help-0

[sour mica]

√(2/3)x - 4 = y+4-4

or √(2/3)x -4 = y

$\sqrt{\frac{2x}{3}} - 4= y$

[ocean seal]

Bacter10Fr4g is not fr0g

[sour mica]

which you can rewrite as

$y = \sqrt{\frac{2x}{3}} - 4$

[ocean seal]

Bacter10Fr4g is not fr0g

[alpine sable]

√(2/3)x = √(y + 4)^2 = y + 4
√(2/3)x = y + 4
√(2/3)x - 4 = y?

[sour mica]

yes

[alpine sable]

That's the answer?

[sour mica]

yes

this new y obtained this way is the inverse function

[alpine sable]

YES

f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
(2) x = 3(y + 4)^2/2 (2)
2x = 3(y + 4)^2
(2/3)x = (y + 4)^2
√(2/3)x = √(y + 4)^2 = y + 4
√(2/3)x = y + 4
√(2/3)x - 4 = y
f-1 (x) = √(2/3)x - 4

OH MY GOSH

Next.

[sour mica]

plot that

[alpine sable]

1. MIKE and his friend are playing a number - guessing game. MIKE asks his
   friend to think a positive number, then add four to the number. Next, square the
   resulting number, and multiply the result by 3. Finally, divide the result by 2. If
   you are his friend and you get a result of 50,
   (a) write an inverse function that will give you the original number and
   (b) determine the original number.
   (c) graph

[sour mica]

oh, put x = 50

in the inverse function

[alpine sable]

Huh?

So.. f(50)?

[sour mica]

f-1(50)

[alpine sable]

oh

(a) f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2

(b) (2) x = 3(y + 4)^2/2 (2)
2x = 3(y + 4)^2
(2/3)x = (y + 4)^2
√(2/3)x = √(y + 4)^2 = y + 4
√(2/3)x = y + 4
√(2/3)x - 4 = y
f-1 (x) = √(2/3)x - 4

(c) ...

[sour mica]

no no no

all that was only (a)

[alpine sable]

JUST A!?

[sour mica]

We are on to (b) now

[alpine sable]

(a) f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
(2) x = 3(y + 4)^2/2 (2)
2x = 3(y + 4)^2
(2/3)x = (y + 4)^2
√(2/3)x = √(y + 4)^2 = y + 4
√(2/3)x = y + 4
√(2/3)x - 4 = y
f-1 (50) = √(2/3)x - 4

(b)

(c) ...

[alpine sable]

Is it that table?

[sour mica]

yes

[sour mica]

wdym?

you just have to calculate f-1 (50) using this function f-1 (x) = √(2/3)x - 4

whatever that ugly number is, is the original number

[alpine sable]

Is that correct?

[sour mica]

YES

[alpine sable]

B!!

So what's B?

[sour mica]

You have to calculate the inverse, to find the original number

[alpine sable]

How-

[sour mica]

you just have to calculate f-1 (50) using this function f-1 (x) = √(2/3)x - 4

[alpine sable]

Hmm

Can I show you something?

Based on this example first

[sour mica]

Sure

[alpine sable]

That box

Is that letter b?

[sour mica]

That is for c

[alpine sable]

Then..

[sour mica]

c is graph

[alpine sable]

what do I do

[sour mica]

put 50 in place of x, and calculate the expression

[alpine sable]

f-1 (50) = √(2/3)x - 4

f-1 (50) = √(2/3)(50) - 4

[sour mica]

yes

[alpine sable]

Damn idk how to fraction

[sour mica]

idk? just leave it as is

for exam times

or use a calculator for homework, but keep the fraction too

[alpine sable]

So that's the answer?

[sour mica]

yes

[alpine sable]

can't I try solving it?

Is that really the answer

[sour mica]

I mean there isnt really a way to simplify it

[alpine sable]

So that's the answer?

[sour mica]

YES

[alpine sable]

OKAY-

(a) f(x) = 3(x + 4)^2/2
y = 3(x + 4)^2/2
x = 3(y + 4)^2/2
(2) x = 3(y + 4)^2/2 (2)
2x = 3(y + 4)^2
(2/3)x = (y + 4)^2
√(2/3)x = √(y + 4)^2 = y + 4
√(2/3)x = y + 4
√(2/3)x - 4 = y
f-1 (x) = √(2/3)x - 4

(b) f-1 (50) = √(2/3)x - 4
f-1 (50) = √(2/3)(50) - 4

(c) ...

[sour mica]

do this thing

[alpine sable]

okeh ez

Imma send it to you when Im done

:3

[sour mica]

Sry, I gotta go out. Maybe someone else might come around and help

good luck

[alpine sable]

THANK YOU SO MUCH

AND IM SORRY FOR ALL CAPS

hehe :3

Just gonna...

@cedar juniper Yoink

Hello?

[cedar juniper]

Huh?

[alpine sable]

Help me with math ples

[cedar juniper]

What's rhw question

[alpine sable]

Just needed to graph rn

It's Inverse Function

can you check it for me

[cedar juniper]

Seems fine

[alpine sable]

just need to do graph

[cedar juniper]

Manually?

