help-26

[neon iron]

3n^2 - 12
So 3(n-4)^2

3xn = 3n
3x-4 = -12

and uh

the squared comes in somewhere

[neon iron]

not quite. when you factorise with 3, what do you get

unless it's 3(n^2-4)

[neon iron]

yes that is correct, but you should make sure you understand

3 x n^2 = 3n^2

I get that

Okay. so we have $3n^2-12=3n^2-3*4=3(n^2-4)$

[thorny flame]

AimaneSN

[neon iron]

now you should factorize $n^2-4$

[thorny flame]

AimaneSN

[neon iron]

n(n-4)

[neon iron]

Not true, expand it to see why

that's equal to what ?

n^2-4n ?

[neon iron]

Yes, so it's not really $n^2-4$

[thorny flame]

AimaneSN

[neon iron]

(n-2) (n+2)

[neon iron]

Yep!! correct

now replace this factorization in the initial fraction

you should get the result you're looking for

OH

U GENIUS

KITH

Ty very much

.close

[topaz sinew]

Channel closed

Closed by @rocky tinsel

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.

[shell iris]

Can somebody help me with this page the first 3 questitons

[shell iris]

And I wanna know if I got the right answer

[topaz sinew]

@shell iris Has your question been resolved?

[topaz sinew]

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.

[quaint musk]

4. If you are tracking a particular stock's price increase, use the formula [(New Price - Old Price)/Old Price] and then multiply that number by 100.

= (1.37-1.29)/1.29 × 100
= 6.2%

[quaint musk]

5. If the price decreased, use the formula [(Old Price - New Price)/Old Price] and multiply that number by 100.

= (589-456)/589 × 100
= 22.6%

[topaz sinew]

@quaint musk Has your question been resolved?

Channel closed

Closed by @quaint musk

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.

[thin oak]

how do you graph

[topaz sinew]

Please don't occupy multiple help channels.

[thin oak]

$$f\left(x\right)=\frac{\sqrt{x-2}}{\sqrt{x-2}}\frac{\sqrt{6-x}}{\sqrt{6-x}}x$$

[thorny flame]

Chunkin

[thin oak]

desmos graphs like this

[thorny flame]

Results provided by WolframAlpha

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

Requested by Chunkin#4952

[thin oak]

wolfram graphs like this

which one is right

[silver valve]

because 2 < x < 6 is the domain

[thin oak]

wait yo

your right

[silver valve]

wait its passing through x = 0, y = 0 lmao idk

ah .... wolfram is simplifying your expression

so there should be holes at x = 2 and x = 6

[thin oak]

I think wolfram understands but is just graphing wierd ig

[thin oak]

ye desmos shows that

ok cool this makes sense

.close

[topaz sinew]

Channel closed

Closed by @thin oak

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.

[lime thorn]

How do I use sin to find x

[shut spear]

what is sin45?

[thin oak]

show ur work here

I'll tell u if ur correct

[rocky dragon]

if you havent learnt calculating sins and cosins and tangents of angles yet you can enter that in your calculator

[thin oak]

where did he go

[shut spear]

but they should probably use the triangle since it's given

[rocky dragon]

the way you should set up your work is || sin45= x/20||and then use algebra to get x

[topaz sinew]

@lime thorn Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[frosty nacelle]

why isnt it 32/3t^3

This is my work

[hazy pumice]

the acceleration function is constant, not linear

you misread what was given

[frosty nacelle]

ohhhhhh

fs

ffs

[topaz sinew]

@frosty nacelle Has your question been resolved?

[topaz sinew]

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.

[native lake]

All I need is a hint

A point in the right direction

Since my brain is not functioning rn

[neon iron]

what's the question ?

[native lake]

The picture

a/(b+c) + b/(a+c) + c/(a+b) = 4

[split igloo]

that's an equation, not a question

[native lake]

Solve for a,b,c

My bad forgot to put it in the picture

[topaz sinew]

@native lake Has your question been resolved?

Channel closed

Closed by @native lake

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.

[lean osprey]

can someone explain this to me? i tried understanding it myself. All I understand is that we need to isolate abcde to find their values and that they are constant. im a complete beginner to this

[topaz sinew]

@lean osprey Has your question been resolved?

[topaz sinew]

@lean osprey Has your question been resolved?

[neon iron]

so in the equation plug in x=-1 and ur done

[lean osprey]

okay but how would i know to do that, if i didnt look at the solution

[neon iron]

its instinct based

practising problems helps u spot them

[knotty ledge]

You kind of just have to notice that plugging in x=-1 gives you a+b+c+d+e on the right hand side

[lean osprey]

🧍‍♂️ ..i

OH

I SEE IT NOW

tyty

but wait

it says x>0 so why can we use -1?

[neon iron]

mb, that shouldnt be legal

but the solution

[lean osprey]

🤔 ...

[neon iron]

oh, it just says x>0 becos its undefined for x=-2

else its just a polynomial after cross multiplication

[lean osprey]

??

so its saying x is greater than 0 because we are not sure that x is -2

?

i got it now

.close

[topaz sinew]

Channel closed

Closed by @lean osprey

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.

[willow kelp]

Want a step by step solution

[topaz sinew]

@willow kelp Has your question been resolved?

[pallid hare]

dude you cant just expect people to come here and give you answers

for a "step by step solution"

you geniuenly have to have a question or not understand the problem

[topaz sinew]

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.

