help-26

[raven sparrow]

Are you sure everything is right with the statement (df/dx, df/dy, the answer you're given)?

Because according to the answer you say it should be,
df/dx = 1/(x^2 y) - 1/x and df/dy = 1/(x y^2) + 1/y, both of which don't fit the original derivatives you had.

[lethal star]

my bad

it was ln(x/y)

in the answer

now what is the mistake?

[raven sparrow]

This still won't fit though. The second term of the y derivative has to be -1/y^2

[lethal star]

let me check

[lethal star]

this is the original equation
Mdx + Ndy = 0

so I multiplied by 2

and it is exact

so df/dx = M
df/dy = N

am I right

ok i found my error

thnx for helping

y2

i'm still not getting ln(x/y)

[lethal star]

how do I find phi(x) now

[raven sparrow]

Recheck your derivative in x you shouldn't have the 1/y term in there

[lethal star]

ok so how do u calculate phi(x) from there?

just solve it normaly?

or separate x and y terms and comapre

[raven sparrow]

It's the same thing you did earlier

But with the right df/dy to start with.

After integrating w.r.t. y you get

$f = \frac{-1}{xy} - \ln{y} + \phi(x)$

[thorny flame]

Azyrashacorki

[raven sparrow]

And then $\frac{\partial f}{\partial x} = \frac{1}{x^2 y} + \phi^\prime(x)$

[thorny flame]

Azyrashacorki

[lethal star]

so i have an equation in $\phi'(x)$
how to proceed from there

[thorny flame]

Pogram

[raven sparrow]

Well you compare it with the other expression you have for df/dx, just like you had done earlier.

$\frac{\partial f}{\partial x} = \frac{1}{x^2 y} + \phi^\prime(x) = \frac{1}{x^2 y} + \frac{1}{x}$

[thorny flame]

Azyrashacorki

[raven sparrow]

So what is phi'

[lethal star]

1/x

[raven sparrow]

Yeah so then phi is ln(x) + c

[lethal star]

what if i dont get such a straightforward result

[raven sparrow]

You will

It's sort of baked into the equations if it's exact

[lethal star]

okay

thanks

a lot

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[sullen briar]

i got a different answer, why am i wrong?

[sullen briar]

holup lemme get the screenshot from my ipad

oh wait i shoudlve changed the =49 in the first part to a 0

but still im wrong

<@&286206848099549185>

[uncut sentinel]

i think on the left side, u should've added a -49 instead to cancel out the +49 u added

[sullen briar]

ohhh wait

[uncut sentinel]

so then u would get a -87 on the second step

[sullen briar]

tyty

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[timber schooner]

when finding theta

and using tan

do i do absolute values

so

$tan^{-1}(\frac{1}{1}) \$ or $\ tan^{-1}(\frac{-1}{1})$

[thorny flame]

pixel

[timber schooner]

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[timber schooner]

i have to express this in the form x+yi

my answer was

$6(-\sqrt{3}+i)$

[thorny flame]

pixel

[timber schooner]

is that right?

woo

how did they get 2/4 as 'r'

cause i got -1/2

rather than the 1/2 that they got

[neon iron]

for z1 did you take the minus sign common ?

[timber schooner]

hmm?

wdym

[neon iron]

show me your working

[timber schooner]

well its on book and my phone is

dead

😭

but uh

anyway only thing im confused about is r value

so ill use latex

$\frac{-\sqrt{3}}{2\sqrt{3}} = \frac{-1}{2}$

[thorny flame]

pixel

[neon iron]

???

where did the sqrt 3 come from ?

[timber schooner]

what

wdym

[neon iron]

did you convert them into cis form ?

[timber schooner]

oh my god

im so silly

💀

i literally popped the 'x' value in z1 and z2

[neon iron]

ohhhh

[timber schooner]

divided those two

and called it a day

😭

im so silly

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[small orchid]

how do i solve this?

[neon iron]

you can either find alpha and beta

and build a new polynomial whos roots are 2alpha+1 and 2beta+1

or

you can do it without finding the roots

[neon iron]

although this is a simpler method

[small orchid]

im confused in the new polynomial part

should i get 2(alpha+beta +1+1) ?

[neon iron]

are you doing the second method ?

[neon iron]

yes

wat

wait

no

2(alpha+beta) +1+1

[small orchid]

ok

👍

and for the product it should be 4(alphaxbeta)+1

[neon iron]

❌

(2aplha+1)(2beta+1)

does that simplify to 4(alphaxbeta)+1

?

[small orchid]

4(alphaxbeta)+1?

[neon iron]

:/

[small orchid]

4(alphaxbeta)+1

[neon iron]

no

[small orchid]

i have no clue

[neon iron]

do you know how to expand

(a+b)(c+d) ?

