help-0

[celest zinc]

6(r-2)(r-1/2)=0

Yeah, sadly I cannot help you with that unless I guess what you did

[chrome plank]

I got it, thanks a lot

I really mean it

[celest zinc]

🙂

[chrome plank]

.close

[lone heart]

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[surreal kindle]

okay so I just need help understanding something

[surreal kindle]

heres graph 1

and heres graph two

the equation for the first graph is

so 4 would be the a value

pi/20 is the k value

and 5 is the c value

to get from graph 1 to graph 2, I thought that I would have to transfer it right 10 units

but it's only actually moving a quarter of the period

for example: a period is 20 units, and I want to move it a quarter way to the right

but the only way that I can move it quarter way to the right is by putting the input for HALF of the period

sorry hard to explain over text

[devout summit]

Period is not 20 units here.

[surreal kindle]

in other words how can I find D value

okay wait

how would i get the period to 20 units?

I just realized this now

a is the amplitude right

so would K be pi/20 since 20 is the length of the period

and c is the center axis

[devout summit]

In both your graphs, period = 40

[surreal kindle]

frick so the problem isnt the d value then

okay just to confirm

a is amplitude

wait sorry im all over the palce rn

how would I get a period to be 20 units?

[devout summit]

Which "a"?

[surreal kindle]

cuz the equation y=asin(k(x-d))+c

used for translations

[devout summit]

Ok understood

[devout summit]

Why would you want that?

[surreal kindle]

thats just the requirement for my assignment

i was given a graph with a period of 20 units

amplitude of 4 units

central axis of 5

and the lowest point is in contact with the y axis

im pretty sure i got the amplitude right

as well as the central axis and the phase shift/horizontal translation(D)

so i think the problem is with my K value

so i guess i got the wrong thing wrong

how would I find the K value from a periodic function is my question

didnt realize my period wasn't 20 until now

this is the way that my teacher put it

360/period=D value

if i put 360 then it obviously doesn't work

but one full rotation is pi on a normal sin periodic function

[devout summit]

Wait. Shouldn't that be = k?

[devout summit]

One full rotation is 2π on normal sin function

[surreal kindle]

yes K

[surreal kindle]

oh i see

ohhh

so thats where my problem is

okay i changed pi to 2pi

it works

Thank you so much!!!!!

.close

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[placid trellis]

b

[placid trellis]

the ans 432 but i didnt get it

[lone heart]

@placid trellis Has your question been resolved?

[placid trellis]

<@&286206848099549185>

[shell widget]

@placid trellis You have 4 consonants(MDCL) and 3 vowels(AEI). To form the four letter words we need, we need 2 consonants and 2 vowels. So we have (4C2)(3C2) and finally since arrangement matters here, we add a 4!.

(4C2)(3C2)(4!)

[placid trellis]

but four letters

[shell widget]

yes?

[placid trellis]

isnt that 8

[shell widget]

wdym?

[placid trellis]

idk maybe i understood thing wronly here

4c2 means we choose 2 out of 4 right?

[shell widget]

Yes,

[placid trellis]

and the remaining 3c2

why we add 4!

?

[shell widget]

Because when doing 4c2 and 3c2, arrangements dont matter

but in the final result, we need arrangement to matter

we chose a total of 4 letters so we add 4!

[placid trellis]

ouh so if five letters 5! ?

thanks!

[shell widget]

np

[placid trellis]

appreciate this

eh wait

why c instead of p

[shell widget]

it says contains 2 consonants(and so it must contain 2 vowels as well)

[placid trellis]

i got the a) by using P is that wrong?

[shell widget]

we dont know which consonants and which vowels, so we account for the number of possibilities of choosing

in the end we account for the arrangement by adding the 4!

depends on how u did it tbh

[placid trellis]

okay thanks again

[placid trellis]

are u free rn?

[shell widget]

kind of

[placid trellis]

im about to cry

\

im trying to relate but i fail to see

[shell widget]

ok so i had to search this since i didnt know it myself, you need to use P(A | B) = 1 - P(A' | B)

' stands for complement

and im assuming the bar in your pictures is the complement as well

[lone heart]

@placid trellis Has your question been resolved?

[placid trellis]

Ouh

Its okay then thanks!

[lone heart]

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[supple laurel]

nvm

.close

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[humble marsh]

Could someone please explain how this works I’m completely lost and I have a quiz on this tomorrow

[fathom mantle]

you just plug in the values you are given then compute to solve for r

[humble marsh]

I’m confused on how it becomes 442/3 we have never been taught this and our teachers says we are supposed to know it and we can’t ask her for help outside of school

[fathom mantle]

you either use a calculator or do mental math

[humble marsh]

I get how it equals 442 but is it 3 as the denominator because it’s the denominator in the original problem?

[fathom mantle]

Yes, if you do the calculations

[humble marsh]

Ok thank you

Could I ask for help with one more problem

[fathom mantle]

sure, ask

[humble marsh]

How do I find the values of sine and cosine using tan=5/12

Is it just sohcahtoa?

