help-39

[pearl pond]

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[uncut coral]

Can someone quickly verify my answer

[cinder bane]

b + c vector is correct
But b-a vector is not

[uncut coral]

also for this q. why is it not DB?

[uncut coral]

would it be flipped for b - a ?

[cinder bane]

Yeah B - a
Gives you the vector that comes from the tip of a to the tip of b

So that if you added it to a you get B

[uncut coral]

ah that makes much more sense

thank you that explains my other question too then

[cinder bane]

Ok
Any other thing?

[uncut coral]

No thats it

thank you :)

[cinder bane]

You are welcome

[uncut coral]

.close

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[cobalt lichen]

r u allowed to do that ?

[cobalt lichen]

if yes why if not also why ?

[next dove]

you can provided that x and x^4-5 both are greater than or equal to 0

if not then you can't separate even roots

[cobalt lichen]

okay

thanks

.close

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[pearl pond]

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[sterile pecan]

how to check if it's monotone?

[pearl pond]

Please don't occupy multiple help channels.

[pearl pond]

@sterile pecan Has your question been resolved?

[pearl pond]

@sterile pecan Has your question been resolved?

[round patio]

!1c

[pearl pond]

Please stick to your channel.

[round patio]

@sterile pecan please close this channel

[sterile pecan]

.close

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[rocky plank]

I'm not sure how to do the second one. Moreover how to go about it and try to visualize the answer. This question is part of a math olyimiad book.

[restive moss]

bruh

whats ur question

[rocky plank]

the second one

root within root one

[pearl pond]

@rocky plank Has your question been resolved?

[restive moss]

no

[rocky plank]

<@&286206848099549185>

[sleek gazelle]

Where is the question

[rocky plank]

@sleek gazelle

the second one

[sleek gazelle]

Ok

Let me try

[oak quiver]

Multiply √5+2 by 2

Do you see anything?

[rocky plank]

no

2√5 + 2

[oak quiver]

Whole square?

[oak quiver]

[rocky plank]

yea i grt the rationalizing factor

[oak quiver]

2√5 + 4

4 not 2

...

[rocky plank]

ok

yea

[oak quiver]

?

[rocky plank]

yea 5+4

= 9

[oak quiver]

Wait first rationalize it

Then send the fraction again

[midnight haven]

yeah

,rotate

[oak quiver]

https://media.discordapp.net/attachments/908078029778083872/1292149285118541836/rn_image_picker_lib_temp_49ad5426-4463-4876-b2f7-3651bb6a092a.jpg?ex=6702af4c&is=67015dcc&hm=b62ebde962fa481d2be43feb0466a3519d15e425405482c859b3bf00ba8cdebb&

[midnight haven]

.rotate

thanks

[oak quiver]

,rotate

[rocky plank]

something like this?

[oak quiver]

SOF?

[rocky plank]

yea imo

[midnight haven]

@rocky plank is this question from imo workbook

[rocky plank]

yes

[oak quiver]

Lol

Class?

[midnight haven]

are u an indian

9th

[rocky plank]

there is no working given behind

[faint cedar]

A

[oak quiver]

You forgot the roots

[rocky plank]

yes

[midnight haven]

me too

[rocky plank]

for what

[oak quiver]

Underoot

[oak quiver]

I am

[midnight haven]

do you understand hindi

[oak quiver]

Hn bhai bilkul

[rocky plank]

root into root cancles out right

[midnight haven]

i have a video for you

[oak quiver]

Nhi

[oak quiver]

No

[rocky plank]

then?

[oak quiver]

[oak quiver]

Dm

[oak quiver]

Lemme do it and send

[rocky plank]

k

[oak quiver]

Understand?

@rocky plank

[rocky plank]

yea

but where did the 2 come from

[oak quiver]

Root 4

[rocky plank]

oh

yea

[oak quiver]

What class are you from?

[rocky plank]

9th

[oak quiver]

Dam

@midnight haven this guy is in 9th

[rocky plank]

so basically when you do √ into √ then inside terms get squared and the outside root still stays

[oak quiver]

Hmm

Can you write and send

[rocky plank]

ok

[midnight haven]

https://tenor.com/view/stepping-step-stomp-stomping-big-dogs-gif-18191398505017438766

[midnight haven]

did u see the video

it is good

[rocky plank]

no

im eating rn

[rocky plank]

@oak quiver

something like this

[oak quiver]

Oh no

That's (a-b)(a+b) = a²-b²

[rocky plank]

oh im a dumbo

√-1

= i or 1

[midnight haven]

do you want the expalnation

[rocky plank]

idk

[rocky plank]

sure

[compact ridge]

your first line is on the right track

after multiplying everything, including using the difference of two squares on the bottom

you should get $\frac{\sqrt{3+\sqrt{5}}+\sqrt{7-3\sqrt{5}}}{\sqrt{4}}$

[jolly parrot]

higher's secret twin brother

[compact ridge]

then you should learn the techinque for denesting square roots

suppose $6 + 2 \sqrt{5} = (a + b \sqrt{5})^2 = a^2 + 2ab \sqrt{5} + 5b^2$

comparing surd and integer parts, $a^2 + 5b^2 = 6$ and $2ab = 2$

so you get a quadratic equation

[jolly parrot]

higher's secret twin brother

[compact ridge]

or you can just guess what a, b are

we use 6 + 2 sqrt(5) here cause the coefficient of sqrt(5) needs to be even

so your final answer will be something divided by sqrt(2)

can you continue? finish this one and the two other nested square roots

you need to multiply all the insides of the square roots by 2 as well

before you start

[oak quiver]

I think this is a lot for him

Way too complicated for his grade

[pearl pond]

@rocky plank Has your question been resolved?

