain of g(x)

and if u wont evaluate f(x) first u might end up solving ur question the wrong way

[carmine spire]

ahh so the innermost function?

[crimson sedge]

yea that's how u start doing them

x should also lie in the domain of f(x)

so u gotta check that too

[carmine spire]

Alright I might have to come back here soon, but thanks guys

.close

[cedar kiln]

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Closed by @carmine spire

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[crimson sedge]

np

[cedar kiln]

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[snow imp]

prove

[crimson sedge]

anything that u have tried so far?

[snow imp]

tried

[crimson sedge]

!show

[cedar kiln]

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

[snow imp]

wait

i tried to bring a zero

but didnt work

@crimson sedge can u pls do it?

[crimson sedge]

i cant see a 0 building up either

i think we should just break it?

im not really sure either

[cedar kiln]

@snow imp Has your question been resolved?

[cedar kiln]

@snow imp Has your question been resolved?

[crimson sedge]

!showwork

[cedar kiln]

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

[cedar kiln]

@snow imp Has your question been resolved?

[cedar kiln]

Channel closed

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[cedar kiln]

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[past sonnet]

why do i have to use 3?

can i not use 9?

[crimson sedge]

You can but you just have more cases

[steel heart]

if cube of a number is divisible by 3, then it is divisible by 3^2 and 3^3 as well

so, you can use 3 instead

[past sonnet]

so i should go for the lowest multiple?

excluding 1?

[crimson sedge]

I don't think that's a good reason

It doesn't always work like that

[steel heart]

it does

3 is a prime number so it does

[crimson sedge]

Say you wanted 7th powers mod 9

You can't just look at 7th powers mod 3

[past sonnet]

what do u mean by mod

[crimson sedge]

You just look at the remainder

(a=b mod c iff c divides a-b)

[past sonnet]

can i follow this logic?

[past sonnet]

I see

[crimson sedge]

Not always

Like if you already know that there are only 3 possible remainders since the question is telling you it's like that, then you probably just need to check for 3

Like here it works because you want cubes and phi(9)/3=phi(3)

But sussity skibidi you know

[past sonnet]

I see

quick q

is this associativity?

[past sonnet]

what does phi mean

[crimson sedge]

phi(n) is the number of remainders mod n coprime with n

[past sonnet]

I see

ty

[crimson sedge]

Like it's some number theory stuff, I'd say that unless you're quite familiar with it, you can't really say why you only need to check for 3 instead of 9. Maybe in general you could just try for 3 and if you don't get anything nice just do for 9. And in general for any other prime powers etc

[past sonnet]

I see

ty

[cedar kiln]

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[analog wind]

Need help w disc math

[neat raven]

!da2a

[cedar kiln]

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/

[neat raven]

hehe

[analog wind]

7a 7b

when it says "for some integer k,i" does it mean for all integers??

[steel heart]

yes

[analog wind]

so
7a -1,1
7b 0?

cuz 0 is not integer

[steel heart]

0 is an integer

[analog wind]

oops

so its
7b 0,2?

[steel heart]

wbt when i = 1

[analog wind]

1-1 =0

[steel heart]

wbt when i = 2

ah yes mb

you're right

[analog wind]

okay thanks bro

im prestudying so its difficult just reading the book in advance

how to close

[steel heart]

.close

!done

[cedar kiln]

If you are done with this channel, please mark your problem as solved by typing .close

[analog wind]

.close

[cedar kiln]

Channel closed

Closed by @analog wind

Use .reopen if this was a mistake.

[analog wind]

👍🏻

[steel heart]

[cedar kiln]

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[agile meadow]

could really use some quick help on these questions please

[steel heart]

which question exactly?

[agile meadow]

all of them lol

one more

[orchid island]

In first question a=1

1

[agile meadow]

yea,i dont wanna waste your time,but if you can just gimme the solutions,ill be able to figure out the rest✅

im sure itll take ages to explain all these

[orchid island]

Looks boring questions because all r very easy

[agile meadow]

yea,but im dumb asf

[undone halo]

Where are you getting these

Why is all in a video

[orchid island]

Instagram 😂😂

[agile meadow]

yea

[undone halo]

Where did your friend get this

Quite peculiar

[orchid island]

U need only answer or explanation also

[undone halo]

!status

[cedar kiln]

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

[orchid island]

?

[undone halo]

!nosols

[cedar kiln]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[agile meadow]

its a revision worksheet,probably has some of the question coming in the nxt exam so im using this to short cut learn

if no can do,then ill be off

[undone halo]

I cant really do 1 since I dont have much knowledge

For 4, do you have an idea on what sqrt(x) looks like?

