help-17

[tepid sable]

Yeah

Oh

Add 2pi or something LIEK that

[calm light]

since this is degrees, we need to add 360 but yeah

[tepid sable]

I mean add 360 degrees

[calm light]

we can convert to rad after

[tepid sable]

Yeah so 311.4096

[calm light]

ok, so what quadrant is that in?

[tepid sable]

4th

[calm light]

alright, and what other quadrant has negative sine?

[tepid sable]

First

[calm light]

remember that sine represents the y-value on the unit circle

where else is the y-value of the unit circle negative?

[tepid sable]

3rd quadrant

[calm light]

yes

so, let’s think about what angle in the third quadrant would give us the same result

[tepid sable]

I would say reflect it over the years axis

[calm light]

alright

now how could we get the angle from that?

[tepid sable]

Subtract 180 which is 131.4096

[calm light]

but don’t forget that the third quadrant starts at 180

[tepid sable]

Oh right

[calm light]

so you’ll need to add another 180

[tepid sable]

So I’m back at 311.4096

[calm light]

add 180 to that

or do you mean 311.4096

[tepid sable]

That’s what I meant

Yeah

Mb

[calm light]

you need to subtract the negative angle from before from 180

[tepid sable]

Huh. I got 179.99996

So do I round up and say it’s pi?

I mean I think it is

[calm light]

should be 180-(-48.59)

[tepid sable]

Oh

228

.59

[calm light]

yep

those should be the only 2 solutions in that interval

[tepid sable]

So 311.4096 and 228.59?

[calm light]

yep

[tepid sable]

Thank you so much, the teacher picked some quiet kid to example the problem and I couldn’t hear them

[calm light]

lmao poor kid

[vocal sleet]

@tepid sable Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

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.

[hushed frigate]

,rotate

Please help me with this question

[hushed frigate]

I am stuck at this step

Please help 🙏

[mellow oyster]

multiply top and bottom by sec^2, then rewrite the bottom sec^2 as 1 + tan^2, then let u = tanx

[hushed frigate]

But what about the pi/2 how do I integrate

The pi/2 is out of domain of tan

How do I do it

[mellow oyster]

limit of tanx as x approaches pi/2 from below is infinity

[hushed frigate]

Can you please show it

I mean how to I change the limits

[mellow oyster]

when you make the u sub, the lower bound becomes tan(0) = 0 and the upper bound becomes tan(pi/2) = infinty

[hushed frigate]

Since when substituting tanx as u I'll have to change the limits right?

[mellow oyster]

yes

[hushed frigate]

Oh right

[mellow oyster]

the integral is over the interval 0 < x < pi/2

so you want lim as x approaches pi/2 of tan(x)

[hushed frigate]

So I just write infinity and it becomes improper integra?

[mellow oyster]

yes

specifically since you're approaching pi/2 from below

[hushed frigate]

Ok bro I'll do wait

[mellow oyster]

limit is infinity

[hushed frigate]

,rotate

Now I'll substitute

[hushed frigate]

,rotate

[hushed frigate]

Is this correct?

[mellow oyster]

yes

[vocal sleet]

@hushed frigate Has your question been resolved?

Channel closed

Closed by @hushed frigate

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.

[formal obsidian]

im always getting 10/3ft/s

and its not the right answerr

$\frac{15}{6}=\frac{x+y}{y}$

[twin meteor]

vinch

[formal obsidian]

where y is the length of the shadow of the dude

and x is the distance from the pole to the dude

kinda looks like this

$\frac{dx}{dt}=5$

[twin meteor]

vinch

[formal obsidian]

and im finding $\frac{dy}{dt}$

[twin meteor]

vinch

[formal obsidian]

that's all the information i can give

[surreal basin]

you also forgot that x at this moment in time is 40

[formal obsidian]

yup

[surreal basin]

this equation could be written simpler as (x+y)/15 = y/6 instead, try using that variant then redoing the work

[formal obsidian]

and that kinda throws the wrench

[formal obsidian]

alrightt

@surreal basin i'm getting $6x+6y=15y$

[twin meteor]

vinch

[formal obsidian]

the problem is if x=40, i cant really do that

if I implicitly differentiatie this, $6\frac{dx}{dt}+6\frac{dy}{dt}=15\frac{dy}{dt}$

[twin meteor]

vinch

[formal obsidian]

now i know what dx/dt is

[surreal basin]

also youre finding d(x+y)/dt not dy/dt

[formal obsidian]

ohh

[surreal basin]

also you should consider subtracting 6y from both sides

bit of improvement overall

[formal obsidian]

wait huh?

then how would i even get d(x+y)/dt?

[surreal basin]

...

dx/dt + dy/dt

you still find dy/dt

then you

actually as a question, if you knew dx/dt and dy/dt, how would you find d(x+y)/dt

[formal obsidian]

find x+y first?

then differentiate it w repsect to t

[surreal basin]

you find dx/dt
and you find dy/dt
then you add them together

[formal obsidian]

wait, that's possible??

i never knew that lmao

[surreal basin]

that didnt seem to click when I said dx/dt + dy/dt the first time

what did you think I was doing

[formal obsidian]

uhm idk?

so your just adding the rates of x and y

that makes sense

i actually got the correct answer now

[formal obsidian]

but is it a general property?

[surreal basin]

x + y = x + y

dx/dt + dy/dt = d(x + y)/dt

yes

[formal obsidian]

dang

alright thanks!!

