help-17

[mild flower]

$\frac{ \blue{\frac{x+9}{9x}} }{\orange{9+x}}$ right?

[twin meteor]

hayley!

[round pasture]

I do this because of this, where (9x) is b

[mild flower]

can you confirm that what i wrote is what you meant?

the blue and orange thing?

[round pasture]

once I set the denominator equal for the above two fractions, yeah

right before the purple, if that is what you mean

[mild flower]

$\frac{ \blue{\frac{x+9}{9x}} }{\orange{9+x}} \cdot \frac{ \purple{9x}}{\purple{9x}}$

[twin meteor]

hayley!

[mild flower]

this is what we're doing next

[round pasture]

I'm following

so there's only a 9x at the denominator I think right

[mild flower]

i hope i typed this right...
$\frac{ \lp\blue{\frac{x+9}{9x}}\rp \cdot \purple{(9x)} }{\orange{(9+x)} \cdot \purple{(9x)} }$

[twin meteor]

hayley!

[mild flower]

right?

[mild flower]

that's correct yes

when i say "multiply top and bottom" i mean the entire top and bottom

[round pasture]

omg thank you so much

I understand now

if I close the channel does everything delete

[mild flower]

no, it stays

forever

[round pasture]

ok that's good cuz I don't want it to lol

thanks again

.close

[vocal sleet]

Channel closed

Closed by @round pasture

Use .reopen if this was a mistake.

[mild flower]

the channel will be renamed but you can get it by searching from:crazyblob

[vocal sleet]

Available help channel!

Send your question here to claim the channel.

Remember:
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[vast shale]

Hey im trying to understand how a recursive formula works

theoretically i should be able to solve every single problem here

if i understand how it works

<@&286206848099549185>

What

[split heart]

You mean how do sequences work?

[vast shale]

Yeah

Recursive formula

im in algebra 1

for background info

[split heart]

Let's start with a problem

Choose one

[vocal sleet]

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

[vast shale]

dude thats not time efficient

make it 10 minutes

[ornate ember]

lol no. It's the discord's rules. It's set at 15m for a reason

[split heart]

We're doing charity work here dammit

[vast shale]

Lol

[split heart]

Anyway, what question did you pick

[vast shale]

lets start with 1

[split heart]

Okay so you have 3, 8, 13, 18, ...

[vast shale]

Yep

[split heart]

What's the pattern

[vast shale]

Pattern is +5

each time

[split heart]

Good. So the recursion formula is $s_n = s_{n-1} + 5$

[twin meteor]

TooManyCooks

[split heart]

where s_n is the next term in the sequence

[vast shale]

what does s stand for and n

just so that im not confused

[split heart]

i just called it s for 'sequence'

[vast shale]

Ok

[split heart]

n is just an integer. Here it coule be 1,2,3,4,...

So

[vast shale]

Yip

But can I ask why is it n-1 and not n+1 and all that

thats what trips me up

[split heart]

Here $s_0 = 3, s_1 = 8, s_2 =13$ and so on

[twin meteor]

TooManyCooks

[vast shale]

Yep

[split heart]

the n-1 or n+1 doesn't matter

[vast shale]

is it always n-1?

[split heart]

they're called "dummy index"

you can always adjust them to whatever you like

it could be n

n+2

n-6

[vast shale]

oh ok

[split heart]

As long as you establish what the starting point is

In my case, I started with n = 0

s_0 = 3

[vast shale]

ya

[split heart]

so for n = 1

You plug in s_0

[vast shale]

its 8 right

[split heart]

Yes

exactly

[vast shale]

ok you plug in

s(0)

[split heart]

$s_1 = s_0 + 5$

[twin meteor]

TooManyCooks

[vast shale]

oh cool underline is subscript

[split heart]

Then if you want the next term in the sequence $s_2 = s_1 + 5$

[vast shale]

Ah ok

[twin meteor]

TooManyCooks

[split heart]

Then you just keep going

[vast shale]

so then 8 to 13 would be s3 = s2+5

[split heart]

Yep! You got it!

[vast shale]

so the equation is

hold on i need to write this out

[split heart]

Go ahead

[vast shale]

$s_n=s_{n-1}+5$

[split heart]

you wanna use "s_{n-1}"

[vast shale]

Ah ok

Lol

[twin meteor]

intracatholic

[vast shale]

how does texit work

[split heart]

It's just a programming language that's supposed to standardize the writing format for papers

As to "how" it actually works, you might wanna google that

[vast shale]

oh

its a programming language? that is a bit funny

[split heart]

It's not really like other language that are meant for calculations

it's for typesetting

Kinda like HTML

[vast shale]

what is typesetting

[split heart]

It's just a way things are arranged when something is being published. Usually journals or articles have a very particular format on margins, font, fontsize etc.

