help-27

[woven radish]

Umbraleviathan

[hybrid snow]

Other than the fact that $x = \log_9(0.5)$ which is what you have written down

[woven radish]

Umbraleviathan

[supple knot]

The rule is not wrong

Log of base 1 isn't defined

You're always going to run into something new

It isn't good to memorize all possibilities of log, but rather the definitions and few properties

https://mathinsight.org/logarithm_basics
Start there

The second one is wrong

1/(-2) is perfectly defined

And -2 <0

[devout snow]

Channel closed

Closed by @quiet glade

Use .reopen if this was a mistake.

[devout snow]

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.

[barren garden]

How do u simplify this further

Can I take out a 14pi from the 15 since its a multiple of 2pi and write it as pi - pi/4?

[supple knot]

,tex .exp rules

[woven radish]

riemann

[supple knot]

Yes this works

[devout snow]

@barren garden Has your question been resolved?

[devout snow]

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.

[alpine tapir]

what does 2 mean

[weak cove]

it means

augment the identity matrix (m x m) onto A

and then reduce it to B U

[devout snow]

@alpine tapir Has your question been resolved?

[alpine tapir]

thank you

[devout snow]

Channel closed

Closed by @alpine tapir

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.

[dire sentinel]

Help

[dire sentinel]

Freshman here attempting to graduate highschool early through the EGP and I’m wondering what knowledge would be useful to reach benchmark on the ACT

I took a pretest for it called the CERT and got 22/40

[devout snow]

@dire sentinel Has your question been resolved?

[devout snow]

@dire sentinel Has your question been resolved?

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[devout snow]

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.

[devout snow]

Please don't occupy multiple help channels.

[willow sedge]

Can someone check

[upper schooner]

Rest are fine

[devout snow]

@willow sedge Has your question been resolved?

[devout snow]

@willow sedge Has your question been resolved?

Channel closed

Closed by @willow sedge

Use .reopen if this was a mistake.

[devout snow]

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.

[shrewd holly]

After how many years will only 4 g of the sample remain? (Round your answer to the nearest whole number.)

[shrewd holly]

he half-life of cesium-137 is 30 years. Suppose we have a 14-g sample.

basically onyl for c

i got a and b already

<@&286206848099549185>

[acoustic leaf]

set your function equal to 4 g, then solve for t

[shrewd holly]

how do i solve for t

[acoustic leaf]

you can use logarithms to cancel the exponent

[shrewd holly]

smart

ill do that

[shrewd holly]

know anything about rxponential functions?

[acoustic leaf]

what about them?

[shrewd holly]

i got some auestions for them

after i solve this ine

[acoustic leaf]

go ahead and post them when you're ready

[shrewd holly]

what log function shoukld i use

the answer to thr firdt and secon dwas this

but how do i use logarithimic function in this

theres no e

natural log

[acoustic leaf]

,tex .log rules

[woven radish]

cloud

[acoustic leaf]

the power rule is very helpful here

[shrewd holly]

how do i seperate them

??

these are the expo i have 30 min to solve 4 probelms

im not sure i can do it in time

[acoustic leaf]

what do you want to work on first?

[shrewd holly]

the one we were wroking

on

im not sure how to@seperate it

[acoustic leaf]

you have an equation 4 g = (your function of t)
you can take the logarithm of both sides to solve for t (it may be easiest to take base 2)

[shrewd holly]

so

log(4)?

[acoustic leaf]

that's one side of the equation

[shrewd holly]

o

i see

log(4)=log(14)(1/2)^(t/30)

is thatr ifht

[acoustic leaf]

yes

then you can use log rules to simplify and solve for t

[shrewd holly]

ok

now i need help with question 4

this quesiton is so confusing part b

i weote 20000e^0.11t

and it says its weong

like what

how do i solve for t/30?

[shrewd holly]

i got 21 but it says its weong

…

[acoustic leaf]

,tex .log rules

[woven radish]

cloud

[shrewd holly]

is it correct

[shrewd holly]

^

i got 9 minutes

its over

[acoustic leaf]

start by using the product rule to separate the 14 then use the power rule to take out the t/30

[shrewd holly]

I GOT IT

54!!

years

now i need help with

number 4

hurry

@rare pivot

[shrewd holly]

help

4. a) is 20000

how do i solve for b

[acoustic leaf]

if every hour it multiplies by some factor, then you can divide by that factor to get the population an hour before

repeat until you get to hour 0

[shrewd holly]

what does h th at mean

???

[acoustic leaf]

in exponential growth, if you have the population at hour 2, then you multiply by its hourly growth rate to get the population at hour 3

but you can also take the population at hour 3 and divide by the hourly growth rate to get the population at hour 2

[shrewd holly]

???

what do u mean

oh i see

thanks

i finish sll of them

its dus

due

3 of them werent do rip 😭

i did like 8 assignement 12 question each for 4 hrs

on 3 questions not done not bad

kinda sad

😒

[acoustic leaf]

i would recommend planning to do homework on a day it isn't due, so that you have spare time in case it takes longer than expected

[shrewd holly]

how do you have better time management

i need asvice

i have terirble time management

[acoustic leaf]

it helps to keep a list of things that need doing, then designate some time every day to working on that list, with things that are due sooner on the top of the list

[devout snow]

@shrewd holly Has your question been resolved?

