help-0

[lone heart]

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[fickle musk]

thnx

[lone heart]

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[karmic rapids]

,, x^2-y^2 = (x+y)(x-y)

[ocean seal]

illuminator3 (#eric4honorable)

[dense sierra]

Oh yes I know that but how do I would I use it?

[tall topaz]

you know what x+y is

Substitute that into the first equation

[dense sierra]

Oh

And do I square root 45 to get x-y?

[tall topaz]

Huh?

$(x+y)(x-y) =45$

[ocean seal]

Pure

[tall topaz]

Then you know x+y is 9

So $9(x-y) = 45$

[ocean seal]

Pure

[tall topaz]

So what’s x-y?

[dense sierra]

5?

[tall topaz]

Yes

Now you have a simultaneous equation to solve

[dense sierra]

W8 its a simultaneous equation???

Wft

My teacher is werid

Anyways ty

.close

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[alpine sable]

In how many ways can 45 be written as a difference of 2 perfect squares?

Also does the answer change if the question is phrased like " find all the integral values for x and y where x^2 - y^2 = 45" ?? Thank you

[tall topaz]

Express x^2 - y^2 as a difference of two squares

Then Prime factorise 45

Then see the combinations of 2 numbers that multiply to 45

[alpine sable]

What is the final answer btw?

[tall topaz]

Idk

,w solve x^2 -y^2 = 45 where x and y are integers

[ocean seal]

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[alpine sable]

Does that count as 6 ways? Or a lot more cuz its + or - in some cases?

12 ways i guess

[tall topaz]

Well it says difference of perfect squares

[alpine sable]

Oh wait thats true.

So 6 ways i guess. I got it.

Thank you bro

[tall topaz]

Np

Btw you should try solving it yourself

[alpine sable]

Yeah i actually got 6 ways. I did it in another way tho.

X^2- y^2 = (x+y) (x-y). 45 has 6 factors. Substituted those factors in the equation and did trial and error.

I lack concepts of this. This is definitely not the way to solve it lol

[lone heart]

@alpine sable Has your question been resolved?

[noble gorge]

If I have 650 tangerines, how many can I give to 20 people equally such that I have left a minimum of 5 tangerines available to be eaten per day, for 10 weeks?

[lone heart]

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[tall topaz]

Just plug in 0 and solve for b

[alpine sable]

after I derive

?

[plain flame]

after you derive yes

[tall topaz]

Oh yeah mb

Didn’t see that but yeah still the same

[alpine sable]

ok 1 sec

[tall topaz]

Also derive is not the correct verb

It annoys me every time

[plain flame]

differentiate 🙂

[abstract fractal]

Differentiate is too long

Too many letters

[alpine sable]

yeah

[plain flame]

just ddx it bro

[lone heart]

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[deep creek]

Help

[deep creek]

How did he simplify this?

https://www.youtube.com/watch?v=B69XKPdwDMI&list=PLrDd_kMiAuNmSb-CKWQqq9oBFN_KNMTaI&index=7&ab_channel=MakkuZjAileron

Somebody help, please

[wary stream]

Well, one he created that example so he already knew how it was going to get simplified
Two, you can use k maps to simplify boolean expressions

[deep creek]

K maps?

What?

[wary stream]

Yes k maps

Full name is Karnaugh map

[deep creek]

I don't know what that is

[wary stream]

That's a method to simplify expressions

[deep creek]

My lecturer told me to simplify it using boolean identities

It doesn't make any sense

[wary stream]

Just a ton of manipulation

And using identities

[delicate stag]

hi

i need help

[deep creek]

I tried and it doesn't make sense

[delicate stag]

im trying to do this guys pls help

[wary stream]

#❓how-to-get-help

[delicate stag]

Idk

[wary stream]

Read it

[delicate stag]

@wary stream I haven't been moved yet

[wary stream]

?

[ebon finch]

$\bar{x}\cdot\bar{y}\cdot\bar{z} + \bar{x}\cdot y\cdot\bar{z} + x\cdot\bar{y}\cdot\bar{z}\
\bar{x}\cdot\bar{z}\cdot\left(\bar{y} + y\right) + x\cdot\bar{y}\cdot\bar{z}\
\bar{x}\cdot\bar{z}\cdot\left(1\right) + x\cdot\bar{y}\cdot\bar{z}\
\bar{x}\cdot\bar{z} + x\cdot\bar{y}\cdot\bar{z}$

[deep creek]

Uh

[ocean seal]

VardhanR

[wary stream]

Read #❓how-to-get-help because this channel is occupied meaning you don't ask in an occupied channel

[deep creek]

I don't get that

[ebon finch]

i suggest writing it like this (with bars and dots and pluses) so that it is easier to observe things that can be factored out (although that might just be me and u might be comfortable with NOT, AND and OR)

[wary stream]

First step to second step, is what I like to call, reverse distribution

Factor out the common terms from the first two terms

[deep creek]

So factor out NOT

[ebon finch]

factor out NOT(x) AND NOT(z)

[deep creek]

Okay

Is that de Morgan rule?

