help-13

[crimson sedge]

you take cases

case 1:

a > x

case 2:

-a > x

[dapper mulch]

doesnt that become
(a,inf) and (-a,inf)?

and the union would be (-a,inf)?

[opaque root]

Also, your question is not correct

[crimson sedge]

no

also i dont know which range you have for x

or anything

pls just

!original

[cedar kiln]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[dapper mulch]

im just trying to find domain for
sqrt(4-x^2)

[crimson sedge]

hint: sqrt(x) exists if and only if x>=0

[dapper mulch]

ye

when i do that

4-x^2 >= 0
-x^2 >= -4
x^2 <= 4
x <= +-2

and then the domain goes [-2,2]

[opaque root]

You get |x|<=2

[dapper mulch]

oh so it goes
x <= 2 and x > -2?

[opaque root]

=

[dapper mulch]

why doesnt it go +-2 tho?

[opaque root]

Because sqrt(x^2) is |x| and sqrt(4) is 2

[dapper mulch]

oh , i was putting +- on the wrong thing

[opaque root]

U put sqrt in both sides

[dapper mulch]

yeah , i wrote it wrong my bad

[opaque root]

And u have ti know where things come from

[dapper mulch]

ok im confused

doesnt the domain for x>= 2 go [2,inf) and x>-2 go (-2,inf)?

[opaque root]

You have this

|x| <= 2

Correct?

We check the limits

If x = 2

|2| <=2 is true

If x>2 that inequality is false

For example |3|<=2 is false

Now the other side

X=-2

|-2|<=2 is true

[dapper mulch]

ok i understand

[opaque root]

If x<-2

Then again is false

So x is between -2 and 2

-2 <= x <= 2

[dapper mulch]

understanding this way is easier , my teacher was trying to make us find domains of both sperately or smthing

[opaque root]

[-2, 2]

[dapper mulch]

ty

[opaque root]

Welcome

[dapper mulch]

.close

[cedar kiln]

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[cedar kiln]

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[tribal bear]

Hello, could someone help me to compute this sum ? Ty !

[tribal bear]

(ping me pls)

[odd verge]

What is n?

[next hornet]

use choose formula

[dusk finch]

Is n some fixed number?

but yeah, use the factorial form

[cedar kiln]

@tribal bear Has your question been resolved?

[tribal bear]

an integer

[tribal bear]

I used it

but still doesnt work

[odd verge]

What is the exact value of n

[tribal bear]

no precised value it is just a random integer

[odd verge]

Then it might not be defined for k>n

Would it?

[cedar kiln]

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[tribal bear]

no u right n is supposed >=k

[odd verge]

Yes

So n ≥ m too

So n might = m

So the sum could be = 1

Let me solve assuming n≥m

[tribal bear]

and so how do u conclude ?

[odd verge]

Multiply the two things

[tribal bear]

i did it

but i'm not able to recognise any special formula

[odd verge]

Ok and what did you get

[tribal bear]

i get

$\frac{m!(m+c-k)!}{(m-k)!(m+c)!}$

[wraith dagger]

5 pl / 3 m

[tribal bear]

idk how do u sum that formula

[odd verge]

You can't find a definite sum

[tribal bear]

prove it

[odd verge]

Find the sum of a+b+c
Where + is ordinary addition

@tribal bear

[tribal bear]

no but u still can find a simplified expression

an expression without the sum

depending of n and m

[cedar kiln]

@tribal bear Has your question been resolved?

[odd verge]

Answer the question

a+b+c

[cedar kiln]

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[queen sundial]

Can someone help me with this?

[brave aspen]

I would start by finding the derivative

Derivative will give you an expression for the slope of the tangent line

As the first derivative can be thought of as the "tangent line slope generator"

[queen sundial]

for derivative i got -1/(x-1)^2

[brave aspen]

Did you do quotient rule for that?

[queen sundial]

yeah

[brave aspen]

If so then yes

Ok then so that thing is the slope

Could you write an equation for the tangent line at any arbitrary point?

[queen sundial]

can yuo just use point slope?

[brave aspen]

Yea any form you like

Point slope is very convenient

[queen sundial]

but then for m should i just plug in -1/(x-1)^2

[brave aspen]

Yess

Exactly

[queen sundial]

so would it be y-5=-1/(x-1)^2(x+1)???

[brave aspen]

Yea

[queen sundial]

but it asks for the equations

so theres more than one

[brave aspen]

Yes

Because right now

You have an equation with 2 variables

You need to find another equation to solve

Maybe you already have one

[queen sundial]

???

[brave aspen]

Well the other equation is

[queen sundial]

what is the other equation

[brave aspen]

f(x) = y

Because of course the original function should be true

Then you have the system

[queen sundial]

wait can you reiterate the two system equations

so one is the point slope form

[brave aspen]

The other is the original function f

y = x/(x-1)

That is also true in this system

[queen sundial]

and then i set them equal to each other?