[devout snow]

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.

[slender yoke]

hi

[devout snow]

Please don't occupy multiple help channels.

[slender yoke]

.close

[devout snow]

Channel closed

Closed by @slender yoke

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 bay]

F(x) = x^3 sinx

A. Local maxima is 0
B. Local minima is 0
C. X=0 no maxima no minima
D. Maxima is 1

[thin inlet]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[thin inlet]

!showwork

[devout snow]

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

@tiny bay Has your question been resolved?

[devout snow]

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.

[stiff folio]

How to move with this one

[surreal night]

,rotate

[stiff folio]

Missed you

I tried converting all to tan

[surreal night]

:3

[stiff folio]

And also to sin

[stiff folio]

You thinking something?

[devout snow]

@stiff folio Has your question been resolved?

[restive river]

oh

i see we are looking at a interesting problem here

have you acomplished anything yet?

@stiff folio

[stiff folio]

Failures only sire

Got terms reduced when converted to sin

[restive river]

can i dm

[stiff folio]

Yeah sure sure

[devout snow]

@stiff folio Has your question been resolved?

[stiff folio]

<@&286206848099549185>

. close

.close

[devout snow]

Channel closed

Closed by @stiff folio

Use .reopen if this was a mistake.

[devout snow]

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.

[sinful pilot]

I dont understand, how can i represent a complex number on the complex plane.
I get that a is the real part and bi is the imaginary, however i cant get how a+bi=z

[sinful pilot]

Like shouldnt be a and b vectors?

[wild creek]

all real vectors are horizontal

and all imaginary vectors are vertical

[elder ermine]

treat the complex number as a vector and 'a' and 'b' as X and Y components of it

and i is a scalar which rotates the vector by 90 when multiplied by it

in clockwise sense

ofc

[sinful pilot]

I treat z as a vector but still dont understand how a+bi=z in this geometric sense

[wild creek]

do you vizualize the vectors a and bi if a and b are real numbers?

or not?

[sinful pilot]

Yes i think so

[wild creek]

and you dont know how to add vectors then?

whats the step that troubles you?

[sinful pilot]

Like a and b are vectors? This step mostly

[wild creek]

so you dont

for any real number a

its vector representation in the complex plane is the vector (a,0)

for any real number b

the vector representation in the complex plane of ib is the vector (0,b)

so now

a+ ib 's vector representation is the sum of the vector representations of a and ib

so its (a,0) + (0,b) = (a,b)

[sinful pilot]

Can we view a and b as both vectors and simple numbers?

[wild creek]

yeah

numbers are vectors

even in R

but you'll discover that later

because i'm assuming you didnt take linear algebra yet

for now

use the idea of a vector representation

i think its easier

but the vector representation follow the exact same rules as the numbers themselves

(because its well made)

[sinful pilot]

Idk it was very wierd to me that, our teacher introduced a and b as vectors and than we made calculations seeing them as numbers

[supple knot]

Is z a complex number or complex vector?

[sinful pilot]

If we think algebraically its a complex number but if geometrically its a complex vector (i think)

[supple knot]

...

It's your class

What did your teacher say z is

[sinful pilot]

Complex number

[supple knot]

Then a and b are just real numbers

[sinful pilot]

And if he would have said complex vectors?

[supple knot]

Then a and b would be vectors

[sinful pilot]

And in the polar form what are cos and sin? Are those vectors?

Because im also not seeing how would a vector z be equal to r(cos x +i sin x) if cos sin and r are numbers

[supple knot]

Polar form per coordinate

But you're not learning complex vectors

[sinful pilot]

Ok

Well thanks both of you

.close

[devout snow]

Channel closed

Closed by @sinful pilot

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.

[dim plume]

is this working out correct?'

[dim plume]

?

no i just need help

because i got this working from a website

and its different from my own

and I'm confused

[winter patrol]

what's your work

[dim plume]

I got

from Friends house ---> motorway ( 20minutes)

Motorway ( 4 hours)

Motorway ---> home (25 minutes)

rest (30 minutes)

TOTAL = 315 minutes

315 minutes --> 5.25 hours

its not right?

[winter patrol]

still alright so far

[dim plume]

in the mark scheme it says 4:45 + 30 = 5:15

i think that's wrong

[winter patrol]

they're using time notation to represetn hours and minutes

note that they're using : and not .

[dim plume]

yes

[dim plume]

so this is the total time she took?

[winter patrol]

yes

[dim plume]

what do i do from here

[winter patrol]

how many minutes is 0.25 hours

[dim plume]

15

[winter patrol]

yes

[dim plume]

oh

5 hours

• 0.25 hours

so that just 5 hours and 15 minutes

thanks

.close

[devout snow]

Channel closed

Closed by @dim plume

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.

[inner pasture]

Where has the 26c1 come from ?

[tall knoll]

Number of ways to pick 1 card from the remaining clubs and diamonds

[inner pasture]

thanks

.close

[devout snow]

Channel closed

Closed by @inner pasture

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.

[onyx cedar]

A plane drops 4 bombs on a target. The probability that a single bomb will hit is 0.3.
To destroy a target it is enough for one bomb to hit the target.
What is the probability that the target will be destroyed?

[onyx cedar]

whats wrong?