Which rule to factor that out?

[wary stream]

Like I said, I like to call it reverse distribution

[deep creek]

Okay

So

Distributivity

I am confused

I need special help lol

[ebon finch]

it is like factoring out variables

[deep creek]

:/

[ebon finch]

$axy + bxy = xy(a+b)$

[ocean seal]

VardhanR

[deep creek]

That's easy to understand

[ebon finch]

here, there is NOT(x) and NOT(z) instead of x and y

[deep creek]

Just gonna put this here

https://media.discordapp.net/attachments/490557019623915520/1025478438582222848/unknown.png

[deep creek]

X and y where?

The green box

[ebon finch]

x and y here needs to be replaced with NOT(x) and NOT(y)

[deep creek]

Okay

[deep creek]

What about this

Need help

[ebon finch]

this is how to get from step 1 to 2

and then de Morgan's maybe?

[deep creek]

I just don't understand the way he did it

😦

[lone heart]

@deep creek Has your question been resolved?

[deep creek]

Help

Ahhhhh

Someone

[lone heart]

@deep creek Has your question been resolved?

[lone heart]

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[vernal cedar]

hi how do i do this

[autumn pasture]

cosine rule

[vernal cedar]

ok but like

[vernal cedar]

what if its not a right angle triangel

[autumn pasture]

it’s fine tho

it can be applied to non-right

[vernal cedar]

rlly?

[autumn pasture]

yea

if we were dealing with right angles tri

we wouldn’t rly be using this

[vernal cedar]

how do i do it then

[autumn pasture]

cosine rule

[vernal cedar]

is it the same if its not a right triangle

[weary wyvern]

Cosine rule for right triangles is just pythagoreas

[autumn pasture]

yea

[autumn pasture]

cosine/sine is for non-rights I think

[vernal cedar]

so i would just do cos^-1(4sqrt2/7) ?

[autumn pasture]

uhhh

how’d you get that

did you use the formula

[vernal cedar]

i learned trig like yesterday and im in grade 10 so like

im not too sure on this stuff

[autumn pasture]

or are you using adjacent/hypotenuse

[vernal cedar]

yeah

[autumn pasture]

because we can’t use this unless we know it’s right angle

[vernal cedar]

ohh

ok then i dont know how to do it

[autumn pasture]

for non-right angle triangles

[vernal cedar]

thas what i learned with cos

[autumn pasture]

we use sin/cosine rule

cosine rule has a formula

$a^{2} = b^{2} + c^{2} -2bc\cdot{cosA}$

[ocean seal]

duckiescute!

[autumn pasture]

https://youtu.be/9CGY0s-uCUE

here you go!

[vernal cedar]

alr thanks ill try figuring it out

[autumn pasture]

no prob!

[lone heart]

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[orchid wraith]

Consider three circumferences C1, C2 and C3, all centered at the same point O, whose respective areas are 4π, 3π and 2π. From a point A on Ci a tangent line is
drawn to C2, where B is the point of tangency, and a tangent line is drawn to C3, where C is the point of tangency. If B and C are on the same side of OA, determine the value of angle BAC.

[orchid wraith]

C1*

[lone heart]

@orchid wraith Has your question been resolved?

[lone heart]

@orchid wraith Has your question been resolved?

[lone heart]

@orchid wraith Has your question been resolved?

[orchid wraith]

<@&286206848099549185>

[orchid wraith]

.closee

.close

[lone heart]

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[indigo gust]

hey could i get some help?

[indigo gust]

its chemistry, but it involves algebra and manipulating equations

Im trying to get equations 1.7 and 1.8 using equations 1.5 and 1.6

Ive gotten 1.7, stuck on 1.8

(ignore 1.13) this was my final answer

for 1.8 I'm having difficulty figuring out why we have Pc

and a subtraction

Pa and Pc are values for Pi

as though its p1 p2

<@&286206848099549185>

[lone heart]

@indigo gust Has your question been resolved?

[indigo gust]

<@&286206848099549185> sorry for double ping, has been another 20 minutes

[lone heart]

@indigo gust Has your question been resolved?

[lone heart]

@indigo gust Has your question been resolved?

[lone heart]

@indigo gust Has your question been resolved?

[lone heart]

@indigo gust Has your question been resolved?

[vague niche]

[lone heart]

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[violet idol]

Hi

[violet idol]

Can the result of a logarithm be negative?

