help-36

[paper crane]

yes right here

[stone wagon]

um

idk why you are doing this, you are given that t=10 in that case

you are supposed to solve it with the 1% case

this is useless lol

[paper crane]

ah i see

[paper crane]

so how would i solve

it

i still get a different answer

[stone wagon]

you have that N=0.01*N_0

so $0.01N_0 = N_0\cdot(1/2)^{t/35}$

[soft zealot]

artemetra

[stone wagon]

the N_0's cancel out

giving $0.01=(1/2)^{t/35}$

[soft zealot]

artemetra

[stone wagon]

and you just solve that

@paper crane

[final saddle]

@paper crane Has your question been resolved?

[paper crane]

time cant be negative tho ?

[final saddle]

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[thin shard]

cosx-2x=0

[thin shard]

solve for x

[nova iron]

where did you get the question?

[thin shard]

my friend asked me how to solve it

[warm python]

you'd probably want to use a graph

[nova iron]

you can use newton's method and go thru with like 4 iterations if you wish

[warm python]

or a polynomial series to solve it

[nova iron]

or any other root finding algorithms

[thin shard]

i don't know the method

[nova iron]

what grade are you in?

like uh

what is this assignment for? trig?

calc?

[thin shard]

i don't know how to do that either

[thin shard]

11th

[nova iron]

and you know calculus?

[thin shard]

trig i think

[thin shard]

partialy

[nova iron]

well u can't do much with trig lol

[thin shard]

okay thanks for the help

we probs havent learned how to solve it

[nova iron]

u can't "solve it"

[vital surge]

do you have a calculator near you

[thin shard]

yes

[vital surge]

does it have trig functions on it

[nova iron]

you're allowed to use a calculator?

[thin shard]

yes

[thin shard]

yes

[vital surge]

ok perfect

[nova iron]

bruh

[vital surge]

here’s what i want u to do..

0. make sure your calculator is set to radians
1. type in a number (like 8)
2. take the cos() of that number
3. divide the result by 2
4. repeat steps 3 and 4 for a very long time

[dreamy pumice]

😂

8 is too big

[thin shard]

damn ok

[vital surge]

my bad. use 88888 instead

[dreamy pumice]

it would be before pi/2

[thin shard]

i know the answer is less than 0.7

wait

[dreamy pumice]

damn how

[nova iron]

are we assuming a calculator with limited functionalities here?

why are we even doing the repeated division and trying to look at values of x where the repeated division converges to just x

[thin shard]

i tried what he just told me a minute ago

[dreamy pumice]

i see

there is no sure like answer tho

its just a transendental eqn

[vital surge]

u need to do the process a bit more

[thin shard]

does that mean i can use lim?

[thin shard]

yea i can tell

[dreamy pumice]

well i mean

you can try using terms of cosx expansion

taylor series'

but that wont be too accurate as well

[thin shard]

i was just wondering if there was a way to solve it with like equations yk

[vital surge]

wt r u talking about

[thin shard]

i dont know what that is

[vital surge]

i am being dead serious when i am telling u if u have a calculator this is the best way of finding ur answer

[dreamy pumice]

taylor series is something you will learn in calc

anyway even that wont be too useful here nvm

[vital surge]

and Taylor series will NOT help you solve this problem

yes thank you

[dreamy pumice]

Mqnic method is best

[vital surge]

it's actually a slightly interesting property abt the cosine function that a process like this even works

further reading https://en.wikipedia.org/wiki/Dottie_number

[thin shard]

0.450184 is extremply close

[thin shard]

by using this

.close

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[prisma heart]

Need help

[prisma heart]

Factorization using the sign change rule. (I kinda get it. But I'm dumb)

[fast arrow]

Mind showing an example of the problem you have?

[prisma heart]

Sure

Sorry my camera is bad

U think I'm dumb for not understanding this? (I don't blame u)

[fast arrow]

Nah, not at all, we were all there at some point

Do you understand the following rule

ab + ac = a*(b+c)

[prisma heart]

I understand the general rule. I'm just not understanding the sign change

[prisma heart]

Yeah

[fast arrow]

ok

now, a doesn't have to be a single number, it can be an expression as well

what would this factorize to

(x-1) * 4 + (x-1) * 3

[prisma heart]

(x-1)*4+(x-1)*3
= (X-1) (4-3) ?

Idk why I'm so slow

[fast arrow]

why is it 4-3?

Where did the - come from?

[prisma heart]

Bec x-1 is in both if the 2 brackets, canceling one of them out. So the numbers inside the second bracket get replaced by the numbers outside the bracket

I live in Africa

It's probably different here

[royal schooner]

maths is maths everywhere

[prisma heart]

M( 3m-2) -n(2-3m)

[fast arrow]

Oh, no, you misunderstood how that works

[prisma heart]

= m (3m-2) +n (3m-2)
= (3m -2) (m+n)

[fast arrow]

Good

[prisma heart]

Why is typing on my phone like this so difficult 😭

[fast arrow]

So is this correct?

