help-0

[alpine sable]

Really? thats a rule?

[mortal trellis]

something like that, yes. surely you covered that in your course at some point

that's what makes gaussian quadrature optimal

cause it can't get better than that

[alpine sable]

Ahh, i mustve missed that

One thing

give me a min

Nevermind, alright thanks a lot finally someone who actually helped

Have u taken numerical methods before? if i need help later is it alright if i ping u?

@mortal trellis

[mortal trellis]

no, just ask as usual and maybe I'll see it

[alpine sable]

Alright, thanks again

[lone heart]

@alpine sable Has your question been resolved?

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[uneven nebula]

This does not make any sense?

Arrh

Never mind

maple is just stupid sometimes

[alpine sable]

Stavanger?

[uneven nebula]

Staveanger?

[alpine sable]

Ja alltså studerar du på uis?

[uneven nebula]

DTU

Denmark

[alpine sable]

oohh aight

[uneven nebula]

What about you?

[alpine sable]

Norway

UiS

[uneven nebula]

Oh I thought your language seems similar

to dnaish

danish

[alpine sable]

Yeah haha

But wait, on this problem its 4 nodes right, but that means 2*4-1=7, but we have degree 6?

ahhh nevermind u said its accurate Up To

[lone heart]

@uneven nebula Has your question been resolved?

[uneven nebula]

Actually I have a follow up question

How do i show that LHS is the same as the RHS

I think I can start by using my 2. in the 3.

<@&286206848099549185>

[lone heart]

@uneven nebula Has your question been resolved?

[wild trail]

Which LHS and RHS are they talking about?

[uneven nebula]

The ones at 3. prove the statement

Oh I see

I have made a mistake in the beginning

[uneven nebula]

I meant left hand side and right hand side

[wild trail]

As in what is on the lhs and what's on the rhs

[wild trail]

huh?

[uneven nebula]

RHS:

[wild trail]

They are clearly not equal

[wild trail]

We wanted to prove T(n), it's assumed true for n=j and then we want to show it is true for n=j+1 to complete the induction

[uneven nebula]

Yes

I have corrected a mistake from earlier

Maybe that was the reason they weren't equal

[wild trail]

Oh yeah, this is correct now. I was confused cause there was no summation there

wait a min

[uneven nebula]

Okay

[wild trail]

It's still wrong

[uneven nebula]

Maybe I should start from scratch

should i do that?

[wild trail]

It should be -> 1 + (1 + 3*1) + (1 + 3*2) + ... + (1 + 3*j) = (3j + 2)(j + 1)/2

That is what you would assume for induction hypothesis

[uneven nebula]

Alright

[wild trail]

(ie the part where you "Assume n=j")

[uneven nebula]

Okay

[wild trail]

And you want to prove -> $1 + (1 + 3 \cdot 1) + (1 + 3 \cdot 2) + ... + (1 + 3 \cdot j) + (1 + 3 \cdot (j+1)) = \frac{(3(j+1) + 2)((j+1) + 1)}{2}$

[ocean seal]

numbpy

[uneven nebula]

I'll write it down

[uneven nebula]

Is it right so far?

[wild trail]

Yes but why are you writing the = part. You are supposed to prove it right?

[uneven nebula]

Oh yeah mb

I forgot

[wild trail]

First line after "prove the statement is true for n = j+1" is ok but for later ones just keep the lhs part

[uneven nebula]

Yes

[uneven nebula]

What can i do from here?

[wild trail]

Just proceed as you are doing here

You'll need some algebraic manipulations

[uneven nebula]

I can do some manipulations here right?

manipulations

[uneven nebula]

I think i've made a mistake again

[wild trail]

Looks good to me

In cases like these you might wanna simplify the rhs

[uneven nebula]

Ok

[wild trail]

Just do some rough and see if they are coming as equal

[uneven nebula]

I don't think it is equal?

[uneven nebula]

What do you think?

[wild trail]

I found the mistake

[wild trail]

Here, check 3rd line

More like going from 2nd to 3rd there's a mistake

[uneven nebula]

Is it the fact that i divided it by 2?

[uneven nebula]

I don't see the mistake unless it is because I divided it by 2?

[wild trail]

Yes, you divided by 2 without multiplying by 2

equation 2 and 3 aren't equal

[uneven nebula]

Like this then?

[uneven nebula]

is this right?