$log_2x = negative$

[ocean seal]

Raid

[alpine sable]

yes

[gray isle]

yes

[alpine sable]

x = 1/2

[gray isle]

,w ln(1/e)

[ocean seal]

Results provided by WolframAlpha

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Requested by ramonov#0921

[violet idol]

damn

ty guys ❤️

didn't think about an example like that

[alpine sable]

just think about the exponents

[violet idol]

because I was watching at the definition of a natural domain of a function

[alpine sable]

or the graph

[violet idol]

So if I have f(x) = log_2x

[alpine sable]

yes, x can't be negative

[violet idol]

And I have to find the natural domain

its domain would be R>0 ?

because the logarithm arguement can only be > 0

[alpine sable]

wait log (2x) base 2 ?

[violet idol]

$f(x) = log_2x$

[ocean seal]

Raid

[alpine sable]

all positive real numbers excluding 0

[violet idol]

so the codomain

is the entire R

because the codomain would be the result of the logarithm

[alpine sable]

no that's range

[violet idol]

Which can be negative or positive, so R

what do you mean?

[alpine sable]

you are talking about range ?

[violet idol]

I am talking about the natural domain

i don't know if the translation is correct

[alpine sable]

i see

[violet idol]

If I have this function, then how can I find the natural domain?

[alpine sable]

if you are talking about range

then all real numbers

[violet idol]

all real numbers

for the codomain

[alpine sable]

yep

[violet idol]

but the domain is R > 0

If I hav

$f(x) = 2^x$

[ocean seal]

Raid

[violet idol]

then its domain and codomain are both R

right?

$R \rightarrow R$

[ocean seal]

Raid

[alpine sable]

domain can be r yea

but

nvm

[violet idol]

ahahaha

If I have

[alpine sable]

yea

[violet idol]

$f(x) = x + 7$

[ocean seal]

Raid

[alpine sable]

but range won't be R

[sonic drum]

hmm codomain sus

[violet idol]

the domain would be R and the codomain R + 7 ?

[violet idol]

what do you mean?

[sonic drum]

yes

[violet idol]

which range? XD

[sonic drum]

this

ig.

[violet idol]

do you mean range = domain?

[violet idol]

why?

[sonic drum]

[lunar tide]

range of this is 0 to infinity

[violet idol]

guys do you mean range as domain?

[lunar tide]

no

[violet idol]

then whats range

[lunar tide]

all possible values that the function can give

[violet idol]

isn't the domain?

[lunar tide]

the domain is all values if x for which a function is defined

[violet idol]

so range is all result values?

[lunar tide]

yes

[violet idol]

is the codomain basically

I mean the image

[alpine sable]

look domain is all possible of value that you can put in function which will give you a definite value

[violet idol]

yep

So If I have f(x) = x +7

Domain is R

And range (codomain) is R + 7 ?

[lunar tide]

yes

no

[violet idol]

why?

[lunar tide]

range is also R

R + 7 is meaningless

R is a set

[violet idol]

y right I mean y>=7

[lunar tide]

no

[violet idol]

y as an element of the codomain

[lunar tide]

put x = -7

you get 0

[violet idol]

Oh fuck

I wrote x

is x^2

XD

[lunar tide]

what

[violet idol]

f(x) = x^2 + 7

XD

[alpine sable]

and codomain is like a loose range if you get what i mean xd

[lunar tide]

now its 7 to infinity

[violet idol]

domain R codomain y>=7 ?

[alpine sable]

like it's lazy way to call it a range but actually contains value which may not come from the function

[lunar tide]

yea

[alpine sable]

like you defined a function 2^x

it's range will nevr have a negative number or 0

[violet idol]

got it

[alpine sable]

but you can say codomain on R

[violet idol]

but the domain could include 0

but the codomain couldn't

or at least the range

[lunar tide]

yea cuz you cant raise 2 to some number to make it 0

[violet idol]

yep

ty guys for the help ❤️

.close

[lone heart]

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[alpine sable]

honestly i just forget about codomains XD

since i don't have to deal with complex functions or anything

[lone heart]

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[chrome vortex]

for 3c.

wouldnt it be f(x+4)?

which is just 3x+1+4 = 3x+5

[lavish yoke]

yes

[chrome vortex]

ok thought i was hallucinating or something

[charred heron]

yes

[dapper veldt]

Ye

[chrome vortex]

thank you

.close

[lone heart]

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[alpine sable]

the length is 2 units

could be cm, meter anything but doesn't matter

it's just a unit

[fallow zealot]

Then how can I determine the coordinates of B or C

[alpine sable]

ab = co = 2 units

[vocal lark]

why is 1/0 infinity?