[brave aspen]

Yes that's one way

That will get you the x values where the tangent line equation has the point (-1, 5)

[queen sundial]

is there an easier way

[cedar kiln]

@queen sundial Has your question been resolved?

[crimson sedge]

everyone speak portuguese?????

[cedar kiln]

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[lucid iris]

im confused

so i set it up as

65 = 80e^(-10k)

and finding k

i got ln(13/16) / -10 = k

but when i go to check

its wrong

[dawn junco]

wym check ?

@lucid iris

[tribal bear]

here u can't

but u can with the sum

[lucid iris]

its something with epon growth and decay

but it was like 80(13/16)^(t/10)

the asnwer

i don't understand that part

[dawn junco]

well did you try getting the function from the k you got ?

you know the function is 80*e^kt, that's what you assumed when setting up the equation

just plug it in

[lucid iris]

oh ok

like plug till it gets 65?

[dawn junco]

no

[lucid iris]

hm

[dawn junco]

you know k=ln(13/16)/whatever

[dawn junco]

replace k by its value here

and simplify

[lucid iris]

oh ok

i see

.close

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[shadow pollen]

hi guys here Does anyone know how I can download and install: LabView"

[plucky owl]

Google this

[dire geode]

Don't occupy a math help channel for non math questions

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[tired crystal]

Can someone please help me I can’t figure out how to isolate theta

[tired crystal]

I’m 99% sure I have the derivative right but after that all my work could be incorrect

And I think you can just disregard the 0.75m since the question has nothing to do with mass my teacher did a question on the bored and he just completely disregarded one of the terms because it didn’t have anything to do with his solution but I could be wrong…

<@&286206848099549185>

[runic garnet]

,w differentiate (0.75sin(x) + cos(x))^(-1)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by northsteve

[tired crystal]

Why did you differentiate that equation?

[runic garnet]

thats how we maximize?

thats what u did lol

it looks like ur off by a factor of -1

but in the end it doesnt rlly matter

[tired crystal]

I differentiated the F=0.75M(0.75Sintheta+costheta)^-1

Then i set that answer equal to zero

[runic garnet]

ya i did the same except without the 0.75M cuz its just a constant

thats being multiplied

[tired crystal]

So I don’t need to include the 0.75M when i differentiate?

[runic garnet]

right, so u set this equal to 0

[tired crystal]

And then I solve for theta right? That’s what I’m stuck on

[runic garnet]

u can leave it outside of the differentiation part

$\dv {x} 3x = 3 \dv {x} x$

[runic garnet]

this is basically what im talking abt

and then once u differentiate and set equal to 0, u just divide both sides by 0.75m

so it doesnt rlly matter

[runic garnet]

yes

[runic garnet]

so set the numerator and denominator of this equal to 0, individually

$\sin(x) - 0.75 \cos(x) = 0 \newline \newline (0.75 \sin (x) + \cos (x))^2 = 0$

[tired crystal]

I just can’t understand it, pissing me off would you just restart completely if you were me and use that derivative you showed me?

[runic garnet]

the derivative i showed u is exactly what u had, except u were off by a factor of (-1)

look at the last line where u wrote F'

thats what i got

that last simplified thing

@tired crystal see it?

[tired crystal]

Not really lol

Anyway you can voice call quick?

[runic garnet]

nah

[tired crystal]

Like that f’ is completely different

[runic garnet]

no its not

look what u simplified to

bro just look 😭

u have it right there

right underneath

[tired crystal]

That’s not simplified the line down I set it equal to zero and moved the 0.75/0.75sintheta +cos theta over on the other side

[runic garnet]

honestly i think u just have to add the fractions

but looks like ur missing an 'm' somewhere

so maybe u shd restart

[tired crystal]

You can just disregard the m

All I need help with is isolating theta

[runic garnet]

dont u have to show work? if u just ignore it, it wont make sense

id say just restart

its not that intensive of a derivative anyways

[tired crystal]

So how would you approach it?

[runic garnet]

$fm \dv {F}{\theta} [(f \sin(\theta) + \cos (\theta))^{-1}]$

[tired crystal]

Okay so I’ll do that quickly give me a sec

Correct? And then set that equal to zero?

[runic garnet]

not correct

u brought the -1 to the inside

instead of the outside

[tired crystal]

So just make that whole bracket on the bottom negative?

[runic garnet]

no

because the negative doesnt distribute to the square like that

u have to keep the negative on the outside

[tired crystal]

Im sorry im actually an idiot

So at the top then?

[runic garnet]

yea that works, u can do that if u want

and keep the fm outside the dF/dtheta

and then just divide it out when u set equal to 0

[tired crystal]

So now I set that equation equal to zero?

[runic garnet]

well show me the equation

oh wait

u sent it lol

lemme see

yea, on the top, it should be (-1)(0.75cos - sin)

parentheses around everything

[tired crystal]

Okay done

[runic garnet]

otherwise, it looks like the - is only for the cos

[tired crystal]

Can I distribute it into the brackets

Making it + sin and -cos

[runic garnet]

correct

did u keep the fm there too

[tired crystal]

So that’s where I’m at once I set equal to zero and move the denominator over

[runic garnet]

wait wait

[tired crystal]

I didn’t keep fm

[runic garnet]

ok u should divide both sides by fm to get rid of it with the 0

[runic garnet]

kept it outside like this

but anyways

[runic garnet]

why are u setting the numerator and denominator equal here?