[alpine sable]

yeah gonna send it to you once Im done

[cedar juniper]

Okay

[alpine sable]

Okay

@cedar juniper Do you know how to use demos?

[cedar juniper]

Yes

[alpine sable]

Doesn't work

[cedar juniper]

You have to do

(X,Y)

(1,37.5)

Or you could just type the function

[alpine sable]

How-?

[cedar juniper]

Wait

[alpine sable]

oh

@cedar juniper

It's not working

[cedar juniper]

You have to put it in the square root

[alpine sable]

how

[cedar juniper]

Rn there's nothing in the square root

Type

Sqrt

Then 2/3x

[cedar juniper]

Put x inside the bracket

Wait

S should be small

Type

sqrt

[cedar juniper]

.

[cedar juniper]

;-;

Just use the symbol then

And put the 2/3 x inside the root

[alpine sable]

Idk how

[cedar juniper]

√(2/3x)

[cedar juniper]

Put a bracket inside the root

And type

If you click there it will let You type inside

[alpine sable]

Can I see how

[cedar juniper]

.

[alpine sable]

Skibidi

[cedar juniper]

Put the 2/3 x inside the bracket inside the square root!

You can see the faint outline

[alpine sable]

CAN YOU JUST TYPE IT OUT

NOTHING IS WORKING

[cedar juniper]

√(2/3x)

Try this

[cedar juniper]

Huh

((2/3) x)^(1/2)

Try this

[cedar juniper]

Yea

Good job

[alpine sable]

That's it?

[cedar juniper]

Yup

[alpine sable]

For an Inverse Function, Is this suppose to look like Inverse Function? @cedar juniper ??

[cedar juniper]

Yes

See how it's rotated by 90 degrees

If you want the perfect graph

[alpine sable]

okie

Next problemmmm

WAIT

2.The SHS officers are planning for a SHS Prom. The allocated budget for decorations, sounds, and other miscellaneous expenses is ₱100,000.00 and an additional ₱1500.00 for meal expenses for each guest. The organization received an amount of ₱200,000.00 from its external
stakeholders.
a. Write the total allocated budget as a function of the number of guests.
b. Find the inverse of the function.
c. State the domain and range for this situation.
d. Find the possible number of guest for a budget of ₱200,000.00

@cedar juniper

Okie help me

[cedar juniper]

What are you struggling with

[alpine sable]

Most of them-

Idk how to do letter a

@cedar juniper

[cedar juniper]

add the money

[alpine sable]

which one-

[cedar juniper]

Readdd

They are getting 100k + 200k always

And 1500 per person

[alpine sable]

so..

100 + 200 (1500) ?

[cedar juniper]

Huh

Explain

[alpine sable]

wait

100,000 + 200,000 (1500)

because that money is how much people give in a day?

[cedar juniper]

Why are we multiplying 200000 and 1500

[alpine sable]

Because...

idk..

[cedar juniper]

Okay

Write the total budget as a function of number of guests

Let's assume the number of guests is x

And budget is y

If the budget increased by 1500 per guest

Y = ?

[alpine sable]

Isn't budget y?

Then 1500

[cedar juniper]

Just 1500?

What if there were 2 guests

[alpine sable]

...

1500 = 100,000 + 200,000

??

[cedar juniper]

...

[cedar juniper]

Read that in your head again

Does that seem right?

[alpine sable]

y = 100,000 + 200,000??

...

1500 = 100,000 + 200,000

[cedar juniper]

That's so close

[cedar juniper]

How did we get here from there

[alpine sable]

The budget is 1500...

[cedar juniper]

No ;-;

Read the question again and ping me

[alpine sable]

@cedar juniper 100,000 + 200,000/1500

[cedar juniper]

And this is the budget?

[alpine sable]

yes

[cedar juniper]

Why are we dividing now

[alpine sable]

To get the exact budget

@cedar juniper ???

[cedar juniper]

Bro wdym the exact budget

What is 1500

What does ₱1500 represent in this question

[alpine sable]

additional meal expenses for each guest

100,000 + 200,000

That's the equation??

@cedar juniper

[cedar juniper]

That's the fixed budget

[cedar juniper]

Yes so our budget will increase as we add more people

We need a function of x!

[alpine sable]

So..

x! = 100,000 + 200,000

[cedar juniper]

Are you being genuine or trolling

[alpine sable]

NO.

IM SERIOUS.

PLEASE

IM NOT GOOD WITH WORD PROBLEMS

[cedar juniper]

Give me a min

2.The SHS officers are planning for a SHS Prom. The allocated budget for decorations, sounds, and other miscellaneous expenses is ₱100,000.00 and an additional ₱1500.00 for meal expenses for each guest. The organization received an amount of ₱200,000.00 from its external
stakeholders.
a. Write the total allocated budget as a function of the number of guests.

Okay so you they give you a word problem

Write down what you know

miscellaneous expenses = ₱100,000

Amount from external stake holders = ₱200,000

Additional expenses per guest = ₱1500.00

Do you agree?

