help-33

[rocky pilot]

how was 1/3x^3-2x^2+10 obtained?

[still temple]

says that

you have to anti derive

the inside

then plug in the bounds

[paper raptor]

$\int x^n\dd x=\frac{x^{n+1}}{n+1}+C$

[elfin berry]

FancyBredFries

[dire spire]

power rule of integration and constant rule

[still temple]

except since it’s bounded you don’t need the C

so disregard the C

[paper raptor]

also $\int f(x)+g(x)\dd x=\int f(x)\dd x+\int g(x)\dd x$

[still temple]

aspect

[elfin berry]

FancyBredFries

[paper raptor]

but the power rule is defined on an indefinite so it's important to have it :)

[still temple]

when you solve out

using ftc

[paper raptor]

otherwise you wouldn't have a rule, you'd have just a constant

[still temple]

it always cancels

[rocky pilot]

brain not braining

[still temple]

do u went pen paper

help

?

[rocky pilot]

I plugged in a online calc and its getting a complete diff answer so yeah

that would help

[still temple]

mkay

lemme go grab

[paper raptor]

which online calc?

[rocky pilot]

emathhelp.net

[paper raptor]

try WolframAlpha

idk what emathhelp is, but wolframalpha is like the go to when you get to math like this :)

[dire spire]

or https://www.integral-calculator.com/

[paper raptor]

integral calculator is good for well...

integrals

[rocky pilot]

Idk emathhelp is useful but idk why it gave me a diff answer

its an integral calc

[paper raptor]

W|A is like a handyman

good at a little of everything

[rocky pilot]

yea it still give me a diff answer

[paper raptor]

,w int x^2-4x+10

[elfin berry]

Results provided by WolframAlpha

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

Requested by XxMrFancyu2xX#6050

[paper raptor]

just distribute

those are the same

[rocky pilot]

oh wait

[still temple]

if i’m not completely stupid this should be

the pen paper

[marsh citrus]

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.

[still temple]

u told him to

use calculator

lol

no?

[rocky pilot]

is this just not further simplified into the other answer?

[still temple]

wdym?

[rocky pilot]

Is this

[still temple]

the calculator

[paper raptor]

yes

[still temple]

is giving u

algorithmic

[rocky pilot]

not further simplfied into that

[still temple]

answer

it is

probably

lol

idk tbh

wait it’s not

[paper raptor]

there are exactly the same

[still temple]

wait it is

yea they are

[rocky pilot]

Yeah I know they are but the first one isnt further simplifed yes?

[still temple]

yes

[paper raptor]

it's best to keep in the form 1/3x^3+...

[still temple]

but typically you don’t simplify it

yea

[dire spire]

you dont need to simplify it further to turn it into that

[rocky pilot]

bruh what

this changes everything

wdym

[paper raptor]

i need to go to bed clearly damn, sorry almost gave some really bad advice lmao

[rocky pilot]

😂

ur good I was just confused cuz the calculators would like further simplify it so I thought I had to do the same

but if I can just do it like the way we talked abt then we'

re good

[dire spire]

simplifying it is just extra unnecessary algebra

[paper raptor]

btw it's standard that whenever we integrate something that looks one way we put the antiderivative in form of the integrand itself, like if the integrand is in terms of radicals we don't keep the antiderivative in terms of fractional powers, but in radicals :) (at least what I was taught)

[dire spire]

esp when you werent asked to

[rocky pilot]

math itself is unnecessary, lets just go back to caveman terms bro

[dire spire]

[rocky pilot]

jk but yea I just dont like this unit of integrals

[dire spire]

no one does

[rocky pilot]

😂

ight well thanks

.close

[marsh citrus]

Channel closed

Closed by @rocky 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.

[woven harness]

how do i do (iiI)

given mean is 0.2

std deviation is 0.04

i found -2.5<z<2.5

how do i find the values

[urban bobcat]

using central limit theorem

[woven harness]

for iii?

isnt that for i

[urban bobcat]

part i says justify why u can use central limit theorem

part iii says to actually use it

[woven harness]

i alr did i and ii

i need help for iii

[urban bobcat]

yes i know

so u found ur mean and standard deviation yes

for the proportion of heads

[woven harness]

yes

[urban bobcat]

in part b

ok

so what was the mean and standard deviation u found

[woven harness]

.

[urban bobcat]

ok

so do u have a calculator or device

[woven harness]

yes

[urban bobcat]

that can do normal distribution calculations

ok

in that device

enter that the mean is 0.2

and the standard deviation is 0.04

and then u can say the lower limit is 0.1 and the upper limmit is 0.3

does u calculator do that?

[woven harness]

no

i dont think so

not even in the syllabus

<@&286206848099549185>

[marsh citrus]

@woven harness Has your question been resolved?

[woven harness]

.close

[marsh citrus]

Channel closed

Closed by @woven harness

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.

[dry musk]

I really don't understand the difference between a and c here..

because we don't even know the force in the y direction..? couldn't it theoretically be either?

and there's no units lol

oh well now that i think abt it

i guess c makes it look like it's also accelerating in the x?

idk

i feel like i need a better explanation

[marsh citrus]

@dry musk Has your question been resolved?