[compact ridge]

it's doable if you break it into smaller steps

they're halfway there

they just need to learn this very useful and common technique

and practice it 3 times

https://www.desmos.com/calculator/sl2ugbo5tu

also working is here

[pearl pond]

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[oak quiver]

Do you any factors of this?

[compact ridge]

what factors did you try?

one should stick out to you if you know your divisibility rules

[midnight haven]

3 is a factor of 13533

[compact ridge]

do you know how to test for divisibility by 3?

[midnight haven]

1+3+5+3+3 = 9

9 is divisible by 3

[oak quiver]

Bro don't tell the answer

[midnight haven]

ok

[compact ridge]

also that's not 9

[midnight haven]

sorry

[oak quiver]

English or maths?

[midnight haven]

15

[oak quiver]

Tell me the divisibility rule of 2

[midnight haven]

and even numbers

[oak quiver]

Yes but incomplete

[oak quiver]

Bro

[midnight haven]

oh

sorry'

[oak quiver]

.

Ok so is that number divisible by 2?

Now 3

Ok so what will be the new number

That is?

?

Yes

We don't need decimal in this

Now check for 3 again

[autumn fossil]

he is right

[oak quiver]

Yes mb

[autumn fossil]

you will have to try higher primes here

[oak quiver]

Yeah

[autumn fossil]

like 7, 11, 13, 17..

[oak quiver]

Now should we check for 4?

No, should we?

This is 4511.00

Not 451100

lol

Should we check for 4?

[autumn fossil]

What's your native language btw?

[oak quiver]

French?

lol

[autumn fossil]

english ig then

[oak quiver]

Kk

We didn't have to check for 4 cause 2 isn't divisible so 4 can't be

I have heard of it

Now what is rule for 5?

[kind trail]

﷽

𝓯𝓻𝓮𝓪𝓴𝔂

[oak quiver]

Yes but incomplete

And 0

Is 4511 divisible by 5?

Now should we check for 6?

Yess

Rule for 7?

[autumn fossil]

just divide it by 7 then

[oak quiver]

Yeah

[autumn fossil]

and see if you get a remainder or not

yeah

indeed

[oak quiver]

Yes

What class are you in?

Wait a few more years

Yeah

Now let's check for next number

8?

[midnight haven]

Is the question still the factor tree

[oak quiver]

Yes

[midnight haven]

oh

[oak quiver]

Wait do you know about prime numbers?

Yes

So while finding factors you should only check for prime numbers

Doing it for composites is redundant

Now skip 8, 9, 10

And directly check 11

Cos they aren't prime

[compact ridge]

,w 13533 factorise

[jolly parrot]

Results provided by WolframAlpha

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

Requested by sooouth.

[compact ridge]

I was helping with some senior secondary stuff

oh woah 13 is there

well 533 is a multiple of 13, 520 + 13

and I didn't type the number wrong, I checked and it's 13533

I mean yeah this is a sus question, cause how do you know that 347 is prime

there is a trick cause you only need to check prime factors up to sqrt(347)

note that 19^2 = 361

so you have to check 17, pain

but ye

bye

.close

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[hearty gust]

can someone tell me what this notation means?

in my multivariable class we only got introduced to
$$\nabla f = (f_x, f_y, f_z)$$ (and to it in n dimenions aswell)

but i have no clue what $\nabla_n$, $\nabla_x$, and $\partial_n$

[jolly parrot]

rhurhuzz ☆

[hearty gust]

uhmmm

for context

[jolly parrot]

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

[plush bramble]

nabla_x is just the gradient in the spatial coordinates (not time)

If there is no time dependence then nabla_x is the same as nabla

[hearty gust]

so like

in this case is $\nabla_x u(x,t) = u_x$

[jolly parrot]

rhurhuzz ☆

[hearty gust]

?

[plush bramble]

When x is one dimensional, the gradient is the same as the derivative

Double check with your book's index for notation

[hearty gust]

what about in 2d for example

[plush bramble]

Every math book at this level should have one

[hearty gust]

its just lecture notes unfortuantly

its not really defined elsewhere... :(

afaik

[plush bramble]

https://en.m.wikipedia.org/wiki/Neumann_boundary_condition

Read the pde section

Same thing I said

[hearty gust]

ty!

