help-0

[alpine sable]

anyone here

[hollow zephyr]

just ask

smh

<@&286206848099549185>

[blazing oak]

Wow

[reef olive]

,w x'=t-x

[ocean seal]

Results provided by WolframAlpha

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Requested by ᲼᲼᲼᲼᲼#5213

[reef olive]

mens

[plucky seal]

How would I find the arc?

Arc DE is 120

But what's arc CE and DC?

[reef olive]

draw line from D to midpoint

and then use the formula for arc pi*angle(rad) = arc length

so angle = 120 / pi and convert to degrees

and then from that u can work out all angles and all lengths using trig

theres probably an easier way to do it though 😦

[plucky seal]

Ok ty

[hallow herald]

Hi

can someone help me with this problem?

[clever frigate]

Can I get some help doing this partial fraction decomposition?

(i just need to decompose whats inside the angle brackets)

[velvet pelican]

@clever frigate try the form A/s^2 + B/(s^2+a^2)

In this case, you don't actually have to square both sides. A transformation of 12cos(x) + 5sin(x) = 13cos(x - arctan(5/12)) works. In general, when you square both sides, you need to plug the solutions back into the equation to ensure they satisfy it.

[hollow zephyr]

yeah but we didn't have arctan

I feel like in this case I just need to say that sin x > 0 and go from there

[velvet pelican]

I mean you can square it

just substitute the solutions back

to make sure they make sense

[hollow zephyr]

true, thank you

that works

[velvet pelican]

welcome

[alpine sable]

apparently 1.5 is the incorrect answer, i thought the arc length is always the same as the inside angle

can someone explain or help what i do here?

[velvet pelican]

the arc length = radius * angle @alpine sable

[alpine sable]

?

ill just copy paste ur question if u care so much

if cot theta < 0 which quadrant does the terminal side of the angle lie

[alpine sable]

If a product has a 100% rating with 10 customers, the real rating could be something else than 100%, like 95% because the chances of getting the first 10 reviews 100% are still high. How can I calculate the range of what values the "real" rating most likely to be (100% is most likely mathematically, but there are also other values that are also likely)?

[real sinew]

I've heard a simple way to do so is to add on two more simulated ratings of 100 and 0

There's probably a better way though

[graceful bloom]

I have a problem

[alpine sable]

Yeah I know but it feels like cheating because I don't know where it came from. I also can't find any other information to this.

Or maybe I have but they use anothef example and the math flew over my head

[real sinew]

You can really only go by past data.

If there is no past data, then it is kind of arbitrary

You could assume there is a normal distribution of ratings where the mean is near 100 but lower, and there is a chance that the normal curve intersects with 100.

But there's no way of knowing the mean

Without past data

It doesnt have to be normal either, it could be another distribution intersecting with 100

[alpine sable]

I know but you could calculate how likely it is to get 100% for your first 10 reviews if you have a lets say 95% rate

So 100% is most likely and then it goes down

[real sinew]

You could calculate it if it is purely random

If it isnt purely random, then you would need an idea of where the true rating would lie

[alpine sable]

Let's say purely random

[real sinew]

Then you have 10^10 for randomly getting 10 ten times

So not likely lol

Oh I just saw the 95 percent rate

So say you are using a normal distribution, that would be the mean but you still dont know the standard deviation

Let's say we go with the 100 and 0 idea I said earlier, that would give you an estimated rating of 11/12

,calc 11/12

[ocean seal]

Result:

0.91666666666667

[alpine sable]

Is there a formula to plot all the chances from 1-100% of getting the first 10 reviews 100%

Yeah but he never said where he got that "add 2 true and one false" thing from

[real sinew]

There is no formula unless you have a distribution (normal distribution is a safe bet here), mean (which could be 95%) and standard deviation (which we have no clue here)

[alpine sable]

I don't think it would be a normal distribution because the chances of the seller having 100% is most likely

[real sinew]

If you had a percentage in mind, (say 1 in x times you will get 100% rating) we could calculate the standard deviation

Oh I see

Possibly a normal curve with a mean at 100% and anything higher rounds to 100%

[alpine sable]

Hmm

Yeah possibly. I'm going to watch 1b3b video again and see if I can get some more clues. I'll come back

[slate marsh]

Hey guys, is there a way to quickly find a number who's product has a certain remainder ? for example x*(2^32) must have a remainder of 0.5, what would be x

[real sinew]

Alright good luck

[real sinew]

You're not dividing anything so there's no remainder

[slate marsh]

sorry I meant decimals

[real sinew]

Oh ok

Are you working with floating point decimals on a computer? Or just in general?

[slate marsh]

yeah on excel at the moment

[real sinew]

Hm

[slate marsh]

im just trying to reverse engineer a sequence of number because Solver can't solve this

[real sinew]

Ok

What I would do is solve x for various examples. Like solve x for 0.5, 1.5, -0.5, and look for a pattern in x values

[slate marsh]

the other thing i noticed is that a single digit change can vary totally the resulting decimals, like even one digit change on a 32 digit number

and there is no actual way of seeing progress

like if im getting closer or further from the correct number

[real sinew]

Multiplying anything by 2^32 makes it hard to get precise values

Because that number is so large

[slate marsh]

im wondering if maybe we could do this by step

[real sinew]

A computer will likely round the number

[slate marsh]

because mutiplying by 2 is easy

[real sinew]

Ok. x*2 has a decimal of 0.5

So some examples are x=0.25, 0.75, 1.25, etc

So the formula is 0.25 + n/2

Where n is any integer

[slate marsh]

alright I see

[real sinew]

If you try it with x*(2^2), and want 0.5 in the decimal, then you get 0.125, 0.375. So In that case the formula is 0.125 + 0.25n

[slate marsh]

interesting so there is actually a pattern

[real sinew]

So it seems the formula in general is (0.25/p) + 0.5pn, where p is the power that 2 is raised to

So for 2^32 you get 0.25/32 + 0.5n/32

Where n is any integer

[slate marsh]

so now i can use solver to test some options ?