[small orchid]

ac+adxbc+bd?

[neon iron]

no

it is
ac+ad+bc+bd

[small orchid]

ok

[neon iron]

now try multiplying (2aplha+1)(2beta+1)

[topaz sinew]

@small orchid Has your question been resolved?

[topaz sinew]

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[tranquil hazel]

can someone guide me through the process of this question like. Do i have to convert it to standard form, if so then how? or if I can do it without converting it to any form

[tranquil hazel]

ping me

[fallow igloo]

!status

[topaz sinew]

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

[tranquil hazel]

1

!status 1

[topaz sinew]

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

[fallow igloo]

Do you know the difference between selection B and C?

[tranquil hazel]

no

what is that

[rapid wyvern]

is this the highest quality graphs you can get

[tranquil hazel]

insult my guy

[rapid wyvern]

because i cannot tell any difference between a/c and b/d

[tranquil hazel]

wdym

[rapid wyvern]

can you zoom in

[tranquil hazel]

a/c b/d

[rapid wyvern]

to each graph

[tranquil hazel]

ah

ok

[rapid wyvern]

choice 1 looks very similar to choice 3

[tranquil hazel]

this is basically the question

i want to convert it to standard form

but can you even convert it to standard form

[rapid wyvern]

sure why not

[tranquil hazel]

like wont it change it completely

[rapid wyvern]

standard form being

y = mx + b

or something like that right

[tranquil hazel]

no

standard is

[rapid wyvern]

ax + by = c

[tranquil hazel]

yes

[rapid wyvern]

its already in standard form

3x - y >= 5

[tranquil hazel]

or wait sorry

not standard form

[rapid wyvern]

slope intercept?

[tranquil hazel]

mx + b

yes

[rapid wyvern]

ok

have you tried converting it into slope intercept form

[fallow igloo]

The difference is the inclusion or not

[rapid wyvern]

ah

[fallow igloo]

If you look closely

[tranquil hazel]

inclusion?

[rapid wyvern]

the line is either dotted/undotted

or complete

broken

whatever the term is

[tranquil hazel]

ye

[rapid wyvern]

ok so

[tranquil hazel]

dotted means less or more than

[rapid wyvern]

notice how the equation calls for >=

[tranquil hazel]

and undotted equal and more or equal and kless

[rapid wyvern]

so therefore the line must be complete/undotted

so you can cross out both choices which are dotted

now i know you might want to do the graphical method but i will share what i would do

3x - y >= 5

[tranquil hazel]

yes

[rapid wyvern]

now

go test if the origin makes the equation true

that is check if (0,0) makes the inequality true or false

[tranquil hazel]

ehm

what does that mean?

[rapid wyvern]

3(0) - (0) >= 5

[tranquil hazel]

can i ask why is that necessary?

[rapid wyvern]

trust in the process

[tranquil hazel]

ok

[rapid wyvern]

now is this true or false

[tranquil hazel]

its just going to be 0 more or equal to 5

[rapid wyvern]

obviously its falae

false

correct?

[tranquil hazel]

what do you mean by false?

[rapid wyvern]

0 >= 5

is not true

[tranquil hazel]

no not true

[rapid wyvern]

yea so false

[tranquil hazel]

false

[rapid wyvern]

ok now

notice how the two graphs at the bottom either contain (0,0) or they dont

[tranquil hazel]

they all have a origin point dont they

[rapid wyvern]

yes

but the shaded region

[tranquil hazel]

oh yes

[rapid wyvern]

either contains (0,0) or it doesnt

now youve shown that 3x - y >= 5

doesnt have (0,0) as a solution point

because 0 >= 5

is not true

correct?

[tranquil hazel]

yes

[rapid wyvern]

now

do you know what the shaded region means?

[tranquil hazel]

yes

[rapid wyvern]

ok

[tranquil hazel]

all the possible answers

[rapid wyvern]

now which of the two bottom graphs contain (0,0)

in the shaded region

[tranquil hazel]

the third one

[rapid wyvern]

well youve just shown that (0,0) isnt an answer to 3x - y >= 5

so it cant be that one

so that leaves you with only 1 option

[tranquil hazel]

what do we check every single one like that?

oh i get it

so we elimated the dotted ones

and the that contains the origin point is the answer

you dont even need to convert it to anything

or am i wrong

[rapid wyvern]

well the answer doesnt contain the origin

[tranquil hazel]

oh

[rapid wyvern]

but its close

[tranquil hazel]

bigger is to the right

and small is to the left right?

[rapid wyvern]

whar

[tranquil hazel]

like bigger that colors to the right

because its more than

and smaller than goes to the left

into the negatives

so its the one that doesent have the origin?