That's what Tex is for. It makes it easy for people to obey those rules

[vast shale]

oh

lol

so its like rich text

</i>

[split heart]

It's not just that. It makes it easy to obey format because you can download packages that arrange the words for you in certain orders

[vast shale]

oh nice

ok 2nd one

oops

[split heart]

haha

I will let you try that out first

What's the pattern

[vast shale]

4, -12, 36, -108

its a loopty loop

the pattern is -4

times

so s1 is 4

s2 -12

huh this is similar to quadratics

like domain and range

[split heart]

Are you sure about that?

think of it again

[vast shale]

yeah

i am sure

oh wait

its -3

😛

oh ew

i meant to send : P

not 😛

[split heart]

So write the recursion formula

[vast shale]

$s_n=s_{n-1}*-3$

[twin meteor]

intracatholic

[split heart]

You got it

Although I would write it as -3 s_(n-1)

[vast shale]

wait what

[split heart]

$s_n = -3 s_{n-1}$

[twin meteor]

TooManyCooks

[split heart]

that's all i meant

[vast shale]

ohh

ok

[split heart]

I think you got it

Let's do geometric sequence next

[vast shale]

ok hold on

i need to writtle this down

[split heart]

Take your time

[vast shale]

wait what does it mean by describe the sequence

[split heart]

what you just did

"add 5"

"multiply by -3"

[vast shale]

lol!!

[split heart]

mathematically, describing the sequence is writing the formula

[vast shale]

lel

[split heart]

You're doing pretty good

[vast shale]

number 3 is confusing

it went from +4, to +6, to +9

[split heart]

8 12 18 27?

[vast shale]

yeah

s1 = 8

s2=12

so it added by 2 then 3

confused

[split heart]

Here's the trick

When in doubt, you want to check one of two things

the difference between the terms

or their ratio

or a combination of both

[vast shale]

what do you mean by that

[split heart]

You checked the difference

[vast shale]

yep

[split heart]

You said it goes +4, +6, +9

[vast shale]

yeah

[split heart]

So there's no clear pattern there

[vast shale]

yeah

[split heart]

Try taking the ratio

[vast shale]

ratio?

[split heart]

take 12/8

then 18/12

then 27/18

[vast shale]

oh

12 div by 8 is like

1.5

[split heart]

ok

what's the next one

[vast shale]

then 18/12 is like 1.5

then 27/18 is 1.5

let me write that down in my study notes

also man im in 8th grade

too young for algebra 1

ok now

how would I write that

goodness gracious my spelling

anyway

would i write that as 1.5*s(n-1)

[split heart]

This particular flavor of sequence is called a 'geometric sequence'

In this particular case the sequence is $s_n = 8\left(\frac{3}{2}\right)^n$, where n start from 0

[twin meteor]

TooManyCooks

[split heart]

so s_0 = 8

s_1 = 8* 3/2

s_2 = 8 * (3/2)^2

and so on

[vast shale]

my goodness you are some type of recursive formula genius

[split heart]

nah this is just practice

you see patterns easily when you know what to look for

[vast shale]

Ok

so i just need to times s0 by the ratio

however many times I do that is determined by N

Wait hold on

is it to the POWER or multiplied?

why to the power?

[split heart]

Because to get to the next term, you multiply the previous one by the same number

here you keep multiplying with 3/2

so every new term in the sequence is another power of n

[vast shale]

i dont get it

[split heart]

Which part?

[vast shale]

why is it to the power

your explanation didnt really make sense to me

[split heart]

I see. so you don't know the relationship between products and exponents?

[vast shale]

I guess not

[split heart]

That's fine

All you need to know is that if you multiply something by itself several times, you can write it as an exponent

For example $a \times a \times a = a^3$

[twin meteor]

TooManyCooks

[vast shale]

yea

[split heart]

Okay so in your sequence you have $s_0 = 8 \ s_1 = 8 \left(\frac{3}{2}\right) \ s_2 = 8 \left(\frac{3}{2}\right)\times\left(\frac{3}{2}\right)$ and so on

[twin meteor]

TooManyCooks

[split heart]

Do you agree?

[vast shale]

wait

[split heart]

Recursively, the formula is $s_n =\frac{3}{2} s_{n-1}$

[twin meteor]

TooManyCooks

[vast shale]

i think i doubted you because I thought 2.25 would have

a decimal outcome when mult by 8

[vast shale]

so thats my actual answer

[split heart]

Okay

I just expressed the answer in terms of $s_0$

[twin meteor]

TooManyCooks

[split heart]

You can write it the way you did too

[vast shale]

is it just me or is it supposed to be 3/2^sn-1

[split heart]

What do you mean?

[vast shale]

its supposed to be 3/2 to the nth power right

[split heart]

You can write it that way

If you write it in terms of $s_0$, you get $,s_n = s_0 \left(\frac{3}{2}\right)^n$

[twin meteor]

TooManyCooks

[split heart]

If you write it in terms of $s_{n-1}$, you get s_n =\frac{3}{2} s_{n-1}$

[twin meteor]

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

[split heart]

They both give the same sequence

Just different way of saying the same thing

[vast shale]

oh how

[split heart]

What do you mean

[vast shale]

how is 3/2*s_n-1 equal to 8(3/2)^n

[split heart]

$s_n =\frac{3}{2} s_{n-1} = \left(\frac{3}{2}\right)\left(\frac{3}{2}\right) s_{n-2} = \left(\frac{3}{2}\right)\left(\frac{3}{2}\right)\left(\frac{3}{2}\right) s_{n-3}$

[twin meteor]

TooManyCooks

[split heart]

Eventually you will reach $s_0$ but by that point you will have 3/2 multiplying itself n times

[twin meteor]

TooManyCooks

[vast shale]

OH

OK

YOU FORGOT THAT LITTLE DETAIL

THANKS

sorry for caps

that wasnt to be mean

I just unlocked more realization

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

@split heart

[split heart]

yes?