[agile meadow]

nope,why do you think i came here,dont try explaining coz its pointless,i learn by question and answer,then i fnd out how they go together

[undone halo]

Ok

So you know how when you input a negative number in square root

[agile meadow]

erroer

[undone halo]

You cant do that because it becomes imaginary and that isnt real

[agile meadow]

yuh ok

[undone halo]

Well the graph of sqrt(x) is just like that

It does not pass through the negative numbers

But it goes to positive infinity

So sqrt(x+1) will look somewhat like that, going to positive infinity

Now do you know what value of x must be so that sqrt(x+1) = 0?

[orchid island]

Wtf

[orchid island]

x=-1

Then y=0

[undone halo]

Yes

So that means that when x = -1, y = 0

[orchid island]

So correct ans is B

[undone halo]

Therefore B is the answer

[agile meadow]

kk

[undone halo]

For question distance

A(5, -2)
B(15, -2)
C(10, -8)

Correct?

[agile meadow]

yea

[undone halo]

Ok

Ill assume you dont know how to get the distance of 2 points even though the formula is right there

But basically its just the pythagorean theorem

[agile meadow]

thx

[undone halo]

d = sqrt((x1-x2)^2+(y1-y2)^2)

Since were trying to find length AC

Whats the x-value of point A

[agile meadow]

broda,why you still tryna teach me,just close this channel

[undone halo]

you close it then

.close

[cedar kiln]

@agile meadow Has your question been resolved?

[cedar kiln]

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[craggy lintel]

so

in this quesiton

[craggy lintel]

what's the steps/thingies i should do cuz im confused i dont think i ever learnt this

[crimson sedge]

do u know genral equation for parabola

[craggy lintel]

yeah its

uh this one right?

y=a(x+k)h right

or other way around

a+h)k

[craggy lintel]

y = a(x-h)^2 + k

[steel heart]

where h is what?

[crimson sedge]

You're allowed calculators?

[craggy lintel]

I am?

[steel heart]

it's not necessary ig

[craggy lintel]

I mean y eah i dont need one

[craggy lintel]

h is our vertex iirc?

h is the x value

[steel heart]

x coord of vertex but yeah

[craggy lintel]

and k is our y value

[craggy lintel]

so i mean ik this but they're asking for the distance from the x axis to the top of the circle

that's 12.1 feet right?

[craggy lintel]

i mean i dunno how to find the equation of botht he line and parabola, what do i do?

[steel heart]

ig no

[craggy lintel]

then how would i find it?

because i'm really confused on this question lol, ive never seen it before

[steel heart]

i am stuck on that x-axis to top of the circle part

if you get the solution lmk

[craggy lintel]

alright

i dont know if 15 minutes has passed yet, just about

<@&286206848099549185> can anybody else help me with my problem?

[floral salmon]

In the first I'm sure they want you to find the length of the red segment in the image.

[craggy lintel]

ok so, how the heck do i do that, like do i take 12.1-4.54

[floral salmon]

that wouldn't give it, would it? Calm down.

[craggy lintel]

? i didnt mean to offend lol

[floral salmon]

does this ring any bells on how to do it?

[craggy lintel]

uh, no :(

I dont think so

but seeing that L is getting my gears grinding

[floral salmon]

right triangle, Pythagora's?

That's not a L, it is a denotation for a right angle

[craggy lintel]

Oh

OH OH OH

sorry

holy crap so sorry

i understand

so ok, so we got 12.1 as our h value and half of 14.3 as our O value right?

sorry wait O or A i made a mistake i think

[floral salmon]

what do you mean by h and O values?

[craggy lintel]

Opposite and Hypotonuse value

hypotenuse

[floral salmon]

Lets call them by colors or something instead since whats opposite and adjacent is not clear directly.

I marked the triangle with red, yellow and blue sides, refer to them as such.

[craggy lintel]

sorry my bad

so R^2=Y^2+B^2

and we have our R and Y values right?

[floral salmon]

yes, we want B

[craggy lintel]

b= 9.761

[craggy lintel]

is this correct? ^

[floral salmon]

yes, use that to find the red segment in this image

[craggy lintel]

ok so now i have 19.522

this line would be 19.522

[craggy lintel]

oh is it because its the r of the semi circle?

do i find the semi circle

Im really sorry btw, just really confused rn

[floral salmon]

no worries, they want the red segment here, it cannot be 19.522 (too big), how did you arrive at this conclusion?

[craggy lintel]

well i took Blue and multiplied it by 2,

ik it can be 19.522

even if it isnt scaled

but i thought i could solve for the area of the semi *circle

[craggy lintel]

so i take it not the area of the semicircle

[floral salmon]

no, we don't want any areas for now, just the length of that small segment.

[craggy lintel]

im sorry i dont know how to find it then(the length)

[floral salmon]

Do you see any relationships between the green, blue and red line segments here?

[craggy lintel]

its a tiny rectangle?

well i mean the green line is the blue line and the red line combined

[floral salmon]

no, like their lengths

[craggy lintel]

oh, i mean no i dunno

[floral salmon]

yes, so R + B = G

We want R, so R = G - B

do we have the values of G and B?

