help-0

[unique dune]

,w find the intersection of x +2y = 1 and x -y = 4

[ocean seal]

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[unique dune]

nah

could u show ur work

[lone heart]

@harsh lantern Has your question been resolved?

[harsh lantern]

I think i missed a step and got confused

I substituted x=-2y-y

[lone heart]

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[lone heart]

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[quiet sonnet]

Can someone explain simplest radical form for me, i do not really understand it

[gray isle]

is there a question you're working on?

[lone heart]

@quiet sonnet Has your question been resolved?

[quiet sonnet]

Number 169

[gray isle]

the want you to express the result in the form
p * sqrt(q)
where q is an integer and doesn't have any perfect square factors (other than 1)

[quiet sonnet]

It is not making much sense, do you think you could walk me through doing one of the problems

[gray isle]

if your issue is just about radicals in simplest form, then i'm gonna skip past those problems and focus on that concept

a common one to start with would be simplifying
$$\sqrt{8}$$

[ocean seal]

ℝαμOmeganato5

[gray isle]

have you encountered something like that before?

[quiet sonnet]

Yes i have but it was quite a while ago

[gray isle]

ok

the idea is to apply
$$\zqrt{ab} = \zqrt{a} \cdot \zqrt{b}$$
and have $a$ or $b$ be a perfect square. repeat if needed

[ocean seal]

ℝαμOmeganato5

[gray isle]

for sqrt(8), that has a factor of 4 (which is a perfect square)
and to simplify you can express that as
sqrt(4) * sqrt(2)
which can then be simplified to
2sqrt(2)
and that would the simplest radical form for that expression as 2 doesn't have any perfect square factors other than 1

does that make sense?

[quiet sonnet]

It is starting to make more sense

Now if i go back to question 169 that i showed you can you somewhat write it out step by step if it is not too much to ask

[gray isle]

try attempting it yourself first

[quiet sonnet]

Ok

I know how to solve for (X) but taking that answer and putting it into simplest radical form is what kees stumping me

[gray isle]

show what you've done so far

[quiet sonnet]

Usually I do my work in my head

[gray isle]

don't do it in your head

wheres 14.8 coming from

[quiet sonnet]

I had tried to solve this one earlier and that is what i got but i do not remember exactly

[gray isle]

well start again

make a new attempt with the info i gave you

[quiet sonnet]

Ok

[gray isle]

and do not use a calculator to calculate the sqrt or something and get a decimal approximation

ideally do all the work by hand

and show me when you get to a line like
x = sqrt(some number)

[quiet sonnet]

X=14.8 after rounding

[gray isle]

i'm sure you're able to do the first few steps

which is just pythagoras

and a little algebra

start from the second line you have there

with the goal of getting B or x by itself

getting 14.8 implies that you were able to do that,
just don't use the calc to round the value to 14.8

[opal tundra]

just put a=6 and c=16 into the pythagoras equation and find b

[quiet sonnet]

X= 14.8

[gray isle]

and show me when you get to a line like
x = sqrt(some number)
just don't use the calc to round the value to 14.8

i'm assuming that you did sqrt(some number)
and then rounded to get 14.8
what was that some number

[quiet sonnet]

220 I believe it was

[gray isle]

yes

ok good

so you should have the line
$$x = \sqrt{220}$$
in your work

[ocean seal]

ℝαμOmeganato5

[gray isle]

which was what i wanted from you

now

going back to this

the idea is to apply
$$\zqrt{ab} = \zqrt{a} \cdot \zqrt{b}$$
and have $a$ or $b$ be a perfect square. repeat if needed

[ocean seal]

ℝαμOmeganato5

[gray isle]

can you identify any perfect square factors of 220

[quiet sonnet]

No

[gray isle]

can you list out some factors of 220

or do something like a factor tree

[quiet sonnet]

Im embarrassed about how bad my memory is

[gray isle]

or prime factorisation
or any method that gets you any factors

can you identify any factors of 220

[quiet sonnet]

20 for an example

[gray isle]

ok, and what's the corresponding factor?
20 * what = 220

[quiet sonnet]

11

[gray isle]

ok.

now can you identify any factors of 20 or 11
ideally perfect squares

[quiet sonnet]

Sorry if my bad memory is annoying

20: no perfect squares

[gray isle]

can you identify any factors of 20

actually its quite small, so can you just list them all

[quiet sonnet]

1 - 20, 2 - 10, 4 - 5

[gray isle]

and check those carefully, apart from 1,
are any of those values perfect squares

[quiet sonnet]

🫥

I feel stupid

Yes

[gray isle]

which one

[quiet sonnet]

2 - 10

[gray isle]

no

neither 2 nor 10 is a perfect square

[quiet sonnet]

4

[gray isle]

yes

and try applying what i mentioned at the very start

[quiet sonnet]

Can you re type it

I cant find it

[gray isle]

start reading here:
#help-0 message

[quiet sonnet]

The ab = a • b

?

[gray isle]

that's one part of it

[quiet sonnet]

Which part do you mean

[gray isle]

well you ignored all the square roots

$$\zqrt{220} = \zqrt{20} \zqrt{11}$$
you've identified that $20 = 4 \cdot 5$ and that 4 is a perfect square
so try simplifying that by following what I did with the $\sqrt{8}$

[ocean seal]

ℝαμOmeganato5

[gray isle]

using 20 = 4 * 5
and sqrt(ab) = sqrt(a) * sqrt(b)
sqrt(20) = ?