[alpine sable]

so coordinate of c is (-2,0)

[lethal pelican]

its not i think

its undefined

[vocal lark]

yeah

i was studying trignometric ratio

it was showing tan90 is 1/0 which is infinity

[viscid pawn]

Impossible basically

[dense temple]

1/0 is not in the real number set

[fallow zealot]

Oh yeah

[viscid pawn]

tan(pi/2) isn't even defined on the tan function

[fallow zealot]

Now I got it

Yo you guys don’t check here fam

Piss off this my channel rn

[alpine sable]

lmao

[daring patrol]

This is other people channel guys

[vocal lark]

ok

[viscid pawn]

it's the limit at ]-π/2 ; π/2[

[viscid pawn]

aight sorry

[viscid pawn]

please switch channels

[lone heart]

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[turbid gust]

@short vessel

[turbid gust]

@short vessel

bot

@short vessel

HELP

Bot

[tall topaz]

What’s going on here…

[turbid gust]

@short vessel asked me to open this

[tall topaz]

Okay…

[autumn pasture]

uhh

[lone heart]

@turbid gust Has your question been resolved?

[lone heart]

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[woeful tartan]

(4x^(3) * y + 28x^(2)y^(2) - 36 y^(2))/12x^(4)*y^(4)

[woeful tartan]

$(4x^3 * y + 28x^2 * y^2 - 36 y^2)/12x^4 * y^4$

[ocean seal]

sombie

[woeful tartan]

how would i factorise this to the lowest factor?

i tried

$(2 * 2 * x * x * x + 2 * 2 * 7 * x * x * y * y - 2 * 2 * 2 * 2 * y * y * y)/ 2 * 2 * 3 * x * x * x * x * y * y * y * y$

[ocean seal]

sombie

[woeful tartan]

i tried this

[fierce prairie]

you don't need to expand it like that

find the greatest common factor in the numerator

[alpine sable]

try taking 4y^2 common

[fierce prairie]

4y, not 4y^2

[alpine sable]

yep

[woeful tartan]

as in?

[fierce prairie]

you can divide each term by 4y

[alpine sable]

express the numerator as a product of 4y

[woeful tartan]

so

$4y(4x^(3) * y + 28x^(2)y^(2) - 36 y^(2))/4y(12x^(4)*y^(4))$

[ocean seal]

sombie

[alpine sable]

yea

[woeful tartan]

$4y(4x^3 * y + 28x^2 * y^2 - 36 y^2)/4y(12x^4 * y^4)$

[ocean seal]

sombie

[woeful tartan]

then i divide it all with each other?

[fierce prairie]

well you need to divide each term by 4y to factor it out

for example: $4x^3y = 4y(x^3)$

[ocean seal]

Kihei

[fierce prairie]

but do that for all the terms

[woeful tartan]

what if its like

y ^ 2

[fierce prairie]

well the whole term is

$28x^2y^2$

[ocean seal]

Kihei

[woeful tartan]

yes

[fierce prairie]

so divided by 4y?

[woeful tartan]

7x^2y

$7x^2y$

[fierce prairie]

yup

[ocean seal]

sombie

[woeful tartan]

hmmm

[fierce prairie]

so you can factor out 4y from all of the terms in the numerator

[woeful tartan]

so i divide each of them with it

[fierce prairie]

$\frac{4x^3y + 28x^2y^2 - 36y^2}{12x^4y^4}$

[ocean seal]

Kihei

[fierce prairie]

yeah exactly

[woeful tartan]

4x^3 * y = x^3

$4x^3 * y = x^3$

[ocean seal]

sombie

[woeful tartan]

yes?

[fierce prairie]

mathematically wrong but yes I get your point lol

dividing 4y

[woeful tartan]

yes i meant that

okay so

$x ^ 3 + 7 * x ^2 + y - 9y$

[ocean seal]

sombie

[woeful tartan]

divided by

$3 * x ^ 4 * y ^ 3$

[ocean seal]

sombie

[woeful tartan]

right

now i divid x^3 with x^4?

[fierce prairie]

well you can't so that's your simplest form

$\frac{x^3 + 7x^2y - 9y}{3x ^ 4y ^ 3}$

[woeful tartan]

3 + x * x * x * x * y * y * y

[ocean seal]

Kihei

[woeful tartan]

i cant proceed any further

[fierce prairie]

yeah but you can't simplify from there because there isn't a greatest common factor

mhm

[woeful tartan]

okay

thanks a lot kihei

.close

[fierce prairie]

np

[lone heart]

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[dense temple]

Hello I have a problem, I have to tell wether that function is derivable and continuous in the entire real numbers set. The problem I have is that I know by replacing that it's possible to have a and b with different values than what i have defined but still i am not sure, but if the answer is still a yes i dont know how to prove it

sorry if my english is not good in the images

i don't know if i have done something wrog maybe

[strong rain]

well

a cannot be 0

it must be -1

[dense temple]

why?