[prisma heart]

I guess not

[thin shard]

is that saying M( 3m-2) -n(2-3m) equals m (3m-2) +n (3m-2)?

[prisma heart]

Yes

[prisma heart]

Wait

I'm dumb

It's also later here. I'm kinda tired. But I'm mainly dumb

[fast arrow]

Let's try this

x * y + x * z =

?

[prisma heart]

xy + xz

I'm not stupid

[fast arrow]

yes but now factorize it

[prisma heart]

Is it even possible?

[fast arrow]

why wouldn't it be?

[prisma heart]

Ok I'm lost

(xy) (xz)

[fast arrow]

if ab + ac = a * (b+c)

then what is

xy + xz = ?

[prisma heart]

That would be

X *(y+z)

[fast arrow]

good job

now, xy - xz ?

[prisma heart]

X * (z-y) ?

[fast arrow]

how come?

[prisma heart]

How do u type so fast?

[fast arrow]

magic

[prisma heart]

Sure

[fast arrow]

why did z and y switch places?

they don't

they shouldn't

[prisma heart]

Yeah I see that

[fast arrow]

the solution is x * (y - z)

so whatever evil place switch magic you were taught

forget it

that's something else

you'll see later

now

[prisma heart]

No

It was my fault

I was just a little confused

[fast arrow]

5x + 5y = ??

[prisma heart]

I'm sick u see. Have an infection

That's it

No

Sorry

5* (x+y)

[fast arrow]

good

now

10xy - 10xz

[prisma heart]

10*(xy-xz)

[fast arrow]

ok

but couldn't you also factor out the x?

[prisma heart]

Yeah

I was going to delete it

[fast arrow]

so what's the simplest form then?

[prisma heart]

10x*(y-z)

[fast arrow]

good

now

(x-1)y - (x-1)t

[prisma heart]

Oh. We put the coefficients in front

So

y(x-1)-t(x-1)
= (X-1) (Y+t)

[fast arrow]

good

now

(x-1)y+(1-x)r

oh wait

hold on

[fast arrow]

why

is this

[prisma heart]

Holding

[fast arrow]

y+t?

[prisma heart]

Sign change

[fast arrow]

what sign change?

why sign change?

[prisma heart]

Sorry

I see my mistake

[fast arrow]

sign change only when the orders are different

like in this example

(x-1)y+(1-x)r

see how here it's x-1

and then the other is 1-x

[prisma heart]

Yeah

[fast arrow]

here you do the sign change

but if they're the same

you don't

[prisma heart]

Damn u type fast

Vinnige persoon

[fast arrow]

so this is wrong, it should be (x-1)*(y-t)

So now, what's (x-1)y+(1-x)r ????

[prisma heart]

(x-1) (y-r)

[fast arrow]

good

now

(x-43) * 45y-(43-x) * 877t

[thin shard]

idk if i understand what you're getting wrong but here
y(x-1)-t(x-1)
= (X-1) (Y-t)
=(x-1)(-(t-y))
=(x-1)(-t+y)

[fast arrow]

he's getting the reverse switcheroo wrong

like (a-b) * c + (b-a) * d = (a-b) * (c-d)

but he's applying it when it's not needed as well

[prisma heart]

(x-43)*(45y + 877t)

I feel like this is wrong

[fast arrow]

where did the r come from?

lmao

anyway, it's correct

now

[prisma heart]

Hmm sure

[fast arrow]

here's a big boy

(234 - x)y + (x - 234)z - (x - 234)t

[prisma heart]

I had to write it down

[fast arrow]

Hmmm... let's break it down

(234 - x)y + (x - 234)z - (x - 234)t

Notice how the first parantheses are in reversed order

let's flip the order and put a - to compensate for it

-(x - 234)y + (x - 234)z - (x - 234)t

Like so

Now if we take the x-234 to the from we are left with

(x-234)*(-y+z-t)

Another way to do it would be to flip the other two parantheses instead

so

(234 - x)y + (x - 234)z - (x - 234)t

would become

(234 - x)y - (234-x)z + (234-x)t

and this is now

(234-x)*(y-z+t)

[prisma heart]

Hmm

Never did this kind before

[fast arrow]

well think about it this way

(a-b)c + (b-a)d

we can rewrite this

as

(a-b)c - (a-b)d

so you can reverse the order in the brackets

if you change the sign in front of it

[prisma heart]

Ok

Verstaan

[fast arrow]

Try to do yourself first

[prisma heart]

No

[fast arrow]

[prisma heart]

Fine

Evil

I'm confused

[fast arrow]

What part confuses you?