[real sinew]

Yes

[slate marsh]

is it (0.5n)/32 or 0.5(n/32) ?

[real sinew]

A cleaner way to put it is n/64 + 1/128

Or (2n+1)/128

[slate marsh]

so if put n=10 i get 0.1640625

oy yeah i can just mutiply until .5

my bad

[real sinew]

Yeah you multiply that by 2^32

[slate marsh]

actually it removed the 5

704643072

[real sinew]

Oh wait

[slate marsh]

yes

[real sinew]

I did 2n when I think it should be n^2

In several places

Let's try 2^3

2^3 times x = something.5

That's what you want right? A number with .5 at the end?

[slate marsh]

yeah

[real sinew]

I'm busy atm

[slate marsh]

yo this is occupied dude

2^n times x would be handy

[real sinew]

So I'm getting 0.0625, 0.1875

[slate marsh]

so that i can choose the exponent

[real sinew]

That's what I'm hoping to find

So when exponent is 3 you get 0.0625 + .125n

.25 .125 .0625 for the first number and .5 .25 .125 for the second

So lemme think this through

[slate marsh]

not eash

easy

im having trouble getting my head around it

[real sinew]

0.5^(1+p) + n* 0.5^p

I believe that is it

Where p is the value in 2^p

And n is any integer

So for 2^32 you have 0.5^33 + n*(0.5^32)

[slate marsh]

trying to make it work but havent managed to find a number n yet

[real sinew]

I'm trying it in wolfram alpha and that formula is correct

[slate marsh]

oh but maybe the final 5 is too far away

for excel

to account for it

[real sinew]

Unless I misunderstood your problem

Let n =10

,w (0.5^33 + 10*(0.5^32)) * 2^32

[ocean seal]

Results provided by WolframAlpha

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Requested by crabchurch#2749

[real sinew]

In goes n, out goes n.5

[slate marsh]

this seems perfect

let me plug this through to my python program

for some reason i get 10.000000000116415

ah got it

but when i think about it it's not exactly what i had in mind

although this is very useful for me

but for an other case

let me give you an example

[bronze pawn]

any idea about an identity for α^2 +b^2 +gamma^2 in terms of the coefficients of a cubic equation

[real sinew]

This channel is occupied atm

[slate marsh]

3648289171/(2^32) is 0.84 something

now if I divide this big figure by 2, the remainder is 0.5, if i do it again it is 0.75, and the third time is 0.375

now my problem is that i wanted to find this big number given the decimals

and the resulting division

[real sinew]

I would help but I dont have the time. I actually have to go

Good luck

[slate marsh]

ah ok thanks

bye

[haughty plaza]

Not sure whether its b or c

[solar tapir]

Not gonna tell you the answer

But

IQR = 3rd quartile - 1st quartile

Median= 2 quartile

Work from there

A symmetric distribution is a type of distribution where the left side of the distribution mirrors the right side

[strong furnace]

distribution should be symmetric about mean/median

[alpine sable]

a=1000+50w is this linear?

[naive belfry]

yes

there's a constant rate of change (y =mx+b)

[alpine sable]

thx

[lucid shuttle]

Guys

How do I go from e^ to ln?

[oak chasm]

@lucid shuttle You generally don't. You usually combine them to eliminate both of them. What problem are you solving?

[lucid shuttle]

I need to go from N = 4500 x e^0,0463t

to

t = a x ln( b x N)

[oak chasm]

Are the xs multiplication? If so, no need for them.

[lucid shuttle]

yes x means times

so 2 x 2 is 4

[oak chasm]

You start with this?
$$N = 4500 e^{0.046t}$$

[ocean seal]

Chai T. Rex

[lucid shuttle]

yes

0,0463 actually but yes

[oak chasm]

OK, so solve for t by getting t alone on one side.

What can you do first to get it closer to t on one side by itself?

[lucid shuttle]

divide by 4500

both sides

[ocean seal]

Chai T. Rex

[oak chasm]

OK, what next?

[lucid shuttle]

uhm

I think there is a special rule I need to apply

a^x = q

is x = ^a log (q)

?

or nah?

[oak chasm]

https://www.chilimath.com/wp-content/uploads/2020/03/log-rules.gif

These are the logarithm rules.

See rule 3?

Sorry, rule 6.

[lucid shuttle]

yes I see

Ooooh okay

very nice

[ocean seal]

Chai T. Rex

Chai T. Rex

[oak chasm]

Does that make sense?

[lucid shuttle]

how nice

well, following the rules I assume yes

Without the rule I would have never came up with that

[oak chasm]

Yeah, the rules are nice.

[lucid shuttle]

but the question is not finished yet I believe

[lucid shuttle]

I need this form

[oak chasm]

OK, what do you need to do next to get t by itself?

[lucid shuttle]

divide by 0.0463

both sides

[ocean seal]

Chai T. Rex

[lucid shuttle]

omg

thank you so much

https://tenor.com/view/spongebob-rainbow-yes-imagination-gif-9320583

[oak chasm]

No problem. So, it's just normal algebra with the new log rules.

[lucid shuttle]

I see

Have a nice day

[oak chasm]

You too.

[night sinew]

for this problem. wouldn't it be a positive degree?

[charred marlin]

Hey, would this be 6/10 or 6/26 I’m confused if I should be finding the answer out of all males or of all students

[night sinew]

since the reference angle has to be always positive. but i'm not sure if its either 30 or -30 because it's directly asking us to calculate sin^-1(-1/2)

[oak chasm]

@night sinew What angle gives a sine of 1/2?

