help-0

[alpine sable]

there is no t *

You're calculing the ammount after 1 month which is a constant

So yes with t=1 it works

Now you begin over with S1 as the first ammount

So you need to add interest rate and repayment

[tawny lion]

right

so

I am still confused on how to express it relative to the second month

sorry

[alpine sable]

Sure

So we calculated our ammount for the first month

From our initial ammount P

No we're month 2

So our new "initial ammount" is S1 right?

[tawny lion]

oh

yes

hmm

I can't think of it sorry

I am trash at math lol

[alpine sable]

Take the time

[tawny lion]

wouldn

wouldn't*

it be

so essentially this expression is our new P right?

[alpine sable]

right

[tawny lion]

the P(1+I/100)

[alpine sable]

you don't need to put the expression in it's easier to calcul with S1

[tawny lion]

to what?

[alpine sable]

nevermind

[tawny lion]

alright that makes sense actually

what about the -R

[alpine sable]

Yes

The repayment is the same each month i think

[tawny lion]

how come we get $R \left [1 + \left [1 + \frac{I}{100} \right ]$ though

[ocean seal]

kurama
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tawny lion]

(negative R)

like why do we multiply 1 + I/100

ah wait

it's because the entire expression earlier is P, right?

so we're subtracting it such that we have just -R

I think I got it, not sure

(I mean that it's essentially our new P if that makes sense

idk

[alpine sable]

Yes

Write S2 with S1

Then you replace S1 with the expression we find earlier

Then you look at both expressions of S2 and you try to find that it's equal

[tawny lion]

S2 with S1? how do you mean

[alpine sable]

By factorising and developing

S2= ....s1...

[tawny lion]

right okay that makes sense

what about ii?

[alpine sable]

Then induction

[tawny lion]

ohh

that is smart

[alpine sable]

It works with n=2 so we suppose Sn is true, show that Sn+1 is true

[tawny lion]

I'll repost the q so I can look at it while I talk to you if you dont mind

so would it be S1 + S2 + . . . + S_n-1?

or no wait

we would have

I'm not sure actually

[alpine sable]

I suggest you express Sn+1

[tawny lion]

$S_{k+1} = P(1+I/100)^{k+1} - 100R/I ((1+I/100)^{k+1} - 1)$

[ocean seal]

kurama

[alpine sable]

Now you need to express Sn+1 with Sn

[tawny lion]

wouldn'

uhh

I just had it in my head but now I'm not sure

I'm not sure how to do that

it's not really direct so I'm not sure but I'

would imagine that it's Sk + . . . = S_k+1

not sure what the . . . would be though

[alpine sable]

Where do you write latex thingy?

[tawny lion]

I'm confused

what latex thingy?

[alpine sable]

For the bot to write the expression

[tawny lion]

oh

$

$ . . . $

[crystal crag]

u need to learn the syntax sadly

[alpine sable]

Alright

[tawny lion]

wouldn't it be also easy to represent this as a summation maybe? could help with the induction I guess, it would be a pain though

sorry for taking up your time I'm just really shit with word problems

especially of this nature

[alpine sable]

Don't worry about that

It's just calculus so yes it would be like

[tawny lion]

you can do this with calculus?

[alpine sable]

$S_{k+1}=P(1+I/100)^{k}(1+I/100) - 100R/I((1+I/100^{k}(1+I/100)-1)$

[ocean seal]

Zamarus

[tawny lion]

right

[alpine sable]

Then you know Sn so you need to find the sum Sn+....

[tawny lion]

yeah

the . . . is what I'm stuck on

aaaaaa

[alpine sable]

Lucky us we can factorise 1+I/100

or can we

[tawny lion]

[limpid snow]

Can someone explain standard form like I did slope intercept?

[uncut tapir]

Yeah I think the point of standard form is you can find the intercepts quickly by setting either X or y =0

[wary stream]

Troll?

[mystic ravine]

wow

was that a joke

or in real?