[prisma heart]

Idk

[fast arrow]

how would you approach this problem?

[prisma heart]

What happens at the last part?

At the beginning I know u divide and the x comes out alone with on a power of 1

It's the second term I'm confused

[fast arrow]

try to factorize y from the last 2 terms

[prisma heart]

Idk

I'm not getting anywhere

[fast arrow]

First 2 terms are x^2 and 2xy, factor out x from them , the second two terms are xy - 2y^2 factor out y from them

[prisma heart]

X^1 and y^1

[fast arrow]

ye

[prisma heart]

Idk if I'm doing it right or correct anymore

(-2xy) (+2xy)

[fast arrow]

hmmmm

[prisma heart]

It's not it

[fast arrow]

let's first loot at x^2 + 2xy

when you factor out x it becomes

x * (x+2y) right?

[prisma heart]

Yes

[fast arrow]

xy - 2y^2

what about this

when you factor out y

[indigo owl]

The problem no j is straight up expansion of ( a-b)^3

[prisma heart]

Y*(2xy)

Probably wrong

[fast arrow]

ye wrong

try again

[indigo owl]

It's simple a = p , b=2q

[fast arrow]

oh and sorry I misswrote up top

x^2 - 2xy = x * (x-2y)

it should be this

I misswrote both as +

[indigo owl]

Problem I is simple

[prisma heart]

Doubt this is it

[indigo owl]

Take x common from x^2-2xy and y common from xy-2y^2

[prisma heart]

Y*(y+2x)

I know ur probably annoyed with me

[prisma heart]

Ur making me more confused!!

[fast arrow]

we have

xy - 2y^2

[indigo owl]

No it's one step solution try it

[fast arrow]

that's l ike xy - 2yy

which is like yx - y2y

which is like

y * (x-2y)

[prisma heart]

Ok

I won't waste ur time anymore

Sorry for being an inconvenience

.close

[final saddle]

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[indigo owl]

@prisma heart wait

[prisma heart]

Yes?

Ok bye

[indigo owl]

@prisma heart here is the solution

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[fallen patrol]

can you take a look on the domain of cotx here

why is it 0 and pi

arent cot 0 and cotpi undefined

[vale harbor]

0 isnt in range

Neither pi

[static pier]

*domain^

[fallen patrol]

but its in the domain column

[static pier]

Rounded brackets tho

[vale harbor]

(0,pi) means 0 to pi not including them

[fallen patrol]

wtf

[vale harbor]

[0. Pi] means 0 to pi including them

[fallen patrol]

thats a damn weird way of describing something that isnt there

[vale harbor]

Lol

[fallen patrol]

bro rlly

is that how you read these bracket things

[vale harbor]

Yea

[fallen patrol]

can you check the first one in the top column, the domain of sinx

[static pier]

Tbh, its fairly standard, looks nicer than greater than and less than strings

[fallen patrol]

domain of sine is all real nos

what is this then

[vale harbor]

Yes its shouldve been all but its probably like that because its taken as inverse of arcsin

[fallen patrol]

.close

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@wispy root Has your question been resolved?

[fallen patrol]

you can take 1/3 common from the series

it would become much simpler

[fiery pecan]

(41-2)/3=13

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[fallen patrol]

??

didnt your teacher tell you to take the 1/3 out of the series

[mental root]

you don't have to take 1/3 out of the series

you can view the common difference as just being 1

[fallen patrol]

yea but these fractions look kinda difficult to solve

so i js thought you could eliminate them

[mental root]

yeah both approaches work

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[silent apex]

i completed the square and got this

how do I find the centre now?

[final saddle]

@silent apex Has your question been resolved?

[silent apex]

<@&286206848099549185>

[final saddle]

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

[limber summit]

@silent apex still here?

[silent apex]

yea having dinner

[limber summit]

https://chat.openai.com/share/a9fb82af-ef54-4649-a6ac-658f8cd6f2ad

[sonic crystal]

!nogpt

[final saddle]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[silent apex]

thats wrong ig

😅

[silent apex]

can you help with the question please

[final saddle]

@silent apex Has your question been resolved?

[silent apex]

<@&286206848099549185>

[echo torrent]

Are you trying to graph it?

[silent apex]

no

i just wanna know its centre

[silent apex]

.close

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[gray acorn]

how do i detremine the sum of this serie

[mint orbit]

simplify first

what do you get when you simplify the summand

@gray acorn u vanish?

[final saddle]

@gray acorn Has your question been resolved?

[gray acorn]

sorry had to leave for a bit

okay ill simplify ut

.close

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[woeful gull]

Can someone help me factor this expression?

[cloud zephyr]

Is that $4x^2 -16 + 15$

[soft zealot]

Adrien-Marie Legendre

[woeful gull]

Yes sir

[cloud zephyr]

What have you tried?

