help-0

[barren portal]

^

[devout yew]

yes because they are the same?

[lament forge]

...so you think $\frac{4}{3} = \frac{3}{2}$?

[ocean seal]

bee [it/its]

[barren portal]

you have get your basics ready mate, get a pre algebra book and start doing

[gray isle]

fractions are simplified by cancelling a factor common in both the numerator and denominator

and NOT subtracting the same value from the numerator and denominator

[devout yew]

in short i can not cancel if their are part of addition or subtraction and i can only cancel when they multiply?

[gray isle]

only cancel common factors

as demonstrated above with

$\frac{ab}{ac}$ simplifies to $\frac bc$ as
$$\frac{ab}{ac} = \underbrace{\frac aa}_{1} \times \frac bc = \frac bc$$

[ocean seal]

ℝamonov

[gray isle]

$$\underbrace{\frac{1}{1+1}}{\frac 12} \redneq \underbrace{\frac{1 \red{-1}}{1+1\red{-1}}}{\frac 01 = 0}$$

[ocean seal]

ℝamonov

[devout yew]

ty, I belive I got it

.close

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[scenic wedge]

can i have some help this is really easy i know it but i just dont know how to do it

[solemn juniper]

Have you used L'Hopital's rule?

[thorn tapir]

L'Hopital Rule

Which means f(1+2x) + f(1+6x) also need to satisfy conditions

[cyan seal]

x -> 0, so f(1+2x) is f(1 + 2 • 0) = f(1) = 0

Same for f(1 + 6x)

If you use L'Hopital, you have to use the same reasoning again @scenic wedge

[thorn tapir]

Yes

[scenic wedge]

umm

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[hollow condor]

Our number system uses the base 10. these three sums are from another number system 13:15=31 10x10=100 6x3=24. what is the base for this number system?

[hollow condor]

Please help!!!

<@&286206848099549185>

[cedar sail]

Yes?

[hollow condor]

Can u help me?

Pleaseeeee

[cedar sail]

I think yes, is it algebra?

[hollow condor]

Don't think so

[cedar sail]

What is it?

[hollow condor]

Not sure

Here is the question

I have no idea lol

[hushed locust]

we can think of the base of our number system as a variable, say x. then each number is
first place + second place * x + third place * x^2 and so on
for example in base 10,
564 is 4 + 6 * 10 + 5 * 10^2

[hollow condor]

ye?

[hollow condor]

Wym by first place and second place

[hushed locust]

first place is the farthest right digit, second place is the second to the left digit, and so on

[hollow condor]

oh

Then what i do

[hushed locust]

so we express each equation in terms of our variable and solve for it

[sage igloo]

base 16?

[hollow condor]

Nope

some reason its base 7

But

I actually don't know why

It doesn't give you proper reasoning

[hushed locust]

so in base 10, we think of our numbers as having a ones place, tens place, hundreds place and so on:

$8924 = 4 \cdot 10^0 + 2 \cdot 10^1 + 9 \cdot 10^2 + 8 \cdot 10^3$

But if we replace the 10 with some variable $x$, we can express a number in any base $x$ that way

[ocean seal]

cloud

[hollow condor]

how u get 8924

oh nvm

but how

<@&286206848099549185>

I still don't know

[exotic belfry]

what is the question?

[exotic belfry]

if 6x3 = 24 for base y, this means 6x3 = 2y+4 -> solve for y.
10x10=100 for base y means (1y+0)(1y+0)=1y^2+0+0 -> gives no information as it is always true.
13+15=31 for base y means 1y+3+1y+5=3y+1 -> solve for y.

[hollow condor]

oh so its 7?

But how did u get 2y+4 and like algebra

[exotic belfry]

thats the definition of a numbersystem, and cloud has explanined it

[granite inlet]

The tens place here is representing one set of complete "y" and you can think of the ones place as a remainder

That's how they got 2y+4

[hollow condor]

That's what the answer told me

lol

[granite inlet]

Yes

[hollow condor]

It doesn't make sense

[granite inlet]

Think about it this way when you're in base 10

You group numbers up to 10 before you move into the next digits place

[exotic belfry]

exactly 10 base 7 means 1x7+0, 11 bas 7 means 1x7+1, 12 base 7 means 1x7+2 ...

[granite inlet]

Hence why we count up to 9 then we add a 1 in the next digit place and 0 in the ones place

[hollow condor]

Huhhhh

[granite inlet]

10 really means as a number one whole set of 10 which is the 1 and 0 remainder which is the 0

In base 10

For example base 2 you count

0 1 10 11 100 101 110 111 1000 1011.. etc.

Oh sorry

Our numbers are ill equiped for counting in bases other than 10 that's why it looks weird but you should think of them as what the digit in each place means

[hollow condor]

o

[granite inlet]

The first digit is always a remainder

The 10's place is how many complete sets of the base you have, aka in base 10 it's the 10s place in base 7 its the 7s place etc.