[wild trail]

yes, follow this

[uneven nebula]

This is where i am at now

I don't know what to do from here

[uneven nebula]

Do you have any suggestion

[wild trail]

Easiest would be to just expand both lhs and rhs completely and compare

[uneven nebula]

Alright i'll try it

[uneven nebula]

I think it is equal but I

am not sure

I differs a little bit

[wild trail]

are u using some software or something?

[uneven nebula]

Yes

Maple

[wild trail]

just do it be hand, it's faster and less confusing

maybe not faster

[uneven nebula]

okay

[uneven nebula]

it is not the same

[wild trail]

both should be equal to 3j^2 + 11j + 10

[uneven nebula]

But the thing is they aren't

[wild trail]

left one is the lhs?

[uneven nebula]

yes

No

Left one is the rhs

[wild trail]

U should recheck calculations

[uneven nebula]

I guess I could try again

[uneven nebula]

it just does not get equal at all

[wild trail]

okayy, the rhs is 3j^2 + 11j + 10 right?

What are you getting as the lhs?

[uneven nebula]

Or this for example

There is actually a example of the answer

But I tried to solve it myself

I could show that one

[wild trail]

yeah

[wild trail]

Can you try expanding the lhs by your hand step by step and then post the picture

[uneven nebula]

I'll give it a try why not

The way I see it acually

On the answer here, he does not expand the RHS

He only expands LHS

Which is the same result i got earlier

In this one. The RHS is on the left

[wild trail]

I mean doesn't really matter what you expand as long as you get both sides as equal

[uneven nebula]

You know what actually it is equal

When I look at how the answer has done it

i understand it now

[uneven nebula]

Thank you for your help

I'll just close this tab now, cause I understand it now.

[wild trail]

Sure

[uneven nebula]

.close

[lone heart]

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[primal galleon]

I'm trying to solve the differential equation y'' + ay' + by = 0, and I've found that the solution is y = 3e^-x + 2e^2x.

However, I'm having trouble determining the constants a and b, as well as the initial conditions for x = 0 that give just this solution.

Correct solution: a = -1, b= -2, and initial condition y(0) = 5 and y'(0) = 1.

Can someone help me understand how to arrive at this answer? I'm really struggling to understand the steps involved.

Any help would be greatly appreciated!

[lone heart]

@primal galleon Has your question been resolved?

[lone heart]

@primal galleon Has your question been resolved?

[lone heart]

@primal galleon Has your question been resolved?

[tacit arch]

it's hard to distinguish what's given information and what you've showed. can you just show the original problem

[molten pivot]

i don't think this is possible to determine uniquely

there should be infinitely many such 2nd order linear constant coeff. DEs that have this as a particular solution

wait actually

this is homogeneous

which means everything is much simpler

our characteristic poly is:

(r+1)(r-2) = r^2 - r - 2

so our DE is:

y'' - y' - 2y = 0

then we take our particular soln:
y(x) = 3e^-x + 2e^2x
and just find y(0) and y'(0)

that's it

[lone heart]

@primal galleon Has your question been resolved?

[lone heart]

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[open shard]

Hello

[open shard]

Can someone help with calculus homework

[long axle]

Send it

[open shard]

Well it’s a test

I can send questions tho

[long axle]

We don’t help on tests

[open shard]

Okay

Sorry

[last ether]

.close

[lone heart]

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[last ether]

Be lucky you didn't post it

[lone heart]

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[last ether]

It legit says to four decimal places

Which you didn't do

You truncated, not rounded

If the digit next to it is 5 or greater, round up

Otherwise round down

The digit next to the fourth decimal is 6, which is greater than 5, so raise 0 to 1

[tribal haven]

4 decimal places

[lone heart]

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[vague sedge]

solve for x

[tribal haven]

construct an isosceles triangle

[lone heart]

@vague sedge Has your question been resolved?

[vague sedge]

I tried that

i got this but couldnt proceed

[wanton hare]

+oh

nono

not that way

[tribal haven]

in which way is that triangle isosceles

[vague sedge]

nvm it isnt

[wanton hare]

u gotta do it in between 40°

[vague sedge]

thought it was the same thing you were talking abt

[wanton hare]

so that u get an isosceles

[vague sedge]

i see..