[rapid wyvern]

thats another observation yes

[rapid wyvern]

yes

its the option at the very bottom

[tranquil hazel]

but it could have the origin and still go to the right

what then?

is the origin necessary or is it just to use like a point to look at when deciding which side the graph goes to

[rapid wyvern]

its just a test point

the easiest test point

[tranquil hazel]

I see

so its like a marker

at which you look at to decide if its bigger or smaller than

thanks for the help

Its a time saver

[rapid wyvern]

btw if you do want to convert to slope form

3x - y >= 5

move the 3x to the other side

-y >= -3x + 5

[tranquil hazel]

I see

[rapid wyvern]

then multiply both sides by -1

which flips the inequality

y <= 3x - 5

thats slope form

[tranquil hazel]

I see

is that the only way?

or are there other methods

like for example switch the y intercept and y sides

[rapid wyvern]

theres probably more but its the one i use

[tranquil hazel]

ok

thanks a lot

you explain everything very well

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[topaz sinew]

@grave delta Has your question been resolved?

[topaz sinew]

@grave delta Has your question been resolved?

[grave delta]

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[heavy musk]

Translation: Given f(x) = 5x + 2/2-3x, find f'(x) and integral f'(x) dx.

[heavy musk]

Can someone help me with this?

the photo sent after translation lol

[spark fiber]

well to take the derivative of that you should use quotient rule

ok thats terrible quality

[heavy musk]

hmmmm

I think I skipped this in differentiation 💀🙏

sorry @spark fiber can u help me to put the number with this rule?

i need example

[heavy musk]

<@&286206848099549185>

[sly relic]

bro just plug in these parts

[heavy musk]

wdym

[sly relic]

You got 5x+2/2-3x

Function

[sly relic]

So there is a rule

[heavy musk]

idk how to put the number

[sly relic]

f(x) = 5x+2 here

g(x) = 2-3x

[heavy musk]

i see

[sly relic]

So then

[heavy musk]

ill try

wait

[sly relic]

By quotient rule

[heavy musk]

thats differentate of 5x + 2?

[sly relic]

Nah look

You got task to differentiate 5x+2/3-2x

Yes?

[heavy musk]

yea

[sly relic]

You can use quotient rule. (5x+2/3-2x)' = ( (3-2x)(5x+2)' - (5x+2)(3-2x) ) / (3-2x)²

Bcz f(x) is 5x+2 and g(x) is 3-2x

[sly relic]

So we just plug in by this rule

[heavy musk]

i seee

[sly relic]

Solve it

[heavy musk]

what does the ' mean

[sly relic]

Derivative

[heavy musk]

like this?

@sly relic

[sly relic]

No

You need to differentiate parts with '

Not multiply with another

[heavy musk]

ohh

okay

[sly relic]

Gtg wait pls

[heavy musk]

wait is it (3-2x)'?

the second one

(5x+2)(3-2x)' or no '

[sly relic]

Yes

I forgot

To write it

[heavy musk]

okay

@sly relic so after I differentate it, should I multiply it?

[sly relic]

Yep

[heavy musk]

alright

am I right so far? @sly relic

[sly relic]

Ur right

[heavy musk]

wait isnt it g(x) = 2 - 3x?

[sly relic]

It is

[heavy musk]

so its all wrong

[sly relic]

Why

[topaz sinew]

@heavy musk Has your question been resolved?

[heavy musk]

because u said it is 3-2x?

[sly relic]

Where is the connection

[sly relic]

Look here

[heavy musk]

what

[heavy musk]

this

isnt it suppose to be (2-3x)²?

[sly relic]

Oh sorry

Yess

[heavy musk]

is this right? new one

[sly relic]

So ye

Im gonna sleep

Goodnight

Bye

[heavy musk]

yea its 2:04am

[sly relic]

idk what am means, i live in country where is 24h system

[heavy musk]

what

[sly relic]

There is 2 systems

12 hours and 24 hours

[heavy musk]

yea ik

like

14:00 is pm

2:00 is am

[sly relic]

It is 23:06 now

For me

[heavy musk]

then its 23:06 pm

[sly relic]

11 pm

You mean

Ah I know understood

So

[heavy musk]

it is the same lol, more accurate

[sly relic]

Good luck

[heavy musk]

alright

[sly relic]

Bye

[heavy musk]

got it by myself xd

.close

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[uncut willow]

How do i calculate the variance based on this?

[glacial adder]

what test did you use?

you need to use the sample variance here

[topaz sinew]

@uncut willow Has your question been resolved?

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[granite ermine]

need help

[granite ermine]

with this

[manic wave]

Maybe try complex sine

Also is there a reason why it's in the u world?