[fathom mantle]

Well, draw a triangle first

[humble marsh]

Ok

[fathom mantle]

you have 5 and 12. You need three numbers. How can you get the last number?

[humble marsh]

Pythagorean theorem

[fathom mantle]

Correct

[humble marsh]

Thank you this is just stressing me out so I’m overthinking everything

[fathom mantle]

Good luck on your quiz tomorrow !

[humble marsh]

Thank you very much

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[ripe shuttle]

for this question

ive done cscx/secx + cosx/sinx but it does not work

[buoyant kayak]

yeah that's not right

[ripe shuttle]

should i like get the same denominator first

[buoyant kayak]

no, you're trying to use even/odd

$\cos{(-x)}=\cos{x}$

[ocean seal]

a disappointing son

[ripe shuttle]

this is wrong

[buoyant kayak]

yes it is

[raw shard]

you aren’t applying them being even/odd correctly

[ripe shuttle]

o im not?

[raw shard]

no

you’re basically saying they’re all even there

[ripe shuttle]

OK got it

but whats the next step

[raw shard]

simplify the fractions

i suggest recalling that csc and sec are reciprocals of sin and cos

[ripe shuttle]

i got it

[raw shard]

now remember that a/(b/c) = (ac)/b

[ripe shuttle]

how do you know what to do next

[raw shard]

recall what cos(x)/sin(x) is equal to

i’m sure you can do the rest

[ripe shuttle]

okk thank you lemme try

OK

I GOT IT

thank you sm

can i ask more than one math question

[raw shard]

yes

[ripe shuttle]

ok for this one

i think i did top 2 steps right

what does secxcosx = to

[raw shard]

sec(x) = 1/cos(x)

[ripe shuttle]

OOOOOOOOOO

1/cosx * cosx = 1

so it all cancels out

so =1

thank u

[raw shard]

@ripe shuttle do .close if you’re done

[ripe shuttle]

i still got a couple questions

[raw shard]

ok that’s fine

[ripe shuttle]

wait can i

cross cancel out one of the cos

[pliant zephyr]

yes u can

[ripe shuttle]

what can i do next

oh i think

1/csc^2x

[buoyant kayak]

it wouldn't be 1/(csc^2(x))

[ripe shuttle]

huh

[buoyant kayak]

just csc^2(x)

[pliant zephyr]

1/cos^2x=cosec^2(x)

then u get it

[ripe shuttle]

OK

is this right

[buoyant kayak]

seems okay

[ripe shuttle]

thank u

confused

do i multiply top and bottom by 1+cosx

[plush quail]

Yes, and you don't need to turn the top into 1/csc

[lone heart]

@ripe shuttle Has your question been resolved?

[lone heart]

@ripe shuttle Has your question been resolved?

[plush quail]

Yeah, you then do $\frac{-sin-cos sin}{sin^2}=-\frac{sin}{sin^2}-\frac{sin cos}{sin^2}=-\frac{1}{sin}-\frac{cos}{sin}=-csc-cot$

[ocean seal]

pastalover69

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[pine monolith]

https://discord.com/channels/@me/927435681637212170/928877144183033937

[pine monolith]

the first one

[sly mantle]

we cant see dms

[jagged imp]

"this link is to a server or channel you don't have access to" pogchamp

[pine monolith]

oh lol

https://drive.google.com/file/d/1TgsiAzp9jICDOILBBOUKXEBem_nfwm7Y/view?usp=drivesdk

Now try

The first one

Is it

a=-x
B=x
C=-x²

poggers

@jagged imp here it is

till then

i will be trying

[jagged imp]

I think you misunderstood the problem. You want a triple of integers (a,b,c) such that all of them are roots of the equation x^3+ax^2+bx+c=0. -x, x, and -x^2 are not integers

Not even constants, as a matter of fact

[pine monolith]

oh

oh so it wants to put a in x^3,b in x^2 and c in x such that the equation becomes true

right?

[jagged imp]

no. I'll use an example of an "almost" solution to explain it. However, the triple im gonna show you is not a solution to the actual problem since the problem requires distinct integers, and 0, 0, and 0 aren't distinct. Suppose (a,b,c)=(0,0,0). Then, the equation is x^3=0. We then check that 0 is a solution. 0^3=0 so it is. Since each of a, b, and c solves the equation x^3=0, (a,b,c)=(0,0,0) is a solution.

[pine monolith]

oh

so it just wants me to keep the coeficients in this way that they multiply wit x^3,x^2,x and add up to gimme 0

[jagged imp]

I'm struggling to figure out what you mean by that so I can't really tell you its a valid summary.

[pine monolith]

ok

soo

how to appproach the true solutions

i now understand the meaning of the question

ok i guess

i will have to ping

lol

sorry

@jagged imp

[jagged imp]

Vieta's formulas should do some good work here.

[pine monolith]

its probably not for a 8th grader right?