[still temple]

only difference acc to me is that A looks like parabolic curve

and the path it follows is parabola ig as constant force -> m*a

[marsh citrus]

@dry musk Has your question been resolved?

[marsh citrus]

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.

[upbeat needle]

Does anyone know how to do this without table values?

[marsh citrus]

@upbeat needle Has your question been resolved?

[marsh citrus]

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.

[lethal bridge]

Trying to find the region bounded by the curves y = x^3 + x^2 and y = x^3 - 1 from 0 to 3.

[lethal bridge]

I think I did something wrong trying to find points of intersection here

also I'm not sure if I drew the right graph, I just set them equal to eachother and drew that

was I supposed to draw y = x^3 + x^2 and y = x^3 - 1?

ok yeah im pretty sure

that is the wrong graph

[lethal bridge]

im suppposed to draw these (probably)

[terse turtle]

,ask x^3+x^2=x^3-1

[elfin berry]

Results provided by WolframAlpha

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

Requested by chlamydia.3844

[terse turtle]

you're good

[lethal bridge]

but Ive never dealt with imaginary roots before

like

ever

[terse turtle]

and yeah graph them both to see what the area is

it just means no intersection

[lethal bridge]

so my only bounds are from 0 to 3 ?

[terse turtle]

yes

[lethal bridge]

ah okay

I know what x^3 looks like but x^3 + x^2 is there like a trick to graph that

[terse turtle]

factorise it

[lethal bridge]

do i set x^3 + x^2 = 0?

[terse turtle]

why

[lethal bridge]

to find roots

oh

you mean like

x^2(x + 1)

what then?

[terse turtle]

you know how to graph cubics right

[lethal bridge]

yeah

[terse turtle]

describe it

[lethal bridge]

it starts at the origin and has a point of inflection

it is concave down below the x axis and concave up above the x axis

[terse turtle]

that's just x^3

how about just polynomials in general

[lethal bridge]

oh in general

uh

kinda broad but like

they got curves that are concave up and down depending on the multiplicity

idk what else to say about that

[terse turtle]

the general features used for sketching polynomials are x,y intercepts, stationary points and inflection points

we find the x intercepts by factorising the function into linear factors

stationary and inflection points aren't necessary here

[lethal bridge]

okay

@terse turtle like this?

Shouldn’t say -1 btw I accidentally wrote a - on the x axis

so do I take the integral of both functions at 0 to 3 and subtract them

like

$\int_{0}^{3}\left(x^{3}-x^{2}\right)-\left(x^{3}-1\right)dx$

?

[elfin berry]

water beam

[terse turtle]

should be + in the first bracker

[lethal bridge]

ih yeeah

otherwise its good?

$\int_{0}^{3}\left(x^{3}+x^{2}\right)-\left(x^{3}-1\right)dx$

[elfin berry]

water beam

[terse turtle]

yeah

[lethal bridge]

and I found A to be 12

area

cool cool

thanks

.close

[marsh citrus]

Channel closed

Closed by @lethal bridge

Use .reopen if this was a mistake.

[marsh citrus]

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.

[halcyon lichen]

how to solve ?

[halcyon lichen]

okk

i stil dont get it

[marsh citrus]

@halcyon lichen Has your question been resolved?

[marsh citrus]

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.

[lyric root]

I'm trying to factor quadratics, the problem that I'm facing with is I do not understand the process of factoring when the coefficient of ax^2 is not 1. For example as you can see in the picture the first example was easy and I understood the logic behind it as well, however when the coefficient of x^2 is 10 I'm having difficulties to understand-
The first step by the video is to multiply the leading coefficient(10) with the constant term(-6) to get -60, then the process almost the same that we have to find two numbers that add up to 11 and multiply to give -60. That is straightforward, however I do not understand the logic behind multiplying 10 by -6.

[leaden monolith]

So when there’s a ≠ 1

First you check can you factor a from the entire quadratic

This is the easiest and most obvious thing to do

Clearly you can’t here

[lyric root]

Yeah

that's clear

[leaden monolith]

Ok second way you start breaking the 10 into parts

[leaden monolith]

Where you have (x…)(x…)

Try (10x…)(x…)

Then try (5x…)(2x…)

Then give up if it doesn’t work

It should work if it’s factorisable by hand

[lyric root]

wdym by try?

[leaden monolith]

Well you’ve got there the +- signs I see

How do you know what goes after the x

[lyric root]

I mean yeah that's my question

[leaden monolith]

I mean when a = 1

How do you find the other numbers

[lyric root]

I'm looking for two numbers that when you multiply you get c and when you add you get b,

[leaden monolith]

Right exactly

And you test pairs of numbers that multiply to c

[lyric root]

Yeah

and add to b

[leaden monolith]

Ok but now instead of just adding the 2 numbers together

You need to multiply one of them by 10 before adding

[leaden monolith]

That’s this one

If you can’t make b this way

[still temple]

OH

[lyric root]

Jeez, chatgpt copy

[leaden monolith]

Chatgpt is bannable btw

[still temple]

thought i could help

[leaden monolith]

If you can’t make b this way

No problem

[lyric root]

No worries

[still temple]

ill delete it if u want

[leaden monolith]

Multiply 1 number by 2 and the other by 5 then add

Can you make b?

