help-0

[vale wigeon]

after the wheel rolls t units its center will be at (0,0) and the point will have risen t radians above its starting position on the wheel

br

brb*

[timber cobalt]

I think x would be t+cos(t) and y would be 1 +sin(t)

[lone heart]

@timber cobalt Has your question been resolved?

[vale wigeon]

that's what that gives you

[timber cobalt]

How do I combine them into 1 curve?

[lone heart]

@timber cobalt Has your question been resolved?

[lone heart]

@timber cobalt Has your question been resolved?

[undone jay]

why can't we separate cosx/1+sinx as cosx/1 + cosx/sinx? cosx/sinx could then turn to cotx?

[timber cobalt]

.close

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[alpine sable]

Can anyone help me solve the second question (for a friend), I know BCD is 192 but idk what from there

[gaunt siren]

i feel like BCD should be 146

[alpine sable]

Can I see the math pls I kinda wanna understand it too

[gaunt siren]

RCD is 108 (regular pentagon)

BCR is 180-84 = 96

BCD = 360-(108+96)= 360-(214) = 146

also 192 would be ridiculous as an interior angle cant be more than 180

well a regular cant, at least

but then the exterior angle would be 34

360/34 is not a whole number

[alpine sable]

108?

isn't it 72?

[gaunt siren]

interior is 108

exterior is 72

exterior angles always add up to 360

pentagons have 5 sides

360/5 = 72

[alpine sable]

yess

I am so stupid

Right wait

n-2x180 for interior angles right?

[gaunt siren]

yerp

which would be 540 for a pentagon

540/5 = 108

am i stupid?

[alpine sable]

No im stupid

[gaunt siren]

i swear they couldve made the isoceles angles 41 and 41

adn it would've been perfectly fine

[alpine sable]

Mkay so

it's 156

cuz uh

84+108 is uh

192

360-192=156

Right

then

(n-2)180=something something

idk the equation tho

15 sides

how did he get 15 tho

[lone heart]

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[river aspen]

hello is anyone free

[river aspen]

i need a quick help

patterns and sequence

[tacit arch]

why quick

[river aspen]

i am stuck in this question

i have to finish within 30 min

and i have like 15 more questions to go

[tacit arch]

why 30 min?

[river aspen]

instructed by our profs for this exercise

[tacit arch]

is that when your test is due?

[river aspen]

its due today but 30 mins is the only given time for this exercise not a test exactly

the pattern does not make sense or I am approaching it wrong

[tacit arch]

and what grade is this problem

or year

[river aspen]

1st yr

[tacit arch]

1st year of what?

[river aspen]

college

[tacit arch]

1st year college is usually calculus

what topics is your professor teaching

[river aspen]

we are in pattern sequence and statements my course is more on business

[ionic jewel]

i also do not see the pattern but they are always silly rules

[gaunt siren]

lol same

at first i thought the numbers were rotating clockwise but thats clearly not it

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@river aspen Has your question been resolved?

[lone heart]

@river aspen Has your question been resolved?

[lone heart]

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[forest cobalt]

oh it's you again

allo

[fresh rune]

hey

i need help

[mellow grail]

Quotient rule

[forest cobalt]

quotient rule

[fresh rune]

?

[forest cobalt]

product rule works too if you're brave

[fresh rune]

wait

i got it

[mellow grail]

U got it?

Aight

[fresh rune]

i mean to say

i got the quotient rule written down sorry

[mellow grail]

Ah K

So apply it

Then show work

[fresh rune]

i gotta try it first gimme a sec

the thing is

idk how to diifferentiate trig functions

[mellow grail]

🤦‍♂️

[fresh rune]

🥲 have mercy

[forest cobalt]

https://tenor.com/view/recess-detweiller-tj-thats-rough-thats-not-good-gif-15753069

[mellow grail]

https://youtu.be/_niP0JaOgHY?si=PMxLuxpr0jC5Pa8n

[mellow grail]

I would recommend you watch this

[fresh rune]

ok

ill be back then

[near apex]

Okay, Terminator.

[fresh rune]

._.

.close

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[lost spruce]

hi

[lost spruce]

can i get help

with this problem?

<@&286206848099549185>

[odd nest]

a

[lone heart]

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[strong junco]

try a few values and see if they work. By inspection it looks like x = -1 is a solution. Then as x = -1 is a solution you know that (x+1) is a factor

now you can factor the equation to be (x+1)(ax^2+bx+c) and you can figure out that unknown quadratic using polynomial long division

and then you can solve the quadratic like you normally would

[mellow grail]

By rational root theorem, the roots of a polynomial will be of the form a/b if the polynomial has rational roots, where a is the factors of the constant term, and b are factors of the coefficient of the the variable with the highest power (also called leading coefficient)

[strong junco]

You can just also use an online software like symbolab if you're really down bad to find the answer without doing any work

XD

[lost spruce]

symbolab fell off

[mellow grail]

I would highly discourage this, except if you want to check whether your answer is correct and you don't have an answer key