[surreal basin]

np

[formal obsidian]

apparently i was missing to add dx/dt to dy/dt lmao

.close

[vocal sleet]

Channel closed

Closed by @formal obsidian

Use .reopen if this was a mistake.

[vocal sleet]

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.

[vast shale]

I'm not sure what to do to solve this expression

[vast shale]

I get the gist of inverse trig functions

Just not this question

[sullen shoal]

That is basically arcsine(1/root2)

So assume some x = arcsine(1/root2)

So then sinx is 1/root2

U can solve it from there ig

@vast shale

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[vocal sleet]

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.

[tender isle]

Is my graph on the second screenshot correct for the task in the first screenshot?

[gaunt frost]

How is (a-b)² = a²-2ab+b²?

[tender isle]

wait did I open in the wrong chat?

[glacial osprey]

#❓how-to-get-help

Unless the question you asked has some sort of deep-ish maybe relation to what they asked

[oblique kettle]

yes, seems all good to me, nice

[tender isle]

thank you 🙂

.close

[vocal sleet]

Channel closed

Closed by @tender isle

Use .reopen if this was a mistake.

[vocal sleet]

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.

[regal otter]

Help me with dimensional analysis please. I have trouble on the second question. Please check the answer to my first question also. This is for my general physics class.

[icy plume]

first one is correct

[regal otter]

And second pls?

I'm having trouble because the given is grams per cubic CENTIMETER while the other is kilograms per cubic METER

[icy plume]

That is no problem since you can look at both units seperately

[regal otter]

I'm still confused 😕

[icy plume]

You know that 1g = 0.001kg. For the volume you know that 1cm = 0.01m, so a factor of 10^-2

now if you want to convert cm^3 to m^3, you also need a factor (10^-2)^3

[regal otter]

Ohhh

So it's going to be 10^-6 ?

[icy plume]

exactly, your factor is 0.001/10^-6

You can use this to multiply with your original value of 11.3 to get your final answer

[regal otter]

Hmm ok I'll try that

[vocal sleet]

@regal otter Has your question been resolved?

[regal otter]

Uh I can understand but I still have difficulty with the dimensional analysis

Do I first convert 11.3g/cm^3 to g/m^3?

Then it would be like this..?

[vocal sleet]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[regal otter]

.reopen

[vocal sleet]

✅

[oblique kettle]

you have a tendency to convert by multiplying by fractions haha

sometimes its simple but sometimes its tricky

consider converting by substituting!

like...

[regal otter]

Because my teacher taught us to use dimensional analysis, I might get deduction

[oblique kettle]

yes, but like...

1 kg = 10^3 g

so: 1g = 10^(-3) kg

right?

[regal otter]

Yeah I know... but how do I make it like the dimensional analysis

Because even if the answer is the same, the method isn't

[oblique kettle]

i understand :d

[regal otter]

So can you help me please?

[oblique kettle]

yes, im thinking about it

the g/kg is correct

remains the cm3/m3

[regal otter]

I can't wrap my head around it

[oblique kettle]

its easy, dont think too much about it

all you need is these 2

which you know

1 kg = 10^3 g

1 m3 = 10^6 cm3

let me show you how to proceed

$\rho = 11.3 , g/cm^3 = 11.3 \cross \frac{1 , g}{1 , cm^3} \cross \frac{1 , kg}{10^3 , g} \cross \frac{10^6 , cm^3}{1 , m^3}$

you see how i did it?

the same way you did for the first question

1st fraction to convert g to kg, and 2nd to convert cm3 to m3, obviously..

[twin meteor]

Emily

[regal otter]

Isn't the second one supposed to be 1 kg=10^3g?

[oblique kettle]

yes yes, my bad

[regal otter]

Then denominator would be 1000m^3?

[oblique kettle]

why

$\rho = 11.3 , g/cm^3 = 11.3 \cross \frac{1 , g}{1 , cm^3} \cross \frac{10^{-3} , kg}{1 , g} \cross \frac{1 , cm^3}{10^{-6} , m^3}$

[regal otter]

because its 10^3?

[oblique kettle]

theres this way too

$\rho = 11.3 , g/cm^3 = 11.3 \cross \frac{1 , g}{1 , cm^3} \cross \frac{10^{-3} , kg}{1 , g} \cross \frac{1 , cm^3}{10^{-6} , m^3}$

[twin meteor]

Emily

[oblique kettle]

what, no

1 m3 = 10^6 cm3

[regal otter]

Ah alright. So the final answer is 0.0113kg/(10^-6) m^3 ?

[oblique kettle]

after crossing out 1 g with 1g and 1 cm3 with 1 cm3, you're left with

$\rho = 11.3 \cross \frac{10^{-3} , kg}{10^{-6} , m^3}$

[twin meteor]

Emily

[oblique kettle]

what about 10^(-6) !!!

[regal otter]

It's 0.00001?

[oblique kettle]

you want to simplify before plugging into your calculator, or not?

cuz you can just do 11.3 * 10^(-3) / 10^(-6)

[oblique kettle]

idk why you didnt divide by 10^(-6) here!

$\rho = 11.3 \cross \frac{10^{-3} , kg}{10^{-6} , m^3}= \frac{11.3 \cross 10^{-3}}{10^{-6}} ,, kg/m^3$

[twin meteor]

Emily

[oblique kettle]

you can punch that into the calc right away

[regal otter]

I get it now. Sorry. Thank you so much for helping me.