[alpine sable]

Yes

[cedar juniper]

Okay

Do you understand what this means

Write the total allocated budget as a function of the number of guests.

[alpine sable]

200,000 = 100,000 + 1500

[cedar juniper]

Bro

[alpine sable]

IM TRYING.

[cedar juniper]

Write in words what this means

I dont want the answer

Explain the question

[alpine sable]

It tells me to write the total buget for the number of guest

[cedar juniper]

Good job

Can we assume the number of guests as x?

[alpine sable]

Yes

[cedar juniper]

What would the additional budget be for x guests?

[alpine sable]

100,000

[cedar juniper]

Where did you get that from

Wheres the x

miscellaneous expenses = ₱100,000
Amount from external stake holders = ₱200,000
Additional expenses per guest = ₱1500.00

[alpine sable]

wait

1500

1500 = x

[cedar juniper]

Explain

[alpine sable]

Because it's getting the addition budget

and it says there additional

therefor

150,000

[cedar juniper]

Um

If they wrote

Miscellaneous budget is ₱100,000.00 and an additional budget ₱1500.00 for each guest. The organization received an amount of ₱200,000.00 from its external
stakeholders.

Is this easier to understand?

[alpine sable]

yes

[cedar juniper]

If the number of guests are x

What would the budget be

[alpine sable]

1500

[cedar juniper]

Literally sobbing rn

[alpine sable]

IM SORRY

[cedar juniper]

Lets say you are organizing your birthday party

You have saved up $100, your mom will pay you $5 for each friend you invite, your dad gave you an extra $50

If you were inviting 5 friends

How much money would you use

[alpine sable]

Easy

(100 + 5 + 50)/ 6

[cedar juniper]

Bro what

[alpine sable]

what?

[cedar juniper]

Where did the 6 come from

[alpine sable]

5 friends + you...

[cedar juniper]

Is this a language barrier?

[alpine sable]

what did I do wrong-

[cedar juniper]

Why are we dividing by 6?

[alpine sable]

5 FRIENDS

AND YOU

5 + 1

[cedar juniper]

WHY ARE WE DIVIDING

[alpine sable]

6

TO GET THE TOTAL AMOUNT

[cedar juniper]

WHAT DO YOU MEANNN

You have saved up $100, your mom will pay you $5 for each friend you invite, your dad gave you an extra $50
If you were inviting 5 friends

[alpine sable]

OF MONEY I WILL USE TO EACH FRIEND

[cedar juniper]

WE DONT NEED PER FRIEND

WE NEED TOTALLL

[alpine sable]

THEN 100 + 5 + 50

[cedar juniper]

We are so close

100 + 50 is correct

your mom will pay you $5 for each friend you invite

[alpine sable]

WAIT

(100 + 50) (5 x 5)

[cedar juniper]

We were so close

[cedar juniper]

Explain

[alpine sable]

I have 100 dad gave me 50

Mom is giving me 5

to spend it on each friend

Therefor, 5 x 5

[cedar juniper]

All of this is correct

Why did we decide to multiply 100 + 50 and 5*5

[alpine sable]

What-

[cedar juniper]

.

[alpine sable]

oh

100 + 50 - 5 x 5

[cedar juniper]

WE ARE SO CLOSE

Why are we subtracting

Are you just trying every single operator

[alpine sable]

To get the total amount

[alpine sable]

yes

[cedar juniper]

why

;-;

[alpine sable]

Because

Idrk the answer

[cedar juniper]

Its okay

Dont worry about it

Uh how about this

Your mom will pay you 1$ for each time you do your chores

You did your chores 5 times

How much would she pay you

[alpine sable]

5$?

[cedar juniper]

Yup

[alpine sable]

...

[cedar juniper]

You did your chores 10 times

How much would she pay you

[alpine sable]

10$

[cedar juniper]

You did your chores x times

How much would she pay you

[alpine sable]

...

[cedar juniper]

You have no right to complain

[alpine sable]

0...

1

???

[cedar juniper]

0?

[alpine sable]

3>>

6??

4??

[cedar juniper]

Okay you are trolling

[alpine sable]

2??

[cedar juniper]

Bye

[alpine sable]

NO

[cedar juniper]

Ask someone else

[alpine sable]

PLEASE

I DON'T REALLY KNOW

@cedar juniper

THERE WAS NO NUMBER INVOLVE

[cedar juniper]

Do you have trouble understanding what x is?

[alpine sable]

SO I DIDN'T KNOW WHAT NUMBER IS THERE

[cedar juniper]

Do you know what a variable is

[alpine sable]

yes

[cedar juniper]

Do you just multiply or add the numbers you see and submit an answer?

[alpine sable]

yes

[cedar juniper]

;-;

Dont

[alpine sable]

WHA WHY?

[cedar juniper]

How did you get to calculus

[alpine sable]

...