[mellow grail]

From here, do what @strong junco suggested

[lost spruce]

dumb it down for me

what i need

is a visual example

which shows the steps

[strong junco]

You can also figure out this unknown quadratic by just collecting like terms instead of doing polynomial long division

ok i got you

9x^3 + 27x^2 + 29x + 11 = (x+1)(ax^2+bx+c)

because if you input x = -1 into that equation its a solution so you know (x+1) is a root

now we know a has to be 9 and c has to be 11 and using that we can figure out that b = 18

[lost spruce]

idk if this is asking for a lot

but can u write it on paper

it getting over complicated on text

[strong junco]

aight

[lost spruce]

ty

[strong junco]

can you have complex roots yet?

because 9x^2+18x+11 doesn't have any real solutions

and idk if you've encountered complex numbers in your course yet

[lost spruce]

jus started doing this i believe

[lost spruce]

idk tbh

prolly not

but not too sure

[strong junco]

well the answer should just be x = -1 then

because it factors to be (x+1)(9x^2+18x+11) and you can check the quadratic expression urself to see the solutions for it

[lost spruce]

yea thats only part of the answer

[strong junco]

but yeah they're complex solutions

[lost spruce]

ima be real idk how to do this yet

i need like a visual example to use

[strong junco]

just chuck the quadratic equation into the quadratic solution formula and you can figure out the complex solutions

[lost spruce]

so i can use it to learn how to do the other problems

[strong junco]

its nearly 2am for me i gtg

[lost spruce]

oh

alr thanks, gn

[lone heart]

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[lone heart]

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[vale wigeon]

!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

[unkempt robin]

Here you have a system of two equations with two unknowns.

Do you know the different ways you can solve this type of system?

There's one that's handed to you on a silver platter here

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[silent linden]

hello could someone clarify something for me ?

[rustic meadow]

I have a short conceptual question for myself

Oh sry

[silent linden]

youre fine

which value do i use for a ? it says a>0 am i missing something ?

[pallid scarab]

Any value for a

a is an unknown positive constant

[lone heart]

@silent linden Has your question been resolved?

[silent linden]

so i could substitute any value as long as its >0 ? any recommended values which simplify easily ?

[mortal trellis]

no you are probably supposed to calculate the value of the integral in terms of a

[silent linden]

thats possible what i was thinking, ive never come across a problem like this so im curious to know

could i get a scoot ? lol i know about the trig substitution, and (sqrt) cubed portion its just the value

[lone heart]

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[alpine sable]

is it possible to explain why when a numbers digits added up are divisible by 3 the number is divisible by 3 as well?

[muted hornet]

yeah. do you know modular arithmetic

[alpine sable]

im in prealgebra, i know numbers decimals percents etc..

[muted hornet]

hmm okay. maybe someone else can give a lower level explanation, but i'll do my best

if a and r have the same remainder when divided by 3, we write a = r (mod 3). for example, 4 = 1 (mod 3)

it turns out that if a = r (mod 3) and b = s (mod 3), then ab = rs (mod 3). so ab and rs have the same remainder when you divide them by 3. also, it's true that a + b = r + s (mod 3), so a + b and r + s have the same remainder when divided by 3.

since 10 = 1 (mod 3) (10 has a remainder of 1 when divided by 3), we get 10^2 = 1 (mod 3) (because 10 * 10 = 1 * 1 (mod 3)), 10^3 = 1 (mod 3), etc by applying the multiplication rule

if you have a number like 213, then 213 = 2 * 10^2 + 1 * 10 + 3. but this has the same remainder as 2 * 1 + 1 * 1 + 3 = 2 + 1 + 3 when you divide by 3, by the sum rule (and the multiplication rule)

so 213 and 2 + 1 + 3 have the same remainder when divided by 3

so 213 has a remainder of 0 when divided by 3 if and only if 2 + 1 + 3 has a remainder of 0 when divided by 3

so 213 is divisble by 3 if and only if 2 + 1 + 3 is

[alpine sable]

ok mod means remainder right, modulus right?

[muted hornet]

yeah

[alpine sable]

ok this looks like something i can understand but i dont want u to stick around while i decode it all, i want to thank u for the great explanation.

[muted hornet]

okay someone else can probably help if you need more assistance. i'm going to go work on my bike

good luck!! it's not too horrible, it just takes a bit of reading and thinking

but its sort of self-contained

[mortal trellis]

if you want a bit less mod stuff: if you have abc a three digit number, then that means 100a+10b+c. now you have 100=99+1 and 10=9+1, so abc=99a+9b+a+b+c. the first part 99a+9b=3(33a+3b) is definitely divisible by three, so the question reduces to whether a+b+c is divisible by 3

same idea, just slightly different words

[alpine sable]

ok awesome

ty

.close

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[alpine sable]

.close

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[bitter sinew]

I need help on this ratio

[bitter sinew]

<@&286206848099549185>

[noble salmon]

Well can you at least show it?