[vast shale]

So my equation is

s_n=3/2*s_n-1

[split heart]

ok

that's right

[vast shale]

But how does the equation work

I dont get it

oh wait

oh so i just multiply the terms by 3/2 and i get the answer

Ok

moving on to 4 ill try to do it on my own

[vast shale]

placeholder text

[split heart]

Good. I'm about to do something else right now, but I'll try to keep tabs on your work if you need help. If I don't respond in more than 10 minutes, DM me

[vast shale]

Hey

what the flip is an arithmetic

like in recursive

ik arithmetic as only basic math like multiplication, division, addition, and subtraction

[split heart]

It just means you add a fixed number to the sequence

Kinda like problem 1

Geometric is when you have to multiple by a number

like in the previous problem, you had to multiply by 3/2

[vast shale]

also, what is "common difference?"

[split heart]

Subtract the adjacent terms. If their difference is the same, that's it

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

Channel closed

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• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[vast shale]

need help understanding these two truth tables. Quick questions on discrete mathematics

[restive tundra]

What don't you understand about them?

[vast shale]

are we able to call so its easier to ask?

i'd really appreciate it

[restive tundra]

I actually don't have a mic sorry

[vast shale]

okay ill try my best to ask properly

wait i think i got it sorry

i was lookin at it the wrong way

[restive tundra]

wd, nw

[vast shale]

btw are you a cs major?

[restive tundra]

No I do maths but I have done quite a bit of logic

[vast shale]

is there any resource i could use online to help me better understand discrete math?

[restive tundra]

Idk sorry, I learnt from lectures and lecture notes, I realise that's not much help

[vast shale]

no no you're good

[restive tundra]

Good luck

[vast shale]

i understand these things intiutively but when it comes to articulating on a piece of paper

i have a hard time

[restive tundra]

Yeah ik what you mean, it's definitely a skill

[vast shale]

how do i close help?

!close

[vocal sleet]

@vast shale Has your question been resolved?

Channel closed

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

Can someone help me here? I’m confused how I got an answer with a non elementary integral

[twin meteor]

Jérémy

[near relic]

that

[flat whale]

,w int log(log(x))dx

[twin meteor]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[flat whale]

You treated x like a constant. That's incorrect

[near relic]

but isn't it treated in terms of x because I'm integrating in terms of u?

[flat whale]

You didn't do the substitution correctly

x = e^u

[near relic]

how so?

[flat whale]

Step 1

[near relic]

but that just means x = x no?

[flat whale]

That's also true

u = u too

[near relic]

I'm confused as to where this is getting at.. At what point did I mess up?

[flat whale]

But you're not substituting correctly if you're only picking some variables to substitute and not others

[flat whale]

.

[flat whale]

You have to replace x with this

[near relic]

u = ln(x)

du/dx = 1/x

dx/du = x

dx = xdu

In here?

😵‍💫 I'm so confused

[flat whale]

This is right so far

But you need to replace x in terms of u

[flat whale]

.

[near relic]

Oh so I can't have x's remaining

[flat whale]

Yes that's right

[near relic]

how did you find that x = e^u though?

[flat whale]

.

Solve for x

[near relic]

oh right

so instead I should end up with the integral of ln(u) * e^u du

and now I have to do integration by parts which is probably where the "Non elementary" stuff happens

I understand now, thanks!

.close

[vocal sleet]

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

hello

I don't understand this question

well i have gathered some information

[rugged orchid]

Do you know polynomial long division

[upbeat plaza]

Well yeah and the factor/remainder theorem as well

[rugged orchid]

Well we need to construct our cubic from the 3 roots

Divide it by x-1

And equate the remainder to 8 and find k

[upbeat plaza]

You mean like If f(2)=expression provided

[rugged orchid]

At least that’s how I would do it

[upbeat plaza]

sorry

f(2)=0

[rugged orchid]

No I mean a cubic with roots a b c can be rewritten as (x-a)(x-b)(x-c)

[upbeat plaza]

and substitute 2 into the expression=0

let me send a pic wait

@rugged orchid I don't get it

[rugged orchid]

You’ve been given the 3 roots

[upbeat plaza]

Can you do it in that way?

[rugged orchid]

They are 2, 3 and k

[upbeat plaza]

Like I haven't heard of the method you're talking

instead i substitute f(x)=0

but i know how to divide polynominals

[rugged orchid]

I don’t know what that’s doing (but it’s possible I don’t know your method that can work)

[upbeat plaza]

ok but u can teach me ur method

[rugged orchid]

It’s very possible I don’t know the best way and maybe there is one

But I would go (x-2)(x-3)(x-k)

Expand

Long division by x-1

Equate remainder to 8

[upbeat plaza]

why x-2

wait

i know how to do it

but i don't get it why it should be x-2

[rugged orchid]

Those are the roots of the cubic

2, 3 and k

[upbeat plaza]

but they didn't say roots of cubic though?