[acoustic leaf]

you're computing the probability that exactly 1 bomb hits. but the target will still be destroyed if more than 1 bomb hits

[onyx cedar]

oh

[acoustic leaf]

what may be easier is to calculate the probability it won't be destroyed, which is the probability that 0 bombs hit

[onyx cedar]

so
n = 4
p = 0.7
k = 0?

and then 1-pn(k)

[acoustic leaf]

p is the same

[onyx cedar]

still wrong

@acoustic leaf

[acoustic leaf]

why did you change p to 0.7?

[onyx cedar]

its not 0.7 it 1-p

1-0.3 = 0.7
and 0.3 to the 0 is 1

[acoustic leaf]

ok so that gives the probability it doesn't get destroyed, so then we need to find the probability that it does get destroyed

[onyx cedar]

you're right, its ok

thanks

[devout snow]

@onyx cedar Has your question been resolved?

Channel closed

Closed by @onyx cedar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[strong willow]

what about -inf?

[teal copper]

i think its the same

since you are taking the abs

[strong willow]

same as?

[acoustic leaf]

how can a sequence go to -infinity, when you're taking the absolute value?

[thorn crane]

D'Alembert's test works for sums with a constant sign

and this work is usually on positive sums

[strong willow]

correct

[thorn crane]

when a sum is negative or diverges to minus infinity, we arbitrarily multiply by -1, which is exactly what the absolute value is here for

[pseudo basin]

where

[thorn crane]

so TLDR: -inf or inf it doesnt matter as long as it diverges

[strong willow]

ok

[zealous flume]

Tomorrow my maths class 10th pre board (india) exam

[strong willow]

tnx all

[zealous flume]

Any advice

[strong willow]

.close

[devout snow]

Channel closed

Closed by @strong willow

Use .reopen if this was a mistake.

[pseudo basin]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[devout snow]

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.

[mystic gulch]

hiii helpp

[devout snow]

Please don't occupy multiple help channels.

[jade oak]

close one of your channels. Also you should show your work or explain what you are thinking and give a specific method you want to focus on first

[devout snow]

@mystic gulch Has your question been resolved?

[devout snow]

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.

[iron vessel]

is this right?

idk how the exponents work along with brackets

[devout snow]

@iron vessel Has your question been resolved?

[iron vessel]

.close

[devout snow]

Channel closed

Closed by @iron vessel

Use .reopen if this was a mistake.

[devout snow]

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.

[crude anvil]

Just quick thing I was pondering: Can n! ever end in n zeros?

[crude anvil]

I would assume not

[low holly]

I don't think so

If my reasoning is correct, that would require that n! be divisible by 10^n, which requires that n! be divisible by 2^n, which requires that there be at least n even numbers between 1 and n.

[crude anvil]

oh yeah

That’s complete right?

[low holly]

actually, does the last part follow 🤔

I don't think it does (because a single even number can contribute multiple factors of 2)

[devout snow]

@crude anvil Has your question been resolved?

[devout snow]

@crude anvil Has your question been resolved?

[devout snow]

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.

[nova whale]

how do i find the stationary point and determine if max,min or saddle point

[nova whale]

f(x, y) = x^2y^2 - 4xy + 6x - 6*y

What i've gotten seems awfually complicated

[cold bough]

how is the gradient you have got ?

[nova whale]

this will become a 2nd degree polynomial

surely i've made a mistake somewehre

[cold bough]

maybe could be useful to do this

then you will get a first degree equation in x

and you can find 1 x such that f_y=0

and then you get y

[nova whale]

wdym

but i would like to find the cirital points first

then find the hessian matrix

[cold bough]

yes ...first solve f_y=0 by using y=...

[cold bough]

i haven't mentioned the hessian matrix

[nova whale]

ok but i would still like to do that

like this?

[cold bough]

yes

now the x squared are simplified

[nova whale]

yh

this ought to equal 4x

6+8x/x^2 -6

-4x

x^2 cancle -6 cnacles
and we have 8x-4x = 4x

4x=0

which means x=0

[cold bough]

ok...but you cannot use x=0

[nova whale]

oh

[cold bough]

because you are assuming that x is not zero

[nova whale]

oh yh true

[cold bough]

here

[nova whale]

yh i see

[cold bough]

so you have no solution

[nova whale]

but then it wont have a solution

yh

what do i do then

[cold bough]

the set of critical points is empty

the empty set is the set with no elements

[nova whale]

what does that mean for the function

[cold bough]

in particular there is not local min or max (so in every point you will find a direction such that the function will increase or decrease )

maybe i can graph it

sorry but the graph is not too clear

[devout snow]

@nova whale Has your question been resolved?

[devout snow]

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.

[tiny bay]

Limit n tends to infinity [n!/n]^1/n

[deft hemlock]

What have you tried

[tiny bay]

Stirling approximation

[deft hemlock]

And how did that go?

[tiny bay]

1/e (2πn)^1/2n

[deft hemlock]

Great

[tiny bay]

What should I do next?

[deft hemlock]

Now u just have to evaluate n^1/2n

I claim the 2pi part can be ignored… you can figure that one out 😉

For that maybe ||take a log||

[tiny bay]

2π/e n^1/2n

[deft hemlock]

No

[tiny bay]

2π/e (e^2nlogn)

[deft hemlock]

Missing a minus somewhere and there shouldn’t be a 2pi

[tiny bay]

So 2π/e

[tiny bay]

What?