[bitter sinew]

k

it is a unit rate ratio

$60 for 5 imported pounds of coffee

cost per pound

ok ill write the problem

[lone heart]

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.

[bitter sinew]

Caffeine Castle buys bulk coffee to sell. The cost of 5 pounds of imported coffee is $60. What is the unit rate in cost per pound?

@noble salmon

[unkempt robin]

So, it's 5 pounds / 60$. Turned around, it's 60$ / 5 pounds

[ocean seal]

USS-Enterprise

[unkempt robin]

To get cost per pound, simply divide by 5

[bitter sinew]

tysm bro

.close

[lone heart]

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[bitter sinew]

.repoen

reopen

.reopen

[lone heart]

✅

[bitter sinew]

wait wats 0 divided by 5

[unkempt robin]

Why do you need that?

And it's 0

[bitter sinew]

9*

60*

dang i cant type

[unkempt robin]

It's 12

[bitter sinew]

ty

ooh 5/9 + 1/4

this ez

6/36 and simplify = 1/6

[unkempt robin]

What?

[bitter sinew]

i was doin a problem

[unkempt robin]

Ah

[bitter sinew]

oh a volume problem? no prob

8ft. x 1ft. x 2ft. is 16 cubic feet

oh no

6,355 / 40

idk this one

Help plz

nvm

@unkempt robin HELP

<@&286206848099549185>

[lethal citrus]

Can you send the question, I don’t see any

[bitter sinew]

k

The hallway is 440 in. long. 2.5 feet of the hall isn't carpeted. What is the length, in inches, of the hall that is carpeted?

there

@lethal citrus

<@&286206848099549185>

[lethal citrus]

Man wait

!15min

[lone heart]

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.

[bitter sinew]

!15min

[lone heart]

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.

[lethal citrus]

What’s 2.5 feet in in. ?

[bitter sinew]

12 in. in a foot right??

so is it 24.6 in. ?

[lethal citrus]

wouldn’t it be : the length of the hallway - length that isn’t carpeted

[bitter sinew]

no it said is carpeted

[lethal citrus]

I mean : the length which is carpeted = the length of the hallway minus the length that isn’t carpeted

[bitter sinew]

ty

415.6

415.4*

[lethal citrus]

Actually I’m not American so I don’t know how to convert feet into inches so maybe that is it or maybe not

[bitter sinew]

hollup

How many fourths are in 2 wholes?

bro thats obvious

8

i need help on number 15. the question is: A recipe called for 2 1/3 cups of broth. which shows how to double this amount

<@&286206848099549185>

!15mins

[lone heart]

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.

[lethal citrus]

Don’t ping the helpers every time you have a question

[bitter sinew]

ok

a b or c tho?

[lethal citrus]

What do you do when you double something ?

[bitter sinew]

x 2?

so it is b

thx bro

.close

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[bitter sinew]

.reopen

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✅

[lethal citrus]

Why ?

[lone heart]

@bitter sinew Has your question been resolved?

[lone heart]

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[glacial valley]

Did I do this right?

[silent linden]

oh man statistics ? , if you plugged everything in correctly it should be right, variance and SD is hard to mess up, you can verify your answer online using a SD and variance calculator, if your answers match up you did it correctly

[glacial valley]

I’m just not completely sure about the x’s within the question and how I should plug it in because it’s not a data set

[silent linden]

as long as you have the sum of all obs, sum of all squared obs , and the number of obs , SD can be calculated

[silent linden]

re check your calculation, i see 39 then it jumps to 29

[glacial valley]

Oh you’re right thanks

[silent linden]

anytime :3

[glacial valley]

Yup you’re right I was so confused what I was doing wrong lol

.close

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[tight thunder]

guys this must be a bloody misatke

6 to 5

must be a 6 man!?

oh

.close

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[wraith adder]

i have no idea how to do this

[upbeat gorge]

First, do you know graph transformations?

[lone heart]

@wraith adder Has your question been resolved?

[wraith adder]

sort of like vertex form stuff

[upbeat gorge]

Ah so you were introduced to it with quadratics I see

Yeah so the principles are similar

Horizontal stretching and shifting, vertical stretching and shifting, reflections, stuff like that

[rustic meadow]

What does the +3 mean in this case

[upbeat gorge]

Given $f(x)=x^2$ as the parent function, what happens if I have $g(x)=x^2+3$?

[ocean seal]

CST

[lone heart]

@wraith adder Has your question been resolved?

[lone heart]

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[simple hemlock]

how would you graph this?

[rose void]

Since it's from -infinity to 6 iinclusive then put a closed circle at -6 then closed circle at 1,6

[simple hemlock]

okay

what about this?

[lone heart]

@simple hemlock Has your question been resolved?

[chilly idol]

This would be a open circle at -8 and -1/7 with a line in between
To graph (3, +inf) you would have to do a open circle at 3 and a continous line going +inf

Since their is a union their will be a gap in between (-8, -1/7) and (3, +inf), this gap cannot satisfy the equation (x+3)/(x+8) < (x-1)/(x-3) so it will not be graphed.