[tired crystal]

To isolate theta I thought

[runic garnet]

but whats on the other side of the equals sign

in the previous line

[tired crystal]

Just df/dtheta

I thought no?

[runic garnet]

right

now, rewrite ur derivative and set equal to 0

[tired crystal]

And then you just set your derivative to zero

[runic garnet]

then we will go from there

[tired crystal]

Okay

I’m confused about dividing the fm part out

Since we don’t need it since it’s a constant I don’t even think he will care if I include it or not

[runic garnet]

well if its in the original formula, i suggest keeping it in, just to be safe

but if u feel its fine, then we'll move on

[tired crystal]

He had an example where he just got rid of it when he set equal to zero

So wait how do I do it? I will just to be safe

[runic garnet]

right, thats what im suggesting to do

u have to keep it for all the steps until u set equal to 0

[tired crystal]

If would be 0.75m correct?

[runic garnet]

yea, sure, or u could keep it fm

doesnt rlly matter

[runic garnet]

ok well close lol

u forgot the 0.75m on the top right

and it should be on the other side of the second dF/dtheta

[tired crystal]

Lmao I’m really sorry

Where do I put it on the top right sorry

[runic garnet]

ok see on line 1

u differentiated and u got

[tired crystal]

Yes

[runic garnet]

(-1)(0.75sin - cos)^-2 ...

right there

the 0.75m just disappeared

[tired crystal]

Yes so can I just put it infront of that whole equation?

[runic garnet]

yea

[tired crystal]

Okay

[runic garnet]

and then on the second line

it should be on the other side of the equation

[tired crystal]

It’s Going to be messy I’m going to fix it after I solve

[runic garnet]

lol line 2 still

other side of the equation, not other side of the dF/dtheta

[tired crystal]

Ohhh okok

[runic garnet]

ok now when u set it equal to 0

u didnt distribute the -1

u only gave it to the -0.75cos

[tired crystal]

Oh my bad should be +sin

[runic garnet]

yea

[tired crystal]

I was working on this shit for like 2 hours and it just hurt my brain plus im working rn I feel brain fried

Ok it’s corrected

[runic garnet]

ok cool

so now, to find critical points,

set the numerator equal to 0

and set the denominator equal to 0

[tired crystal]

Separately?

[runic garnet]

yes

[tired crystal]

Done

[runic garnet]

ok, now we want to solve

[tired crystal]

Can I move sin over and then cos over making it 0.75=sintheta/costheta which will equal tantheta and then move tan to the other side by taking the inverse?

[runic garnet]

$\sin (\theta) = 0.75 \cos (\theta) \newline \newline (0.75 \sin (\theta) + \cos (\theta))^2 = 0$

[runic garnet]

YES

[tired crystal]

For the first line right what about the other one we set equal to zero that’s squared what happens to it

Would be -0.75 actually

[runic garnet]

what would be -0.75?

[runic garnet]

still not understanding how its -0.75

tell me ur steps how u got that

[tired crystal]

Oh actually nvm I’m overthinking it

[runic garnet]

well what did you do

[tired crystal]

I have no idea now that I look at it again what I was thinking

[runic garnet]

yea, i mean add 0.75cos() to both sides, and then u get tan() = 0.75

so what do u have for the first eqn

[tired crystal]

So taninverse(0.75) right?

[runic garnet]

yea arctan(0.75)

thats a potential angle

but we have to check the others first

so now onto the second equation

what do u think we should do

[tired crystal]

I would say expand the brackets and then foil but idk

[runic garnet]

no

if we had the eqn

(4x)^2 = 0

how would u solve

without expanding/distributing the exponent

[tired crystal]

Make it a root? Idek tbh I’m lost abit

[runic garnet]

wdym by make it a root

not tryna be rude or anything, but this stuff should be second nature to you if ur doing calculus

[tired crystal]

No offence taken lol, we are just starting up classes again and I’m in a college course for instrumentation control engineering technology last year was just basic derivatives and integrals that I found very easy and some of this stuff is just weird to me

[runic garnet]

ah ok i see

alr

so for the second eqn, wdym by make it a root

[tired crystal]

Like turn the power into a square root but I guess you kinda can’t even do that like it wouldn’t make sense

[runic garnet]

u cant "turn" the power into a sqrt

but u can take the sqrt of both sides

[runic garnet]

so what happens to this

[tired crystal]

doesn’t it just become 4x

We did that last year I forget lmao

Because square root of 0 is just 0 and the square root will cancel the power out

[runic garnet]

yea, so what does the equation become

[tired crystal]

4x=0

[runic garnet]

good

now back to ur problem

what should we do

[tired crystal]

Take the square root of both sides

[runic garnet]

yes

what do u get upon doing that

[tired crystal]

0.75sintheta+costheta

[runic garnet]

give me the full equation

[tired crystal]

Excuse how messy it is

[runic garnet]

ok now what should u do

[tired crystal]

Same as last time?