[strong rain]

let's substitute on the last branch

x = 2

then we will have

$$ \frac{-2}{2\sqrt{2}} + \frac{3}{\sqrt{2}}$$

[ocean seal]

Eraldo Coil

[strong rain]

but this can be simplified into

[ocean seal]

Eraldo Coil

[dense temple]

but wait

isn't it possible to analize the first two branches as if the third one didn't exist and then when you get results for the first two you analize them with the 3rd?

[strong rain]

sure

and thats what I did

first you solve for b

and you find b = 4

[dense temple]

yes

[strong rain]

then you use the third branch to find a

[dense temple]

but why the third

there is no a in the therd branch

a and b are both in second

[strong rain]

yes, but there's no a in the first either

[dense temple]

i know

[strong rain]

you have 3 variables

[dense temple]

yes

[strong rain]

you must have 3 equations to find correlate the 3 variables

you use the first branch to find one of the variables

then you use the other branch to find the other variable

[dense temple]

i don't understand what you mean

[strong rain]

for the function to be continuous,

the values of each branch must be the same

when the function jumps

in this case

the function jumps at x = 0

and x = 2

at x = 0

[dense temple]

yeah

[strong rain]

you have the first and second branch

and at x = 2

you have the second and third branch

[dense temple]

mhm

[strong rain]

so you have to equal the first with the second branch

[dense temple]

yes

that's what i did

[strong rain]

and then the second branch with the third branch

when you equal the first branch with the second

you get that b must be equal to 4

[dense temple]

yeah but before equaling second and first branches i want to find wether first and second are derivable or not

[dense temple]

yes

and to get a i must equal with third?

is that what you meant?

but what i want to say is

[strong rain]

aaaaa

[dense temple]

what if b has another value?

[strong rain]

I understand the problem

alright

[dense temple]

mmm

so

is a=0 then?

[strong rain]

you're right but wrong

[dense temple]

oh

[strong rain]

for the derivative to exist

a must be 0

sure that's right

BUT

to be continuous

a must be -1

so since

[dense temple]

to be continuous with the third branch you mean?

[strong rain]

yes

[dense temple]

ah but i havnt arrived to that part yet

my problem is a different thing

[strong rain]

oh

sorry then I must have missunderstood

[dense temple]

ahah no problem

so my problem is that

i got a=0 and b=4 so that the content inside the square root in the second branch isnt negative right?

but

the problem comes when i know by replacing a and b with different values that there are more possibilities for that

but i dont know how to prove it

for example, when you said that a=-1

that also can be possible as long as b is equal or bigger than 1

well not always now that i think of it

but

yeah

there are more posibilities and idk how to prove them

[strong rain]

sorry for what ?

for the square root to not be negative ?

[dense temple]

i mean

[strong rain]

the reason why a must be 0

is because of the first branch

[dense temple]

mmm

yes but

[strong rain]

when x = 0

the derivative on the first branch is 0

[dense temple]

ooohhh i thikn i understood it

[strong rain]

and on the second branch must also be 0

[dense temple]

ok so i am going to say one thing and please tell me if its corect or not

[strong rain]

sure

[dense temple]

so first of all we need the second branch to be in set R and for that the content inside of its squareroot cant be negative because square root of a negative number is not in R. So for that there are many possibilities for a and b but if it's anything other than a=0 and b=4 first and second branches wont be continuous and/or derivable?

[strong rain]

yes

[dense temple]

GREAT

lfkjaslkf

im so happy

i have been the entire afternoon with thi

s

[strong rain]

but don't forget the third branch

[dense temple]

yeah i'm going to do it now

now that i have the first and seocond

thank you so much, really

[strong rain]

no problem

[twin fiber]

hi

[strong rain]

you will find that a must be -1, for the function to be continuous, but as you saw with the derivative, a must also be 0, for the function to be continuous,

[twin fiber]

i have a question about scientific notation

[dense temple]

please do your question in an available channel

[strong rain]

$$ a = 0 $$
and
$$ a = -1 $$

[ocean seal]

Eraldo Coil

[twin fiber]

ok

[dense temple]

so it cant be continuous in both sides at the same time?

[strong rain]

no, or the function wont have a derivative on the first part

[dense temple]

i mean if 1&2 are 2&3 cant be?

[dense temple]

ohh i understand

ok thank you very much ill take that into account

great

[strong rain]

no problem!

if you have any more questions just ping

[dense temple]

oh ok thankyou!

[lone heart]

@dense temple Has your question been resolved?