[granite ermine]

What's the u world

Did some substitution to get to this

That's why

[icy rapids]

Use the limit theorem

[cursive patrol]

not solvable in the conventional sense

[cursive patrol]

can you show the original integral

[topaz sinew]

@granite ermine Has your question been resolved?

[granite ermine]

Hmm

Ig

[topaz sinew]

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[fathom marlin]

be x e R , the result of the calculation (sin x + 7 cos x)^2 + ( 7 sin x - cos x)^2 is egal to

we should just use the formula a^2 +/- 2ab + b^2

[verbal hound]

yes

[fathom marlin]

so sin^2 x + 14sinx cosx + 49cos^2 x + 49 sin^2 x - 14sin x + cos^2 x

[verbal hound]

yes

[fathom marlin]

50 sin^2 x + 14sinx cosx + 50cos^2 x - 14sin x

if we add them

[verbal hound]

no

[fathom marlin]

(idfk if we can add them like this

oh

damn

[verbal hound]

50 cos^2 x

not 51

continue

[fathom marlin]

50 sin^2 x + 14sinx cosx + 50cos^2 x - 14sin x

so

uh

[verbal hound]

-14 sinx cosx

not just sinx

they cancel out

please recheck your work

[fathom marlin]

sin(x)^2 + 14sin(x)cos(x) + 49cos(x)^2 + 49sin(x)^2 - 14sin(x)cos(x) + cos(x)^2

[verbal hound]

yes

[fathom marlin]

i did 2a in the second one not 2ab

too much make it not work huh

[verbal hound]

exactly

now, continue

[fathom marlin]

sin(x)^2 + 49cos(x)^2 + 49sin(x)^2 + cos(x)^2

the 14sinxcosx cancel each other

[verbal hound]

yes

[fathom marlin]

50cos(x)^2 + 50sin(x)^2

[verbal hound]

yes

[fathom marlin]

now

what

we just

use 50 as a common factor?

[hollow dagger]

now use sin(x)^2+cos(x)^2=1

[verbal hound]

this

[fathom marlin]

oh okey

so

50cos(x)^2 + 50sin(x)^2 = 1

?

[verbal hound]

no

try again

[verbal hound]

do this

[fathom marlin]

50(cos(x) + sin(x) ) ^2

?

[verbal hound]

yes

[fathom marlin]

so

[verbal hound]

m=no

no

no

50(sin^2x+cos^2x)

[fathom marlin]

oh

mb

yeah

[verbal hound]

now continue

[fathom marlin]

50(sin^2x+cos^2x) = 50 * 1

[verbal hound]

yes

[fathom marlin]

then we square it ?

[hollow dagger]

no

[verbal hound]

you got your answer

why square it

[fathom marlin]

oh

yeah

mb

thxx

[verbal hound]

np

[fathom marlin]

with this much i'll get a 50 on the test hopefully !

(god may i pass it

[verbal hound]

🙏

good luck!

[fathom marlin]

THANKS

I HOPE I WONT FAIL MATH CLASS

OTHERWISE YOU'LL SEE ME IN SUMMER HERE

[verbal hound]

you wont, I believe in you

just chill

and do everything step by step

[fathom marlin]

THANKS @verbal hound !

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[gaunt bone]

how do i determine a?

[fickle pelican]

we want displacement in the y coordinate = 50

have u learnt kinematics?

[gaunt bone]

yes

[gaunt bone]

mhm

okay

how do we proceed with this?

[fickle pelican]

are u aware of these

where u_y = 48sin(53.1) and u_x = 48cos(53.1)

[gaunt bone]

yes i am

[gaunt bone]

uh this not so much

oh wait its just y and x component yes i do

[fickle pelican]

we want displacement of the y component to be 50

so we find the time at that point

get it till here?

[gaunt bone]

ytes

i just have different formulas than you

im trying to make them work like yours

and find t

okay i got it

[fickle pelican]

so u will realize

u get 2 solutions

right?

[gaunt bone]

yes cuz its a parabolic formula

okay i got the answer tysm!

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[fickle pelican]

npp!

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[neon iron]

is the direction vector for this one m(a,3,b)
or m(a,-3,b)?????

cuz im getting 3 but gpt is telling me its -3?

r = a + td

its the one given to us

or do u mean the ax +by +cz = d

[thorny flame]

..,,

[neon iron]

yes

yep

kinda honestly its tricky to spot that it belongs to the denominator

could it also be that

(a,3,b) is equivalent to (a,-3,b) ?

since its the same direction vector, but in opposite direction

how come

a and b are constants, so the signs dont mean anything until we actually find the value

hmm

let me focus on waht u said then

i half get it

isnt it fair to say that the denominator b also cant be affected by the sign? since the skeleton of the equation says its b, not -b?

so b is a constant but x isnt

x is a variable

so we cant change its sign

thus the denominator must take the sign

i see

its hard to spot

but yea as u said

like now i know

yep thank you

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[astral blaze]

yes, that is true. but what is the question again?