[pearl pond]

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[tacit abyss]

you have to prove this

[tacit abyss]

i cant find my mistake

en means and

of means or

[pearl pond]

@tacit abyss Has your question been resolved?

[tacit abyss]

<@&286206848099549185> 🙏

[dry atlas]

?

[tacit abyss]

ok that makes so much sense ty!

.close

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[rare holly]

is it not 8.91x10 power 9?

[signal atlas]

Nah. Addition of two numbers should be around the same order of magnitude as the number with the largest magnitude.

Try writing one of the numbers to have the same exponent as the other number

[rare holly]

wdm

[signal atlas]

If I do 100000 (10 power 5) + 10000 (10 power 4) I get 110000 (around 10 power 5), not 1000000000

[rare holly]

so we do 6.31+2.6?

which is

8.91

then the powers dont we just multiply it?

[signal atlas]

Almost but not quite

[rare holly]

we times it?

idk bru

[signal atlas]

Can you write out the original numbers in normal form

[rare holly]

631000+26000

[signal atlas]

Alright now write out 8.91 x 10^9 (^9 meas power 9)

[rare holly]

wait why?

[signal atlas]

This is the original answer u got.

I want you to see that it will not match up and maybe get an idea why we dont multiply the powers

[rare holly]

it dosent match

then wht should have we actually done?

[signal atlas]

Yes it is like 10000 times bigger than you would expect. This is because you shouldnt multiply the powers

When we add to numbers in scientific notation we need both numbers to have the same power. Then we just add the numbers infront

For example $3 \cdot 10^5 + 5 \cdot 10^5 = 8 \cdot 10^5$

[jolly parrot]

Nekoyashiki Yuki

[rare holly]

noo

i was trynna uderstand it

[signal atlas]

I just made 1 edit

Sorry

[rare holly]

kk is fine

ooooo i see

6.31+0.26?

[signal atlas]

Yes nice

[rare holly]

6.57x10 power of 5?

[signal atlas]

Yup

[rare holly]

WWWW

les goo

why this wrong

[signal atlas]

Seems right. Maybe you need a non zero number before the decimal

[rare holly]

but isnt half 0.5?

[signal atlas]

Yes but this may not be in standard form yet (I do not know how it is defined for you). Like standard form would not have 0.xxxx * 10^6 it would be x.xxx * 10^5.

[rare holly]

bru

i see

the ans should be correct tho

[signal atlas]

Yes the answer u gave is equivalent numerically

Try 5 x 10^5

[rare holly]

it was this

i put in my calc

[signal atlas]

Yeah

[rare holly]

why is it tht

when i do non calc

appeard 0.5

ooo

ik

bc we need a hole number

[signal atlas]

Kinda

The front number needs to be between 1 and 10

[rare holly]

yh kk got it ty

[pearl pond]

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[pearl pond]

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[stiff mauve]

could someone explain me how the nullspace would be a subset of R^n, and how columnspice would be a subset of R^m

[stiff mauve]

linear algebra

[sharp vigil]

for an $m \times n$ matrix the null space is the set of vectors which result in \vb 0 when multiplied by the matrix. the vectors must be in \R[n] to perform the multiplication. the column space is the span of the column vectors of the matrix, and the column vectors are in \R[m].

[jolly parrot]

cloud

[stiff mauve]

ohh, so is the nullspace in the equation Ax = b, any x for which Ax = 0?

[sharp vigil]

yes

[stiff mauve]

thank you so much

.close

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[runic holly]

can anybody help ?

[boreal ember]

where is x?

[vocal lark]

it's on the smaller triangle

use LoS

[boreal ember]

ahh i see

[vocal lark]

@runic holly

[boreal ember]

you need sin, cos or tan

[vocal lark]

LoS = "Law of Sines"

oh

wait

you can just use similar triangles, lol

x/113 = 21/84

simpler

[boreal ember]

yeah

[runic holly]

I got it nevermind guys

[pearl pond]

@runic holly Has your question been resolved?

[pearl pond]

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[gritty cave]

linear transformations should fulfill two criteria

aT(x) = T(ax) and T(x) + T(y) = T(x + y)

given that x,y are vectors of the vector space

the best way to check is take two arbitrary vectors, x and y, and put them into the transformation

[frank goblet]

you would wanna check this

to do so, you use arbitrary vectors as spruce leaf said

[gritty cave]

so to do A, take x = x1, x2, x3, and y = y1, y2, y3

T(x + y) = T(x1 + y1, x2 + y2, x3 + y3) = (x1 + y1, x2 + y2, -(x3 + y3)
T(x) + T(y) = T(x1, x2, x3) + T(y1, y2, y3) = (x1, x2, -x3) + (y1, y2, -y3) = (x1 + y1, x2 + y2, -(x3 + y3)

[frank goblet]

like this

which would give us this

(though spruce leaf's notation is clearer)

[gritty cave]

you do a similar check for scalar multiplication

so check if aT(x) = T(ax)

if both conditions are met, then it must be linear

if you wanna save time, you can check both conditions at the same time by doing T(ax + y) = aT(x) + T(y)

i can type it out in latex for you if what i wrote isnt clear

yeah it takes a bit to get used to all the notation stuff

if you want, you could even define \Vec{x} as (a, b, c)

just make sure its clear what youre defining the variables as

[frank goblet]

i personally think its easier to read when the vectors are vertical, like here:

[gritty cave]

yeah that does look cleaner

[frank goblet]

as for how to show two terms are equal, if it is hard to find out if they are equal, it can be a good tactic to set them equal and rearrange to get something obviously equal. when we only use equivalence rearrangments, this can be a proof. otherwise this can give useful ideas.