[dense temple]

(actually yes, and am grateful for it but i want to keep the thread open in case i have more questions)

[lone heart]

@dense temple Has your question been resolved?

[dense temple]

@strong rain

a doesnt give me -1

it gives me 1

and b gives me 0

[strong rain]

mind showing ?

why did you change b ?

keeping b = 4

for the function to be continous

a must be -1

after solving the first and second branchs

we have established that , b = 4, and a = 0

now looking at the second and third branchs, keeping b = 4 and a = 0

you should come at an impossible solution

in this case

KEEPING b = 4 and a = 0

[ocean seal]

Eraldo Coil

[strong rain]

substituting x = 2 , a = 0 and b = 4

you have

[ocean seal]

Eraldo Coil

Eraldo Coil

Eraldo Coil

[strong rain]

which is impossible

[dense temple]

sorry i was abscent

one second

i will show you what i have deon

maybe there's something wrong

what's wrong here?

ok i've just seen an erro

r

hold on i correct it and i resend images

ok i corrected but b is still 0 and a is still 1

@strong rain ?

[strong rain]

what you did isn't wrong

but

you're complicating this here

after you find a and b

[dense temple]

it's what they said we had to do in class

[strong rain]

the thing is,

you're calculating a and b again

that's why you get different values

it's normal

you're getting the conditions in which the second and third branches are continuous and have a derivative

but these conditions are different

from the ones you already found

[dense temple]

yeah

[strong rain]

so what you can also do

is keep the first conditions you found, b = 4, and a = 0

[dense temple]

but you know, there is one problem with what you have typed above

the problem is that they requier us to do this without replacing x by a number

[strong rain]

wait they don't allow you to ?

[dense temple]

no

we have to do it without replacing x by a number

it's a rule

because also, we have to find the result for the entire R set not only a particular case

so idk what to do

@strong rain

[alpine sable]

Id just write no

[dense temple]

what?

[alpine sable]

Thats the question

[dense temple]

uh?

wdy

m

[alpine sable]

Tell if its continuous and diff in entire R

[dense temple]

no but

you have to jutify

[alpine sable]

The a cant be two values at a time

[dense temple]

and tell explicitely in which cases its continuous and/or derivable

[dense temple]

yes but you have to say when a equals this, then that happens when a equals this other thing then that other thing happens

[alpine sable]

can someone solve this problem?

[dense temple]

stuff like that

[dense temple]

post in another thread

[alpine sable]

Its continuous for a=-1

Never differentiable

[alpine sable]

this is a help channel

[dense temple]

yeah that's between 2nd and 3rd but betwen 1st and 2nd its a=0

[dense temple]

but i am using it take an avilable one

haven't you read the #rules and #❓how-to-get-help ?

[alpine sable]

Wdym? Checking continuity at x=0 gives us b=4

[dense temple]

hold on i am going to send you the full thing

[alpine sable]

Im talking about just continuity

[dense temple]

yeah but to explain what do i mean i have to show you the first part

[alpine sable]

Show

[alpine sable]

Dude

[dense temple]

yes?

[alpine sable]

Just check continuity first over R

[dense temple]

but

that's what im doing aswell

[alpine sable]

Ur 3rd image is checking the differentiability for which u get a=0

[dense temple]

yes

[alpine sable]

Which isnt wrong, but that doesnt mean the function isnt continuous for a=-1 and b=4

[dense temple]

yeah i know

[alpine sable]

So thats the first part of the answer

[dense temple]

yes yes i had that clear

but

the problem is

[alpine sable]

The second part should be never differentiable

[dense temple]

that i dontknow how you get a=-1

[alpine sable]

I checked continuity at x=2

[dense temple]

but how did you do itç?

[alpine sable]

Lhl and Rhl at x=2

[dense temple]

i dont know what Lhl and Rhl is

[alpine sable]

Left hand limit and right hand limit

[dense temple]

aah

ok

that's what i did to

[alpine sable]

But this i meant the second part of the question, the part asking about differentiability

[dense temple]

yeah yeah but i mean

checking the continuity at x=2 i didnt get a=-1

[alpine sable]

Show your work

[dense temple]

ignore first half

it begins in We

[alpine sable]

Use b=4

You already have that

[dense temple]

but what if with b=4 x=2 is not continuous?

[alpine sable]

Why wudnt it be

[dense temple]

idk

i am going to try

[alpine sable]

You got b=4 from continuity at x=0

Now use trying to check continuity at x=2

[dense temple]

ok i am going to try

do i ping you when i am done or not?

ok now yes

this time i got a=-1

[alpine sable]

Then for b=4 and a=-1 function continuous over R

Now check differentiability at x=0, and ull see u get a=0

[dense temple]

yes i did get a=0

at x=0 differentiability

[alpine sable]

But if u change a to 0, its no longer continuous

[dense temple]

yeah

that's true

it's not continues in the second part

but what about the first one?