Sorry i am new to this chapter

[rugged orchid]

They said roots of f(x) = 0 are 2, 3, and k

[upbeat plaza]

yeah?

ok

@rugged orchid ?

[rugged orchid]

Well then the cubic has this form

[upbeat plaza]

and then what did you do

[rugged orchid]

Lol keep reading

I wrote out my steps

[upbeat plaza]

oops sorry

[rugged orchid]

This is the next step after writing the cubic in that form

[upbeat plaza]

but my teacher haven't thought me any method to involve anything in the dividend with variables

Like the dividend can only have the variable of x

it can be long but there should be only variable which should be x

[rugged orchid]

Well 2, 3, 5, 10, k, same thing

[upbeat plaza]

tbh i get what you're trying to say

and i know how to work it out

but I don't get the concept of why it should be (x-2)(x-3)(x-k)

Why should i subtract it

[rugged orchid]

Okok wait

I’ve been told that there is a much easier way

I’m so sad I missed it

[rugged orchid]

But this is still the correct first step

[upbeat plaza]

the way you said is easy as well but i don't know why it should be negative

[rugged orchid]

Well think about it

If my function f needs to be 0 at 2

[upbeat plaza]

please

[rugged orchid]

ie. f(2) = 0

[upbeat plaza]

ok

i get it

thanks

[rugged orchid]

I just need to slap a (x-2) somewhere

[upbeat plaza]

I get it

let me try and let you know

[rugged orchid]

Anyway, the easy method is just to do f(1) because that does the same thing as dividing the polynomial by x-1

[upbeat plaza]

yeah

and?

[rugged orchid]

You can just do f(1) = -8

[upbeat plaza]

and then what should i do after i solve it

[rugged orchid]

Using this

[rugged orchid]

You can just solve this is equal to -8 when x = 1

[upbeat plaza]

yeah yeah ik how to solve

a+b+c=-9

[rugged orchid]

So you’d write f(x) = (x-2)(x-3)(x-k) because you know the cubic looks like this

[upbeat plaza]

this is the answer i got

[rugged orchid]

Then you have f(1) = -8

So just plug them in and solve for k

[upbeat plaza]

@rugged orchid This is the answer i got

for solving f(1)==-8

[rugged orchid]

Where did a + b + c come from

[upbeat plaza]

by solving f(1)=-8

Hey?

[rugged orchid]

Yes

Where does a b c come from

[upbeat plaza]

from the expression f(x)=x^3+ax^2+bx+c

[rugged orchid]

Don’t worry about that expression

[rugged orchid]

Worry about this

[vocal sleet]

@upbeat plaza Has your question been resolved?

[vocal sleet]

Channel closed

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[vocal sleet]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[honest heath]

$e^{e^{\ln\pi+\frac{i\pi}{2}}}$

[twin meteor]

goobybalooby

[honest heath]

how can i simplify this and express it as a point in polar?

[paper depot]

well you could just work downward couldnt you

like

$e^{\ln(\pi) + i\pi/2} = e^{\ln(\pi)} \cdot e^{i\pi/2}$ ...

[twin meteor]

Ann

[honest heath]

i have that but as an exponent on e

[paper depot]

and?

that shouldn't stop you from manipulating it the way i showed you

unless you have some kind of weird allergy

[honest heath]

right i have that, sorry

i have...

$e^{\pi e^{\frac{i\pi}{2}}}$

[twin meteor]

goobybalooby

[honest heath]

but i need to do more to it to find the polar coordinates, right? or am i being dumb

[paper depot]

what's $e^{i\pi/2}$?

[twin meteor]

Ann

[honest heath]

$[1,\frac{\pi}{2}]$

[twin meteor]

goobybalooby

[paper depot]

ok but what number has magnitude 1 and angle pi/2?

[honest heath]

i, right?

ohhhhh i see

shit

thank you very much lol

.close

[vocal sleet]

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[vast shale]

Can someone help me? I'm stuck on this

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

@vast shale Has your question been resolved?

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[tidal trail]

Y is it not
A < x < C ?

[ornate ember]

Because you have an inflection point at b, which means it’s no longer concave up

From B to C it’s increasing but it’s concave down

[tidal trail]

Ah I see
Thanks :)

.close

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[hollow acorn]

.open

[hollow acorn]

Given points ABCD, I need to solve for t in A+t*AB, where B reaches collinearity with CD

[vocal sleet]

@hollow acorn Has your question been resolved?

[hollow acorn]

Nvm figured it out. If anyone cares the solution is cross(CD,{0,1,0} to get the perpendicular vector for CD, t = dot(C - A, CD_perp) / dot(AB, CD_perp)

.close

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[upbeat plaza]

PLEASE HELP

[upbeat plaza]

from what my teacher said i have to make it (x-2)(x-3)(x-k) and then solve it.

[fathom drum]

evaluate f at 2

you know the result is going to be 0, by the Factor Theorem

do the same for 3 and k

[upbeat plaza]

is what my teacher said and ur method the same?