[quiet sonnet]

You confused me a little

[gray isle]

where

don't overthink

[mellow relic]

Whatever comes in ur mind just write it down to ur notebook
That would be helpful

[gray isle]

the main idea as mentioned earlier is the extract perfect square factors as the square roots of those will be nice integers
which leads to simplification

for sqrt(8), that has a factor of 4 (which is a perfect square)
and to simplify you can express that as
sqrt(4) * sqrt(2)
which can then be simplified to
2sqrt(2)
and that would the simplest radical form for that expression as 2 doesn't have any perfect square factors other than 1

having identified 4 as a factor of 8 and knowing that 8 = 4 * 2
i expressed sqrt(8) as sqrt(4) * sqrt(2)

similarly you've identified 4 as a factor of 20 and knowing that 20 = 4 * 5
how could you express
sqrt(20)
?

[quiet sonnet]

So just sqrt 256

?

[gray isle]

you're going backwards and mixing things up now

[gleaming sparrow]

how did he get to this conclusion?

[gray isle]

forget about 16,6,36,256 you're done with those numbers

you applied pythag to get sqrt(220), forget about those other numbers now

[hollow fable]

chaos theory

lorenz attractor

[quiet sonnet]

Ok

[gleaming sparrow]

its pretty cool right?

[lone heart]

@quiet sonnet Has your question been resolved?

[lone heart]

@quiet sonnet Has your question been resolved?

[lone heart]

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[lone heart]

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[humble garnet]

Can someone help me with probability please

[humble garnet]

<@&286206848099549185>

[median oar]

What are you stuck on

[humble garnet]

I am stuck on A

[vale wigeon]

ok, do you know what a CDF is generally

[humble garnet]

mhmmm no

[vale wigeon]

ok do you at least know what the acronym stands for

[humble garnet]

Ye

[vale wigeon]

ok then what is it

as in

what does CDF mean

[humble garnet]

Cumulative distribution function

[vale wigeon]

so you know this word but you forgor what it means, did i get that right?

[humble garnet]

Is that what u mean

yee

[vale wigeon]

ok then it's time to remind you: the CDF of a random variable $X$ is denoted $F_X$ and is defined as $$F_X(x) = P(X \leq x)$$

[ocean seal]

Ann

[vale wigeon]

have you seen this before

[humble garnet]

Yep

[vale wigeon]

do you see what to do now or should we go into more detail

[humble garnet]

Let’s go into more detail

Let’s do A

[vale wigeon]

ok let's see

given a random variable X specified via its density function f, and an interval [a,b],

how do you calculate P(a ≤ X ≤ b)?

[humble garnet]

Isn’t it b-a integration sign f(x)

B on top

[vale wigeon]

well that is quite horrible notation but maybe you could write it down on paper

[humble garnet]

😭 okay hold on

[vale wigeon]

why are the a and b off to the left of the integral symbol 😭

what are they doing there

[humble garnet]

Oopsies

[vale wigeon]

i've seen them to the right, and i personally prefer them directly above and below, but left??

anyway yes this is correct

you integrate the density over the interval you want

in this case it's no different

so one might also write $F_X(x) = \int_{-\infty}^x f(t) \dd{t}$

[ocean seal]

Ann

[humble garnet]

Yep

[vale wigeon]

now work out what this integral evaluates to for your density function in the following cases:

• x ≤ 1
• 1 ≤ x ≤ 2
• 2 ≤ x ≤ 4
• 4 ≤ x

think about which parts of the piecewise definition of f are relevant for which case

[humble garnet]

Mhm

[vale wigeon]

that or you could think about properties of CDFs to take some shortcuts (e.g. you can say instantly what value the CDF will have when x is outside the range [1,4])

[humble garnet]

Mhm hm

[vale wigeon]

would you like to work this out yourself now

[humble garnet]

Let do it together 🥺

[vale wigeon]

ok so here is your density function

[humble garnet]

Yes

[vale wigeon]

if x ≤ 1, what will int[-∞, x] f(t) dt work out to?

(this one is easy)

[humble garnet]

First one……………….

Oh wait

[vale wigeon]

don't overthink it

[humble garnet]

0

[vale wigeon]

right.

ok

now what if 1 < x ≤ 2?

note also that in this case $\int_{-\infty}^x f(t) \dd{t} = \int_1^x f(t) \dd{t}$ --- think about why this makes intuitive sense too

[ocean seal]

Ann

[humble garnet]

?

[vale wigeon]

missing dt

[humble garnet]

Oh right

[vale wigeon]

but ok i guess so far so good

so that's our thing for 1 < t ≤ 2

[humble garnet]

Ye

[vale wigeon]

now work out the case 2 < t ≤ 4

[humble garnet]

Same thing?

[vale wigeon]

the integral from -∞ to 1 will break into the integral from 1 to 2 + the integral from 2 to t

there is a way to avoid working out the former of these a second time

[humble garnet]

Erm

I’m not sure got to do this part

.close

[lone heart]

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[hexed kiln]

A dishonest seller marks up his articles by x% and gives
discount of y%. Besides he gets x% more amount per kg
from the manufacturer and sells y% less per kg to
customers. If ‘x’ is a root of the equation (a2 + 600 = 50a).
Then what is difference between his maximum and
minimum profit percentage?

[lone heart]

@hexed kiln Has your question been resolved?

[lone heart]

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[glacial sinew]

i=i(not)*e^(-t/RC) ; i(not)=2 then di/de=?

[glacial sinew]

<@&286206848099549185>

[iron crystal]

what

[glacial sinew]

this

[vale wigeon]

what's i(not)

also di/de?

[glacial sinew]

Its like i0

[vale wigeon]

why not call it i_0 then

[glacial sinew]

Thats just differentiation

Oh thats something new

I learnt

[vale wigeon]

also it's spelled "nought" not "not"

[glacial sinew]

aight thanks for the english classes but could ya help me in the sum

[vale wigeon]

ok but like what do you mean by derivative wrt e

[glacial sinew]

wut

[vale wigeon]

i=i(not)*e^(-t/RC) ; i(not)=2 then di/de=?