[craggy lintel]

green is 12.1 and blue is 9.76?

[floral salmon]

yes, so you can find R.

[craggy lintel]

ok so r=2.34

[floral salmon]

seems good, that's the answer to the first question (2.34 ft).

[craggy lintel]

yay! ok, so now i gotta find the equation of the circle (x-h)^2 + (y-k )^2 = r^2

[floral salmon]

yes, identify the radius and the middle point of the circle. Remember that the gray lines (dotted and filled) are the coordinate axis.

[craggy lintel]

alrighty gimme a second

ok so the radius is 12.1?

[floral salmon]

yes

[cedar kiln]

@craggy lintel Has your question been resolved?

[craggy lintel]

no sorry mr bot

im still solving

@floral salmon (x-0)^2+(y-9.761)^2=12.1^2

is this right?

[floral salmon]

no, $(x-0)^2$ is correct but $(y-9.761)^2$ is incorrect, what is k here?

[wraith dagger]

Crystopher

[craggy lintel]

vertex

oh

you mean

ok

our vertex y value is is (0,9.761)

WAIT I MADE A MISTAKE

ITS -

-9.761?

and then its y+9.761

[floral salmon]

yes, that was the mistake you made, it should be $(y+9.761)^2$

[wraith dagger]

Crystopher

[craggy lintel]

so sorry

[floral salmon]

no worries, so the answer is $x^2+(y+9.761)^2=12.1^2$ for question 2

[wraith dagger]

Crystopher

[floral salmon]

For the next, I don't know how they taught you to do that, there are several ways, is there some method, formula or similar you normally use for find equation of parabolas?

[craggy lintel]

i dunno 💀

[floral salmon]

anything you know about parabolas?

[craggy lintel]

i mean yeah y=a(x+k)h

[floral salmon]

this one $y = a(x-h)^2 + k$?

[wraith dagger]

Crystopher

[craggy lintel]

yeah soirry mb

ok hey i took another case

because i got the area of a circle wrong

fml

im going to just start again, and speedrun it

[craggy lintel]

yeah ik they're an asshole for doing so

[floral salmon]

I have to go for a moment, I leave you with insights on the parabola formula you know. In $y=a(x-h)^2+k$ apparently $h$ is the x-coordinate of the parabola's vertex, $k$ is the y-coordinate of the parabola's vertex. I don't know what $a$ represents, or rather how to find it easily, I would personally select some arbitrary point on the parabola after finding h and k and solving for $a$ using it.

[wraith dagger]

Crystopher

[cedar kiln]

@craggy lintel Has your question been resolved?

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[cedar kiln]

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[craggy lintel]

alright so i'm back

[craggy lintel]

gonna redo this question because i wont be able to sleep otherwise

[dull oxide]

!status

[cedar kiln]

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

[craggy lintel]

1

[craggy lintel]

1 because i tried and got it right then wrong again and its pissing me off that i cant get it right

[dull oxide]

Set up an equation for the parabola and circle

[craggy lintel]

wait onesecond

first off i gotta solve for distance to the x axis right?

so ik how to do that i think

[craggy lintel]

so what's that first step i should take?

[dull oxide]

Probably to write the equation of the circle

[craggy lintel]

ok so

.close

[cedar kiln]

Channel closed

Closed by @craggy lintel

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[cedar kiln]

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[echo sleet]

Can someone verify to which domain can we extend $f(x,y) = x \sin (\frac{\pi}{xy})$ by continuity? Idk if my separation in two limits is valid

[wraith dagger]

vascomarq

[echo sleet]

I think this is wrong but I don't have other aproach

[cedar kiln]

@echo sleet Has your question been resolved?

[mental trail]

when "y->0" part is not very well justified

If you want to show it's discontinuous

first of all you're approximating xsin(pi/xy) as pi/y when y -> 0

which is not true

since sin(t) approximates t but ONLY when t->0

not when 1/t -> 0

[mental trail]

you used the same "approximation" as well when x->0 I didn't notice that

it's not true

if you want the correct approach :

for when it should be extended by continuity : ||squeeze theorem||
for when it shouldn't be extended by continuity : ||show that you can approach multiple different values (ie take y_n = 1/(nx) and y_n = 1/((n+1/2)x) for different limits)||

[cedar kiln]

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[crimson sedge]

@livid trellis here right

[crimson sedge]

now what

[mortal hemlock]

!help

[cedar kiln]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[livid trellis]

you can send your problem here

[crimson sedge]

so far i tried racionalizing but it still leads to undefined

[mortal hemlock]

$\lim_{x\to 4}(x-3)^{\frac{x}{\sqrt{x^2+9}-5}}$

am i reading this right?