[wanton hare]

then u can find the angle of the sector

[vague sedge]

140

[wanton hare]

total angles in a quadrilateral will equal to 360°

use that to calculate x

[vague sedge]

i cannot find a way to proceed

sorry im dumb rn

[potent wave]

if you’ve bisected the other acute angle and you got 20°

you’ve got 20° + 20° + 40° + 140°

add those values together then subtract it from 360°

if not

then you know at least that one angle on the other triangle is 20°

[vague sedge]

yea i get 140

but that number is the sum of x and bottom left angle

i got this in another way it jst came up on my mind

[wary stream]

Honestly, I would have used the concept of central/inscribed angles if you know that

[vague sedge]

wait what

im not smart enough

[wary stream]

<@&268886789983436800>

[rapid tapir]

bruh

[next brook]

b&, thanks.

[wary stream]

If you know this concept, you can apply it. You found what the central angle was, the 140 degree

[vague sedge]

Oh this

Thank you very much

[lone heart]

@vague sedge Has your question been resolved?

[lone heart]

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[golden scaffold]

does anyone about the Taylor series

[golden scaffold]

I want to know about Taylor series

pls help me in it

[tribal haven]

google taylor series i guess

personally lamar's notes got me through entirety of calc just fine

[wary stream]

Google

[tacit arch]

Go watch YouTube videos or Khan academy. Help channels are for specific problems you've already attempted

[golden scaffold]

ok

thanks

[lone heart]

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[lone heart]

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[jade cosmos]

im unsure how to prove if it is absolutely convergent, conditionally convergent, or divergent

I think I should use root test

then take the limit to infinity of that

so it would get me zero

[alpine sable]

Would alternating series test not work here

[jade cosmos]

yes but

im trying to prove absolute

well disprove it

[alpine sable]

Oh no it wouldn't this will go to 1

The limit of that sequence that is

[keen plinth]

classic dwmt test

[jade cosmos]

dwmt?

[keen plinth]

dont waste my time

[jade cosmos]

lol

[keen plinth]

the terms in a convergent series must ->0

[jade cosmos]

yea

so is the answer div

[keen plinth]

or is it curl

[alpine sable]

Oh yeah I'm dumb

Because a_n goes to something other than 0 so (-1)^n(a_n) must also go for something other than 0

[keen plinth]

it just doesnt converge

[alpine sable]

Yeah

Diverges

U can use nth term lol

[jade cosmos]

still a little confused

so was my use of root test right?

[keen plinth]

this seems a little sus

how did you even get the -(n^2)^1/n

[jade cosmos]

ah wait

i see where I messed up

okay okay

so when I test for abs cgt what test should I use

Cause if i just use the div test it gets me infinity / infinity

[alpine sable]

I think ratio test is a bit overkill though

[jade cosmos]

ik

direct comparison i think would get me it

i use a function smaller

so 1/n^2

nope

not that

uh

[lone heart]

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[sterile idol]

Hello. I’m trying to find an expression for the the one in blue. I’ve tried this so far but now I’m stuck as I need to find the sum of terms with powers in GP

[tacit arch]

Are you missing a 9 on 9cos(x)

[sterile idol]

Yeah, sorry

9cos(9x)

I can’t find any other way of simplifying this further

[tacit arch]

What makes you think this even converges?

Outside of when x is of the form (2k+1)pi, I doubt this even converges

[sterile idol]

This doesn’t converge, I just need to find a more compact expression

[tacit arch]

Doubt it exists

[sterile idol]

Oh no

[lone heart]

@sterile idol Has your question been resolved?

[golden scaffold]

obtain Taylor series for f(x,y)=e^x cos y powers of x+y

i need help in this

[tribal haven]

#❓how-to-get-help

[golden scaffold]

obtain Taylor series for f(x,y)=e^x cos y powers of x+y

[tribal haven]

#❓how-to-get-help

[lone heart]

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[west glen]

hi guys

[strange meadow]

Question?

[west glen]

.close

[lone heart]

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[west glen]

.reopen

[lone heart]

✅

[west glen]

sorry

couldnt send messages for some reason

I got this question

but i keep getting 0.15 m/min as an answer

im not sure how i got it wrong

[strange meadow]

Do u have ur workingV

[west glen]

yeah 1 sec

did it do it wrong

[strange meadow]

Yes u did

You can’t treat r as a constant in the second line

R is a function of h

[west glen]

oh ok

[strange meadow]

Use the fact the radius is 12/5 of the height

Or use product rule

Either works

[west glen]

oohhh so you sub it in and differentiate it

right?

[pliant cedar]

yeah

[west glen]

thxx

.close

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[green folio]

Finally help 0.

