help-10

[safe stirrup]

Je crois avoir compris mon truc ci-dessus. Je patente quelque chose et je poste une image.

Would this reasoning make sense for matrix of permutation?

[pseudo swift]

Ouais ça marche

Par contre la traduction est limite

Les matrices de permutation c'est un autre concept qui existe aussi

On dit plutot "change of basis matrix"

Changement de base quoi

[safe stirrup]

Je suis actuellement dans les matrices de passage ahah..

Les matrices de permutations me disent de quoi, mais je ne me souviens plus ahah.

[pseudo swift]

Enfin bon les matrices de permutation c'est un cas particulier de matrices de passage en vrai, donc c'est pas faux ce que tu dis, c'est juste trop spécifique

[safe stirrup]

Mais si vous me dites que mon raisonnement fait du sens, J'ai totalement compris les changement de base alors. ça sert à "comparer" deux vecteurs de bases différentes en convertissant l'un vers l'autre base.

[pseudo swift]

Oui exactement

[safe stirrup]

Ok good j'ai totalement compris.

Et ça a donne que la matrice de passage revient à faire un produit matriciel de deux matrices.

Ok good, c'est résolu, merci.

.close

[obtuse pebble]

Channel closed

Closed by @safe stirrup

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tall nebula]

How to find area of these shapes?

[safe stirrup]

You can view this as multiple triangles

Do you have the length of a side?

For example, you have 4m for the hexagon.

You could use some pythagore or sin/cos/tan to find the whole length oh the haxagon, then divide it in two to find the distance to the center... if you have learned about these.

[tall nebula]

Could you do the hexagon one I understand the other two

[safe stirrup]

Sure, hold on.

Sinc ethis is a perfect hexagon, the red triangle should be isocele, thus have 2 equal side.

Does that make sense?

[tall nebula]

Yea

But can you also do this

Make it 5 triangles

[safe stirrup]

The current issue is finding precisely this length to the center.

So my approach was to find the whole length from one side to the other. as such in blue

[tall nebula]

Isn't this also possible

[safe stirrup]

Then, once you have this whole blue line

You can cut it in two

and get the triangle.

[tall nebula]

This is quite complicated Isn't making 5 triangles easier

[safe stirrup]

Let's try your approach

What would be the distance of the orange line?

How would you find it?

[safe stirrup]

Keep that close please to undertand later.

[tall nebula]

That's my question that's what I'm confused about I would find the green and do sin of 30 but I can't find it for some reason

[safe stirrup]

Now that I think about it, it would be possible somewhat.

First we need to know what are the angles of the triangle.

[tall nebula]

120 degree yea

[safe stirrup]

360 / 8

Then divided by two, to get the angle between orange and green

And you would be able to use tan to get the orange line.

Wow I did not think of doing it this way 😄

The blue is 360 degrees

You have 8 triangles. Thus we divided in 8.

Then we divide in two because we want the angle of one of the two triangles we made.

[tall nebula]

So could you find it for me please and show calculations so I can understand

[safe stirrup]

Yes.

[tall nebula]

Thanks

[safe stirrup]

adjacent would be the height you would use to find the area of the triangle.

IE the orange line.

[tall nebula]

OK thanks

[safe stirrup]

Does that makes sense? It is an interesting problem.

[tall nebula]

But is this not possible with sin

[safe stirrup]

With sin, you would find the green line

As with sin, it would be opposite / hypothenuse

[tall nebula]

Ok is this the easiest way? Because I have a test soon

[safe stirrup]

It looks much easier than my approach earlier.

And would apply to any size of polygon basically

you could try with a square just to be sure.

Remember that once you get the area of the triangle, you will need to multiply it.

[tall nebula]

I have a question

Is this possible

Because it's isocleles

[tall nebula]

And the vertex is 45 each base would be 67.5 eliminating use for tan

@safe stirrup is it possible?

[safe stirrup]

Where does 67.5 comes from

[tall nebula]

Each base because the triangle is 180 and vertex is 45 so 180-45/2

[safe stirrup]

For the square or the octogon?

Ooh for the octogon. Yes you could do that

[tall nebula]

Octagon

[safe stirrup]

to use sin instead.

Good point.

As long as you respect the sum being 180, and the correct division (SOHCASTOA), you will be fine.

[tall nebula]

Ok thanks

Close.

.close

[obtuse pebble]

Channel closed

Closed by @tall nebula

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[errant crane]

so far im at $$ \frac{2\sin t}{1-4\cos t} $$ but idk what to sub in for t

[warm shale]

morphine_addiction

[obtuse pebble]

@errant crane Has your question been resolved?

[sour mulch]

well you know what the y-coordinate is

(and the x but it will be easier using y)

can you find t from there

[unreal musk]

(assumedly you need both to narrow down t, hence them giving it)

[sour mulch]

yes, i didn't think of that

[errant crane]

so $\arccos{\frac{1-1}{2}}$?

[warm shale]

morphine_addiction

[sour mulch]

yes

[errant crane]

so i did $\frac{2\sin(\frac{\pi}{2})}{1-4\cos(\frac{\pi}{2})}$ which got me 2 but the answer is -2

[warm shale]

morphine_addiction

[sour mulch]

[errant crane]

i dont understand that

[sour mulch]

so if you find 1-2cos(pi/2), is that the same as 4-pi/2

nope sorry

pi/2 - 4 sin pi/2

is that the same as 4 - pi/2

[errant crane]

4-pi/2 is negative

[sour mulch]

so they're not the same

what does that tell about the value of t you got

because if it's the right one they should be

[errant crane]

but what did i do wrong?