If you can’t you give up because it’s not doable by hand

[lyric root]

I dont really get it, I mean the first part must be this

[leaden monolith]

You give up because 1, 10 and 2, 5 are the only pairs of Integers to multiply to 10

Ok so let’s say you have -6 there

[lyric root]

But how do you figure out what goes after x

[leaden monolith]

So it’s either 1 6 or 2 3

Clearly

[lyric root]

Yeah

but what do you replace -6 with?

[leaden monolith]

1*10 and 6*1 is 16 or 4

Very far from 11

1*1 and 6*10 is 61 or 59

Even further from 11

[lyric root]

I dont understand, where?

[leaden monolith]

-6 is in the question

[lyric root]

where did you plug -6 in?

[leaden monolith]

You have 10x² + 11x - 6

[lyric root]

Yeah but I dont get the logic, like the trying stuff that you do

I understood it when it was with just x^2

[leaden monolith]

Ok

Let’s look at this

(10x + m)(1x + n)

What do we get when we expand this

[lyric root]

10x^2 + 10bx + ax + ab

[leaden monolith]

Ah I shouldn’t have used those letters

Let me change it

[lyric root]

okay no worries, I appreciate your help

In the video btw, she's using the AC method

[leaden monolith]

10x^2 + (10n + m)x + nm

Lol I’m not gonna lie idk what AC method is

I do factorisation by intuition and experience

[lyric root]

What @still temple copied

[lyric root]

dont really know what this supposed to represent

[still temple]

bro what

even though i copied from chatgpt

[leaden monolith]

What the heck

This AC method looks ass

[still temple]

i know what ac method is

[leaden monolith]

It’s just a very procedural way of intuition

[still temple]

and easy

[lyric root]

didnt say you did, you just copied it

[still temple]

bro yes i copied it

[leaden monolith]

https://txwes.edu/media/twu/content-assets/images/academics/academic-success-center/A-C-Method.pdf

[still temple]

but i know what it is before i copied it

[leaden monolith]

Are these the steps you’re doing

[lyric root]

Can you explain it then?

[still temple]

bet

explain how it works

or what it is

[lyric root]

How do you use it to solve the problem I've sent

[still temple]

oksy

[lyric root]

I think so

[leaden monolith]

I think AC can be good but sometimes requires as much experience as doing it my way

[still temple]

the problem is 10x^2 - 11x - 6 right?

so

multiply first and last term

[lyric root]

Yeah I mean, understanding it in a deeper level would be way much beneficial

[still temple]

=-60

[lyric root]

I can read thru the pdf as well, I can solve my problem with the ac method I just dont understand the point of it

[leaden monolith]

I can try to help explain but there’s a lot of moving parts

[still temple]

do u know what math is

[lyric root]

I want to question everything not just accept a method that I'm using.

[still temple]

u dont need a point to find a solution

[leaden monolith]

I think the AC method complicates thing due to needing to factorise AC which can be much tougher than just facotring c

Cos AC is just bigger

[still temple]

mathematician just wants to win a nobel and learn math

[leaden monolith]

Bigger = harder to factorise

[still temple]

no

[lyric root]

I dont care about the solution that much I just wanna understand the why of every step I'm doing

[still temple]

its actually easy

i just told chatgpt to explain as if the person is new

[leaden monolith]

Look I’m not too certain on this AC method but I can show you how I intuit factorising quadratics

[still temple]

lmao

[lyric root]

The method is easy, but understanding the why is the hard. I mean everyone can read thru a pdf but actually understand what's going on under the hood is way much beneficial

[lyric root]

I'd love to see

[leaden monolith]

It’s just a combination of quick mental arithmetic and lots of practice

[still temple]

u told me ur point

whats there to argue about

both are same

[leaden monolith]

So let’s take the question as an example

[still temple]

yall just used at something

done.

[lyric root]

Okay

[leaden monolith]

I need to factorise 10x² + 11x - 6

[lyric root]

yep

[leaden monolith]

I’m gonna assume the numbers are Integers

[lyric root]

yep

[leaden monolith]

I look at them

Can I factor 10, 5 or 2 from the entire thing to make it easier (smaller coefficients = easier)

No, so we’ll have to live with the 10

[lyric root]

why cant you, 5x \cdot 2x?

[leaden monolith]

.

Can I factorise 10, 5, 2 from everything

[lyric root]

Ohh yeah you're right

[leaden monolith]

So 10x² + 4x - 6 I can factorise a 2 from everything

[lyric root]

apologies

[leaden monolith]

Here I can’t

Well I know in (kx + n)(hx + m) which is what I will have

I know kh = 10

nm = -6

[lyric root]

yeah, got it so far

[leaden monolith]

Ok I’m gonna ignore the - signs because they don’t really matter

It’s not a big deal you’ll see later

[lyric root]

okay

[leaden monolith]

So 10 can be 1 10 or 2 5

6 can be 1 6 or 2 3

[lyric root]

yep

[leaden monolith]

(This gets really hard to think about with negatives, you’d have to say -1 6, 1 -6, -2 3, 2 -3)

That’s why I’ve just temporarily ignored them

[lyric root]

Yep, gotcha

[leaden monolith]

Ok now comes the mental arithmetic

Our goal is to make 11

Positive negative doesn’t matter if it you can’t get it it probably means it’s not doable