[upbeat musk]

Q1: How does X being an input value affect the process of getting

2x-5, 3x+1

Q2

2x-5 3x + 1
6x + 2 -15x - 5
What do you do at this step?

Q3
What are the rules of factoring? Can one simply make any number into whatever they want, so long as the other numbers end up multiplying to get the original value?

Q4
Explain in verbal form the concept of each constituent concept and part of the problem and what the overall goal of the problem is.```

[astral blaze]

Oh wow, that is a lot. what question do you want a help or what do you not understand?

[upbeat musk]

All prior attempts have failed to result in my understanding; I assume this is the best solution given the circumstances. You may also use this as a guide to help clarify the parts outside my comprehension.

[upbeat musk]

I do not understand the processes, goals, or reasons behind the result of (2x-5) (3x+1).

[astral blaze]

ok... we can start step by step.

Let's start from the product itself

(2x-5)(3x+1)

do you know how to multiply those out?

[upbeat musk]

Because they are quantities being multiplied and not individual numbers, you must multiply each constituent part by each other constituent part to combine them.

[still dirge]

A good strategy.

[astral blaze]

so it seems like you know how to do this already. I will be quick then. Notice that when you multiply things out, you will see that the constant term will be the product of the last two numbers.

So, from (2x-5)(3x+1), you can tell right away that the final polynomial will be something - 5

[still dirge]

https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/janvee-variables-01-1602217580.png

[astral blaze]

and notice that the first term (2nd degree term, or x^2 term) will be the product of the two leading x term (in this case, it is (2x)(3x) = 6x^2)

so... really if you have a polynomial like 6x^2-13x-5, you know that whatever (ax+b)(cx+d) you want to have, bd = -5 and ac = 6. You also know that ad + bc = -13 from this formulation

you can guess the numbers that satisfy those equations to decompose or factoring the polynomial

it might be too abstract. But really, you can guess the number. You can solve it algebraically but that requires you to know how to solve the equation formed by polynomial degree two

the product of the backs is what the back of the polynomial is

the product of the fronts is what the front of the polynomial is

and the cross sum is what the middle of the polynomial is

[still dirge]

Define "product of the backs," and "product of the fronts," along with what front and back mean in this context.

[topaz sinew]

@upbeat musk Has your question been resolved?

[still dirge]

[upbeat musk]

hmmthonk

It is time for me to give up.

All attempts have failed.

This problem is not solvable though traditional approaches, possibly due to lack of core conceptual teaching methods by most teachers.

Meta-aware processes have been inert during my trek.

P is for pragmatism.

Efforts to solve this problem are abated until further notice.

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[late frigate]

am i correct so far?

[vernal matrix]

,rcw

[late frigate]

cos(4t) should be cos(2t)

tho

in the integration

just noticed 😅

[acoustic pecan]

oh dear

[late frigate]

is it wrong?

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[late frigate]

hm

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[neon iron]

Does anyone have any fun ways to self-study maths starting from college algebra? I'm a normie who gets distracted easily so I wanted to know if you guys had a stimulus or philosophy that helps you guys put in the time to voluntarily sit down and study math whilst maintaining focus on the material during your studies.

[rose sierra]

Are you studying for school or just for fun?

[cinder sequoia]

youtube math content is quite entertaining

watch some channels like 3blue1brown and blackpenredpen

[neon iron]

Studying in my spare time at work and at home

[ember spoke]

when you say "college algebra" do you mean like group theory or like coordinate plane stuff

[neon iron]

I bought a textbook from Blitzer titled college algebra in an effort to build the skills needed for the next level which is Trigonometry from what I heard

[ember spoke]

ah ok so the latter

yeah, that's a good step

[neon iron]

I've watched 3b1b but his content doesn't seem like it's aimed at me as I'm learning basic concepts like rationalizing exponents

[cinder sequoia]

maybe organic chemistry tutor and khan academy?

[keen venture]

Khan is easy to recommend

[neon iron]

Mhmm

[keen venture]

As his website does do the full curriculum thing

[neon iron]

Ah ok

[cinder sequoia]

unfortunately there’s not really a fun way to study when it’s still basics like algebra, but there are some pretty good resources out there when you get out to at least the calculus level

just any way to make it not boring, like challenge questions, integration bees, exam priblems

[keen venture]

A book is a good idea! You may find your brain trying to get you away from the book, unfortunately learning to ignore that urge is useful

[neon iron]

I find that I get the urge when I use my phone to find a solution for a question as I don't have many resources to ask for help without checking my messages

But I believe this place is a reliable resource when I get stuck

Another thing I also wanted to ask is what topics should I expect to learn and in what order to do calculus?