[rain lotus]

Hi

[rain lotus]

,rotate

[rain lotus]

Did I do anything wrong? I checked the answer on the answer sheet and I’m so far from it but I just don’t know what I did wrong

[hearty spoke]

Would help if you finished the problem instead of getting 80% of the way there and stopping, but it looks fine so far

[willow kelp]

I understand the problem I just have no idea how to deal with differential equations with mutliple y terms

[pallid hare]

well if you want that

go to

https://symbolab.com

[topaz sinew]

@rain lotus Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[mild fractal]

subject: quadratic equations | axx + bx + c
question: the difference between (x-5)^2 and (x+5)^2 is based on whether b is less than or greater than 0 right

[mild fractal]

like

if equation is x^2 + bx + 25

then factored form would be:

(x-5)^2 if b < 0

or (x+5)^2 if b > 0

right?

[pure fulcrum]

no, since there are only 2 values that satisfy the equation (x-5)^2 and (x+5)^2, which is -10 and +10

[tall wolf]

^

I felt like that was a trick question lol

[pure fulcrum]

if b = 1 or something else, then you have to find another factor form

[mild fractal]

wait thats not what i meant

idc abt the solution

factored form would be ONLY (x - 5) ^ 2 if b < 0

right?

[pure fulcrum]

oh, if you are talking about (x-c) ^2 form , if c > 0, then you are correct, b should be always less than 0

and vice versa

[mild fractal]

ty

.close

[topaz sinew]

Channel closed

Closed by @mild fractal

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.

[frosty cape]

Helo

[frosty cape]

If g(x)=x+15 then whats gog(x)

Is it

x+30

?

[empty sail]

Yes

[frosty cape]

And

Can u answer one more question

11

Q-11 a gof(x)=(x+1)^3 fog(x)=x^3+1

Is it?

[topaz sinew]

@frosty cape Has your question been resolved?

[loud dawn]

Are those equal?

[topaz sinew]

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 storm]

?

[topaz sinew]

Please don't occupy multiple help channels.

[floral storm]

Ok

[obtuse rover]

So for the rate of change we can use the same formula that you used in the first one. m = (y1-y2)/(x1-x2)

To do this we need two points on our line. We can use any two points to do this.

[floral storm]

Thank You

[obtuse rover]

Let's make this easier on our selves and use the point (0, 0) and for the second let's use (1, 75).

[floral storm]

You’re helping with the problem with the graph right?

[obtuse rover]

Yes, did you want help with the top one?

[floral storm]

Yeah just finishing it up to get the initial value and function rule

But yes I also need to do the bottom one lol

[obtuse rover]

Gotcha, So the initial value is typically referring to the 'y' value of the function when our 'x' value is 0

I don't know how you were taught to find it but I think the best way is find your function rule first. Since it looks like we are dealing with linear functions we will be using the 'y=mx+b' formula

y=mx+b where 'm' is your rate of change and 'b' is your y-intercept or initial value.

We already know our 'm' so we can plug that into the equation. y=(2/3)x + b

To solve for 'b' lets replace the x and y with known values and then solve for b

We can use the point (3, -1).

So now our equation looks like -1 = (2/3)*3 + b

Do you feel comfortable solving for b from there?

[floral storm]

Yes thank you

[hazy flare]

yo

I need help

[obtuse rover]

No problem. Let me know if you want help with the bottom one.

[floral storm]

Yes Please

[floral storm]

you the goat bro

[obtuse rover]

So the only thing left on the bottom one is to find the value of 'b'. Since 'b' is the initial value and will also let us finish our function.

What is nice about this one is b is also the y-intercept value and we can get that from the graph.

[empty sail]

Don't do people's work for them

[floral storm]

Who are you?

[empty sail]

A person

[floral storm]

Do you have any sort of authority orrr 😭

[empty sail]

I know how the server works more than you do

The goal of the server is to teach, not do people's work for them

[floral storm]

Well I’m pretty new to this math server yo

[obtuse rover]

Sorry, I was trying to explain the problem thoroughly as I could but I could probably do that a different way.

[floral storm]

I’m literally learning though and I’m putting thumbs up emojis to confirm that I’ve written it down and understood it

[empty sail]

Meaning people who help, should ask questions, engage, see if the user can answer said questions

IE for this question, asking if they know slope formula, and assist if they stuck

[floral storm]

You’re like a creator of this discord?

[empty sail]

No, but I've been here long enough to understand how this server works

[floral storm]

So like you go around the different channels and tell people what to and what not to do?

[empty sail]

I help people too

[empty sail]

@obtuse rover This is what I mean

[floral storm]

I get that but why do you care 😭 respectfully

[empty sail]

Because you need to learn, not be feed the answers

Learning means be engaged

[floral storm]

I’m learning though as he’s doing that I’m understanding what he’s talking about which is why if you scroll up you see Thumbs Ups on his messages indicating that I get what it meant and it’s making sense

[sweet shard]

It's still against the rules to be fed answers. Period

[floral storm]

Alright I guess whatever you guys say

Are all the people with colored names good with mathematics?

[empty sail]

Yes, you may get what they meant, but if you were to be given you're own problem, could you do it all on your own, without memorizing the process?

[floral storm]

Good point I guess

[empty sail]

Green = helper
Darker blue = active
Light blue (like mine) = very active
Lighter blue = mods

[topaz sinew]

@floral storm Has your question been resolved?

Channel closed

Closed by @floral storm

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.

[worn light]

Im having trouble on question 4-6 can someone help me?