[woeful gull]

Here I can show you

I prob went wrong somewhere

6f

[cloud zephyr]

How did 60x^2?

Also why -16x?

[woeful gull]

Huh

Where you see dat

[lethal estuary]

is it -16x or -16

[woeful gull]

Ohhhh

Thats -16x

Oops

The equestion is supposed to be -16x

[woeful gull]

What was the other

Question

[lethal estuary]

try figuring out how you could factor into two expressions that, when distributed, equals the function

so it could be (4x - a)(x - b), or (2x - a)(2x - b), etc.

[woeful gull]

Hmm

I mean I know

[lethal estuary]

I think there's a trick, but trial and error works here. since you know a*b = 15

[woeful gull]

15 makes it

Mmmhm

[lethal estuary]

(I don't know any tricks to do it)

[woeful gull]

Oh

lmao

Wait I cant just factor the first one by 6?

[lethal estuary]

no

[woeful gull]

Hmm

How would I get it to (4x-x) then

[lethal estuary]

4x - x = 3x, but I'm sure that's not what you mean

[woeful gull]

naw im just talking bout this

[lethal estuary]

well you know a*b = 15, so what are the only possible values for a and b here?

[woeful gull]

5 and 3?

[lethal estuary]

right

so let's say we now have (cx - 5)(dx - 3). you want c * d = 4. and also -3c - 5d = -16, so 3c + 5d = 16

there are only a couple combinations of c and d that will work for c * d = 4

so you can try both

[woeful gull]

isint it just

C = 2

D = 2

[lethal estuary]

yup

so 4x^2 - 16x + 15 = (2x - 5)(2x - 3)

[woeful gull]

iiiii mightt be cooked for tommoroowww

lemme seeee

Thanks sir

Figured it out

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@woeful gull Has your question been resolved?

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[silent apex]

how can i do these type of questions

can someone help please

[humble swift]

u know determinants?

[silent apex]

yes

[humble swift]

if yes then the determinant of coefficient matrix of the equations should be zero for the system to have infinite equations

ie

[silent apex]

i calculated that

i got two values

[humble swift]

mhm

[silent apex]

-2 and 1

[humble swift]

okay

[silent apex]

how do i check now

which one is correct and which is not

[humble swift]

how do i type it

[silent apex]

can you write it on paper

[humble swift]

u should replace the x coefficients in the determinant by values of the 'c' and make it zero

[silent apex]

and send a pic

[humble swift]

im on laptop

this cam not good

[fringe heart]

mcq ez brute force 😃😃😃😃😃😃

[silent apex]

ill have to calculate a lot determinants in that way

[humble swift]

only 2 bro

[humble swift]

thats an option

[silent apex]

hmm

i had a question

if i take lambda = 1

then the equations become

x - 2y + z = -2
x - 2y + z = 1
x - 2y + z =1

[fringe heart]

personally i’d never bruteforce unless it was on a test or contest lmao

[silent apex]

would these have infinite solutions?

[fringe heart]

gotta learn

[humble swift]

yea true

[humble swift]

that got no solution

[silent apex]

because parallel planes?

[humble swift]

yep

1 and 2 are parallel

2 and 3 are coincident

[silent apex]

hmmm

so if i take lambda = -2

ill have to calculate 3 determinants no?

@humble swift

[humble swift]

why so?

only 2

[silent apex]

which 2

[humble swift]

coefficient and one with replaced with c

[silent apex]

the coefficient one would obviously be 0, because we chose lambda -2 right

and about replacing the determinant with c, ill get 3 determinants no?

one in which the first column is replaced, one in which 2nd column is replaced and one in which 3rd is replaced

ill have to calculate all three of these right?

[humble swift]

no only one u replace

[silent apex]

i replaced it

[humble swift]

replcae x column by c column

[silent apex]

done

i got 0

then

?

[humble swift]

thats it

[silent apex]

see it says here that all three should be 0

[humble swift]

yepp

[silent apex]

and if any det is not 0

[humble swift]

idk i always use only 1

[silent apex]

then it will be inconsistent

[silent apex]

isn't that wrong

[humble swift]

idk man i get it everytime

[silent apex]

you're missing the case for when the system is inconsistent

coincidence?

😭

[humble swift]

yea i verify options tho

[humble swift]

prolly

[silent apex]

hmm makes sense

so ill have to calculate all three

to be sure in the exam

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@silent apex Has your question been resolved?

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[tropic barn]

someone help in the first part of 6th question

[shadow tinsel]

Try let a^3 = t and factorise

[sinful flume]

take a^3 commmon

[tropic barn]

cant

im getting 8t^2+5t+1

which has complex roots

[shadow tinsel]

You can’t use complex roots?