[fathom drum]

only slightly different

[upbeat plaza]

I evaluated f(2) and I got 4a+2b+c=-8

[hybrid flicker]

What you're suggesting is unnecessarily complicated

[fathom drum]

Ok

[upbeat plaza]

just teach me guys

[hybrid flicker]

Keep the closed form

[upbeat plaza]

ok and then

[hybrid flicker]

This is a very good factored form

We know the remainder by (x-1) is -8

[upbeat plaza]

so i just leave it (x-2)(x-3)(x-k)

[hybrid flicker]

Yep

[upbeat plaza]

Yeah

[hybrid flicker]

And so if you evaluate at x = 1, what should you get?

[upbeat plaza]

like i substitute x=1 in the first expression like f(1)=-8?

[hybrid flicker]

Yes it's substitution

But not in the first expression

[hybrid flicker]

In this one

[upbeat plaza]

Sorry my bad in the closed one

[hybrid flicker]

Yes, factored form

[upbeat plaza]

(1-2)(1-3)(1-k)
=(-1)(-2)(1-k)
=(2)(1-k)
=2-2k

[hybrid flicker]

Yes

[upbeat plaza]

and then what should i do

[hybrid flicker]

What is this also equal to?

This is f(1)

[upbeat plaza]

-8

[hybrid flicker]

Yes!

[upbeat plaza]

so

it is gonna be

2-2k=-8
8+2=2k
2k=10
k=5?

[hybrid flicker]

Correct !

[upbeat plaza]

oh my gosh! Thank you so much

i was cracking my brain entire day and everyone was teaching me all those complicated ways

thank you so much!!!!!

: )

[hybrid flicker]

No problem 👍

[upbeat plaza]

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[river kettle]

How do I do this?

[livid tapir]

🅱️ythagorean theorem and if you need the direction also then trig

[fathom drum]

do you understand what the question is asking

[river kettle]

So do I connect the vectors tip to tail or something?

[fathom drum]

yes

and then compute the magnitude and angle

[river kettle]

What angle am I looking for?

[fathom drum]

That is the magnitude

the one adjacent to 70

[river kettle]

Like this?

@fathom drum ?

[fathom drum]

yes

[river kettle]

Okay

[fathom drum]

not quite

you’ve double counted the tan

[river kettle]

So I got the measurements wrong?

[fathom drum]

no, it should either be tan theta is 55/70, or theta is arctan 55/70

but not both

[river kettle]

Oh ok

By the way

Would I need to answer this in just degrees or minutes and seconds type stuff

[fathom drum]

should be just degrees

[river kettle]

So I’ve found both the hypotenuse and angle

How do I write my answer

Like do I say relative velocity, 89 kph, 36 degrees or something idk

[fathom drum]

you’d write 89 kph with 36.25 deg west of north or something

[river kettle]

Okay cool

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[viscid sparrow]

hello, i dont understand how the square root of x turned into 2x

[timber cypress]

Original question please

Anyways

The multipled 2√x on both numerator and denominator

Fo2√x

[viscid sparrow]

ahhh thank you

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[river kettle]

The left is a solution to the question on the right but my working out I got this

Where do they get the bearing stuff?

[paper depot]

,calc atan(55/70) * 180/pi

[twin meteor]

Result:

38.157226587369

[paper depot]

think you fucked up somewhere with the arctan

[river kettle]

I must’ve read something wrong or put something wrong into the calc then

[paper depot]

you would have given the bearing as N38W, which is the same as their 322°

[river kettle]

How are these the same?

[paper depot]

they measure bearing as a clockwise angle from north

0 to 360

like there are two formats you can give bearings in

either (N/S)(0-90)(E/W), or as that

converting from one to the other requires little more than looking at, or being able to reproduce, a compass rose.

[river kettle]

oew

So If i gave my answer in

N38degW

i would still be correct?

[paper depot]

best ask your teacher what form they want it in.

like value-wise you're correct, it's only a question of which two otherwise equally valid forms is the one wanted

and whether they even care

in the absence of special instructions requiring the answer to be given one way or the other, i personally would accept either one.

[river kettle]

well its a late for that since my 2 week exam block is coming up and we dont have anymore classes

my teacher said they purchased this test off of somewhere

so it probably has different marking guidelines

[paper depot]

do you not have contact w your teacher via email

[river kettle]

well I do

ig i can email her. is it worth it over this?

[paper depot]

why not?

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[fossil python]

hello, why can't i just eliminate the middle portion of the domain? the first first and last part already excludes 4 and 5 right?

[paper depot]

what's your function

is it something like 1/((x-4)(x-5))?

[fossil python]

yes

my bad left that out lol

[paper depot]

and you claim (4,5) should be thrown out of the domain too, yes?

[fossil python]

yes

so itll just be (- infinity, 4) U (5, infinity)

is this not the same?

[paper depot]

but why throw it out tho

what's wrong with values of x lying strictly between 4 and 5?

[fossil python]

ohhhhhh

okay i get it now

ty

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[pale nova]

Absence - for example a number
Absence rate - in %
Right?