[chilly idol]

The reason why we have a open circle is because in the original equation
(x+3)/(x+8) < (x-1)/(x-3) their is a <
This less than sign does not have a equal to it

For example if we had the equation x <= 2
We would have a closed circle because it is less than OR EQUAL TO

Hope this helps ping me if you need a further explanation @simple hemlock

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[languid raft]

3 and 4

I don't know what it's asking or how to do them

[rotund shoal]

Do you know what a tangent is?

If so, explain what it means

[languid raft]

i know what the tangent line is yeah

hrm

okay, I don't really know how to explain it

[rotund shoal]

Well, what features does it have in relation to function?

[languid raft]

its the instaneous rate of change at a specific point

[rotund shoal]

Right, so I would recommend working with the function first

as the line is already established

Have you tried finding f'(x)?

[languid raft]

yeah

I got 2kx

[rotund shoal]

Correct

What can you tell me about the gradient of the line?

@languid raft

[lone heart]

@languid raft Has your question been resolved?

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[winter badger]

C pls

[lone heart]

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[royal thorn]

someone please help me with this

[honest hare]

I need help to study for the shsat, I’m so worried, it’s killing me

[lone heart]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[royal thorn]

<@&286206848099549185>

[bitter sinew]

?

[lone heart]

@royal thorn Has your question been resolved?

[royal thorn]

.close

[lone heart]

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[reef flame]

I don't understand how they got 2x+5 and -3y+1

<@&286206848099549185>

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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.

[lone heart]

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.

[safe lance]

you want the values of f(x), right?

[reef flame]

Yeah

[safe lance]

but you only know the values of some operations over this man:

so, lets call our new x' = 1/2(x-5), that is 2x'+5 = x

[safe lance]

oo, sorry, you DONT want the values of f(x), you want the values of y = -3f(1/2(x-5))+1

[reef flame]

I already figured it out just now thanks anyways

.close

[lone heart]

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[stiff summit]

How would you solve 1/6y+3/8x=24? Put in form of y=mx+b

[bleak geyser]

do u mean $\frac{1}{6y} + \frac{3}{6x} = 24$

[ocean seal]

ahaan

[stiff summit]

I meant the 3/8

[stiff summit]

3/8

Hello?

@bleak geyser

[lone heart]

@stiff summit Has your question been resolved?

[alpine sable]

Show on a piece of paper

or

make it easier

to read

[hardy urchin]

$\frac{1}{6}y + \frac{3}{8}x = 24$

[ocean seal]

Amir

[stiff summit]

Yes

[hardy urchin]

multiply both sides of the equation by 6

[stiff summit]

All sides?

What if you get 2.25 for on of ur answers

[lone heart]

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[stiff summit]

I have 1y+2.25=144

.reopen

[lone heart]

✅

[alpine sable]

whats going on

[hardy urchin]

y+2.25x=144

[stiff summit]

What do I do next?

[alpine sable]

why work in decimals

[stiff summit]

Bc that’s what I got when I did 3/8*6

[alpine sable]

whats the equation or expression

orignal one

there might be a easier way to go at it

[stiff summit]

1/6y+3/8x=24

[alpine sable]

okay

[stiff summit]

I times 6 to both sides

[alpine sable]

okay then what

[stiff summit]

I got 1y+2.25x=24

[alpine sable]

well first off keep the co-efficient of x in fractions

and second you forgot to do the otherside of the equation

so its currently unbalanced

[stiff summit]

I meant 144

[alpine sable]

ok good

so

now

[stiff summit]

My bad

[alpine sable]

instead of going into messy decimals

we should keep it in fractions to make it easier to compute

is it asking to simplify?

or solve

[stiff summit]

It’s asking to find the slope

[alpine sable]

for a vairable

[alpine sable]

ohhhh

this is a slope question

[stiff summit]

Yes

[alpine sable]

so your in the wrong format we shouldnt be solving it

y = mx+b

thats what we are trying to get that into

[stiff summit]

Ok

[alpine sable]

one secondd...

[stiff summit]

So was I still on the right track

[alpine sable]

no we were on a whole diffrent rail line

this is easier

[stiff summit]

Oof

[alpine sable]

do you know how to rearange equations?

like transform that into a format like y = mx + b?

[stiff summit]

1/6=3/8+24?

[alpine sable]

no

We still need vairables to define the lines

[stiff summit]

I was going to say move to everything to one side

[alpine sable]

Yes.

so first thing is to isolate 7

y*

on one side

so if we do indeed multiply by 6

we end up with y + 18/8x = 144

so from there how would we make sure y is alone on one side?

while everything else is on the other side

[stiff summit]

By subtracting it

[alpine sable]

yes

so after we subtract it what are we left with

[stiff summit]

18=144-y

144x

[alpine sable]

no, we kinda got messed up there

make sure to keep the co-efficent of x with x

while you keep the 144 to the side

[stiff summit]

18/8x=144-y

Yeah I realized that

[alpine sable]

now we could be that, but dont you think we could just move the X and its multiplyer while keeping Y?

less work right?