[jagged imp]

Depends on the 8th grader. I think the majority of 8th graders could understand it given enough time and guidance. But I also think the vast majority of 8th graders couldn't solve it at all without guidance. If you want some fun competition math problems that are "made for 8th graders" I might suggest checking out the amc 8

https://artofproblemsolving.com/wiki/index.php/2020_AMC_8

[pine monolith]

i have done that

[jagged imp]

I also don't have a great understanding of the mathematical literacy and knowledge of an average 8th grader

[pine monolith]

i asked one friend that i made here to gimme some question that they think that it is hard for em

[jagged imp]

With these kinds of problems, a lot of it just comes down to practice

[pine monolith]

oh

that friend whom i asked is a 8th grader

and said that they were able to solve just 2 of it

i donno how to even approach it

*doubts his intelligence

[jagged imp]

Don't pin your self worth on how well others are doing. If your friend can solve 2 of those they're a very highly above average 8th grader

do you know where those problems are from?

[pine monolith]

they said

its from

asc

ok so now

i am just trying to do the same thing

in a simplified version

the equation is

ax+by=0

i am first doing this one

i would inform about the updates

[lone heart]

@pine monolith Has your question been resolved?

[pine monolith]

Nope

[pine monolith]

@jagged imp should not there be like infinite such a and b

In this case

Help

[lone heart]

@pine monolith Has your question been resolved?

[lone heart]

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[broken gorge]

Hello! Could someone please help me understand the error in my solution? This is the solution given in the book, it uses odds

[broken gorge]

ah

crap that won't do

one sec I'll just send a picture

Sorry, I don't quite follow

Ah. I'm sorry. No wonder I felt like I was banging my head against a brick wall on this problem

Okay. It matches up perfectly now. Thank you so much

I can't imagine how much more time it would've spent me skipping over the first sentence

.close

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[alpine sable]

I need help at math just dm me

[alpine sable]

is there some kind of tutor here ?

[severe sluice]

send the question here please

[alpine sable]

Ok wait

I need help at principal amount unknown

@severe sluice

[severe sluice]

do you know what those words mean

if yes

this should be simple

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@alpine sable Has your question been resolved?

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[orchid pulsar]

solved part a. Can i get help with b?

[orchid pulsar]

answer for a is sqrt(3)e^(5pii/6)

for b is the complement of z same as z but raised to the power of negative instead?

[alpine sable]

$\mathop{conj}(re^{\theta i}) = re^{-\theta i}$

[ocean seal]

Matthew8

[orchid pulsar]

alright and in that case do I just apply r*(cos(theta)+isin(theta))?

[alpine sable]

Since the question asks you to give the answer in the form $a+ib$, you probably want to do that

[ocean seal]

Matthew8

[orchid pulsar]

ok and I get (-3-sqrt(3)i)/2)^6

do I need to compute it the long way now?

[alpine sable]

Why don't you apply the power before writing $e^{\theta i} = \cos(\theta) + i\sin(\theta)$?

[ocean seal]

Matthew8

[alpine sable]

This will help https://en.wikipedia.org/wiki/De_Moivre's_formula#Relation_to_Euler's_formula

[orchid pulsar]

ohhhhh rightt

ok i got it now

thanks!

[lone heart]

@orchid pulsar Has your question been resolved?

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[glad sluice]

please help

[lone heart]

@glad sluice Has your question been resolved?

[alpine sable]

What have you tried, can you spot some symmetry?

[glad sluice]

I tried using a^2 + b^2 + c^2 = -2
but that just complicated it more

[alpine sable]

Hi frens

[lone island]

Have you tried vietas formula?

[lone heart]

@glad sluice Has your question been resolved?

[glad sluice]

how would I use those?

i know i will have to use those, but i can't get in what way

should I simplify

[lone island]

I'm not sure

I haven't solved it yet myself

[glad sluice]

okay

[lone island]

Ofc, finding a,b and c is always an option

[glad sluice]

oh lord no

[lone island]

Lmao

[glad sluice]

2 of them are complex

that's hell

[lone island]

You're in for hell either way tbh

[glad sluice]

[lone heart]

@glad sluice Has your question been resolved?

[lone heart]

@glad sluice Has your question been resolved?

[wild tundra]

.reopen

.close

[lone heart]

@glad sluice Has your question been resolved?

[smoky isle]

carry the on dude

easy stuff

[lone heart]

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[alpine sable]

Hi could someone please help me?

I have tried dividing and that wasn’t correct

[strong hornet]

well average speed is just

speed = |v| = ∆x/∆t

= displacement/time

[alpine sable]

What is the triangle?

[strong hornet]

it just indicates

change

you'll see it later when you're introduced to slope

ok so for the question, you can just plug in the values

so

your displacement will be 15 miles

and the elapsed time will be between 45 and 50 minutes

[alpine sable]

15/45?