2

[small trellis]

It only has one root though, as far as I'm aware

so how is it allowed to be misleading by stating "roots", instead of "root"?

[wary stream]

It's one double root

[alpine sable]

@tawny lion I sent you a pm

[wary stream]

2 roots that appear at the same location

[rose onyx]

don't you use the discriminant to solve that?

[small trellis]

Yes,

[rose onyx]

so you would do b^2 -4ac = 0

[small trellis]

How is it not just 1 root?

[rose onyx]

if it's = it's 2 identical roots

[wary stream]

It's one root that appears twice

So technically roots

[small trellis]

I've been lied to then

in my text book it says "one root"

if it = 0

[rose onyx]

'one repeated root' is what we are told

[small trellis]

Ok, let me check what it actually says

[rose onyx]

then it it's > than it's 2 distinct roots

and <, no real roots

[small trellis]

actually, I can't, because the login to the site with my textbook is acting up for some reason

[wary stream]

Aka imaginary roots or complex roots

[rose onyx]

ye exactly

[mystic ravine]

i know the answer

but i am not understanding it

can anyone help

[uncut tapir]

Which part don't you understand?

[mystic ravine]

p[5]=5^3+5^2-2*5+5

[uncut tapir]

That comes from the remainder theorem

[mystic ravine]

ohh yeah right

thx

[uncut tapir]

No worries

I'm guessing they included it as a check you calculated the remainder correctly

[mystic ravine]

yep

[low delta]

tex X<\frac{1}{2}

nah dont mind me imma write

|X-1|<1/2 so this is the equation we had

but somehow teacher turned that into 1/2<X<3/2

and my question is how> xD

[topaz scaffold]

Because of the absolute value

[low delta]

so from right side it added 1

but my problem is left side

[topaz scaffold]

$x-1< \frac{1}{2}$ or $-(x-1)< \frac{1}{2}$

[ocean seal]

RipeOrange

[topaz scaffold]

Because it's the absolute value of (x-1)

[low delta]

oh thnx

got it

Thank you

[topaz scaffold]

Np

[languid sleet]

I have a doubt on probability. If an event E occurs once every minute on average, what is the probability that E doesn't occur for some segment of one minute? can we even answer this?

[amber marsh]

someone help with this

idk where to start

someone worked it out

but idk what they mean

like where did

(theta - sin theta) come from?

why is it there in the first place

[languid sleet]

you can find area(AOC) and area(COB) (both triangles) in terms of theta and r. area of shaded portion is ${\pi}r^2*(t/2\pi)$ - area(COB)

[ocean seal]

jellyfish

[amber marsh]

whats t?

lentgh?

[languid sleet]

theta

[amber marsh]

oh

[languid sleet]

the sector's area will scale with angle

so t/2pi times full area

[amber marsh]

ok i get i need to do that

but what is (theta - sin theta)

why is it there?

[languid sleet]

you'll get that expression when you equate area(AOC) and 3*area of shaded region and simplify

[amber marsh]

the last line

why did they convert

sin theta to (theta - sin theta)

[languid sleet]

they have mistyped - as = in first line second occurrence

[amber marsh]

-as?

i dont get what u mean by that

[ebon quail]

how do i locate the window

[ocean seal]

jellyfish

[amber marsh]

ohhhh

now it makes sense

i overcomplicated it

[amber marsh]

thx a lot man

[languid sleet]

im guessing it's where the 55 contour formed, at 15 ft 🤔

you don't multiply theta_0 by |theta| in the numerator ig

[alpine sable]

Yeah sorry. I got it now.

Been a little rusty. Thanks btw.

[languid sleet]

happens

[upbeat helm]

out of curiosity

How would I get the reciprocal of a decimal without converting it to a fraction

is it possible?

[languid sleet]

are calculators allowed?