Wait no we can’t

Can’t do that either fuck

[runic garnet]

how did u get 0.75 + cos

it was 0.75sin

[tired crystal]

Can I do that?

[runic garnet]

no

if u divide one term by 0.75, u have to divide all terms by 0.75

[tired crystal]

Would that be the right approach to do?

[runic garnet]

no

[tired crystal]

Hmmmm

[runic garnet]

u wanna get the sin and cos on opposite sides

[tired crystal]

Okay

So

0.75sintheta=costheta

-costheta

[runic garnet]

yes

now what

[tired crystal]

Now divide sin over?

[runic garnet]

keep going

on the right track

[tired crystal]

I forget what -cos/sin equals isn’t it cot?

So it would it be -cottheta

We haven’t learnt to much about those trig functions yet

[runic garnet]

yes

so -cot(theta) = 0.75

so now what

[tired crystal]

We would isolate theta from -cot

[runic garnet]

ok but how

[tired crystal]

We haven’t learnt much about those trig functions at all

[runic garnet]

well its basically exactly what u did with the tan

remember?

[tired crystal]

What’s the inverse of cot

Yes

Is there a cot inverse button on calculator?

[runic garnet]

not sure

[tired crystal]

But is that what you would do?

[runic garnet]

but yea its arccot

so -cot = 0.75

cot (theta)= -0.75

then take arccot of both sides

[runic garnet]

yes

,w arccot(-0.75) in degrees

[wraith dagger]

Results provided by WolframAlpha

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

Requested by northsteve

[runic garnet]

what does that solution tell u

in a physical context

like reading the problem

[tired crystal]

That the angel that minimizes the force would be 36.87degrees

Our first solution

[runic garnet]

and why is that?

why not the -53.13?

[tired crystal]

Because that would also be 126.87 degrees which is larger

Than the 36.87

[runic garnet]

not quite

if we're pulling something at a negative angle, what does that mean

[tired crystal]

Abit confused

[runic garnet]

that means ur pulling from the floor

like an angle of depression

but the problem states that we're pulling at an angle of elevation

meaning it cant be a negative angle

[tired crystal]

Okok I understand now

Brother thank you so much

[runic garnet]

yea np

[tired crystal]

So that’s our final answer it’s all good?

Wanna check this over quick you’re a genius lmao

[runic garnet]

should be right

[runic garnet]

nah im not

[tired crystal]

Yes you are

What did you major in or what did you take

[runic garnet]

ok for these, just use derivative-calculator.com

its free and really good

just type these in ther

[tired crystal]

Okok

[runic garnet]

im studying actuarial math +data science rn

[tired crystal]

Appreciate it man and that’s awesome

I might branch out into electrical engineering if I can wrap my head around some of this stuff I’m in Canada idk about your our education system is wonky

[runic garnet]

i see

[tired crystal]

You*

[runic garnet]

yea im from the nyc area

alr gl

cya

[tired crystal]

Yessir, again thank you so much brother you’ve been great help

Have a good night man

[runic garnet]

u2

[cedar kiln]

@tired crystal Has your question been resolved?

[cedar kiln]

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[limpid brook]

Gr 12 data management!

so for e) i did it correct and i did 126 - (5C1 x 4C4)

but i dont understand why im getting the wrong answer for f???

I wrote:

126 - (4C2 x 5C3) - (4C1 x 5C4) - (4C0 x 5C5)

and instead of getting 45 (which is the answer), im getting 46??

nvm

i got it

zlol

ik why

.close

[cedar kiln]

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[cedar kiln]

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[tired crystal]

Just looking to have these answers looked over if I messed up where did I go wrong?

[cedar kiln]

@tired crystal Has your question been resolved?

[tired crystal]

No

<@&286206848099549185>

[dreamy void]

looks all good

[tired crystal]

Do you think I can show my steps anymore to get anymore marks or should that get me full marks?

Teacher is a weird marker he will take them out for not putting brackets in right spot n stuff

[dreamy void]

nah they are really fine, don't over do it

in an exam i wouldn't waste too much time on making it obviously clear

[tired crystal]

It’s not a exam just a assignment, thank you

Just wanna make sure I get perfect on it lol

[cedar kiln]

@tired crystal Has your question been resolved?

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[full matrix]

i wanan do $-b/2a$

[wraith dagger]

Roach

[full matrix]

but i don't have a B what do i do

do i just set it 0?

[livid hound]

4x^2 - 6 = 4x^2 + 0x - 6
b = 0

[full matrix]

so my equation would be $4x^2+0x-6$

[wraith dagger]

Roach

[full matrix]

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[oblique moth]

How can I do this? And what is the answer?

[odd seal]

is that a 1/a or 1/9?

whatever it is, substitute it where "t" is, then evaluate it

[oblique moth]

My bad, is 1/a and T is an X.