[tropic barn]

no

factorize

[shadow tinsel]

If you’re not meant to factorise with complex roots, then all you can do is take a^3 out as a common factor

[tropic barn]

well its supposed to be factorized by the formula a^3+b^3+c^3-3abc

idk how to apply it

8a^6 can be

(2a^2)^3

and 1 is 1^3

but what about 5a^3 part

[shadow tinsel]

(5^(1/3)a)^3?

[tropic barn]

thats too complex the answer looks v simple

i tried making it 6a^3-a^3 but i guess that doesnt work either

oh wait

it works

.close

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[young verge]

How do I calculate this?

[young verge]

What am I doing wrong?

[formal trail]

when entering a negative number like -2, you have to use the (-) button rather than the subtraction button

[long wraith]

For real?

Is it a Ti calc thing?

[young verge]

Where is the (-)?

[formal trail]

it's a quirk of the texas instruments calculators, yes

bottom right, next to enter

[young verge]

oh

ah alr

makes sense thanks

[long wraith]

Sound so stupid lmao

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[dire terrace]

its wrong but idk where i messed up

[humble swift]

i think its right

whats the ans?

[thin coral]

Its wrong at integral-calculator.net

Hol up

[lapis sinew]

Hi

[dire terrace]

my other term is wrong but idk how

[humble swift]

maybe changing to sin^-1 will solve the prob?

cuz u got in sec^-1

[dire terrace]

changing what

[humble swift]

changing sec^-1 to sin^-1?

[dire terrace]

no but like my theta is=arcsec(2x)

can i just use another theta?

is that what you mean

[magic sparrow]

Yes, you can

I’d check that your expressions aren’t actually equivalent or just differ by a constant

Before concluding you’re incorrect

For trig sub sometimes you can use different substitutions

[humble swift]

yes

[dire terrace]

wait my fking

8cos^2x is wrong lol

.close

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[tranquil pine]

Someone check my work pls

🙏

[desert mantle]

write words

is this supposed to be ln^(n+1) or ln(n+1)

[tranquil pine]

The second

Ln(n+1)

[desert mantle]

ok in what world was anyone supposed to read it like that

[tranquil pine]

..

But did I do it?

[desert mantle]

why is 1/n > 1/ln(n+1)

[tranquil pine]

It is?

[desert mantle]

you wrote a bunch of symbols without any justification of why they should be true

[tranquil pine]

Ok how should i do it?

[desert mantle]

answer this

[tranquil pine]

Ok

I see i was wrong

Just checked it

@desert mantle ?

[desert mantle]

yeah its wrong. so thats a fundamental flaw in your proof

[tranquil pine]

So

How should i do it?

[desert mantle]

well what are you trying to say

[tranquil pine]

I need to prove the limit of the sequence using the definition of a limit

[desert mantle]

ok and what did you try to do here

your execution was flawed, but the idea wasnt

[tranquil pine]

Fine i get that i am terrible

But how do i actually do it

I have seen some youtube videos and the did something similar

[desert mantle]

not what I said

[desert mantle]

see, you arent far off

but what did they do

[tranquil pine]

I guess Step one is to express a distance[ an-L] which is less then any arbitrary distance you can pick

And then find an input P in witch every number greater than P gives a lesser distance

[desert mantle]

ok, let me rephrase what you tried to do. you wanted to bound |a_n-0| < eps. the left side just turns out to be a_n. then instead of eps, you wanted to compare a_n with 1/n, knowing that you pick n so that 1/n < eps

yes?

[tranquil pine]

Yes That was my try

[desert mantle]

ok good

but it failed because 1/ln(n+1) is not smaller than 1/n

[tranquil pine]

Yes

[desert mantle]

the flaw here is that you tried to compare a_n to 1/n, both depending on the same number n

what if you tried comparing a_n to 1/k and pick k so that 1/k < eps

and then n depending on k

[tranquil pine]

I don't seem to understand

Do i need to find a function greater than an?

[desert mantle]

in some sense yes but I dont think that viewpoint is helpful

lets suppose that k=2

to make it a bit easier to think about

we want that a_n < 1/2

for big enough n

how big would n have to be

[tranquil pine]

I don't know

[desert mantle]

solve the equation

[tranquil pine]

I need to solve an inequality for that

[desert mantle]

yes

[tranquil pine]

Ok fine i will do it

Greater then e^2 +1

[desert mantle]

good

so to rephrase, if n>=e^2+1, then |a_n - 0 | < 1/2

yes?

[tranquil pine]

Yes

[desert mantle]

now can you do the same but with 1/k ?