[cinder sequoia]

make sure you have a really solid understanding of algebra and precalc, including trig

nothing like exponents or logs or unit circle should be a problem for you

then start with limits

move onto derivative definition, then derivative rules, then some properties/theorems involving derivatives, implicit differentiation and related rates and optimization problems, then cover the definition of the integral via riemann sums, then properties and basic rules of integration, then fundamental theorem of calculus, then some more integration techniques like u-sub, then applications of integration like areas between curves and volumes of revolutions and stuff

then calc 2 stuff so like more integration techniques, some basic differential equations, and then sequences and series, and then power series

basically just following the order of most textbooks on calc 1/2

[neon iron]

Sounds good, do you recommend that I go through a trig textbook before moving onto calculus books?

[cinder sequoia]

maybe not a whole trig textbook but just know the six functions, any identities/formulas involving them, their domains and ranges, what their graphs generally look like, and how to find the values of all six of them given an angle in the unit circle

[neon iron]

Oh ok, thanks for the help guys

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[marsh roost]

Let f : D → R, with rule f (x) = –3x + 1 has range [−2, 7).
The domain, D, of f (x) is ?

[marsh roost]

whats the difference between square and round brackets ?

[unique crypt]

the square means -2 is included and the round means that 7 is not included

[marsh roost]

so the domain is -2, 1

what would the brackets be

[topaz sinew]

@marsh roost Has your question been resolved?

[rare anchor]

the brackets mean that specific number is/is not included in the domain

for example, the square bracket next to the -2 in this case indicates 2 is part of the domain, while the round bracket next to the 7 indicates 7 is not part of the domain itself

everything in between them is part of the domain though, if thats the confusing part

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[upbeat musk]

Sup

[upbeat musk]

On that last question.

How is (2x-5) (3x+1) equal to the question it was derived?

[pearl fog]

how is it not?

[gleaming reef]

well to check it

just expand it out (2x-5)(3x+1)

2x(3x+1) - 5(3x+1)

[upbeat musk]

Also how did they factor 13x away? Are they able to Simply delete it by making sure the other things will end up creating it when multiplied?

[upbeat musk]

K

[haughty wren]

Sort of yes. That‘s a technique of factoring

[full turtle]

Do u know how to use the cross methods

[upbeat musk]

6x+2x & 15x+5

What next?

[upbeat musk]

No?

[upbeat musk]

Yes, but how did they attain that result in particular while doing that? And what do you mean "sort of?" What rules, general ideas, or concepts am I missing?

[haughty wren]

The cross technique they‘re speaking of most likely. There are a couple methods for factoring, but one of them involves "making sure you create one term from the others" as you said

[full turtle]

So is something like this

[upbeat musk]

Wait so that WAS the method?

That I spoke of?

[haughty wren]

Yeah. You had a good intuition

[upbeat musk]

Hmmm.. a bunch of squiggly lines with random numbers on the left..

And the same on the right with a final factored answer?

Replace what I said with what they actually are.

[upbeat musk]

You're making me wonder if the perfect problem solving strategy is literally just finding ANY solution that solves a problem because so long as it would work it would have to be a truthy solution

Because before I had no way to validate if any one answer would be correct

[haughty wren]

For a lot of problems in maths you can verify your answer

[full turtle]

Just ignore the one on the left

[upbeat musk]

Kk

[haughty wren]

In the case of factoring, just expand, and check if you get the original equation back

[full turtle]

So basically u have to try out different components to to able to derive to your answer

[upbeat musk]

Why is X thick and what is the purpose of the graphing line?

[upbeat musk]

I see

[full turtle]

The X means times so like 2x times 1

[upbeat musk]

https://media.discordapp.net/attachments/1015759484708208792/1045835008012714017/a_3a6633f55a6525e045c618e50b97782a12.gif

[upbeat musk]

Reason?

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[lament stirrup]

Can I have some help with this

[lament stirrup]

<@&286206848099549185>

[thorny flame]

You must be a bot manager to use this command!