[oblique kettle]

yw!

[regal otter]

.close

[vocal sleet]

Channel closed

Closed by @regal otter

Use .reopen if this was a mistake.

[vocal sleet]

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.

[dire harbor]

um super embarassing but can anyone help

[vast shale]

we meet again

[dire harbor]

oh hey its you

lol

finished my long assignment now its just my easier quiz

im not sure how i got everything wrong twice but yeah

im assuming i made a mistake from the start with the series

[vast shale]

aight lemme see

i can see you used the expansion directly which we studied earlier

but

[dire harbor]

yeah arctan

i assume i did the arctan 5x series right

i guess i just messed up with multiplying the 1/x

[vast shale]

yeah seems like that

expansion seems correct

[desert hornet]

Your integration step is wrong

You forgot the (2n+1) that was already there in the denominator

Also didn’t understand where you got 2n+2 from

[dire harbor]

oh its you again too

[vast shale]

i think she tried multiplying by x and dividing , but the 2n + 2 doesnt make sense

[dire harbor]

oh wait, is thedenominator supposed to be (2n+1)(2n+1) instead of what i did

[desert hornet]

Yes

[dire harbor]

ah ok

yeah thats my bad im not that good with the integral power rule

is everything else with the integrated series correct

[desert hornet]

Yes

[dire harbor]

ok great

i will redo the rest too

ty

[desert hornet]

,w series of arctan(5x)/x at x=0

[twin meteor]

Results provided by WolframAlpha

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

Requested by shikhargupta1207

[dire harbor]

thank you

[vocal sleet]

@dire harbor Has your question been resolved?

Channel closed

Closed by @dire harbor

Use .reopen if this was a mistake.

[vocal sleet]

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.

[heady quest]

Prove that the plane of the plane angle corresponding to an even angle is perpendicular to its edge.

hi so what is that line in the middle

why did they make an angle

And how do i prove this

[vocal sleet]

@heady quest Has your question been resolved?

[vocal sleet]

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.

[plain aurora]

how do i do thisd

[knotty lynx]

Informally, all you have to do is consider how many times that loop iterates for different values of n

[knotty lynx]

Say n = '7', how many times does the loop iterate

[vocal sleet]

@plain aurora Has your question been resolved?

[vocal sleet]

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.

[vast shale]

where does the convolution come from

.close

[vocal sleet]

Channel closed

Closed by @blissful zenith

Use .reopen if this was a mistake.

[vocal sleet]

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.

[gilded cedar]

hi

[gilded cedar]

in order to solve this

my books says

i have to simplify to that

but how can i just "know" to simply to this

how am i suppose to know that

[oak magnet]

Its partial fractions

[brittle charm]

add +1 and -1 in numerator to x^2

then split that

[gilded cedar]

how?

[oak magnet]

He explained well

[gilded cedar]

okay yes, but how can i know to do that, it seem to randomly coming out of nowhere

[oak magnet]

But mostly, its A + B/(x^2 +1) = x^2/(x^2+1)

And try to find A and B

[brittle charm]

it becomes an general observation while you solve multiple questions like this... me too was confused at start when I was learning but gradually you will be able to see these simplification things as you solve these type of questions

[brittle charm]

yea can do this way too

[oak magnet]

If this was x^3/(x^2+1) for example, it would have been like Ax + B + C/(x^2+1)

(Didnt check but B is probably 0 )

[gilded cedar]

thanks

.close

[vocal sleet]

Channel closed

Closed by @gilded cedar

Use .reopen if this was a mistake.

[brittle charm]

wait

[brittle charm]

I guess they just divided it

[vocal sleet]

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.

[vocal sleet]

@tacit escarp Has your question been resolved?

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

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.

[pulsar cliff]

how do i do this

[hard atlas]

to find the first term you plug in n=1 into the formula

but the question for the common difference makes no sense, there is no common difference

[pulsar cliff]

uhmm

finding first term and second term

[pulsar cliff]

and how I'm gonna do the fraction

[hard atlas]

you know how fractions work, right?

if you plug n=1 into the formula it looks like $1+\frac31$

[twin meteor]

Denascite

[pulsar cliff]

ohh

3+1+1?

[hard atlas]

no

[pulsar cliff]

ohh

wait

3+1 divide by 1

?

[hard atlas]

no

[pulsar cliff]

😥

[pulsar cliff]

how

[hard atlas]

you first compute the fraction $\frac31$ which means 3 divided by 1

[twin meteor]

Denascite

[hard atlas]

so thats equal to 3

afterwards you compute 1+3 = 4

[pulsar cliff]

ohhh

and the second term

n=2

ohhh

so

the first term is 4

and the second term

[hard atlas]

are you still there?

[pulsar cliff]

yes

[hard atlas]

have you tried computing the second term?

[hard atlas]

no

[pulsar cliff]

?

[hard atlas]

how did you arrive at 2.5

what grade are you in

[pulsar cliff]

10th grade

meow

[lucid bane]

maybe it would help to write it as n+(3/n). You are interpreting it as (n+3)/n

[hard atlas]

well you need to learn to interpret fractions correctly without having unnecessary brackets

[pulsar cliff]

😖

my friend just gave me a .5 common difference

[hard atlas]

?

well your friend is also wrong

there is no common difference for this sequence

[pulsar cliff]

💀

[hard atlas]

but thats not the problem here

you are unable to compute 2+3/2

you desperately need to revise fractions

[pulsar cliff]

our teacher told us first to find the first and second term

then subtract them to each other to find the common difference

[hard atlas]

that works for other types of sequences

the type of sequences that have a common difference

this one does not have a common difference

[hard atlas]

(those are called arithmetic sequences or arithmetic progressions)

[pulsar cliff]

hhmm oky

one last question

[lucid bane]

!noans

[vocal sleet]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[vast shale]

Oh

[lucid bane]

!nosols

[vocal sleet]

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

[lucid bane]

you know k and m, and you know a_k and a_m

so you can solve for d, which is the common difference.