[cedar kiln]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[oblique moth]

Hmm well I'm sorry, but I'm asking this because I tried to do it by myself and I don't know if it's correct.

[worldly chasm]

That looks correct to me, but you can simplify the expression

[oblique moth]

"Simplify"?

[odd seal]

make it look nicer

[worldly chasm]

Multiply by a^2/a^2

But be sure to also note that a≠0

[oblique moth]

I still don't understand how. 😅

[worldly chasm]

\begin{align*}
f(t) &= \frac{2t}{t^2 + 1} \
f\qty(\frac1{a}) &= \frac{2 \frac1{a}}{{\qty(\frac1{a})}^2 + 1} \
&= \frac{\frac{2}{a}}{\frac1{a^2} + 1} \
&= \frac{\frac{2}{a}}{\frac1{a^2} + 1} \cdot 1 \
&= \frac{\frac{2}{a}}{\frac1{a^2} + 1} \cdot \frac{a^2}{a^2} \
&= \frac{\frac{2}{a} \cdot a^2}{\qty(\frac1{a^2} + 1) \cdot a^2} \
&= \frac{2a}{1 + a^2}
\end{align*}

(subject to the restriction that a ≠ 0)

@oblique moth ^ does the above help?

[oblique moth]

Holy, that's awesome, thank you so much.

.close

[cedar kiln]

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[worldly chasm]

No stop come back

The point wasn't to work the answer just, do you understand the steps?

.reopen

[cedar kiln]

✅

[worldly chasm]

Like can you explain why I multiplied by a^2/a^2

Hi you're back with me again 👋

[oblique moth]

I understand you multiply a² / a² to simplify it, since 1 is the same as a² / a².

Then multiply it with this to get the result, am I correct?

[oblique moth]

Holy never thought people would really care about learning here, thank you so much.

[worldly chasm]

Yes, but why a^2 / a^2 specifically and not some other value

What about your expression above shouts to me that a^2/a^2 specifically should be the form of 1 that I multiply by?

[oblique moth]

Because a x a = a²?

[worldly chasm]

Because in the denominator you have 1/a^2 and that's the largest power of a in any denominator in the fraction

So if I multiply everything in the fraction, top and bottom, by a^2, then I'll be left with a regular fraction rather than a compound fraction

[oblique moth]

I think I understand.

[worldly chasm]

So if I showed you the following fraction, what would you multiply by?

[
\frac{\frac1{ab} + \frac{b}{a^2}}{\frac{a}{b^3} - \frac{1}{ab^2}}
]

[wraith dagger]

OmnipotentEntity

[oblique moth]

B³...?

[worldly chasm]

Would b^3 / b^3 cancel out any of the a's in the denominator?

[oblique moth]

🥹

[worldly chasm]

It's a little tricky, but the answer is a^2 b^3 / a^2 b^3

Because you need a^2 to wipe out all of the a's (the largest power of a is found in b/a^2), and you need b^3 to wipe out the b's.

[oblique moth]

Common denominators, right?

[worldly chasm]

Yup! Exactly correct

[oblique moth]

In this case, you grouped a & b to wipe them all, no?

[worldly chasm]

Yup

[oblique moth]

Oh okay, thank you so much again.

||Can I close the post? 🥹||

[worldly chasm]

.close

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[worldly chasm]

Thanks for sticking around!

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[versed fulcrum]

Hello

[versed fulcrum]

Not sure why this is wrong

[worldly chasm]

!show

[cedar kiln]

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

[versed fulcrum]

30 = v(3.9) -> v = 30/3.9

60 = v_avg(10.8) -> v_avg = 60/10.8

[versed fulcrum]

And I substracted v from v_avg

[worldly chasm]

So if we let v_boat be the speed of the boat, and v_river be the speed of the river, then we have

3.90 hr (v_boat + v_river)km/hr = 30.0 km
6.90 hr (v_boat - v_river)km/hr = 30.0 km

Do you see why? @versed fulcrum

[versed fulcrum]

I understand that

I guess substitution is the best way?

[worldly chasm]

That's one way

You can also just eliminate v_boat by subtracting the two equations from each other

Well you need to divide both equations by 3.9 and 6.9 first

Respectively

[versed fulcrum]

Okay

I see

Thank you so much!

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[torn lake]

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[serene bison]

determine the intervals on which the function is continuous: f(x) = [[x+3]] looks like this (look at image), can someone explain what this means?

[muted bear]

your book or teacher should have specified

thats not standard afaik

[serene bison]

hmm, do you know what it is stood for commonly for

or it can basically be anything

[idle crystal]

normally [] is used for the floor functions sometimes but ive never seen [[]]

[muted bear]

i have also seen it used for floor

but there are many ways people write floor

[hot crag]

interestingly, those double brackets are used in things like R[[x]] to mean the ring of all formal power series in x with real coeffs

[serene bison]

the answer says its discontinuous at c and continuous at (c,c+1) for all integers

[hot crag]

probably floor then

[serene bison]

what is floor exactly

[hot crag]

rounding down

floor(3) = 3

floor(3.4) = 3

floor(-1.5) = -2

etc

[serene bison]

so like this

[hot crag]

uhhh

not quite

oh wait no nvm

that's correct, yeah.

the color scheme confused me

[serene bison]

so the example up here is incorrect?