[topaz sinew]

Channel closed

Closed due to the original message being deleted

[worn light]

I just need a way to solve those ones

So i can solve the other questions

Heres what i have currently

And i dont know how to proceed

What am i supposed to do with the fraction 106/16

[shut spear]

Are you allowed a calculator

[worn light]

Yes

Its just homework im having trouble with

[shut spear]

Think of which trig function of that angle allows you to utilize sides a and b

[worn light]

Idk

Thats what im having trouble with

[shut spear]

so let’s start with sin

[worn light]

Id ont know how to deal with fractions

Okay

[shut spear]

oh wait

i didn’t even read the question im sorry

[worn light]

Its alright

[shut spear]

you can simplify 106/16

[worn light]

How?

[shut spear]

both are even numbers

[worn light]

16 can go to 4 right

And 106 idk 😭

[shut spear]

if they’re both even, it means that they are divisible by 2

[topaz sinew]

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.

[worn light]

106 is equal to 53 right

[worn light]

If divided

And 16 is 4?

[shut spear]

yup

no

we’re just dividing the numerator and denominator by 2

[worn light]

Oh 16 is 8

After that what am i gonna do with the factors?

Okay then?

[shut spear]

find the square root

of the fraction

[worn light]

Ok

53 doesnt have a square root

[shut spear]

yeah so leave it with the square root sign

[worn light]

So just √53•2?

Or 53√2?

[shut spear]

for the numerator?

or the entire fraction?

[worn light]

Numerator

[shut spear]

it's just root 53

or actually

or you finding the square root of 106/16

or doing it with the simplified one

[worn light]

Huh?

[shut spear]

sorry for the bad phrasing

so like

what's the fraction you have right now

[worn light]

106/16

[shut spear]

ok

[worn light]

Its alright

[shut spear]

so now take the square root of the numerator and then the denominator

[worn light]

The square root of 106 is a decimal

[shut spear]

yeah so keep it as is

[worn light]

Okay so 106/4?

[shut spear]

√(106)/4

[worn light]

Oh okay

Then?

[shut spear]

so now you have c so just do what u normally do for the trig functions

[worn light]

So c is √(106)/4?

[shut spear]

yeah like this (took the ss bc typing it is a bit ambiguous)

[worn light]

Then how do i find the sin theta?

[shut spear]

which side is the opposite of theta

[worn light]

5/4

[shut spear]

ok

and which side is the hypotenuse

[worn light]

√106/4?

[shut spear]

yup

[worn light]

So how do i write that

[shut spear]

so then do the opposite divided by the hypotenuse

[shut spear]

it's division so write the first fraction and divide it by the 2nd one

[worn light]

So 5/4 ÷ √106/4

[shut spear]

yup

bc sin of theta = the opposite over the hypotenuse

[worn light]

But is that even allowed?

I mean fraction on denominator and numerator

Isnt sin supposed to be whole numbers?

[shut spear]

no it doesn't matter

it's just the ratio of the opposite side to the hypotenuse

also im doing hw rn so i can't respond that quick

[worn light]

Oh okay sorry for bothering

Heres what my teacher taught us

[shut spear]

ya

sin in that example is a fraction

[worn light]

Mhm

So i write it as

Like that?

[shut spear]

it should be 5/4 on the numerator

and then simplify

[worn light]

Oh okay

How do i simplify it

[shut spear]

do u know how to divide fractions

[worn light]

Yes

Like that?

I already flipped 106 and 4

[empty sail]

What happened to the sqrt?

[worn light]

What sqrt

[empty sail]

It was sqrt(106), was it not?

[worn light]

Yeah

[empty sail]

Why did the sqrt disappear?

[worn light]

I forgot to add it

I added it now

[empty sail]

You can't just add it

It messes up the math

[worn light]

We were just dividing 5/4 and √106/4

[empty sail]

And still, you can't just insert a sqrt

You messes up the math

[worn light]

It didnt change the answer

[empty sail]

It does

There is a difference between $4 \cdot 106$ and $4 \cdot \sqrt{106}$

[thorny flame]

dldh06

[empty sail]

You did 4 * 106 first, then put in the root, it messes up the math

[worn light]

So like that?

[empty sail]

Yes

[worn light]

Okay

What do i do now

[empty sail]

Multiply fractions

The concept is still the same

[worn light]

20/424

[empty sail]

No

[worn light]

What then

[empty sail]

Do you know how to do $2 \cdot \sqrt{5}$?

[thorny flame]

dldh06

[worn light]

No

[empty sail]

Here, I guess this works
https://www.youtube.com/watch?v=5hT7yYZr-ng&ab_channel=eHowEducation

[worn light]

Okay thank youu

Ill get back to you later after i watch the video and showered

My brain is dying

Okay byee

OH WAIT OMG THANK YOU SO MUCH

THAT EXPLAINS EVERYTHING

My teacher didnt teach us that so i was very confused

[topaz sinew]

@worn light Has your question been resolved?

Channel closed

Closed by @worn light

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.

[neon iron]

A common math doubt ,,
This doubt doesn't specific on any math branch ,,

What is the meaning of this if someone written like this p(x) , V(G) etc ...
What this represents?

[neon iron]

.close

[topaz sinew]

Channel closed

Closed by @sterile thunder

Use .reopen if this was a mistake.

[trim zenith]

.open

fuck this

[vernal vale]

you okay?

see #❓how-to-get-help

[trim zenith]

nah

thx

[vernal vale]

you need to create a new channel

well, claim an open one

[vernal vale]

did you figure it out?