[deft hemlock]

What is the limit of c^1/n for any positive constant c

[tiny bay]

1

[deft hemlock]

Correct

[tiny bay]

,w 2^1/n n tends to infinity

[woven radish]

Results provided by WolframAlpha

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

Requested by gitoo0451

[deft hemlock]

So what do you get from here

[tiny bay]

,w limit n tends to infinity (n!/n)^1/n

[woven radish]

Results provided by WolframAlpha

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

Requested by gitoo0451

[deft hemlock]

Ah did u mean to say n^n

Instead of n at the bottom

[tiny bay]

Yes n^n

[deft hemlock]

So this equals lim 1/e n^1/2n

Can you find what lim n^1/2n equals?

[tiny bay]

@deft hemlock

[deft hemlock]

What is this picture

Ah i meant can you find the limit of n^1/(2n)

[tiny bay]

e^(2nlogn)

Infinity

[nova whale]

i am back, what do i do? the question is find if it is min, max or saddle point. and this isnt any of the options

[deft hemlock]

You have to open a new channel

[nova whale]

my bad

didnt see

[deft hemlock]

No, its e^(log(n)/(2n))

[tiny bay]

Ohh yes

e^(infinity/infinity)

I'm gettting infinity

,w limit n tends to infinity n^{1/2n}

[woven radish]

Results provided by WolframAlpha

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

Requested by gitoo0451

[tiny bay]

,w log ininity/ininity

[woven radish]

Results provided by WolframAlpha

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

Requested by gitoo0451

[devout snow]

@tiny bay Has your question been resolved?

[devout snow]

@tiny bay Has your question been resolved?

[deft hemlock]

UI shouldnt be

log(n)/n tends to 0

[tiny bay]

,w limit n tends to infinity log(n)/n

[woven radish]

Results provided by WolframAlpha

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

Requested by gitoo0451

[tiny bay]

.close

[devout snow]

Channel closed

Closed by @tiny bay

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.

[restive ginkgo]

.close

[devout snow]

Channel closed

Closed by @restive ginkgo

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 atlas]

I know a and c are correct for sure

just want to know why b and d are incorrect,

concept is fine, dont need notations and precise proof

<@&286206848099549185>

SOMEONE

[devout snow]

@limber atlas Has your question been resolved?

[limber atlas]

.close

[devout snow]

Channel closed

Closed by @limber atlas

Use .reopen if this was a mistake.

[devout snow]

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.

[swift knoll]

I'm trying to find the radius of convergence of $$\sum _{k=1}^{\infty }\arctan \left(\frac{1}{k}\right)x^k.$$ Appreciate any hints.

[woven radish]

Philip

[swift knoll]

When I apply the ratio test, I get a sequence in the numerator and denominator that tends to 0. Maybe I should apply L'Hospital's rule then?

[wild creek]

if you want a hint do you know an assymptotic equivalent to arctan?

at 0?

[swift knoll]

hmm, are you alluding to $$ \arctan\left(\frac{1}{x}\right) = \frac{\pi}{2}-\arctan(x)?$$

[woven radish]

Philip

[wild creek]

no

i mean arctan(x) = x+o(x²)

when x approaches 0

[swift knoll]

ah ok, so just the taylor series

[wild creek]

yeah just the first term of the expansion

i'm not calling that a series

but yes

[swift knoll]

ok, however, to get the radius of convergence in this case, I'd need to use some test, right?

[wild creek]

x^k arctan( 1/k) = x^k/k + o(x^k/k)

so if series of x^k/k converges

then the original series does

so yeah ratio test

is easy

[swift knoll]

yeah, ratio test would do it I think, even using L'Hospital's would probably work, but maybe a bit more work 🙂

[wild creek]

use the simplest proof

[devout snow]

@swift knoll Has your question been resolved?

Channel closed

Closed by @swift knoll

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.

[thorn bramble]

Between 5 and 6 o'clock, the hour and minute hands are perpendicular to each other twice. These two moments
How many minutes is the distance between?

[pseudo basin]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[thorn bramble]

3

4

[lusty sapphire]

!show

[devout snow]

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

[thorn bramble]

minute hand goes 6 degrees per minute

hour hand goes 0.5 degrees per minute

if we think that hour hand does not move so minute hand would go 5.5 degrees per minute

the angle is 90 at the beginning rest is 270

[lusty sapphire]

I do not think this is correct

[thorn bramble]

that is correct

[brave vapor]

Nah

[supple knot]

Explain your reasoning

[thorn bramble]

360 degrees ---------> 12 hour

360 degrees ----------> 720 minutes

[pseudo basin]

it is

[pseudo basin]

hang on what?

[thorn bramble]

0.5 degrees -----------> 1 minute

[pseudo basin]

oh, you mean at the first moment they're perpendicular

[pseudo basin]

it is correct swr

[lusty sapphire]

Oh

you are right

I am bad at clocks

[thorn bramble]

we want to get 90 degrees so 270 - 90 =180

now i tjink that we shoul go 180 degrees and the speed is 5.5 degrees per minute so 180/5.5 = 32.72727...

is it true ??