[night sinew]

30 degrees

[oak chasm]

Do you know the unit circle?

[night sinew]

i don't have it memorized but i can understand it well

[oak chasm]

OK, so sine is the y value when it hits the circle.

So, you get 1/2 at an angle of 30 degrees counterclockwise from 0 degrees.

You get -1/2 at an angle 30 degrees clockwise from 360 degrees.

So, 360 - 30 = 330 degrees is one place.

You also get -1/2 at an angle 30 degrees counterclockwise from 180 degrees.

So, 180 + 30 = 210 degrees.

Does that make sense?

[night sinew]

yeah, like it's coterminal angles?

[oak chasm]

No, those two aren't coterminal.

They're in different quadrants.

[night sinew]

so it would still equal to +30 degrees?

[oak chasm]

No, what's the sine of 30 degrees?

[night sinew]

wait no i see it

it's -30 degrees

[oak chasm]

Right, that's one of them.

There's two that aren't coterminal.

[night sinew]

one is in QIII

180 + 30 = 210 yeah

and 360-30, 330 QIV

[oak chasm]

Yes, that's right.

[night sinew]

thank you

[oak chasm]

No problem.

[radiant elk]

does anyone know how to start this problem? i don't really know where to begin

#21 btw

[radiant elk]

not sure if i'm allowed to ping <@&286206848099549185>

[oak chasm]

@radiant elk You asked the question and waited 15 minutes, so it's fine.

[radiant elk]

ok

[amber mountain]

Im verifying identities and dont recognize these symbols

can I see them as variables?

[tawdry pollen]

https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

[wary stream]

Those are Greek letters, alpha and beta, and yes you can use them as variables

[tawdry pollen]

I would use this website it has all the formula and identities

[wary stream]

They weren't referring to not knowing the identities. They didn't know what the Greek letters meant

[tawdry pollen]

I realized that as soon as I sent the message lol

[amber mountain]

Oh ok so its the same an X and Y

[wary stream]

Yes

[amber mountain]

its just to establish two different thetas, ok got it

[mighty sinew]

@radiant elk are we assuming the circle has unit radius?

[radiant elk]

uh what does that mean- sorry I dont understand

[mighty sinew]

Radius = 1

[radiant elk]

sure i guess, I think I just have to prove that the triangles are similar tho

[mighty sinew]

Ahh thought its 22 mb

[radiant elk]

oh ok

[mighty sinew]

hint: prove that the two triangles have the same angles. Ah, and BAC = 90 degrees @radiant elk

[radiant elk]

i think there is a theorem to prove that angle BAD and angle DAC are congruent, but in order to prove that the triangles are similar, don't I have to prove two pairs of congruent angles?

nvm i figured it out, thx anyways

[fallen night]

Hello, I need to solve this for a and b

I've split it into three equations

but now i can't isolate the variables

hmm

could I maybe divide the first by [1]?

[wary stream]

I would use elimination/substitution to find a and b

Like set one equation equal to a, and plug it into another to find b

[fallen night]

yes that is what i am trying to do

i just don't know how to get a you know

or how to get b either

[wary stream]

So for equation 1, set that equation to a

[fallen night]

yes

how do i do that?

hmm, do i do -b*[2]?

[wary stream]

Given $$ a + 2b = 0$$, set that equation to a

[ocean seal]

dldh06

[fallen night]

what about the brackets?

can I just ignore them?

[wary stream]

It's a constant

[fallen night]

no the brackets

[2]

[wary stream]

Yeah

That's a constant

Like I don't have to do [2]*x every time, right? I can say 2x

[fallen night]

oh you mean (2)*x

[wary stream]

I can say [2]*x too

They all mean the same, right?

[fallen night]

no these are equivalence classes on modulo 5

which i don't know what that means either

so [2] is all numbers that are 2 if you divide them by 5

[wary stream]

They're brackets, it's just a notation. So technically [2] * x, (2) * x, and 2x, all mean the same

[fallen night]

they're equivalence classes 😩

and i don't know how to get rid of them

[subtle mantle]

you could rewrite each equivalence class as [a] = (5k_1+a), [b] = (5k_2+b) for some k_1, k_2 in Z if you want to move the problem into Z

[fallen night]

interesting

i'll try that, thanks

[subtle mantle]

alternatively you could just treat them as normal numbers and divide/multiply keeping in mind that 0=5

cause Z/5Z is a field so division is all fine

[fallen night]

alright

[lunar garden]

does anyone know how to solve this?

[radiant elk]

sides of similar triangles are proportional

try to figure it out using that information?

@lunar garden

[lunar garden]

Yeah im no sure how to find the missing sides

Do i have to find LMN first?

[radiant elk]

uh

i dont know what that is sorry

but how I did it was

NL / LH = ML / LG

so if NL is 10 x more than LH

then ML is 10x more than GL

idk if that makes sense to u

[lunar garden]

Yeah i'm still confused

Thanks for the help tho

[radiant elk]

uh sorry

ok i wil try to explain it better

if you put the side lengths into a fraction

you would get 70/x = 7/10

[wary stream]

Set proportions $$\frac{NL}{ML} = \frac{HL}{GL}$$, right?

[radiant elk]

then cross multiply to find x

[ocean seal]

dldh06

[radiant elk]

yep thats right ^

wait not NL

nvm

it is NL

[lunar garden]

Ok so i cross multiply them to get the answer?

[wary stream]

Plug in the values that you know

[lunar garden]

NL is 70 Right?

and ML is unknown

[wary stream]

$$\frac{NL}{ML} = \frac{HL}{GL}$$
$$\frac{70}{x} = \frac{HL}{GL}$$

[ocean seal]

dldh06

[wary stream]

So far so good, right?

[lunar garden]

yeah

[wary stream]

What other values do you know?