[crimson sedge]

yup

[wraith dagger]

Flappie

[mortal hemlock]

what happens when you just fill in x=4

[crimson sedge]

the power becomes 4/0

[mortal hemlock]

ah right, whoops

[crimson sedge]

dw gang

[mortal hemlock]

okay, lets just look at the exponent $\lim{x\to 4}\frac{x}{\sqrt{x^2+9}-5}$

[wraith dagger]

Flappie

[mortal hemlock]

what have you tried?

[crimson sedge]

racionalizing

truns into (x(sqrt(x^2 + 9)+5x))/(x^2-16)

asked chat gpt but i didn't understand what it was doing

[mortal hemlock]

!nogpt

[cedar kiln]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[mortal hemlock]

have you thought that it might not exist?

try taking left side and right side limit

[crimson sedge]

wym

[mortal hemlock]

like $\lim_{x\to 4^+}$ and $\lim_{x\to 4^-}$

[wraith dagger]

Flappie

[crimson sedge]

true it might not but since i couldn't find it i thought why not ask

[crimson sedge]

yeah i haven't seen this

idk how to proceed with that

[mortal hemlock]

how do you normally show that a limit doesnt exist?

[crimson sedge]

well, in my uni, as far as i'm aware we haven't had any of those

[mortal hemlock]

youve never had a limit that doesnt converge?

[crimson sedge]

someone in a different server said to subsitute with t

[crimson sedge]

that doesn't exist?, i mean so far no i don't think

[mortal hemlock]

just t?

[crimson sedge]

in my material i mean

[crimson sedge]

didn't give any further info

[mortal hemlock]

,w graph x/(sqrt(x^2+9)-5)

[wraith dagger]

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Requested by flappie.

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[crimson sedge]

nope

[cedar kiln]

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@crimson sedge Has your question been resolved?

[livid trellis]

basically when the limit aproaches 4 from 3.9999, it aproaches to -infinity

and when it aproaches to 4 from 4.0000000...1

it aproaches to infinity

but there is no limit for 4

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[shrewd hornet]

what "as many as" mean in 2 times as many as 9 ?

[mortal hemlock]

If I have 4 apples

And bob sitting next to me has 8

Bob has 2 times as many apples as I

[shrewd hornet]

2 times as many as 9, the second as is not clear to me

[austere ember]

that is just english for multiplication, the second as doesn’t do anything

2 times as many as 9 is just 2*9

[mortal hemlock]

It's like saying "as soon as" or "as quick as" etc

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[brisk nova]

Find the exact time between 9 and 10 when the hour hand and
minute hand are symmetric about the 12 o'clock position.

[brisk nova]

what do hey mean by symmetric about 12 oclock

[mortal hemlock]

Left-right symmetric

Imagine x axis is 9 to 3

Y axis 6 to 12

Then symmetric around u

[dreamy void]

<@&268886789983436800>

[mortal hemlock]

<@&268886789983436800>

[atomic tendon]

Huh

This question is interesting

[brisk nova]

wait i still dont get it

[atomic tendon]

Has to be between 9 and 9:15

[mortal hemlock]

Well, between 9:10 and 9:15

[brisk nova]

ohh

[atomic tendon]

Will it be 9:12?

[brisk nova]

so the angle made should be equal

[celest seal]

hint: the hour hand travels at 1/60th the speed of the minute hand (why?)

set up an algebraic equation and solve

(the minute hand starts at 0 degrees, the hour hand at 270 degrees...)

[brisk nova]

hmmm..

is it

[atomic tendon]

Could simplify it using the constraints flappie set

It can only be between 9 and 9 :15

[brisk nova]

is it 9:12

i got it from 90-6x=0.5x

which give x=12

[atomic tendon]

Holy intution

[brisk nova]

?

ohhh

[atomic tendon]

I guessed

[brisk nova]

damn

nice

thx

bye

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[civic coral]

What’s the evaluation trick at the end of the video

I cannot understand

[dreamy void]

you are showing yourself btw

[civic coral]

Im aware it

[nova snow]

selfie

u can screen record with an iPad btw

[cedar kiln]

@civic coral Has your question been resolved?

[wanton sail]

I'm assuming this is 11:54 of this video? https://www.youtube.com/watch?v=bOXCLR3Wric

He explains it in the rest of the video

Have you already watched the rest

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[strong merlin]

Hi! Why does x become 1/x and 3x^2 become 3?

[scenic stirrup]

think about $\sqrt{\frac1x+3}\cdot x,$ specifically moving $x$ inside the square root

[wraith dagger]

Vѳrtєx-

[strong merlin]

wouldn't that just make it x + 3 in the square root?