[lyric root]

I mean that should be in the middle, not sure what you mean here

[leaden monolith]

I’ll clarify

[leaden monolith]

We have these numbers

[leaden monolith]

And these numbers

[lyric root]

yep

[leaden monolith]

And we want to “make” 11

But there’s some rules

We need to multiply the factors of 6 by the factors of 10

Then add to 11

Or subtract

So let’s say I picked 10 1 and 1 6

[lyric root]

yeah

[leaden monolith]

If I pair the 10 with the 6

I’m in 61 or 59 land

Wayyy too far from 11

If I pair the 10 with 1

I’m in 16 or 4 land

[lyric root]

wait so (10 + 1)(1 + 6)?:

[leaden monolith]

Closer but still far

[leaden monolith]

Yes

[leaden monolith]

(10x + 1)(1x + 6)

See how the 10 and 6 are in different brackets

That’s what it means to be “paired” together

[lyric root]

Ohh okay, that's really good to know

[leaden monolith]

Because when I expand I’ll have to multiply the 10x and 6 together

[lyric root]

Yep

[leaden monolith]

That’s how I’m getting these numbers

10 * 6 +- 1 * 1

Way too far from 11

Even pairing the 10 with 1 is still too far

10 * 1 +- 1 * 6 = 16 or 4

[lyric root]

But how do you know that the middle term(11) will be this?

[leaden monolith]

We want to make 11

[leaden monolith]

So far we are trying this

[lyric root]

You mean we want 11 to be in the middle surrounded by 10x^2 and -6?

[leaden monolith]

Yes

[lyric root]

okay

[leaden monolith]

I want to make (km +- hn) = 11

Because that’s the x term

I don’t know if it’s add or minus or whatever

Doesn’t matter for now

[lyric root]

But you cant have km, since k is with x

[leaden monolith]

So what this tells us was that picking 1 10 and 1 6 was bad

[leaden monolith]

No the expanded form is (km + hn)x

,w expand (kx+n)(hx+m)

[elfin berry]

Results provided by WolframAlpha

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

Requested by frosst

[leaden monolith]

See the middle

[lyric root]

yeah okay

[leaden monolith]

hnx + kmx = (hn + km)x

[lyric root]

Yeah that's clear

[leaden monolith]

Do you follow this

[lyric root]

I do, but in this case what should have been equal to 11?

[leaden monolith]

Ok after we chose 1 10 and 1 6

[lyric root]

yeah

[leaden monolith]

Do you understand this part

(10x +- 1)(x +- 6) gives 61x or 59x when expanded

[lyric root]

Yeah that's clear

[leaden monolith]

And you understand the other paring?

[lyric root]

but what happens when we pair the 10 with 1

[leaden monolith]

(10x +- 6)(x +- 1)

We get either 16 or 4

[lyric root]

Yeah that's clear

[leaden monolith]

Ok so no 11 to be found

[lyric root]

yeah

[leaden monolith]

That means this is wrong

Now here’s where intuition and experience comes in

We want to make 11

I look at 10 1 and 1 6

Doesn’t look like I can make 11

I won’t even try

[lyric root]

That's what I dont have 😄

[leaden monolith]

I actually skip striaght to 2 5 and 2 3

These are some nice small numbers that look like they can make 11 the easiest

[lyric root]

(2x +-3)(5x+-2)?

is this what we are doing rn?

[leaden monolith]

Not so fast yet

I have an extra comment to give

[lyric root]

Yep

[leaden monolith]

But also you should now realise that if my question was 10x² - 61x + 6, the factorisation is very obvious

Whoops forgot the x

But you can see now that the 61 is ringing alarm bells saying pair the 10 with 6!!!

[lyric root]

yeah

that's clear

[leaden monolith]

So that’s a kind of intuition you will develop with this method

Ok back to the question

[lyric root]

yep

[leaden monolith]

(2x +- 3)(5x +- 2)
Or
(2x +- 2)(5x +- 3)

We don’t know yet but let’s try

[lyric root]

yeah

[leaden monolith]

The answer is the first one

But let’s say we didn’t try that first

Let’s say we tried the 2nd one first

We would go 2*5 and 3*2

That gives 10 and 6 so I’d get 16 or 4

Which is still bad I want 11

[lyric root]

Yeah

[leaden monolith]

Ok what about the first one

You try say it

[lyric root]

15 and 6 so you'd get 11!!!! or 21

[leaden monolith]

What

15 and 6 gets you 9 or 21

Lol

[lyric root]

shit

😄

[leaden monolith]

It’s not 6

[lyric root]

why?

[leaden monolith]

(2x +- 3)(5x +- 2)

[lyric root]

isnt 35 and 32

[leaden monolith]

We’ve paired 2 with 2 and 3 with 5

No there’s 2 2’s not 2 3’s

[lyric root]

I mean 3 times 5 and 3 times 2

[leaden monolith]

Put a \ before your star

It overrides the formatting

[lyric root]

okay

[leaden monolith]

isnt 3\*5 and 3\*2

[lyric root]

okay so I'll expand it. 10x^2 +- 4x +- 15x +- 6

[leaden monolith]

Aha

That’s not a 6

[lyric root]

now I'm confused

what is it then?