[glacial sinew]

I am asked to find the rate of change of current at t=0.3

i_0=2

[vale wigeon]

but why is it not written as di/dt

[glacial sinew]

Waitttt

Mb mb

It has to be di/dt

my apologies

[vale wigeon]

so $i=i_0e^{-\frac{1}{RC}t}$

[ocean seal]

Ann

[glacial sinew]

Yeee

[vale wigeon]

do you know how to differentiate e^(kt) where k is constant

[glacial sinew]

No i dont

[vale wigeon]

what about just e^t

[glacial sinew]

Yea i knwo that

[vale wigeon]

ok what's d/dt (e^t)

[glacial sinew]

Its just e^t right

[vale wigeon]

yes

do you know the chain rule

[glacial sinew]

Yea

[vale wigeon]

wonderful then please work out the derivative of e^kt for me

[glacial sinew]

So it will be e^kt * k(d(t)/dt)?

[vale wigeon]

bit of an obtuse way to put it but technically correct

what is dt/dt

[glacial sinew]

its 1?

[vale wigeon]

yes

[glacial sinew]

so its just k* e^kt

[vale wigeon]

so e^kt becomes ke^kt when differentiated

yes

[glacial sinew]

Ohh ok ok

But wait a min

[vale wigeon]

you now have all that you need really

[glacial sinew]

I gave you a bit of incorrect info so my fault

Here t, R and C is also given

So wont they become constants too?

R = 6 * 10^5 and C = 0.5 * 10^-6

@vale wigeon you there?

[vale wigeon]

the next time you ask i will disappear

R and C are constants, t is not

you're calculating a derivative with respect to time

[glacial sinew]

did i do smthg wrong?

[vale wigeon]

no

[glacial sinew]

uhh then why that sudden comment

[glacial sinew]

anyways lets start from here

[vale wigeon]

you can replace the constants R and C with their values at any point but i recommend doing it only at the end

[glacial sinew]

But when you like differentiate a constant it becomes 0 no?

[mellow relic]

Yes

[glacial sinew]

that isnt really helping

that just messes up the entire equation

[vale wigeon]

sure when it is on its own

but like you're getting some kind of tunnel vision here i think

you know the derivative of e^kt is ke^kt

it's just that your k looks like -1/(RC)

[glacial sinew]

so we differentiate even constants in chain rule?

this is very confusing

[mellow relic]

U r differentiating it with respect to time right ?

[glacial sinew]

Yes

[mellow relic]

Differentiate it one time then put value of it t = .3

[vale wigeon]

you're not differentiating k alone you're differentiating kt

[glacial sinew]

ok ok

I got a glimpse of it

[glacial sinew]

Here are we just suppose to ignore the fact that t here has a value which makes it a constant?

[mellow relic]

After differentiating all will remain same but u will get multiply it with -1/RC

[vale wigeon]

no

t is not a constant

t is the variable with respect to which we are differentiating

the fact that we want the derivative at a specific value of t doesn't change that

i think i am going to leave this to @mellow relic tho

[mellow relic]

Ok

[glacial sinew]

So could you like continue

[mellow relic]

Ok give me hint where u r

Like u r having trouble differentiateing it ?

[glacial sinew]

YEs

[mellow relic]

e^somthig after differentiating it will remain same but we need to differentiate x too which is power of it

And differentiation of x is 1 so it's doens't matter if this equation happen to us
But we have e ^ kx
It's differentiation will be e^kx times k

[glacial sinew]

right i got that much

[mellow relic]

And k in ur case is -1/RC

[glacial sinew]

yes

[mellow relic]

Multiply it with that same eq

And put value

Find out rate

[glacial sinew]

Aight got it

Could you help me understand the chain rule ?

I have learnt it several times but cant seem to get a grasp of out

it*

w8 w8

i figured it out

Thanks for the help @mellow relic

[mellow relic]

Np

[glacial sinew]

Thanks a ton!!

.close

[lone heart]

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[outer steeple]

do u calculate the same if the space diagonal is facing the left? like in this picture

[mellow relic]

Ig Yeah

For magnitude yes

[outer steeple]

alright thanks

.close

[lone heart]

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[blissful hornet]

The options are
0.5
1.5
2.5
3.5
The ans is only 0.5, but I ended up getting 0.5 and 2.5, not sure how

[lone heart]

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[mellow tendon]

hello, can someone give me a linear equation i just wanna see if i can solve it

[lethal belfry]

in how many variables

[mellow tendon]

like a easy equation but not that easy

[lethal belfry]

hmm, okay

5x+3=2

to start

[mellow tendon]

sorry, i just came

[lunar saddle]

@mellow tendon try this

[mellow tendon]

5x + 3 = 2
5x = 3 - 2
x = 2

[lethal belfry]

uh, no

what is 3-2?

[mellow tendon]

1

[lethal belfry]

okay, so what is 5x?

[lethal belfry]

here

5x=3-2

right

[mellow tendon]

i would know how to solve without 5x

[lethal belfry]

so what is 3-2

[vast harbor]

2-3

[mellow tendon]

if it the equation was x+3=2

[lethal belfry]

oops, right

[lethal belfry]

wel, okay, do you want to learn how to solve this type of problem now?

[mellow tendon]

wait what

im so stupid

i cant believe i just

[lethal belfry]

You aren't stupid. Calm down

[mellow tendon]

so this is all right, but x = 1 is here?

if x = 1 was there would it be correct

[lethal belfry]

well, no
5x+3=2
5x=2-3
5x=-1

[noble stirrup]

is anyone here learning ai right now and want to enhance his \her maths skills can be my freind

[lethal belfry]

Does it make sense until here?

[mellow tendon]

i knew it was first 2-3

[mellow tendon]

yes

[lethal belfry]

okay, so now what you do is divide both sides by 5

[vast harbor]

#discussion

[mellow tendon]

which

[lethal belfry]

Okay, so you have 5x=-1, yes?