And you continue in that fashion, how many groups of 10 10s do you have is 100

How many groups of 7 7s do you have is 100 in base 7

[hollow condor]

OOO

Ohhhh

Tyy

[granite inlet]

No problem, again the reason it looks bizzare is because we're really writing all these things in base 10 when we don't really mean it

Our system for representing these things isn't very good

[hollow condor]

lol

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[hollow condor]

/close

?!

[civic panther]

Did you want to close it?

.close

bruh

[lone heart]

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[alpine sable]

This question just amazed me. Am done with the answer keys error.

Is it really asking me to find the number of digits in

312 × 28

???

💀

[alpine sable]

Maybe they did error during typing

[thorn tapir]

Ah

No it's okay

Number of digits in a any number is floor(log_10 n)

[alpine sable]

Whaat

[thorn tapir]

Yeah

Try it

[alpine sable]

OHHHH

Wait

[thorn tapir]

Sorry, that plus 1

Yeah

[alpine sable]

Got ittt

[thorn tapir]

This works because the numbers are all in base 10

If base b, just change the logarithm base

[prime badge]

not exactly

[vale wigeon]

i have a feeling that the INTENDED expression might have been 3^12 * 2^8

because as is like

,calc 312 * 28

[ocean seal]

Result:

8736

[vale wigeon]

four digits

[alpine sable]

I remember my teacher told me smth abt base 10 in characteristics and mantissa too

[prime badge]

oh true

[alpine sable]

Could be

[thorn tapir]

For any number $a_1a_2a_3...a_n$ in base $b$, it can be expressed as

$a_n \cdot b^0 + a_{n - 1} \cdot b^1 + ......... a_1 \cdot b^{n - 1}$

[ocean seal]

Riku

[alpine sable]

I will note it down

[thorn tapir]

This extends to fractions too

[alpine sable]

Hmmm

[thorn tapir]

b will just take negative exponents

Floor(log_10 n) works because it's finding the power of 10 closest to n which is less than n

The number of digits in that specific power has to be the number of digits in n

[alpine sable]

I see

[thorn tapir]

Like say

99

[alpine sable]

I wonder if its in my current curriculum

Btw

[thorn tapir]

Closest power which is less than 99 is 10 itself

Has 2 digits

99 too

[thorn tapir]

Probably not

[alpine sable]

Agree

[alpine sable]

How can i solve this then

They gave me value of log 2 with base 10

[thorn tapir]

Take common log of that whole thing

Use log properties

[alpine sable]

Hmmmmmm

Oof i cant

[thorn tapir]

$\log_{10}(3^{12}2^{8}) = \log_{10}(3^{12}) + \log_{10}(2^8) = 12\log_{10}3 + 8\log_{10}2$

[ocean seal]

Riku

[alpine sable]

But i dont need to find their log

I need to find their digits

[thorn tapir]

Floor of this log is the number of digits

[alpine sable]

Damn

[thorn tapir]

Here n = 3^12 * 2^8

[alpine sable]

Yes

[thorn tapir]

We just showed that no

[thorn tapir]

Now use the values given

And find the floor

[alpine sable]

😮

I think

I can do this now

[thorn tapir]

Yess

[alpine sable]

But i dont think floor log property is coming in my curriculum soon

[thorn tapir]

Yeah they just put the question there I guess

But it isn't too difficult, maybe it was put to check if you are familiar with the notion of counting digits and seeing the connection of number of digits with the powers of 10

The idea uses logarithm

You did mention you teacher mentioned bases in class

So i think that's why it was asked

You just didn't have the formula for it

[alpine sable]

Hmmm

Could be

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[plain hill]

how can i solve it?

i try to start by using the formula sin(a+b)=sin(a)cos(b)+cos(a)sin(b)

but now idk how to countinue

[tawny condor]

there is a formula for sin(A)sin(B)

you should use that instead

[plain hill]

werner formula?

this?

[tawny condor]

I think so

yes

use that

[plain hill]

okk, now i try it

[tawny condor]

pi/6 and pi/3 nicely add up to pi/2

and pi/3 - pi/6 is pi/6

[plain hill]

one question, in the formula i have cos(a-b), this mean cos((pi/3 - a)-(pi/6 + a)) ?

[tawny condor]

yes

wait no

its pi/3 + alpha

(pi/3 + alpha) - (pi/6 + alpha)

notice that the alphas cancel here

[plain hill]

yes

so became cos(pi/3)-(pi/6)

[tawny condor]

where did all the alpha go

$\sin\parens{\frac{\pi}{3} + \alpha} \cdot \sin\parens{\frac{\pi}{6} + \alpha} = \frac{1}{2}\parens{\cos\parens{\parens{\frac{\pi}{3} + \alpha} - \parens{\frac{\pi}{6} + \alpha}} - \cos\parens{\parens{\frac{\pi}{3} + \alpha} + \parens{\frac{\pi}{6} + \alpha}}}$

[ocean seal]

RedstonePlayz09

[tawny condor]

lots of parenthesis but hopefully this is understandable

[plain hill]

yeah i see

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[upper prism]

d

[upper prism]

the functional equation from a bridge is
f(x) = -0,00293(x - 124)² - 45
Calculate the range of the bridge

How to do that?