[austere ember]

if this makes it easier, $\sqrt{x + 3x^2} = \sqrt{x^2 (\frac{1}{x} + 3)} = \sqrt{x^2} \cdot \sqrt{\frac{1}{x} + 3} = x \cdot \sqrt{\frac{1}{x} + 3}$

[wraith dagger]

neil

[wanton sail]

^ what neil said

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[viral sequoia]

what does y=2*f(x) mean?

[viral sequoia]

y = f(x)?

im confused why its in my assignment

like duh yeah?

why not just f(x)=2x

[ancient lodge]

"y is the same thing as f(x)" is something that's technically wrong but that usually works as a conceptual shortcut for more elementary stuff

[ancient lodge]

ex. you could define y to be 2f(x), like here

Basically, y is twice the function f(x)

[ancient lodge]

So if f(x)=2x, then y=2(2x)=4x

[viral sequoia]

ah

makes sense

ty

[ancient lodge]

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[carmine spire]

I don't really understand besides like points and graphs, how is this the answer (can't show steps because I don't anything)

[carmine spire]

since g is the innermost function I thought it would be -1 but its 1

[austere ember]

f(g(0)) means find out what g(0) is and then plug that as an input into f and see what f outputs

when you plug 0 into g, you get -1

and when you plug -1 into f, you get 1

[carmine spire]

but how did you plug it in when it doesn't have like f=x^2 or g=x+2

or smt

oh wait

its for g my fault

so under the g column and look for 0

and -1 is under the f(x) column

I see

is that correct

Ah okay, thank you

Have a nice day

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[wild belfry]

Hey I got pretty far on this one but I forget the next step

(x+3)(x+4)/(x+1)(x-9)

(-4+3)(-4+4)/(-4+1)(-4-9)

(-1)(0)/(-3)(-13)

What do I do next? Is the answer just 0?

Ok I just checked, I guess it is

lol

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[woven meteor]

$\int :x^2cot^2x:dx$

[wraith dagger]

Clarence

[woven meteor]

Is there a clean way to solve this integral with just using the basic formula/integration techniques?

[crimson sedge]

is solving it with byparts fine ?

[woven meteor]

Yes

I tried using integral calculators, but they result in using dilogarithms which I know nothing about

[crimson sedge]

nvm

[muted bear]

,w integral of x^2 cot^2 x dx

[wraith dagger]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by garlicbredfries

[muted bear]

its nonelementary

[woven meteor]

shucks there's no way for it to be simple then

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@woven meteor Has your question been resolved?

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[silver terrace]

Hello,
I'm currently attempting to solve this problem, however none of my work matches the correct solution. I've tried different workarounds but couldn't figure out how to reach the solution. Can I get some assistance with solving this? Thanks

[jaunty thunder]

@silver terrace

I have checked it. Your Gaussian elimination is correct.

The point is to let x = k.

Then solve for -y + 3z = -2, and t - 2z = 1

[gleaming gust]

this is the correct answer

[silver terrace]

i think i understand but that wasn't a possible answer in the set of answers i was given

which is what confused me

the bottom solution [1; 2; 0] is a valid solution, and [k; 3k/2 + 1/2; k/2 - 1/2] is as well

[gleaming gust]

right

second one is not right

[silver terrace]

also, i don't quite understand this; where is t - 2z coming from?

[jaunty thunder]

from the second row of augmented matrix

[jaunty thunder]

the bottom one is not the unique solution.

[silver terrace]

i get that ; but i'm not sure how to get the 3rd option since its the correct one with infinite solutions

[gleaming gust]

this is the final solution for your problem

[silver terrace]

is there some way to get from that solution to this form? or is the set of possible answers they gave me incorrect

[gleaming gust]

let's suppose that

1+2t=k

then you can get the solution

from the above condition, you can derive the following result

t = k/2 - 1/2

right?

super easy

[silver terrace]

oh yeah i see that now

[gleaming gust]

how old are you?

[silver terrace]

im 18

[gleaming gust]

oh I see

university?

[silver terrace]

yeah

[gleaming gust]

good

do not hesitate to ask any questions

okay?

[silver terrace]

thank you

[gleaming gust]

you are welcome

[silver terrace]

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[marsh vigil]

Maybe a bit too specific but I'm trying to find a way to calculate the angle a camera is viewing a face in 3d graphics at.
So if it was viewing from straight up that would be 90 degrees.

[marsh vigil]

I have access to surface normals. I would prefer to use them if possible

[cedar kiln]

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.

[marsh vigil]

This isn't for a class. I'll draw it out, one moment

[upper abyss]

How do you define "angle between camera and surface" here?

[marsh vigil]

My art skills are unrivaled

[marsh vigil]

Like if I were to draw a line between the point it's sampling from what the angle would be compared to the surface

Sorry, this is for a programming related thing

[civic magnet]

you know the distance?