[sour mulch]

what's cos(-pi/2)

[errant crane]

0

[sour mulch]

the same as cos(pi/2)

so you have to remember that there are multiple values of t such that cos t = 0

[errant crane]

ye cos its symmetrical

[sour mulch]

you have to use the x-coordinate to find which is the right one

[errant crane]

how would i know pi/2 is wrong tho bc its still in the range

[sour mulch]

either you look at the graph and realise the gradient should be negative (you got positive) and go and try another value of t

or you check to see if pi/2 gives you the right x-coordinate (it doesn't)

[sour mulch]

that's what this was about

[errant crane]

alight, so bacically try a bunch of things until it looks right

practice should help

[sour mulch]

it will

and remember whenever you take an inverse trig, remember that there are multiple values

(which may need to be negative)

[errant crane]

i didnt know that, i know when u divide by a cos/tan/sin 0 is a solution but didnt know the inverse thing

thanks for the help

.close

[obtuse pebble]

Channel closed

Closed by @errant crane

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[silver torrent]

say I have a point A in 3d space, and I want to rotate it around the origin by $\theta ,\varphi$. How would I do that?\
I dont know too much about trig btw, go easy on me

[warm shale]

DerTheo

[tired shell]

you find A in spherical coordinates, add those angles, and convert back if you want

[silver torrent]

is there an easier solution though?

[tired shell]

uh there are rotation matrices that do it for you

[silver torrent]

no clue what that is

I mean I have heard of it

[tired shell]

technically you have to say if you want to rotate by theta first or phi first

[silver torrent]

oh right that matters I think

does it though?

[tired shell]

rotation matrix is just a big formula that you multiply by your point to get the new point

[silver torrent]

ok

[tired shell]

this thing apparently

[silver torrent]

so cartesian(rotate(spherical(A))) basically

[silver torrent]

yeah Ive seen that

[tired shell]

yea if you convert to spherical it's just adding numbers

if you want to go cartesian to cartesian you use the matrix

[silver torrent]

ok

thanks

.close

[obtuse pebble]

Channel closed

Closed by @silver torrent

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wanton dune]

how can i find series representation of this around zero?

[wanton dune]

i know that d/dx(1/(1-x))=1/(1-x)^2

and that

but what should i do now

should i just derive that series?

[tired shell]

yea

[wanton dune]

so ill get $\sum_{n=0}^\infty nx^{n-1}$?

[warm shale]

Slowaq

[wanton dune]

but wolfram says its equal to this

$\frac{1}{(1-x)^2}=\sum_{n=0}^\infty (n+1)x^{n}$

[warm shale]

Slowaq

[wanton dune]

why?

[lapis charm]

That’s the same thing

[lapis charm]

Because the first term of this is 0

[wanton dune]

ah alright i see it thx

.close

[obtuse pebble]

Channel closed

Closed by @wanton dune

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[deft gazelle]

I am completely stuck

[restive gorge]

what have you triederino?

[deft gazelle]

I dont know where to begin

[glass dagger]

Maybe you could notice that the integral of a sum is a sum of integrals

[deft gazelle]

i noticed that

[glass dagger]

and you probably know how to integrate a constant function

[restive gorge]

you can also pull out scalars

[deft gazelle]

but do i try and get the basic f(x) and g(x) functions like solve what they are

[glass dagger]

You could try multiplying the very first equation by 4

and just see what happens

[deft gazelle]

ohh then it would be the integral equal -12

i just dont know how to stary evaluating the other problems

[glass dagger]

It's a good exercise and I don't want to spoil every detail of the solution so you should probably give it a few minutes and think about it on your own

[deft gazelle]

if i know from (-2,4) f(x)=-12 how would i love the one where it is from (4,-2) (f(x)-3)dx

i know i can start by flipping so its (-2,4) -(f(x)-3)dx

[glass dagger]

One additional hint I'll give is that exchanging the bounds of integration amounts to multiplying the value of the integral by -1

[deft gazelle]

i see that

[glass dagger]

yeah exactly

I think you have what it takes to solve the full problem

[deft gazelle]

do i substitute the f(x) for -12

I am stuck

especially for the next equations where its a different integral and i have to find it

[deft gazelle]

do you have anymore tips

[glass dagger]

Begin by writing each of the integrals as a sum of two integrals

(except the first and the third one)

If you integrate a constant function then just compute the integral

[glass dagger]

and recall this trick

[deft gazelle]

for an answer i got -6

for the first one

i have no idea if thats right

[deft gazelle]

wait do you mean do that for the fist given equation or the first equation i am solving?

[glass dagger]

I get 30 for the first one

[glass dagger]

For the first given equation

and in general for the integrals you're given

[deft gazelle]

im not getting that answer

[deft gazelle]

is there any visual examples you could send

[glass dagger]

Maybe I made a mistake. Maybe if you solve the second one then we can see if we agree on the second one

or maybe you can show your working and I can try to see if it makes sense

[deft gazelle]

sorry its messy, my eraser is failing me

[deft gazelle]

are you able to see the image?