[slow nebula]

yeah im a bit confused on how i tell if they equal

[slow nebula]

idk if im doing this right

this is for B

[frank goblet]

,rotate

[frank goblet]

now write what T(v)+T(w) would look like

you would get two vectors. When you add them up, you would get a new vector

then you can compare this vector with the previous one

but yes, the 4 is the important part here

the 4 is added each time we apply T, therefore T(v)+T(w) will have a +8

yes, thus it is not linear

exactly

i would also highly recommend watching 3blue1brown's series on linear algebra. In my experience, intuition wasn't really teached in algebra. He however gives a lot of visual intuition which can be really helpful.

https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

👍

[pearl pond]

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[summer imp]

Your sign is wrong in the first component

It should be 8+6

[pearl pond]

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[forest sun]

hi, trying to figure out if these are false. Stuck on on what to do. I am highly certain that both are false as antiderivative of -sinx would be cos x and ln|sinx| of cot

[forest sun]

but i am not sure if that's what i should have done

[feral sedge]

Yes they are both wrong

[forest sun]

.solved

[pearl pond]

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[feral sedge]

Your explanation for why the first one is wrong doesn't make sense

[forest sun]

the first one?

the -sinx?

[feral sedge]

Yes

[forest sun]

this part?

like the whole all of it

[feral sedge]

Like, saying that this is wrong because the antiderivative of -sin is cos

Isn't that what they used

[forest sun]

hm true

wait

then do i just have to solve the int?

to prove that its wrong

[feral sedge]

More or less ig

[forest sun]

also do you perphs know why they would write this here

like does it help anything

[feral sedge]

I have an idea but it's a dumb thing to write

[forest sun]

.reopen

[pearl pond]

✅

[feral sedge]

part of the "mistake" that person made with this problem

[hollow owl]

u can say he substituted the limits without integrating

[feral sedge]

He didn't though

[hollow owl]

no what the person did

sin0 = 0?

[feral sedge]

I have a feeling you're about to spoil the problem

Ah well

[hollow owl]

ok ill mind my business

[feral sedge]

The problem is the uselessness of -sin(0) = 0 is much more obvious then the actual mistake in the problem so it's just confusing to write

[forest sun]

i mean i don't need to solve the problem so i'll just leave it alone

.solved

[pearl pond]

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[lost stirrup]

If all the ice on the planet (38,000,000 km3) melted, almost all the water would end up in the ocean. The ocean has a total area of ​​360,000,000 km2. If this surface remained constant and the water from the melted ice was distributed uniformly over the entire length of the ocean, the height that the water level would reach would be 1.06 x 10-1 km. Do you agree with this answer? Develop a procedure to justify your answer

[lost stirrup]

the -1 that accompanies 10 is a 10 raised to the -1

the same with km3, km2

[oak quiver]

V = A*h

Can you tell me in this case what V, A, h would be?

[lost stirrup]

i dont know

what is v, a and h

[oak quiver]

Try guessing

[lost stirrup]

height

volume

area

ig

[oak quiver]

You can even compare the units from the data given in the question

I mean according to the data

[lost stirrup]

im spanish thats why i dont understand somethings that can be easy for u

but the things that i said are right?

[oak quiver]

Yes

I was asking the value like V=?

Not the full form

[lost stirrup]

area would be 360,000,000
volume 38,000,000
height 1.06 x 10-¹

[oak quiver]

Yes

[lost stirrup]

aight

so

[oak quiver]

Use this formula to cross check

And you are done

[lost stirrup]

38,000,000 = area*h

?

oh

[oak quiver]

Yes

[lost stirrup]

ty

[oak quiver]

! Done

[pearl pond]

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

[lost stirrup]

.close

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[polar steppe]

Am I being silly? In this experiment, does order matter or not?

[uneven smelt]

as a sanity check probability is always between 0 and 1

[polar steppe]

yes

but the issue here is picking combinations v perumations. I argue that the order doesn't matter

Because Y is just the number of empty bowls. The first could be empty or the second could be empty.

[gleaming musk]

order shouldn't matter since it just says number of empty bowls

[polar steppe]

okay

I must have done the combinations wrong then

for the denominator, wouldn't it be $3^3$?