[pulsar cliff]

5

[lucid bane]

yes

this allows you to get the first term

[pulsar cliff]

ohh

this was just the start of me being a 10th grader

💀

[vocal sleet]

@pulsar cliff Has your question been resolved?

[pulsar cliff]

.close

[vocal sleet]

Channel closed

Closed by @pulsar cliff

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.

[limber pasture]

But the answer is p > -5/2??

[limber pasture]

I don’t know what’s wrong, I have tried asking ChatGPT, but it just gives me a statement like “to make sure that the expression y^2 - 2(p+4)y + p^2 - 4 < 0 well have to take the opposite”

Im like what the hell, the p value comes from us aiming for < 0, then why do we have to take it as > now??

Btw I’ve checked using Desmos and differentiation and the answer do is p > -5/2.

[honest flame]

Guys

What's the problem

[limber pasture]

Idk

I am confused as hell

[ornate terrace]

ive tried before, chat gpt aint the right thing to ask at all

[limber pasture]

This one too, somehow the answer is k > 2

[limber pasture]

Yeah but I don’t think I have better ones to go to

Same with my chemistry physics and math

[ornate terrace]

whats that second line doing

[limber pasture]

Which question?

[ornate terrace]

ah, you got rid of the fraction didnt you

[limber pasture]

I’m sorry for sending the second one here, it only distracts us🙏

[ornate terrace]

thats a weird way but ok

[ornate terrace]

ill help with the second one first

maybe itll help with the other one

[limber pasture]

Sure

[ornate terrace]

its weird

the second line

[limber pasture]

Oh yeah

[ornate terrace]

you multiplied thr denomatior over right?

[limber pasture]

-y

Slight mistake

Ok this ones solved

[ornate terrace]

this also looks like you solved for the roots and not stationary pts

[limber pasture]

Which one?

Lmaoo this is chaotic but funny

Sorry

[ornate terrace]

the second one

sta pts?

shouldnt you do 1st der for that

[limber pasture]

This is through discriminant

Basically to set when the curve equals some constant

Just for convenience I used y

[ornate terrace]

mk

[limber pasture]

To solve for roots: points of the curve intersecting with the constant

Which is the stat pnts

[ornate terrace]

ok

i might be stupid

you said the discriminant of your thing is more than 0 so it has no real roots?? first q

idk seems weird

[ornate terrace]

did you get the >0 and <0 mixed up or is this something that idk

[limber pasture]

In order for the original equation to have 2 sp, discriminant of x > 0; for the y express to be > 0, discriminant of y < 0; solving gives p < -2.5

I don’t see what’s wrong

If the discriminant of y < 0, y don’t have real roots

In which means that y doesn’t touch the y-axis

Yeah everything seems right to me

Can I call the helpers now?

[ornate terrace]

yea do it imma step away

send the img again for them

[limber pasture]

https://media.discordapp.net/attachments/903463353417072641/1268544483998306305/image0.jpg?ex=66accf9d&is=66ab7e1d&hm=1aea6707a704d1dfb1d5b0115c5e1a2b6fcf78b57959c14aa666b28ee596b2b2&

The answer is p > -2.5, I’m confused

<@&286206848099549185>

[honest flame]

hi

Omg Cambridge question

I'll do my best

[ornate terrace]

yo ima just put this here for a sec. its not the way you want, but it might help?

[limber pasture]

Sure do

Hello, anyone?

Anyone?

[vocal sleet]

@limber pasture Has your question been resolved?

[limber pasture]

<@&286206848099549185>

[honest flame]

sup

[limber pasture]

I am still stuck

I don’t see what the problem is

[honest flame]

-_-

I am askinh

What's the question

[honest flame]

What happened to this

It was right

Jing ping me when ur online

[limber pasture]

@honest flame

[honest flame]

Sup

Yeah

[limber pasture]

This is the question and my try

[honest flame]

The answer was correct

[limber pasture]

But the answer provided was p > -2.5

I got p < -2.5

And I’m very sure that p < -2.5 is correct

But I don’t know how to get it

[honest flame]

oh i see

lemme try

[limber pasture]

Also my teacher specifically asks us to use the discriminant

[honest flame]

I see

We have special methods since I'm asian

[limber pasture]

Lmao

Ngl, when I first know about this method, I thought it’s quite genius tbh

[honest flame]

Yeah

So ans is p>-2.5

Right?