[lunar garden]

HL is 7? and GL is 10

[wary stream]

$$\frac{NL}{ML} = \frac{HL}{GL}$$
$$\frac{70}{x} = \frac{HL}{GL}$$
$$\frac{70}{x} = \frac{7}{10}$$

[ocean seal]

dldh06

[wary stream]

Yep

So how would you find x?

[lunar garden]

do i divide it

[wary stream]

No

What do you need to do first?

[lunar garden]

Cross multiply?

[wary stream]

Yep

[lunar garden]

ok so 700 on the top side then

[wary stream]

What about the other side?

[lunar garden]

7x

[wary stream]

$$\frac{70}{x} = \frac{7}{10}$$
$$700 = 7x$$

[ocean seal]

dldh06

[wary stream]

So how would you find x?

[lunar garden]

now i divide?

[wary stream]

Yep

[lunar garden]

by 7 so is x 100?

[wary stream]

Yep,x = 100

[lunar garden]

Thank you!

[cyan fractal]

I'm currently second guessing myself, so a bit of a basic question.

Does foh(x) = 4(x^3) simplify to foh(x) = 4x^3?

[woeful pulsar]

$f\circ h(x)=4(x^3)$ is the same as $f\circ h(x)=4x^3$ because of PEDMAS, yeah

[ocean seal]

Element118

[cyan fractal]

Alright, thanks!

[vagrant pier]

can someone help me on this

[woeful pulsar]

what have you tried?

[vagrant pier]

i know it's -2 and 1

but how do i know what sign to use

[woeful pulsar]

what is -2 and 1?

[vagrant pier]

the answer

at least

[woeful pulsar]

the answer is not a pair of numbers

you need to come up with the values x such that f(x) is well defined

[dawn frigate]

Hello can anyone help me in a voice channel

[vagrant pier]

ok so can you walk me through the problem

[woeful pulsar]

what are -2 and 1?

they are where the expression (x+2)/(x-1) changes sign, right?

so what happens around them?

[vagrant pier]

ok thank u

[spark shadow]

,rotate

[spark shadow]

Is this correct.?

[muted raft]

I don't think so.

[whole meteor]

guys please help me

Idk how I can get the answer

well

[woeful pulsar]

what is the question?

[whole meteor]

i know the answer but I dont know the explanation

[bold silo]

Can someone give me the answer to a question

[glacial pier]

can someone check 10 calculus questions for me?

[full canopy]

sure i guess

:3

[glacial pier]

dm ok?

[full canopy]

sure

[woeful pulsar]

why not here lol

[woeful pulsar]

probably not

[woeful pulsar]

okay definitely wouldn't have guessed the question.

So you want P(z<=2.15), for that you can just lookup your standard distribution table or tap that into a calculator

[faint root]

what is 30cm2

[glacial pier]

10 question

need to put 10 photos out

because i need to take them seperately

[cyan fractal]

Currently calculating the inverse of a function. I've got x = 3y-7 / y+1, how do I isolate the Y in this case?

Intuitively, I already want to try to do:

x(y+1) = 3y-7
xy+x = 3y-7
xy+x+7 = 3y

But I'm kinda stuck tryting to get that y out of the left side of the equation. I'm making some glaring mistake, but I don't know what it is.

Woop, figured it out

[dusk smelt]

Take xy to the right side

And take y as a common factor

[cyan fractal]

Indeed, thanks!

[quaint crater]

Hi! I was wondering if I had sin2x = 1/2 and I was looking for values of x in radians within a range of 0-2pi would my possible answer be pi/2 or pi/12?

[woeful pulsar]

did you forget your brackets?

remember your brackets next time

[native brook]

anyone know how to put v sub 1 into something like scilab (reference photo): https://gyazo.com/1b17ae95923c51966842deddb19a65c6

[woeful pulsar]

sin 2x=1/2? when you solve it you are solving for x

[quaint crater]

yes, I am trying to solve it in terms of pi (in radians)

[woeful pulsar]

yeah so pi/12 would be one solution

[quaint crater]

Hmm ok so why cant I just divide the whole thing by 2 to get sinx=1, aka x= pi/2?

@woeful pulsar

[dusk smelt]

It's sin(2x)=1/2

2x is the argument of sin, you can't just divide by 2

You need to get rid of the sin first

[oak chasm]

@quaint crater When you have an input to a function, you can't easily take things inside or outside of it unless you have a good reason.

So, with sin(input), you can't touch the input (taking something out of it or putting something into it) unless you have a good reason.

Pretend the numbers are stuck in there.

[quaint crater]

I c ok, thanks!

[alpine sable]

Hello, I am having problems understand orthogonal in linear algebra!

I must determine coordinates of a vector with respect to a basis...but I'm completely lost where to even start.

[muted raft]

The $\textbf{unqiue representation theorem}$ tells us that for any vector $\vb{v} \in \mathbb{F}^{n}$, there exists unique scalars from $\mathbb{F}$ such that $\vb{v}=c_1v_1 + c_2v_2 + \cdots + c_nv_n$ where $v_1, v_2, \cdots, v_n$ are the basis for $\mathbb{F}^{n}$. Recall that those unique scalars, $c_1, c_2, \cdots, c_n$ are the coordinates of the vector $\vb{v}$.

[ocean seal]

zslya

[alpine sable]

I need to understand this...

[oak chasm]

@alpine sable Orthogonal means at a right angle to all the vectors it's orthogonal to.

[alpine sable]

So, the theorem is telling me that to find the equation is to simply multiply the given vector with each vector?

And then, the results of each multiplication are the coordinates?

[muted raft]

This basically means that you need find a way to write vector $\vb{v}$ as a linear combinations of vectors of basis $B$.

[ocean seal]

zslya

[alpine sable]

Oh, okay.