[strong hornet]

so first find the speed when it takes 45 mins to travel 15 miles

and then do the same with 50 mins

[strong hornet]

exactly

now simplify that

[alpine sable]

It’s 0.33333333

[strong hornet]

oh wait

it's miles per hour

[alpine sable]

And 0.3

[strong hornet]

so ur gonna have to convert those minutes

into hours

45 minutes is 3/4 of an hour

so instead of 15/45

you do

15/(3/4)

[alpine sable]

20?

[strong hornet]

yeah

now do the same with

50

50 mins is just

5/6 of an hour

[alpine sable]

5/6

[strong hornet]

yep

[alpine sable]

18?

[strong hornet]

mhm

so ur answer should be e

[alpine sable]

Ohhhh ok thank you!

.close

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[alpine sable]

Sorry but could anyone please help me again?😅

I didn’t try this because I don’t know how

[severe sluice]

use d=vt to calculate the velocity when the plane is travelling against the current

and the velocity when the plane is travelling with the current as well

[alpine sable]

Ok but it says train

At the end

[strong hornet]

probably a typo

[alpine sable]

Oh lo

[alpine sable]

I still don’t understand

[bleak ridge]

Plug in variables to d=vt

[severe sluice]

hi papabread

[bleak ridge]

Yes

[alpine sable]

3200 x 5?

[bleak ridge]

V is velocity

[alpine sable]

3200/5

[bleak ridge]

Yes

[alpine sable]

640?

[bleak ridge]

,calc 3200/5

[ocean seal]

Result:

640

[bleak ridge]

Yes

[alpine sable]

Then what

[bleak ridge]

Do it for other

[alpine sable]

300

[bleak ridge]

Yes

So baseSpeed with the wind is one thing

And baseSpeed against the wind is another thing

You can calculate stuff from there

[alpine sable]

Waits o then what do I do

[bleak ridge]

Say base speed with no wind is v

And wind is w

Try writing the two equations

That I said above

[alpine sable]

D=wxt??

[bleak ridge]

I mean like

Speed with wind = 640

Then speed without wind

[alpine sable]

Yea

300

[bleak ridge]

In terms of v and w

[alpine sable]

Could u maybe write it out?

Please?😅

[bleak ridge]

Well when its with the wind

The wind adds to the original speed

And thats the actual speed

What you calculated

[alpine sable]

Huh

So the wind that they told us

Adds to like 640?

Or 300?

[bleak ridge]

Both

Depending on which direction youre going

[alpine sable]

300+600?

[bleak ridge]

Well youre not sure what the wind is yet

[alpine sable]

True

[bleak ridge]

So hence the variables

v and w

[alpine sable]

Ya

[bleak ridge]

Lemme just say it since its a bit confusing how Im saying it

v + w = 640

v - w = 300

Does that make sense

[alpine sable]

Uh

Nothing works

[bleak ridge]

Wdym

[alpine sable]

I’m think about what v and w could be

[bleak ridge]

Oh

Do you know how to solve systems?

[alpine sable]

Not really

[bleak ridge]

Theres a couple methods

One of which I dont even remember

So

Basically you solve for the same variable in both equations

Then set them equal using that variable as the glue

So like if you had a+b=5 and a*b=3

You could solve for either a or b

Ill do a

a=5-b for the first

a=3/b for the second

Then notice that both equations are equal to the same thing

a

So then both equations are actually equal

5-b=3/b

Then its just algebra from there

[alpine sable]

Ohhh

Ok

Then how would I use that in the question

[bleak ridge]

Uhhhhh

You try solving for v in both

[alpine sable]

Then we don’t even know the w

[bleak ridge]

Youll just keep the value held in the w

Until you can figure it out

Which is whats nice about using variables

You can have absolutely no clue what it is and still use it like a normal value

[alpine sable]

But you need v + w

We don’t know both

[bleak ridge]

The purpose of the first step is to kinda

Brush one of the variables under the rug

[alpine sable]

Which one

[bleak ridge]

So you dont have to worry about it

You can choose

[alpine sable]

V

[bleak ridge]

I said v but either works

[alpine sable]

Okk

640?

W= 640?

[bleak ridge]

That would only be the case if v was 0

Because v+w=640

Youre just trying to get v alone on one side

Just like solving for x

[alpine sable]

That could be any number

[bleak ridge]

Ye

[alpine sable]

Yea soooo

300?

600?

[bleak ridge]

Do you know how to do just normal algebra solving?

Like uhh

5x+3=7

[alpine sable]

Yea

[bleak ridge]

So the whole premise is just doing stuff to both sides to accomplish some goal right

Usually isolating x

[alpine sable]

V=600-w

[bleak ridge]

Yes

But 640

[alpine sable]

640-w=V

[bleak ridge]

Ye

So then whatd the other one be

A couple more steps

[alpine sable]

300 + w= v

[bleak ridge]

Well actully not a couple more

I was thinking of solving for w

Yeah thats right

So now notice

640-w=V
300 + w= v

These two equations are equal to the same exact number

v

Therefore every one of the expressions are equal

640-w is equal to 300+w which are all equal to v

So you can cut out the middle man

And just say 640-w=300+w

[alpine sable]

340

[bleak ridge]

Thats the first step yes

[alpine sable]

Yay ok

So TAHTS v

340 + w= 640

[bleak ridge]

Wait you forgot a step

[alpine sable]

?