I got the result 248

is this right?

<@&286206848099549185>

[thorn tapir]

wait

what

from a bridge

is it about a Projectile?

[upper prism]

bridge bridge

its about a bridge

[thorn tapir]

....do you have the original question, like uh, written somewhere?

[upper prism]

I have if u speak german

[thorn tapir]

i will try translating

just post it

I don't know german though 😭

[upper prism]

Die Fehmarnsundbrücke verbindet die Insel Fehmarn mit dem deutschen Festland. Der parabelförmige Brückenbogen wird durch die Funktion f(x) = -0,00293(x - 124)² + 45 beschrieben
b) Berechne die Spannweite des Brückenbogens. Runde auf Meter

[thorn tapir]

ohhh so the bridge is parabolic

[upper prism]

yes its x²

[thorn tapir]

I'll use this for myself and any others who doesn't know German

span of arch.... hmmm

no no lol I used DeepL

[upper prism]

ok

can u solve it?

[thorn tapir]

for this I think

you need to have a ground

so let's assume it's just the x axis

[upper prism]

ok

ground is x

[thorn tapir]

so the span would be the distance between the two points where this parabola intersects the x axis

[thorn tapir]

which means y = 0

y = 0 is the equation of x axis

so solve the equation $0 = -0.00293(x - 124)^2 + 45$

[ocean seal]

Riku

[upper prism]

isnt + 45 = y?

[thorn tapir]

you will get two x values

[thorn tapir]

wait no?

[thorn tapir]

get the absolute value of the difference between them, that should be the span

[upper prism]

i got x1 = 163,19
x2 = 84,81
span = 163,19 + 84,81 = 248

is this right?

[thorn tapir]

nonono

don't add them

it would be minus

163.19 - 84.81

[upper prism]

why minus

[thorn tapir]

you need the distance between thepoints

[upper prism]

but isnt it 163,19 --84,81 then

cause 84 is in the negative direction

[thorn tapir]

lemme just see

[upper prism]

cause 84 would be in the left direction and thats negative or not?

nooo

wait

that doesnt make sense

both are in the right direction

so its 163.19 - 84.81

[thorn tapir]

this is what desmos shows me

you probably did caluculation mistakes somewhere

[upper prism]

why is the first 0?

[thorn tapir]

what

first is not 0

it's 0.071

[upper prism]

still not 163.19

[thorn tapir]

and also it actually doesn't matter

you can like move around that parabola left and right

still the span stays the same

so the endpoints doesn't matter, the distance between them does

[upper prism]

but why is it 0.071 now

[thorn tapir]

ok let me just solve it

$-0.00293(x-124)^{2}+45 = 0$

[ocean seal]

Riku

[exotic belfry]

why not? your solution is wrong

just draw it

[thorn tapir]

from this you get $(x - 124)^2 = \frac{-45}{-0.00293}$

[ocean seal]

Riku

[thorn tapir]

so x is either

$124 + \sqrt{\frac{45}{0.00293}}$ or $124 - \sqrt{\frac{45}{0.00293}}$

fuck

[ocean seal]

Riku

[thorn tapir]

yeah now makes sense

put these in calculator to see what it is

definitely shouldn't be what you got

yeah

desmos stands correct

[upper prism]

ah ok

thanks

[thorn tapir]

distance in first minus second for this one

then round it off too nearest meter

[upper prism]

so i need to 247,93 - 0,07 then?

[thorn tapir]

yes

[upper prism]

ahhhhhhhhhhhhhhhhh

ok thanks

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[zinc oar]

Is there a formula of some sort to solve this. I've been using the sum of geometric sequence formula and when I check with the answer it is wrong

[solemn juniper]

There is a formula, and it is related to a geometric series

So you should show precisely what you've tried

[normal magnet]

I have a question

[solemn juniper]

#❓how-to-get-help

[zinc oar]

Am i doing it incorrectly?

[solemn juniper]

,rccw

[solemn juniper]

Not quite

20,000 is the amount of the debt at time 0

When you apply this formula, you're looking at the accumulated value of the payments after 5 years

[zinc oar]

Yes from 2009 to 2013

[solemn juniper]

So if 20,000 is the size of the debt at time 0 (2008) and interest is 6%, what is it at time 5? (2013)

[zinc oar]

The amount to be paid with the interest?

So 3000*1.06^5?

[solemn juniper]

Not quite

Perhaps you want to look up "time value of money"

[zinc oar]

👌

[solemn juniper]

The formula you applied that resulted in 17925 is the value of the 5 payments at time 5

Whereas 20,000 is the value of the debt at time 0

You can't compare these directly because they exist at different points in time

[zinc oar]

Oh i see

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[dawn grotto]

please help me

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@dawn grotto Has your question been resolved?

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[dawn grotto]

no

[dawn grotto]

.close

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[ripe oriole]

so I need to find the type of discontinuity here, over x=0

I get to an indeterminate form not sure how to simplify or expand the term

not sure how to deal with floor brackets

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@ripe oriole Has your question been resolved?