[tranquil pine]

You mean an<1/k

[desert mantle]

yes

[tranquil pine]

Ok give me a second

e^k-1

[desert mantle]

ok good

so if n>=e^k -1, then |a_n-0| < 1/k

[tranquil pine]

Yes

[desert mantle]

and now thats your proof

after you write it down properly

[tranquil pine]

Yea

I need some help there too

Do i just write an<1/k

[desert mantle]

no

write down why you need a_n < 1/k

write down what k is

use words

[tranquil pine]

How ?

[desert mantle]

I am unsure how to answer this. you know how to write. just try bringing your thoughts onto a page

try writing enough that someone who reads it doesnt have to try guessing what you thought

[tranquil pine]

ok i will try

[desert mantle]

I have to go. good luck

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[tranquil pine]

hsllo

[humble swift]

what

N is kgm/s^-2

[worldly vale]

kgm/s²

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[peak mica]

i need help

[peak mica]

im not too sure about the coordinates

[ornate spade]

!show

[final saddle]

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

[ornate spade]

@peak mica

[peak mica]

yes?

[ornate spade]

What are the coords you found

[peak mica]

thats the only info they given me

[ornate spade]

!occupied

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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).

[lethal fossil]

Guys am going to cry 😭

[lethal fossil]

I know integration by parts

[peak mica]

so thats the only info gave me, also foir part a where the line passes x at 2, then y may be 0?

[vast sorrel]

open a new channel

[ornate spade]

I dont see how thata related to what i asked

[lethal fossil]

The solution plz

[nova iron]

#❓how-to-get-help

This is not your channel

[ornate spade]

Thats what crossing x axis at point x=2 means

[peak mica]

y-0?

i mean y equals 0?

[ornate spade]

(2,0) is the point yeah

[peak mica]

ohhhhhhhhhhhhh ok thank you

[ornate spade]

Draw for yourself for illustration

Did you also use the parallel line info

To know slope of this line

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[little flame]

Help me brothers with the number 16

[final saddle]

@little flame Has your question been resolved?

[cold gorge]

!status

[final saddle]

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

[cold gorge]

Also

Take that back LEORIO 🗣️

[median lagoon]

there are calculus ways to do this and there are cheesy ways to do this without calculus

which one do you want

also what step are you on, see above

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[fluid swallow]

Hey, can someone explain me where this come please?

[fluid swallow]

I got the expression of xh and yh

but I don't understand how it comes up

[vital surge]

wdym by "got the expression"

[fluid swallow]

I find that xh = xp - (axp+byp+c)/(a²+b²) *a

and yh = yp - (axp+byp+c)/(a²+b²) *b

I already did xh²+yh² but it doesn't work

[final saddle]

@fluid swallow Has your question been resolved?

[humble swift]

Ok consider line ax+by+c=0
Consider point (x1,y1)
To prove distance formula
Draw line normal to ax+by+c=0
Consider it to be passing through (x1,y1)
Now find point of intersection of these lines
Distance between point of intersection and (x1,y1) is the distance formula as it the perpendicular distance

@fluid swallow

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[fluid swallow]

.reopen

[final saddle]

✅

[fluid swallow]

Yes and so it's given by this formula

Ok I think I will just admit why it looks like this ^^

Thank you!

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[mortal berry]

I have read the solution to this problem, but I have doubts about how it works.
A piece of ice, with mass m_1=30g and at temperature t_1=-15°C, is immersed in m_2=50g of water at temperature t_2=60°C. If the system is contained in a container with adiabatic walls, determine the equilibrium temperature t_e.

Procedure:Since the temperature of the water is higher than that of the ice, the ice will rise in temperature, in this case melting will take place and therefore the water will transfer heat to the ice Q_1=m_1 * c_g * (t_0-t_1). So for for fusion to occur, a further heat equal to Q_2=m_1 * λ must be released. Therefore the heat that the water must release is Q_1+Q_2. The water can release the heat Q_3=m_2c at most from t_2 to t_0(t_2-t_0).It occurs that Q_3>Q_2+Q_1.The temperature t_e is obtained from m_1c_g(t_0-t_1)+m_1λ+m_1c(t_e-t_0)=-m_2c(t_e-t_2).

My doubts are: why was that last report used. And also why we used the specific heat in water here:m_1c*(t_e-t_0), and why after the equal sign there is a sign -. Pls help

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@mortal berry Has your question been resolved?

[mortal berry]

<@&286206848099549185>

[mortal berry]

<@&286206848099549185>

[pliant fern]

The walls are adaibatic..so the heat(energy) doesn't escape. Its self contained. The 'heat' flow from the water will equal to the heat flow into the ice. You just equate the two? I don't understand where 'Q_3>Q_2+Q_1' this is coming from.

[final saddle]

@mortal berry Has your question been resolved?