<@&286206848099549185>

[pseudo basin]

yes, that's the answer in minutes

you said your answer disagreed with somebody else's though

is that so?

[thorn bramble]

yes

[pseudo basin]

who was it

[thorn bramble]

they said that the answer is 360 minutes but i said it is a lot

[lusty sapphire]

Yeah that's longer than an hour. That sounds way off

[thorn bramble]

help-1 you would see knief

[pseudo basin]

360 minutes is literally 6 hours

there is no way that could be right

[thorn bramble]

i said it to him

[misty crest]

i was saying it should be half the circle between the two

[thorn bramble]

any way thank you

[misty crest]

half the clock

between the two times

where it can be perpendicular

[pseudo basin]

it is not quite half the clock face

it is a bit more

sure it's two right angles on either side of the hour hand but the hour hand itself moves some distance in that time

[misty crest]

but was it not asking

at any instant where the clock is between hours 5 and 6

how much time or minutes on the clock are between the two times

like there r two times where it can be perpendicular

so what is the minute differential between the two times

is this not what the question asked?

[pseudo basin]

yes it is.

i don't think there was any doubt about it

[misty crest]

so y wouldn’t it be half the amount of minutes in a clock

because a clock is a circle

[pseudo basin]

sure it's two right angles on either side of the hour hand but the hour hand itself moves some distance in that time

[lusty sapphire]

How many minutes is the distance between?
Distance between the two moments?

[misty crest]

no like

[pseudo basin]

sure it's two right angles on either side of the hour hand but the hour hand itself moves some distance in that time

the hour hand doesn't stay in place

[misty crest]

i interpreted it as

there r two times where the hour and minute hand can make a right angle

[pseudo basin]

yes

there are two times

no they are not 30 min apart

[misty crest]

without the hour hand moving

like at that instant

how many "minutes" or degrees really are between those two times

[pseudo basin]

what the fuck are you on about

why would the hour hand not move

[misty crest]

🤦🏼‍♂️

[pseudo basin]

you're trying to shoehorn your wrong answer into this problem

[misty crest]

how?

[lusty sapphire]

Just double-checked my own work. I will also say that this is correct. So good work.

[misty crest]

i’m telling u how i interpret it

[pseudo basin]

and your interpretation is wrong.

[thorn bramble]

Thank you

[misty crest]

what’s the wording of the question again

so it’s saying as the hour hand moves between 5 and 6

not just at a single instant between 5 and 6

[pseudo basin]

here are the positions of the clock hands at the two times in question

overlaid on top of each other

[thorn bramble]

that's why we do 6-0.5=5.5 we consider that hour hand is stable

[pseudo basin]

we consider that the hour hand ISN'T stable

or rather

[misty crest]

yea i wasn’t interpreting it as the hour hand is@lvong

[pseudo basin]

that it ISN'T standing in place

KNIEF

[misty crest]

moving *

[pseudo basin]

DO YOU KNOW HOW CLOCKS WORK

[misty crest]

sure i do

[pseudo basin]

do you know how analog clocks work

[misty crest]

that’s just not what i thought it was asking

[pseudo basin]

the hour hand is moving continuously

always

on like 99% of all analog clocks in existence

[misty crest]

yes i’m aware lol

[pseudo basin]

yeah so

why tf would you assume that it isn't

your interpretation was wrong

[misty crest]

did u read how i explained how i interpreted it? i agree now that i’ve reread it

[pseudo basin]

yes but you dont need to repeat it so many times lol

[misty crest]

but yes i’m aware the hour hand also moves💀

[pseudo basin]

@thorn bramble do any doubts remain unanswered?

[thorn bramble]

no and Thank you for your help

.close

[devout snow]

Channel closed

Closed by @thorn bramble

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.

[restive river]

translation: determine and give reason as to why the following series is either convergent or divergent

clue: show first that the series is positive by analyzing the function f(x) = x - ln(1 + x) for x > 0. use maclaurin expansion to find an appropriate series that the given series can be compared to

[cold bough]

what have you been trying ?

[restive river]

not much, i don't know how to approach it

maybe the ln term can be approximated

to a maclaurin

that is always positive for x > 0

and that expansion is greater than x

making f(x) positive for x > 0

but idk how to use or transfer that into use

nvm this is all incorrect

[cold bough]

do you know that $\ln(1+x)=x-x^2/2+o(x^2)$

[woven radish]

everg

[restive river]

sure

[cold bough]

ok then plug in x=1/n

and get

$1/n-\ln(1+1/n)=\frac{1}{n^2}+o(1/n^2)$

[woven radish]

everg

[cold bough]

$\sum 1/n^2<\infty$

[woven radish]

everg

[cold bough]

do you see why $\sum o(1/n^2)<\infty$?

[woven radish]

everg

[restive river]

how did we get to this

1/n - 1/n - (1/n^2)/2 ...

1/2n^2

did you just eliminate the 2

[cold bough]

sorry i just missed that constant

have forgetten

[restive river]

yes, because 1/n^2 is a convergent p-series

p > 1 --> convergence

@cold bough

[cold bough]

and why sum o(1/n^2) is convergent ?

[restive river]

because p > 1

[cold bough]

but there is an o

[restive river]

idk what it does

[cold bough]

o(1/n^2) is not 1/n^2

is a function in n ...such that lim o(1/n^2) / (1/n^2)=0

so basically you just use it

with a_n=o(1/n^2)

and b_n=1/n^2

and sum b_n converge because p>1

[devout snow]

@restive river Has your question been resolved?