@limber pasture

[limber pasture]

Ya

[honest flame]

Find the derivative of y with respect to x:
dy/dx = ((x - 2)(2x + p) - (x^2 + px + 1)) / (x - 2)^2
Simplify the derivative:
dy/dx = (2x^2 + px - 4x - 2p - 1) / (x - 2)^2
Set the derivative equal to zero to find the turning points:
2x^2 + px - 4x - 2p - 1 = 0
Rearrange the equation to form a quadratic equation in x we get
2x^2 + (p - 4)x + (-2p - 1) = 0
For two distinct turning points, the discriminant (b^2 - 4ac) must be positive
(p - 4)^2 - 4(2)(-2p - 1) > 0
p^2 - 8p + 16 + 16p + 8 > 0
Combining we get
p^2 + 8p + 24 > 0
Factorising:
(p + 2.5)(p + 9.6) > 0
p > -2.5 or p < -9.6
Since p < -9.6 is not a solution (as it would result in a negative number of turning points), we conclude that:
p > -2.5

Question solved

(:

[limber pasture]

Well that’s using differentiation

[honest flame]

Yessir

It's one method

[limber pasture]

I am told to not use that

[honest flame]

um like only discriminant

No differentiation and stuff?

[honest flame]

You could use his answer then

I can explain his answer too

Got any doubts

[limber pasture]

Pure discriminant

No differentiation

Actually it’s just to practice

In exam I’ll probably still choose to use differentiation

[vocal sleet]

@limber pasture Has your question been resolved?

[vocal sleet]

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.

[uneven herald]

Not understanding how they could just add x1000 on this??

[uneven herald]

I get as a method of calculation but they never divide it by 1000 so how is it the right answer??

[magic wasp]

They do?

It's clearly on both the numerator and the denominator

[snow hedge]

They multiplied and divided 1000 at the same time

[uneven herald]

LOL

Ok thanks

[short pilot]

@uneven herald

.close

[uneven herald]

.close

[vocal sleet]

Channel closed

Closed by @uneven herald

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.

[grim bluff]

Could some please help me understand geometrical representation of differentiation?

[tawny nacelle]

hm, you can think of the derivative of a function at a point as the best linear approximation to the function at that point

so the line that "best fits" the curve at that point

[grim bluff]

What do mean by linear approximation?

[vast shale]

https://tenor.com/view/derivative-gif-23137892

i think this is considered linear approximation

[grim bluff]

I think my teacher called it slope

Is it the same thing?

[solid hornet]

Yes

It's a way of finding slope at every point

Of a function

[heavy yoke]

it gives the slope of the tangent line, which is the line which is closest to the function at any given point

[grim bluff]

Ohh

So is dy/dx considered the tangent line?

[vast shale]

yeah

[grim bluff]

Ohhh

Thanks

[vocal sleet]

@grim bluff Has your question been resolved?

Channel closed

Closed by @grim bluff

Use .reopen if this was a mistake.

[vocal sleet]

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.

[cinder frost]

“solve this equation”

can someone guide me on what to do?

[cinder frost]

write now what i’m thinking to do is

rewrite 2logx as

logx^2 - logx^1/2 = 3

[worn dove]

maybe the other way around?

rewrite 1/2logx

[velvet zephyr]

it's easy

take log_2 x common and get your answer.

second term would be -1/2*logx (to the base 2)

[twin horizon]

2logx is logx²

Log(p)-logq

Is log(p/q)

a^Log_a(n)=n

All you need

[sharp lynx]

!nosols

[vocal sleet]

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

[fervent wasp]

Just see sqrt x as x^1/2

[tame cedar]

Understanding the log properties is important. Such as:
m × logn = log( n^m)
loga - logb = log(a/b) etc.

[tame cedar]

Did not know that, I'll keep that in mind

[fervent wasp]

We appreciate your zealousness, but don’t give them the solution

[velvet zephyr]

wait, is m*log n^f = log n^f^m?

or log n^fm?

[tame cedar]

log n^fm

[velvet zephyr]

so m^log n = log n^(1*m)?

[tame cedar]

Yeah

[vocal sleet]

@cinder frost Has your question been resolved?

[velvet zephyr]

yes @vocal sleet

[vocal sleet]

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.

[mental palm]

how many 3 digit numbers are there that have 16 divisors

[red bear]

What have you done so far

[mental palm]

nothing...

I don't know how to solve it

well actually, i do know how to find how many factors a number has

[red bear]

Alright, usually when we count the number of divisors a number has, we consider it’s prime factorization

[mental palm]

however, I just don't know an easier way to do it

because there are many numbers that have 16 divisors like

2^3x3^3

but there are a lot of options

to get these

[red bear]

Yeah, you pretty much need to consider all of those possibilities

[mental palm]

But there must be an easier way

[red bear]

I don’t think there is, and there aren’t that many possibilities

[mental palm]

ok

wait, but these are 3 digit numbers

[red bear]

First, find the number of ways you can write the prime factorization in terms of arbitrary primes p_1, p_2, …

[mental palm]

so, lets consider the posibility of the exponents being 3, 1, and 1

there can be a lot

of options for p1 p2 and p3

[hard atlas]

the product quickly gets too high

there really arent that many options

[red bear]

Yes, but you can find the largest

[mental palm]

oh

ok

[surreal basin]

also Ive just went through all the p1 p2 p3 p4 cases

[mental palm]

can you help with that?

oh thnks

[surreal basin]

as long as you use a calculator youc an go through them quickly

[mental palm]

can you give me how many cases?

[surreal basin]

that doesnt mean Im doing them for you you know

[mental palm]

ok...

[surreal basin]

you need to practice pushing buttons that have digits on them cmon

[mental palm]

so did you get 46, 47, 48, 49, or 50

[surreal basin]

why are you guessing

[mental palm]

because that seems like a lot of cases to go through

[surreal basin]

theres less than 20 of them

you didnt even try to do them

[mental palm]

but the answer choices are 46-50

[surreal basin]

hey

pay attention

[mental palm]

remember, these are 3-digit numbers

[surreal basin]

what did I say

I was counting?