No idea

[cedar juniper]

Im 98% sure you are trolling

[alpine sable]

I AM NOT

PLEASE

IM BEGGING YOU

[cedar juniper]

Okay so when I say

You did 5 chores

You say $5 * 1

Right?

[alpine sable]

yes

[cedar juniper]

So if I say I did x chores

You say?

[alpine sable]

x

1!

1 CHORE

PLEASE.

[cedar juniper]

Whats a variable

[alpine sable]

X and Y

[cedar juniper]

WHAT ARE THEY

[alpine sable]

X AND Y

[cedar juniper]

Did you miss 6th grade

[alpine sable]

No

BECAUSE MOST OF WHAT WE STUDY IS MEMORIZATION

[cedar juniper]

😭

[alpine sable]

WE DIDN'T SOLVE COMPLEX THINGS BECAUSE THEY PUT IT IN A WORD FORM

LIKE

Oh if an ellipse is like this

What is their b and a?

2b and 2a

[cedar juniper]

Thats lame

[alpine sable]

LIKE THAT

OKAY IM SORRY.

[cedar juniper]

No no

Your school

Is lame

Do you want to move this to dms?

[alpine sable]

Sure...

.close

[lone heart]

Channel closed

Closed by @viscid galleon

Use .reopen if this was a mistake.

[alpine sable]

.reopen

[lone heart]

✅

[alpine sable]

2.The SHS officers are planning for a SHS Prom. The allocated budget for decorations, sounds, and other miscellaneous expenses is ₱100,000.00 and an additional ₱1500.00 for meal expenses for each guest. The organization received an amount of ₱200,000.00 from its external
stakeholders.
a. Write the total allocated budget as a function of the number of guests.
b. Find the inverse of the function.
c. State the domain and range for this situation.
d. Find the possible number of guest for a budget of ₱200,000.00

[alpine sable]

@modern skiff

Yeah Im going to pass out any moment

[limpid heart]

200,000-100,000-1500x=y

b. switch x and y for a and make y the subject

c. original function doman = inverse function range, original function range = inverse function domain

d. find x in original function

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

Channel closed

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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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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[marsh ridge]

claim

[marsh ridge]

can someone explains how the ! works in this context

I understand how it works if it's just one number like 2!

but not if it's something + something

[sterile trench]

1 x 2 x 3 .... x (k+1) x (k+2)

[hushed locust]

k+2 is just a number. so for example if k = 5 then k + 2 = 7, so (k+2)! = 7!

[alpine sable]

both excellent responses

gg helper team we cooking

[marsh ridge]

give me a sec to

process

does this make sense

can I just assign it a number

assign k*

[sterile trench]

you can assign, but depends on actual question

[marsh ridge]

alright I think I got it

ty all

.close

[lone heart]

Channel closed

Closed by @marsh ridge

Use .reopen if this was a mistake.

[marsh ridge]

.reopen

[lone heart]

✅

[marsh ridge]

is this just a bug in the question/

is there such thing as an induction question but it's multiplication

wait it's a real question wtf

imma try it

[sterile trench]

just tryna take lcm with general term and see if it makes a pattern

factorise if it needs to be

[marsh ridge]

yeah I have no idea

I'm stuck here if it's even correct

.close

[lone heart]

Channel closed

Closed by @marsh ridge

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rose flax]

how can i simplify 4X^2-4X+7Y^2-3Y+2X^2-Y^2+XY fully?

[zealous ingot]

first combine like terms

[rose flax]

6x^2-4x +6y^2 -3y +xy

[zealous ingot]

i dont think you can simplify more now

unless you want it to be in a specific form?

[rose flax]

would factorising be "simplifying"

[rose flax]

the question hasnt stated anything like it, but it seems so simple if it just wants me to "condense" the equation

[zealous ingot]

i mean not necessarily, this is basically the most simplified form

[rose flax]

huh, could we not go along the routes of

2(3x^2-2x)+3(2y^2-y) +xy?

[lone heart]

@rose flax Has your question been resolved?

[fading depot]

Ill add to previous statements:
Simplify fully would usually mean everything is expanded unless stated otherwise.
The other cases for this includes: graphing, completing the square, and inequalities

This is because factored forms can tell you roots of the equation

[rose flax]

ohh, so i was making it more complicated when i was trying to factorise it after i had simplified it?

[fading depot]

Do you know about completing the square?

[rose flax]

yes, kind of

i am not a pro at it

[fading depot]

Ok as an extension to your question: there are multiple ways to solve a quadratic.
This requires both good use of expanding and factorising

I'll give an example, 3x^2+30x+48=0

When x^2 has a common factor

You can factorise and notice since its = 0 , you can divide both sides

3(x^2+10x+16) = 0

x^2+10x+16 = 0

I was going to go more in detail how you can solve this

But the main note is that for your original question, it was simplifying, not solving a quadratic

4 ways are: factorising, quadratic formula, completing the square, and graphing

[rose flax]

thats what i was confused about, i for some bizarre reason thought it was solving quadratic

thanks bennru!

🙂

[fading depot]

You're welcome

[rose flax]

.close

[lone heart]

Channel closed

Closed by @rose flax

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Send your question here to claim the channel.