[glass dagger]

Your top right integral should have an additional minus sign

because you exchanged the bounds of integration

Then you'll get the same result as me

Well done

[deft gazelle]

ohhhhhh okay thank you

[deft gazelle]

would g(x)dx from the interval of (-2,4) be 9.2

[deft gazelle]

for the second one i got the answer 21.2

[glass dagger]

I get 4.2

[deft gazelle]

wouldnt it be 3+1.2+5

[glass dagger]

Why +5?

[deft gazelle]

cause from (3,4) is 2g(x)dx=10

so wouldnt g(x)dx on that interval eqal 5

[glass dagger]

3+1.2 takes care of first integrating from -2 to 0 and then integrating from 0 to 4

[deft gazelle]

ohhh

thank you

[glass dagger]

no worries ^^

[deft gazelle]

so for my overall answer i got 16.2

[glass dagger]

That makes sense to me. Well done!

[deft gazelle]

Thank you so much, I can do the rest on my own now

[glass dagger]

great ^^

[obtuse pebble]

@deft gazelle Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ripe merlin]

anyone know computer science stuff/

[shut lagoon]

[ripe merlin]

ok

[ripe merlin]

How do I determine the order of this tree?

[obtuse pebble]

@ripe merlin Has your question been resolved?

[ripe merlin]

help

[obtuse pebble]

@ripe merlin Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sacred trail]

Can someone explain 9

I don’t understand why the 1st degree polynomial is negative

When the derivative at that point is positive

[karmic yarrow]

um need more context here

whats the question asking

[sacred trail]

Find the third degree Taylor polynomial

[karmic yarrow]

for??

[sacred trail]

Question 9

[karmic yarrow]

no what formula

[sacred trail]

At 0.5

[karmic yarrow]

what equation do they give u

[sacred trail]

You don’t have a formula

Just given derivatives

[karmic yarrow]

are u sure this is the answer key no?

[sacred trail]

Yea

It’s from the website he gets it from

[karmic yarrow]

But like can u ss the question, there is lack of context here

[sacred trail]

And here’s the question

[karmic yarrow]

could be mistake on answer key

i dont know why it would be negative either

[sacred trail]

Yea I thought so just wanted to make sure

.close

[obtuse pebble]

Channel closed

Closed by @sacred trail

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pure gull]

How to do this I have no clue

[pure gull]

<@&286206848099549185>

.close

[obtuse pebble]

Channel closed

Closed by @pure gull

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dark idol]

What’s wrong

[surreal forge]

looks like you need to simplify and rewrite what you got for d y/dx

[alpine verge]

factor out a -3 from both the numerator and the denominator

[dark idol]

How about this

It says the answer was c

[alpine verge]

in the last bit you simplified wrong

you multiply y to the top and the bottom of the complex fraction

but you forgot to multiply that y to every term in the numerator

[dark idol]

Where

The x times x/y?

[alpine verge]

x^2/y part

[dark idol]

I thought when it’s like that it just means it’s on the denominator/moves there

[alpine verge]

that only applies if all of the terms in the numerator are divided by y

[dark idol]

Oh

How about this

Idk what I was suppose to do so ignore wat I wrote

[alpine verge]

so the equation of a tangent line requires two things

the slope and the point

we can find the slope using the derivative

and we're given the point

[dark idol]

2x+2yy’=0?

[alpine verge]

yep

essentially we need to find dy/dx

or y'

at (3,4)

[dark idol]

So am I suppose to just plug those numbers in

[alpine verge]

yeah

[dark idol]

2(3)+2(4)dydx

6+8dydx

[alpine verge]

and you need to find dy/dx

so like it might be better to solve for that first

and the plug in the numbers

[dark idol]

Dydx=-2x/2y

[alpine verge]

yep

[dark idol]

-6/8

-3/4

[alpine verge]

yep exactly

now we have all the parts and we can just create our tangent line

[dark idol]

How

[alpine verge]

well you have the slope at (3, 4)

we evaluated it to be -3/4

[dark idol]

Oh y-4=-3/4(x-3)?

[alpine verge]

yep thats it

[dark idol]

Ok thanks

.close

[obtuse pebble]

Channel closed

Closed by @dark idol

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[warped zinc]

Did I do his wrong

This

But still got the mark

Cuz theta should be (2 root 5)/5

It's just asking for the triangle

and gives coords btw

if you cant read french

[obtuse pebble]

@warped zinc Has your question been resolved?

[warped zinc]

<@&286206848099549185>

[obtuse pebble]

@warped zinc Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[novel crater]

anyone know how to go abt doing this

all i know abt p value is that it is the lowest value at which we reject the null hypothesis

[obtuse pebble]

@novel crater Has your question been resolved?

[novel crater]

.close

[obtuse pebble]

Channel closed

Closed by @novel crater

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gray forge]

anyone have idea on Lebnitz's rule on Definite Integration?

[obtuse pebble]

@gray forge Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[midnight dust]

can someone explain me why option 4 is correct

[midnight dust]

also I am wondering what the LUB if 4 and 6 is? Its not valid right?

[obtuse pebble]

@midnight dust Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sage dagger]

im on part b but im having trouble with finding the horizontal distance. I know that initial horizontal = final horizontal velocity and im supposed to be using these 3 equations:

the problem im having is that i have u_y, u_x, but i dont have v_y or t so i dont think i can find s. at first i assumed that v_y = u_y since i think its implied it lands at the same height it is launched from so i tried to find t from there but i just get t=0 or s=0 which doesnt help

[sage dagger]

get your own channel

[grand fog]

oh mb

[sage dagger]

delete your messages as well

ur flooding my thing

[grand fog]

there ya go

[sage dagger]

thanks

[obtuse pebble]

@sage dagger Has your question been resolved?