[bleak ridge]

So you took 640-w=300+w

And subtracted 300 from both sides correct?

[alpine sable]

Yea

[bleak ridge]

So you have 340-w=w

Whatd be the next part

[alpine sable]

Uhmm

Idk that one

[bleak ridge]

w is just like x is

If you had 2-x=x whatd you do

To find what x is

[alpine sable]

X=x-2

[bleak ridge]

What would you do to both sides

[alpine sable]

Subtract 2

?

[bleak ridge]

Oh I see

I mean you could

But that doesnt help in isolating x

You wanna start shuffling the variable to one side

[alpine sable]

2=x+x

[bleak ridge]

Yes exactly

Or just 2=2x

[alpine sable]

X=1

[bleak ridge]

Indeed

So then whatd you do for the wind equation

[alpine sable]

340=x+x

340=2x

X= 170

[bleak ridge]

Yes

So now that you know wind

[alpine sable]

Yea

[bleak ridge]

What can you do with your original equations

The two v+w and v-w ones

[alpine sable]

170+340

[bleak ridge]

Yes but just 300

[alpine sable]

Ohh

170+300

[bleak ridge]

Ye

And notice what happens when you plug w into the other one

v+170=640

[alpine sable]

300+170?

[bleak ridge]

Yeah that was for the v-170=300 one right?

Cause v=300+170 using algebra

[alpine sable]

470?

[bleak ridge]

Yeah

Then what do you get when you solve for v using the other equation

v+170=640

[alpine sable]

V = 470

[bleak ridge]

Yes

Its the same

And thats a really good way to check that you got the right answer

The two different equations agree that v=470

[alpine sable]

Yea

[bleak ridge]

So now that you know the speed of the plane without wind

How would you finish off the problem

[alpine sable]

Uhmmmm

What’s the time

[bleak ridge]

Yeah how long it would take to travel 1880 miles

[alpine sable]

1880/60=31.33

[bleak ridge]

Whered you get the 60?

[alpine sable]

Hours

[bleak ridge]

Well you have 1880 miles

And 470 miles per hour

[alpine sable]

Oh lol

1880/470

[bleak ridge]

Yeah exactly

[alpine sable]

4

Ohh so that’s the answer

[bleak ridge]

Ye

[alpine sable]

Could we maybe like review really quick and write it out clearle

[bleak ridge]

Yeah there was a lot

Ill summarize the given values rq

[alpine sable]

Ok tyyy

[bleak ridge]

Trip against wind: 600 miles, 2 hours
Trip with wind: 3200 miles, 5 hours

Trip with no wind, 1880 miles, ??? hours

So first you calculated the speed for each trip

Dividing miles by hours because miles per hour

With wind speed: 640 mph

Against wind speed: 300 mph

Then you know you want to find the base speed of the aircraft, no wind

Which is changed directly by the speed of the wind

So you can set up the two equations

v + w = 640 (can be read as "velocity with wind equals 640")
v - w = 300 (can be read as "velocity against wind equals 300")

And solve using the method for solving systems

Just pick a variable to solve for and cut out the middle man

Then from there its just plain old algebra

Then finally you calculated the final speed and the time it would take to travel 1880 miles without wind

4 hours

[alpine sable]

Ohhh wow

Ok thank you so much!

[bleak ridge]

No problem

[alpine sable]

.close

[lone heart]

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[lone heart]

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[covert agate]

hi

[covert agate]

i don’t understand why for an interval, f’(x) > 0 implies its increasing

i get for an increasing function, for all h > 0 and x, (f(x + h) - f(x))/h > 0

i cant continue from here

help

[buoyant kayak]

positive slope --> increasing

[covert agate]

how to algebraically explain

[severe sluice]

definition of derivative?

[covert agate]

how

[severe sluice]

uhh.... i was just about to say that

[covert agate]

how to continue lol

[severe sluice]

but anyways

$\frac{f(x+h)-f(x)}{h} > 0 \Rightarrow f(x+h)-f(x) > 0 \Rightarrow f(x+h)>f(x)$

[ocean seal]

sam

[severe sluice]

@covert agate

[covert agate]

this is my process

[severe sluice]

(also i'm fake texit, remember me?)

[covert agate]

just the other way round

[covert agate]

(no 😦 )

[severe sluice]

from brilliantians

[covert agate]

wait oh yea

[covert agate]

anyway

this big thing’scalled difference quotient right

[severe sluice]

i don't get what you're saying

[covert agate]

(f(x + h) - f(x))/h

say this is Q(x)

[severe sluice]

but f(x+h)>f(x) is like the definition of "increasing"

[covert agate]

why does Q(x) > 0 imply lim Q(x) > 0

[covert agate]

i cant relate it to limits and by extension derivatives

<@&286206848099549185>

[lone heart]

@covert agate Has your question been resolved?