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[hard patio]

you cant reopen it now

[ripe oriole]

ye I figured lol

[hard patio]

open a new one

[ripe oriole]

gotchu

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[still jungle]

For which k the function is continous at x=1/3

[wet atlas]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[wet atlas]

Show your working if possible

[still jungle]

1

[wet atlas]

Can you tell me what is $\lim_{x\to0}\frac{sinx}{x}=$

[ocean seal]

Encrpyt

[still jungle]

1

[wet atlas]

Great can you tell, what denominator if you took 2 as the common factor

[still jungle]

2(3x-1)

[wet atlas]

Yeah, good,
So look at the numerator and denominator and tell me what do you get

[still jungle]

(sin(3x-1))/2(3x-1)

[wet atlas]

Yeah so what will be the limit, when 3x-1 tends to zero

[still jungle]

I guess 1/2

[wet atlas]

Yes, you got your answer

now equate to the other equation and find the value of K

[still jungle]

just a question do I have to factor the denominator or can I directly apply lhopitals

since the limit is in indeterminate form

[wet atlas]

I mean you can't use lhop in this case, because of the 0/0 form

[still jungle]

but then does'n it become 1/6

the derivative of the nominator is 1

and the derivative of the denominator 6

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[alpine sable]

Hello I have a question

[alpine sable]

Are they the same?

[upbeat hornet]

is i a complex number here?

[alpine sable]

Yes

[upbeat hornet]

are you doing complex analysis?

[alpine sable]

physics

[upbeat hornet]

what is k?

[alpine sable]

Its a wave vector

[vale wigeon]

so it's a constant

the function x ↦ ikAe^(ikx) - ikBe^(-ikx) is continuous in x so yes these are the same

[alpine sable]

Well it has a Dirac function in it

wait

[vale wigeon]

eh?

[alpine sable]

D can be any rational number

k contains a delta function, this means that the wave number itself has a discontinuity right?

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[alpine sable]

.close

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[tired fossil]

In what cases are pade approximants better than taylor series and vice versa?

[alpine sable]

https://mathoverflow.net/questions/122539/the-unreasonable-effectiveness-of-padé-approximation

[tired fossil]

Thks

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[glacial nimbus]

What kind of theorem can or postulate can help me identify it is a parallelogram

[analog falcon]

i would use congruency to prove opposite sides (of bigger parallelogram) are equal

congruency of triangles

in particular SAS congruency criterion

[glacial nimbus]

Omg i didnt even picture that

Ty so much

[analog falcon]

You are welcome 🙂

[glacial nimbus]

If u can

Can u help me with this too

Ik i needa use properties of a rhombus but have been trying and am still lost for 20 min

[lone heart]

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[brisk heath]

how to integrate?

[glacial rover]

What kind of level do you need to know this to?

[brisk heath]

i don't understand your question

[glacial rover]

For example the A level further maths syllabus has the integration of cosec x ( 1 / sin x ) listed in the formulae booklet

So as a result the full steps do not need to be known

[tacit arch]

,w int csc(2x)

[brisk heath]

i'm pre university

[ocean seal]

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[brisk heath]

what is csc?

[glacial rover]

Cosec

[copper delta]

1/sin

[brisk heath]

why are we using log?

[tacit arch]

Multiply top and bottom by cot(2x)+csc(2x)

[tacit arch]

Some trick your teacher would have taught in class

[brisk heath]

that's nothing i know, idk maybe the teacher left it as a kind of challenge or something

[glacial rover]

https://m.youtube.com/watch?v=77ACcWJfZQ4

I recommend you watch this video to understand why it works

It’s not very in depth but the steps are useful

Alternatively, I am year 13 A level further maths so the method I would use to solve it, is simply from the formulae book provided by AQA in the exams

Here we can see the integration for cosec is provided so using base integral rules it is 1/2 ln(tan x)

[thick lynx]

This has been asked on Math StackExchange before:
https://math.stackexchange.com/questions/3275505/evaluate-the-indefinite-trigonometric-double-angle-integral?noredirect=1
and here with 5x:
https://math.stackexchange.com/questions/683119/integrating-csc-5x?noredirect=1

[lone heart]

@brisk heath Has your question been resolved?

[brisk heath]

oh ty

.close

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[alpine sable]

maxima/mimima

[alpine sable]

f(x) = 4x^3 - 18x^2 - 48x + 17

how do i do this

Are you trying to find local or global maxima and minima?

polynomial functions

[alpine sable]

Alright well that doesn't answer my question but on second thought I think I already know the answer so let's continue

Have you seen a problem like this before or learned how to find maxima and minima or is this your first time doing this?

im not english so i just used translate

not sure wtf is means

its my first time

doing this

[alpine sable]

Do you speak English or is everything you say coming from a translator?

i speak english

just some terms

i dont know for example the local ro global

or

Is your native language Arabic?