[green folio]

So the question is

How to understand

Or identify

If a differential equation

Is separable

Or homogeneous

Or will apply linear

Plis hwelp

Umm guys 💀

[strange meadow]

Google it lol

Separable is just when u can separate the variables to two sides

So u just have two integrals

[green folio]

Yee yee I just understood separable

And homogeneous

Linear one is still a doubt

[strange meadow]

https://en.m.wikipedia.org/wiki/Linear_differential_equation

[green folio]

Jesus

Naa bro 💀

Questions like these 💀

[strange meadow]

Integrating factor

[green folio]

No like how am I gotta identify

These type

Between all other diff ewn

Eqns

Mixed in the ques paper

[strange meadow]

Which question

[green folio]

No like the whole ex is linear only

But I feel like I can apply separable as well

Its not visually distinctive

[strange meadow]

Yes but which question are you struggling on

[green folio]

Let's say 3

[strange meadow]

Have you tried anything?

[green folio]

Umm

Yes

I tried linear directly knowing it was linear

[strange meadow]

What

What does that even mean

[green folio]

Coz I knew the exercise is on which one

I applied the process directly

But then I thought abt it

[strange meadow]

Wdym I tried linear

[green folio]

There's a method

[strange meadow]

Have u learnt some process

What is it

What is this process

[strange meadow]

Yes so integrating factor

What’s wrong with using integrating factor

[green folio]

So like

How am I gonna identify

When to apply this method?

[strange meadow]

It says in ur thing

When it’s of that form

[green folio]

I saw some past question papers

They dont mention tho

[strange meadow]

What

dx/dy+P(y)x=Q(y)

[green folio]

Yee they didn't mention in the past question papers and sample question papers

[strange meadow]

When it’s of that form

Then u can use If

IF

[green folio]

What is its like

OHHHH

YEE I SEE SHIT NOW

Bruh why am I so blind?

Tyty

[strange meadow]

bro 💀

[green folio]

Ty ty

.close

[lone heart]

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[alpine sable]

Does having a free variable in this just automatically make it so that a linear combination exists that would = b? or do i just have to do it the long way of row reducing it out

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[frozen hare]

you would have to row reduce it

remember a linear combination from the definition means that $p \vec{v_1} + q \vec{v_2} + r \vec{v_3} = \vec{b}$ where $p, q, r$ are real numbers

[ocean seal]

bluecaps

[frozen hare]

that gives you a system of four equations in three variables

so there if there is no linear combination, the systems of equations would be inconsistent

[iron tree]

@frozen hare can u help me with my question on my channel I made

[frozen hare]

someone else will help you

[serene junco]

Please don't spam other people's channels

[alpine sable]

my apologies got wrapped up in the studying and missed this. Would this mean x1 / x2 / x3 would all need to be = to a real number in this scenario

i row reduced it down and found that x1 = 1, x2 = -1 , x3 = 2

[alpine sable]

when you row reduce it this is the matrix you get ( sorry it's just written in google docs )

But wouldnt it be impossible for the vector b to exist as a linear combination without any numbers existing within row 4 ?

[naive valley]

it's a consistent equation, 0 = 0

if the rightmost number in row 4 were nonzero instead, then it would be inconsistent and no solution would exist

[alpine sable]

oh that does make sense actually

[naive valley]

0 = 0 just means "this equation adds no new information"

[frozen hare]

so this means that there is exactly one linear combination

[alpine sable]

how do i know if its the singular one that they provided?

if there's only 1

[lone heart]

@alpine sable Has your question been resolved?

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[swift spire]

i wrote (x+1)^2 as x^2 + 2x1 + 1^2

[swift spire]

the teacher wrote the final answer as x^2 + 2x + 1

whys that

[vale wigeon]

$2x \cdot 1 = 2x$

[alpine sable]

$a \cdot 1 = a$

[ocean seal]

Ann

♡LexQa♡

[alpine sable]

Oopsie

[swift spire]

oh

[alpine sable]

Double latex

[vale wigeon]

sniped

[swift spire]

ohhh i get it

thank u guys

.close

[lone heart]

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[swift spire]

.reopen

[lone heart]

✅

[swift spire]

hang on

where did the 1^2 go

[alpine sable]

1^n = 1

[swift spire]

oh yeah

so we dont need to write it?

[alpine sable]

1^2 = 1

[swift spire]

yes

oh i get it

the answer is

x^2 + 2x + 1

[alpine sable]

Yes

[swift spire]

ok thanks

.close

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[languid cobalt]

A ladder reaches the top of a vertical wall making an angle of 60 degrees with the ground.

If the height of the wall is 12 ft, find the length of the ladder.

[languid cobalt]

is this the representation of the problem?