[leaden monolith]

That’s a 4 you got there not a 6

[leaden monolith]

You said 15 and 6

You don’t get 15 and 6 that’s wrong

[lyric root]

Ohh yeah I know what you mean now

[lyric root]

yeah

[leaden monolith]

Right and you get 4 because that’s 2*2

[lyric root]

yeah

[leaden monolith]

From this

[lyric root]

so (2x+3)(5x-2) ? Because that's where we have 11x and -6

[leaden monolith]

Yes

If it was -11x

You swap the minus signs

[lyric root]

Yeah

[leaden monolith]

If it’s +19

It’s impossible

[lyric root]

jeez I understand it now, it was a hard enough ride

[leaden monolith]

Because -6 means you have differing signs

And 19 means 15 + 4

[lyric root]

Yeah

[leaden monolith]

So that’s impossible that needs the same sign

But -19x and + 6 is possible

Both can be minus

[lyric root]

Exactly

Thanks very much for your help it is unreal how patient you were and how long you tried to help.

[leaden monolith]

Now go do like 100 questions using this method

(If you want to get good at it)

[lyric root]

Yeah I will practice it

[leaden monolith]

Then you’ll just very easily see how to factorise

It’s very hard to explain because it’s very uh

Intuition based

[lyric root]

This is way better, you actually understand every part of it

[lyric root]

Yeah, I mean you just need experience and practice

[leaden monolith]

I just say it’s factorisation by inspection because often times you just see the right choices straight away

When there are a lot of choices then it doesn’t matter what you do it’ll be hard

I would just plug into quadratic formula haha

Bad numbers are ones with lots of factors

And when the middle number (x term) is like a medium ish number it’s very hard as well

[lyric root]

I mean yeah, that would take hours to solve perhaps

[leaden monolith]

Medium is like 6-20 ish

Best ones are the ones with prime a and/or c

Prime ones have the least factors haha

This also really relies on good and fast mental arithmetic

And don’t worry if it’s a struggle at the beginning, I didn’t even consider extending my inspection method to a ≠ 1 questions until much later on

I used to always used quadratic equation if a was not 1

[lyric root]

Okay, thanks very much for your patient and extremely helpful help

[marsh citrus]

@lyric root Has your question been resolved?

Channel closed

Closed by @lyric root

Use .reopen if this was a mistake.

[marsh citrus]

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.

[stoic tiger]

where is q_j coming from in the second term?

[stoic tiger]

is it some property of derivatives of a function with multiple variables? is it a property of the taylor expansion?

the fuck is going on

3rd term, i should say

[devout mauve]

yes that is the taylor expansion in more than one variable

you have to sum over all second derivatives

and then over all third derivatives. and so on

[stoic tiger]

ok, i imagine this has something to do with the chain rule as well?

similar source of confusion here

pretty sure it has something to due with this

or maybe not

idfk

[marsh citrus]

@stoic tiger Has your question been resolved?

[marsh citrus]

@stoic tiger Has your question been resolved?

[marsh citrus]

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.

[merry yarrow]

can someone help me with this question?

[marsh citrus]

@merry yarrow Has your question been resolved?

[merry yarrow]

.close

[marsh citrus]

Channel closed

Closed by @merry yarrow

Use .reopen if this was a mistake.

[marsh citrus]

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.

[desert prairie]

Anyone able to help me with it

[desert prairie]

With question 28

[twilit grove]

you need to show the figure...

[desert prairie]

The top one

Mb

Mainly neee help with the first one

I know it’s only a one marker

[twilit grove]

well when does sin(2t) = 0

[desert prairie]

When t is pie?

[twilit grove]

and?

[desert prairie]

Pie over 2 and 0?

[twilit grove]

yes. but t=0 would be at point O

[desert prairie]

So t would just be pie over 2?

[twilit grove]

pi / 2, but yes I think so

[desert prairie]

Ok thanks

Could you or anyone else help me with 29 b

Wait nvm

Nvm I do need help

.close

[marsh citrus]

Channel closed

Closed by @desert prairie

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.

[karmic mason]

x = csc (n) and y = csc (n) + cot (n) and if n = 2 get the tangent line

[karmic mason]

<@&286206848099549185>

[tacit vale]

is this supposed to be a parametric curve?

[karmic mason]

ye

[tacit vale]

do you know how to find the equation of a tangent on a regular curve? given the equation?

[karmic mason]

yes

[tacit vale]

find dy/dx at that point, which is the gradient. find x and y at that point. sub into y = mx + c to find c

do the same here

use chain rule to find dy/dx

[karmic mason]

my problem here is that i dont have csc and cot on my calc

[tacit vale]

ah

cosec = 1/sin

or (sin(n))^-1

cot(n) = 1/tan

or (tan(n))^-1

do it like this

[karmic mason]

ye tried that and it gave me the terrifying number of 2 sqrt(3) / 3

my bad n = pie/3

[tacit vale]

yeah youll get something like that

thats alr

wait what

no

n = 2

[karmic mason]

no i typed the n wrong at the biggening

[tacit vale]

ah

[tacit vale]

the yes thats x

y is sqrt(3)

dy/dx you can find

and substitute

[karmic mason]

well when deffrentiating and deviding the answer becomes (-csc(n)cot(n)-csc^2(n))/-(csc(n)cot(n))

which is not very fun to do on the calculator

[karmic mason]

substituting that would make me feel like sisyphus fr

[tacit vale]

not 100% if thats right but hopefully it is

but yeah

its not fun

i dont have a paper w me rn so

[karmic mason]

ye thanks ill try

[marsh citrus]

@karmic mason Has your question been resolved?