[slim storm]

.open

How do I?..

[topaz sinew]

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.

[wild breach]

how would i do (i)?

[topaz sinew]

@wild breach Has your question been resolved?

[wild breach]

<@&286206848099549185>

[thorny flame]

Ariel1300

[wild breach]

yh P(E intersect F) = P(E) + P(F) - P(EUF) right

[blissful acorn]

Yes

[wild breach]

but then you have the -

which doesnt allow me to get upper bound?

[thorny flame]

Ariel1300

[blissful acorn]

Or of any probability of event in general

[wild breach]

P(EUF) <= P(E) + P(F)

[blissful acorn]

yes, but you can find a better bound then: P(E) + P(F)

[wild breach]

i am not sure

[thorny flame]

Ariel1300

[blissful acorn]

but for any event A, the maximum value of P(A) is 1

[thorny flame]

Ariel1300

[blissful acorn]

So the upper bound is 1

[thorny flame]

Ariel1300

[blissful acorn]

@wild breach Do you get this?

[wild breach]

ok yh i got this now

what about part (ii)

[blissful acorn]

Just create something like choosing a random number from 1 to 5 or something

And choose 2 events that matches the given information

[topaz sinew]

@wild breach Has your question been resolved?

Channel closed

Closed by @wild breach

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.

[frozen sphinx]

This is part of a larger problem: I found this table of a transition function, and I need to find a general expression for f(s, a).

[frozen sphinx]

Given this information:

I know there's a pattern here, using modular arithmetic, but I can't see it (after like a day of trial and error) can someone point me in the right direction?

Because then I have to prove my transition function works with the machine via induction, but I can't do that w/out a transition function :,)

\

[topaz sinew]

@frozen sphinx Has your question been resolved?

[frozen sphinx]

<@&286206848099549185> :,)

[frozen sphinx]

<@&286206848099549185>

<@&286206848099549185>

[topaz sinew]

@frozen sphinx Has your question been resolved?

[frozen sphinx]

<@&286206848099549185>

.close

[topaz sinew]

Channel closed

Closed by @frozen sphinx

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.

[iron sapphire]

Help

[iron sapphire]

How do I further simplify this

Am I able to divided by like 2

[mellow venture]

split it into two fractions

[iron sapphire]

Wym

-4/4 and 2/4

[mellow venture]

do u know how to split a fraction into two fractions when numerator is a sum

(2sqrt(2)/4*

[iron sapphire]

It was a quadratic equation

[mellow venture]

$\frac{a+b}{a}$

[thorny flame]

Triangular Hebesphenorotunda

[mellow venture]

how would u split this

[iron sapphire]

Uh

Is it a/a b/a idk

[mellow venture]

a/a b/a what?

what should be inbetween a/a and b/a?

[iron sapphire]

Bruh

[mellow venture]

?

[iron sapphire]

I don’t get what ur trying to say

[mellow venture]

did u mean a/a + b/a?

[iron sapphire]

Yeah

[mellow venture]

alrighty

now do that same thing to yours

[iron sapphire]

Do you put the -4 / 4 ????

[mellow venture]

thats first fraction

what would second be

[iron sapphire]

2sqrt2/4

[mellow venture]

yes

[iron sapphire]

2 radical 2 / 4

[mellow venture]

now simplify each fraction

[iron sapphire]

The answer is This on my math book I didn’t get this

@mellow venture

[mellow venture]

what did u get when u simplified each fraction

[iron sapphire]

-4/4 is -1

[mellow venture]

yes

what about other

[iron sapphire]

And I got 1/2 sqrt 2

Is that wrong

[mellow venture]

no

$-1 +- \frac{\sqrt{2}}{2}$

[thorny flame]

Triangular Hebesphenorotunda

[mellow venture]

is also correct to write

[iron sapphire]

How did they get this answer ?

[mellow venture]

if u add these fractions ur gonna get that

[slow trout]

Is it not correct to just divide each term by a factor of 2? Just curious

[iron sapphire]

This would be correct way to right?

Write *

@mellow venture

[mellow venture]

yes

[iron sapphire]

Alright

That was confusing me

[topaz sinew]

@iron sapphire Has your question been resolved?

[topaz sinew]

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.

[tawdry chasm]

Anyone know what's up with this?

[tawdry chasm]

I'm a little confused there's 2 means

[wide berry]

One is the population mean and one is the sample mean

They use bad notation. Usually a capital letter is used for random variables. We are given $X \sim \mathcal{N}(250,20^2)$. We take a sample $X_1,...,X_{600}$ from this. The mean then has distribution $\bar{X} \sim \mathcal{N}(250, 20^2/600)$. The test statistic is thus $$z=\dfrac{\bar{x}-250}{20/\sqrt{600}}$$

[thorny flame]

1345631

[wide berry]

You would use a small letter for realisations of a random variable (unless you want to go against established norms, which isn't recommended)

[tawdry chasm]

Oh yeah, my bad lol

[topaz sinew]

@tawdry chasm Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[dawn hawk]

A sporting goods stores sells footballs, basketballs, and volleyballs. A football costs $35, a basketball costs, and a volleyball costs $15. On a given day, the store sold 5 times as many footballs as volleyballs. They brought in a total of $3750 that day, and the money made from basketballs alone was 4 times the money made from volleyballs alone. How many footballs, basketballs, and volleyballs were sold?