For example a student attended 10 times but absence 4 days, then you would find how many % 4 of 10, and then it’s 40%, so 100% - 40% = 60% absence RATE does the word rate mean like this?

[paper depot]

60% is the attendance rate.

the absence rate is 40% as you say.

[paper depot]

wait hold on sorry

bad calculations or bad phrasing

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[dapper lotus]

Have I done right so far? How Do I continue?

[somber portal]

We need extra data.
What's the mass of the sun?
What's the mass of a hydrogen atom and of an helium atom?

[dapper lotus]

I use this reference

I feel like I get too small number in the first energy equation

[somber portal]

i'm not getting that on the first line, i'm getting 4.815563291 * 10^-29 kg

[dapper lotus]

Hmm, you mean youre getting that instead of my 4.3229 x 10^-9 ?

[somber portal]

no, on the first line. As in mass diff

per fusion

[dapper lotus]

Oh. How did you calculate? I

Im interested in the total energy released per pp Chain

They did similar here

Could this be correct? @somber portal

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[random wave]

Hello, I have a question about finding a limit of the exponential function of base e.
I don't know how to start from $\forall x \geq 1, \frac{e^{x/2}}{x} \geq \frac{1}{2}$ and somehow end up with $\frac{e^x}{x} \to \infty$ when $x \to \infty$, but it's asked in the exercise. All the ways I would see to find the limit doesn't use that inequality whatsoever, so that makes me be stuck on my side for a bit now ... Does anyone have an idea of how to tackle this ?

[twin meteor]

Epsilia aka Mellow

[worthy citrus]

do you have a picture of the question at hand

[random wave]

I prefered not to since it was all in french ...

[worthy citrus]

its still worth it, we can translate

just helps to see it in its context

[random wave]

Okay okay I see !

Welp here I come

So the 9. (a) asked to determine the equation of the tangent of exp at (0,1), then to justify that the curve representation of the exp function is always below this tangent, then deducing the limit in +inf and -inf of the exp function

The 9. (b) then asks, by using previous results, that I explicit a certain constant a(lpha) > 0 such that for all x >= 1, we have this inequality I wrote before

Here, I used the result from 9. (a). Translating it as an inequality on the values of y=e^x and y=1+x (equation of the found tangent), we get that for all x real, $e^x \geq 1+x$

[twin meteor]

Epsilia aka Mellow

[random wave]

I apply this inequality for the variable X=2x, still targets all the reals

Then factorized x from the RHS

I considered the inequality only for $X \geq 1$, granting me the division by X. I then get the easy chain of inequalities :
[
\frac{e^x}{x} \geq \frac{1}{2} + \frac{1}{x} \geq \frac{1}{2} > 0
]

[twin meteor]

Epsilia aka Mellow

[random wave]

And now I'm stuck on how to use that inequality I just found out for the result :
$\frac{e^x}{x} \to \infty$ as $x \to \infty$

[twin meteor]

Epsilia aka Mellow

[somber portal]

it would be 1/2+1/x > 1/2, since x>=1

[random wave]

Yeah it's really a detail, for now the problem really is not there

[somber portal]

i dont like how that "for now" sounded XD

[random wave]

I'm still stuck ._.

That's just how it's supposed to sound

OW

I think I just understood

Okay so

e^(x/2)=(e^x)^(1/2) = sqrt(e^x)

So $\frac{e^{x/2}}{x} = \sqrt{\frac{e^x}{x^2}}$

[twin meteor]

Epsilia aka Mellow

[random wave]

So the idea would be getting rid of the sqrt, the multiplying by x the inequality

[sterile forum]

Perhaps the idea is that since $\frac{e^{x/2}}{x} \ge \alpha$ you have $\frac{e^x}{x} \ge \alpha e^{x/2}$?

[twin meteor]

Troposphere

[random wave]

Oooooow that's a good idea

(I dunno if mine is good )

[sterile forum]

The whole thing feels rather roundabout to me no matter how we slice it ...

[random wave]

But you're right though, as long as we have a divergent function to inf as a function below what we're studying

Then we get the divergence of the other one as well

Would you confirm this as a valid proof too then?

@sterile forum

[sterile forum]

Looks valid, yes. Would probably be easier to read if instead of the square root you simply square both sides of the original inequality and then multiply by x.

A benefit of your approach over mine is that it's more immediately clear that x/4 goes to infinity, than that e^{x/2}/2 does so.

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[random wave]

The divergence of the exp function has already been shown before so np np !

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[elder obsidian]

help

[elder obsidian]

what is this symbol D, Df(x) and Df(1-x)?

[uneven basin]

Determinant.

It's Sarrus's rule

[elder obsidian]

what does determinant do?

[uneven basin]

The determinant of A is the scalar denoted det(A) defined as the determinant of the family of column vectors in the canonical basis of Kn.

(A is a square matrix)

More clearly

It's a scalar which as property in regard to the matrix

[whole birch]

help

[elder obsidian]

ahh ok

so if i learn matrix, i can understand?

[uneven basin]

Ok:

• reslove the equation n(n-1)>=20 Not that hard.