[obtuse pebble]

@sage dagger Has your question been resolved?

Channel closed

Closed by @sage dagger

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[safe haven]

parallel means same gradient

[static furnace]

gradient being the slope

[obtuse pebble]

@open atlas Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[river falcon]

find radius of the circle

[marsh geyser]

What did u try?

[river falcon]

i found the sides

[errant delta]

and then phythagorus? for half of the triangle?

[river falcon]

but now what

the side of the square inside is 10

but in what way do you split it in terms of r

[paper zenith]

the 8-r and 6-r on hypotenuse can be found using congruence

so 8-r+6-r=10

14-2r = 10

r=2

[river falcon]

can u pls explain how

i cant recall it

[paper zenith]

see the radius is equal

[river falcon]

yes

[paper zenith]

and the hypotenuse is common

and the angle between them is 90 degrees or Pi/2 radians

so by pythagoras theorem, the part of hypotenuse should be equal in both smaller parts of triangles

alternatively, by rhs congruence the parts of hypotenuse must be equal

[river falcon]

huh

[crude coral]

btw there is a formula to find radius of inscribed circle for right angled triangle , i think its
r = (P + B - H)/2
P being perpendicular
B being base
H being hypothenuse
r being radius

is there any info about if the triangle is right angle?

[river falcon]

yeah that gets the correct answer

but i need to do it from scratch

[river falcon]

yes, its right triangle

[crude coral]

what u mean , like prove the formula and then get the answer?

[river falcon]

no

[river falcon]

this way

how do you split the hypotenuse in 8-r and 6-r

i dont get that

[crude coral]

oh ok

orange dots represent the 2 triangles being congruent

yellow dots represent the 2 triangles being congruent

so 8-r = base of 1 triangle = base of 2nd triangle = 8-r

[river falcon]

but how are the triangles congruent

the angle is common and perpendicular is common

but that isnt RHS congruency

[paper zenith]

see, the marked angles are perpendicular by construction

[river falcon]

OH BRUH

im stupid

i was trying congruency for these 2 for some reason

thanks

.close

[obtuse pebble]

Channel closed

Closed by @river falcon

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[river falcon]

find missing term
4 7 7 3
6 1 5 x
5 x 6 1
7 3 4 7

[river falcon]

not really math but yes

[sage geode]

No rules?

[river falcon]

options are 2, 9 and 5 if that helps

[obtuse pebble]

@river falcon Has your question been resolved?

[river falcon]

<@&286206848099549185>

[frosty rivet]

Sum of every row is 21 if x = 9 atleast

[river falcon]

hmm

[frosty rivet]

I feel like the question is missing or something. Do you know the specific subject?

[river falcon]

its just logical question

no specific subject

[river falcon]

this makes sense tho

[frosty rivet]

Then it sounds like it should just be 9

[river falcon]

ig

thanks

.close

[obtuse pebble]

Channel closed

Closed by @river falcon

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[slate lintel]

is there some mysterious cancelling here because shouldnt it be a division by 0 error?

[novel knoll]

Why would there be that?

[slate lintel]

because like 1/(x-1)^3 right

?

1/0

or does it not matter because its in sin function

[novel knoll]

It says for x!=1

So how is (x-1)^3=0?

[slate lintel]

i mean in b

it says f'

[novel knoll]

Thats also only for x!=1

[slate lintel]

uhh i am confused

for part b it says f'(1)

i mean from the calc

it says f' is that

[novel knoll]

I suggest you back up

How did you solve a?

[slate lintel]

ehh

i kinda didnt

really confused bout that too

[novel knoll]

Yeah thats the problem

[slate lintel]

why is it 2

[slate lintel]

like i subbed in n=2 and n=3 here

either way i think am goin to get a division by 0 error for f'(1)

[novel knoll]

No you are not

[slate lintel]

please explain i dont understand 😭

[novel knoll]

For a derivative to exist at a point the left and rhs limits needs to be equal

(And continious)

So for example for n=0 find derivative for x!=1

Take limit from the left and the right

Check if they are equal

[slate lintel]

is this what u meant by taking limits from RHS and LHS?

also this is not continuous because x = 1 breaks it right?

[novel knoll]

Wdym?

[novel knoll]

No meant doing it formally. How do you know your function doesn’t behave differently at 1.0000000000000000000000000001

[slate lintel]

oh

so u meant like

the epsilon definition?

of limits?

[novel knoll]

Or working with limit properties

[slate lintel]

i meant like for a function to be continuous at x=a, then the point at x=a must exist right?

but like subbing in x=1 makes it so that it doesnt exist

[slate lintel]

in this one

[novel knoll]

Again that is not how the function is defined at x=1

[slate lintel]

oh...

[novel knoll]

(And doesn’t make any sense to speak of continuity at points where the function isn’t defined)

[slate lintel]

sorry but ive like

not heard of limit properties

..

is this it?

[novel knoll]

Yes

But I would suggest you find (much) simpler examples before doing that exercise. Because you seem kind of lost

[slate lintel]

yes

i am super duper lost

gotta go back to definitions ig

😭

😭 😭 💀

[novel knoll]

$$f(x)=\begin{cases} x^n\cdot \frac{1}{x} & x\neq 0 \
1 & x=0 \end{cases} $$

[warm shale]

ScapeProf

[novel knoll]

Find smallest non-negative n such that f is differentiable at x=0

[slate lintel]

hmmm

[novel knoll]

Start with n=0

[slate lintel]

ok

sooo x^0 * 1/x

derive that

-1/x^2

?