Also if by any chance you speak French we can go with that instead

nono its fine to use english

i speak a bit of arab and french but english and dutch the most

so lets go w english

Okay so have you ever seen a maxima/minima problem or learned how to do them?

no i havent

If I mention derivatives as a way of finding them, does that ring a bell?

no

no i dont

sorry

i mean i know what they are

i just cant do them

Do you see what all of these maximas and minimas have in common? (except for the one on the top left, ignore that one)

when its below the line

the global and local switch

?

The line is arbitrary

Ignore it

Like, looking at this do you see any way to visually identify maximas and minimas?

[alpine sable]

By the way forget about global vs. local, that's not gonna be important for this question

I can still explain what that means but it isn't important here

yeah please explain

A global minimum is a point that is the lowest of the entire graph

Whereas a local minimum is a point that is the lowest within its neighborhood

For example, the local minimum on the right is not a global minimum because it is not the lowest point of the graph but it is a local minimum because none of the points immediately next to it are lower

And the same logic applies for global and local maximas

@alpine sable Does that make sense?

yhes

yes

so local is the lowest of the area its in

and global

is just the lowest of the entire graph

[alpine sable]

Or highest if we're talking about maximas

ahh

okay

But again while you might need to know this for the future it isn't important for this question

yeah its good to know

[alpine sable]

I'll ask again, do you see what all the maximas and minimas have in common?

they're both at the highest

or lowest?

Hmmm yes but that's not what I was hoping you'd say

Hint: It has to do with slopes

they go in slopes

up

and down

?

Are you talking about how on one side of a minima/maxima the slope will be going up and on the other it'll go down?

yh

Okay that's close enough and in fact it'll help later but for now just focus on the slope at the point itself

oky

okay

Do you see it yet?

they both dont go higher

or lower

than 2?

Than 2??

yes 😭

on the side of the graph

idfk man

Oh right

That has nothing to do with them being maximas/minimas

The answer is that they all have a flat slope

oh

so it goes in a slope

then flat

then slope again?

thats what you mean?

Yes, but all you have to remember is that it becomes flat at the extrema (turns out I didn't have to say "maxima and minima" this whole time)

And do you know how to check whether the slope is flat at a point using derivatives?

no i dont

Do you know how to calculate derivatives?

i dont

How are you supposed to do this problem if you don't have the prerequisites

im not sure

thats why i asked

Can you send the original question?

,w graph 4x^3-18x^2-48x+17

[ocean seal]

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[alpine sable]

Maxima/minima van veeltermfuncties
"Maxima/minima of polynomial functions"

Hmmm

yes

@alpine sable I checked the video from the first QR code and it included f'(x)

Which is a derivative

So I'm assuming you must've seen derivatives in class

i havent

this isnt a book from my class

i bought it myself

im working on it at home

[alpine sable]

Then you should first learn about derivatives

okay

Typically I'd be happy to explain things like this myself but derivatives aren't a simple thing

no problem

thank you

You can now .close this channel unless you have more questions

.close

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[surreal meteor]

how would i know the sub space is the ortonormal basis for standard basis (e_1, e_2) etc from just (x_1, x_2, 0)

it is because it's in R^3 then I know its the standard basis E

[lone heart]

@surreal meteor Has your question been resolved?

[mortal trellis]

wdym

you could take another basis for the space

but clearly e1 and e2 are in the space and span it

so we take those

[surreal meteor]

is the standardbasis e1 and e2 in all spaces?

[mortal trellis]

no

[lone heart]

@surreal meteor Has your question been resolved?

[surreal meteor]

So, why can I just pick that? How do I know it's within that space?

[mortal trellis]

cleary (1,0,0) and (0,1,0) are of the form (x1,x2,0)

[surreal meteor]

So it could've been (2, 2, 0) as well?

It's just because it's easy to show with the standardbasis?

[mortal trellis]

you could also have taken as a basis the vectors (2,2,0) and (13, -57,0)

just would have made everything much more complicated

cause its not orthonormal and stuff

[surreal meteor]

Yes, ah I see!

Yep yep yep!

Okay cool!

Thank you!

.close

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[teal lagoon]

Hi

[teal lagoon]

What am i doing wrong?

[modern sedge]

that sum is 2 * (1+2+3+4...+24+25)

you forgot to multiply it by 2 I guess

[teal lagoon]

Why multiply it?

Isnt that the equation

[modern sedge]

2+4+6+8+10+...+50 = 2 * (1+2+3+4+...+24+25) do you understand this?

[harsh swallow]

the sum you did is 2 times the sum you calculated with the formula

[sharp sail]

That's applies to sum of all natural numbers till n, not even numbers

[modern sedge]

what you did is calculated 1+2+3+4+...+24+25

but you need to multiply it by 2 to get it to 2+4+6+8+10+...+50

[sharp sail]

I found a sylveon

[harsh swallow]

ah shit

[teal lagoon]

What is 2+4+6+....+50=

[harsh swallow]

hides

[sharp sail]

where, it's an open field?