[alpine sable]

That is not the question

[dense temple]

yah but

well

ok good

now i have done differentiability in second part

i got a=-1/2

so just, in the first part it is continuous if a=0 as well right?

[alpine sable]

Pls use intervals

[dense temple]

in what context

each branch has its interval

but that's differentiability between two branches

how would i use intervals to say that i got a=-1/2 when i checked for differentiability

@alpine sable ?

@strong rain ?

[lone heart]

@dense temple Has your question been resolved?

[lone heart]

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[glass tide]

How did they find this probability

[glass tide]

is 0.1 (that is, 10 percent). If there are 35 users, the probability that there are 11 or
more simultaneously active users is approximately 0.0004.```

[merry depot]

binomial distribution

[glass tide]

so x = 11, p = 0.1, q = 0.9, n = 35 ?

[merry depot]

that would give you P_11, yeah.

they want 'at least 11' so you'd add up P_11 + P_12 + P_13 + ,,, + P_35

[glass tide]

so why is my calc saying 0.035 and not 0.0004 ?

oh

gotcha

[merry depot]

.035 is also way to big for just x=11 case. make sure you're putting everything in correctly.

[glass tide]

I am using a website. I think the first one was just bad I guess

this one seems better

[merry depot]

yep, that should work.

[glass tide]

thanks for the help @merry depot

.close

[lone heart]

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[lone heart]

Please don't occupy multiple help channels.

[late basalt]

im stuck pwes help

[wanton pebble]

can u see a pattern

it is 1/n^2/3 + (n^2 +n)^1/3 +(n+1)^2/3

[ivory pivot]

it's very hard

[plain flame]

brackets T_T

[plain flame]

lol prove that then

[ivory pivot]

prove what =

[plain flame]

that its impossible

[lone heart]

@late basalt Has your question been resolved?

[turbid portal]

plug it into a calculator

[ornate condor]

the

person said hard

[plain flame]

(edited)

[ivory pivot]

i said hard

[plain flame]

no im quite sure you said impossible

[late basalt]

lol

[plain flame]

why else would it be edited:)

besides i wouldnt make such a nerd comment if you just very hard lol

[ivory pivot]

because i m not very good at english and maybe i wrote hardy

[ornate condor]

ye

dont bully ppl cuz of english

not good

🥣

[ivory pivot]

😭

[plain flame]

never meant to be dick though

perhaps tone is lost in text ahh well

[late basalt]

are u like a pro bowl with spooner

[ornate condor]

no

im

meng po

[late basalt]

with two bowls and spoons

[ornate condor]

yesh

[late basalt]

maybe if i use difference of squares

[ivory pivot]

there are three terms

[late basalt]

yea but letting the last two be one

[ornate condor]

$\sum_{n=1}^4$

$\sum_{n=1}^4 \frac1{\sqrt[3]{n^2} + \sqrt[3]{n^2 + n}+ \sqrt[3]{n^2 + 2n + 1}}$

like this ig?

no idea if this helps

[fallen verge]

Difference of cubes yall

[ornate condor]

how

🥣

[fallen verge]

Multiply by cbrt n+1 - cbrt n over itself

Diff of cubes simplifies everything over 1

Telescopes the rest

[ornate condor]

no idea but

well

op can try it

[lone heart]

@late basalt Has your question been resolved?

[lone heart]

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[alpine sable]

What is the process of turning complicated stuff into simple algebra equations like F=MA? I know linear algebra using least squares to create aesthetically pleasing graphs when curve fitting, but typically those curve-fitted equations are not simple algebra. I'm sure its also a question of how much error you want. Has anyone calculated how much error is in Newton's F=MA? It is an approximation after all.

[plain flame]

F = MA is derived using differential equations and there is no error at all

[naive valley]

maybe you are conflating two different things

measurement error on one hand

versus newton's law not being true outside of an inertial system on the other

[lone heart]

@alpine sable Has your question been resolved?

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[lone heart]

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[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

Unsure if that is helpful...

this is fucked up bruh

this is an entire AP FRQ

youre better off asking a classmate or some shit

no one here has the attention span to read this

i tried bro haha, everyones unsure

youre in college right

yeah man

what year

first

ok i was gonna say

if you were 2nd year or some shit youd prob be the most qualified and hsit

is anyone here good w financial math, willing to pay for a tutor

to guide me with how to tackle / approach this, not solve it

join a finance discord bruh

i tried finding one that was focused for students, but they're mostly just stock / market related

does your school have office hours and shit

like where older students help younger ones

na im a distant student, so no campus sadly, making it even more hard

back in 20-30

[alpine sable]

i think 2(e) may be in relation to a sinking fund?

actually no, doesnt sound right on second though

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[slate jolt]

wdym by general mathematics?

do you have a link to the content of the course?