[mortal berry]

$Q_3>Q_1+Q_2$ would be that if it is greater, all the ice melts and the equilibrium temperature $t_{e}$ is greater than $t_0$; otherwise the system reaches equilibrium at $t_{0}$ with only part of the ice melted, and it may even be the case that all or part of the water solidifies.

[soft zealot]

BobTheBuilder

[mortal berry]

<@&286206848099549185>

[mortal berry]

.close

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[left echo]

$\int \frac{x^2}{(x^2 - 1)\sin (2x) + 2x\cos(2x)}\dd{x}$

[soft zealot]

jewels!

[left echo]

Back at it with another antiderivative

[vital surge]

woohoo

did you get the x^41 quotient rule one

[left echo]

I did yes

[vital surge]

🎉

[left echo]

Is there a way to perhaps factorize it well

$2(x^2 - 1)\sin x \cos x + 2x(\cos^2 - \sin^2 x )$

[soft zealot]

jewels!

[left echo]

Oh there is

$\frac 12 \int \frac{x^2}{(x\sin x + \cos x)(x\cos x - \sin x)} \dd{x}$

[soft zealot]

jewels!

[left echo]

Is there a way to partial fraction a mixture of trig and polynomials

[hybrid heath]

I don't see why not (not saying this is right or wrong, but it's worth exploring)

[left echo]

I don't see how that's possible though

Atleast for this case

Since the way I'd do it is add some sort of weight to each factor in the denominator

And use it as a difference in the numerator

Actually wait

Let me work on something

[hybrid heath]

@left echo I just tried and you can absolutely decompose the fractions

[left echo]

OMG IT WORKS

[left echo]

YEAH

this is so cool :)

[hybrid heath]

oh yea

you totally have it from here

[left echo]

$-\frac{1}{2} \int \left ( \frac{x\sin x}{x\sin x + \cos x} - \frac{x\cos x}{x\cos x - \sin x} \right ) \dd{x}$

[soft zealot]

jewels!

[hybrid heath]

This was the play-of-the-game idea right here

[left echo]

Now it's just a u sub for each

[left echo]

yep yep

just gotta believe and pull through

😅

[hybrid heath]

good work

[left echo]

Thanks!

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[rustic token]

With what test can I test if this is convergent

[rustic token]

Alternating test is applicable right? Even if it is in denominator

[formal trail]

(-1)^n = 1/(-1)^n so that still works

[rustic token]

Thanks

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[rotund musk]

The additive inverse of the number (-1)³

[serene basin]

Well

What is (-1)³?

[rotund musk]

Uh

1³

?

[serene basin]

No, (-1)³=(-1)*(-1)*(-1), which is equal to ...?

[rotund musk]

1

[lethal totem]

try again

[serene basin]

Not exactly. -1*-1=1. -1*-1*-1=1*-1=-1 🙂

[rotund musk]

So it's -1?

[fast arrow]

define "additive inverse"

[rotund musk]

Opposite

Answer the question 😔

[fast arrow]

You already have your channel

[young minnow]

oh yh

[serene basin]

You search a number s.t. -1+x=0. What could x possibly be?

[rotund musk]

1

[rotund musk]

Can you solve this so I know if my answers are correct

[serene basin]

🤌🏻

[serene basin]

I dont like solving those repetetive tasks, what im here for is learning and helping others understand something in a way that helps them to do it on their own

[rotund musk]

I'm not sure about number 3

I think it's 4

[serene basin]

How did you get 4? 4 is indeed correct.

[rotund musk]

I did 10÷100x 20

[serene basin]

10:100*20?

[rotund musk]

Yes

[serene basin]

Ah, you misunderstood me. I meant how you came to your answer 4 in Problem 3.

I want to know why you are not sure about it. Maths is all about finding steps that you are 100% sure about to get to an answer. So where are you unsure?

[rotund musk]

The question looked scary at first but I remembered the rule

[serene basin]

This is correct btw, well done

[serene basin]

Okay, thats good. Its a typical beginners task on manipulating equations. Be sure that you really understand those basics, you will need them for the rest of your school time, if not lifelong. 🙂

[rotund musk]

1. d
2. a
3. a
4. c
5. b

[rotund musk]

Thanks

[rotund musk]

Are these answers correct?

[serene basin]

Everything but 4), yes
You got the right term for it but you did equate it wrong.

Wait

c) is correct

Wasnt there b) before you edited it?

Nvm

Everything is correct now

[rotund musk]

I'm having a hard time answering this one

[serene basin]

Well, you need to understand that we as mathematicians simplify those reallife problems. For tasks like this, we take for granted that every own event is equally likely. So the probabilty that you draw one predetermined ball is the same for every ball.
This means, its all about the distribution of the colors.
You have 60 balls in total. You draw one. Because its equally likely to draw each of the balls, you just need to think about how many of the balls have a certain property that makes them differ from the rest. Here its the color. So you wont notice which of the green balls you drew. Whe have twenty. Therfore, 2) should be 20/60=1/3.
Now, you should be able to do the rest on your own.