[gray isle]

why is your 60 near the top

[languid cobalt]

mb. it must be in at the bottom

so if this is the problem, why 24 isnt the answer?

[gray isle]

how are you getting 24

[languid cobalt]

sin30 = 12/x?

[gray isle]

why are you doing sin(30)

[languid cobalt]

bc the other one is 60

or should i do sin60 = 12/x?

ohh

[gray isle]

to make less work for yourself, you'd use the given values

[languid cobalt]

there is no adj value

[gray isle]

at the bottom, the angle the ladder makes with the ground

[languid cobalt]

should i get the adj value?

[gray isle]

the angle at the top would be 30°

and you "could" use
cos(30°) = 12/x

not really

they rarely say angle between the ladder and building/wall

[languid cobalt]

i really dont understand the angle of elevation

[gray isle]

angle of elevation is the (acute) angle made with the ground and/or horizontal

[languid cobalt]

its incorrect

[gray isle]

not quite what it wants
they want a simplified radical

do NOT use a calculator to get a decimal approximation

60° is a special angle, you should know the exact value of sin(60°)

[alpine sable]

ok idk if this makes things more complicated

but there are ratios for triangles that are 30 degrees, 60 degrees, and 90 degrees

1:√3:2

2 being the hypotenuse

use it if it helps, if it doesn't just ignore

[languid cobalt]

so the formula for this problem would be

cos(30°) = 12/x?

[gray isle]

both sin(60°) and cos(30°) would work

[languid cobalt]

ok thanks

ill be back as soon as i got another problem i cant solve

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6m away from the wall. The length of the ladder:

is my drawing correct? or the 60 angle must be on the top?

[lone heart]

@languid cobalt Has your question been resolved?

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[swift spire]

how do we solve such equations (i understand what a perfect square is)

[ocean seal]

кαтαηα

[rocky grove]

Hmm

It's a multiplied by a minus b multiplied by b

Or in short

[swift spire]

yeah

[rocky grove]

a^2 minud b^2

[swift spire]

my notebook says it equals to (a+b)(a-b)

[rocky grove]

Yeah

[swift spire]

i dont understand why

[rocky grove]

$(a+b)(a-b) = aa -ab + ab + bb = a^2 - b^2$

[ocean seal]

VulcanOne

[rocky grove]

You expand

And then you simplify

[swift spire]

hang on

why do we bring the -ab + ab

if its not something like (a-b)^2

[rocky grove]

Something like (a-b)^2 has all the terms in between the squares

$(a-b)(a-b) = aa -ab -ab +bb = a^2 -2ab + b^2$

[ocean seal]

VulcanOne

[swift spire]

(a-b)^2 means a^2 - 2ab - b^2

[rocky grove]

+b^2 yeah

[swift spire]

uhhh

oh yeah +b^2

[swift spire]

im not catching up on this tho 😅

[rocky grove]

Hmm

Ok I'll give you something to do

[swift spire]

okk

[rocky grove]

$a(a-b)$

[ocean seal]

VulcanOne

[rocky grove]

Simplify this

After expansion

[swift spire]

aa-ab

[rocky grove]

Alright

$a(a-b) + b(a-b)$

[ocean seal]

VulcanOne

[rocky grove]

Expand this

[swift spire]

$aa-ab + ba-bb$

[ocean seal]

кαтαηα

[rocky grove]

Alrighty that's great

[swift spire]

wait

hang on

shouldnt it be

$a^2-ab + ba - bb^2$

[ocean seal]

кαтαηα

[swift spire]

b^2

for the last one

[rocky grove]

Yeah b^2

Yeah precisely

[swift spire]

which one is correct

[rocky grove]

They're both equal

[swift spire]

oh so the one i just wrote is to make the equation kind of shorter?

[rocky grove]

Yeah

[swift spire]

ohhh ok

[rocky grove]

Simplified

[swift spire]

but i still dont understand the original question

[rocky grove]

Even more simplified when you do ab - ba

ab - ba = ab - ab = 0

So in the end

$a(a-b) + b(a-b) = a^2 +0 -b^2$

[ocean seal]

VulcanOne

[swift spire]

uhh

hang on lemme writ this down

shouldnt the answer be

$a^2-2ab-b^2$

[ocean seal]

кαтαηα

[rocky grove]

Why?