Channel closed

Closed by @cyan pivot

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.

[winter torrent]

y² is why it's 25 in the equation, because it's (5y)²

but that's just how transformation works like

,tex .transformation rules

[woven radish]

hayley

[winter torrent]

it's a little weird but like

imagine the point (1,1) satisfied the original equation, then (1, 1/5) needs to satisfy the new equation, which will be true if we just replace y with 5y

[devout snow]

@iron vessel Has your question been resolved?

Channel closed

Closed by @iron vessel

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.

[raven swift]

help?

$c^2-d^2/d^2+cd-2c^2$

[woven radish]

T2

[supple knot]

What's the question

[raven swift]

how do i put in simplest form

[unique marlin]

Multiply by the conjugate?

It’s going to be trickier since there are 3 terms in the denominator

[raven swift]

?

[strange nimbus]

Assuming it's (c^2 - d^2)/(d^2 + cd - 2c^2), you can factor the numerator and denominator.

[winter torrent]

factor top and bottom

[raven swift]

i dont know how to factor it tho

wait (c-d)(c+d) ?

[strange nimbus]

Right.

Then, you can factor d^2 + d - 2 and use that to figure out how to factor d^2 + cd - 2c^2.

[raven swift]

d^2+d-2?

[strange nimbus]

Right.

What does that factor to?

[raven swift]

where r u getting that?

[strange nimbus]

Well, you usually have v^2 + v + 1 or something like that where you have numbers.

[raven swift]

i have cd

[strange nimbus]

Well, go ahead and factor d^2 + d - 2 and I'll show you how to apply it.

[raven swift]

(d+2)(d-1)

[strange nimbus]

OK, now put in cs on the constants and expand: (d + 2c)(d - c).

[raven swift]

cs?

[strange nimbus]

Yes multiple instances of c.

[raven swift]

i dont understand this

[strange nimbus]

You don't understand what?

[raven swift]

whats the polyonomial idenity

for the denominator

[strange nimbus]

You don't use an identity for it.

[raven swift]

so i just factor it?

[strange nimbus]

You already factored it.

Then, I said put in cs like (d + 2c)(d - c). Expand that and what do you get?

[raven swift]

lets say c is 1

can i factor it?

[strange nimbus]

No, with c.

It's already factored.

You factored it into (d + 2)(d - 1).

[raven swift]

yea but for denominator

[strange nimbus]

That is for the denominator.

[raven swift]

yea

now what do i do

where does C go

[strange nimbus]

This ^

[raven swift]

ij

OHHH

wait chai

do you have any more practice problems?

or any way to practice it

[strange nimbus]

Well, you can do something like (d + c)(d + c) and put random coefficients.

Then, you expand it.

Then you hide the factored form and try to factor the expanded form.

Note that the coefficients can be negative.

[raven swift]

but why does C go into 2c and d-c

[strange nimbus]

So, like (2d + 27c)(d - 2c) = 2d^2 + 23cd - 54c^2.

So, now you hide (2d + 27c)(d - 2c) and factor 2d^2 + 23cd - 54c^2.

Or something like that.

I'm not sure what you mean by c going into 2c and d - c.

[raven swift]

like how did u factor the denominator

[strange nimbus]

Well, you know how you have (d^2 + cd + c^2) if you remove the coefficients?

The d exponent goes down by 1 each time.

The c exponent goes up by 1 each time.

Do you see that so far?

[raven swift]

yea

wait what

[strange nimbus]

Or even better, the exponents in each term add to 2.

[raven swift]

what do u even mean

[strange nimbus]

I don't know what you don't see, so I can't answer that.

[raven swift]

The d exponent goes down by 1 each time.
The c exponent goes up by 1 each time.

[strange nimbus]

Do you know what an exponent is?

[raven swift]

mhm

[strange nimbus]

OK, so, we have d^2 + cd + c^2.

What's the exponent on d in d^2?

[raven swift]

2

[strange nimbus]

What's the exponent on c in d^2?

[raven swift]

1

[strange nimbus]

No, there is no c there, so it's zero.

What's the exponent on d in cd?

[raven swift]

what?

if c is 50

,calc 50^1

[woven radish]

Result:

50

[raven swift]

,calc 50^0

[woven radish]

Result:

1

[strange nimbus]

Right, and it's d^2, which is 1 times d^2, which is c^0 times d^2.

If it was c^1, that would be c and you'd see cd^2.

[raven swift]

ohh because there is no c

?

[strange nimbus]

Right.

So, d^2 has a d exponent of 2 and a c exponent of 0.

What about cd?

[raven swift]

1

for each

[strange nimbus]

OK, what about c^2?

[raven swift]

2

[strange nimbus]

Is that for c or d?

[raven swift]

c

[strange nimbus]

What exponent does d have?

[raven swift]

1

[strange nimbus]

No, d^1 looks like d.

But there's no d there.

d^0 means d isn't there.

Does that make sense?

[raven swift]

what?

where is there no d

[strange nimbus]

Here ^

[raven swift]

ohh ok

yea 0

since no d

[strange nimbus]

OK, so we have d^2 + cd + c^2.