[jolly parrot]

Dylan Armbruster

[gleaming musk]

s

*si

[polar steppe]

I got,
$$
y(1) = \frac{\binom{3}{1} \times \binom{2}{2}}{27}
$$

[jolly parrot]

Dylan Armbruster

[polar steppe]

so, 1/27, 6/27 , 3/27, and 0

wait

I have that reversed I think

would 3 empty bowls be impossible

[gleaming musk]

yes

if we let Y denote the variable

we first need to find P(Y=0,1,2,3)

P(Y=3) = 0

P(Y=2) = 3c2/27

[polar steppe]

did you omit the 1c1

[gleaming musk]

sure

i mean its kinda redundant

if you have chosen 2 bowls to be empty, the nthe last bowl must contain all 3 balls anyway

[polar steppe]

yeah

jsut making sure

darn

so unless I missed something with the rest of the combinations, I still got the same asnwer

.44 rounded off

[gleaming musk]

show me your working out for expected value and variance

[polar steppe]

$$
E[Y] = \sum 0(1/27) + 1(6/27) + (2)(3/27) + 0
$$

[jolly parrot]

Dylan Armbruster

[gleaming musk]

why is it 6/27?

for P(Y=1)

we first pick one bowl to be empty

3c1

[polar steppe]

yes

then 2c2

[gleaming musk]

then we can arrange 3 balls into the remaining 2 bowls

[gleaming musk]

no not quite 2c2

[polar steppe]

there's two bowls left over though. So there's 2 left to be not empty

idk why i had 6

it should be 3/27

[gleaming musk]

just again as a sanity check, does your probability of events add up to 1

it should be a pretty telling sign if thats not the case

[gleaming musk]

how many ways can u arrange 3 objects into 2 groups usch that none of the groups are empty

[polar steppe]

3

oh wait

wait I just don't think I'm following

3c1

we selected 1 empty

now we're left with 2 bowls

from those 2, we can choose 2 to make non empty.

[polar steppe]

why are you doing 3 choose 2?

[gleaming musk]

im not

[gleaming musk]

different concepts

[gleaming musk]

sry i gotta go now tho but its not 3c2

ur probability for each event right now is incorrect

[polar steppe]

what?

for all of them

alrighty..

.close

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[river lodge]

can someone check my answer for 13.b)

[pearl pond]

@river lodge Has your question been resolved?

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[river lodge]

.reopen

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[river lodge]

anyone?

reason im asking is because my answer didnt match the back of the textbook but im not sure why

[light helm]

you'd need to determine whether these values of x make sense in the context of the problem
also for dimensions they want
length,width,height

[pearl pond]

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[midnight haven]

Please check my work

[river jolt]

how'd you get 15625 in numerator

[midnight haven]

I changed no 1 a little

[jolly parrot]

Sending query to Wolfram Alpha, please wait.

[midnight haven]

@river lodge You listed out 3 possible values for x, but those aren't the actual dimensions of the box.

You have to plug each one into the equations for length, width, and height to see which of those x-values "make sense". (there can't be negative dimensions).

The only ones that work in this case are x = 1.64 and x = 7.09.

[jolly parrot]

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An unexpected error occurred while processing your command!
The error has been reported and should be fixed soon.
If the error persists, please contact our friendly support team at our support guild!

Exception

PIL.UnidentifiedImageError: cannot identify image file <_io.BytesIO object at 0x7efe79446110>

[river jolt]

1st is right

but

in second

2^(-24) is not the same as 1/6^24 * 1/3^12

[midnight haven]

huh

oh

Wait ill change mb

I was so confused

[river jolt]

np

[river jolt]

,w 1/2^24 * 1/3^12

[jolly parrot]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by moonguy257

[midnight haven]

yeah

[river jolt]

,w 1/2^12

[jolly parrot]

Results provided by WolframAlpha

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Requested by moonguy257

[river jolt]

yeah

its right

[midnight haven]

okay

can u check the other numbers?

[river jolt]

but you didnt subtract them?

you should do that as thats what the question asked for

[river jolt]

1/256 - 6 is not 255/256*6

[midnight haven]

huh?

[river jolt]

in the 3rd

Q

[midnight haven]

ohh

idk how to solve it

[river jolt]

take the LCM

[river jolt]

fourth is right

[midnight haven]

of which

[river jolt]

of the fractions 1/256 and 6/1

denominators

and combine them

[midnight haven]

idk 😭

[river jolt]

3/4 - 1/3

how'd you solve this

if you don't

then watch

[midnight haven]

thats 5/12

[river jolt]

https://youtu.be/GvLIEiqxS6s?feature=shared

[midnight haven]

i know that but

[river jolt]

yea and how'd you do that

[midnight haven]

idk how to get the lcm lol

wait ill show sol

[river jolt]

forget that part for now

[midnight haven]

oh

12

[river jolt]

you can tell me

[midnight haven]

is the lcm

[river jolt]

yea

[midnight haven]

ahh oky

what do i do after

[river jolt]

wdym after?

[river jolt]

you did this

its over

?

[midnight haven]

so the answer is 2?

12*

[river jolt]

???