[upbeat helm]

yes

[wet nacelle]

if there are calculators then you just divide one by the decimal

i think there could be a trick, though.. to doing it on paper without memorising reciprocals of decimals

[upbeat helm]

so 1/0.6

[wet nacelle]

or maybe you just need to memorise a few and then you can use those to work out any reciprocal of any number

[wet nacelle]

yes

[upbeat helm]

i challenged myself to write a program that divides without using the dividing operation

[weary arrow]

help how do i do the shading part

[wet nacelle]

that'd be like 1/(5/3) which is like flipping the fraction

[upbeat helm]

yea

[alpine sable]

you know what's a polynomial?

[alpine sable]

I Don't rlly know that's why I'm asking for a help

[wet nacelle]

yes! do you know what the definition of a polynomial is

[alpine sable]

No I don't have any idea what it is

[upbeat helm]

its pretty much

[alpine sable]

https://www.mathsisfun.com/algebra/polynomials.html

after reading this, I believe you're set to answer everything correctly!

[upbeat helm]

expression with 2 or more terms

but you need the article to continue

bcz there are types of polynomial

[languid sleet]

just realized i don't know the definition of polynomial

[alpine sable]

Thank you so much

[upbeat helm]

one of those trivial things everyone seems to forget

[alpine sable]

@alpine sable do you also have any links about conic sections?

I searched on google and that was one of the first links

https://www.mathsisfun.com/geometry/conic-sections.html

the same site also has this

[languid sleet]

[wet nacelle]

it depends on the distribution of event Es. event E could happen on the dot every minute and it'd still satisfy "an event E occurring once every minute on average." event E could happen every 59-61 seconds or so a bunch of times so it could balance out rare events that happen immediately after event E or around two minutes after an event E has happened

[languid sleet]

right

[wet nacelle]

instead of thinking of it like windows of one minute where something could happen, think of it like points where event E would occur on average surrounded by points where it could occur

[languid sleet]

this is my homework problem. so it's fake right?

[wet nacelle]

have you been taught distributions?

[languid sleet]

yes, but none is given in the problem

[wet nacelle]

ahh.. they probably aren't expecting you to think too deep about the distribution type whatnot

i hate it when schools do this

[languid sleet]

same. sadly, schools college.

[wet nacelle]

i think it wants you to think of it as a uniform distribution

that'd be a default way of thinking about it.. simple terms considering there's no extra detail

[languid sleet]

if E happened at t = 0, then uniform distribution will gurantee that it happens again in 2 minutes

but that may not be the case?

[languid sleet]

because the distribution must be a line segment with mid point at 1

[wet nacelle]

oops.. you are right

i was trying to say uniformly random

[languid sleet]

meaning?

[wet nacelle]

like a coin toss

there's no bias towards any second

but as time goes on, your luck will dwindle if you're hoping to get straight heads or tails

much like how your luck with dwindle as time goes on when you're hoping for no war

erm.. just pay no mind to the distribution nonsense

[languid sleet]

? anyhow there must be some distribution with expectation of 1 and none is obvious here

i need the distribution to comment about probability, right?

[wet nacelle]

there's a distribution of course

it just doesn't mention what kind

[languid sleet]

yeah, and answer depends on what kind

[wet nacelle]

so just take it like how somebody who doesn't know what distributions are would take it

if there's a war on average every 15 years, then i think there'd be a 50% chance of there being a war at the 15 years mark. it averages at 15, so half of the times the war could have happened are behind you, and the other half are in the future

if you assume the odds stay the same, then in another 15 years the odds of you having not been to war would be 25% (50% x 50%)

if it were 30 years

the question says 25 years

questions like those are very tedious because there's so much uncertainty as to what the question is really asking you to do

and not because it's a mouthful

i hope that helped a little

[languid sleet]

hmm, you're trying to use the fact that half the area is after 15 and half before

ill think about that, thanks a lot for your time

[wet nacelle]

it averages at 15, so the tip of the curve would be at the 15 years mark

[languid sleet]

no, there needn't be any tip at 15 right, its the geometric centre of the curve..?