[fathom mantle]

yo

[covert agate]

hi

can you see my question

[placid zinc]

So yeah, ignoring the limit and using algebra, a positive derivative basically means that the function is increasing on the interval (x, x+h) for h → 0

I think to perfectly explain this, we need to use the definition of the limit. With that in mind, this now says "there exists some real number Δ such that, for all δ<Δ, f is increasing on (x, x+δ)"

[covert agate]

how

[covert agate]

huh

thats not the definition

[placid zinc]

That's the first "how"

[covert agate]

yea i get that

then what

[placid zinc]

For the second, I am filling in a few gaps, but this does use the ε-δ definition of the limit

[covert agate]

?

[covert agate]

this??

[placid zinc]

Ye

[covert agate]

i dont get jt

there’s no ε

[placid zinc]

Let's say the difference quotient was 1. Then, there must be a real number Δ where the function is increasing on (x, x+Δ). If there's no such real number, then the limit was false since the difference quotient would dip below 0 and this wouldn't pass ε-δ

[covert agate]

huh

[placid zinc]

huh

[covert agate]

wdym there must be a number Δ where the function is increasing

[placid zinc]

So a number looks like 5.184 or any other choice

Δ represents some number

[covert agate]

yea

[placid zinc]

A function takes a number and returns another number using some rule

"Increasing" on (a,b) means f(b) > f(a)

[covert agate]

i know

i can’t go from (f(x + h) - f(x))/h > 0 to f’(x) > 0

[placid zinc]

Good thing you don't have to

[covert agate]

????

[placid zinc]

I'm really lost on where you're lost, fam

If you have a question, feel free to ask

[covert agate]

question

to show for increasing f, f’(x) > 0 is desired result

[covert agate]

i think the former is close but i cant go on

[placid zinc]

So what are you asking?

Questions normally have question marks

[covert agate]

how to go from former to latter

[raw shard]

you don’t

because that’s not equal to the derivative

[placid zinc]

Oh, you mean to include the limit

[raw shard]

yeah

[covert agate]

yes

[covert agate]

huh

i believe i didn’t get first principles wrong lol

[raw shard]

i said that because you didn’t include the limit

[covert agate]

uea

how to include limit

[placid zinc]

Let's say the difference quotient was 1. Then, there must be a real number Δ where the function is increasing on (x, x+Δ). If there's no such real number, then the limit was false since the difference quotient would dip below 0 and this wouldn't pass ε-δ

[covert agate]

limit of a constant is apparently a constant

[placid zinc]

I'm sure someone could explicitly write that out, that's a lot of effort for me.

[covert agate]

i’ve caused the server so much trouble recently lmao

[placid zinc]

Okay

[covert agate]

this helps include the limit?

[placid zinc]

Ye

[covert agate]

here (f(x + h) - f(x))/h = 1

lim 1 = 1 > 0

i don’t see how it helps

[placid zinc]

Sorry, you're right I should have been more clear. Difference quotient is 1 at some specific point x

Can be any function

[covert agate]

so this proves the point for some x and some h

asdf

i still dont get it

[lone heart]

@covert agate Has your question been resolved?

[alpine sable]

no

[lone heart]

@covert agate Has your question been resolved?

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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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[dusky quest]

This thing i am asking for is electronic but it's pure maths<
I understood the first part (orange one )it was (a-b-c)^2
but I did not understood (blue part)

[dusky quest]

<@&286206848099549185>

[fathom mantle]

it looks like they used algebra

[dusky quest]

yes but what they did?
and how

I did not understood the blue part

[fathom mantle]

well do you know algebra?

play around with it

[dusky quest]

yes, but I tried and dat wasn't dat great!
is their any formula dat they use like for the orange part it was (a-b-c)^2

[fathom mantle]

no formula. they just moved things

[dusky quest]

yes, I tried dat as well
wait leme show you

even if we shift all dat, where is dat black part ?

and how dat extra -VT came from ?

[fathom mantle]

if you distribute those two, you get what exactly that. if you can't see that then you need a break from math

[dusky quest]

I am so sorry, Maths was always my weakest subject, thats why I came back and trying to understand all basics!

Can you elaborate more what they did and how ?

[fathom mantle]

Sorry, I can't help. Is late. Maybe someone else can help you.

well, first do you know how to distribute?

what is this, (2)(4x)

[dusky quest]

Okay no problem, I apricate your time and you tried !