I need a hint. This is going to be a long process, right?

[muted raft]

Not really.

[alpine sable]

I have to multiply u1*u2 and such???

I hate lectures. They're never helpful.

[muted raft]

You are already given the basis. So just create an augmented matrix and apply elementary row operations to find the solution.

[alpine sable]

Okay >_<
I am the worst at memorizing these concepts. Honestly on the verge of flunking this class >O<

[muted raft]

In other words.

$\bmqty{2 & 1 & -1 & 3 \ 0 & 1 & 5 & 1 \ 1 & -2 & 2 & 4}$

oops

[alpine sable]

So, I just need to get the augmented matrix, solve down to echelon form, then solve from there?

(I wished I knew what I was doing xD)

[ocean seal]

zslya

[alpine sable]

Thank you! Now I know I set it up right.

I kept mixing up ranges and basis >_<

Honestly not sure when it's supposed to be in the matrix as shown, or when I have to solve for variables.

[muted raft]

range and basis are not the same.

Range of some function T means the set of image points of T. Whereas basis means a set of linearly independent vectors that span some vector space.

[alpine sable]

Okay, so far I got $\bmqty{1 & 0 & 8 & 6 \ 0 & 1 & 0 & 1 \ 0 & 0 & -22 & -10}$

[ocean seal]

Tofu

[alpine sable]

I might need to double-check with octave...

[muted raft]

Did you put it on reduced row echelon form?

It doesn't look like it is in rref yet.

[alpine sable]

I just did

Using octave

Hmmm, I think I need general help doing elementary operationgs

Every time I do this, it's hit and miss

So, I believe I got the answer?

Thank you so much @muted raft

I would've never figured it out without you!

But now, I need to figure out why I never get the elementary operations right on paper.

How can i factor this?

Ive done similar questions where I start by common factoring out one of the terms but since one term is squared in this idk where to start

[muted raft]

yeah looks correct.

Just take it slowly.

RREF just requires practice.

[alpine sable]

Thank you so much!!

I'm good for now!

[oak chasm]

@alpine sable First, expand everything.

There's no factor common to all three terms right now.

[alpine sable]

i need the area of this shape. no steps needed. just one answer. plz

[alpine sable]

Oh ok i thought the 3m-n would be

[oak chasm]

@alpine sable Sorry, channel is busy.

[alpine sable]

D:

[willow wolf]

Hi, I was wondering if someone could help me with what i'm doing wrong here? I thought you multiplied the top exponents, and then subtracted the bottom from the top

[oak chasm]

@alpine sable No, factoring means from the whole thing.

@willow wolf Sorry, channel is busy.

[alpine sable]

ohh so since the -5 doesnt have it

it cant be factored

[oak chasm]

@alpine sable There is a trick you can use, I guess.

No, it can.

[alpine sable]

I mean the 3m-n

[oak chasm]

There are two ways, expand everything and then collect like terms and then factor from there.

Or use the quadratic formula, I think.

Not sure on that last one.

Yeah, that'll work.

[alpine sable]

but the quadratic formula wouldnt be factoring which i was instructed to do here right

[oak chasm]

No, it can be used for factoring.

First, check the discriminant.

What's the discriminant?

[alpine sable]

lol i dont think we learned this yet

[oak chasm]

OK, have you done the quadratic formula yet?

[alpine sable]

we used quadratic formula but nvr too factor so ill try expanding

yup

[oak chasm]

OK, the part under the square root is called the discriminant.

What's the value of the discriminant here?

[alpine sable]

so -3(3m-n) * 4(2(3m-n)(-5))

[oak chasm]

Nope, a, b, and c are the coefficients of the "variable" (3m - n).

[alpine sable]

oh wait

im tripping lol

ohh

[oak chasm]

So, a = 2, b = -3, c = -5.

[alpine sable]

so 9-4(2)(-5)

9-40

[oak chasm]

Nope.

Close.

[alpine sable]

9+40

[oak chasm]

Right.

[alpine sable]

49

[oak chasm]

So, is that at least zero?

If it was less than zero, you can't take the square root, right?

So we need it to be at least zero.

And 49 is at least zero.

Does that make sense?

[alpine sable]

yup its much more

yup

[oak chasm]

OK, so do the quadratic formula.

What two results do you get?

$$\frac{3 \pm 7}{4}$$
$$\frac52 \mbox{ or } -1$$

[alpine sable]

2.25 is one

[ocean seal]

Chai T. Rex

Chai T. Rex

[alpine sable]

isnt a=2?

[oak chasm]

Yep.

[alpine sable]

ohh mb i keep messing up the formula

yup i got how u did that

[oak chasm]

OK, now here's how you use quadratic formula to factor.

What's the "variable" here?

[alpine sable]

3m-n?

[ocean seal]

Chai T. Rex

[oak chasm]

The roots are the answers you get from the quadratic formula.

[alpine sable]

ohhh

[ocean seal]

Chai T. Rex

[alpine sable]

yup n then x 2 to make it so its not a decimal

[oak chasm]

Well, not exactly.

I forgot something.

[alpine sable]

it is like that in the answer key tho

[oak chasm]

Put a k out front.

Yeah, but we have to solve for it too.

$k \left((3m - n) - \left(\frac52\right)\right)((3m - n) - (-1))$

[ocean seal]

Chai T. Rex

[oak chasm]

See the k out front?

[alpine sable]

yh but idk what that means?

[oak chasm]

It means fill it in with a number so that when you expand, you get your original expression.

[alpine sable]

so in our case 2

[oak chasm]

So, how can we expand the two parenthesized factors to get just the (3m - n)^2 term?

You know FOIL, right?

[alpine sable]

yeah

[oak chasm]

So, first will give us what?

[alpine sable]

lol i havnt used foil foil ina while but isnt it jus solving the binomials

[oak chasm]

Yes, but we only need one term of the binomial expansion.