[novel knoll]

A necessary condition for differentiability at a point is continuity

So start with checking if continious

[slate lintel]

errr

whats the formal way to do that

because like i'd just sub in like

some small numbers to the left and and right of 0

but.... that clearly isnt it

[novel knoll]

lim x->0+ of 1/x sort of standard, but if you don’t know that you have to use definition to show limit is inf.

But idea is you prove a few formally then use properties of limit once you know a few limits to show everything else

[slate lintel]

hmmmmm

alright

ill look at some more basic examples online and learn this

thanks :)))))))))))))))

.close

[obtuse pebble]

Channel closed

Closed by @slate lintel

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dusky hare]

How do I finish this

It’s calculus

Chain of rule

[crude coral]

why did denominator go from 4x to 8x

also where did the 2 go from denominator

u cant multiply that with 4x+2 cuz 4x+2 has a power of 1/2

[dusky hare]

Oh yeah

What can I do though

The numerator is wrong too apparently

Answer sheet says this

[high lily]

what's 4/2

[dusky hare]

Omds

Thanks

.close

[obtuse pebble]

Channel closed

Closed by @dusky hare

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fallow cosmos]

how to solve this

[cinder nimbus]

pls help someone

someone help?

[high lily]

plug in each value within the domain

[obtuse pebble]

@cinder nimbus Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[grand minnow]

just need to verify if this is the ideal/intended/best way to solve this (i.e., change of base, cross multiply, square root etc so on and so forth)

[grand minnow]

ignore nickname lol my friend set it for me

just call me felei

[sudden sage]

seems fine to me, you could simplify the change of base as 1/log_y (x^2) = log_(x^2) y instead of writing 4 separate logs but it doesn't make much of a difference

[grand minnow]

gotcha thanks

.close

[obtuse pebble]

Channel closed

Closed by @grand minnow

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[native obsidian]

Is it possible to write U in terms of x1,x2,y1 and y2s only?

[bitter pewter]

;l

[obtuse pebble]

@native obsidian Has your question been resolved?

[native obsidian]

not, but it doesn't matter

i'm 90% sure it is impossible

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[river falcon]

W = (1-iz)/(1+z) , z is a complex number, then w is real/imaginary/not defined?

[river falcon]

i already tried

(1+b-ia)/(1+a+ib)

now what

[dark stirrup]

Multiply numerator and denominator by $\overline{1+z}$

[warm shale]

SWR

[river falcon]

.close

[obtuse pebble]

Channel closed

Closed by @river falcon

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[snow herald]

Hey, I've been trying the understand the proof behind undermined coeffecients of linear differential equations with constant coefficients
so generally something of the form $Ly = f$ where $L = p(D) = \sum_{i=0}^{n} a_iD^{n-1}$
So the proof says that we can consider $f(x)$ a solution to a homogenous LDE with constant coefficients
so $f$ would be the general solution to $\tilde{L}y = 0$
considering L and $\tilde{L}$ are both linear operators
We can just take $\tilde{L}(Ly) = \tilde{L}(f) = 0$
let's say $\tilde{L}L = \hat{L}$ we know that the general solution to this, will be f(x) and any solution to $Ly = f$ and any of their linear combinations
So $\hat{L} = \sum_{i = 0}^{n}c_iy_i(x)+ \sum_{i=0}^{n}d_iu_i(x)$

so we can deduct that $y_p = \sum_{i=0}^{n}d_iu_i(x)$
this is the part I don't get:
in which case there are two options either there exists a $u_i(x)$ that has the same root as one of the $y_i(x)$
which means we can see that there exists a solution of the form $b_0x^ry_1(x)$ whith r being the multiplicity of the root of $y_i(x)$ + the multiplicity of the same root of $u_i(x)$ minus 1
or it doesn't in which case $b_0x^ry_1(x)$ r is equal to the mulplicity of the root of $u_i(x)$ - 1

[warm shale]

Mephisto

[snow herald]

why is that that if there are any roots found that match that this is the case?

and can I assume that any solution to using undetermined coeffecients is of the form $P(x)e^{\alpha x}cos(\beta x) + Q(x)e^{\alpha x}sin(\beta x)$ where P(x) and Q(x) are polynomials

[warm shale]

Mephisto

[obtuse pebble]

@snow herald Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[strong aspen]

hi

[strong aspen]

I have sent a suggested solution as well as my work

the thing is we got different Constant

but all the steps seem logically correct

what's wrong

[obtuse pebble]

@strong aspen Has your question been resolved?

[snow herald]

I'll try to help, I'm doing differentials too rn

Oh I think I see it?