[hot crag]

no the example is correct

[serene bison]

so its floor, but how do i know how to get this

[hot crag]

just

look at the graph?

do some limits?

[serene bison]

so [x+3] means it starts from 3 and rounds down?

im confused

<@&286206848099549185> hi can i get brief explanation

[native heath]

Heya!

[serene bison]

how does the floor of x+3 work

[native heath]

I assume that's just floor?

[serene bison]

yes

[native heath]

Can you try floor(x)

[serene bison]

or ren deducted it to be

[serene bison]

so it doesnt matter what value is at 3 here, it will always be discontinuous at c and continuous at (c,c+1) for all integers?

[native heath]

what's c

what does that mean

[serene bison]

c i assume is x?

are you asking a question to clarify

or like to make me think

i think i get it

thanks

.close

[cedar kiln]

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[native heath]

..lmao

[serene bison]

?

[cedar kiln]

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[gilded plume]

when should we rationalise the denominator in trigonometric identities

[cedar kiln]

Please don't occupy multiple help channels.

[gilded plume]

@old ridge

[tropic jay]

When you can actually solve it by doing that

[gilded plume]

the second step

but we can solve it by seperating 1/secA and 1/Tan A

@old ridge

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[tropic jay]

Trigonometry can be solved many ways

So it's upon you which way you can make it work

[cedar kiln]

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[hybrid leaf]

please help me in grade 9 math i dont quite understand how to solve quadratic equations by completing the square

[high bridge]

yall do quadratics in grade 9?

[hybrid leaf]

yeah im so cooked

[high bridge]

don't be, it is more simple than you think

[idle crystal]

what grade normally does it?

[void spoke]

Let's say you have a quadratic ax^2+b-x+c=0

[high bridge]

in canada it is grade 11

[idle crystal]

HUH

[void spoke]

Steps to solve a quadratic by completing the square method.

[hybrid leaf]

dang

[bleak viper]

bruh

[high bridge]

although i learned it in grade 7 in china...

[hybrid leaf]

thats the standard form right?

[idle crystal]

were getting off topic lol

[void spoke]

1. Make the coefficient of x^2 as 1

[hybrid leaf]

hahahah

[void spoke]

Yes

[high bridge]

yeah let oppailol cook

[void spoke]

Ok so 1st step

[hybrid leaf]

ok tysm

[void spoke]

1. Make the coefficient of x^2 as 1

So now if the quadratic is ax^2+bx+c=0

[hybrid leaf]

i should write this down

[void spoke]

How can you make the coefficient of x^2 as 1? Think

[hybrid leaf]

x = 1?

😭

[void spoke]

Do you know what is the meaning of coefficient?

Relax don't cry

9th graders don't cry

[hybrid leaf]

no sir

[void spoke]

Do you what is the meaning of coefficient?

[hybrid leaf]

i dont

[void spoke]

Ok let me explain

[hybrid leaf]

wait

is it the ²?

[void spoke]

No no

[hybrid leaf]

🤧

[void spoke]

the power is the degree of that term

leave let's make it simple

[hybrid leaf]

okay

[void spoke]

We have quadratic
ax^2+bx+c=0

Now coefficient is simply the number/term multiplied to a power of x

Like for example

x^2 is multiplied with a

So it's coefficient is a

x is multiplied with b

So it's coefficient is b

[hybrid leaf]

i see

[void spoke]

Take your time and tell do you understand it

[hybrid leaf]

the letters next to x?

is it

[void spoke]

In general form

Its letters but it is actually numbers

[high bridge]

note: coefficient is a CONSTANT number that is MULTIPLIED with a VARIABLE

[hybrid leaf]

because it represents 1?

[hybrid leaf]

okay

[void spoke]

He gave you the definition you could write

Ok now did you understand it?

[hybrid leaf]

i do

[void spoke]

Good

Ok now tell me

the quadratic is 2x^2+4x+6

What is the coefficient of x^2

[hybrid leaf]

its 2?

[void spoke]

Sure?

[hybrid leaf]

yes

[void spoke]

Good

[high bridge]

ok a more complex one: tell me the coefficient of this term: 18645xyz^152

[void spoke]

I wanted to see the confidence

[hybrid leaf]

yes!

[void spoke]

Give him the answer C

note: coefficient is a CONSTANT number that is MULTIPLIED with a VARIABLE

Remember this is the general definition

[hybrid leaf]

18645

[high bridge]

nice

[void spoke]

Good

Ok so we move to step 1 now

1.Make the coefficient of x^2 as 1

[hybrid leaf]

okay

[void spoke]

Now let's say we have
ax^2+bx+c=0
How will you make the coefficient of x^2 as 1

Think take your time

[hybrid leaf]

divide?