[midnight haven]

5/12

i meant

[river jolt]

yea

[midnight haven]

ahh ok thx

[river jolt]

for 3/4 - 1/3

now similar to this

[river jolt]

try that

3 rd

[midnight haven]

so 1/256 -1/1

[river jolt]

its 6

not 1/1

[midnight haven]

-5 255/256

[river jolt]

,w 6*256

[jolly parrot]

Results provided by WolframAlpha

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

Requested by moonguy257

[river jolt]

no?

[midnight haven]

-1535/256?

[river jolt]

I think u shld watch this

[river jolt]

yea

[midnight haven]

i turned it into whole no

xd

[river jolt]

,w 1/256 - 6

[jolly parrot]

Sending query to Wolfram Alpha, please wait.

[river jolt]

_5 255/256 is not a whole number?

[midnight haven]

wait i mean proper

fraction

[river jolt]

ohh

[jolly parrot]

Something went wrong!

An unexpected error occurred while processing your command!
The error has been reported and should be fixed soon.
If the error persists, please contact our friendly support team at our support guild!

Exception

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[river jolt]

yea you need to clarify that you made it into proper

I thought it was -5 * 255/256

thats why

[midnight haven]

ohh okay

thanks

bye bye

.close

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[fluid socket]

Why is 6÷sin60 =4sqrt3?

[versed mica]

sin(60) = sqrt(3)/2

[fluid socket]

Yeah shouldn't this make it 12/sqrt3

[versed mica]

$\frac{12}{\sqrt{3}} = \frac{12}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

[jolly parrot]

knief

[versed mica]

the sqrt(3) * sqrt(3) becomes 3

then 12/3 = 4

[fluid socket]

Oh okay thanks

.close

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[sterile turtle]

This is for part a

I feel like theres another way of doing it, but if not then thats fine

Why do i have a double root at k=-2 and what does it mean?

If i were to have a double root, I thought it would be at k=1

[pearl pond]

@sterile turtle Has your question been resolved?

[sterile turtle]

<@&286206848099549185>

[late flame]

yes?

[sterile turtle]

This is the bigger question I want answered

[sterile turtle]

.close

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[real shard]

Can someone let me know if I’m going wrong somewhere. I only did the forward part but I feel like this isn’t correct.

[limber glacier]

if w is in the span of v1, .., vm, then there are constants a1, ..., am such that a1v1 + ... amvm = w

also, if u1, ..., un is linearly independent, then the only way of having a1u1 + ... + anun = 0 is by having a1 = ... an = 0

combine these results

kinda seems to be similar to what uve done but im not sure thats what u were thinking of

[real shard]

i see thank you very much. Do you think this proof would be better for the backwards pass? Also, in my contrapositive I said that v1,..,vm,w is lin dep does that not matter since it was stated in the beginning that those vectors are lin ind?

[pearl pond]

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[fluid socket]

What's the easiest way to multiply 320 by 1.25^3 without calculator?

[limber glacier]

320 = 4 * 8 * 10
1.25 = 5/4

Ig

[vestal tapir]

(5/4)³ = 125/64
320/64 = 5
so it's 5*125

[fluid socket]

That's a nice one

Thanks to you two

.close

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[vestal tapir]

honestly (add a quarter three times) is even better

[crisp oasis]

pls help #help-1

[pearl pond]

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[elfin cairn]

I've been stuck on this problem for hours, how do I get the area?

[acoustic path]

consider

the problem gives the rotated graph is tangent to x-axis, and the center of rotation is origin

yes?

[elfin cairn]

ahuh

[vital estuary]

try rotating the x axis to be tangent to the graph instead

[acoustic path]

so

crucial fact here is x-axis passes through origin

[acoustic path]

and yes go from here

[elfin cairn]

ohh okyy thank uuu

.close

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[lethal estuary]

how did we know the top angle is 50

[vital estuary]

because rhe diagram says so

whats the original problem?

[main pollen]

help

my calcualroe no work

0 divded by 1

[pearl pond]

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[cunning patio]

What way am I supposed to display my answer? i dont know what "system of first orders O.D.E's" are

[pearl pond]

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[tacit abyss]

$I = N \setminus {0, 1} \text{ and } A_n = \left{ x \in \mathbb{R} \ \middle| \ \left( \frac{1}{2} - \frac{1}{n} < x \leq 1 \right) \lor \left( \frac{3}{2} + \frac{1}{n} \leq x \leq 4 \right) \right} \text{for n} \in I. \text{What is} \bigcap_{n \in I} A_n \text{equal to?}$

[jolly parrot]

ana

[tacit abyss]

Is it [1/2,1] or [3/2,4]?

[cinder flower]

since 4 is in A_n for every n, it can't be [1/2, 1]

[tacit abyss]

how is 4 in every An?

sorry i have a hard time seeing this visually

[cinder flower]

x = 4 satisfies this no matter what n is

and A_n is the set of all x that satisfy either of these inequalities

[tacit abyss]

but what if x is < 1

then you're in the first inequality

so how do you make it satisfy for all x

[cinder flower]

do you agree 4 is in A_n for every n and this is a new question?

because that's not relevant to 4 being in A_n

[desert tendon]

Is it v or union?