[modern sedge]

it seems like sum of all even numbers between 2 and 50

[harsh swallow]

$2 + 4 + 6 + ... + 50 = 2 * (1 + 2 + ... + 25) = 2 * \frac{25(25+1)}{2}$

[teal lagoon]

Basically Un=2n
And i want S(50)

[ocean seal]

Katharine

[modern sedge]

no, you want S(25)

[modern sedge]

or well it depends on summation bounds and ur definition of S(n)

[teal lagoon]

Ok i got thnxxx

But what is the formula

Cuz i thought it was n(n+1)/2

[modern sedge]

n(n+1)/2 is formula for sum of first n natural numbers

1+2+3+4...+n = n(n+1)/2

[teal lagoon]

What about the 2

In 2*

[modern sedge]

but you had to calculate 2+4+6+8...+50. So you should first rewrite it as 2*(1+2+3+4+5+6...+25), then apply the formula

[teal lagoon]

Ooooh thx

[modern sedge]

once you apply the formula, you will find out 1+2+3+4...+25=25*26/2

[teal lagoon]

Ok thats all thx so much

.close

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[wide mango]

could someone solve for n

[wide mango]

i already did it but im afraid i did it wrong

[sharp sail]

This isn't the full question

[copper delta]

what’s on the other side of =

[wide mango]

dude sorry

i was busy

i didnt notice sorry

[sharp sail]

n is 1/2

[wide mango]

i know

[sharp sail]

so?

[wide mango]

i want to know how would you guys get to it

[sharp sail]

oh

[copper delta]

add the second fraction to both sides

[sharp sail]

just bring n/3.75 to RHS

[copper delta]

then divide by 3.75

[wide mango]

i did it as
n = 3.75/-7.5

but im mostly sure its wrong

[sharp sail]

there isn't going to be -

[hushed wolf]

equalize the denominators

[wide mango]

its because i switched from left hand to right hand

[hushed wolf]

3,75*2=7,5

[sharp sail]

There is already a - in front of n, so changing sign should be +

[wide mango]

ok ok

thx yall

[lone heart]

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[grand cape]

The last part is right here? I meant
R-[-1,3] U {1}
This one 👆

[grand cape]

Some of parts are Turkish here sorry about it.

[lone heart]

@grand cape Has your question been resolved?

[grand cape]

<@&286206848099549185>

[tardy nest]

Huh

[lone heart]

@grand cape Has your question been resolved?

[lone heart]

@grand cape Has your question been resolved?

[lone heart]

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[buoyant zephyr]

Hello, I just need help on making sure I doing correct on differentiate the function y= square root 4-x using chain rule 1/2(4-x)^1/2

[proven leaf]

This looks right except where did your negative go in the final simplification

[buoyant zephyr]

OhI just only missing a negative

[proven leaf]

Ohl?

[buoyant zephyr]

Oh lol

[proven leaf]

Everything else looks pretty good! 🎉

[buoyant zephyr]

Ok thx you

/end

[proven leaf]

make sure you close you channel and have a good day!

[buoyant zephyr]

How do I close

[proven leaf]

.close

[buoyant zephyr]

.close

[lone heart]

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[molten pivot]

Let's say we have a square matrix A. How do I write the matrix B that maps the first row vector of A to the first column vector of A, second row vector to second column vector, so on and so forth?

[tacit arch]

Do you mean transpose?

[vague coral]

^

[molten pivot]

Not quite, let me come up with an example. It should be a linear transformation

i suppose what is desired is the row reduced version of the augmented matrix [A | A^T]

[lone heart]

@molten pivot Has your question been resolved?

[molten pivot]

yep it's just A^T A^-1

[lone heart]

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[native temple]

How to delete an element of a list in ti-basic?

[gleaming granite]

I haven't done TI coding in a long time, but I think you can just do del(Lk, i)

[native temple]

Does this work on ti-84 plus(no ce)

[gleaming granite]

I think so

You can try it out on a dummy program

[native temple]

How to get del()?

[molten pivot]

just press the delete button on the entry

[native temple]

That isn't ti-basic

[gleaming granite]

are you typing on the calculator?

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@native temple Has your question been resolved?

[lone heart]

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[kind snow]

if a 5ft tall person stands in one spot on the equator of the earth for 24 hours, how much farther will that person's head travel than his or her feet as the earth rotates about its axis

[kind snow]

radius of the earth is 4000m

for this problem

5280 feet in one mile

ive tried finding it online and ive found the answer i just dont understand why thats the answer

why is a newly entire circle create cause the guys head ?

why do we add 5ft to the radius of the cirle if hes on top of it ?

where does he get 10pie in the middle of subtracting

[wary stream]

Because the center to the feet is 4000mi but the center to the head of the person is 4000mi + 5ft

[kind snow]

oh i see

but how does that help us find

how much his head will travel compared to his feet

[wary stream]

Because the head is farther from the center, you find out how much the feet travels in 24hr, then find how much the head travels in 24hr, and subtract the two

[kind snow]

24hrs isnt even used in the solution though

[wary stream]

Take a circle with 1ft radius and 2ft radius, do you understand that you have a larger circumference for 2ft compared to 1ft?

[kind snow]

yes

[wary stream]

It's the same logic with the head and feet, the head is farther so it travels more

[kind snow]

but its attached to the feet which are connected to the closer circle ?