[lunar saddle]

is ok

[mellow tendon]

yes

[lunar saddle]

We make mistakes

[lethal belfry]

so now you want to get rid of the 5, yes?

[fallow merlin]

like my parents who made me

[mellow tendon]

yes

is it -0.2

[compact sentinel]

why every number raised to the power of 0 is equal to 1

[lunar saddle]

!occupied

[lone heart]

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 belfry]

YES!

But can you write it as a fraction instead?

[lunar saddle]

try 10x - 24 = 12 next

[mellow tendon]

10x - 24 = 12
10x = 12 - 24
x = - 12

[fallow merlin]

where did the 10 go?

[lunar saddle]

sry i gtg ill let the others help :)

[mellow tendon]

10x = - 12?

[lethal belfry]

Yea!

so now divide both sides by 10

[mellow tendon]

-0.2

oops

is it 12

[vast harbor]

10x=-12 , yes

[lethal belfry]

What is -12 divided by 10

[mellow tendon]

-1.2

i forgot how to divide

why do people keep forgetting math after they learn it?

[lethal belfry]

Lack of practice usually!

[mellow tendon]

so math teachers have to do practices all day? lol

[lethal belfry]

Most of them do some math everyday, yes!

[mellow tendon]

can you give me another equation

[vast harbor]

\begin{align*}
&10x=-12 \
&\text{multiply both sides by } \frac{1}{10} \text{ to get the value of } x \
&\frac{1}{\cancel{10}} \cdot \cancel{10}x = -12 \cdot \frac{1}{10} \
& \rightarrow x = \frac{-12}{10} = -1,2
\end{align*}

[ocean seal]

<rajel />

[lethal belfry]

9x-44=1

[mellow tendon]

9x - 44 = 1
9x = 1 - 44
9x = -43

is it correct

[lethal belfry]

what is 44+1

[mellow tendon]

5

so its 9x = 5 ?

[lethal belfry]

44+1 is not 5

[mellow tendon]

45

[lethal belfry]

yes

so what is 45 divided by 9

[mellow tendon]

5

[lethal belfry]

yes!

[mellow tendon]

oh, so - = - is = +

and + = - is -

[lethal belfry]

what do you mean

basically when you take a number to the other side of the equation, the sign flips

[mellow tendon]

can you give another equation

[lethal belfry]

sure

uh, easier or harder?

[mellow tendon]

hm

you pick

[lethal belfry]

harder?

[mellow tendon]

sure

[lethal belfry]

3x=2x+1

[mellow tendon]

uh

[shell agate]

subtract both sides by something to simplify it

[mellow tendon]

3x = 2x + 1
3x = 1 + 2x
3x = 0.5

[shell agate]

.

[lethal belfry]

almost, can you subtract 2x from both sides

[shell agate]

I don't understand the logic behind how you got 0.5

[mellow tendon]

1 subtract 2

[shell agate]

you see there is an x

multiplied with the 2

and 1-2 is -1

Anyways 5x-x =4x , so you can subtract x terms

[mellow tendon]

how did you get 5x-4 = 4x

or is that an equation

[vast harbor]

he didnt get that

he clearly written 5x-x=4x

not 5x-4=4x

[mellow tendon]

what x could it be

@vast harbor

[vast harbor]

i guess its time to watch some videos or read some articles on equations solving
iirc someone else have send you a video that explains equations very well , if you have watched it you'd learn alot

you can also find exercices online

im saying this because you've been in the same topic for a while now

[mellow tendon]

dude i just asked you what x could it be

[vast harbor]

and i've given you the answer

[mellow tendon]

ur annoying

[vast harbor]

your so fluent in roasting other people

have that deducation in math

[vast harbor]

realised you said something disrespectful , good

[mellow tendon]

weirdo

[lone heart]

@mellow tendon Has your question been resolved?

[lone heart]

@mellow tendon Has your question been resolved?

[lethal belfry]

@mellow tendon you still here?

Still need help?

[mellow tendon]

sure

[lethal belfry]

Okay, back to the question then

3x=2x+1

can you start by subtracting 2x from both sides?

[mellow tendon]

3x=2x+1
3x=1-2x
x=-1

[lethal belfry]

uh, almost

what's 3x-2x?

[mellow tendon]

1

[lethal belfry]

no

try again

[mellow tendon]

-1 ?

[lethal belfry]

3x-2x=1x, yes?

[mellow tendon]

oh so 1x ?

x = 1x is this correct?

[lethal belfry]

x is 1x, yes

so we have 1x on the left hand side

and 1 on the righ hand side

what does that mean?

[mellow tendon]

x = 1?

[lethal belfry]

yes!

[mellow tendon]

do another equation

[lethal belfry]

Harder question or easier question

[mellow tendon]

same as taht

thatz

[lethal belfry]

okay

6x=12+4x

[mellow tendon]

6x=12+4x
6x=4x+12
x=16 ?

[lethal belfry]

what is 6x-4x

[mellow tendon]

2

[lethal belfry]

2 what

[mellow tendon]

2x

[lethal belfry]

yes!

[mellow tendon]

so x = 2?

[lethal belfry]

so 2x=12

[mellow tendon]

oh dang

[lethal belfry]

so what is x?

[mellow tendon]

x= 12?

[lethal belfry]

2x=12

so divide across by 2

[mellow tendon]

x= 1

[lethal belfry]

what is 12 divided by 2

[mellow tendon]

6

[lethal belfry]

so what is x?

[mellow tendon]

x = 6

[lethal belfry]

yes!

[mellow tendon]

can you tell me step by step how did you do that

[lethal belfry]

from which step?

from the beginning?

[mellow tendon]

yes

[lethal belfry]

6x=12+4x
we then subtract 4x from both sides
6x-4x=12+4x-4x
2x=12
We divide both sides by 2
x=6

[mellow tendon]

can u do another equation

[lethal belfry]

I can only do one more for now as I have to study too, is that fine?