[wet nacelle]

yknow or maybe they just want you to use regular binomial distribution xd

[languid sleet]

perhaps

[wet nacelle]

depends on the distribution

personally, i would try writing multiple answers using different methods and then see which one is your favourite

fill in the blanks with each attempt

[languid sleet]

lol

[wet nacelle]

at least you'd get the working marks if you hit the expected method

i haven't done statistics in two years xd but i was pretty good at it so i hope i helped a little

[languid sleet]

i'll try to convince my prof its a fake qn

[wet nacelle]

i'm sure you'll find something similar on the internet

[languid sleet]

yes, thanks a lot

[wet nacelle]

maybe there's a correct approach

no worries

i have to go swimming now

good luck :>

[languid sleet]

enjoy, thanks

[distant valley]

anybody got any tips for understanding ammeters and ohms?

[neat summit]

1 + 1 = ?

[tawny lion]

I'm not really sure what to do here

[remote lodge]

11

[harsh saffron]

0 mod 2

[tropic sail]

sorry i interupted

[vocal grove]

Can someone help me find x?

[glass lichen]

make the LHS 2^(f(x))

then solve f(x)=1/2

[vocal grove]

whats f(x)?

I do not know those terms

I am a idiot

I have been able to get 2^4x / 2^x-1 = 2^-1

But dont know what to do after that

[fading scroll]

You can start by

[viscid night]

try and multiply 2^x-1 on both sides

and then write 16 as 2^4

[fading scroll]

Now use the power propeties

[vocal grove]

This is what I have done so far

I'm just stuck on rearranging everything unless I messed parts up

[fading scroll]

Wait

[viscid night]

how did you do lhs for second line?

it isnt 2.5 its sqrt2

2^1/2 im assuming

[vocal grove]

Its 2^1/2 on the rhs

[small trellis]

I see

[viscid night]

shouldnt be -1

[small trellis]

still not 2^-1

yeah

[vocal grove]

So the start of the rhs right?

[fading scroll]

2^-1 =
/= 2^1/2

[viscid night]

not the second line

[vocal grove]

I'm just confused on how to solved it from the 2nd line

[viscid night]

second line is wrong

[small trellis]

it's 2 square rooted

[vocal grove]

How so?

[viscid night]

the rhs doesnt simplify to 2^-1 as everyone said

Just keep it as 2^1/2

then square both sides in next step

[vocal grove]

Why do you sqaure?

[viscid night]

then take logbase 2 and solve the equation

[vocal grove]

I have never done logs

this is pure maths

[fading scroll]

You can just use the index propeties man

[viscid night]

(2^1/2)^2=2

[vocal grove]

$Can you show me how it should look using this?$

[ocean seal]

gkysyt

[viscid night]

im in phone

too hard to write tbh

but i explained it well enough I think

[fading scroll]

Like
$\frac{10^x}{10^{2x}} = 10^{x-(2x)}$

[vocal grove]

I dont understand what your trying to say, as my teacher never made it look like that

[ocean seal]

THCampbell

[fading scroll]

You got the same base(2)

[viscid night]

youve had to learn about logarithms..

[vocal grove]

I need it to look like this

[viscid night]

yea

its same thing

[vocal grove]

Its my first week of alevels and I never did further maths, so we haven't covered that yet

[viscid night]

well you took logarithm there

[small trellis]

You don't learn about logs in further maths only

[viscid night]

inbetween 4th and 5th line

[small trellis]

You'll learn it later though this year

[viscid night]

just follow what i said

and youll do fine

[vocal grove]

I havent covered it yet though so I cannot do it as it will look very weird to my teacher

[small trellis]

Are you doing bridging work?

[viscid night]

#help-0 message

ignore the log base 2 prt

[vocal grove]

I am on a maths+2 class meaning we just get extra lessons

[remote lodge]

need help with Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)

(1, 3), (2, 6), (3, 12), (4, 24) here's the sequence

it's geometric

[livid jolt]

the time is getting multiplied by 2 each time

[remote lodge]

Yes i know that

i just don't know to write a recursive formula

[remote lodge]

^

[neat summit]

U didn't finish it. 1 1 = 3 😎

[livid jolt]

i think by recursive they are asking u to find the time at x=5 using the x=4 value
so ig u just multiply 24 by 2?