[swift spire]

i did :

[rocky grove]

We have +ab and a -ab

Both cancel out

[swift spire]

wait lemme show u what i did

[rocky grove]

Sure

[swift spire]

i got:

$a^2-ab+ba-b^2$

[ocean seal]

кαтαηα

[swift spire]

ohh wait

-ab+ab is 0

so its a^2 + 0 - b^2?

but why plus 0

if its neither positive or negative

or

0 doesnt count so it would be

$a^2-b^2$

[ocean seal]

кαтαηα

[swift spire]

is this right

[rocky grove]

Yeah

Exactly

It's is known this way since ab and -ab cancel out

[swift spire]

so why is $a^2-b^2 = (a+b)(a-b)$

[ocean seal]

кαтαηα

[rocky grove]

Let's reverse

[swift spire]

ok

[rocky grove]

We have $a^2 - b^2$

[ocean seal]

VulcanOne

[swift spire]

yep

[rocky grove]

Let's add and subtract ab

[swift spire]

why?

[rocky grove]

$a^2 -ab + ab -b^2$

[ocean seal]

VulcanOne

[rocky grove]

So that we can manipulate

The expression

[swift spire]

yeah this is the ssame as a^2-b^2

[rocky grove]

Yeah

Now

[swift spire]

ye

[rocky grove]

Let's take a as a common factor

From a^2 + ab

[swift spire]

ok

[rocky grove]

$a(a+b) - ab -b^2$

[ocean seal]

VulcanOne

[rocky grove]

Lastly

Let's take -b as a common factor

From -ab -b^2

$a(a+b) - b(a+b)$

[swift spire]

what do you mean by common factor?

[ocean seal]

VulcanOne

[rocky grove]

Hmm

3x -6 = 0

Solve for x

[swift spire]

3x = 0+6

3x = 6

x = 6/3

x = 2

[rocky grove]

So it's the same if we did x-2 = 0

[swift spire]

ye

[rocky grove]

3 was a common factor for x and -2

[swift spire]

ye

[rocky grove]

We could have done this: 3(x-2) = 0

Right?

[swift spire]

wait

yeah

[rocky grove]

That's how you take common factors

[swift spire]

so its the same as 2+2 and 2*2

they both give us 4

[rocky grove]

That's a different case

[swift spire]

oh

[rocky grove]

15x^2 -5x + 10

Find the common factor

[swift spire]

wait

we cant solve it

there arent any like terms

[rocky grove]

Yeah

[swift spire]

soo

[rocky grove]

But there is a common factor

[swift spire]

5

[rocky grove]

How did you find it?

And what will the result be when you take the common factor?

[swift spire]

15 5 and 10 are all multiples of 5

[rocky grove]

Alrighty

What's the expression gonna be when you take a common factor

[swift spire]

wdym

[rocky grove]

Like how we changed 3x - 6 to 3(x-2)

[swift spire]

yeah

well 5 isnt even

wait

i dont understand what im meant to do

[rocky grove]

We were supposed to make 15x^2 - 5x + 10 into something like 5(3x^2 -x + 2)

This is taking a common factor

[swift spire]

would it give us the same answer (15x^2 - 5x + 10)?

[rocky grove]

Yeah

Multiply it out

Should work

[swift spire]

wait

yea thats right

[rocky grove]

Now

Let's go back to our questions

We have $a^2 - ab +ab -b^2$

[ocean seal]

VulcanOne

[rocky grove]

We wanna take a common factor of +a

[swift spire]

mhm

+a?

[rocky grove]

Yeah

Positive a

[swift spire]

where is that

[rocky grove]

It's found in a^2 and in +ab

[swift spire]

yea

how do we take the common factor?

[rocky grove]

a^2 = a•a

And you have ab = a•b

So?

You do...?

[swift spire]

a(a+b)?

[rocky grove]

Yeah exactly

[swift spire]

ohh

OH I GET IT

[rocky grove]

[swift spire]

LETS GO

thank you so much!

i also have another question i forgot to ask it has something to do with pythagoras theorm

do you mind?

[rocky grove]

Sure

[swift spire]

ok wait

,rotate

[swift spire]

how do we solve this?

[rocky grove]

Oki you first find lengths

And to do that

You must have your coordinates

Do you have coordinate C?

[swift spire]

I dont think so

[rocky grove]

Hmm

You can get it

[swift spire]

let me check in the book

[rocky grove]

Coordinates C can be found

[swift spire]

oh

[rocky grove]

Through coordinates A and B

1 min brb

[swift spire]

okk

[rocky grove]

Oki I'm back

Did you find coordinate C?