[restive surge]

oh wait

hol on

its about algebra, trigonometry and world geometry, sequences, finance, networks and decision mathematics and statistics

[ornate condor]

lol

isnt alg calculus

[restive surge]

well based on my course, gen math and calculus are kind of related

[restive surge]

Trigonometry
Geometry
Algebra
Function
Arithmetic
Probability
something like that

[slate jolt]

well i think it depends on how deeply you'll study each of these

in what country are you?

[restive surge]

philippines

[slate jolt]

well that doesnt help me

maybe you should ask the professor giving the classes

send them an email

its really hard to help you unless you send us an official link to the content or something like this

or non official

but to see what you'll actually do in each of these courses

[restive surge]

https://www.courses.com.ph/senior-high-school-core-subject-general-mathematics/#:~:text=General Mathematics is one of,Key concepts of rational functions

[slate jolt]

this seems easier than pre calc

but also its applied maths

[restive surge]

ahhh i see

i guess ill advance study in pre calc

[slate jolt]

like all this "business" maths

is just for people who dont want to do maths later

but who want to do economic related stuff

[gusty gorge]

lol I feel like that kind of math is a bit of a waste of time

might as well not learn it and just rely on Excel

[slate jolt]

it is

[gusty gorge]

people who memorize math could just use a good calculator and get the same result

[restive surge]

oh okayy

last question

what would be the hardest topic in pre calc/basic calc

[slate jolt]

actually understanding all the concepts given to you

what is a limit a derivative

not just how to calculate them

[restive surge]

alright, thanks for answering me

i made up my mind that im starting to like calculus

calc seems to be interesting

[lone heart]

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[runic trench]

How do I prove 10+9=19 and not 21

[ornate condor]

MIKUUUUUU

🥣

come drink soup

was that a troll Q

lol

[runic trench]

Thanks for the soup but I have this burning qn

[ornate condor]

literally

count up from 10 9 times

and ull get 19

[runic trench]

Hmmmmmmmmmmmmmmmmmmm

Ok cool

.close

[lone heart]

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Closed by @runic trench

Use .reopen if this was a mistake.

[ornate condor]

LOL

HAHHAHA

🥣

we all need

some soup

🥣

[rustic coral]

write 10 and 9 as arithmetic series with common difference 0 and first term 1

we can rearrange to get an arithmetic series with 19 terms, all of which are 1

[ornate condor]

what even

lol

[rustic coral]

applying the formula for the sum of an arithmetic series, we get 19

🙂

[runic trench]

Wait how’s it still open

[ornate condor]

it

takes awhile

🥣

take some soup

[slate jolt]

[ornate condor]

im

rejected everyday

[lone heart]

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[worldly path]

How do I do part b?

[slate jolt]

f(x) = f(0) + integral from 0 to x of f'(x) dx

so for -4 you need to integrate g(x)

and for 4 you need ot integrate 5e^(-x/3)-3

[worldly path]

oh okay thank you

[long axle]

Hint: ||consider the actual shape of the graph above the -x||

[worldly path]

-sqrt(4-x^2) + 2?

[long axle]

What is that for

[worldly path]

g(x)?

am i overcomplicating this

I don’t understand how I’m supposed to find the integral of the curve from 0 to 4

Unless I’m just supposed to use a calculator

[slate jolt]

(y-2)²+(x+2)²=4

solve for y

to get the equation of g(x)

oh

[worldly path]

but do i ened to do that

[slate jolt]

yeah thats smarter

what you did is better

[worldly path]

oh okay

but for f(4)

is that calculator needed

[slate jolt]

compute the integral

by replacing what f'(x) is

between 0 and 4

[worldly path]

like do antiderivative stuff?

[slate jolt]

yeah

[worldly path]

oh i see ty

is it okay if i keep the thread open until i finisht his part so i can double check if i got it right

[slate jolt]

yeah

[worldly path]

ty

[long axle]

That’s ap practice right

[worldly path]

yea

[long axle]

(I think) all the answers to those r online, not saying u shd just go there and get the answers, but it’s a good resource to double check

[worldly path]

Maybe I'm really bad at googling but I couldn't find them online

Did I do it correctly?

[slate jolt]

you didnt integrate the -3 properly

the exponential term is good though

also you shouldnt write everything right away

make a step where you show your formula

[worldly path]

wait

[worldly path]

wdym

[worldly path]

which formula

[slate jolt]

last line

this is not clear