USING MATRIX

I'm not sure how to set up the matrix for this problem or the right numbers to use for the equations

[empty sail]

What's the cost of the basketball?

[dawn hawk]

25

This is what I got but something isnt right

[empty sail]

Why are you pinging helpers?

This isn't your channel

[dawn hawk]

no its not

[empty sail]

Wtf is going on?

[dawn hawk]

idk this dude just came into this channel

please help

[thorn briar]

sorry about that.

[worthy storm]

why do you say that something isn't right?

it agrees with what matlab finds for the rref

(i'm too lazy to verify it manually)

[dawn hawk]

the problem is it shouldnt be 0's for the other 2

so i kapoofed something

[worthy storm]

other 2 what?

which elements do you mean?

[worthy storm]

why shouldn't it be?

[dawn hawk]

How many footballs, basketballs, and volleyballs were sold?

it should be 3 different nums

and 0 doesnt make sense lol

[worthy storm]

oh

well assuming the original matrix is correct, the RREF is also correct

[dawn hawk]

i dont think the original is correct

thats da problemo

and im not sure how to fix

[worthy storm]

you can see that indeed (0,0,250)^T is a solution to the equations represented by the original matrix

since 250*15 = 3750

ah i just scrolled up higher and saw the original problem, let me read it over

A football costs $35, a basketball costs, and a volleyball costs $15. - there's a missing price for the basketball

[dawn hawk]

oh 25

[worthy storm]

ok thanks

[thorn briar]

A football costs $35, a basketball costs, and a volleyball costs $15. [..] They brought in a total of $3750 that day
35f +25b + 15v = 3750
On a given day, the store sold 5 times as many footballs as volleyballs.
f = 5v
the money made from basketballs alone was 4 times the money made from volleyballs alone
25b = 4 * 15v

(im assuming a basketball costs $25, you seem to have omitted it from your statement)

use those 3 equations to set up your matrix (you'll probably have to "solve them", i.e. put the variables on one side)

here f, b, v are the number of footballs, basketballs, and volleyballs sold respectively

im not sure why you set up every equation to equal 3750

the only case where the 3750 mattered was in the total profit

[dawn hawk]

is this closer

[worthy storm]

i agree with @thorn briar 's equations

[dawn hawk]

ik i messed something up

[thorn briar]

i gave you the 3 equations to use, you seem to have strayed from them

remember that matrices represent systems of equations

for example, the second row of your matrix says that 35f + 15v = 5

which did not come up at all in the problem

(and is certainly impossible, since you can't sell a fraction of a ball)

[dawn hawk]

lol

[worthy storm]

(and in words, it says that you only made $5 from the footballs and volleyballs)

[thorn briar]

there are 3 equations:

35f +25b + 15v = 3750
f = 5v
25b = 4 * 15v

in order to put these in matrix form, you're going to want to move all the variables to the same side. some rearranging gets you this:

35f +25b + 15v = 3750
f - 5v = 0
-60v + 25b = 0

do you see how i did that?

[dawn hawk]

yeah

[thorn briar]

and now that you have 3 linear equations, you can make a matrix out of them.

[dawn hawk]

thanks that answer makes a lot more sense

.close

[topaz sinew]

Channel closed

Closed by @dawn hawk

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.

[neon iron]

Hey in this question I am not sure if I am doing it right.. I did (P google I advert ) = ( P (google) * P(advert I google) ) / P (advert) = (0.5*0.2)/0.4

The thing is that correct to divide by 0.4? like the sum of all probabilities?

[placid root]

hello

im new here

[empty sail]

#❓how-to-get-help

[neon iron]

<@&286206848099549185>

[distant vine]

you have the right reasoning but your P(advert) is off

you cannot sum them like that

[neon iron]

I guess so but I am not sure how to work with P(advert)

[drifting swift]

can i suggest a slightly cheaty but at the same time somewhat intuitive way to solve this problem?

[distant vine]

because your given P(advert | google), P(advert | facebook) and p(advert | new account)

[neon iron]

yes exactly but like I want the total of it idk how to find it except sum or I cant think of anything else rn

[neon iron]

of course

[drifting swift]

imagine a cohort of 100 new users of the website

50 of them sign up with google, 40 of them sign up with facebook, and 10 make a new account

among the google users, 20% click on the ad - that makes 50 * 0.2 = 10 clicks

among the facebook and new-account users, 10% click on the ad - that makes (40 + 10) * 0.1 = 5 clicks

so there are 15 clicks in total

of which 10 came from google users

therefore P(google user | clicked on ad) = 10/15 = 2/3

[neon iron]

omg that makes sense yes

thanks @drifting swift

.close

[topaz sinew]

Channel closed

Closed by @naive temple

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.

[young violet]

i need help with 1

[hazy pumice]

well, n/(n+1) is less than 1 and monotonically decreasing increasing but approaching 1 for all n, right?

so you just need to worry about what happens to (2x)^n

looks like |x| < 1/2

you have answers?

[worthy storm]

n/(n+1) is monotonically increasing, not decreasing. 1/2, 2/3, 3/4, 4/5, ...

[young violet]

i do have answers

[hazy pumice]

ok there you go

[hazy pumice]

ooh you are right

[young violet]

i just dont know how to get there

[worthy storm]

i don't think it affects the outcome

if you want to make it a bit more formal you could use the ratio test

[young violet]

is that the

a2 - a1

or

a1/1-r

[worthy storm]

$\lim_{n \to \infty}\frac{a_{n+1}}{a_n}$

[thorny flame]

OurBelovedBungo

[young violet]

oh

right

[hazy pumice]

I ❤️ you, @deep stone .