[raven swift]

mhm

[strange nimbus]

So, d^2 has a d exponent of 2.

cd has a d exponent of 1.

c^2 has a d exponent of 0.

So, the exponent goes down by 1 each time.

2, then 1, then 0.

[raven swift]

ohh yea

[strange nimbus]

That's for the d exponent.

With the c exponent, we have d^2 with a c exponent of 0.

cd with a c exponent of 1.

c^2 with a c exponent of 2.

So, the c exponent goes up by 1 each time.

0, then 1, then 2.

Does that make sense?

[raven swift]

yea

[strange nimbus]

OK, when that happens it will factor into something like (d + c)(d + c) with whatever coefficients.

Expand (d + c)(d + c) and see what you get.

[raven swift]

isnt that just (c+d)^2?

[strange nimbus]

Yes, but what does it expand to?

[raven swift]

c2 +d2 + 2cd.

[strange nimbus]

Right, so you have d^2 + 2cd + c^2.

Ignore the coefficients, and you can see we got back to d^2 + cd + c^2.

[raven swift]

yeaa

[strange nimbus]

So, (d + c)(d + c) is what we're looking for when we factor it.

With whatever coefficients.

Now expand (d + 1)(d + 1).

[raven swift]

mhm

[strange nimbus]

What do you get?

[raven swift]

we made c into a numbers/coefficient

[strange nimbus]

No, we're not exactly doing that.

We just got rid of c for now.

But what does that expand to?

It used to be (d + 1c)(d + 1c) and we got rid of the cs.

[raven swift]

d^2+2d+1

[strange nimbus]

Almost.

It's d^2 + 2d + 1.

[raven swift]

yea sorry

[strange nimbus]

Do you see how the coefficients are the same as (d + c)(d + c)?

You got 1, then 2, then 1.

[raven swift]

yea

[strange nimbus]

So, the coefficients are the same:

(d + c)(d + c) = 1d^2 + 2cd + 1c^2
(d + 1)(d + 1) = 1d^2 + 2d + 1

So, if you see d^2 + 2cd + c^2, you can factor d^2 + 2d + 1 instead, which is easier.

That factors to (d + 1)(d + 1).

[raven swift]

mhm

[strange nimbus]

And then you multiply the constants by c.

(d + c)(d + c).

So, with yours, you had d^2 + cd - 2c^2. You can get rid of the cs like d^2 + d - 2.

You factor that to (d + 2)(d - 1).

Then, you multiply the constants by c to get (d + 2c)(d - c).

That's only if we have the pattern with d exponents going 2, 1, 0 and c exponents going 0, 1, 2.

Does that make sense?

[raven swift]

i dont get it

sorry

[strange nimbus]

OK, let's try to do d^2 + cd - 2c^2 without that.

How would you factor that?

[raven swift]

so two numbers that multiply to -2c^2 and two numbers that add to cd

[strange nimbus]

Almost.

The d is "the variable", so to speak.

c is part of the coefficients.

So, you need two numbers that multiply to -2c^2 and that add to c.

[raven swift]

wait c is a coefficent?

[strange nimbus]

Yes, if you're using the normal factoring methods, d is like the variable, and everything else is a coefficient.

So, c would be part of the coefficients, but not d.

[raven swift]

ok now im understanding

[strange nimbus]

Like x^2 + kx + 2 has coefficients 1, k, and 2.

[raven swift]

so what do we do from there

[strange nimbus]

OK, so if they add to c, they must be something times c and something times c.

You can't do like 2c^2 + 2c to get c.

You need like 3c + 5c with just cs in both or something to get 8c with a c in it.

[raven swift]

it should be neg 2

no?

[strange nimbus]

Well, we're looking at what they add to.

They add together to give you c.

So, they're probably like 5c - 4c or something.

Does that make sense?

[raven swift]

yea

[strange nimbus]

OK, they both have c to the first power.

Then, you multiply them together to get c^2.

Like 5c times 4c is 20c^2.

Does that make sense?

[raven swift]

yea

[strange nimbus]

OK, so 5c and -4c won't work.

They add to c, but 20c^2 isn't what we want them to multiply to.

[raven swift]

-2c and c?

wait

no

2c and -c

yup

it works

lets gooooo

[strange nimbus]

Good job.

[raven swift]

now what

how do we simplify it

[strange nimbus]

OK, so d^2 + cd - 2c^2 = (d + 2c)(d - c).

[raven swift]

$d^2 + cd - 2c^2 = (d + 2c)(d - c).$

[woven radish]

T2

[raven swift]

mhm

[strange nimbus]

So, we have (\frac{c^2 - d^2}{d^2 + cd - 2c^2} = \frac{(c + d)(c - d)}{(d + 2c)(d - c)}).

[woven radish]

Chai T. Rex

[strange nimbus]

Do you see any factors that can be cancelled?

[raven swift]

no

wait yea

c+d

and d-c

?

[strange nimbus]

No, they have to be the same thing.

[raven swift]

ohh yea

nothing

[strange nimbus]

But one thing you need to know is that -(x - y) = y - x.

To see why, you do:

-(x - y)
-x + y
y - x

Does that make sense?

[raven swift]

yea

yea

[strange nimbus]

OK, so c - d and d - c are negatives of each other.