[mental palm]

the p1 p2 p3, and p4 cases

[red bear]

@thin vale

[surreal basin]

that implies p1, p2, p3, and p4 arent the same prime doesnt it

[mental palm]

yes

[surreal basin]

did it occur to you that 16 can be factored into other primes

if you group them up (2 * 2) * 2 * 2, then thats 3 1 1 as you said earlier

so thats p1^3 p2 p3 that you then also need to search

in addition to p1^3 p2^3 which you also need to search

youre not done yet

[mental palm]

i know

but there are 46-50 cases

[surreal basin]

then you gotta go through them

[mental palm]

and that will take a long time just guess and checking

[surreal basin]

I just did the p1p2p3p4 cases with a calculator

do you need me to tell you how to guess and check quickly?

[mental palm]

what type of calculator

desmos?

or mathway?

or what

scientific?

regular?

[surreal basin]

you dont need a Special calculator to multiply numbers together

you keep in mind the first few primes are 2, 3, 5, ... 31

then you go through them starting with 2 3 5 7

when one goes too big, you skip one

you should eventually end at 2 5 7 13

this will account for less than 20 of the cases

the others should mostly be the same

[mental palm]

do you know how to use stars and bars

just curius

curious

[surreal basin]

not really, what idea do you have

[mental palm]

no i just mean do you know the concept

[surreal basin]

not the explicit formula but the concept should be enough

[mental palm]

like if i have 7 indistinguishable balls and i want to give them to 3 distinguishable people

how many outcomes are there?

do you know the concept

?

[surreal basin]

I asked you what idea do you have

[mental palm]

easy, you just do 6 choose 2

[surreal basin]

you can state the idea and we can see if stars and bars works for this problem

[mental palm]

it won't work

but do you know the concept

[surreal basin]

I said yes

[mental palm]

ok

[surreal basin]

why are you asking me this then if its not related

youre wasting time

[mental palm]

ok

hold on, i'm looking through lecture notes

@surreal basin I don't see anything in my teacher's lecture notes that could help

i think i'm going to guess...

[surreal basin]

youre not guessing

[mental palm]

let me try to do it your way

[surreal basin]

now keep in mind that way works for p1p2p3p4

[mental palm]

but we also have to take into account p1p2p3

and p1p2

[surreal basin]

why do you keep saying obvious things

[mental palm]

idk

[surreal basin]

also shouldnt that be p1^3 p2 p3 and p1^3 p2^3?

[mental palm]

no, i already know the exponents

so yes to that

Ok, well I also have another question

[surreal basin]

yea

[mental palm]

Find the largest two-digit positive integer n such that (n\choose3)(n\choose4) is a perfect square

please excuse the latex, it's just to make it easier to read

[surreal basin]

nw

[mental palm]

so, have you found a method?

[surreal basin]

have you tried writing that out as a polynomial then factoring out the squared terms?

[mental palm]

you don't need to do that...

i don't think

because dr. gao would probably not ask for a polynomial

it probably would be like figuring out what n choose 3 would look like and n choose 4

then multiplying to get

{(n(n-1)(n-2))^2 (n-3)}/144

[surreal basin]

thats literally what I just said

[mental palm]

wait, I think i've got it

oh yeah

[surreal basin]

bruh

[mental palm]

i just didn't realize

it's just a factored out polynomial

[surreal basin]

you need to try things before you say them

[mental palm]

then the answer would be...

84

[surreal basin]

yep

[mental palm]

ok

thnks

I'm gonna close the room now

.close

[vocal sleet]

Channel closed

Closed by @mental palm

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.

[vagrant sonnet]

hello, i need help with these please

[vagrant sonnet]

i really dont know whats wrong

[gentle thicket]

see,
For partial fraction decomposition to work correctly, the degree of denominator must be strictly greater than the degree of the numerator

[vagrant sonnet]

what do we do if its not

[gentle thicket]

we will try to make lesser degree polynomial in numerator by algebric manipulation

[gentle thicket]

you got it or it's still not clear?

[vagrant sonnet]

not really, how do we exatcly make it less

[gentle thicket]

lemme explain

for example take part b
$\frac{x^2}{x^{2}+x+72}=\frac{x^{2}+x+72-(x+72)}{{x^{2}+x+72}$

what's up with it

[loud walrus]

$\frac{x^{2}}{x^{2}+x+72}=\frac{x^{2}+x+72-(x+72)}{x^{2}+x+72}$

[twin meteor]

Samuel

[gentle thicket]

why it didn't work for me?

[loud walrus]

You are missing a closing }

[gentle thicket]

oh frick

thanks

[vagrant sonnet]

where did we get the new bracket from

[gentle thicket]

what we are trying to do is to reduce the degree of numerator

it can be achieved by making some cancellation on both numerator and denominator

[vagrant sonnet]

so we'd need 4 terms now

[gentle thicket]

from here what you need to do is to separate the fractions

[gentle thicket]

that will lead to some cancellation

[vagrant sonnet]

itll go back to the original function no?

[gentle thicket]

yeah cause we just added the x+72 and then subtracted it

so overall we just added 0 to it

[vagrant sonnet]

how does that make the numerator less tho

[gentle thicket]

you have to separate those fractions for it

so it will be
$\frac{x^{2}+x+72}{x^{2}+x+72}-\frac{(x+72)}{x^{2}+x+72}$

[twin meteor]

77²

[gentle thicket]

got it?