[worthy storm]

assuming that limit exists: if the limit is less than 1 then the series converges, if it is greater than 1 then it diverges, if it equals 1 then it's inconclusive

[young violet]

but how do i find R

[worthy storm]

well start by forming the ratio $\frac{a_{n+1}}{a_n}$

[thorny flame]

OurBelovedBungo

[worthy storm]

$a_{n} = \frac{n \cdot (2x)^n}{n+1}$, what is $a_{n+1}$?

[thorny flame]

OurBelovedBungo

[young violet]

uhh

can i simplify it to

(2x)^n +1?

[worthy storm]

how?

[young violet]

cancelling both ns

oh wait

[worthy storm]

no it's $\frac{n}{n+1}$

[thorny flame]

OurBelovedBungo

[worthy storm]

you can't just cancel the n's in that

it won't matter because we're gonna take limits, which will take care of that factor

but for now keep it

[young violet]

ok

so is it just that whole fraction + 1?

[worthy storm]

well you get $a_{n+1}$ by replacing all the n's with n+1

[thorny flame]

OurBelovedBungo

[young violet]

oh

so

(n+1)(2x)^(n+1)/(n+1)+1...?

[worthy storm]

yep

where the (n+1)+1 in the denom is also known as n+2

[young violet]

i see

and i divide that by the original?

[worthy storm]

typesetting to make it easier to see: $a_{n+1} = \frac{(n+1)(2x)^{n+1}}{n+2}$

[thorny flame]

OurBelovedBungo

[young violet]

ty

[worthy storm]

so now $a_{n+1}/a_n$ is what we just got times the reciprocal of the previous one

[thorny flame]

OurBelovedBungo

[worthy storm]

so it's $\frac{a_{n+1}}{a_n} = \frac{(n+1)(2x)^{n+1}}{n+2} \cdot \frac{n+1}{n(2x)^n}$

[thorny flame]

OurBelovedBungo

[young violet]

wow this looks crazy

and if i solve that i should get my R?

[worthy storm]

yeah but it turns out ok

i'll simplify it a bit:

$\frac{a_{n+1}}{a_n} = \frac{(n+1)^2}{(n+2)n}\cdot (2x)$

[thorny flame]

OurBelovedBungo

[worthy storm]

now remember we're taking limit as n -> infinity

that whole first fraction with the n+1 squared over n+2 times n

the limit of that is just 1

so you are left with 2x

[young violet]

ohh

[worthy storm]

so the ratio test tells you that the series converges if 2x < 1

and diverges if 2x > 1

and that's where you get the radius of convergence

2x < 1 is also known as x < 1/2

[young violet]

OHHH

[hazy pumice]

[worthy storm]

so it matches the earlier reasoning

but with a more rigorous justification

[young violet]

okay ty

[hazy pumice]

[young violet]

and for the interval

its just between

its negative and positive?

[worthy storm]

yeah so far you know it converges on (-1/2, 1/2)

and you know it diverges on (1/2,infinity) and on (-infinity, -1/2)

but you don't know yet what happens at x=1/2 and x=-1/2

you have to handle those separately

[young violet]

tysm

[worthy storm]

pleasure

[hazy pumice]

bye, @worthy storm

[worthy storm]

cheers!

[hazy pumice]

he's flying off to answer more in-progress math problems in another city...God bless'im.

:🇺🇲

[topaz sinew]

@young violet Has your question been resolved?

[topaz sinew]

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.

[fallow hollow]

what determines how many critical points a function can have? I know its when the derivative = 0 or anything/0

[fallow hollow]

I found 2 for -3x^5 + 5x^3

[neon iron]

It depends

for each function there are different number of critical points

Ig

What on

Earth

Is that

[rare isle]

for a polynomial there are no more than degree-1 critical points

[placid root]

Sans possessed

btw i just guessing answers for my exam now

atleast he has one

[neon iron]

<@&268886789983436800> @trim zenith is posting random stuff -_-

[placid root]

(Only Math Relevant Topics here boi

[neon iron]

Dude

What on earth are you doing

[fallow hollow]

.close

[topaz sinew]

Channel closed

Closed by @fallow hollow

Use .reopen if this was a mistake.

[rare isle]

can you shut up

[thorn briar]

b&

[fallow hollow]

*3

[topaz sinew]

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.

[rotund tapir]

I'm trying to find the triple integral to convert it to cylindrical coordinates but I'm stuck trying to find the limits

[rotund tapir]

I had let r^2=x^2+y^2+z^2 and r^2=(x-1)^2+y^2+z^2

[topaz sinew]

@rotund tapir Has your question been resolved?

[rotund tapir]

<@&286206848099549185>

[topaz sinew]

@rotund tapir Has your question been resolved?

Channel closed

Closed by @rotund tapir

Use .reopen if this was a mistake.

[topaz sinew]

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.

[topaz sinew]

@queen night Has your question been resolved?

[sweet shard]

this fucking problem

I guess do it by cases. Let P(x) = Q(x)/x^k. Then consider |x| < 1 and |x| >= 1 separately

Use triangle inequality or reverse triangle inequality

[lyric pagoda]

Hmm, maybe I'm being simple-minded but I don't see the problem?