Jun 4, 2024, 5:00 AM

[hazy pumice]

@lament stirrup what have you tried

!status

[topaz sinew]

What step are you on?
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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

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[livid elbow]

number 2, basically solving it on polar coordinates

i got 1/12 but definitely confused because the integral of csc^4 and also if cot (0) and csc (0) should be written as undefined or no

*not

if solved using cartesius also 1/12 but more simplier than this💀

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[livid elbow]

not yet

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[livid bone]

Can I ask a question about a cryptography problem? I think it has something to do with pascal's triangle

[livid bone]

I have 12 strings; the first 4 and the last one are colored gray, while the other ones are red. The gray strings are encrypted, but they're really similar to pascal's triangle structure and content. I have no clues for the red ones. I need to decrypt the cipher of those strings. If you want to, I can send the problem

[odd pagoda]

how should anyone know if they can help you without you sending the problem first

[livid bone]

Yeah u're right 😅

I came up with this

01 = 1 ... 09 = 9
0A = 10 ... 0Z = 35

01 = 1
0B = 11
37 = 55
A5 = 165
4A = 330
CE = 462

And I think the red part may be the password and the gray part the pascal's triangle, so I think that I need to decode the cipher using the gray part and assuming it is pascal's triangle and then decode the red part using the same cipher

[odd pagoda]

well the last row is obviously hexadecimal

so you probably need to translate the red rows from hexadecimal and maybe then a pattern emerges

[livid bone]

I have already tried almost every compatible cipher

No intereseting results

The last row isn't exadecimal I think though, because the decoded text is "
 7 � J � � J � 7 
"

And it's the same pattern as the pascal's triangle

[odd pagoda]

it quite literally is the 11th row of pascals triangle if you translate it from hexadecimal to decimal

[livid bone]

But what about the different values like CE?

[odd pagoda]

462 is 1CE in hex

fair enough I didnt check all of them

[livid bone]

And "14A" is 330, but there's only "4A" in the text

So maybe it has something to do with adding stuff in front of the strings

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@livid bone Has your question been resolved?

[livid bone]

I still don't know how to decrypt the red part

<@&286206848099549185>

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@livid bone Has your question been resolved?

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@livid bone Has your question been resolved?

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@livid bone Has your question been resolved?

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[topaz sinew]

@violet light Has your question been resolved?

[violet light]

<@&286206848099549185>

[sacred rune]

Hint: According to [a・b = |a| |b| cos (θ) ]

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[rare citrus]

can someone please help me with this

[ember lodge]

Show your steps

[rare citrus]

lemme grab my phone

[ember lodge]

k

[rare citrus]

I don’t really know how to use the inequality we’re given

[ember lodge]

umm

cannot help, I'm still doing... sorry

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@rare citrus Has your question been resolved?

[sacred rune]

Take the logarithm and see.

[rare citrus]

nah this questions full cooked

definitely not getting this correct in an exam

here's the solution for anyone curious

.close

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[ember skiff]

How does one get c?

I can't think of any way to do it

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[rough vapor]

,rotate

[rough vapor]

not sure what I did wrong

I couldn't factor b^3=256

[acoustic pecan]

5/4=ab^(-1) 320=ab^3
i assume you did the second divided by the first

it should be b^4

you wrote ab^2=320 erroneously

[rough vapor]

so I am getting exponent from x2?

[acoustic pecan]

its from the point (3,320)

im not sure what you mean

[rough vapor]

yeah that's what I mean

x2

[acoustic pecan]

you cant use terms you havent defined to me

because i dont know what youre referring to when you do so

[rough vapor]

idk typically when you have two points isn't the default x1,y1 and x2,y2

[acoustic pecan]

but idk what youre saying though

the ^4 exponent isnt from a single point

its from using the two equations gained from them

[acoustic pecan]

like here

i dont really get whats going on here, but i know youve written both equations wrong

the first should be -1, not 1

and the second should be 3, not 2

the stuff on the right though loses me

[rough vapor]

yeah what I did wrong was not use the points for b exponenets

[acoustic pecan]

eh? where were you getting them?

[rough vapor]

the stuff on right is distrubting b to equal right

I just thought 1 and 2

like in order

[acoustic pecan]

the a=5/4 b only really makes any sense if you previously said ab^(-1)=5/4

but you dont need to do that

if a=b and c=d then a/c=b/d you can just apply that from the get go to eliminate a

[rough vapor]

Okay I see

I think I know how to do it know

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[grim forge]

Forgot how to solve this

[grim forge]

I know I got this wrong

But I think it’s dividing

Not times

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@grim forge Has your question been resolved?

[grim forge]

<@&286206848099549185>p

[sonic escarp]

if 1500 is 20% what is 100% then?

[grim forge]

1500x80

[sonic escarp]

no

[grim forge]

Divided

[neon iron]

7500

[neon iron]

It’s 7500

[grim forge]

How

[lean brook]

Always make graphs for yourself, it's easier to understand.

If 1500 is 20%, then 100% is x, and you want to know the value of x, that's what you need. Memorize it and you will never have problems with solving these type of questions

[grim forge]

It’s just 20

Not 20%

[lean brook]

Which exercise or which question is it?