[mellow tendon]

absolutely fine, go ahead

[lethal belfry]

a new question?

[mellow tendon]

yes

[lethal belfry]

12x=20+2x

[lethal belfry]

Can you solve this

or should I

[mellow tendon]

i can

[mellow tendon]

u subtracted 4 and 4 '

?

[lethal belfry]

you mean 4x?

[mellow tendon]

yes

@lethal belfry i

[lethal belfry]

sorry

had to plug in my laptop

[lethal belfry]

well, that's what we're really doing

[mellow tendon]

12x=20+2x
12x=2x-20
2x=1
x=2

is this correct?

[lethal belfry]

uh

try again please

[mellow tendon]

x=1?

[lethal belfry]

no, with steps

[mellow tendon]

uh i did 12-2

so thats 2

[lethal belfry]

12 -2 is 2?

[mellow tendon]

-2

[lethal belfry]

or is x =2?

[mellow tendon]

wait no

its 10

[lethal belfry]

12-2 is 10, yes

[mellow tendon]

so is it x= -10

wait, no

i got confused.

[mystic steeple]

U have to divide by 10

[mellow tendon]

i dont know what i have to divide after 10

[lethal belfry]

you have 10x=20

yes?

[mellow tendon]

yeah

[lethal belfry]

now how to make 10x to x

[mellow tendon]

subtraction

[lethal belfry]

using division

[mellow tendon]

yeah but idk how do divide 10 to x

[lethal belfry]

what happens If I divide 10x by 10

[mellow tendon]

it's x=1

[lethal belfry]

you get 1x

right

[mellow tendon]

oh now i knoww

[lethal belfry]

cool

[vernal merlin]

@lethal belfry is your job in mathematics cause you are smart asf

[lethal belfry]

I'm a math major. I'm going into my second year after this summer.

[vernal merlin]

so you are 14 years old ? and you are so smart

[lethal belfry]

no

I'm old, but my age is immaterial here

[vernal merlin]

yeah idk why i stuy every day but in total i have 27% bro look

[lethal belfry]

hmm, if you need help open a. new channel please.

#❓how-to-get-help

[vernal merlin]

math is impossible for me for knowing math so good do you just study every or does it come like this

[vernal merlin]

no thanks i don't really need now

[lethal belfry]

I used to be bad at maths in school( like used to score 60-70%) . Uni math is more proof heavy, which helps

[vernal merlin]

60 is good for me

[lethal belfry]

And yeah practice a lot!

Like spend atleast 2 hours on math a day

[lethal belfry]

anyway, did you get the answer?

[vernal merlin]

what do you want to do with math later ? like working in the nasa or ?

[vernal merlin]

i have something for you

[lethal belfry]

Research at a uni in my home country.

[vernal merlin]

@mellow tendon is it this that you are learning

[mellow tendon]

no

[vernal merlin]

can you show a picture of what ur learning

[mellow tendon]

normal equations

[vernal merlin]

youare in first grade of secundary school ?

[mellow tendon]

yes

[onyx skiff]

SAME!

[lone heart]

@mellow tendon Has your question been resolved?

[lone heart]

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[unborn valley]

would it not be capital b and capital a?

(capital as in derivative)

formula for N(t) has T’(t)

so if T(t) was <a,b>
N(t) would be <-B,A>

[hushed locust]

no

all that the formula is saying is that the normal vector is also a unit vector and it is orthogonal to T(t)

(which comes out of the definition in a somewhat more complicated way)

[lone heart]

@unborn valley Has your question been resolved?

[lone heart]

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[void forge]

Hello, I’m stuck on how to find the domain of a square root within a square root. Please help

[cursive viper]

first, you can watch under the most inside root

for which x is it defined ?

[void forge]

I’m sorry, I’m confused, what are you asking?

[cursive viper]

to first check for which values of x, the sqrt(x²-9²) is defined

[void forge]

Like this?

[cursive viper]

yes but this is wrong

the last line

[cursive viper]

nope, try instead of factorising the first line in this picture

i mean the x²-9²

[void forge]

I can factor it?

[cursive viper]

yes

i can tell how to do if you dont know

[void forge]

Yes please

[cursive viper]

it is a formula basically

(a-b)(a+b) = a²-b²

[void forge]

Ohhh ok

So like (x-9)(x+9)

[cursive viper]

yea

[void forge]

So would I find the domain for each parentheses?

[cursive viper]

no

you must just solve the whole inequality : (x-9)(x+9) >= 0

[cursive viper]

you see where this comes from ?

[void forge]

Yes but I’m confused as to what to do next

[cursive viper]

if you have a * b >= 0

how could this be true, reasonning on the signs of a and b?

[void forge]

One of the variables is 0?

[cursive viper]

hm yea also, but for this : a * b >0

i shouldnt have writen >=

[void forge]

They’re both positive?

[cursive viper]

yes

but there is another way to make it true

[void forge]

There is?

[cursive viper]

yea

[void forge]

I don’t know what that way is

[cursive viper]

-1 * -1 = ?

[void forge]

Ohhh ok

[cursive viper]

siuu

[void forge]

siuu?

[cursive viper]

thats an emote

u scream it when you are satisfied

[void forge]

Ohhh ok

[cursive viper]

but are you still stuck ?

[void forge]

Yes, I don’t know what to do with (x-9)(x+9)>/=0

[cursive viper]

think of this with a = (x-9) and b, the other term

[cursive viper]

i meant, just applying the way of solving a*b >0

not replacing the terms

the 2 soulutions were: a> 0 and b> 0 or, a< 0 and b<0

[void forge]

I’m confused as to how you got those solutions

[cursive viper]

what did you understand here ?