[sweet shard]

what's your idea

[lyric pagoda]

Never mind, I was being simple-minded. It's tricky!

@sweet shard, I'm not sure it's good form to post the link to a homework/self-study problem, but I found a clever solution on SE.

[sweet shard]

i do it all the time

[lyric pagoda]

https://math.stackexchange.com/questions/2280479/domain-over-which-a-polynomial-is-strictly-positive

[sweet shard]

yea they use reverse triangle inequality

or actually even something better with the max

[lyric pagoda]

Nasty problem.

@queen night, take a look, and if you're taking the ISI entrance exam on Sunday, good luck!

[queen night]

Thankyou and yes i am giving the exam.

Are you also giving it?

[lyric pagoda]

Yes, the M. Stat.

[queen night]

Oh....all the best

Btw from where you did(or doing) your graduation?

[lyric pagoda]

No personal questions. :P

[queen night]

Ok sorry

[neon iron]

isi 2017

[topaz sinew]

@queen night Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

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.

[marsh mortar]

,,,

[marsh mortar]

bit of a silly question

But

Can you deduce from the multiplication of two complex numbers whether they are perpendicular or not

I am aware of the dot product of the coordinates, but not looking for that

[wide berry]

No. You need the dot product

[marsh mortar]

ok

thx

.close

[topaz sinew]

Channel closed

Closed by @marsh mortar

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.

[hard furnace]

how I can prove that this set go down?

[topaz sinew]

@hard furnace Has your question been resolved?

[worldly tendon]

a(n+1) = sqrt(a(n) + 6) < a(n)
a(n) + 6 < a(n)^2
simplifies to proving a(n) > 3

Induction:
assume a(n) > 3
then a(n+1) = sqrt(a(n) + 6) > 3
a(n) + 6 > 9
a(n) > 3: TRUE
now initial case a(1) > 12, thus a(1) > 3: TRUE

@hard furnace

[hard furnace]

I need to show it go down

[worldly tendon]

that’s what i just did…

read it

[hard furnace]

ok .close

.close

[topaz sinew]

Channel closed

Closed by @hard furnace

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.

[topaz sinew]

Please don't occupy multiple help channels.

[sturdy oracle]

<@&268886789983436800> Shitposter moment

[topaz sinew]

Channel closed

Closed due to the original message being deleted

[thorn briar]

.close

[visual oracle]

Balls

[topaz sinew]

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.

[fresh sun]

GCD(m,n)=a^4
LCM(m,n)=a^5xb^6 or a^6xb^5

so max is 2 prime divisors

right?

wait no

ok I did it wrong

LCM could be a^4xb^2xc^1

so max 3?

[worldly tendon]

yes, if n = a^4 b^2 c and m = a^4

3 primes

the greatest number of prime divisors for n is achieved when n = LCM, so the question can be reduced to how many prime divisors LCM has.
since 30 = 2(3)(5), the 30 divisors consist of 3 prime divisors

[fresh sun]

ok ty

.close

[topaz sinew]

Channel closed

Closed by @fresh sun

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.

[mossy nest]

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

[thorny flame]

Michal

[topaz sinew]

Please don't occupy multiple help channels.

[mossy nest]

converges or diverges ?

[pure helm]

Try root test

[mossy nest]

idk what it is

or i think that the values approaches 0

if is it what you meant

[pure helm]

$\lim_{n \to \infty} \left ( \frac{1}{(2n - 1)^{n}} \right )^{\frac{1}{n}}$

[thorny flame]

Sup?

[pure helm]

If this is > 1, the series diverges. If this is < 1, the series converges.

If it equals 1, you have to choose another test.

Btw, if the terms go to 0, that doesn't mean the series converges.

For example, 1/n.

Terms go to 0 but the series diverges.

However, if the series converges, then the terms must go to 0.

[mossy nest]

why exponent is 1/n

[pure helm]

For the root test, you take the nth root.

So that means raising to a power of 1/n.

[mossy nest]

hmm

probably im supposed to use convergence criterion

i need to find sequence that is larger and converges

[pure helm]

Ah

comparison test

[mystic cobalt]

hm interesting question

[mossy nest]

yes this is probably it

[mystic cobalt]

need help?

or you figured it out?

[mossy nest]

i need to solve it

[mystic cobalt]

the answer is 1

no?

[mossy nest]

i need only find out if it converges or diverges

using comparison test

[pure helm]

Have you learned that the series 1/(n^n) converges?

[mystic cobalt]

well it diverges, because the limit is 1

idk if it converges

[mossy nest]

no

[pure helm]

Hmm.

[mossy nest]

probably i need to find some geometric sequence

[mossy nest]

but this is geometric sequence

or not ?

[pure helm]

No

[mossy nest]

$\left\frac{1}{n}\right^n$

[pure helm]

Can you tell me any series which converges?

[thorny flame]

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

[pure helm]

Common one

$\left ( \frac{1}{n} \right )^{n}$

[thorny flame]

Sup?

[mossy nest]

thx

[pure helm]

Do you know that the series 1/n^2 converges?

This is a p-series, with p = 2.

[mossy nest]

hmm

idk, in my book were just geometric sequences mentioned

[mossy nest]

and why this is not a geometric sequence ? because of n^n

?

[pure helm]

Because of the (1/n) inside the power of n

the ratio keeps changing

The ratio has to be constant

[mossy nest]

and $\left ( \frac{1}{n} \right )^{2}$

[thorny flame]

Michal

[mossy nest]

power cant be constant ?