Channel closed

Closed by @karmic mason

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.

[marsh citrus]

@grand thorn Has your question been resolved?

[marsh citrus]

@grand thorn Has your question been resolved?

[marsh citrus]

@grand thorn Has your question been resolved?

Channel closed

Closed by @grand thorn

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.

[mint sonnet]

a driver sets out on a journey, for the first half of the distance she drives 30 miles per hour and second half 60 miles per hour, what is her average speed for the entire trip

help?

[marsh citrus]

@mint sonnet Has your question been resolved?

[still temple]

I can explain the answer, but i can't do it well

Let's say the entire trip distance was 1000 miles

[marsh citrus]

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.

[pale drift]

what does the 5 miles due east mean?

[marsh citrus]

@pale drift Has your question been resolved?

[pale drift]

<@&286206848099549185>

[marsh citrus]

@pale drift Has your question been resolved?

[still temple]

@pale drift that means 5 miles to the east

or to the right

compass directions are used in physics and math a lot because they can be defined easily

[pale drift]

so 5 miles to the right of G?

[still temple]

yeah

[pale drift]

ok, thank you

[still temple]

thats what 5 miles due east of G means

no worries

[pale drift]

.close

[marsh citrus]

Channel closed

Closed by @pale drift

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.

[desert sedge]

.close

.open

[desert sedge]

solve for the lenght of t

[still temple]

hypotenuse of the right triangle

use pythag

a^2 + b^2 = c^2

@desert sedge

[desert sedge]

so t^2+b^2 = c^2

[marsh citrus]

@desert sedge Has your question been resolved?

[marsh citrus]

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.

[jaunty anvil]

this is about the topic Bearings

all numbers are in metres

i tried solving (i) myself but then i had no clue what i was doing

<@&286206848099549185>

Bro I don't get this at all

[marsh citrus]

@jaunty anvil Has your question been resolved?

[jaunty anvil]

Broo

I have another problem then

I don't think this is law of sines

It might be cosines I think

But I was absent when they were teaching this and I just don't get it

man nvm im just gonna fail it bro 💀

.close

[marsh citrus]

Channel closed

Closed by @jaunty anvil

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 sundial]

how do you read this ? "S4 ={x∈Z:|x|=−x},"
The way I read this, The set S4 consist of x integers such that the absolute value of x equals to -x.

but does that make sense?? "absolutely value of x equals to -x" is never true, like how can |x| = x just like 1 = -1, or 2 = -2 ... wouldn't it make more sense to write |-x| = x , which i could read it as -x will get its absolute value to x? sorry im new to set notations and mathematics.

[restive sundial]

this is the answer ;;

[pastel leaf]

|x|=-x is true for many integers.
unwind definition of abs value |x|:
x for x>=0
-x for x negative.

now if x is negative then |x|=-x says
-x=-x

[marsh citrus]

@restive sundial Has your question been resolved?

[marsh citrus]

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.

[frail lodge]

boolean algebra

[frail lodge]

how do they get this step?

[marsh citrus]

@frail lodge Has your question been resolved?

[marsh citrus]

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.

[umbral karma]

Quick help?

[umbral karma]

Calc students are bad at basic math sometimes : p

[gray shoal]

You can do 15 divided by 2.5 (got 2.5 from turning that 2 1/2 into a decimal)

[umbral karma]

Ah ok so 6

[gray shoal]

yup

[umbral karma]

Alright easy enough

[gray shoal]

I think thats the answer

I did it on a whim

[umbral karma]

I mean that’s what I got too so hopefully

[gray shoal]

ok

[umbral karma]

.close

[marsh citrus]

Channel closed

Closed by @umbral karma

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.

[unreal bridge]

I dont even know where to start...

If Im(z) =/= 0 , then z is imaginary. Thus, z = -z'

But where do I go from there? Multiply by the conjugate?

[young owl]

no

Im(z) =/= 0 doesn't mean z imaginary

1+i is not imaginary but Im(1+i) =/= 0

to solve this, I think you use 6z + 2/z = r for some real r
so 6z²-rz+2 = 0, then z' verifies it too

[unreal bridge]

lemme try it

dont think that works

this is a sample solution

[young owl]

that's wrong, in the question they say 6z+2/z is real

but in your last screen, they say 8z+2/z

[unreal bridge]

yeah its just different numbers

its the same question with randomly generated numbers, the sample solution is just showing the workings of how to do it, but I dont understand the 1st part already

[young owl]

8z+2/z is real, so it means Im(8z+2/z) = 0

that's what a real is, a number that has 0 as imaginary part

but then, Im(8z+2/z) = Im(8z)+Im(2/z) = 8Im(z)+2Im(1/z)

= 8Im(z)+2Im(z'/zz') = 8Im(z)+2/zz' Im(z')

because zz' is a real (it's |z|)

they got it out of the Im with the trick of writing 1/z as z'/zz'

then they use that Im(z') = -Im(z)

and they're back to having only Im(z)

to solve the equation "for Im(z)"

then since it's non 0, 8-2/zz' has to be 0

and now you solve for zz'

[unreal bridge]

hmm ok thank you very much!