[void forge]

That was in response to understanding what the emote meant

[cursive viper]

ah, i thought you understood the answer lmao

so

if you have a * b > 0 , do you agree that if a> 0 and b> 0, it is true ?

[void forge]

Yes

[cursive viper]

and same if a<0 and b<0 ?

[void forge]

Yes

[cursive viper]

so if (x-9)(x+9) >0 , it means that either (x-9)>0 and (x+9) >0 or another solution

that i let you find

[cursive viper]

if you understood this ofc

[void forge]

Ohh ok

I have to go, I have a class in 5 minutes, I appreciate your help!

[cursive viper]

np

[lone heart]

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[summer dirge]

does this proof look okay?

[summer dirge]

this is Prop 5.37. that I reference

[lone heart]

@summer dirge Has your question been resolved?

[lone heart]

@summer dirge Has your question been resolved?

[lone heart]

@summer dirge Has your question been resolved?

[lone heart]

@summer dirge Has your question been resolved?

[lone heart]

@summer dirge Has your question been resolved?

[summer dirge]

oh well

.close

[lone heart]

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Closed by @summer dirge

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[woeful zenith]

Probably a question for stackexchange

[frank blade]

help

[leaden bobcat]

works for me

[blissful temple]

why is this help channel still up

[lavish cave]

didnt cllose yet

[blissful temple]

maybe this help channel is not properly embedded? @summer dirge

[lethal belfry]

.close

.reoopen

.reopen

[lone heart]

✅

[lethal belfry]

.close

[lone heart]

Channel closed

Closed by @lethal belfry

Use .reopen if this was a mistake.

[lavish cave]

.solved

[lethal belfry]

Hopefully this works

[lone heart]

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[brave junco]

Im supposed to simplify this

And

The answer I got

Was

10x-2-3x^2

While the correct answer is 22-3x^2

[stuck ether]

what did you do

[brave junco]

I’ll sjpw

Show

[vale wigeon]

sign errors are pretty likely in this kind of question

so yes show what you did

so we can hunt the mistake down

[vale wigeon]

ah.

[brave junco]

Idek what happened here

[vale wigeon]

5x+10 - ( 3x^2+9x-4x-12 )

you missed those parentheses

[brave junco]

Huh

Wait

Those two parentheses become one huge one?

[vale wigeon]

yes bc that whole thing is getting subtracted

[brave junco]

Oooooooooooooh

[stuck ether]

you can imagine the - there as (-1)(3x-4)(x+3) aswell if that makes sense

[brave junco]

Ohhhh I get it tysmmmm

.close

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[dapper sequoia]

ch

[dapper sequoia]

ask

Uhhmmmm

.close

[lone heart]

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[dapper sequoia]

@swift basalt i've been wai'ng for soo long

[swift basalt]

In case that there is a Vector-space, with the dot product $\langle\cdot,\cdot\rangle$. For all subspaces $U,W\subseteq V$, the direct sum $U+W$ is defined as.
$[U+W={u+w|u\in U,w\in W}]$
how can I show, that $V=U+U^\bot$?

[ocean seal]

McMake
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vale wigeon]

!occupied

[lone heart]

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).

[vale wigeon]

(sorry, this channel still has somebody else's name on it.)

[swift basalt]

oki

he just closed it so I thought its fine

tz for the info

[dapper sequoia]

Hey Ann, i want to close it

.close

[vale wigeon]

it's already closed

the bot has a rate limit for channel modification

• there is a grace period during which a channel can be reopened

[dapper sequoia]

Oh fine, Okayy

[lone heart]

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[cinder sundial]

Ugh

How should I memorize them

The proofs for them is kinda counterintuitive IMO

[lavish cave]

the first one is just a definition

exponential and logarithmic functions to the same base are inverse functions

[lavish cave]

then you can write $a^{\log_a x \cdot \log_a y}$

[ocean seal]

south

[cinder sundial]

Does it explain anything

The formula

[lavish cave]

it's a useful property I guess

[lavish cave]

so that's the case of $f^{-1} (f(x)) = x$

$f(f^{-1} (x)) = x$ would be $\log_a (a^x) = x$

[ocean seal]

south

[cinder sundial]

I cannot see it is relevant to the formula

[lavish cave]

yes

look at how x was rewritten here

[cinder sundial]

The definition of headache

Can you explain it in simple terms

[cinder sundial]

I cannot see they are relevant as well

I think I should just grin and bear it

[lavish cave]

$x^{\log_a y} = (a^{\log_a x})^{\log_a y}$ first

[ocean seal]

south

[lavish cave]

replace x first

then use (a^b)^c = a^(bc)

[lone heart]

@cinder sundial Has your question been resolved?

[lone heart]

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[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[sick tangle]

for question 2 i never know if i add 1 when i work out Q2

so do i do
(95+1)/2 or 95/2

[mossy reef]

Where are you getting 95 from?

[sick tangle]

by adding the freq

to work out the position

[mossy reef]

You should do (95 + 1)/2.

[sick tangle]

why not 95/2

[mossy reef]

Rather than 95/2, think of it as n/2. If you had exactly one datapoint, meaning n = 1, would it make more sense to use (n + 1)/2 = 1 or n/2 = 0.5 for the median?

[sick tangle]

adding 1 to n

to get 1

right?

the thing is

ive seen examples of not adding 1

coz of that im like hella confused on when or not to add 1

okay i found one

it says n/2 in bottom right

[onyx swallow]

can you show the full comment on the bottom right?

[sick tangle]

yea sure

[onyx swallow]

it means that if n/2 is not an integer, you round up your value.

If it is, then you take average between n/2 element and n/2+1 element

[sick tangle]

for these questions shall i always add 1 for the Q2 value? as well as Q1 & Q3

[onyx swallow]

for example, n=3, the "middle" of the data would be the second position, and you notice that this is precisely 3/2 rounded up (since 3/2 is not an integer).