[wary stream]

Because that's not how you find circumference

[wary stream]

But the head is farther from the center than the feet

[kind snow]

yes but the feet and head move together

?

im sorry if im missing the point

[wary stream]

Yes it moves together but the head is farther from the center than the feet are

[kind snow]

okay yes the head is farther

wait

idk man

okay so after 24hs rotating on the earth axis

his head will travel farther

because its farther away from the center

[wary stream]

Yes

So you need to find how much the head travels and how much the feet travels

[kind snow]

so the rotation of the circle and middle circle are connected how

[wary stream]

Are you referring to the middle circle that has the radius of 4000mi here?

[kind snow]

yes

[wary stream]

That's the radius from the center to the feet

[kind snow]

okay lemme see then

so because its farther from the center it'll have to travel more to make a rotation

even though its connected to the feet which is closer to radius

[wary stream]

What is "it"? Feet or head?

[kind snow]

head

my bad

[wary stream]

Yes the head and feet are connected to the body but vertically from the center, the head is farther away from the center of the earth compared to the feet

[kind snow]

yes

how does that relate to the rotation of circle itself though

[wary stream]

Because the earth makes one full rotation in 24hr

One full rotation relates to circumference

So you find the circumference using the distance from the center to the feet and the center to the head

[kind snow]

okay to make it simplier for myself

technically the circle the heads apart of

the new radius

okay wait

that made no sense

OH

i think i get it now

[wary stream]

Do this, stand up and imagine this. From the center of the earth to your feet, is one radius distance, and from the center of the earth to your head is another radius

[kind snow]

yes i imagined i was on a ball

so its not according to that one circle its according to each radius

thats why i was confused

i think

[wary stream]

Yes there's two different radii

[kind snow]

cause of this guys head theres new circle

i minus the 2

and get the difference thats been travel

between the 2 circles rotations

[wary stream]

Yes

[kind snow]

i get it now

thank you

ima try to solve it now

okay

i ran into a problem

so i get a difference of 12.6

not 31,4

like the answer that i showed

[lone heart]

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

[kind snow]

okay so after solving for both circumferences

then subtracting them by eachother i got this number

12.5663706213

but the answer i found online

had a different answer

i followed the same steps

except 1

which dont understand where they got a number from

[wary stream]

That's not showing your work

What did you get for the circumferences? How did you calculate said circumferences?

[kind snow]

okay so i did 4000 x5280 + 5

first

and got 21120005

then multiplied it by 2 pie

and got 132700905.104

then i did 4000 x 5280 x 2 pie

132700873.688

and got 12.6

wait those numbers look right

ima try again

okay nvm

i got the right answer

idk how i got that last answer

i got that answer twice

so idk

[wary stream]

Not sure, you did the work

[kind snow]

thank you though

i got the answer

is there a way i can close this now

that its been answered

[wary stream]

Use .close to close a channel

[lone heart]

@kind snow Has your question been resolved?

[lone heart]

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[cerulean talon]

composite function g ⭕️ f(x) and state it’s domain

that circle is there cos there’s no open circle symbol

[trail sage]

you can just write it as gf(x), its understandable

[cerulean talon]

ok

so basically

i’ve plugged the f(x) into x

[trail sage]

What do your textbook/notes say about the domain of composite functions? This should be almost immediate

[cerulean talon]

and i’ve put it into (x+2)(x-2)

[cerulean talon]

we haven’t actually done this in class

it’s stuff we’ll be doing soon

[trail sage]

ah your studying ahead?

[cerulean talon]

but it’s apart of our general assignment

[cerulean talon]

yes

[trail sage]

Lets start by thinking about what domain means

what is the domain of a function?

[cerulean talon]

so basically, i’m at 2/(x+2)(x-2)

[cerulean talon]

any number that x can equal

[trail sage]

hmm i just realised, you dont have a domain for f and g?

[cerulean talon]

when i put it on mathway, it was this

[cerulean talon]

wym?

[trail sage]

For a function to be defined, you need to have both a rule and a domain

The question just gives us the rule of f and g but doesnt specify their domain

[cerulean talon]

want the full question?

[trail sage]

yes, the question is not solvable without that

[cerulean talon]

here

[trail sage]

the rule of the composite is correct btw, you just replace all the “x” in the equation of g(x) to get g(f(x))

[trail sage]

This is a lousy question tbh

[trail sage]

but presumably if the question wants you to state the domain of the composite of the form ^

just think about what values this expression cannot take

[cerulean talon]

if i plug in any number on my calculator it has a result

of course if i do like 999999, it shows as 0 since decimals can’t show it

same with -99999

[trail sage]

how about you try the number 2

[cerulean talon]

oh yeah

2 doesn’t sork

[trail sage]

do you know why it doesn’t work?

[cerulean talon]

it cancels out the bottom to 0

2/0 isn’t possible

[trail sage]

yep, could you think of another number that doesnt work?

another number that turns the bottom to 0

[cerulean talon]

/2

*-2

[trail sage]

thats exactly what this means

[cerulean talon]

ok i think i got it

[trail sage]

every number but 2 and -2

[cerulean talon]

yeah

i get it now

thank you so much!!