[tacit abyss]

idk i dont see why 4 is in every An

[cinder flower]

it's supposed to mean or

[tacit abyss]

it stands for or

yea

[desert tendon]

thanks

[cinder flower]

fix n. a given x is in A_n if and only if x satisfies at least one of these inequalities

[cinder flower]

and 4 satisfies this one (for any n)

[cinder flower]

like, this is what the set builder notation means

this is how A_n is defined

3/2 + 1/n <= 4 <= 4 is true for any n. that's all

[tacit abyss]

okay yeah

[cinder flower]

we can also say things like, if 3/2 + 1/2 <= x <= 4, then x satisfies this inequality for all n

[desert tendon]

open intervals

[cinder flower]

no

[desert tendon]

explain plzz

[cinder flower]

finding a similar thing to say about this condition will lead you to the answer

[cinder flower]

wait did you mean "is it [1/2,1] union [3/2,4]" or were you asking if the answer was a) [1/2,1] or b) [1/2,1]

[tacit abyss]

the first one

[cinder flower]

oh

[cinder flower]

sorry i misunderstood and thought the second thing, that's why i brought this up. but that answer isn't right still

[desert tendon]

(1/2,1]U[2,4]

[tacit abyss]

what do i change then

[cinder flower]

!nosols

[pearl pond]

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.

[cinder flower]

especially wrong ones

but yes (1/2,1] U [2,4] is close to correct

[desert tendon]

[tacit abyss]

i dont see it

😭

[cinder flower]

so from here any x in [2,4] satisfies this inequality

so \cap A_n includes [2,4]

[tacit abyss]

yea

[1/2,1]U[2,4]

[cinder flower]

and then you want to say something similar for the other inequality

[cinder flower]

yep

[tacit abyss]

ah

[desert tendon]

sorry my bad

[tacit abyss]

this chapter breaks my brain

[cinder flower]

[tacit abyss]

okay i think i got it

tysm

[cinder flower]

[tacit abyss]

its just confusing w when the x is included its a little different

[desert tendon]

may you tell the answer

[cinder flower]

yea. it's a lot of symbols to digest

what ana said

[tacit abyss]

its this

[desert tendon]

In equation 1st n-> infinity for answer

[cinder flower]

[tacit abyss]

yea

but you had to close the interval

[desert tendon]

whyyyy

[cinder flower]

well just ask yourself if 1/2 satisfies this inequality for every n

the answer is yes

[desert tendon]

no

[cinder flower]

so 1/2 is included

wdym no

[desert tendon]

read the question first

[cinder flower]

1/2 - 1/2 < 1/2
1/2 - 1/3 < 1/2
1/2 - 1/4 < 1/2
1/2 - 1/5 < 1/2
...
all true statements

[desert tendon]

ok ok

[tacit abyss]

ok im closing

tysm layla 💓

[desert tendon]

It's like 1/2-0.00000000000000000000000000000000000000000000000000000000000001

I got it

tysm

[cinder flower]

[tacit abyss]

.close

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[copper matrix]

@agile ridge i believe you need to check derivatives in 2 dimensions

i.e. check that $\pdv{f}{x}$ and $\pdv{f}{y}$ both exist at the origin

[jolly parrot]

Ginger

[copper matrix]

ah wait sry

what you did works too, since you leave both x and y arbitrary

try a special case tho, try $y = 0$ fore example @agile ridge

[jolly parrot]

Ginger

[pearl pond]

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[wary owl]

determine all integers 𝑛 such that 𝑛−4 divides 3𝑛+24
im looking for an elegant solution

[wary owl]

ping me if u got the anser

[verbal whale]

n=4 case apart, I'd do it this way: $$\frac{3n+24}{n-4} = \frac{3n-12 + 36}{n-4} = \frac{3n-12}{n-4} + \frac{36}{n-4} = \frac{3(n-4)}{n-4} + \frac{36}{n-4} = 3 + \frac{36}{n-4}$$

[jolly parrot]

Alberto Z.

[verbal whale]

So now you have to find all possible factors of 36, and equate each of them to 𝑛-4

[wary owl]

thats the solution i found too

[verbal whale]

$n - 4 \in {\pm 1, \pm2, \pm3,\pm4,\pm6,\pm9,\pm12,\pm18,\pm36}$

[wary owl]

i was js wondering is there was a more elegant method

[wary owl]

it said all intigers

so take into account negative divisors too

[jolly parrot]

Alberto Z.

[verbal whale]

Do you think this is not elegant?

[wary owl]

probably is

how abt this

[gleaming musk]

i feel like this is about as elegant as it get

[wary owl]

Let 𝑎∈𝑁and 𝑛∈𝑁Show that if 𝑎divides both 𝑛+4and 2𝑛−3then 𝑎 is a divisor of 11.

uh oh

[plucky python]

u can't really do much better

[plucky python]

whenver you end up with a solution set like i.e. this, then you can't really improve upon it too much

ig you could alternatively present it as

n - 4 | 3n + 24 <=> n-4 | 3n+24 - 3(n-4) = 36

so n-4 is a factor of 36 and hence (write solution set here)

[wary owl]

alright

[verbal whale]

So n can be ${4\pm 1, 4\pm2, 4\pm3,4\pm4,4\pm6,4\pm9,4\pm12,4\pm18,4\pm36} = {3,5,2,6,1,7,0,8,-2,10,-5,13,-8,16,-14,22,-32,40}$

[jolly parrot]

Alberto Z.