[alpine sable]

so (3m-n)(3m-n) which is 9m^2-6mn+n^2

[oak chasm]

So, see how the first terms of each binomial have (3m - n) in them?

Nope.

[alpine sable]

yea

[oak chasm]

We don't want to do that.

See how no other pair of one from the first binomial and one from the second make (3m - n)^2?

[alpine sable]

lol honestly im quite confused but ik for a fact that she probably will just want us to factor I understand most of this and got the same answer if i make it so it isnt a decimal I think ill jus try to expand n solve

[oak chasm]

$$\mbox{First: } (3m - n)(3m - n) = (3m - n)^2$$
$$\mbox{Inner: } \left(-\frac52\right)(3m - n) = -\frac52 (3m - n)$$
$$\mbox{Outer: } (3m - n)\cdot 1 = (3m - n)$$
$$\mbox{Last: } \left(-\frac52\right)\cdot 1 = -\frac52$$

[ocean seal]

Chai T. Rex

[oak chasm]

See how I did FOIL?

@alpine sable

[alpine sable]

1 sec lemme read it rq lol

lol honestly i dont get it but fr man thx for the help i got to what i needed im gonna continue reviewing the other concepts for now if thats finee tysmm for clearin it up

[stark gate]

I need help with this question pretty difficult for me to solve

the line y=(3)/(4)x+A passes through the points (B,-3) and (9,c). Determine tha values of A,B, and C

I asked a few hours ago no one responded

<@&286206848099549185>

[alpine sable]

btw @oak chasm i think i got how my teacher does it just assigns a variable to the common term aka a=3m-n and then it factors normally off that n rewrites a in its full form at the end if that makes sense

[raven plaza]

does anyone

understand this

How would I prove

tanx=sinx/cosx?

[vital delta]

can i ask matlab questions here ?

[muted raft]

#computing-software might be better choice @vital delta

[harsh acorn]

what does question mean as "type of triangle" does it means that is it right , isso, acute or other triangle?

or it asks for how much side length combinations does this triangle have?

[dusk smelt]

I think it means this

Based on the example they provided

[harsh acorn]

then how can i solve it?

all i know is side's length cant be bigger then other side's sum and cant be smaller than other length's difference

[dusk smelt]

That's a combination question I believe

[obsidian mango]

can anybody teach me this quesiton

[harsh acorn]

channel is occupied

[obsidian mango]

i am not getting the logic of this one

[dusk smelt]

This channel is in use

Don't just paste it question here randomly

[obsidian mango]

i don't understand i mean does this channel is made for only one quesion...where i am wrong...

[harsh acorn]

#❓how-to-get-help

[dusk smelt]

Facepalm

[obsidian mango]

so like when one question isn't solved till then i can't ask any other quesiton right?

[oak chasm]

Right, you have to find a channel that's not busy.

[muted raft]

Move to another channel which is not on use.

[obsidian mango]

ok...great....

[muted raft]

Pick a channel and ping me

[harsh acorn]

$$ x+y+z= 26$$
$$ |x-y|<z<x+y$$

[ocean seal]

Hyl1s

[harsh acorn]

$$z_{max}=12$$

[ocean seal]

Hyl1s

[harsh acorn]

and $$z_{min}= 2$$

[ocean seal]

Hyl1s

[harsh acorn]

so i just put numbers and count them?

[alpine sable]

Guys

The answer says its over 12

hi

is this a combination

and should it be 5C2?

<@&286206848099549185>

[stable umbra]

Yes

[alpine sable]

is my 5c2 correct tho

[stable umbra]

It's correct

[alpine sable]

thank you anand babu

[toxic dust]

I always find these questions confusing, with the quotient rule. Can someone help me clear that

<@&286206848099549185>

[alpine sable]

you should've waited 15 minutes to use that tag breh

[harsh acorn]

and channel is occupied

[stable umbra]

@toxic dust are you talking about differentiation using quotient rule?

[toxic dust]

Yeah

[stable umbra]

Here
"u" is the function in the numerator
and
"v" is the function in the denominator

[alpine sable]

Ye

[tardy scarab]

$$1 + 1

$help

$1+1

Ayo

[alpine sable]

??

[nimble frost]

$$2$$

[ocean seal]

Destreaux

[charred raft]

Could someone help me answer

-17(-9)

[floral jungle]

i got priority, the answer is 153

could someone help me through with this problem
ik the speed is dy/dx, we know dx, but how do we get dy with the cos(0.5x)
since its not the same variable

[alpine sable]

use chain rule

[floral jungle]

we can use calculator for this problem

i just don't know what to do w the x

[alpine sable]

yep u can , but when differentiating the term cos x/2

u get a term of dx/dt

by chain rule

now sub the value of dx/dt given to u seperately

Plug t =2, x =-3

U get dy/dt

[floral jungle]

so derivative of cos x/2 = -1/2 sin x/2 right?

[alpine sable]

Ye

[floral jungle]

and you sub in dx/dt and x = -3

and then you find the derivative of the rest?

[alpine sable]

Ye u had a whole

equation of y

[floral jungle]

yeah

[alpine sable]

solving this big derivative u will get

dy/dt

U then find dx/dt

and then speed is resultant of these two, use pythagoras

[floral jungle]

so if you find the derivative of cos1/2x what do you do with the rest of the equation

cuz like don't u needto find the derivative as a whole

not part by part

[alpine sable]

Rest of equation is in t

u r differentiating wrt t!

So the other terms would only be in t

[jaunty sierra]

Express cos162 in terms of cosine of another angle between o and 180 degrees

[floral jungle]

hm ok gimme a sec

[upper kayak]

is this channel open?