But when n=4, the middle should be 2nd or the 3rd element, and you can calulate 4/2 (this is an integer) which gets you 2, and you take average between the 2nd, and 2+1=3rd element

[sick tangle]

ok thanks

[onyx swallow]

it is ok to always add 1

[sick tangle]

for question 3 i dont add 1 to median right?

[onyx swallow]

in fact (n+1)/2 tells you what the actual middle is

[sick tangle]

wb q3 and q1

[onyx swallow]

if, say, 367.5 is the output, then both 367 and 368 could be the middle since we are working with positive integers

[onyx swallow]

what does Q1 and Q3 stand for?

[sick tangle]

1st quartile and 3rd quartile

1/4 of data and 3/4 of data

[onyx swallow]

in this case, assuming ascending order, (n+1)/4, and 3(n+1)/4tells you the cutoff.

you can try and prove this fact, its quite intuitive

[onyx swallow]

for example n=5, so we have elements numbered 1,2,3,4,5 you are trying to find the "middle" element.

[sick tangle]

thank u

it makes sense now

clears a lot of stuff up

but wb grouped data

[onyx swallow]

the idea is to make it an inteval, and try and find the middle of the interval [1,5] (or [1,n] more generally). This just turns out to be (n+1)/2

[onyx swallow]

np

[sick tangle]

final question

[onyx swallow]

what is grouped data?

oh actually that looks more complicated, i don't think i know enough definitions surrounding that to answer, maybe someone else will help

[sick tangle]

the one in question 3 is grouped data

[sick tangle]

that is okay

thanks a lot btw!

[onyx swallow]

oh wait i think this should be (n-1)/4+1, and 3(n-1)/4+1, but they don't make too much of a difference

(n-1) is the length of the interval, (n-1)/4 is a quarter of the length, and +1 because we are starting at 1.

[onyx swallow]

but tbh, your teacher might have a different convention when it comes to this and how to calculate this. so you should double check with the resources you are given

[sick tangle]

okay

[onyx swallow]

https://www.desmos.com/calculator/wtnjpeqbcc you can fiddle around with this graph to get some intuition for the other cases

[lone heart]

@sick tangle Has your question been resolved?

[lone heart]

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[cursive wharf]

.close

[rare kayak]

hi, this is my first time asking a doubt here so im sorry in advance if this is the wrong channel. Anyways, how would you go about finding the correct function for the second graph? The first one was pretty simple i just recognized the sin function

[void bear]

Lol.

This ain't the wrong channel.

[rare kayak]

thanks for the clarification

[astral apex]

Ok so see for the negative value of x function gives positive positive value of y so function Highest degree x coefficient has to be negative and it's giving both positive and and negative infinity so it has to be odd degree function

[rare kayak]

okay....

[unreal flicker]

well there are a couple ways

[rare kayak]

please tell me the simplest one

ive been away from math for a year, so im super rusty rn

[unreal flicker]

honestly this is probably the easiest way

[rare kayak]

the answer they provided is option 6

which im super confused about, if anything i was thinking the answer would have a cube

something with x^3

[unreal flicker]

I don't think that's correct

let me just graph it for you

[rare kayak]

yeah it seems to be wrong

the green line seems similar

but its not been offset

[unreal flicker]

oh wait yeah yeah

[rare kayak]

its f'(x)

[unreal flicker]

apologies about that

[rare kayak]

so we got to integrate it right?

[unreal flicker]

oh, you've done integration?

[rare kayak]

np

[rare kayak]

yeah

its just been a year so im super goofy at it now

[unreal flicker]

yeah that's probably the easiest way

[unreal flicker]

yeah that's just the +C

[rare kayak]

okay now coming back to the question, how do i just figure out the answer without integrating each option like a chad?

[unreal flicker]

but you can also set the derivative equal to zero

you'll get 3 solutions of x which satisfy f'(x)=0

[rare kayak]

can you explain this

im really having trouble remembering how to do that 😅

i was so good at calculus back in high school, scored 87% in math

[unreal flicker]

when the derivative of a function is zero that means it's either a local maximum, minimum or a saddle point (as you can see in the graph 2, at zero for a moment the gradient seems to become zero but it's not a maximum or minimum point)

[unreal flicker]

I know the feeling man, but don't worry it's not that difficult to get back on track

[rare kayak]

okay i think i understood this

[unreal flicker]

the derivative essentially gives the gradient of the graph. You can figure out where there is EITHER a local maximum, minimum or a saddle point by equating the graph to zero because at those points, the graph f(x) has a gradient zero

if you precisely want to figure out whether the graph's gradient is positive or negative you can make a chart with the values you got for f'(x)=0

[rare kayak]

i did some simplification and now i have f'(x)=x^2(1-x)(1+x)

so those are the 3 zero points you mentioned

so x= -1,0,1

[unreal flicker]

exactly

[rare kayak]

oooo i remember making this type of table😆

[unreal flicker]

if you check the sign using the 3 values you got you can see the variation of the gradient such as this

[rare kayak]

yeah

okay i think i've got a working theory

[unreal flicker]

and just in case, you should check the values f'(x) approaches for the limits as x->infinity and x->negative infinity

[rare kayak]

these are the three points of inflection

[unreal flicker]

yep

checking the inflection points is probably the easiest way without integrating

btw, I like your pfp 😅 used to love that show

[rare kayak]

goated

[unreal flicker]

fr man

is there anything else you would like to know?