[swift spire]

i think

is it:

(1,0)

[rocky grove]

Hmm

[swift spire]

wait

[rocky grove]

The x coordinate is correct

Btw

[swift spire]

wdym

[rocky grove]

Draw a straight line connecting B and C

[swift spire]

OH

(-1,0)

[rocky grove]

Hmm

[swift spire]

no

no hang on

i made a mistake

y is -1

no

[rocky grove]

Yep

[swift spire]

why

[rocky grove]

It is

B and C lie on the same y coordinate

And A and C lie on the same x coordinate

[swift spire]

so its 1,-1

[rocky grove]

Yep

[swift spire]

ohhh

[rocky grove]

Now let's find lengths

[swift spire]

Ok

[rocky grove]

What's the length of AC?

[swift spire]

how do we find that

do i count the cubes

[rocky grove]

Something like that yeah

But you don't count cubes

You find the difference in y coordinates

Since they have the same x coordinate

Right?

[swift spire]

Yeah

[rocky grove]

So

A is (1, 5)

And C is (1, -1)

What's the difference of y coordinates

Or in other words

Δy?

[swift spire]

5?

[rocky grove]

Nope

[swift spire]

hang on

we're meant to find the length from -1 to 5?

[rocky grove]

Yeah

[swift spire]

ohh

6

[rocky grove]

Yepp

[swift spire]

yay

[rocky grove]

Oki now length BC

[swift spire]

ok

[rocky grove]

Same concept but on x coordinates

[swift spire]

hmm

2

[rocky grove]

Yepppp

[swift spire]

ohhh and then we just do normal pythagoras theorm?

[rocky grove]

Exactly

[swift spire]

THANK U SO MUCH

[rocky grove]

[swift spire]

really thank yo so much for your time i have an exam tomorrow and ive tried asking the teacher but she didnt reply (yet atleast)

thank you :))

[rocky grove]

I'm happy I helped you :)

[swift spire]

:)

see u!

.close

[lone heart]

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[tacit dome]

Two cyclists left at the same time from Vilnius to Kaunas, the distance between which is approximately 100 km. The first drove at a speed 10 km/h higher than the second, but stopped on the way for 50 minutes. At what speed must the first cyclist travel in order to arrive in Kaunas no later than the second cyclist?

[tacit dome]

Inequality

[woeful pulsar]

what have you tried so far

[tacit dome]

I was only thinking how to write it as inequality.

100<10x<?

Maybe something like that?

[woeful pulsar]

what is the variable you are using?

[tacit dome]

10km/h

[woeful pulsar]

there's one unknown right? so might as well use the speed of the first cyclist

[tacit dome]

Where we should use it?

[woeful pulsar]

basically you can express everything in terms of the speed of the first cyclist

[tacit dome]

But we should do something with 50 minutes, right?

[woeful pulsar]

So we are trying to compare the amount of time both cyclists took

right?

[lone heart]

@tacit dome Has your question been resolved?

[tacit dome]

Yes

[lone heart]

@tacit dome Has your question been resolved?

[lone heart]

@tacit dome Has your question been resolved?

[woeful pulsar]

so can you write an expression for the times?

[tacit dome]

(100/x) + (5/6) <= 100/(x - 10)

[woeful pulsar]

hmm yeah, now solve this inequality

probably move everything to one side

[tacit dome]

ok

[tacit dome]

.close

[lone heart]

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[polar otter]

i cant really understand what negative angle means

[alpine sable]

basically

sine is an odd function right

[polar otter]

yes

[alpine sable]

so basically

f(-x) = -f(x)

[plain flame]

look at the unit circle

[alpine sable]

but basically what a negative angle means is

[rustic ruin]

so positive angles are ones which have an anticlockwise direction sense and negative angles are the ones which are taken clockwise

[alpine sable]

this.

[polar otter]

so

negative angles

have negative cosines

according to this formula

then lenghts of the triangles will be negative

[plain flame]

you dont really encounter negative angles in real life

[polar otter]

according to law of sines

am i stupid?

[plain flame]

well can you show me a triangle with negative angles

[alpine sable]

negative angles don't exist in a triangle

[polar otter]

where do they

exist

than

in circles?

[alpine sable]

hmmm

in a unit circle

[polar otter]

what

is

unit

circle

like in complex numbers?

[plain flame]

this

[polar otter]

oh

thanks

[plain flame]

you only need to understand the top right quadrant though

and then you can deduce the rest

so its less bad than you might think hahah

but yeah its a bitch

[polar otter]

thanks a lot

[alpine sable]

basically first quadrant everythig is positive

second quadrant sine is positive

third quadrant tan is posiitve

fourth quadrant cos is positive

[polar otter]

okey

thanks

[runic badge]

Is it possible?

to solve...