In a box, there are red, green, blue, yellow and black marbles. There are 200 marbles of each color. At least how many marbles do you have to pick from the box to guarantee that you have picked 100 marbles of the same color?

i'm terrible at stats

[strong furnace]

consider the worst case for such problems

[misty quiver]

help

[rich kestrel]

worst case scenario: you pick 99 of each color; then the next marble u pick will satisfy 100 marbles of the same color

so 99*5 + 1 i think

[woeful pulsar]

don't just give answers

[rich kestrel]

sorry

you have 5 colors; worst case you pick 99 of each, missing one from each

then the next marble will have to be part of those 5 colors, and one of the colors will have 100 in them

[vale wigeon]

this is not stats, this is basic counting / pigeonhole principle

[upper kayak]

Ok

[vale wigeon]

but yes, thelonewolf has explained the reasoning behind the answer here

[wispy olive]

How is the line it passes through = 8,5.
It's slope is obvious but can you explain me how the line it passes through has the point 8,5?

[wispy olive]

Ummm anyone?

[harsh acorn]

$$y=-4(x-8)+5$$

[ocean seal]

Hyl1s

[harsh acorn]

and in (8,5) $$x= 8$$

[ocean seal]

Hyl1s

[harsh acorn]

put x in the equation

$$y = -4(8-8)+5=5$$

[ocean seal]

Hyl1s

[harsh acorn]

if u try other points like (5,8) or (-5,-8) and put x in the equation you will not get the y

so they are wrong

[formal edge]

anyone understand this? I don't really get how to change it from a series to the sigma notation

[wispy olive]

I see.

[wispy olive]

Okay.

[harsh acorn]

why questions has marks

[wispy olive]

Woahhhhhhhh.

[formal edge]

cuz it a two part question ://

[wispy olive]

Oh crap what a huge mistake I made.

I thought we have to find the values.

Instead of substituting the values from the answers.

Ahhh.

What an idiot I am.

[alpine sable]

how does that even happen

there’s no info abt any of their current or past ages

my brain cells are fried

[formal edge]

K = 4d <--- kevin is 4x daniel

K = d + 6 <--- kevin is 6 years older than daniel

4d = d + 6 <--- They both equal K, so they're equal

[alpine sable]

ik but

[formal edge]

3d = 6 simplified

d = 6/3 = 2

if daniel is 2 then kevin is 4*2

[formal edge]

kevin is 8 and daniel is 2

[alpine sable]

these are only options

[formal edge]

put 8

[harsh acorn]

anyway it is course challange

you should do it by yourself

so you can know your weakness

[alpine sable]

ikk

i just wanna know

[harsh acorn]

answers and solutions are given after the questions tho

[alpine sable]

i just never heard of that

[wispy olive]

But how do we know that it passes through (1,7)!?

[alpine sable]

how abt the plus 6 years?

[wispy olive]

Anyone?

[alpine sable]

you have to check

look at the graph

see if the line passes thru that point

[formal edge]

@alpine sable

[wispy olive]

I have to make the graph.

From the equation given.

[alpine sable]

after that we ain’t gotta add 6?

[formal edge]

wym

it just plugging in numbers

[alpine sable]

oh okay

[alpine sable]

do that then

[wispy olive]

Bro what?

I asked a question.

[alpine sable]

simplify as much as you can

[wispy olive]

@harsh acorn ?

[formal edge]

have u ever heard of desmos?

[alpine sable]

ohh

yea

[wispy olive]

I want to do it myself.

[formal edge]

you are, you're plugging in the numbers yourself 🤣

[harsh acorn]

just check it in equation

put 1 in x

[alpine sable]

you need to simplify the equation

[harsh acorn]

and 7 in y

and check

[alpine sable]

PH

oh

that’s

simple

[wispy olive]

Huh?

[alpine sable]

why didn’t i think of that 💀

[harsh acorn]

(1,7)

[alpine sable]

replace the x and y

[harsh acorn]

what is x there

and y

[alpine sable]

with the cords you wanna check

[wispy olive]

But why?

Why that number of all numbers?

[alpine sable]

if the equation works out it is

[harsh acorn]

actually there are infinite possible points

but in answers

there are only 1 right

[wispy olive]

Yeah I know.

[alpine sable]

bc your looking if the line passes thru those points right

[harsh acorn]

you just need to check

which one can be possible

[wispy olive]

But why should I try substituting (1,7) out of all?

[harsh acorn]

oh

you need to check all of them tho

[wispy olive]

Here we are just given the equation.

[harsh acorn]

when u find the right one

[wispy olive]

Not MCQ.

[harsh acorn]

just take it

[alpine sable]

that’s actually really smart

i legit never thought of that 💀

[wispy olive]

How do we know that (1,7) passes through y−7=−3(x−1) ?

[alpine sable]

7 is x and 1 is y

replace the x and y in the equation

[harsh acorn]

just put them in the equation

[harsh acorn]

dont give the exact answer tho

[wispy olive]

😒

[alpine sable]

if the equation works out then you know the line passes thru

WHAT

[harsh acorn]

wrong lol

[alpine sable]

i’m trying 😭

oh

[harsh acorn]

x is 1 and y is 7

[alpine sable]

yea

[harsh acorn]

first one is x

[alpine sable]

other way around

[harsh acorn]

second one is y

[alpine sable]

i keep mixing that up 😭

[wispy olive]

But how do we know?

Reasoning please?

[harsh acorn]

it is the order

(1,7)

first x always

and second y

if there are z coordinate, z is 3rd

[wispy olive]

How do we know that particular point passes through the line made when the equation is graphed?

[harsh acorn]

you need to know that particular point's coordinate first and check in the equation

or

you can draw the graph

and look at the point's place

try in desmos

[alpine sable]

what does that even mean

[harsh acorn]

perpendicular

[wispy olive]

Line OA is perpendicular to line OC.