[rare kayak]

im still tryna figure out how after finding the inflection points im supposed to deduce what the function is out of the many options that are given

[unreal flicker]

this plot is probably the easiest way

[rare kayak]

i dont like how the graph has wierd bulges

[unreal flicker]

if the gradient goes from - to +, a local minimum
is the gradient goes from + to + or - to - that's a saddle point

• to - is a local maximum

[rare kayak]

yeah i got that

[unreal flicker]

yeah the weird budge at x=0 is the saddle point, the gradient becomes zero

[rare kayak]

ahhhh

its really not clear from the graph given in the question

[unreal flicker]

yeah 😅

that's how questions are sometimes, at least where I live

but in general, if there are weird budges and stuff in a polynomial graph, that means there's a saddle point

[rare kayak]

got it

[unreal flicker]

if there's anything else you'd like to ask, just give me a text. I have to go now 😅

[rare kayak]

no nothing else, thanks for the help it was really nice of you to take the time

.close

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[alpine sable]

Can I send an assignement I need help with ?

[alpine sable]

I asked Chat GPT to translate so I'm not sure if it's perfect

Let E be a K-vector space, and F a subspace of E.
We define the relation R on the vectors of E by:

∀(x, y) ∈ E², x R y ⇔ y - x ∈ F. 

1. Show that the relation R is an equivalence relation.

2. For every x ∈ E, specify the class of the vector x.

For every x ∈ E, we will denote by x + F the class of the vector x in E. We denote E/F as the set of the quotient E/F.

3. Show that the operations:
   (a, b) ∈ E/F × E/F, (a + F) + (b + F) = (a + b) + F and λ ∈ K, λ(a + F) = (λa) + F
   are well-defined.

4. Show that the set E/F equipped with the operations + and scalar multiplication thus defined forms a K-vector space.

We say that the subspace F is of finite codimension if the space E/F is of finite dimension. In that case, we denote:

codim(F) = dim(E/F) 

the codimension of the space F.

5. Show that the space F has finite codimension if and only if F has a finite-dimensional supplementary subspace G in E.

I'm struggling with the fifth question

The other are trivial tbh

[mossy reef]

<@&268886789983436800>

[alpine sable]

<@&286206848099549185>

[lean depot]

Please don't message random users like this.

[alpine sable]

k

So can you help ?

[alpine sable]

Can I ping <@&286206848099549185> again ?

[lean depot]

I would suggest not doing so

If you want people to answer your question, it's a good idea to:

• be specific about what your question is
• show what you've tried already

Helpers are volunteers, not waiters on-call

[alpine sable]

https://tenor.com/view/jerry-hungry-tom-and-jerry-feed-me-mouth-gif-11590925

GIVE ME MY ANSWER

NOW

[lean depot]

When you say "assignment," is this just homework or is this going to be graded?

[alpine sable]

It's not graded but the teacher wants us to do our best

NEC PLUS ULTRA !!

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@alpine sable Has your question been resolved?

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[candid whale]

Can someone help me prove that the sum of the interior angles of a triangle is 180 degrees?

[north rover]

<@&268886789983436800>

[lilac fulcrum]

phishing scam?

[edgy walrus]

draw a line through Z that is parallel to the base of the triangle

[candid whale]

ah ~ i see

is this right?

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@candid whale Has your question been resolved?

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[summer swallow]

Curios why demos isn’t showing an oblique asymptote for the function y = 6x^2/(x+2). Equation for the oblique asymp I got was y = 6x-12

[summer swallow]

Wait uhh maybe I’m just not zoomed out enough

.close

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[cobalt pumice]

hello! does anyone have textbooks for algebra or just highschool math in general ranging from grade9-grade12?

[errant thorn]

can someone tell me the answer to this? It looks easy but i just wanna compare my result cause im kinda lost rn ill send an image

[alpine mason]

@cobalt pumice i would recommend the book Alegbra CCSS for algebra 1

[mossy reef]

!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).

[cobalt pumice]

woould it be this? https://www.thecorestandards.org/Math/Content/HSA/

[alpine mason]

yeah that would be it

[cobalt pumice]

got it, tysm!

.close

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[drifting badger]

My work so far
$$\vec F=\langle4y-4z,4z-4x,4x-4y\rangle$$
$$\nabla\times\vec F=\langle-8,-8,-8\rangle$$
normal vector is $$\langle1,1,1\rangle$$
$$\int_{S}\langle-8,-8,-8\rangle\cdot\langle1,1,1\rangle ds=\int_{S}-24ds=-24\cdot\pi\left(\sqrt{\frac23}\right)^2=-\frac{48\pi}{3}$$

[ocean seal]

Definite Articles

[drifting badger]

the issue is that $$\frac{-48 \pi}{3}$$ is incorrect so idk where my mistake is

[ocean seal]

Definite Articles

[drifting badger]

feel free to spam ping me

[lone heart]

@drifting badger Has your question been resolved?

[drifting badger]

<@&286206848099549185> halp pls

nvm i figured it out myself

the answer was $$\frac{-16\pi\sqrt3}{3}$$

[ocean seal]

Definite Articles

[drifting badger]

.close

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[ember locust]

<@&286206848099549185>

Can somebody help me study for my 7th grade math SOL reatake

[mossy reef]

!da2a

[lone heart]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

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[mossy reef]

!noping

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Please do not ping individual helpers unprompted.

[mossy reef]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[ember locust]

What speak english

Hello

Can somebody help me

[lavish cave]

you should ask questions about a specific exercise you have

"can someone help me study" is not how the help channels work

[ember locust]

Then is there anybody that can help me study

[lavish cave]

https://www.khanacademy.org/math/geometry-home
if you want to practice try Khan Academy

[lavish cave]

let me rephrase: how do you want people to help?

[ember locust]

My 7th grade Math sol retake

[lavish cave]

okay, what topics are in your retake

[misty rune]

hey south could you help me? im on the math help modopotasio and no one is trying to help me

[ember locust]

Proportions

And dilation

[lavish cave]

I'm sorry that's happening

but I can't juggle multiple things like that at once

[lavish cave]

try Khan Academy honestly

[ember locust]

Ok

[misty rune]

its ok but is there anotehr person that can help me?