[raven swift]

yea

[woven radish]

Chai T. Rex

[raven swift]

multiply by -3

so we only have e

3*

[strange nimbus]

No, you can't do that, because you'd have to do it to both sides, but there's no other side here.

Try it with a calculator.

[raven swift]

well u get -1

if u divide

[woven radish]

Chai T. Rex

[strange nimbus]

If you divide anything other than 0 by itself, you always get 1.

Does that make sense?

Like 4 divided by 4 is 1.

[raven swift]

mhm

[strange nimbus]

OK, so that with one negative sign is always -1.

(\frac{x}{-x}) or (\frac{-x}x) or (-\frac{x}x) are all -1.

[woven radish]

Chai T. Rex

[raven swift]

yea

agreed

[strange nimbus]

So, we can divide c - d by d - c to get -1.

[woven radish]

Chai T. Rex

[strange nimbus]

Does it make sense how I got that?

[raven swift]

yep

[woven radish]

Chai T. Rex

So, we have \(\frac{c^2 - d^2}{d^2 + cd - 2c^2} = \frac{(c + d)(c - d)}{(d + 2c)(d - c)} = -\frac{c + d}{d + 2c}\) and \(d - c \ne 0\).

[raven swift]

so i cant cancel oujt that neg sign?

ok i got it i think chai

yea

i got what u got

[strange nimbus]

Well, you can by multiplying it by the top or bottom, but then you get (\frac{-c - d}{d + 2c}) or (\frac{c + d}{-d - 2c}).

[woven radish]

Chai T. Rex

[strange nimbus]

OK, one thing is that you have to write "and d - c isn't 0".

Because that used to be a factor in the denominator.

So, if it was zero, the denominator would multiply together to be 0.

And you can't have a 0 denominator.

[raven swift]

wait wdym d-c isnt 0

why not

[strange nimbus]

With (\frac{(c + d)(c - d)}{(d + 2c)(d - c)}), you have ((d - c)) in the denominator.

[woven radish]

Chai T. Rex

[raven swift]

yea

but negative sign doesnt cancel ouiit

tho

right?>

[strange nimbus]

If d - c is zero, then you have (\frac{(c + d)(c - d)}{(d + 2c)\cdot 0} = \frac{(c + d)(c - d)}0).

[woven radish]

Chai T. Rex

[strange nimbus]

Does it make sense why you'd have 0 as the denominator if d - c was 0?

[raven swift]

ohhh yea

yea

sorry i forgot about that

yea

asymptotes we learnt that

chai any more tips solving these types of problems?

[strange nimbus]

Well, we can't have 0, so we can't have d - c = 0 here, so d - c is not equal to 0.

And you have to write that because your answer doesn't show the reader that d - c can't be 0 anymore.

[raven swift]

yea

[strange nimbus]

No, the main thing is to factor the top and bottom, then look for common factors in the top and bottom (remembering that c - d and d - c can be cancelled if you put a negative sign in front of the fraction).

And then, if you cancel a factor, write that that factor can't be 0 so that people can see that.

[raven swift]

ohh yea

yea i understand it now

thx tho for telling me

c is a coeffcient

that helped a lot

any more tips? or problems?

[strange nimbus]

Yeah, when you have one main variable, anything else is part of a coefficient.

Well, to make problems, you just write something like (\frac{(d + c)(d + c)}{(d + c)(d + c)}) and fill in some coefficients for the ds and cs.

[woven radish]

Chai T. Rex

[strange nimbus]

Then, you expand the top and bottom.

[raven swift]

idk im having trouble with polynomials for algb 2

[strange nimbus]

Make sure to make some of the factors cancel because they have the same coefficients.

Then, you get a new piece of paper and write down the expanded form, hide the old piece of paper, and simplify the thing on the new piece of paper.

Well, Khan Academy is a free website. They have video lessons and practice problems.

Let me see.

[raven swift]

thank you

[strange nimbus]

Here's the section for factoring in their Algebra 2 course: https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-factor.

[raven swift]

thank you

[strange nimbus]

You're welcome.

[raven swift]

.close

[devout snow]

Channel closed

Closed by @raven swift

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

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

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

[uncut moss]

the integral of x^n is x^(n+1) /(n+1), with x evaluated from the lower to the upper limit.
here n = 1.

[tiny bay]

Yes but here i didn't understand [x] part

x^2/2

[lost laurel]

the differential variable is a constant on a given interval , are you sure the question is right?

[fervent sundial]

d[x] is 0 everywhere

except for integral values of x

[tiny bay]

I didn't understand the question actually

[quiet delta]

Then would you integrate at integral values of x or just add the integral values?

I mean like x²/2 then put integral values and add or just put 0+1+2+3+4?

[lost laurel]

I think the integral would just be 0 everywhere , except at integral points , where it isn;t defined

[quiet delta]

Why isn't it defined at integral points?

Wait a minute I get it the answer will be 0 as d(of any constant)=0

[lost laurel]

take the limit. of [x] at 3, as you approach it from the left, (sqy 2.99999999...) you get [2.99999999]=2

but [3.0000000.....1] say is 3

[quiet delta]

But you have to integrate x

Not [x]

You have to int x wrt [x]

[lost laurel]

yes, which is a constant in a given interval

[quiet delta]

So I don't think it has anything to do with the limits