[marsh vigil]

Yes

From camera to the point I assume you mean

[civic magnet]

then it's plain trigonometry

[marsh vigil]

I was thinking that it could be done with taking the distance betweem that point and another. Issue is I'm not confident that I could get another point for reference. If possible I'd prefer to use the surface normal to calculate it as that's readily available, but I'll give that a go and see if it works

[floral arrow]

I don't see why you'd need the distance

You have your camera position C, your point on the surface P, and the surface normal at that point, N

Make the vector PC and compute the dot product between it and N

Then use that: https://en.wikipedia.org/wiki/Dot_product#Geometric_definition

[marsh vigil]

I saw the dot product online but I couldn't figure out how it worked/how to use it

[floral arrow]

The angle you drew here would be 90º - arccos(PC dot N / (|PC| |N|))

[marsh vigil]

I theory you could take the camera's coordinates, checking point coordinates, and a reference point on the surface's coordinates, then calculate the distance between the 3 of them and their angles.

[floral arrow]

I kinda mispoke, you do need the distance since you need |PC|, but don't go making a triangle just to use basic trig, use the dot product instead

[marsh vigil]

So:
arccos( dot( (P * C), N) / (abs(P * C) * abs(N) ) )?

[floral arrow]

No, P and C are points, the vector PC is C-P

[marsh vigil]

Cool, I can do that fairly quickly I think. One moment

[marsh vigil]

Would this output the degrees of the angle?

[floral arrow]

If your arccos outputs degrees, yes

[marsh vigil]

I'm gotten something working, though for some reason the output is 0 in places where it shouldn't be. To double check the formaula is:

PC = (xyz of camera) - (xyz of point)
arccos( dot(PC, N) / (abs(PC) * abs(N)) )

[floral arrow]

Yes

abs being the length of the vector

[marsh vigil]

Just to double check, the output of this would be a vector 3, right?

[floral arrow]

of what?

[marsh vigil]

This

The normal would be a vector3

[floral arrow]

A "normal" is a normal vector, yes

"normal" just means orthogonal to the surface

[marsh vigil]

So what would the individual xyz outputs be? I've gotten it working (mostly, my code seems to be a mess as usual). Would they be the angles on the x, y, and z axis?

Sorry, I'm kinda awful with all of this stuff, I'll be doing some reading in the coming days

[floral arrow]

Not sure what you mean

[floral arrow]

This is an angle

I don't know what individual xyz outputs you want

An angle in 3D space is the same as an angle in the 2D plane

It's a number in degrees or radians

You can get the corresponding angles in the xy, yz, xz planes but that would be projections, I don't think that's what you want

[marsh vigil]

Sorry, to clarify I'm not trying to get a specific xyz output. I'm just wondering what the xyz outputs of this are

[floral arrow]

Again, not sure what you mean, this gives you an angle, not xyz coordinates

[marsh vigil]

Ok that explains it. I'm getting a vector output Are all of the inputs here numbers?

[floral arrow]

You seem truly confused about the types of objects you're handling

PC and N are vectors

PC dot N is a number

[marsh vigil]

I thought that, but dividing the dot product of PC and N by a vector gives a vector, at least in what I'm using

[floral arrow]

|PC| and |N| are lengths

[floral arrow]

.

Not sure how you divide by a vector tbh

[marsh vigil]

I see. I know the issue. I meant a 3d point in space. I think I'm gonna try to figure out how to actually get the lengths of the Normal which would, in theory, solve the problem

[marsh vigil]

The thing doesn't technically do that, it just takes the input number and makes it a vector then divides vectors 1 and 2

Thanks for the help! I'll probably just need a reference point which shouldn't be too hard to calculate (hopefully). Sorry for all the trouble!

[floral arrow]

Doesn't seem very useful but fair enough

[marsh vigil]

Well if you wanted to get the inverse of a vector you would do 1 / vector

Or if you wanted to decrease the rate of change you could do vector / 2

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[sturdy island]

problem number 13

[long arrow]

well

you already have your slope m = -1/2

right

[atomic tendon]

I saw u asking about this exact question yesterday

[cedar kiln]

@sturdy island Has your question been resolved?

[sturdy island]

ya

i did not get it

[sturdy island]

<@&286206848099549185>

Can you tell me that we have to take both reciprocal intercepts

[long arrow]

nope

It refers to reciprocals of a new line

[sturdy island]

Can you tell me how to solve

[long arrow]

yes

[sturdy island]

cuz i am solving using this

x/1/a + y/1/b = 1

[long arrow]

yeah good

now you know that reciprocals are (a,b) (of x, y respectively)

[sturdy island]

yup

[long arrow]

and the questions says a new line has reciprocal intercepts on both axes

[long arrow]

ah, nope, that's false

x/a + y/b = 1 (general form)

[sturdy island]

ya

[long arrow]

and now it means that e.g. xb + y/b = 1

since they're their own reciprocals

a = 1/b

[sturdy island]

nope do not understand this point

[long arrow]

or b = 1/a but it's same

[sturdy island]

ohh

ok

a = 1/b or b = 1/a

[long arrow]

yeah

plugging it into our equations it gives

xb + y/b = 1

now we use slope m = -1/2

xb + y/b = 1 ---> y = -b^2x + b

hence, -b^2 = -1/2

[wraith dagger]

Modus

[long arrow]

now:

y = -1/2x +/- sqrt(2)/2

2y = -x +/- sqrt(2)

x + 2y +/- sqrt(2) = 0

Therefore b) is an answer.