[strong aspen]

ok

thanks

[snow herald]

when distibuting the 3/4

I think it essentially gets absorbed into the C

so you can technically multiply this C by 3/4 to get rid of it, at leat that's how your solution sheet did it

[strong aspen]

btw that's x^1/3

[snow herald]

they absorb everything into the C

[strong aspen]

yeah I got that

but is it technically still correct my solution or teachers solution is correct

[strong aspen]

ln(x) = 0 if x=1 so left term at the end would cancel out and give C^3

[strong aspen]

but logically my solution for question A is right but it doesn't do sm like this?

anyways feel free to try the question for yourself w/o looking at the answer to learn

[snow herald]

hold on I'm looking into it

My assumption would be, you have to absorb everything you can, before you can plug in numbers

I think that's the issue, but if I were you I'd wait for someone who knows more about it then me

<@&286206848099549185>

[strong aspen]

I'll just ask my teacher tomorrow, or if anyone is down to answer please do it in my dms 🙏

.close

[obtuse pebble]

Channel closed

Closed by @strong aspen

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

@astral radish Has your question been resolved?

Channel closed

Closed by @astral radish

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[long roost]

can someone explain why the summation becomes this, its been a long time since i've dealth with summations

[long roost]

in the previous step it was this

i understand changing the index and bringing the second p outside since its a constant not too sure about the rest

after looking into sums of infinite geometric series i understand why we get the denominator but i dont understand the numerator

<@&286206848099549185> any ideas?

.close

[obtuse pebble]

Channel closed

Closed by @long roost

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rugged rampart]

Stuck on question 3G and 3h

[knotty thorn]

!status

[obtuse pebble]

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

[rugged rampart]

1

[knotty thorn]

these are soled the same way as you presuambly did during question 2

get rid of the brackets, and then rearrange to solve for x

[rugged rampart]

I never done 2

[knotty thorn]

the same way you did any other question in 3

[rugged rampart]

So I simplify it

[knotty thorn]

Yes

[rugged rampart]

So it becomes like this

How does it become in its simpliest form

[knotty thorn]

expand each bracket individually

do one side at a time: first, what is 4(2x-3)

sorry that's f)

[rugged rampart]

So it will be

[knotty thorn]

2(1-x)

i mean

[rugged rampart]

What question is that

[knotty thorn]

3g)

[rugged rampart]

Ok

It will be 2x1-x

[knotty thorn]

try and use the asterisck * to mean multiply on here as it gets a little confusing otherwise

2(1-x)

can you get rid of the brackets and simplify here

[rugged rampart]

Okay

Okay

2*1-x

X doesn't have a value

Well it does but not in this

I need to remove the brackets

and then find the value for x

[knotty thorn]

right now im only asking you to expand out 2(1-x) in isolation

ignore the left hand side of the equation; what is the expanded form of 2(1-x)

[rugged rampart]

so it become 2*1-x

[knotty thorn]

it becomes 2 - 2x

[rugged rampart]

how

[knotty thorn]

2(1-x) you can think of as 2 multiplied by 1, + 2 multipled by -x

[rugged rampart]

If 2*1= 2 then it will be 2-x

[knotty thorn]

the brackets are important

2 is not only multiplied by 1, but also the -x

there is a difference in saying 2(1-x) and 2*1 - x

2(1-x) = 2*1 + 2*-x

this is the same for any bracket with a number multiplying it: they times each number individually, not just the first one

[rugged rampart]

Ahhhh

[knotty thorn]

for example in 3a), 2(x+3) will simplify to 2x+6

not 2x+3

[rugged rampart]

is it because of it like this

2*3+x

but done in the same way just shown differently

[knotty thorn]

be careful with your notation with brackets especially now that you know they are different

i am unsure if you mean 2*(3+x) or 2*3 + x

[rugged rampart]

I am just stressed because i have a junior mathematical challenge

It's confusing me

[knotty thorn]

do not worry, once you have this concept down you will find these questions fine

[rugged rampart]

that's just helped me now

[knotty thorn]

would you still like help with g) or would you like to go over the other questions in 3)

[rugged rampart]

I will like to go over the other question in 3 then work my way up

May i be excused for a moment

[knotty thorn]

sure, @ me when you're back

[rugged rampart]

Okay

[rugged rampart]

Actually can I do it tomorrow as I will be more energised

Yes because the second a cancels out

[knotty thorn]

sure, have a read of https://www.mathsisfun.com/algebra/expanding.html if you need a resource in your own time

[rugged rampart]

Thanks

[obtuse pebble]

@rugged rampart Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[floral siren]

hello

[floral siren]

"find the sum of the given series, or show that
the series diverges (possibly to infinity or negative infinity)"

im not sure how to approach this problem

any tips?

[restive gorge]

you can use comparison test

[floral siren]

what is that about?

[restive gorge]

finding a smaller series that still diverges

we find a smaller series by making the denominator bigger

any ideas?

[floral siren]

1/2a

but why does that work?

i think im suppose to use one of these

or this

[warm shale]

𝔸dωn𝓲²s

𝔸dωn𝓲²s

[restive gorge]

I dont think they help

[floral siren]

so

the sum using 1/2n is smaller obviously

[restive gorge]

yes

[floral siren]

but how does that help me

[restive gorge]

if you were to make the partial sums of a diverging series bigger then it diverges still

like it makes it worse

[restive gorge]

that is the comparison test theorem

[floral siren]

hmm i was not taught that yet

oh well

[restive gorge]

i thought you used it previously somewhere else

[floral siren]

oh

[restive gorge]

what are the options you have other than these 3 theorems above

[floral siren]

next chapter is about comparison test

anyways

i dont think i understand partial sums

if i have a series

partial sums is the sum of the first n terms ?

and this thing here confuses me

[restive gorge]

well the word suggests it already

say you have a sum n = 0 to infinity with a_n

a_1 is a partial sum

a_1 + a_2

a_1 + a_2 + a_3

a_2 + a_3 is

[floral siren]

a_2 + a_3 is not a partial sum?