[dusky quest]

it is gonna be 2 * 4x

[fathom mantle]

what? no is 8x

What I did is just distribute. goodnight. I hope someone helps

[dusky quest]

Goodnight mate! Thanks for help

[lethal tendon]

in the second equation you have a term $$-2\cdot(v_{IN}-V_T)\cdot v_{OUT}$$

expand that for me

ah hold on

[ocean seal]

dino dik

[dusky quest]

ahh
-2vIN --2VT

-2vIN+2VT

[lethal tendon]

yeah, then multiply both by v_OUT

then you get your black term

[dusky quest]

-2vIN * vOUT + 2VT * vOUT

[dusky quest]

wait

[dusky quest]

Ohh Yeah, thanks mate, I was scratching my head from so long!
I really appreciate you help

i got it now

Dmmm I wated one hour for this lol
why I couldn't see like you say!
Thank-you again

[lethal tendon]

like what the other helper said, there's no formula to do this. You just have to practice factoring and identifying like-terms

[lethal tendon]

[dusky quest]

yeah, I will do some practice with factoring

[lone heart]

@dusky quest Has your question been resolved?

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[lone heart]

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[feral moth]

How do I get U-value when I only have area, thermal conductivity and temperature difference?

[lone heart]

@feral moth Has your question been resolved?

[lone heart]

@feral moth Has your question been resolved?

[feral moth]

.close

[lone heart]

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[alpine sable]

. I’m going back to the a

.clise

.close

[midnight sand]

How would you do x²>x+5

[solid cargo]

Bring all to the lhs, complete the square

or just use the wavy curve method

[molten zenith]

Do you know the answer ? I have got one but i am not sure if it is correct or not ? @midnight sand

[lone heart]

@midnight sand Has your question been resolved?

[midnight sand]

no

[midnight sand]

idk this method*

[solid cargo]

ohk then for that ull have to see an article or something for that....

[midnight sand]

I only in year 8 👀 👍🏻

[solid cargo]

hmm...is the answer that x>(root(21)+1)/2 or x<(-root(21)+1)/2?

[midnight sand]

i'll just ask my teacher on monday then

[midnight sand]

idk

there is no answer shet

[solid cargo]

okk

[midnight sand]

the ks4 aqa maths book that my ScIEncCE teacher bought me does not even explain how u do it

[warped steppe]

im not sure but u can rearrange to get x^2-x-5>0 then solve for the quadratic

[midnight sand]

okai

.close

[lone heart]

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[alpine sable]

Α = 8 Χ 1/2 + (5+2³ - 3 1/2 Χ 2)
Β = 1 : 1/4 - (8+4² - 5 1/2 Χ 4)

[alpine sable]

3 1/2 is mixed number and so is 5 1/2
1/2 and 1/4 are fractions

<@&286206848099549185>

oh oops didnt read after 15 mins

sorry

hello?

[molten zenith]

You are just supposed to solve the equation ?

A=10

B=2

[alpine sable]

no

make a calculation

@molten zenith

the stuff in the brackets is calculated first

[molten zenith]

Ikr ?

These answers are correct right ?

[alpine sable]

bro

i need a calculation

to get the answers

[molten zenith]

Step by step ?

[alpine sable]

yes

(5+2³ - 3 1/2 Χ 2) is calculated first

same for B

[alpine sable]

i did this:
5+2³ = 13
13 - 3 1/2 = 13 - 7/2 = 9.5
9.5 x 2 = 19
19 + 8 = 27
27 - 1/2 = 13.5

could you confirm if thats right

my friend said everything is correct up to the last one, which he isn't sure about

[molten zenith]

Ik something is wrong but couldn’t pinpoint it

Just a sec

Ok get it, u cant minus 7/2 from 13 bcz of bodmas rules

1st solve 3 1/2*2 then minus it from 13

[alpine sable]

6?

[molten zenith]

BODMAS= brackets of division multiplication addition and subtraction

[molten zenith]

Yeah so 4 from outside+6=10 which is the answer i gave at start

[alpine sable]

your handwriting is

well

i cant really tell what you're writing at 4+(13-7/? x ?)

[molten zenith]

No denominator left, simply 4+(13-7)

[alpine sable]

so.. now for B

Β = 1 : 1/4 - (8+4² - 5 1/2 Χ 4)

[alpine sable]

8+4² = 24
24 - 11/2 = 18.5
18.5 x 4 = 74
1 : 1/4 = 0.25
74 x 0.25 = 18.5

damn

you found something different

💀

ok so now

can you help me with 2 more

@molten zenith

[molten zenith]

Yeah sure

[alpine sable]

"(this guy) has 2 pipes. the length of pipe A is 3 4/5 meters and the length of pipe B is 1 1/2 meters longer than pipe A. (this guy) requires 10 meters of pipe in total, how many more meters does he need to buy?"

"(this woman) bought three pieces of cloth with a total length of 12 meters. cloth A is 4 3/5 meters and cloth B is 5 2/8 meters. what is the length of the third cloth?"

wrong channel

go get your own

[alpine sable]

@molten zenith

[molten zenith]

0.9 metres (yeah i am asian so i write meter as metre)

[alpine sable]

@molten zenith

[alpine sable]

can you please do the calculation?