I dont really get it tbh but ill try again

have a nice day 😄

.close

[marsh citrus]

Channel closed

Closed by @unreal bridge

Use .reopen if this was a mistake.

[marsh citrus]

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.

[still temple]

hello i need help im not sure with my answer

[stoic saddle]

,rccw

[stoic saddle]

is this... an equation you were given as-is?

or was the goal to factorize x^4 - 324x^12?

[still temple]

yes i think soo we need to find the factor smth

[stoic saddle]

"find the factor" is a bit strange as far as wording goes

[still temple]

how to factor in two different squares

im not sure with my answer..

[main timber]

Your answer would be wrong for only one thing (understanding that the expression "x^4 - 324x^12" must be factored) Because when you factor it you should get "x^4(1-18x^4)(1+18x^4) " and not "x^4(1-18x^4)x^4(1+18x^4)"

To notice this, check by operating "x^4(1-18x^4)x^4(1+18x^4)" and you will see that you will get "x^8 - 324x^16" and not "x^4 - 324x ^12"

[still temple]

ohh okayy thanks!

[small kindle]

can someone help me find this using derivatives

[waxen dust]

!occupied

[marsh citrus]

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).

[main timber]

Not at all!

[marsh citrus]

@still temple Has your question been resolved?

Channel closed

Closed by @formal hearth

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.

[sour sphinx]

how do you find range of functions

[sour sphinx]

i understand domain

[main idol]

find the domain of its inverse function

[marsh citrus]

@sour sphinx Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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.

[broken pond]

"show that the polynom has exactly one reell zero point?

like where its 0

i understand that you are supposed to derive

and then equal to 0

and its greater than 0 which means its + as in the graph is positive

but i dont understand how to get the "exact one reell zero point"

[wet holly]

Here u can just show it's monotonous

[broken pond]

what does that mean?

like a

function to he power of 3?

[leaden monolith]

Monotone means the derivative is always positive or always negative

Although…monotone applies to non continuous functions too

But you have a continuous and differentiable function

I could suggest the use of MVT and IVT

[broken pond]

umm i need to see what those are

[marsh citrus]

@broken pond Has your question been resolved?

Channel closed

Closed by @broken pond

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.

[brave pumice]

is my graph correct?

[brave pumice]

nvm

this one

💀

[marsh citrus]

@brave pumice Has your question been resolved?

[marsh citrus]

@brave pumice Has your question been resolved?

[brave pumice]

.close

[marsh citrus]

Channel closed

Closed by @brave pumice

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.

[rich herald]

hey

[rich herald]

According to the solution I did everything right except i the power -8 should be -9 apparentely

<@&286206848099549185>

Help

[unborn condor]

where does the 3000/1.05 come from on the left?

also, what's that 20'000 supposed to be?

[rich herald]

sorry the -20k isnt part of the series

idk in the solution they took out the 3000/1.05 just like how i wrote it

i didnt completely understand that part either tbh

[unborn condor]

dont use the top apostrophe as separator, if you do need a separator use half a space

[rich herald]

okay my bad

[unborn condor]

also, i dont know where you're getting the 1.05^-k, since 1+0.5=1.5, not 1.05

[rich herald]

ah its meant to be .05

[unborn condor]

Okay. I'm gonna ignore the -20k and work only with the original sum

[rich herald]

Okay perfect thanks

[unborn condor]

sum from k=0 to 8 of 3000/[(1+.05)^(k+1)] is equal to 3000* sum from k=0 to 8 of 1/[(1+.05)^(k+1)]

[rich herald]

okay

if you want i can send the provided solution

[unborn condor]

the sum from k=0 to 8 with index k+1 is the same as the sum from k=1 to 9 with index k

[rich herald]

Ahhh yeah

[unborn condor]

so now you have:
sum_1_9 of 1/1.05^k

which is the same as
sum_1_9 of 1.05^-k

[rich herald]

yeah

i follow so far

[unborn condor]

this is a geometric series

[rich herald]

i understand now i just dont know why they took out 3000/1.05

[unborn condor]

for easier computation of the series

[rich herald]

but then where does -9 come from

or did they do t+1

wait i think i get it now

[unborn condor]

they do it in only one step, i would not do that

[rich herald]

yeah me neither haha i think thats what confused me

[unborn condor]

as you can see it's definetly not obvious

the 3k out is simple

now, the first 1/(1.05) would be inside the sum when the limits are 1 and 9

but since it's multiplying every term there, you can take it out and then you change the limits of the sum from 0 to 8

[rich herald]

ah yeah that makes sense

I wish they wouldve expanded a bit more though lol

but thanks a lot its much clearer now

.close

[marsh citrus]

Channel closed

Closed by @rich herald

Use .reopen if this was a mistake.

[unborn condor]

and then they use this

[rich herald]

ahh yeah

thats useful

thanks a lot

[unborn condor]

np

[marsh citrus]

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.

[plucky parcel]

hello

[plucky parcel]

ok, so basically i forgot why i added a 1

3^x = 3^50 + 3^50 + 3^50
3^x = 3*(3^50)
3^x = 3^(1+50)

[worthy trellis]

are you aware of laws of exponents?