[remote lodge]

it's this

[livid jolt]

yeh but that formula is asked in the part c

i found this online

[remote lodge]

wait i figured it out,

[livid jolt]

yeh looks good

[alpine sable]

Stuck on this problem, can someone help me please?

Guys how do I represent limits in Newtonian Notation of Integration?

For example y = sinx

I need to calculate area from 0 to 10

How do I represent it in limits?

[alpine sable]

Nevermind, I went back over the problem just now and I got the answer

Advanced Placement

[still ravine]

thanks

[alpine sable]

You're welcome

how do i find dy/dx in ln(x+y) = x ?

[glass lichen]

implicit then isolate

or isolate for y then differentiate is imo easier

[magic warren]

is question A just trial and error

[glass lichen]

you can set up 2 equations for a

then solve the system as much as you can

[alpine sable]

if i isolate for y i get y = e^x - x, so dy/dx is e^x - 1?

[glass lichen]

yes

[alpine sable]

but i've been told dy/dx is x + y - 1

[magic warren]

@glass lichen thanks

[alpine sable]

ez

math is so easy

[glass lichen]

$\frac{1+y'}{x+y}=1 \ y'=x+y-1$ but you know $y=e^x-x$ so $$y'=x+y-1=x+(e^x-x)-1=e^x-1$$

[ocean seal]

Mosh

[alpine sable]

oh

[glass lichen]

it just depends on if you want the derivative as a DE or as an explicit function

[alpine sable]

is it wrong to say it's e^x - 1?

[glass lichen]

no

[alpine sable]

could anyone confirm if $f(x)=\frac{4}{10}x * \frac23$ is the correct answer?

[ocean seal]

Lambdalo

[alpine sable]

I mean the correct way to calculate it, and then if 225 is the correct solution

[lime sequoia]

Hi, can someone help me with these problems?

apparently I should use integrals that lead to inverse trigonometric functions and inverse hyperbolic trigonometric functions

[hushed pasture]

second one, let u = e^x

and you will see it

[zinc roost]

Hey can anyone help and explain this to me

We can vc if u want I just fell asleep in class and dont understand anything on this paper

[lime sequoia]

Thanks, I'm going to try it right now

[magic geyser]

(12,-8) what's 12 and - 8?

[zinc roost]

it says give the new coordinate of the point (12,-8) after each of the following transformations

[magic geyser]

yeah

[zinc roost]

so im guessin after u find the coordinate for the number given u put how far it is from 12,-8?? irdk I was sleep when she explained

[magic geyser]

for 1 just multiply 12 and - 8 by 2

5 divide it by 1/2

2 by 3/4

[zinc roost]

so for the first one

24,-16 is my answer?

[magic geyser]

yes

[zinc roost]

for 2 i got 16 and -10.6 so I rounded up to 11

so 16,-11?

@magic geyser

[fringe spindle]

first one rewrite as (1 + e^(2x) - e^(2x))/(1 + e^(2x)) = 1 - (e^(2x))/(1 + e^(2x))

[magic rose]

Hey, so I was doing out some long division algebraic polynomials and I came across an issue.

I understand the whole process but the x^2 divisor changed it up as I'm used to just x-1 or a divisor without squares

So when you do the 5x^2/x^2 = 5 part,

you obviously bring that to the top so u can multiply out

so 5(x^2-1) = 5x^2-5,

What happens to the -5 since it's obviously not like terms or an x so u cant use it.

where did the -x come from

And what should I do in the future if I come across such a problem.

<@&286206848099549185>

[twilit flicker]

Quick question if a point is undefined is it a removable or nonremovable discontinuity

[zenith bough]

a and b are two vectors.
If ( 2a - b ) ⊥ ( a + b)
and ( a - 3b ) ⊥ ( 2a + b)
what is the angle between vectors a and b?