[stiff summit]

We

Yes

[alpine sable]

So instead lets keep y there and move the x and its multiplyer to the otherside making it negative

and canceling out from the original side

subtracting it

[stiff summit]

Y=144-3/8x

[alpine sable]

18/8x*

dont forget that step

but yes

now for the next step we dont need it but it will make it easier to compute, so why dont we move the 144 to the end of the second expression making it -18/8x + 144

it would make it easier to see the y = mx + B

now what are we left with?

[stiff summit]

Y=-18/8x+144

[alpine sable]

very good

now, can you see the y = mx + b in that equation?

[stiff summit]

Yes

[alpine sable]

great

did your teacher teach you the fourmla y = mx + b or is that new to you?

[stiff summit]

They taught us if

It

[alpine sable]

alright so whats the slope in the equation

[stiff summit]

-18/8x

[alpine sable]

half right, but the x is not apart of the slope that is the x cordinate

so just -18/8

and from there what can we simplify that to?

[stiff summit]

-9/4

[alpine sable]

great!

thats your awnser

[stiff summit]

I have one more question

[alpine sable]

Yea?

[stiff summit]

1/2+2/5t-1=1/5t+t

[alpine sable]

okay unforunately i cant help you right noiw

my discord acount is hacked

just ping helpers

[stiff summit]

Ok

[alpine sable]

i need to delete the account

[stiff summit]

Sorry

[alpine sable]

np

good job

[stiff summit]

<@&286206848099549185>

My helper can’t help any more

Apparently their account got hacked

[alpine sable]

make y the subject of the formula

[stiff summit]

1/2+2/5t-1=1/5t+t

[alpine sable]

what

[alpine sable]

do you understand what i mean?

y = something

you have 1/6y+3/8x=24

[stiff summit]

I need help with the other problem

Not that one

[alpine sable]

? i read from pins

[stiff summit]

I already had help with that one now I need help with this one

[alpine sable]

whats the problem

[stiff summit]

1/2+2/5t-1=1/5t+t

[alpine sable]

yes and?

[stiff summit]

How to solve it?

[alpine sable]

do you know how to simplify this

adding like terms

variables on one side

[stiff summit]

Ye

[alpine sable]

go on

[stiff summit]

Like what do I need to simplify

[alpine sable]

...

[alpine sable]

solve for what exactly t?

[stiff summit]

Yes

[alpine sable]

...

go on

[stiff summit]

How do I get the variables to one side?

[alpine sable]

5x + 3 = 6 - 3x

how do you go about this?

[stiff summit]

6-3

And -3x-5

[alpine sable]

an equation please

[stiff summit]

-3x=-5

[alpine sable]

no

[alpine sable]

we had this

[stiff summit]

Yes

[alpine sable]

you isolated the variables and the constants

what is the full equation

[stiff summit]

I subtracted -5 from -3 and got 8 and then I took -6 from 6 and got 0

[chilly idol]

So you got -3 = -8x

[stiff summit]

Yes

[alpine sable]

5x + 3 = 6 - 3x
5x+3x = 6-3

do you see what i did

[stiff summit]

Yes

[alpine sable]

finish simplifying

and we get to your question

[stiff summit]

2/7

2/8

[alpine sable]

what is 2/7

[stiff summit]

2/8!

[alpine sable]

what is 2/8!

[alpine sable]

what were we doing here btw

[chilly idol]

So your saying that you got 2/8 for x? We are solving for x

[stiff summit]

Yes

That’s what I meant

[chilly idol]

Thats not quite right

Lets take it back a step

[stiff summit]

@alpine sable is this ur first time helping someone out?

Ok

[chilly idol]

As said by Sen we have 5x+3 = 6-3x

[stiff summit]

Yeah I have that

[chilly idol]

The easiest way to do this is to add 3x to both sides of the equation

Then subtract 3 to both sides

[stiff summit]

But the they put both like terms on the same side

[chilly idol]

As said by Sen

[chilly idol]

Explain

[alpine sable]

hmm so what is the equation then

we started with 5x + 3 = 6 - 3x

we then isolated the variables 5x + 3x on one side and the constants 6-3 on the other side this is all to get x

so when you simplify what do you get for x

[stiff summit]

5x + 3 = 6 - 3x
5x+3x = 6-3 is what they had

[alpine sable]

night remind me again why we are doing this?

[alpine sable]

...

[chilly idol]

Yes, and if you add the like terms... you'll get ||8x=3||

[chilly idol]

This was her orginial equation?

[stiff summit]

That’s what we started with

[stiff summit]

I messed up a little

[chilly idol]

So Sen you used 5x +3 = 6-3x as a way to test her skill?