[pure helm]

Nope

Okay, can you prove 2n - 1 >= 1.5 for n>=2?

It is pretty easy.

If you cant prove it, we'll get to that later

Put in n=2, n=3, you'll see 2n-1 is > 1.5

[mossy nest]

$ \frac{1}{(2n-1)^2} = \left ( \frac{1}{2n-1} \right ) ^2 \leq \left ( \frac{1}{2} \right ) ^n $

oh

[pure helm]

$\frac{1}{(2n-1)^{2}} = \left ( \frac{1}{2n-1} \right )^{2} \leq \left ( \frac{1}{n} \right )^{2}$

[thorny flame]

Sup?

[mossy nest]

i made a mistake

[pure helm]

Can you do what I told you?

[mossy nest]

$\frac{1}{(2n-1)^{2}} = \left ( \frac{1}{2n-1} \right )^{2} \leq \left ( \frac{1}{2} \right )^{n}$

[thorny flame]

Michal

[mossy nest]

for n > 3 for example

[pure helm]

Okay, that's a good try.

[mossy nest]

yes, i will take a look

[pure helm]

But you have [1/(2n-1)]^n

Not [1/(2n-1)]^2

If you manage to prove that 2n - 1 > 1.5 for n >=2

Then you will have (2n-1)^n > (1.5)^n

And so [1/(2n-1)^n] < [1/(1.5)^n]

And [1/(1.5)^n] is a geometric series which converges with r = 1/1.5 < 1

[mossy nest]

uhm got it

[mossy nest]

is it a problem ?

(1/2) will be bigger always

[pure helm]

this isnt true btw for n>=1

[mossy nest]

i know

[pure helm]

You need to basically find some number c such that 2n - 1 > c for some n >= N

where c > 1

and then you have [1/(2n-1)]^n < (1/c)^n

And since c > 1, your ratio 1/c is < 1

and thus the geometric series converges

I used c = 1.5, you can use c = 500 or anything > 1 really

[mossy nest]

ok thanks for help

[pure helm]

np

[mossy nest]

.close

[topaz sinew]

Channel closed

Closed by @mossy nest

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.

[mild oasis]

I need to find a number that :
Has sum of digits = 6
Divides 2 but not 4
Has 8 divisors
Has sum of divisors divide 10
And last but not least
Its not equal to 16k + 14 (for any k)

[mild oasis]

Rn ive got that it must have 3 prime factors

$$2 , _ , _$$

[thorny flame]

Pluton

[long stirrup]

i found it

just guessed

[mild oasis]

Lol

The question states can you guess the number? So its a yes/no question lol

I mean if theres 2 numbers ig its a no

[long stirrup]

how did you figure out what you did?

why 3 factors?

[mild oasis]

Bc if it has 3 prime factors its divisors are
1
A
B
C
AB
AC
BC
ABC

If it has more or less it doesnt have 8 divisors

[long stirrup]

that's not true

[mild oasis]

How so

[long stirrup]

54

has 2 prime factors

but 8 divisors

[mild oasis]

Umm what are its 8 divisors?

[long stirrup]

54 1 2 3 6 9 18 27

[mild oasis]

Just checked it has 4 prime factors

[long stirrup]

yeah

4 or 2

depends if you count duplciates

[mild oasis]

Oh so i need to count duplicates too

[long stirrup]

the one i guessed does have 3 though

[mild oasis]

And i got
$$(c + 1)(b + 1)$$
Must be divisible by 10

[thorny flame]

Pluton

[mild oasis]

Absolutely useless

I aint checking infinite prime solutions to that

Its basically a guessing game

Ok its time.
Im going to see the solution

... ok

,close

.close

[topaz sinew]

Channel closed

Closed by @mild oasis

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.

[tiny ginkgo]

I believe this is implicit differentiation

and I think the chain rule is involved

[hazy pumice]

Chain rule, I don't think so

But it isn't hard

Product rule is here

[tiny ginkgo]

Okay would you say bring one side of the equation to the other?

[hazy pumice]

I guess implicit differentiation is kinda chain rule

Just wait for dy/dx to fall out and solve for it

dy/dx will appear in the second and third terms

Factor it out

And solve for it

[tiny ginkgo]

4xy+y^3

[hazy pumice]

Those are the second and third terms, before differentiating

[tiny ginkgo]

4(y+x(y'))+3y^2

[wary oak]

there is chain rule involved

d/dx [y(x)]^3

[tiny ginkgo]

okay should we set that up first

[hazy pumice]

...

@tiny ginkgo just differentiate each term one at a time

We ("implicitly") assume that y is a function of x

[tiny ginkgo]

3x^2 + 4(x+y d/dx(y)) + 3y^2 = 2x

[hazy pumice]

Thats why the step (yes, chain rule) when we differentiate a term with y in it is to do dy/dx...since we don't know exactly what function y us, only that it is a function of x

[tiny ginkgo]

ahhh i see

[hazy pumice]

I'm in Dr Strange

Not starring, just watching

x^3 + 4xy + y^3 = x^2 + 39
Differentiating
3x^2 + 4x(dy/dx) + 4y + 3y^2 (dy/dx) = 2x

I think you got this far but notation is off

[tiny ginkgo]

4y okay

so now cancel variables?

or y's?

[hazy pumice]

You just need to isolate and solve for dy/dx

...and then plug in the given values for x and y

[tiny ginkgo]

so it'd be 4x+3y^2

=2x