[vagrant sonnet]

so now we divide x^2+x+72 by x+72

[gentle thicket]

huh no

x+72 is in numerator

we are dividing it by that quadratic expression

[vagrant sonnet]

how would that go

[gentle thicket]

you got upto that?

[vagrant sonnet]

ye

[gentle thicket]

so what do you get after simplifying it?

[vagrant sonnet]

-x-72/x^2+x+72

or 1/x^2

[gentle thicket]

yeah but missing something

[vagrant sonnet]

im bad at maths

[vagrant sonnet]

1-this

[gentle thicket]

where does that same form

[gentle thicket]

yup

[vagrant sonnet]

ok so now we have 1-(x+72)/x^2+x+72

[gentle thicket]

so now since the degree of numerator is less than the degree of denominator, you can use partial fraction decomposition here

[vagrant sonnet]

can u help out with that

[gentle thicket]

bro for partial fraction decomposition you have to factorise the denominator

maybe try analyzing the given example

[vagrant sonnet]

1-A/x-9+B/x+8

?

[gentle thicket]

you sure about that factorisation?

[vagrant sonnet]

nevermind

it gave me roots

which im guessing is wrong

.close

[vocal sleet]

Channel closed

Closed by @vagrant sonnet

Use .reopen if this was a mistake.

[vocal sleet]

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.

[vast shale]

According to the graph, AB = R√2 and mBD = 53 degrees. Calculate the slope of AB

[rare swift]

Join b with the center so the angle made will be 53degrees and so thr x and y coordinates can be found
Join a with center as ab is r√2 and oa and ob are r angle aob will be 90de gress and so angle aod will be 90+53 and so coordinates of a can be found then use distance formula to find eq and then slope

[vast shale]

so thr x and y coordinates can be found
mm how?

oh

w8

I know

[rare swift]

Rsinx Rcosx

[vast shale]

mm this I don't know why

oh

w8

[rare swift]

Then you need to learn polar coordinate system

[vast shale]

those are the coordinates

[rare swift]

For a unit circle y = sinx and x = cosx

[vast shale]

of B

Yes

I haven't learned that for coordinates

but for triangkes

[rare swift]

Then learn it lol

[vast shale]

That's what I am doing

[vast shale]

where do I use thag

if I replace that in the equation y = 4/3 x the R gets canceled out

perhaps with the distance formula

and AB

?

mm no

<@&286206848099549185>

I have
B: y = 4/3 x
A: y = -3/4 x

[rare swift]

Yess find the coordinates of b and a in terms of r then use the distance formula

To formulate an eq of line

Y= mx + x where the coeff of x is going to give you slope

[vast shale]

A (4/5 R; -3/5 R)
B (3/5 R; 4/5 R)

[rare swift]

And then use distance formula

[vast shale]

like R = Xsec(x)

for B

[rare swift]

I'd say first apply distance formula and then write r in terms of x to find the coedd

[rare swift]

Yess

[vast shale]

distance formula for what points

AB?

[rare swift]

A and B

[vast shale]

How should I name the variables

[rare swift]

Yes cause we want the eq of line ab

[rare swift]

What variables?

[vast shale]

of the coordiantes

[rare swift]

Let variables of a be x1 and y1 and b be x2 and y2

Dosent really matter tho

[vast shale]

(x1 - x2)^2 + (y2 - y1)^2 = 2R^2

[rare swift]

The ans?

[vast shale]

?

[rare swift]

Is this the ans you're getting ?

[vast shale]

for the problem obs no

[rare swift]

No is this the distance your getting 2r²

[vast shale]

yes

(x1 - x2)^2 + (y2 - y1)^2 = R^2 2

is the same

if u want

it like that

idk

perhaps you confused

2r^2 with (2r)^2

idk

what should I do next

I am not getting the plan

like I am visualizing a system maybe

but don't know with which variables

[rare swift]

Wait I fcked up give me some min

[vast shale]

oh ok, don't worry

[rare swift]

Tan 8 degrees

[vast shale]

Yes

How

?

[rare swift]

I extended the line to meet the x axis so we have y / x = tan x which will give us slope

[vast shale]

Ohh wow, right, that's smart

so 1/7

thankss

[rare swift]

Wlc

[vast shale]

.close

[vocal sleet]

Channel closed

Closed by @magic pine

Use .reopen if this was a mistake.

[vocal sleet]

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.

[candid ledge]

can someone please help me understand this

[candid ledge]

I dont really understand the notation they used to describe L

or how they came up with it

[vocal sleet]

@candid ledge Has your question been resolved?

[vocal sleet]

@candid ledge Has your question been resolved?

[sweet flower]

Okay this isn’t my field, but it looks like the center circle denotes accept states, starting at the left side. Since the empty word (?) is allowed n=0 is permitted. Then on the right following the arrows, ø->a->b gives ab which is acceptable, otherwise continue to ->a->b which is acceptable… therefore any number of ab combinations is permitted. Therefore (ab)^n where n is an element of the integers greater than or equal to zero builds the language

It’s in set-builder notation

[vocal sleet]

@candid ledge Has your question been resolved?

[vocal sleet]

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.