[restive gorge]

it is

it's part of the sum

[floral siren]

okay

but what do they mean with "sequence of its partial sums"?

[restive gorge]

You can define $\sum_{i = 1}^{\infty} a_i$ as $S_n = \sum_{i = 1}^{n} a_i$

Then if the sequence $\lim_{n \to \infty} S_n$ converges then so does the series

[warm shale]

𝔸dωn𝓲²s

[restive gorge]

it's pretty much useless

to be honest

[floral siren]

well look

maybe

[restive gorge]

it's basically

[floral siren]

i can use this

[restive gorge]

the ver same thing

[floral siren]

to solve

[floral siren]

this

[restive gorge]

yea

then show

$\lim_{n \to \infty} S_n = \lim_{n \to \infty} \sum_{k=1}^n \frac{1}{2k-1}$

[floral siren]

but wdym with sequence?

[warm shale]

𝔸dωn𝓲²s

[floral siren]

a sequence is not a sum...

[restive gorge]

bro

you can have sequence of sums

[floral siren]

lets say

1 + 2 + 3 + 4 + 5 ...

so you mean

the sequance if this partial sums is:

{1, 3, 6, 10, 15 ...} ?

[restive gorge]

yea

[floral siren]

alright well so in order for me to see if the the sequance if this partial sums converges, i must find a formula for {1, 3, 6, 10, 15 ...} right?

[warm shale]

𝔸dωn𝓲²s

[restive gorge]

yea

but to find that is pretty difficult

[floral siren]

im just wondering if i can use this

for this

[restive gorge]

for any series

[floral siren]

.

because

in this chapter

we didnt learn

[restive gorge]

well you would have to go till infinity

[floral siren]

comparason test

[restive gorge]

if the partial sums are finite then it always converges

because it stops at some point summing up

but with infinity it doesn't

and finding a closed form is pretty difficult

series is not a sequence, but you can rewrite it as one

[restive gorge]

.

S_1 tells you the partial sum at n=1
S_2 at n=2
...
S_k at n=k

and that resembles a sequence

if you were to do it infinite times (basically take the limit to n->oo) and if that converges then the series converges

it's a basic and important thing

but doesnt really help to solve these

[floral siren]

yeah... i guess i will just move on to the next chapter and learn comparason test

i have exam in calculus in 3 days

so much more to learn...

but i will try my best, thanks for the help! 😄

.close

[obtuse pebble]

Channel closed

Closed by @floral siren

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[pastel wren]

wut

[violet timber]

why is there brackets

or i mean why do you need to put brackets

[pastel wren]

you mean (-2)^3?

[violet timber]

yes why is that in brackets

[rain tiger]

cause -2^3 and (-2)^3 are different things

[pastel wren]

say x=-2

so sqrt(x^2) = sqrt((x)^2)=sqrt((-2)^2)

its just to distinguish that the whole -2 is taken to third power

not just the 2

for third power it doesnt change much

but for even powers would

[violet timber]

i know that but it didnt ask rewrite the number (-2) it said reqrite the number -2

[pastel wren]

but (-2)=-2

its just agreed upon notation if you write -2^n it means -1 times 2^n

[rain tiger]

its actually kinda confusing to explain just think about it this way If u do -2^2 it will be -4 while if u do (-2)^2 its 4

[violet timber]

yes i understand that

100%

but right here there is no brackets

so why do we change it

[rain tiger]

thats just cause if its put by its self its fine you dont have to put brakets

[pastel wren]

from this context its obvious you take (-2)^3

if they asked for -(2^3) it would be clear they ask for that

[violet timber]

ok

[obtuse pebble]

@violet timber Has your question been resolved?

@violet timber Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[violet timber]

is a repeating decimal rational?

[violet timber]

like is 33.33333333333333333333333333 rational since it repeats?

[glacial obsidian]

Yes

A decimal number is rational if and only if it repeats

They are the same thing

[violet timber]

but like 34.35 is rational righ

but 36.3234242348320407395873204983725098790932578329085473209573259032879450 (image it keeps going)

is irrational right

[glacial obsidian]

Yes, but it can be written as 34.350000000... which repeats

[glacial obsidian]

Correct

[obtuse pebble]

@violet timber Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tight sail]

i think 3 and 5 are wrong

[obtuse pebble]

@tight sail Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[violet timber]

my calc gives an error when getting the root of a negitive number

will the number allways result in a negitive

(like can i just do it without negitive then add back the negitive no matter what the ro ot is 4th root 5th root etc

[tired shell]

error for the cube root?