Remember:
• 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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crude mortar]

guys wait lim x--> x_0 f(x) = f(x_0) means that f(x) is continous at f(x_0) right? so if it wasn't, f(x_0 ) wont exist or what, i dont get how the above limit would prove continuity

[pallid scarab]

f is continuous at x_0

[exotic canopy]

consider $f(x) = \begin{cases} 2 \text{ if } x = 0 \ x \text{ otherwise} \end{cases}$

[ocean seal]

artemetra

[crude mortar]

yeah but how does the limit prove that

[crude mortar]

ok

[graceful wedge]

ik im dumb but please someone explain how to solve this 😞

[exotic canopy]

what is $\lim_{x\to 0} f(x)$

[ocean seal]

artemetra

[crude mortar]

2

[exotic canopy]

you sure?

[crude mortar]

umm im not sure i just started with limits but ig

[exotic canopy]

what is f(0.0001)

[crude mortar]

hmmm

[tacit arch]

https://image-static.collegedunia.com/public/image/2e4c0b26f27e3d6403a2a8a22c0bfa6c.png

[crude mortar]

yes but how does the 3rd point come about

[tacit arch]

it doesn't in artem's example

[crude mortar]

that makes sense it should be x, but in that case when ever solving the differnce quotient, we cant take dela x as 0 right?

im still confused

if the last point is true

how is a function continous at x=0

[exotic canopy]

mine isn't

i was giving a counterexample, sorry

[crude mortar]

👀

so were u right?

[exotic canopy]

what this really means is that near a, the function is close to the value at a

[crude mortar]

but that would be true if the function is discontinous as well

[exotic canopy]

why?

[crude mortar]

ohhh wait

if its discontinous at a

as it approaches a

and a is like at lets say 1

then the function apporaches the value of a on that grpah

but if a continus again from a jump somehwere, it would be ideallty having a differnet value thats close to it

idk if that makes sense

ok nah im confused

@exotic canopy can a continuity have a case where lim from lhs and lim from rhs are unequal

[exotic canopy]

nope

wait wdym lhs rhs

[crude mortar]

like appraoching from the left

and approaching from the right

[exotic canopy]

ah

the limit doesn't exist if the right sided and left sided limits don't agree

[exotic canopy]

yeah!

[crude mortar]

ok but then in a removable continuity

the example i gave doesnt hold true

[exotic canopy]

*removable discontinuity

[exotic canopy]

yes because the function isn't defined at the discontinuity

[crude mortar]

ah so in a removble continiuity, the limx->a f(x) = f(a) is true but f(a) is not defined?

[exotic canopy]

that's the thing, you can't say "= f(a)" cuz f(a) is not defined

[crude mortar]

so both things must be defined

ohh

[exotic canopy]

yep

[crude mortar]

so in a jumped disconitnuity for example, f(a) is defined though?

[exotic canopy]

it is but then the limit and the value don't agree

[crude mortar]

oh ok so both things must agreee

[exotic canopy]

yep

[crude mortar]

got it!

tysm man for ur help!

[exotic canopy]

if this confuses you less you can let $\lim_{x\to a} f(x) = L$ and $f(a) = V$, so continuity would occur if:\

• $L$ is a thing\
• $V$ is a thing\
• $L=V$

[ocean seal]

artemetra

[exotic canopy]

no problem!

[crude mortar]

ok this makes way more sense

tysm again!

also what aobut the thing u wer saying

[crude mortar]

this thing

[exotic canopy]

yes

[crude mortar]

so what would be the answer to the quesiton u actually said

[exotic canopy]

there, L exists and L=0

but f(0) = V = 2

so L ≠ V

so it's not continuous

[crude mortar]

lim x-> 0 f(x) = ?

[exotic canopy]

0

[crude mortar]

but

how do yk that?

u are only given it can be 2 or x

[exotic canopy]

the limit doesn't care what happens AT 0, only at what happens AROUND 0

[crude mortar]

around lim x->0 f(x) = x

[exotic canopy]

f(1) = 1
f(0.1) = 0.1
f(0.0000000001) = 0.0000000001

[exotic canopy]

precisely

[crude mortar]

so how can it be 0?

u have to take it as x

not 0 right

[exotic canopy]

wdym

[crude mortar]

u said L exists and L=0

[exotic canopy]

well x tends to 0

[crude mortar]

oh shit yeah

[exotic canopy]

$\lim_{x\to 0} f(x) = \lim_{x\to 0} x$ (because in the limit $x \neq 0$)

[ocean seal]

artemetra

[exotic canopy]

$= 0$

[ocean seal]

artemetra

[exotic canopy]

have you covered the epsilon-delta definition of a limit?