[void spoke]

Ok

But divide by what?

[high bridge]

divide by ?

[hybrid leaf]

divide by a

[void spoke]

Yes he is understanding

Good

Ok so you divide by a

Now after dividing by a what will you get?

[hybrid leaf]

x² is 1

[void spoke]

x^2 or coefficient?

Be confident and answer

[hybrid leaf]

coefficient

[void spoke]

Good

Ok we had ax^2+bx+c=0
You divided by a
So what will you have now

Think

[hybrid leaf]

wait

[void spoke]

Ok

[hybrid leaf]

umm

can i send a image from my book

[void spoke]

Ok

[void spoke]

Oh

[high bridge]

your textbook is over-complicating it.....

[void spoke]

So they don't want to do the standard way

[void spoke]

They want to do the fashion way

Ok so what we do is

[hybrid leaf]

fashion way sucks

[void spoke]

Ik

But quick question

[hybrid leaf]

?

[void spoke]

1.Is it necessary for you to do according to the book

Or you can become Gauss?

[hybrid leaf]

i think it is necessary

[void spoke]

Oof

[high bridge]

oof

[void spoke]

Oh no

[hybrid leaf]

💀

[void spoke]

Ok so let's take a different way to the answer

you know (a+b)^2 ?

[hybrid leaf]

oh okay

i dont

[high bridge]

step 1: recognizing binomial squaring pattern

[void spoke]

No

💀☠️

Bro speaks facts but tough

[high bridge]

ok let's start from 0 then

[void spoke]

Yes

Do you know (a+b)^2

C?

[hybrid leaf]

i dont

[high bridge]

um you know your distributive properties right?

[hybrid leaf]

no 😭

im dumb

[high bridge]

like 2X(3+5)=2X3+2X5

[void spoke]

Okok

See

I belive he knows

He learning quadratic he might be knowing it

[hybrid leaf]

oof

[void spoke]

Say yes C 💀

[high bridge]

they probably just didn't recognize the name

[high bridge]

say yes to this at least lol

[void spoke]

Do you know ax(b+c)=axb+axc ?

[hybrid leaf]

i dont bro sorry

[void spoke]

💀☠️

[high bridge]

huh????

[hybrid leaf]

no 💀

[void spoke]

Bro how are you studying quadratic then

[hybrid leaf]

frick

[void spoke]

What

[hybrid leaf]

i was watching a video

[void spoke]

Bro was right

He is cooked

[high bridge]

bruhhhh you are studying ahead???

[void spoke]

But still 9th graders don't cry

They face it fr

[hybrid leaf]

thats the same with what i was taught

[high bridge]

oh ok

[void spoke]

Ok so we begin with properties of multiplication

💀☠️

[hybrid leaf]

can i send it

[high bridge]

let's actually start at 0 ig lol

[void spoke]

What ?

[void spoke]

Ool

Lol

You will send what you are taught?

[hybrid leaf]

i can understand the first things

[void spoke]

You understood coefficient that's great

But there are two problems

1.you need to do the book way
2.you don't know the d I s tri butive property

[hybrid leaf]

like example for x² + 4x -12 = 0

[high bridge]

nonononono

you are currently not ready for this

[hybrid leaf]

i guess not really

[high bridge]

you need to know your basics before you start quadratics again

[hybrid leaf]

i forgot 💀

but i ask for one last help so i can understand

[high bridge]

basically, the distributive property is a law of multiplication that ALWAYS works

for example:

if you do 2X(3+5)

[void spoke]

Ok

[high bridge]

it gives you 16

and if you do 2X3+2X5

it still gives you 16

notice how you can brea apart the bracket into 2 sections?

that is how distributive property works

[hybrid leaf]

yesss

[high bridge]

so you recall distributive property now?

[hybrid leaf]

i do

[high bridge]

good, now let's go to this

(a+b)^2

when you square something, it is basically multiplying it by itself

so (a+b)^2 can be turned into this (a+b)X(a+b)

[hybrid leaf]

mhm

[high bridge]

now if you use distributive property on the first a+b you get this

(a+b)Xa+(a+b)Xb

now use distributive property again you will get this

aXa+aXb+aXb+bXb

remove the multiply sign cause algebra do not like it

a^2+ab+ab+b^2

combine the two ab terms

a^2+2ab+b^2

so there we go, you get this

(a+b)^2=a^2+2ab+b^2

that is your binomial square expansion (formula?, different places decides to call it formula or not)

[hybrid leaf]

(a+b)² = a² + 2ab + b²

[high bridge]

this is the most important thing we have tried to conclude all this time, you should prob jot it down if you cannot rememeber this

[hybrid leaf]

okay

i get it

[high bridge]

nice now next step

notice how your equation is ax^2+bx=c?

[hybrid leaf]

yeah

[high bridge]

so your way of doing it is multiplying both sides by 4a

you should try

[hybrid leaf]

4a(ax² + bx) = 4ac

[high bridge]

yes now use distributive property, break the bracket

[hybrid leaf]

4a^2x^2 + 4abx = 4ac

[high bridge]

nice

notice how 4=2^2?