[sturdy island]

how you do this

[long arrow]

I've already removed the irrationality

[sturdy island]

B is correct option

How is b2 = 1/2

[long arrow]

slope is what stands next to x

y = -b^2 * x + b

hence here -b^2 is a slope

and from the question we know slope of a new line is m = -1/2

hence -b^2 = m = -1/2

[sturdy island]

ok

[long arrow]

multiply both sides by (-1) to get

b^2 = 1/2

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[knotty yoke]

Where should i start with

.close

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[sinful lichen]

Hello could anyone help me rearrange this eqaution to =t?

[dull oxide]

you need quadratic formula

[sinful lichen]

Yeah so true thankyou

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[surreal juniper]

So, this is actually a physics problem, but since physics has a lot of math, I thought it would be appropriate. I know that this question is about torque, but I just don't know how to start or what to do.

[surreal juniper]

.close

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[hexed dirge]

I need a hint to address this problem

[cedar kiln]

@hexed dirge Has your question been resolved?

[flint plinth]

is there a transpose missing somewhere on the LHS?

[hexed dirge]

No [a,b,c] means (a \dot ( b x c)), and RHS is a determinant

[flint plinth]

oh, i misinterpreted what [a,b,c] means

[hexed dirge]

$[a,b,c] = a \cdot (b \times c)$

[wraith dagger]

dtaa0673

[dense hornet]

have you proved that the triple product of $\mathbf{a}, \mathbf{b}, \mathbf{c}$ is equivalent to det$(\begin{bmatrix}\mathbf{a}&\mathbf{b}&\mathbf{c}\end{bmatrix})$?

[wraith dagger]

waler

[hexed dirge]

thank u, I got the point

.close

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[novel ginkgo]

0.489 x 0.592 x 0.798 x 0.875 x 0.23 is there a shortcut to answer/approximate the anser for trhis?

[astral bay]

well you can replace some of the numbers with numbers that are fairly close and you'll get an answer that's fairly close

for instance 0.798 is pretty close to 0.8, and 0.8 is a lot easier to compute with

[novel ginkgo]

owow right right thank u !!!

[runic garnet]

,calc .5*.6*.8*.9*.2

[wraith dagger]

Result:

0.0432

[runic garnet]

,calc 0.489 * 0.592 * 0.798 * 0.875 * 0.23

[wraith dagger]

Result:

0.04649104908

[runic garnet]

Ah ha

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[scenic vale]

why does n- fm <= Fm-1 imply none of fi1, ..., fin can be fm

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[hollow loom]

Can anyone explain where the (x-3) came from at the bottom there?

[livid hound]

point slope formula

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[spring coyote]

84000$ is amount after tax, tax was 25%, is it correct to then do 84000 * (1+0.25) = 105000? I feel like its not good

[spring coyote]

so 105000 is amount before tax

[mortal hemlock]

if x is the amount before tax, then subtracting 25% of x from x you should get 84000

x(1-0.25)=84000

[spring coyote]

yes this fail so thats why i sad

[mortal hemlock]

this is different than from what you wrote

[spring coyote]

x-x*0.25=84000

i solve for this very nice?

[mortal hemlock]

this is correct

[spring coyote]

very nice!

🧃🏞️

[mortal hemlock]

so what do you get as answer?

[spring coyote]

112000

[mortal hemlock]

indeed

[spring coyote]

very nice!

🍔🫚

[mortal hemlock]

https://tenor.com/view/sachabaroncohen-borat-greatsuccess-gif-3983519

[spring coyote]

https://tenor.com/view/sathya-sai-baba-gif-8766847

[astral bay]

the issue here is that "decreasing by 25%" and "increasing by 25%" aren't inverse operations, even though it does kind of sound like they should be

simpler example: if you take 2, decrease it by 50% (now you have 1), then increase it by 50%, you get 1.5, which clearly isn't 2

[spring coyote]

ye

you are financially literate

so how much money are you making ? 😄

do you profit from all this mafs bruv

mans

I got bussines finance test

in a FEW HOURS

[mortal hemlock]

two thousandths of a million

[spring coyote]

😮

crazy finance

[mortal hemlock]

frfr

(you should calculate how much that is)

[spring coyote]

hmmm

[astral bay]

ok wait what unit is that in

[spring coyote]

1/2000 * 1milly

?