[trail sage]

glad to help

[cerulean talon]

i have one more question tho

i’ll attempt it first, but i’ll come back later if i need help

ty!

.close

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[keen orbit]

I've ruled out A and B

if there are 5 vertices, then there is at most 4 degrees per vertex, and at most 4*5=20 total sum of degrees, thus 20/2 = 10 maximum edges

so A and B are ruled out

I guess D would make sense

because in order for a graph to be complete, a would need to be connected to all other 4 vertices?

[carmine reef]

Yeah that's correct

01101
10010
10010
01101
10010

K2,3 for the record

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@keen orbit Has your question been resolved?

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[cerulean talon]

hello, i need help with a question

[snow pebble]

what question

[cerulean talon]

By using the discriminant, or otherwise, explain why the graph y = 9x^2 - 6x + 3 only exists in the first two quadrants of the Cartesian plane

[snow pebble]

uhh

[ocean seal]

marc

[wild trail]

This is just a scaled quadratic

[snow pebble]

yeh

[cerulean talon]

yeah ik that, but the second part i’m not getting

[ocean seal]

marc

[cerulean talon]

am i saying because it’s 9x^2?

yeah

[ocean seal]

marc

[snow pebble]

plot the points using $(-D/(4a) , b/(2a)$

[ocean seal]

Buttercup

[cerulean talon]

ohh

okay

[wild trail]

Negative discriminant means no reals roots means the graph will always be above x-axis

[ocean seal]

marc

[cerulean talon]

and because it’s a positive 9x^2, it’s in the top 2 quadrants

[ocean seal]

marc

[cerulean talon]

okay that makes sense yeah

[snow pebble]

lol

[wild trail]

Yeah but 9 > 0 so it's a downward parabola

My bad

[cerulean talon]

so if discriminant is positive it’s below, and negative on top?

because the 9x^2 is positive it’s on top

ohh okay

yeah i get that

[wild trail]

Tbh there's a much easier way to see this

[cerulean talon]

if it were -9x^2 it’s on bottom yes?

[snow pebble]

true

thats what i was about to say lol

[wild trail]

$9x^2 - 6x + 3 = (3x - 1)^2 + 2$

[ocean seal]

numbpy (anti glomed)

[wild trail]

Thus the graph will always be 2 or above

[cerulean talon]

not sure i get wym

okay so the discriminant is -72

meaning it doesn’t touch the z axis

*x

[wild trail]

(3x - 1)^2 will always be greater than equal to 0

[cerulean talon]

how do i know that it will be in the top two quadrants?

[wild trail]

Hence, (3x - 1)^2 + 2 will always be greater than equal to 2

[cerulean talon]

why did you factor it exactly?

[wild trail]

Completing the square

[cerulean talon]

wait so

okay

i get it

thank you

.close

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[lavish dagger]

Hello. I need some friend for my work. No need any ability and time. And I will pay. please dm anybody interesting.

[wary stream]

First this server is all voluntary, meaning it's free help

And two, if you need help with math, because this server is voluntary, you can just post a question you're stuck on and someone who is available can help you

[snow pebble]

how much will u pay?

@lavish dagger

[gleaming granite]

https://tenor.com/view/dinero-plata-cash-money-rich-gif-19790979

[wary stream]

You do realize that replying to a message pings the person right? Unless you turned it off so you didn't have to ping them a second time

[snow pebble]

k bruh

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@lavish dagger Has your question been resolved?

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[oblique stirrup]

Not exactly mathematics but can I get an explanation of why it says to add 6e^- to the right hand side

[oblique stirrup]

Prior to that the charge is 14+ and 2- so 12+ total so I wouldve assumed it to add 12e^-

[hushed locust]

we're just trying to bring the total charge to the same as the other side, which is currently 2*3+ = 6+

[oblique stirrup]

6+ on left side and on the right side I see 2-, +, and 6e^- so -7 total on the right

[hushed locust]

you have to multiply each charge by the number of moles

[oblique stirrup]

isnt that the first thing i did

2-, 14+, 6e^-

[hushed locust]

so -2 + 14 - 6 = 6

[oblique stirrup]

oh i see

.close

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[grim pelican]

how do u do this im genuinely confused😭

[vale wigeon]

well there's 6 regions here

so 6 options for martina's first move

examine each one for which responses Zahra has to it

[full frost]

there’s one that’s a obvious answer

[alpine sable]

Just like simulate the game in your head

pick a piece and try to compute the best possible moves

Your goal is to shade the most area

[full frost]

that’s not true

[vale wigeon]

for example, suppose Martina shades in region 1 first. which moves does Zahra have in this position, and which ones lead to a win by whom?

[vale wigeon]

no, it is not.

[alpine sable]

Oh those rules are weird?

[vale wigeon]

@grim pelican

[vale wigeon]

no, the rules are not weird. you just misinterpreted them.

the goal is to leave the other player w/o a move.