@fickle ridge please delete

[molten zenith]

Okayy ;-;

[alpine sable]

sorry if its a bother

[molten zenith]

Its alright

[alpine sable]

`oh god

it's not horizontal

and it hurts my neck

lmao

[molten zenith]

Sorry my bad

[alpine sable]

its ok

there we go

better

[alpine sable]

can you tell me how you did the calculations cause its kinda confusing me lol

[molten zenith]

Btw i like to use decimal system, you can use mixed fractions bcz this seems to be your mixed fractions exercise

[alpine sable]

can you please re-take this in horizontal cause i cant understand what your writing

i see 12's and 19's but i dont know if they're 12 or 19

[molten zenith]

1st i have converted mixed fractions into improper fractions, then taken lcm and then somple division

[alpine sable]

184+210??

[alpine sable]

ty

also i did something by myself but i'm not 100% sure about it

can you confirm?

[molten zenith]

ok send it

[alpine sable]

"find the most common multiplier"
8, 15, 20 | 2
4 15 10 | 2
2 15 5 | 2
1 15 5 | 5
1 3 1 | 3
1 1 1

7, 5 70 | 5
1 1 10 | 7
1 1 5 | 5
1 1 1 | 5

12. 24, 8 | 2
    6 12 4 | 2
    6 6 2 | 2
    6 6 1 | 3
    2 2 1 | 2
    1 1 1

i think this is the most common division instead of multiplier

[molten zenith]

Idk if the multiplier has to be common in all of them or not

[alpine sable]

it does

you can google Ε.Κ.Π (greek term) to learn more (you can use google translate for that)

[molten zenith]

Then 1 for both 1st and 2nd ques and 4 for 3rd

Are these hcf questions ? (Highest common factor questions)

[alpine sable]

184 + 210?????????

[alpine sable]

i think thats what it is in english idfk

[molten zenith]

Basic lcm bro

This was for 184+210 question

You know how to do LCM bro ?

[alpine sable]

i dont remember

i'm stupid

[alpine sable]

under 3 4/5 is 12/5 or 19/5 and under that is 19/5 or 12/5?

[molten zenith]

Thats why, revise the concept, it is imp for higher standards too, it is one of the most imp operation

[molten zenith]

19/5 only

[alpine sable]

i'm in a hurry, can you please do it for me? my school is starting in 2 days and i thought this shit easy but it aint and now i'm panicking

[molten zenith]

That is 3*5+4/5 (mixed to improper)

If u just need to right the answers then just copy mine

[alpine sable]

bro

for that LCM or whatever

can you please do it for me i need to hurry

[molten zenith]

LCM is a concept, i have already used it in the answers and they are correct

[alpine sable]

nono

that

8, 15, 20

find the most common multipleir

[molten zenith]

Actually tbh i dont know what those question are, i have never done them in my school but probably an application of them

I am just seeing the numbers and it is obv that they have no number common between them

Like 8 and 15 have nothing in common, but 8 and 20 have 4 as their common factor

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[alpine sable]

i thought about proving that M is the centre of the parallelogram but couldnt find any solution

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[bold panther]

is this how i should replace t with?

[hearty frost]

f(t) = 4.9t^2

f(t+h)=4.9(h+t)^2

just replace, expand and solve these

[bold panther]

but when i expand that equation theres still a left over t in 9.8th

[hearty frost]

yes? take h common and cancel it

[bold panther]

yh but theres still t left

[hearty frost]

yes?

thats the realtion with velocity

9.8t ig?

[bold panther]

system says that its wrong :(

[hearty frost]

i just helped you with question you asked me, your approach from the start might be wrong

[lone heart]

@bold panther Has your question been resolved?

[bold panther]

.close

[lone heart]

Channel closed

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Use .reopen if this was a mistake.

[lone heart]

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[snow seal]

Im looking for the best book to learn algebra, im a beginner and know the bare basics of algebra and i would like to master algebra. what book would you guys recommend me to study algebra?

[hearty frost]

https://youtube.com/playlist?list=PL0o_zxa4K1BUeF2o-MlNpbRiS-oE2Kn6J

[snow seal]

do you also have one regaring statistics?

[hearty frost]

just write on youtube

[snow seal]

is there a book you'd recommend to learn algebra

[hearty frost]

your highschool books?

which std you are

[snow seal]

.close

[lone heart]

Channel closed

Closed by @snow seal

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.

[edgy cape]

Can someone explain to me how

3/2(3x-5)^-1/2 becomes 3/2(5)^1/2 when x=0

like what happened to the negative

I thought you can't do negative roots

[abstract fractal]

They plugged in x=10/3, not x=0

[lone heart]

@edgy cape Has your question been resolved?

[edgy cape]

why would they do that when I am supposed to show that x=10/3 at the intersection

[abstract fractal]

They're first assuming that p is 10/3, and then showing the tangent line does indeed go through the origin

Thus showing the assumption correct

[edgy cape]

how does that show that it goes through the origin without using x=0

[abstract fractal]

They first find the tangent line at x = 10/3. Then one can see that by plugging x = 0 in to the tangent line equation, we get y = 0, in other words, the line goes through the origin

[edgy cape]

ohhh i understand

[edgy cape]

thanks