[uneven basin]

Yep

Determinant are used in more thing than just matrixes

But learning whta determinant are is required to aboard matrix for higher levels

So

[elder obsidian]

i am grade 10 :((

[whole birch]

im in 11th

[whole birch]

oh

[uneven basin]

Well don't worry

For me I learned what determinant were after that

[elder obsidian]

wow

ok thanks for that

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[golden kite]

so anyone here can provide an answer about this sign: ➗️
i would like to know the exact meaning of it

[soft walrus]

$a\div{b}=\frac{a}{b}$

[twin meteor]

MrFancy

[whole birch]

isnt this sign is used for division?

[golden kite]

yes that what i have been taught but some people doesn't see it that way

[viral copper]

Deprecated from 4th grade onwards

[golden kite]

for example here
8➗️4(2+2)=?

[viral copper]

1/2 for PEMDAS and 8 for BODMAS

Whatever you follow

[golden kite]

so the answer of the above can be either 1 or 16?

[viral copper]

wat

[golden kite]

this

[viral copper]

I just gave you the answers

[golden kite]

alright thanks

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[exotic delta]

Using the replacement rule, show that each of these conditional statements is a
tautology. Conditional statements can help to simplify the statements below.
a. [~p ∧ (p ∨ q)] → q
b. (p → ~q) ∨ (~r → p)

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[scarlet garden]

I did the problems, but I just am confused on what they mean by defining vectors and matrices

[livid tapir]

Honestly not sure. Maybe it's asking you to give them variable names?

I'm assuming you already wrote out the matrices and vectors

[scarlet garden]

I see ty I’ll figure smth out ig

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[vast shale]

For this problem https://i.imgur.com/r5Xwv9s.png you need to find an equation for the volume of water at time t. The equation is 9(h(t)^2), but how is that? I honestly have no idea how this was achieved lol

[teal topaz]

So to solve this you find the area of the right triangle

and then multiply by 9

Except you can't really find the area of the triangle without at least 1 other measurement

[vast shale]

So then h(t)^2 or height squared = area of the right triangle. As far as I know the area of a right triangle is 0.5bh, so how does h(t)^2 even fit in?

[teal topaz]

So for 0.5bh, that would actually be the volume of a triangular prism

if we make it 0.5lw then it would be the volume, but I guess it's kind of the same thing

Since this is an isosceles right triangle, the right angle obviously is 90 degrees (right), but that makes the other 2 congruent (isosceles), making for the angles 90, 45, and 45

[vast shale]

Just realized that was only the cross section not the actual trough- read your questions thoroughly kids aint no way I spent more than 5 minutes on this 😭

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[vast shale]

how do i turn the quadratic formula into turning point formula

[meager dock]

Formula for x coordinate of a turning point is -b/2a

If thats what you're asking

[vast shale]

oh i see but how do i get the f(x) = -2x + x + 1 into the a(x+p)^2 + q format

[pale perch]

you would first factor out the coefficient of $x^2$ to get $-2[x^2-\frac{x}{2}] +1$

[twin meteor]

AℤØ

[meager dock]

"+p" in "(x+p)^2" is the amount of units you shift your graph on the axes

So if you want to shif it 2 units to the right, you'd use (x-2)^2

[vast shale]

oh yea i see now

[meager dock]

"+q" is the same, just for the y axes

And "a" is how much you stretch(or shrink) your graph

[vast shale]

thank you

[meager dock]

So in your instance it would be something like f(x) = -2x^2 + x + 1 --> g(x) = -2(x+5)^2 + x

[vast shale]

thank you so much 🙏

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[snow narwhal]

did I do this correctly?

[flat whale]

,w diff (4+e^x)^6 / 6

[twin meteor]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[flat whale]

Yes

[snow narwhal]

thanks, can I ask something else

so the part where I cancelled out the e^x and the e^x

was this decision correct? Because someone told me earlier that it was wrong to do so in a different problem

[flat whale]

Algebraically it's fine. Mathematically, no. Up to the rigorous standard your teacher expects of you

[snow narwhal]

specifically this problem

[flat whale]

Oh that

No

[snow narwhal]

I don’t understand

[flat whale]

e^x * e^x = e^(2x)

[snow narwhal]

oh I see now

since before it would be multiplying

instead of cancelling out

it’s still possible to continue after the e^2x right?

I’m having trouble visualizing the way I wanted to solve it

[flat whale]

You should be writing the integral in terms of x and not u

You have to replace all x variables with u at once, not in multiple steps

Write e^x in terms of u

[snow narwhal]

This is what I did instead

but I do feel more comfortable the other way

ty tho

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[wanton cairn]

Trapezium/Geometry question

A trapezium ABDC is shown. Its base AB has a length a, its height is h and CD has length b. E and F are at the midpoints of AD and BC respectively. Find EF in terms of a and b. (I'm not sure where to start, I thought perhaps vectors could help but that's only a guess)

[turbid forum]

you should be able to set up similar triangles

what i did was label the intersection of CB and AD as G, then use similarity between GEF and GAB

@wanton cairn

[wanton cairn]

Ohhh ok can you give me a sec to think about this

I understand the similarity but im not sure what to do next

Could I say EF/AB = GF/GB

Im not sure what the next step is

EF = a(GF/GF*2) ?

does that make EF = 1/2 a

@turbid forum (sorry for the ping)

[turbid forum]

oh, sorry for not seeing the messages

[turbid forum]

where did you get this equation?