[tardy reef]

you can do it the same way. a | n+4 means a | 2n+8. This means a | 2n-3 and a | 2n+8. So a | (2n+8)-(2n-3) or a | 11

[wary owl]

wow

[verbal whale]

{-32, -14, -8, -5, -2, 0, 1, 2, 3, 5, 6, 7, 8, 10, 13, 16, 22, 40} U {4} = {-32, -14, -8, -5, -2, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 13, 16, 22, 40}. This should be the complete set of solutions @wary owl

[wary owl]

for some reason tho when i tried asking chatgpt this question it got stuck and started trying different values for the solution. how it struggle with such an exercise but be able to solve much more complex ones

[tardy reef]

chatgpt is so easy to gaslight, it would change even the correct answer if it ever found it

Dont trust it for at least like 3 more years

[wary owl]

fr tho

ty to yall btw

uh

seperate question

are there any good math books for 1st year highschool

10th grade

[gleaming musk]

what curriculum are u studying from?

are u US education or somewhere

[wary owl]

french curriculum

i dont trust us 😭

[gleaming musk]

yeah im gonna be honest im in an australian highschool and the textbooks are not great either

the answers for the textbooks are wrong 50% of the time

[wary owl]

??

what

[gleaming musk]

everything is a lot more online now tbf, u could probably study mosto f the stuff ahead of time from online resources as long as u know like a roadmap of what u need to study

[wary owl]

hm

its not the source material

im more interested in the exercises

cause we both know u cant learn math without exercises

my thoughts are very scattered i have a diff question

i think ill ask in general dicussion

ty tho

[pearl pond]

@wary owl Has your question been resolved?

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[short orchid]

guys, why am i wrong for d?

[cursive wraith]

how did you get that

lemme check

[cursive wraith]

yeah whatever it is something's wrong in that value

what formula did you use?

[pearl pond]

@short orchid Has your question been resolved?

[short orchid]

area to find the segment

[cursive wraith]

yeah but what did you do to get those numbers

[short orchid]

i got 41.47 from the area of segment

and 8 from the triangle

:w

[cursive wraith]

how did you compute that

[short orchid]

like this

[cursive wraith]

and what is 4.1470

[quaint lantern]

The arc

No?

[short orchid]

OHHH WAIT

😭😭😭

[cursive wraith]

you wrote the formula yourself

guess which value is not correct

[short orchid]

its supposed to be 0.9273 😭

omg

[short orchid]

thank youuu so much

took me a long time to realize 😇

btw guys

we can make an equation from a graph when given 3 random points right?

by using y=ax^2 + bx + c

[cursive wraith]

depends on what you want to link them to

if you have 3 points with distinct x-coordinates, you can make a unique y = ax^2 + bx + c

three unaligned points will also give you a unique circle they all lie on

(x-a)^2 + (y-b)^2 = r^2

[short orchid]

ohh

[cursive wraith]

etc

[short orchid]

how do we make the 3 coordinates become part of y = ax^2+bx+c tho?

[cursive wraith]

well if you have three points, say (2,3), (3,4) and (4,7)

and you want a,b,c such that y = ax^2+bx+c goes through all of them

if you remember the exercise with the line previously

that a line given by equation y = ... means that a point (x,y) is on it IF and ONLY IF y = ...

[cursive wraith]

same logic goes for a curve defined by this equation

so we have 3 equations to solve for a,b,c:

(2,3) lies on the curve, meaning 3 = a(2)^2 + b(2) + c

(3,4) lies on the curve, meaning...

etc

[short orchid]

ohhhh

okayyy thank you so muchh

i have another question 😃

[cursive wraith]

ask away

[short orchid]

for c, why is the second method wrong?

holdon this is the question

[cursive wraith]

you're solving for 10x - x^2 <= 9

which you simplified to this

[cursive wraith]

except you got the signs wrong

when x > 9, what's the sign of x-9 and x-1?

[short orchid]

it’s greater than and equals to

[cursive wraith]

?

[short orchid]

wait i’m supposed to reply to this one 😭

[cursive wraith]

ok sure, when x>=9, what's the sign of x-9 and x-1?

[short orchid]

wait i don’t understand

[cursive wraith]

suppose x is greater or equal to 9

is x-9 greater than (or equal to) 0? smaller than 0?

same for x-1

[short orchid]

yes x-9 is greater than or equal to 0

[short orchid]

greater than or equal to 1

[cursive wraith]

uuuhh sure

but x-1 compared with 0

which is bigger

[short orchid]

x-1?

[cursive wraith]

ok

so x-1 >= 0 right?