[plucky parcel]

the question is what is x

[plucky parcel]

if you multiply two number with same base you can add their exponents?

[worthy trellis]

$a^m \times a^n = a^{(m+n)}$

[elfin berry]

Deol

[worthy trellis]

yes

here you have $3^1 \times 3^{50}$

[plucky parcel]

but the 3 here 3*(3^50)

doesnt have a square

[elfin berry]

Deol

[plucky parcel]

3^51

or can i say instead of 3*(3^50)

i write this 3^1 *(3^50) ?

[worthy trellis]

no one said that it had to be a square

yes

[plucky parcel]

so even if its not a square

and it has the same bas

you add the exponents

no matter what

[worthy trellis]

yes

[worthy trellis]

yes you can

you should be able to take it away from here, yes?

[plucky parcel]

ye

3^x = 3^(1 + 50)

3^x = 3^51

x = 51

[worthy trellis]

yes that looks fine to me

[marsh citrus]

@plucky parcel Has your question been resolved?

Channel closed

Closed by @plucky parcel

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.

[obtuse locust]

Connections between triangle numbers, house numbers and square numbers

All are natrual numbers

House number figure can be made with square number and triangle number figure

Square Number figure can be made with 2x Triangle number figure

[obtuse locust]

True or false?

[marsh citrus]

@obtuse locust Has your question been resolved?

[unborn shale]

the question is highly unclear. please write the original question verbatim, and possibly show your work. Photos of the problem are accepted.

[obtuse locust]

Top = triangle

Middle = Square

Bottom = House

Triangle numbers: 1, 3, 6, 10 ...

Square Numbers: 1, 4, 9, 16 ...

House numbers: 1, 5, 12, 22 ...

[unborn shale]

\begin{align*}
t_k &= \frac{k(k+1)}2 = \frac12k^2 + \frac12k\
s_k &= k^2\
h_k &= ??
\end{align*}

[elfin berry]

luke1337

[unborn shale]

why is 2 not a house number?

1 is a triangle number
1 is a square number
so 1 + 1 = 2 is a house number?

[obtuse locust]

@unborn shale i have no idea bro

[obtuse locust]

This is just what I am thinking

But it might be false

[unborn shale]

triangle number is half a square plus half a line?

[obtuse locust]

example: sqaure number 9 (9 dots in square) and triangle number 3 (3 dots in triangle)

and you can make it look like house

this is what i think

[obtuse locust]

sqaure number not same i think

just triangle number is half of what square looks like

[unborn shale]

not exactly half, see equation above

[obtuse locust]

oh so its true that

Natrual numbers and that you can make a house

with the square and triangle

House number = 12 Triangle Number = 3 Square Number = 9

So this are the only connections I can think of

between the different type of numbers

[unborn shale]

So you're saying that
\begin{align*}
t_k &= \frac{k(k+1)}2 = \frac12k^2 + \frac12k\
s_k &= k^2\
h_k &= s_k + t_{k-1}
\end{align*}
?

[elfin berry]

luke1337

[obtuse locust]

ye this

@unborn shale

[obtuse locust]

what is K?

In like sk = k^2

k^2?

Oh nvm understand

So like if its figure 5

The square will contain 25 dogs

Dots*

[unborn shale]

yes

\begin{align*}
T_n &= \frac{n(n+1)}2 = \frac12n^2 + \frac12n\
K_n &= n^2 = T_n + T_{n-1}\
H_n &= K_n + T_{n-1}
\end{align*}

Looks like it

but i think your textbook already has the solution?

[unborn shale]

Like this

[elfin berry]

luke1337

[obtuse locust]

Ye but thanks for explaining. I wouldve understand it Worse if you didn’t help

i close now 😁

Ty

.close

[marsh citrus]

Channel closed

Closed by @obtuse locust

Use .reopen if this was a mistake.

[unborn shale]

nw

[marsh citrus]

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.

[visual sparrow]

Hi

[visual sparrow]

How to find the limit of this equation

[high pine]

is it

[elfin berry]

Modus

[visual sparrow]

Yes but x

[visual sparrow]

How can i solve it tho

[high pine]

conjugate

multiply by conjugate

then simplify

[marsh citrus]

@visual sparrow Has your question been resolved?

[marsh citrus]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[marsh citrus]

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.

[lyric bay]

Hello

[lyric bay]

How do I solve

Without using LH?

This is how far I got

[proper zodiac]

Do you know the limit as (stuff) goes to 0 of tan(stuff)/stuff

[still temple]

remember thats when lim goes to zero of sinx/x is 1

[lyric bay]

Yea

[lyric bay]

Where's sinx/x

[still temple]

before u get here

[proper zodiac]

So try and manipulate your expression to have something of that form

[still temple]

((sin4x/cos4x )5x)

[astral junco]

yeah exactly

[still temple]

split it in 2

[lyric bay]

$\frac{\tan\left(4x\right)}{x}\cdot\frac{1}{5}$

[elfin berry]

LE SSERAFIM

[lyric bay]

Like this?

[proper zodiac]

Good start

What do we need on the bottom now?

[lyric bay]

tan4x/x is going to be 1