[sonic escarp]

1500 is 20%

[grim forge]

Ah

So then that means I can do 7500/.03

For 30

[sonic escarp]

7500 times 0.3 for 30%

[grim forge]

Thank u I got it

[topaz sinew]

@grim forge Has your question been resolved?

[sonic escarp]

you got it but the question is not resolved?

[grim forge]

Yes,sorry,it was my final assignment online so I fell asleep

[sonic escarp]

if its unsolved then ask, if its solved then type .close

[sonic escarp]

.close

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[rough vapor]

I guess problem one is an evolution of problem 2 ?

idk how to solve it

.close

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Please don't occupy multiple help channels.

[clever citrus]

oh bra

my bad

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[clever citrus]

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[spare grail]

can someone help me

[topaz sinew]

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/

[spare grail]

im really shit at anything math related, i need help taking away big and small numbers. like the fastest way

[acoustic pecan]

you mean subtraction?

[spare grail]

yes

[acoustic pecan]

any example

[spare grail]

if someone asked me what 40 - 23 i wouldnt have any idea ill have to get a calculator

[acoustic pecan]

you can split it into (40-20)-3 if thats useful

[spare grail]

wdym

[acoustic pecan]

you can subtract 20, then 3

40 -> 20 -> 17

there are more hardy methods though

[cinder sequoia]

there's a procedure similar to addition where you put the numbers on top of each other and go column by column from right to left, but there's an additional concept called "borrowing" when the top number is less than the bottom number

if you look up "borrowing and subtraction" you'll probably get a nice video that demonstrates this

[acoustic pecan]

https://youtu.be/r3qKojj4g4g

this may be of use to you

[spare grail]

ill give it a watch

for example if someone asked me on the spot whats 14 - 9 for example ill have no idea

[acoustic pecan]

hm

im not sure how to help with that besides practicing truthfully

over time it becomes almost automatic

[spare grail]

even in ur head not on paper?

[acoustic pecan]

unless its a crazy number, yeah

[spare grail]

how do u study ? i never studied when i went school and every time ive tried to study i get really bored and end up not doing it

likle my mind just wonders off

[cinder sequoia]

for addition/subtraction, it's less about studying and more about memorizing some stuff at least in the lower 2 digit numbers

flashcards and online worksheets would be useful

[spare grail]

i mean generally tho

whats flash cards

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[neon iron]

Bingo is a game in which each player has a square card with k
lines (horizontal) and k columns (vertical), where k^2 distinct numbers taken from the
set {1, 2, 3, . . . , N}. Numbers are drawn one by one and players must mark on the
card the drawn numbers. We have two game types, A and B.
Mode A: Here, whoever completes the entire card wins the game.
(a) Calculate the total number of bingo cards.
(b) Two cards are said to be equivalent if whenever one of them is a winner, the other is also a winner. Once a card is fixed, calculate the number of cards equivalent to it.

[neon iron]

i found a) n!/(n-k²)!
b)k²!

its correct?

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@neon iron Has your question been resolved?

[opal vault]

yeah, both are correct

[neon iron]

okok thanks

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[pastel oracle]

A looks right to me

for B, given what they wrote it's right. I wonder if it's a typo and they wanted h'(4)

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[gleaming solstice]

So i was watching this video that helps with my hw but the guy goes from step 1. to step 2. but I dont understand how or why the pi changed to pi/2 and why the x changed to 2x. Can someone help explain this to me?

[pastel oracle]

because 2 * 1/2 = 1, so the equation doesn't change

[gleaming solstice]

so

does he multiply it by 1/2?

because wouldnt that make the x = x/2

[pastel oracle]

no

in step 1, there is 1 x

in step 2, he changes it to 1/2 and 2, because their product is still equal to 1

[gleaming solstice]

wait

so

you can multiply the x by two and the pi by 1/2 to keep it all the same?

[pastel oracle]

yes

[gleaming solstice]

okay that clears it up

thank you

.close

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[sacred rune]

for the last time I post the qs

[sacred rune]

The Chinese is talking about determining whether there is convergence, and if so, determining whether there is absolute convergence or conditional convergence.

How can I solve (1)?

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[charred rampart]

ratio test?

[sacred rune]

math homework...

[charred rampart]

no

ratio test

like rhe math tool

[sacred rune]

the difficulty is determining whether there is absolute convergence or conditional convergence?

It's certainly convergent.

it seems that it's conditional convergence

[sacred rune]

the L = 1

<@&286206848099549185>

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[sacred rune]

.reopen

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✅

[sacred rune]

<@&286206848099549185>

[fallow igloo]

You still haven’t solved it?

[sacred rune]

Yes

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@sacred rune Has your question been resolved?

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@sacred rune Has your question been resolved?

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[turbid holly]

what is the question?

[neon iron]

I need to find xy/z

Knowing that it is equal to 2y,(6)