[hybrid leaf]

wait

why =

[high bridge]

lmao 2 squared is 4

[hybrid leaf]

my brain is overheating

[high bridge]

ummmmm, maybe you should come back next time?

take a rest if you cannot handle it

[hybrid leaf]

i should!

mad mod bro thank you so much for the help

[high bridge]

np

[hybrid leaf]

ill try to understand better

[high bridge]

and when would you like to meet next time?

[hybrid leaf]

@void spoke too

[hybrid leaf]

nono its fine

[high bridge]

ok

ig cya

[hybrid leaf]

i feel like its about to turn into free online tutoring 💀

[hybrid leaf]

alr bye

.close

[cedar kiln]

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[hybrid leaf]

.close

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[balmy breach]

Here can I just consider volume to be a function of diameter?

[normal cipher]

Yes

Volume is 3/4 r^3 π or something

[balmy breach]

that would mean, $$V=(3(2x+1))^3\times \frac{4}{3}\pi$$

[normal cipher]

Then dy/dx

[balmy breach]

and then differentiate this wrt x?

[wraith dagger]

PianoDolphin

[cedar kiln]

@balmy breach Has your question been resolved?

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[ivory gull]

why do they divide by 2?

i don't get their reasoning. i understand how they got 25! tho

[raven shard]

25! instead of 26! accounts for the fact the necklace can be rotated
division by 2 accounts for the fact the necklace can be mirrored/flipped

[ivory gull]

what does being " worn either way around" mean?

[cedar kiln]

@ivory gull Has your question been resolved?

[ivory gull]

this is a necklace and i don't get how the necklace can be mirrored

when a necklace looks like that

[cedar kiln]

@ivory gull Has your question been resolved?

[cedar kiln]

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[brave nova]

I have ask this question once but I forgot to check the notifications, i am sorry. Can you guys please help me with this question again. I don't know how to differentiate it using chain rule. I have found x, x= 4 or 1.

[fiery plaza]

!occupied

[cedar kiln]

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).

[fiery plaza]

y = x + 4(x-5)^-1

Misstyped it, edited^

[brave nova]

oh I was confused

thank you

[fiery plaza]

That's just the rearranged formula btw

Does that give you an idea of how to differentiate it?

[brave nova]

is it -1/(x-5)^2 ?

[fiery plaza]

You forgot about something

And your power is wrong

y = x + 4(x-5)^-1

Type out the steps you do 1 step at a time

Just focus on the 4(x-5)^-1

Then I can correct you, at the end I'll summarise the method if you haven't quite got it

[brave nova]

thanks I will try again just a min

[fiery plaza]

np

[brave nova]

dy/dx = 1 - 4/(x-5)^2 ?

Idk how to proceed step by step cuz the questions before weren't like this.

[fiery plaza]

Okay, it was a bit confusing because you didn't keep it in the same format as me which is why I asked for step by step and not the answer, but yes

so, we rearranged the original to get 4(x-5)^-1

You multiply the whole thing by the power

-4(x-5)^-1

You lower the power by 1

-4(x-5)^-2

Then you multiply by the differential of what's inside the brackets
Differential of x-5 is just 1

So your answer is -4(x-5)^-2

If you want it in fraction form then you are completely correct, that gives you -4/(x-5)^2 !

[brave nova]

Thank you. in no.5 i can just assign "u = x-2" and y= 8/u^2 then dy/du = =-16u^-3. But i didn't know how to do step by step with this one.

So it's correct now? Thank you so much for helping me.

[fiery plaza]

You need to substitute u back out

But yeah everything up to that point looks correct

[brave nova]

Hey i got the answer correct. Thank you so much

.close

[cedar kiln]

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[cedar kiln]

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[midnight linden]

what is this

oh

wait nm

nvm im good

[cedar kiln]

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[lusty pawn]

use vietas formulas

[crimson sedge]

Is this a test?

You aren't supposed to ask test questions in this server

[fallen silo]

Put x = 1/2-alpha and find the value of alpha

Then substitute that value of alpha in the question

[crimson sedge]

It's unmarked 🤨

[brazen dagger]

Be careful next time @weary pike , you can ask doubt but no live test questions

<@&268886789983436800> FYI^^

[fallow steppe]

.close

[cedar kiln]

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[devout wing]

i need help with 3b please. it's non-exact differential equation

[honest rover]

50 runes for 25 dollars
150 runes for 50 dollars
500 runes for 150 dollars
evaluate how good of a deal 150 runes and 500 runes are from 50 runes

[lusty pawn]

!occupied

[cedar kiln]

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).

[devout wing]

<@&286206848099549185>

[cedar kiln]

@devout wing Has your question been resolved?

[covert cipher]

3b?

[devout wing]

yes please

[covert cipher]

you just need to make 2 key observations

try distributing the dx and dy and arrange the like terms together