Are you in grade 6th or 7th or something, just asking.

[topaz cosmos]

can someone help me out

[wispy olive]

Oh wow question 1 has been free since some time.

All questions go here or what lol.

[harsh acorn]

stop multiposting

[alpine sable]

no

[wispy olive]

Then?

[alpine sable]

8th

[wispy olive]

Same.

[formal edge]

do you know how to do b? 🥺

[harsh acorn]

i think you need to telescope

for second answer

first one is given already

[vestal widget]

yes i'll try

[muted raft]

bruh lmao

you don't just give away the answer

[harsh acorn]

i tried to say that lol

[formal edge]

arigato gozaimasu

[muted raft]

Just apply ratio test

It is not that hard....

If you actually put in some effort...

[formal edge]

im still a beginner im sorry

[alpine sable]

$help

oops

😭

[muted raft]

don't be sorry but put in some work...

[alpine sable]

$ 5^3*10/5 $

oh

[muted raft]

no space before and after $

[alpine sable]

ah

hi

[vestal widget]

??

[formal edge]

thank you in japanese hehe

[vestal widget]

For b goto https://youtu.be/yYxzq_O18Mg

[wheat prawn]

could someone help me on how to solve this by substitution

[ruby parcel]

basic question

this answer would be right just as (n+12)(n-2) would be right

[wheat prawn]

how is that a basic question

we to subsitute y and get x

@ruby parcel

[ruby parcel]

what

i said my question was basic

[wheat prawn]

oh

[warm iron]

Since the value for y is simultaneous for both of the equations, you can equate them

Then simplify the whole square terms

[wheat prawn]

@warm iron i dont like fractions

[vestal widget]

On 2nd equation multiply 2 on both side then add it with 1st one

[wheat prawn]

i tried

im not doing something right

[ruby parcel]

ik my question was stupid but can someone answer it please

isnt it right cause multiplication is commutative

[vestal widget]

Don't open square.....

[wheat prawn]

y

[vestal widget]

Just add it with 1st equation then u got y value

[wheat prawn]

what do you mean

like this?

[glossy current]

Yes

[wheat prawn]

then its that?

[glossy current]

Yes

[wheat prawn]

then this?

[glossy current]

No

[wheat prawn]

what did i do wrong

[glossy current]

Just compare

It's wrong

[warm iron]

You can't distribute the -2 since the expression is inside of the square

[glossy current]

,ask simplify -2(x-2)²+14

,ask Simplify (-2x+4)^2+14

See they're different

[ocean seal]

Results provided by WolframAlpha

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

Requested by Darkness#5004

Results provided by WolframAlpha

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

Requested by Darkness#5004

[glossy current]

Also

Why do you need to throw -2 in

$-2(7-(x-2)^2)=(x-2)^2+2$

[ocean seal]

Darkness

[glossy current]

There are 2 ways to solve it
One way is to break $(x-2)^2$
Second way is to substitute $t= (x-2)^2$

[ocean seal]

Darkness

[vestal widget]

I think finding y value first is easy

[wheat prawn]

wdym

[vestal widget]

Afterthat put the y value anyone equation and find x value

[wheat prawn]

no we are trynna find x

first

thats what the teacher wants

[glossy current]

You can find y

From y you can find x

[vestal widget]

So there's no problem

[wheat prawn]

yea but its really confusing

we learnt the whole unit in 3 days

and you adding this

makes it more confusing

[vestal widget]

Solve the quadratic equation u will get 2 value

Of x

[wheat prawn]

yea

[glossy current]

Well can you solve this

$-2(7-(x-2)^2)=(x-2)^2+2$

[ocean seal]

Darkness

[wheat prawn]

awx

sec

ok this is confusing now

[glossy current]

Why

what is (x-2)²

Do it slowly if you are confused

[wheat prawn]

x^2-4x+4

now times that by 2?

[glossy current]

Write it as replaced of (x-2)² first

Like this

[wheat prawn]

wdym

[glossy current]

$-2(7-(x^2-4x+4))=(x^2-4x+4)+2$

[ocean seal]

Darkness

[wheat prawn]

ok

[glossy current]

Then break the inside bracket first

What is $-(x^2-4x+4)$

[ocean seal]

Darkness

[vestal widget]

$-2(x-2)^2+14 = (x-2)^2+2$

[ocean seal]

Aman Verma

[vestal widget]

$3(x-2)^2 = 12$;
$(x-2)^2=4$;
$x-2=+-2$;
$x=2+-2$;
$x=4,0$

[wheat prawn]

ok that is much easier to understnad

i dont get this tho

[wheat prawn]

$-x^2+4x-4$

[ocean seal]

Roberttt

Aman Verma

[glossy current]

$-2(7-x^2+4x-4)=x^2-4x+4+2$

@wheat prawn Now simplify it

[ocean seal]

Darkness

[feral pine]

I cant rlly read the question, can you send a better image @modern aurora

also what is 'desi' supposed to be?

[modern aurora]

'desimetre'

better?

[wheat prawn]

@glossy current $-14-2x^2-8x+8=x^2-4x+4+2$

[modern aurora]

open original

[ocean seal]

Roberttt

[wheat prawn]

$-2x^2-8x-6=x^2-4x+6$

[ocean seal]

Roberttt

[wheat prawn]

$-x^2+4x=0$

[ocean seal]

Roberttt

[glossy current]

solve it

[wheat prawn]

$0=x^2-4x$

[ocean seal]

Roberttt

[glossy current]

bruh

[modern aurora]

i asked a question here

like it went trash

[wheat prawn]

@glossy current

?

[glossy current]

solve it

[wheat prawn]

factor?

[glossy current]

Yes

$x(x-4)=0$

[wheat prawn]

(x-2)(x-2)

[ocean seal]

Darkness