[crude mortar]

no

ig i should do that first then

[exotic canopy]

no, no need

[crude mortar]

its weird how first we dont take x as 0 but later we do

[exotic canopy]

i understand

[exotic canopy]

but this is the most important step i would say

f(x) = x for all x that are not 0

so we can replace it with just x

but the limit of x (forget f(x)) at 0 is 0

[crude mortar]

i think i get this

[exotic canopy]

in a slightly more formal language, we can make x arbitrarily close to 0 but not 0

so the function will return that arbitrarily small value

[crude mortar]

the x inside f(x) and x are not the same x i supopse, our professor did tell us about this before the start of the lecture

[exotic canopy]

but in analysis we often equate the notions of being arbitrary close to something as being that thing itself

[crude mortar]

yeah i can get it now

i think i got decently confuserd bout the notation as well

but i got it

[exotic canopy]

yeah that's understandable

[crude mortar]

so again tysm for ur help! i havent been able to udnerstand this from so long and u finally helped me get it

ill close the ticket now

.close

[lone heart]

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[lone heart]

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

[nocturne lintel]

Use Intercept theorem

@hybrid needle

[lone heart]

@hybrid needle Has your question been resolved?

[hybrid needle]

Nope I'm still stuck

@nocturne lintel what's that?

[nocturne lintel]

DB and EA are parralel ?

[nocturne lintel]

if so then CD/CE=CB/CA=DB/EA

[hybrid needle]

I can send you a whole pic

[nocturne lintel]

ye

[hybrid needle]

There

[nocturne lintel]

From my knowledge it can only be solved like this

but it doesnt say that DB and EA are parallel so...

[hybrid needle]

Hmm

[nocturne lintel]

Did you see intercept theorem in class ?

[hybrid needle]

No I've just started the new year

[nocturne lintel]

so intercept theorem is only usable if :
Two lines crossing by a point(in case C) are both also crossed by two parrallel lines (DB and EA)

if im not clear say it

@hybrid needle

and the theorem is that the small part (CD or CB or DB) on the big part (respectfuly CE; CA; EA)

(So CD/CE or CB/CA or DB/EA)

[hybrid needle]

It's e to a but I need to find answer for it

[nocturne lintel]

Are all equal to each other CD/CE = CB/CA = DB/EA

what measurement do you have ?

[hybrid needle]

It's cm

[nocturne lintel]

not the unit the value

like CD=8cm

[hybrid needle]

Not sure

[nocturne lintel]

of what ?

the explanation ?

[hybrid needle]

Yes

[nocturne lintel]

ok

so CE and CA both pass through C

[nocturne lintel]

and B∈[CA]

D∈[CE]

And supposing (DB) is parrallel to (EA)

then CD/CE= CB/CA

and CD/CE = CB/CA = DB/EA

Im going to sleep if you didnt understood (which I can understand), just ping Helpers

[hybrid needle]

It's all good I went from 0.1 to 10.5 and got answer

[lone heart]

@hybrid needle Has your question been resolved?

[hybrid needle]

Yes

[lone heart]

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[rapid flare]

ez

[rapid flare]

.close

[lone heart]

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[supple cloud]

I dont even know what is wrong here

[supple cloud]

also, the last two equations in the peice wise function for the second graph are wrong

nvm, imma sleep

too sick for this

.close

[lone heart]

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[lone heart]

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[gloomy ridge]

I'm not sure what I'm doing wrong here...

Write a quadratic function with real coefficients and the given zero. (Use x as your variable.)

7 + 2i

7 + 2i, 7 - 2i

(x -7 -2i)(x -7 + 2i)

x^2 -7x + 2ix -7x + 49 -4i -2ix + 14i + -4i^2

x^2 -7x + 2x -7x -2x + 49 -4 + 14 + -4

x^2 -14x + 55

[jagged cobalt]

-14i not -4i

[gloomy ridge]

?

[jagged cobalt]

third line

but what did you do on the line after

it looks like you just deleted any i

somehow

[gloomy ridge]

yeah

[jagged cobalt]

(you cannot do that)

2+3i is not equal to 2+3

[gloomy ridge]

how do I get rid of i then?

what I did worked on 2 of the other equations

[jagged cobalt]

youll notice that the imaginary terms cancel out if you look closely

like +2ix and -2ix

and also note i^2=-1

[gloomy ridge]

oh

well

everything makes much more sense now

.close

[lone heart]

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[lone heart]

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[limpid heart]

how can i integrate e^x^2

[lone heart]

Please don't occupy multiple help channels.

[long axle]

It’s pretty rough

,w intégrate e^(x^2)

[ocean seal]

Results provided by WolframAlpha

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

Requested by northsteve

[limpid heart]

what does erfi mean

[long axle]

Error function I’m p sure

[limpid heart]

ok

thank u

.close

[lone heart]

Channel closed

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[remote heron]

it is not

it is -i erf (iz)

[lone heart]

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[glass silo]

heeeeelp plsss

[lone heart]

Please don't occupy multiple help channels.

[torpid dirge]

u can look at the ratio of those two triangles with respect to BCP

[glass silo]

mmmh how?

[opal lintel]

Hi guys, I have a question: Can I get the number inside the sin? Would it be right or would it be wrong?

[high crest]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[torpid dirge]

whats the ratio of QPB:BPC

what is the ratio of BCP:APD

[lone heart]

@glass silo Has your question been resolved?