[wanton cairn]

EF/a = GF/GB ?

[turbid forum]

what i did was calculate GE in terms of AD, then compare it to AG to find GE/AG which i could use to find EF/AB

[wanton cairn]

EF = a(GF/GB) = EF(GF/GF*2) (since g is the midpoint of CB)

[turbid forum]

g is not the midpoint of cb

f is

[wanton cairn]

oohh oops

[turbid forum]

i set AD to be, say, x, then found GE by subtracting ED and GD

ping me if you make any progress lol

[vocal sleet]

@wanton cairn Has your question been resolved?

[turbid forum]

should i like show you my work?

[wanton cairn]

Yes please im so confused

I understand the similar triangles but I'm not sure how to work out GE in terms of AD

[turbid forum]

Hopefully this is correct lol

[wanton cairn]

How did you get GD = b/a+b *x ?

[turbid forum]

so x is obviously AD

but because of similar triangles we know AG to GD has to be a to b

and that AG+GD = x

so from there you can solve

but it's helpful to just sort of memorize that relation

[wanton cairn]

I understand the rest of your steps but can you explain why GD = b/a+b * x

btw tysm for your help so far

you've been so helpful

[turbid forum]

do you understand why AG to GD is a to b?

[wanton cairn]

umm no not really

[turbid forum]

since angle CGD = angle BGA and because of parallel lines GAB = GDA and GDC = GAB, we know triangles GBA and GCD are similar

by AA basically

[wanton cairn]

Ohh ok I understand that now 👍

Wait but how does that mean AG to GD is a to b?

[turbid forum]

if they're similar the sides have to also be in the same ratio

and AB corresponds to CD in the similarity statement

[wanton cairn]

Ohh ok I see

But how does GD = b/a+b * x

[turbid forum]

we know AG+GD = x

so we can like solve if we want to

GD = b/a * AG, substitute and solve

(1+ b/a) times AG = x
(a+b)/a times AG = x
AG = a/(a+b) * x

[wanton cairn]

Ohh ok I think I understand now

Ohhhhhh I see how you got the solution now

Wow that makes a lot more sense now

Then you can do EG/AG to get the ratio between the similar sides and apply it to EF/a to get (a-b)/2

Tysm for your help

I really appreciate it ♥️

@turbid forum

[turbid forum]

of course!

[wanton cairn]

Thanks once again for your time ik it took really long haha

.close

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[vast shale]

Is it minutes cause it wouldnt make sense to be 6hour.40hour but it would make sense for it to be: 6hour.40 mins and also because 1hr and 10 mins would be 1hr.10mins? I didnt know after the point of an hour, it represents minutes

[vast shale]

Is this how it is?

[spiral inlet]

I'm not sure I understand your question but 6⅔ hours is 6 hours 40 minutes

[granite oxide]

What does “.” mean

[vast shale]

I never knew that

[vast shale]

Thanks and u too @granite oxide

.close

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[delicate totem]

.

[lament grail]

Im just confused on how to do this

so far i converted the tan into sin/cos

thats about it

[ornate ember]

can you use L'Hopital's rule? you have the 0/0 form

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@lament grail Has your question been resolved?

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[fresh cove]

This is the Vandermonde matrix

My question is

How can I prove it invertible by changing the basis of the family of interpolating Lagrange polynomials to the canonic base
towards the canonical base.

[flat whale]

Why do you need to do that at all

Can't you just prove its determinant is nonzero

[fresh cove]

Well

The problem is about this

I have to prove it invertible by using two methods

[flat whale]

Can you just show the original problem/question with screenshot or pic

[fresh cove]

I have it but in French

The first method is using the kernel

And I did it

[fresh cove]

But im stuck here

Here’s the problem

Im stuck at 1/b

<@&286206848099549185>

[chrome rock]

i only can read english

[fresh cove]

Okay I’ll use translation for 1)b
Here we have the vandermonde matrix I have to prove it invertible by using the change of basis matrix of the family of interpolating lagrange to the canonic basis

<@&286206848099549185>

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[ashen patrol]

I think the answer to this question is yes since every single point on one function is also on the other function. Therefore every point would be invariant right? I also cant think of a reason it could be wrong

[ashen patrol]

<@&286206848099549185>

[nocturne spade]

!15m

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<@&286206848099549185>

[ashen patrol]

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[sharp atlas]

I need help with this

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[safe sedge]

gcf/hcf of 1800 and a is 180, dumb question but its confusing me

[craggy coral]

a=2^23^25

[safe sedge]

still confused 😭

[craggy coral]

Sorry a=(2^2)x(3^2)x(5)

[safe sedge]

i need to find out a and b, not change the numbers in the sequence, im pretty sure

<@&286206848099549185>

[spiral inlet]

is that really meant to be 33 in the middle?

if so, it's not factored completely

are you sure you didn't mean 3^3?

[safe sedge]

this the og question

[spiral inlet]

that has to be a mistake