@fast arrow 😔

[rotund musk]

So for the first answer I divide 30 by 30

[serene basin]

No, not 30/30. In total, we habe 60 balls. Out of them, 30 are white.

[rotund musk]

Yes 30 are white and the others are 30

So we should divide?

@serene basin

[serene basin]

You always divide the "undistinguishable" amount by the amount

[rotund musk]

So yes

Btw I have to more questions

2*

Three consecutive natural numbers, their sum is 18 . Find these numbers

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[thin field]

help

[final saddle]

Please don't occupy multiple help channels.

[magic sparrow]

Please stick to #help-28 and don't open multiple channels @thin field

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@wet drum Has your question been resolved?

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@wet drum Has your question been resolved?

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[shrewd perch]

Hey so I need help with a bit of projectile motion, so in this question. I wasent able to prove for part i and when I checked the solutions it said for the i component = Vcosx and the j component Vsinx - gt you sub in 0 into the x for cosx and sinx...why is that?

[final saddle]

@shrewd perch Has your question been resolved?

[quiet zinc]

you can just use S= ut+ 1/2at^2 in the y direction

[shrewd perch]

im sorry i dont know what that is

I don't think ive learnt that yet

[quiet zinc]

not faimiliar with equations of motions??

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@shrewd perch Has your question been resolved?

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[shrewd perch]

yea I am the time equations but idk what the one ur talking about is

[shrewd perch]

Ill show u the solutions. I just wanted to know for that questions why they sub in 0 as the angle

Like how do u assume its 0

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@shrewd perch Has your question been resolved?

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@shrewd perch Has your question been resolved?

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[stoic forum]

A glass in the shape of a rectangular parallelepiped has the sum of its edges equal to 48 cm, and the width, length and height are consecutive natural numbers. In the glass, tea is poured to the height of 4.5 cm.

[stoic forum]

How many litres of tea are in the glass?

If in the glass a cube of sugar with the edge = 2 cm is added, what will happen to the tea?

Im lost

<@&286206848099549185>

[hollow sierra]

wtf

oh

you need to find the tea volume bro

[stoic forum]

How

Length × width × 4,5?

I'm lost

[hollow sierra]

nuh

that is the tea volume

[stoic forum]

Why not

[stoic forum]

.

[hollow sierra]

but that not gonna help you to find the length and width

so in order to find the tea volume we need to figure out the length and with first

[stoic forum]

a cuboid has 12 edges

And sum of all edges is 48

Edge = 4cm?

[hollow sierra]

wait

[hollow sierra]

so we have 24^2=length^2+width^2

[stoic forum]

Wait what

[hollow sierra]

we are talking about this shape right?

[stoic forum]

Yes

[hollow sierra]

so we have another 24^2=height^2+width^2

[stoic forum]

Where did you get 24 squared from

[hollow sierra]

what is the edge sum mean?

does it like d1+b1?

[stoic forum]

If you add all the edges of the cuboid the sum is 48

[hollow sierra]

wait

doesn't it make the whole thing easier

[stoic forum]

Yes but I'm in the 5th grade

This is still difficult

[hollow sierra]

so you have 4 height+4length+4width=48

[hollow sierra]

wait wtf

[stoic forum]

What

[stoic forum]

So width + length + height is 12 cm

[hollow sierra]

yes

[stoic forum]

Ok

That means they are 3, 4 and 5 cm

[hollow sierra]

yes sir

so the height is 5 cm ( tea pour is 4.5cm)

and width and lenght are 3 and 4

[stoic forum]

Ok

Volume of glass is 3 × 4 × 5 then

[hollow sierra]

just use 3x4x4.5 then /1000 to have liter of tea

[stoic forum]

What

[stoic forum]

Isn't that the volume of the tea

Ou

And volume of glass?

[hollow sierra]

it will split out

[hollow sierra]

is bro really grade 5?

[stoic forum]

Yes

Why

Do you need proof or

I can show my math book

[hollow sierra]

no

I don't just surprise

[stoic forum]

Oh k

[stoic forum]

How did you get there

[hollow sierra]

you can figure it out on your own ngl

xd

[stoic forum]

But idk

This is too difficult for me

Whatever

.close

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[proud echo]

Why is this correct?

[proud echo]

Question 4

[simple basalt]

Because

The volume of the ball is 4/3 x r^3 x ㅠ

Yk what I mean

[proud echo]

?

4/3

And then time r power 3

[simple basalt]

That’s the formula but the question already gave the volume of the ball

So only thing u need to consider is the ratio

(diameter of tennis ball)^3x10:(diameter of the beach ball)^3x10

[proud echo]

Ohhh

Ok