[alpine sable]

yes

[chilly idol]

I want to be on the same page as you

ok good

[stiff summit]

That was not how I was taught

[alpine sable]

do you know how to solve equations

[chilly idol]

What did you mess up on? We can take it slow for you to understand. It would be better if you could send us a picture of your work

[stiff summit]

I erased it when you came into the picture so let’s just start over

[stiff summit]

Yes, but you’re not good at explaining it.

If that’s okay

[chilly idol]

Uh ok. Lets start with a basic equation, as a little side quest. Lets say we want to solve for x in the equation 3x+5 = 0

What would we have to do first?

[stiff summit]

You want to take 5 and -5 by itself and do it to the zero

[chilly idol]

Remember the whole idea of solving for x is to isolate x to one side of the equation and leave the constant on the other side

[chilly idol]

Yes good

So when we do this we will get 3x = -5
Remember we are doing -5 to both sides of the equation!

[stiff summit]

That’s what I said

[chilly idol]

The 3 is being multiplyed by the x, how do we cancel out something thats being multiplyed?

We need to do the opposite of multiplication.

[alpine sable]

np i'll leave it to bing

[stiff summit]

So it’s -5/3x

[chilly idol]

Yes

no you made a mistake

Don't divide by 3x
Only divide by 3

[stiff summit]

Ok

[chilly idol]

Remember we are leaving the x variable on one side of the equation

Thats the whole idea of solving for x

[stiff summit]

I know sorry,

[chilly idol]

Don't be sorry

You are doing a good job

So now we have x = -5/3

[stiff summit]

Yes

[chilly idol]

This is it

We are done

Thats how you solve for x

lets go back to the original question

[stiff summit]

Ok

[chilly idol]

This one here

We first have to find the common denominator

Man I wish I could used the texit tool 😦

[stiff summit]

Ok

[chilly idol]

Hold one sec

Hold on

[stiff summit]

10?

[chilly idol]

nah wait for a minute

[stiff summit]

Why

[chilly idol]

This is what we have

For reference t is writen as capital T

For no confusion with the + symbol

[stiff summit]

Ok

The common denominator is 10. Right?

[chilly idol]

No we have variables in the denominator as well

Give me a minute to figure this out

[stiff summit]

Yes, but don’t we have to find the same denominator for all of them? Ok

[chilly idol]

I feel like im going to pass out

[chilly idol]

It would be preferrable that we find the same denominator on both sides so we cancel out and add up the numerators. I'll show you

[stiff summit]

Ok

[stiff summit]

Honestly, same

[chilly idol]

Sorry but I don't think i can do it

I gotta go to bed

Use the helper ping which is this

<@&286206848099549185> @stiff summit Needs help on solving for x

[chilly idol]

Equation is here

[stiff summit]

Ok

@tall talon

[lone heart]

@stiff summit Has your question been resolved?

[lone heart]

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[lone heart]

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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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[alpine sable]

Hi, tried using logarithmic differentiation to find y’, is this correct?

[alpine sable]

This channel’s taken

[lone heart]

@alpine sable Has your question been resolved?

[serene junco]

seems right, but you didn't really need logarithmic differentiation, since you didn't have any variables in your exponents

you could have just used the product and quotient rules

[alpine sable]

The question actually made me use logarithmic differentiation

[serene junco]

oh

well

[alpine sable]

Yeah I guess I could’ve

[serene junco]

either way, yeah looks good 👍

[alpine sable]

Thanks!

[serene junco]

np 👍

[alpine sable]

I actually have another question

How am I supposed to differentiate y = (sinx)^(lnx)

[serene junco]

now, in that case, you do have a variable in the exponent

so you do need logarithmic differentiation

[alpine sable]

I think I got it

Hold on

[serene junco]

watch out, you forgot to actually take the log on the right side

your second line should be

ln(y) = ln(x) ln(sin(x))

not

ln(y) = ln(x) sin(x)

[alpine sable]

This is better right

[serene junco]

yes looks good

[alpine sable]

Last question

Quite similar

But

y’, considering x^y = y^x

Would be

Cleaner like this

[serene junco]

I think everything's right except this 1/y came out of nowhere

let me check one more time

[alpine sable]

You’re right it did pop out of nowhere

I fixed it

[serene junco]

I think, on the left you have $\ln(x)- \frac{y}{x}$, not $\frac{\ln(x)-y}{x}$

[ocean seal]

tatpoj

[serene junco]

it seems like you inadvertantly switched betwee these two

[alpine sable]

Where’s the mistake?

[serene junco]

wait one sec, I think you're right

[serene junco]

yeah my bad, you got it

[alpine sable]

No worries, I’m working on other stuff too

Perfect!

Just one last thing, if you don’t mind

I have no idea where to start

[serene junco]

The hint is a big hint

y = x^y

[alpine sable]

Is y = x^x^(…)?

This wouldn’t make sense though

It would give me

x^x^(…) = x^x^x^(…)

[serene junco]

isn't this true?

[mellow knoll]

An infinite amount of x's is still infinite whether u remove one or not

[alpine sable]

So it is infinite

[serene junco]

it may converget to something finite. let's find out

[serene junco]

do you agree that this is true?