2/2000 * 1 milly?

2/1000 * 1 milly

finala naswer

[mortal hemlock]

2/1000*1000000

[spring coyote]

Im smart im best

great sucess

im college

[mortal hemlock]

https://tenor.com/view/borat-borat-very-nice-verynice-thumbs-up-gif-25080066

[spring coyote]

college learn from me

but yo

i gotta go

learn bussines finance

cos the test is like

[mortal hemlock]

goodluck with your exam bro

[spring coyote]

top 5 hardest thigs

i my college

they make test so that you fail

but all other things are easy

ad u ca cheat easily

but this 1 is like

they make theoretical part

circle a b c or d

exactly to fool the feeble minded

but as i know 2 thousands of 1 milljo ic ant fail

[mortal hemlock]

if youre done use .close to close the channel

[spring coyote]

.close

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[tribal kite]

Problem 2

I got all integers excluding p^n where p is a prime, and n is any integer greater than 0

Can someone check if I'm right

[mortal hemlock]

what about 3^1?

or 7^0

[tribal kite]

sorry I meant is NOT P^n

my bad

[mortal hemlock]

ah okay

[tribal kite]

since all composite numbers with m*n will

then there's p^n and composite^n

[tribal kite]

composite should still work

[mortal hemlock]

but composite can be a multiple of a prime

so 4^1 would work

but 2^2 wouldnt?

[tribal kite]

that wouldn't

since p^n

[mortal hemlock]

so you want a composite with different factors?

[tribal kite]

I'm excluding all p^n even if it can be put in composite form

[mortal hemlock]

m and n are different

[tribal kite]

or m^n where m is composite also works

so just p^n will not

like 4^2 is still excluded

[tribal kite]

^but that's just because it can be put in m*n form maybe

Since like 6³ can be put into 12*18

[azure swift]

,w Wilsons theorem

[wraith dagger]

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Requested by .4slan

[azure swift]

Might help

If you’re allowed

[silver oar]

2^3?

[azure swift]

Also if not

I think you might make use of induction

[silver oar]

Factorize m

If m is a product of at least two different primes to any power

All of them individually will be smaller than m and therefore will appear in (m-1)!

If m is of the form p^n with n>2

Then p^1 and p^(n-1) will appear in (m-1)!

However, it's easy to prove that if m is of the form p^n with n=1 or 2, then m does not divide (m-1)!

[tribal kite]

wait that's true

[tribal kite]

it's an olympiad problem, anything is fair game lol

(just that searching up probably isn't)

[tribal kite]

also yeah that kinda solves everything, thanks lol

.solved

[cedar kiln]

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[brisk nova]

heeeeeeelppppp

[mortal hemlock]

try making a drawing

[wicked mantle]

What have you tried?

[brisk nova]

yeH

[wicked mantle]

!show

[cedar kiln]

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

[brisk nova]

kk

its not much

[wicked mantle]

Better than nothing

[brisk nova]

ts only a diagram

[wicked mantle]

It’s ok

[mortal hemlock]

,rotate

[brisk nova]

i thought getting equations and equating

but i canly think of 1

wwhich is area of ABC

hellooooo?

anyone there?

wait if u construct BE pependicular to AC

sin 2c=BE/x

cosc=BE/5

its there any relation btwn sin 2c and sin c

[muted timber]

yes

[brisk nova]

sin2c=sinccosc right

[muted timber]

no

sin2c=2sinccosc

[brisk nova]

thn?

[muted timber]

you can use the law of sines

[brisk nova]

wait i made mistake

its sinc and sin 2c

[muted timber]

you know that angle in B is 180°-3c

[brisk nova]

yes

[muted timber]

and you know that sinB/5=sinC/x=sinA/(x+2)

[brisk nova]

yeah

[muted timber]

so go compute stuff

[brisk nova]

ohh

thx

[cedar kiln]

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[wicked mantle]

Did you actually solve it?🤔

[mortal hemlock]

!original

[cedar kiln]

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.

[brisk nova]

yet to compute

[wicked mantle]

Alr, have you done computing?

[brisk nova]

but why occupy if im practically there

no

[wicked mantle]

I don’t think computing would work tho

[brisk nova]

why?

[wicked mantle]

How are you going to tackle sin,cos,x simultaneously?

Have you thought about it?

[brisk nova]

using sin(2x)?

[wicked mantle]

no

[brisk nova]

.reopen

[lyric narwhal]

what's the question?

[wicked mantle]

@lyric narwhal

[brisk nova]

.

uhmm

[lyric narwhal]

ah okay

[wicked mantle]

I doubt the solution

[lyric narwhal]

could use cosine rule here

[brisk nova]

im not allowed to use trig

[lyric narwhal]

...?

[brisk nova]

sooo i kinda dithced

[lyric narwhal]

there's no way to solve it without trig