I think it's impossible.

[lone heart]

@polar otter Has your question been resolved?

[lone heart]

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[bitter lintel]

I’m having trouble solving this ratio test. I want to simplify it but I can’t find a way to do it.

[lone heart]

Please don't occupy multiple help channels.

[bitter lintel]

.close

[lone heart]

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[ember wadi]

What is the square root of 43,098,124?

[alpine sable]

calculator

[echo socket]

Prime factorization if you wanna do it with just paper and a pen

[ember wadi]

If I want to multiply 230098 hectometre to mm, ho do i do it?

[echo socket]

Hecto means 100 iirc, right?

[last ether]

10

I think

[ember wadi]

I stink at maths

[last ether]

Or 0.1

Oh wait

What

[alpine sable]

h = 100

[last ether]

One hecometer is 100 meters

Okay

I apparently don't know units

[ember wadi]

i feel u

[echo socket]

1 hectometer = 100 meters = 100 * 1000mm

So 1hectometer = 100 000mm

[ember wadi]

tyy

mi teacher (Miss Carol Smith) taught us like this:

King: K : Kilo

Henry: H : Hecto

Died: D: Deca

Mother: M: Metre

Didn't: D : Deci

Cry:C:Centi

Much:M:Milimetre

@ocean seal

230098 hectometre to decimetre

[echo socket]

Just add 5 zeros to the number

[ember wadi]

oo

[echo socket]

Also is it me or that memorisation thing is absolutely useless?

[lone heart]

@ember wadi Has your question been resolved?

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[ember wadi]

. reopen

[lone heart]

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[quaint jay]

Hi I need some help with best way to divide something.

[quaint jay]

I have 4 pieces of wood that are 96 inches

I beed to make 17 cuts

need*

4x 24.5 inches 6x 26.13 inches and finally 7x 19 inches

[golden canyon]

I think you don't have enough wood

4 * 96 = 384 total inches

4 * 24.5 + 6 * 26.13 + 7 * 19 = 387.78

[quaint jay]

im sorry that last one is supposed to be 6 x 19

[golden canyon]

oh, okay

I think the best approach is to just guess some arrangements and see if they work or not

*planning btw, not cutting immediately

[quaint jay]

Theres no formula or anything for this?

Was hoping to stumble on some formula to save me work future wise

[golden canyon]

just use as much of one piece of wood as possible with as little wood left over I think

maybe you could cut out a couple pieces of paper

or just glue the 3 pieces of wood together

into one long piece

[quaint jay]

They are 2x4s heh

If I did glue them together that would be very tricky for my miter or table saw

well 5x 19= 95

So then it becomes 4x 24.5 6x26.13 1x 19 into the remaining 3

[golden canyon]

2 * 24.5 + 1 * 19 + 26.13

this is also kinda close to 96

plank 1: 5x 19
plank 2: 2x 24.5 + 19 + 26.13

than you have 2x 24.5 and 5x 26.13 left over

hmm, that won't work out

you should probably distribute the 26.13 as equally as possible over the 4 pieces

[quaint jay]

I feel like there has to be a formula or something for this

[golden canyon]

maybe there exists a tool online that does this for you

[quaint jay]

What type of math is this?

[golden canyon]

https://www.opticutter.com/cut-list-optimizer

"cut multiple planks of wood into pieces of certain lengths online tool" this is what I googled

[golden canyon]

combinatorics I guess

not really sure

[golden canyon]

I don't think you have enough wood

[quaint jay]

I do what ill do is use that second board there

leaves me with about 3-4 inches

ill glue that to whats left with from one of the 3rd

[fallen verge]

Youre gonna need a 5th 2by4by96

Or buy 2by4by120s

[quaint jay]

Balls I dont wanna go to lowes lol

[fallen verge]

Unfortunately youre a little short

[quaint jay]

or

Shave that half an inch off

Really appreciate that opticutter link

[lone heart]

@quaint jay Has your question been resolved?

[lone heart]

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[nova swallow]

There are known points A, B, C, D, which do not belong to one plane, with coordinates: A (-1, -1, 6), B (-1, 0, 2), C (-1, -2, 5), D (-3, -3, 1)
Find the coordinates of point M, the vertex of base ABCM.

[nova swallow]

how do I solve this?

[limpid turret]

What is base abcm supposed to be