[next burrow]

Would someone mind helping me step by step through this

[mellow oyster]

well for the add on loan, your total interest is given by your principal multiplied by your annual interest rate multiplied by the number of years

6700 * 0.05 * 3 is where the 1005 interest comes from for that loan

then your total payment with the dealer would be the 300 down payment plus the 6700 you borrow plus the 1005 interest on that

add those up, divide by 36 since you make a payment every month for 3 years, and that's your monthly payment with the dealer

[vocal sleet]

@next burrow Has your question been resolved?

[next burrow]

sorry for not responding

[vocal sleet]

@next burrow Has your question been resolved?

[vocal sleet]

@next burrow Has your question been resolved?

Channel closed

Closed by @next burrow

Use .reopen if this was a mistake.

[vocal sleet]

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.

[vast shale]

hello im doing a question on partial fractions and i dont know the decomposition for cubic polynomials....

[gentle thicket]

you know about synthetic division?

polynomial division

?

[vast shale]

long division?

[gentle thicket]

yeah if that's what they call there

[vast shale]

am i supposed to do long division first ?

[gentle thicket]

see there is a condition for partial fraction decomposition to work

[vast shale]

okay ill try

[gentle thicket]

the degree of numerator has to be strictly less than the degree of the denominator

[vast shale]

OK 👍🏻

thanks mate

.close

[vocal sleet]

Channel closed

Closed by @mild kiln

Use .reopen if this was a mistake.

[vocal sleet]

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.

[heady quest]

Find the focus, vertex, axis and directrix equations of the following parabola.

where did the +9 come from

In the first three lines

[gentle thicket]

they added it intentionally to form a perfect square in left hand side

[heady quest]

but how do i know which number to add

this seems hard

[gentle thicket]

see if you have $x^{2}+2{\cdot}a{\cdot}x$

[twin meteor]

77²

[gentle thicket]

you'll try to add a "a^2" term

which makes it $(x+a)^2$

[twin meteor]

77²

[heady quest]

i have no idea what you just said

[gentle thicket]

I just said that you have to try to form a perfect square

it is not always a definite procedure

you've to think about it calmly and understand it

[heady quest]

yknow what ill just skip this question

im sure they wont give us hard stuff like this in the test

.close

[vocal sleet]

Channel closed

Closed by @heady quest

Use .reopen if this was a mistake.

[gentle thicket]

that's not hard😭

[vocal sleet]

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.

[tardy jetty]

Hi, I had a question about formulating statements and one of which was say “If a series converges, we know that the sequence {an} as n->inf is 0 or the nth term is 0” and from contrapositive “If the nth term is not 0, the series does not converge; it diverges” I also know it is not proper to say “If the nth term is 0, the series converges” as we know the statement is true only with the condition that when the series converges the nth term is 0.

So my question was is there an example of when the nth term is 0 but the series diverges? Thanks.

[tardy jetty]

Note: infinite series

Forgot to clarify

[inner osprey]

when you say "the nth term is 0" do you mean "the limit of {a_n} as n approaches infinity is 0"

[tardy jetty]

yes I just edited

[inner osprey]

answer is yes. for example, consider the p-series 1/n^p where p isn't greater than 1

[tardy jetty]

as p approaches 0?

[tardy jetty]

ohhh

tysm!

wait nvm

[tardy jetty]

sorry last question

when p<1, doesnt the sequence {a_n} as n->inf approach infinite and not 0

[inner osprey]

no

that is p < 0

for 0 < p < 1, {a_n} approaches 0

[tardy jetty]

OHHH

fire 🔥

[inner osprey]

indeed 🔥

[tardy jetty]

i love math

ty chat

.close

[vocal sleet]

Channel closed

Closed by @tardy jetty

Use .reopen if this was a mistake.

[vocal sleet]

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.

[graceful grail]

If sin10°=k, sin280°=?

[short pilot]

Sin(270+10)

[graceful grail]

Ik that

[short pilot]

So

[graceful grail]

And that turns into -cos10

[short pilot]

Ok

and (sin10)^2+(cos10)^2=1

[rare swift]

Make a right angle triangle with hypotnouse 1 and perpendicular k and find it's base

[graceful grail]

And the answer is -sqrt(1²-k²)

[rare swift]

Yea

[graceful grail]

What

[short pilot]

Do u know

[rare swift]

U can also use that

[short pilot]

sin^2x+cos^2x=1

[graceful grail]

Oh wait

Im dumb

Ty

I didnt notice that

.close

[vocal sleet]

Channel closed

Closed by @graceful grail

Use .reopen if this was a mistake.

[short pilot]

Nvm

[rare swift]

Fair enough

[dusty jolt]

Wait... Is this sin and cos channel?
Trigonometry?

[vocal sleet]

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.

[gentle thicket]

erm
what you are supposed to do here?

[honest flame]

Yea ig

[olive stag]

prime factor tree is correct way?

[honest flame]

uh no i think

Bro just strike off

[olive stag]

there is image linked in message

[honest flame]

Square and root

-_-

[olive stag]

how do i find root of 229.7

[honest flame]

Bro strike off square and root

you get same value tf

[olive stag]

can u use more mathematical term than strike off idk what that means

[loud walrus]

(Sqrtx)^2 = x

[honest flame]

((229.7)^1/2)^2

Square root is written as

[olive stag]

can you prove that

[honest flame]

Power of half

Sure I can prove it

consider x as a term

[olive stag]

ok i know what to do but i need proof

[honest flame]

Proof of problem or proving the strike off thing?