[glass silo]

oh right they have the same base but amm

[torpid dirge]

amm?

[glass silo]

srry im a little lost with the area problems

[torpid dirge]

first this

[glass silo]

mmmh

[torpid dirge]

what do u know about them

[glass silo]

is the ratio of their heights? something like that?

[torpid dirge]

yes

[lone heart]

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[sacred fable]

what does this 2m thing mean? Is it just a second angle?

[torpid dirge]

twice the angle

[tardy stag]

m√1 is the measure of angle 1

m√2 is the measure of angle 2

(these are in degrees)

this is saying that the measure of angle 1 is two times the measure of angle 2

so maybe angle 1 is 68° and angle 2 is 34°

[lone heart]

@sacred fable Has your question been resolved?

[sacred fable]

Okay thank you so much!!

[lone heart]

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[west breach]

Hi

[west breach]

Can someone help me with this one question

I just dont get how it works

27w^2 + 18w - 16
/
9

Like i dont get how im supposed to divide 16 by 9

[tacit arch]

What are you supposed to be doing

Factoring?

[west breach]

Dividing it

They explained it that i should
Seperate them like

27 /9

18/9

But 16/9 doesnt work so i dont get how im supposed to do that part

[sharp plaza]

just leave it as -16/9

[west breach]

Wait

Let me send a photo

This

So its gonna be 3w^2 + 2w -16?

So its just gonna be 1?

So 3w^2 +2w -1?

[sharp plaza]

,rotate

[sharp plaza]

you do realize you dont have to get a whole number right

it is perfectly acceptable to have a fraction there

[west breach]

Huh

Oh

So this is right?

[sharp plaza]

-16/9 is just -16/9, you dont have to simplify it further

yeh

[west breach]

Alright thank you

[sharp plaza]

is there some other contex to this problem we dont know about?

[west breach]

I was so confused

[west breach]

Im preparing for an exam tmrw

No youtube video is helping me with this

And the slideshow doesnt even explain it like you guys did

[sharp plaza]

what was the original problem? or was it just that?

[west breach]

Here

It only explained the ones you could divide

It doesnt explain the ones you cant

I tried tutorials but i still dont get it

[west breach]

Just that this is the only lesson i dont understand

[sharp plaza]

well you can just think of x's as any other number

then apply the exponent rule to them, if you divide the exponents subtract

so (x^3)/x

is the same as

x^(3-1)

since x has an exponent of 1 because: x^1 = x

[west breach]

Alright thank you

I dont know if i can memorise this tho

[lone heart]

@west breach Has your question been resolved?

[lone heart]

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[summer dirge]

[normal summit]

how would you solve 9d i know you replace the 24,000 with p(t) but i literally can’t do anything further than that

and you aren’t supposed to use some crazy method as this unit is “ characteristics of polynomial functions “

[lone heart]

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[limpid heart]

i simplified the numerator into something like [cos(nx)]^1/n

not sure what to do next

[valid lava]

I made a ai tutor app its free if you want to download it it can solve ur problem and explain it through step by step

[limpid heart]

my appstore is in china

it can't download most of the apps

<@&286206848099549185>

[gaunt sonnet]

yes

@valid lava wats the app name

[limpid heart]

.close

[lone heart]

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[knotty tangle]

.reopen

.close

.reopen

.reopen

asdfasdasdf

asd

[knotty tangle]

as

asd

f

why is this not workin

nvm

it works

[hushed locust]

you have claimed the channel. note for future that messages starting with . do not count for opening a channel

[knotty tangle]

okh

ty

bro

what grade ru

in

??????????????????

[limpid heart]

whats ur question

[rose iris]

theyre prolly just in a crisis rn

[summer dirge]

do we have a question?

if not, then I'll close this channel in 5 min

.remindme 5min close if nothing is asked

[lone heart]

Created reminder close if nothing is asked (#help-0 message) for <t:1728534261:f>

[knotty tangle]

yo

anyone

here

<@&286206848099549185>

[lone heart]

@summer dirge asked to be reminded <t:1728533961:R>, close if nothing is asked

[knotty tangle]

i need help

[summer dirge]

can you post your question?

you haven't posted anything but requests so far

[knotty tangle]

so basically how do find the domain and range from a function a equation smth like this

?

https://tenor.com/view/anyone-here-tumbleweed-john-travolta-pulp-fiction-where-are-you-gif-22041899

<@&286206848099549185> s

how do find the domain and range from a function a equation smth like this

[summer dirge]

do you know what the graph of x^2 looks like?

[knotty tangle]

no

[summer dirge]

it's a parabola

[knotty tangle]

oh

i just want linear

functions

for now

[knotty tangle]

cuz that what my schools teachin

f(x)=−x+2

[summer dirge]

then why are you asking how to find the domain and range of a quadratic function?