[violet timber]

👍

since the number inside is negitive

[tired shell]

huh that's pretty weird

you can just ignore the negative and add it in the end yea

an odd root of negative is negative

[pseudo swift]

did you actually use a cube root on your calc ?

you only said "root"

[violet timber]

But if the root is positive

How do I know

[violet timber]

Yes just said root since other questions have different roots

[tired shell]

odd root of a positive is positive
even root of a positive is both negative and positive because reasons

[violet timber]

Positive root of a negative number isn't possible right

[tired shell]

even root of a negative is nothing yea

since when you multiply negative numbers it goes back and forth + and -

[violet timber]

The root of a positive is always positive right

[tired shell]

4*4=16 and -4*-4=16

sometimes people just do the positive number though yea

[violet timber]

But it's not possible to find right

[tired shell]

yea you can't find the 4th root of -100 or whatever

[violet timber]

So positive root of positive is positive

Odd root of positive is positive

Odd root of negative is negative

Positive root of negative isn't possible

[tired shell]

👍

[obtuse pebble]

@violet timber Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[peak silo]

I have a math project where we are making new casino games and playing them in class. One of the tasks is to determine the probability of each possible outcome within the game. Currently my game is where a deck of 18 cards (all but Aces, Kings, Queens, Jacks, and Jokers are removed) are laid down on a table (face down of course) and the player has to choose 4 of the cards. Prior to selecting the cards the player bets on what outcome is going to happen (ex. 3 Aces are chosen) and depending on how rare the outcome determines the pay out for winning. Additionally if they get a joker it trumps the payout upon being drawn, red joker meaning they automatically win an amount determined by spinning a wheel and a black means they lose. I am having trouble though for one of my outcomes: the probability that a pair of any kind is present in the 4 cards drawn. Currently I am getting a ~103% chance of it happening ((16C1 * 3C1 * 12C2) / (18C4) = 1.03...). I understand that the probability of it happening is very high and that I should not add the ability to bet on it in the game but it is making me question all my other calculations for the other outcomes. I am feeling quite stupid right now as this feels like a very simple oversight and any help will be much appreciated. Thanks in advance.

[raw torrent]

For the pair of any kind does it include pair of jokers

[peak silo]

No...

[raw torrent]

Ok

What is the 3C1 for

[peak silo]

The idea was that there are only 3 cards that can create the pair with the first card selected and only choosing one of them to create a pair

[raw torrent]

I’m thinking

4c2 for the pair

12c1

8c1

Just thinking

[peak silo]

Ah I see...but any card can be a pair hence the 16c1 then the 3c1 because with 4c2 I thought that it would mean you need to decide which card you need the pair to be

[raw torrent]

It’s been a while since I did probability but

I remember my teacher saying to start off with the most specific

So that’s why I started with 4c2

Idk I might be tripping

Let’s see what others say

[peak silo]

Yeah I typically do it that way too but I didn't see how that would work here considering whatever the first card drawn is determines what the second card must be (not literally first and second card but hopefully you get what I mean)

[raw torrent]

Actually mine is wrong it needs to start with 4c1 and then 4c2 p sure

[peak silo]

4c1 determining which card value (Jack, Queen, King, or Ace)?

[raw torrent]

Yea

Ugh now I’m thinking 4c14c23c14c12c1*4c2

Wait

Discord format

[peak silo]

Lol I got ya

[raw torrent]

Ugh now I’m thinking 4c1 x 4c2 x 3c1 x 4c1 x 2c1 x 4c2

[peak silo]

Huh lemme check...I know I can get the answer by figuring out the probability of not getting a pair (1-(4c1 * 4c1 * 4c1 * 4c1) / 18c4)

Unless that is wrong as well

HUh yours got me 113% so something isn't quite right...

[peak silo]

This gave me ~92%

[raw torrent]

Of getting a pair?

Or not

[peak silo]

Of getting a pair

[obtuse pebble]

@peak silo Has your question been resolved?

Channel closed

Closed by @peak silo

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[uncut verge]

Was sent this proof by my teacher, but it is wrong. Any ideas on the actual inductive process to take? The idea is to prove that the degeneracy for the nth level is 2n^2

[tired shell]

what's the full question? n^2+n+1 isn't (n+1)^2

[uncut verge]

exactly my issue

lemme translate the question real quick

it's in spanish

To find the possible states for a certain n ∈ N, we proceed as follows

nevermind

probably the mistake is that it should be 2(2n+1)

he missed a two

if someone else notices something else lmk

[obtuse pebble]

@uncut verge Has your question been resolved?

[obtuse pebble]

@uncut verge Has your question been resolved?

[uncut verge]

.close

[obtuse pebble]

Channel closed

Closed by @uncut verge

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[humble kraken]

well there are 12 ways to arrange 12 tasks

and each group of 2 tasks can be arranged 2! ways or 2P2 ways

and there are 6 groups

and since it doesnt specify the order of the groups, we can assume it doesnt matter and say its 6!

[zenith raft]

what

there are 2 questions and the answers to neither of them are 6!

[humble kraken]

so couldn't u just do (12!/(2!^6) * 6!)6!?

[humble kraken]

i wasnt finished

[zenith raft]

that sounds too big still

it's significantly bigger than the answer to the first question

and the answer to the second question should be smaller than that

[humble kraken]

i was tryna answer second question sorry, shouldve specified that

[zenith raft]

yea i was just trying to give a sanity check for it

using the first question

[humble kraken]

but first question could just be that same thing but without the 6! at the end right

so just (12!/(2!^6) * 6!)

that makes 10395

[zenith raft]

the first question you can think of as number of functions from the set of tasks to the set of people

and there are 6^12 of those

[humble kraken]

oh yeah u right

[zenith raft]

and the answer to the second question should be smaller than that right?

but (12!/(2!^6) * 6!)6! > 6^12

[humble kraken]

yeah probably

i havent rlly learnt much counting theory yet tho so im not too good at it

[zenith raft]

counting is hard

[next crescent]

for #2 would it be C(10,2) * C(8,2) * C(6,2) * C(4,2) * C(2,2) ?

[zenith raft]

not quite but sounds like a good idea