[alpine sable]

Yup

[serene junco]

then you can use logarithmic differentiation from here

you don't have to worry about anything infinite

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

I’m too zoned out to finish this right now

I’ll come back to it tomorrow

Thanks for your help

[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:
• 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!

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[lament brook]

I am so confused, pease help

[nimble fern]

do you know what is "limit method"?

[lament brook]

i think its the f(x+h)-f(x)/h

^ as h-> 0

[nimble fern]

very good

[nimble fern]

so you can first do that and see what you got

[lament brook]

thats the part im confused on

i got some big number

[nimble fern]

show please

[lament brook]

ok one sec

[nimble fern]

oh ok lemme check

[lament brook]

tyty

[nimble fern]

i was checking the numerator right now and i think it's wrong already

[lament brook]

oops

[nimble fern]

do you have steps?

[lament brook]

yes, but its super wrong

Ignore the pencil part

[nimble fern]

I'll check bow

,rotate

[lament brook]

ohh thats what the command is, i thoguht it was .flip

[nimble fern]

ohhh

[nimble fern]

.

[nimble fern]

you didn't calculate the 2nd part of the numerator

and the first part of yhe numerator it's +6hx instead of +3hx

[lament brook]

is it okay if you send you work? i am a visual person 😅

[lament brook]

ohhh

ive been factoring for 5 hours straight aaaaaaaa my brain is not working

[nimble fern]

(3x+3h-1)(2x+2)-(3x-1)(2x+2h+2)
6x²+6x+6xh+6h-2x-2-6x²-6xh-6+2x+2h+2
6x+8h-6

4(x+h+1)(x+1)
4(x²+hx+2x+h+1)

[lament brook]

tytyty

thebn after this step do you substitute h as 0?

[nimble fern]

you night (not sure) need to do something more to simplify it in order to get rid of the h at the denominator

[lament brook]

true

[nimble fern]

btw, keep the denominator without factorizing is better

[lament brook]

yeah

wait but if i do get the euation, how do i find the tangent line?

do i need to find the derividanct of f(x)?

then plug in 3 to find y

and finally do the euqation

[nimble fern]

since you already found the derivative, you just plug x=3 to find the

• point on the curve at x=3
• slope of the tangent at x=3

[lament brook]

ah okay tyty

[lone heart]

@lament brook Has your question been resolved?

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[lone heart]

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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.

[lament brook]

how do i start?

[lone heart]

Please don't occupy multiple help channels.

[lament brook]

.close

[lone heart]

Channel closed

Closed by @lament brook

Use .reopen if this was a mistake.

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.

[shy wigeon]

help

[lone heart]

Please don't occupy multiple help channels.

[shy wigeon]

hi

can you help me with my homework

[alpine sable]

So for the LHS the circle theorem you need is that "opposite angles in a cyclic quadliteral add to 180"

Forget the little quad, that's not the quad we mean, we mean the bigger one, what's the opposite angle to 110?

[shy wigeon]

uhh

y and x?

[alpine sable]

y is the one you want

y + 110 is 180

[shy wigeon]

ya

[alpine sable]

So you can get y

[shy wigeon]

so y is 180?

[alpine sable]

No, y + 110 = 180

[shy wigeon]

and what do i do with the 180?

[alpine sable]

Well this is an equation, you should be able to solve it to find what y is

[shy wigeon]

wait im thinking

180 - 110?

[alpine sable]

Yes

[shy wigeon]

wait'

i should get 70

y = 70?

[alpine sable]

Yes

[shy wigeon]

and i need to get x now

[alpine sable]

You need another circle theorem

[shy wigeon]

how

[alpine sable]

The top right one

[shy wigeon]

oh so 110 % 2 = 55?

x is 55?

[alpine sable]

No

It's not a division first off, and second you used the wrong angle

You want to work out the O bit first then you can do 360-that for X

[shy wigeon]

360 - 110?

[alpine sable]

That's not O, use the circle theorem in the top right

O is 2 × y

[shy wigeon]

ya

is it 140?

70 x 2

hey

im stuck

can you help me with my homework

[alpine sable]

Yes but you need to actually try

It's 140

From there you can get x

[shy wigeon]

i am stuck at all of that question

can you helpme

[alpine sable]

Jesus fucking Christ no

[shy wigeon]

sorry

[alpine sable]

I'm sorry I hope you're trolling

[shy wigeon]

no

i am for real

1 question?

help me with 5 and 6 please

[alpine sable]

The second is exactly the same logic as the first

I've already laid out all the steps

[shy wigeon]

ok

[shy wigeon]

ok im gonna try do it 1 by 1

@alpine sable x is 220?

hey

hey

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[shy wigeon]

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[deep grotto]

i have a problem regarding distribution i never encountered before:

[deep grotto]

$12x - \frac{x+4}{x-4}$

[ocean seal]

marty

[deep grotto]