[knotty tangle]

i searched it up a web

bro sry

f(x)=−x+2

thats a linear

function how do i find the domain and range

without a graph

bro stop typing and respond

alr

[summer dirge]

at this level, you can think of the domain of a function is the set of all values that you can input into the function without "breaking" anything, e.g. division by zero

[knotty tangle]

ik that

[summer dirge]

I am doing my best to respond as fast as I can

please be patient

[knotty tangle]

sure

[summer dirge]

right, so we have a line

[knotty tangle]

yep

[summer dirge]

is there any value we can plug into the line that "breaks" the function, e.g. division by zero?

[knotty tangle]

no i hope so

[summer dirge]

there isn't. indeed

so the domain is the maximum one possible

,, \operatorname{Dom}(f) = \R

ugh

[knotty tangle]

tf

is that

[ocean seal]

higher!

[knotty tangle]

what is that

mean

bruh

[summer dirge]

just notation

[knotty tangle]

f(x)=−x+2

f(x)=−x+2

f(x)=−x+2

f(x)=−x+2

FIND THE DOMAIN AND RANGE

[summer dirge]

read it as "the domain of f is equal to R"

that is your answer for the domain

R

the real numbers

[knotty tangle]

idk what ur talkin abou

[summer dirge]

if you want, write it as $(-\infty, \infty)$

[knotty tangle]

i need a simpler

way

bruh

[ocean seal]

higher!

[knotty tangle]

BRUH

[summer dirge]

there is literally not a simpler notation

I don't know what you want

[knotty tangle]

i want a simple way

to

find the domain

[summer dirge]

you're asking for the domain, which is all of R

[knotty tangle]

and range of a equation

isnt r the range

or smth

idk

[summer dirge]

the way to find the domain is to look for any faulty values

[knotty tangle]

im new bruh 😭

i dont what ur talking bro

:((

[summer dirge]

you already said (correctly) that there are no inputs that can break our function f(x) = -x + 2

so the domain must be every possible real number

[knotty tangle]

dude what grade ru

in

?

[tacit arch]

Higher than you

[summer dirge]

I'm a 2nd year uni student, but I don't see why this is relevant

[knotty tangle]

BRUH

[summer dirge]

it has nothing to do with my grade

[knotty tangle]

NO WAY

IM A 7th grader

dude

and i have to learn this

shi

[summer dirge]

why does that matter

[knotty tangle]

Idk

[summer dirge]

I'm giving you the answer!

[knotty tangle]

okh

bro

[summer dirge]

the domain of f is R

[knotty tangle]

ty

what the helllll

wait

a

sec

[summer dirge]

waiting

[knotty tangle]

wait

[summer dirge]

https://tenor.com/view/pusheen-pusheen-cat-pusheen's-best-friend-pusheen-loading-computer-gif-7565637198389470946

[knotty tangle]

wai

[lone heart]

@knotty tangle Has your question been resolved?

[lone heart]

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[lone heart]

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

I know it's probably got something to do w gcd

but i can't figure it out

also i can use a computer to work this out

[lone heart]

@placid flume Has your question been resolved?

[worthy finch]

you can use libraries like itertools to find

[placid flume]

I'm trying RN an approach but it's incredibly slow

I'm not great w code so if u find a better way pls tell

[worthy finch]

also what did you mean by maximum number of change

[placid flume]

So for example they can get 130 by doing 60,30,20,20

What's the maximum number that can be

[worthy finch]

oh so you want maximum number that is not 120

[placid flume]

Yh

[worthy finch]

from itertools import combinations_with_replacement

coins = [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]
max_sum = 0

for r in range(1, len(coins) + 1):
    for combination in combinations_with_replacement(coins, r):
        total = sum(combination)
        if total != 120:
            max_sum = max(max_sum, total)

print(max_sum)

try this (this will probably work)

[placid flume]

It ran but it gave the answer 720? Which is wrong

[worthy finch]

are repeats allowed

[placid flume]

Yes 👍

Sorry if that isn't clear

[worthy finch]

if you want i can make it write the combination

so i can also see what is the mistake

[placid flume]

Yh pls do

I'm tryna digest the code myself as well

[worthy finch]

(60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60)

it made maximum with this

oh

you didnt say subset

bruh

"no combinations of coins will make exactly 120p"

so no subset will be 120

[placid flume]

What's the maximum possible value

[placid flume]

Yh

[worthy finch]

i made it wrong that's why

i thought it was something else

[placid flume]

:(

[worthy finch]

using subset slows code a lot

[placid flume]

:((((

[worthy finch]

is it 168

[placid flume]

No sorry

[worthy finch]

119?

[placid flume]

No

Cos 130 is greater

<@&286206848099549185>

[placid flume]

<@&286206848099549185> imma close this in a few mins if no significant progress is made pls help me

.close

[lone heart]

Channel closed

Closed by @placid flume

Use .reopen if this was a mistake.

[lone heart]

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[sleek fog]

Simplifie Arctan(√1+x^2 - x)

[sleek fog]

It sound stupid and ez

But my brain some how not pulling together the pieces

Tried chatgpt but it just gives me not understandable answers

[ocean seal]

bacc the sigma😔🤞