$\frac{12x^2-48x}{x-4}-\frac{x+4}{x-4}$

[ocean seal]

marty

[deep grotto]

i represented 12x as a fraction with the common denominator

and the right term had a negative sign in front of it

when I now want to compose this fraction together as a single fraction, do i distribute the negative sign over (x+4) to become (x-4) ?

as in, A or B ? :

[wanton umbra]

(-1)(x+4)

[deep grotto]

okay, so i distribute

[pale kestrel]

uh

you put brackets

[deep grotto]

which then can be distributed

[pale kestrel]

youre technically writing this with fractions

the brackets are implied with the notation

[deep grotto]

aha, right, this makes sense

so because we're dealing with fractions we're dealing with brackets, and then naturally we distribute

i was assuming this but i don't think i ever came across this at least consciously

still somewhat new to thinking naturally about distribution 🙂 thank you anyhow. Then I assume the answer would be

$\frac{12x^2-48x-x-4}{x-4}$

[ocean seal]

marty

[deep grotto]

after distribution (obv didn't simplify x)

[pale kestrel]

yes, but dont skip the middle step

when doing workign

,,\frac A C - \frac B C = \frac{A - B}C

[pale kestrel]

as in, id write this always because skipping it often leads to mistakes

[deep grotto]

so basically to write out the brackets before distributing ?

at least in this case where i want to distribute

[pale kestrel]

before this, i would write

[deep grotto]

yes okay, i see

i would also do so but with the stuff im currently doing i try to minimize space used on my sheet

so i try to do distribution in my head also for my own practice and to consciously apply it

[pale kestrel]

yeah well, mental arithmetic is actually generally bad practice

that ppl highschool ppl pick up

mental algebra - as opposed to writing all your steps out

[deep grotto]

yeah i get ur point, i would skip stuff that made mistakes a lot, perfect example for me was simplifying fractions and not really knowing why it worked, then i started explicitly writing like *4 next to nom. and denom. and it has helped a lot

[pale kestrel]

👍

[deep grotto]

i don't write down the bracket expansion because it's a step i'm very conscious about rn (even having me ask this question here) but i try to be explicit about everything i can

thank you for your advice i really appreciate it

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[pseudo schooner]

hello I need help here how can I get the mass cuz I don't understand anything from the professor and first time to take chem

[languid bolt]

V = 27 000 cm^3 right?

[pseudo schooner]

yup

[languid bolt]

And density is 0.0025 kg/cm^3

[pseudo schooner]

yup

[languid bolt]

that would mean that every cm^3 would be 0.0025 kg in mass

so what would 27.000 cm^3 be in kg?

[pseudo schooner]

27000(0.0025)?

[languid bolt]

yes

you're welcome

[pseudo schooner]

67.5 so thats the mass?

[languid bolt]

,calc 27000*0.0025

[ocean seal]

Result:

67.5

[languid bolt]

yes

kg

in kg

dont forget

[pseudo schooner]

so thats the answer or theres more process?

[languid bolt]

that should be it

[pseudo schooner]

ok thx

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[pseudo schooner]

.reopen

[languid bolt]

Here are the three equations to use:

Mass = Density x Volume.
Density = Mass ÷ Volume.
Volume = Mass ÷ Density.
@pseudo schooner

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✅

[pseudo schooner]

tysm

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[pseudo schooner]

.reopen

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✅

[pseudo schooner]

my classmate sent me her answer but I dont understand

how did she get that mass?

[vale wigeon]

,rccw

[vale wigeon]

quite messy handwriting she's got

but she could only have gotten the mass as volume * density

[pseudo schooner]

but its 7.5×10^-2 if converted in scientific notation

[vale wigeon]

you cannot drop the units

[pseudo schooner]

what

[vale wigeon]

ok, let's walk through the calculation step by step

volume = (30 cm)^3 = 27,000 cm^3 = 2.7 * 10^4 cm^3

agree or disagree

[pseudo schooner]

aggree

[vale wigeon]

ok

density = 0.0028 kg/cm^3 = 2.8 * 10^-3 kg/cm^3 = 2.8 g/cm^3

agree or disagree?

[pseudo schooner]

agree

[vale wigeon]

mass = volume * density
=> mass = (2.7 * 10^4 cm^3) * (2.8 g/cm^3)
=> mass = 7.56 * 10^4 g

agree or disagree?

[pseudo schooner]

agree thx for explaining it to me

btw how did it become gram?

[vale wigeon]

10^-3 kg = 1 g

1 gram is 1/1000 of a kilogram

[pseudo schooner]

ok thx so much

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[bleak geyser]

HIII

[bleak geyser]

I got good sleep

I’m ready to go

[wanton umbra]

,rccw

[bleak geyser]

I know we have to factor the top

[wanton umbra]

ok

[bleak geyser]

,tex $\frac{x^2+2x+4x+8}{x-2} <= 0$

[wanton umbra]

ok

[ocean seal]

ahaan

[bleak geyser]

If u factor it I get a non similar factor than the denominator