[dark granite]

please don't multipost your question. You posted this question in question 4 channel at 3:26pm. You'll see I also answered your question too.

[zenith bough]

I tried using the dot product [ if a /dot b = 0 then angle between a and b is 90 deg ]

but i cannot get anything meaningful out of it

pls help <@&286206848099549185>

[ancient saddle]

Hello, you have those 2 pairs of perpendicular vectors, so you know what their dot product is

You will get 2 equations which you can use to find a•b, then you can find the angle

[zenith bough]

its zero right?

[ancient saddle]

yes

[zenith bough]

ok, i dont really understand your solution, i know ( 2a - b ) is perpendicular to ( a + b), but i also know that ( a - 3b ) is perpendiculat to ( 2a + b)

how do i get a dot b out of that?

[ancient saddle]

(2a - b)•(a + b) = 0
2a•a + 2a•b - a•b - b•b = 0

[zenith bough]

thanks a lot

x*x is x^2

sqrt(x) = 3

it goes like this : ..... 540=4 * 3x * 5x => 540=60* x^2 => x^2=9 => x = 3

well x*x is x squared, how do you not know that??

if a is vector and * is dot product,
is a*a = 2a

?

it's very basic question i know, but I don't really understand vectors that much

[elder belfry]

@zenith bough a +a = 2a

[kindred warren]

since there are two envelopes, you have to put a '2' infront of p, and since there are 6 paperclips left over, add a 6 at the end

so it's 2p + 6

[zenith bough]

ty

[cerulean vine]

2p+6

[boreal ruin]

One of the most common reasons why drivers speed is because:

[remote agate]

hello, this is a pretty easy question. Could someone convert 7860 kg/m3 in kg/cm3, cause i would say it's 7860^6 kg/cm3 but that's wrong... could someone show me the process please?

[zenith bough]

1m = 100cm

(1m)^3 = (100cm)^3 =>> 1m^3 = 10^6 cm^3

[vestal aspen]

What’s 126 diminished by the product of two consecutive integers? (Translated to algebraic expression)

[remote agate]

i know that but it doesnt work lol

[zenith bough]

bro i showed you how to convert m^3 to cm^3

[remote agate]

i know how to do that but the answer is wrong

but kg stays the same

i don't really have to convert it

well no i have a point kg should change too logically? but idk how to do that...

[zenith bough]

7860 kg/1m^3 => 7860 kg / (10^6cm^3) = 0,007860kg/cm^3

[zenith bough]

@remote agate

[remote agate]

why is it negative tho

i'm sorry i'm confused thanks for the help, but what am i dividing with?

ooooooh

i get it

thanks

[small pumice]

i need help with thoose 3

[zenith bough]

i guess we will just do it for you

[fathom sequoia]

Hi guys, I need help - I think I did something wrong here. I don't know how to simplify this any further:

[wary stream]

Is this some sort of exam?

[small pumice]

no

hw

[frigid hatch]

lol

[zenith bough]

yeah, you can just send it here anytime and someone will do it for you

🤡

[wary stream]

I'm hoping this is sarcasm

[zenith bough]

yeah haha, i hate people that are like that

[wary stream]

I mean the directions says it all. Find the equivalent expressions, the pair of expressions that are equivalent, and expand and collect like terms

[alpine sable]

Yeah if you take the time you can do it

[fathom sequoia]

Is it possible to simplify this:

if it's fully simplified I get the green tick but if not I get the blue one so Idk how to simplify it more

[alpine sable]

Maybe $\sqrt[4] {\dfrac{1}{u^{3}}}=\dfrac{\sqrt[4] {1}}{\sqrt[4] {v^{3}}}$

[ocean seal]

Zamarus

[fathom sequoia]

ok it still says I need more simplifying:

[alpine sable]

obviously $\sqrt[4] {1}=1$

[fathom sequoia]

should I just skip this

[ocean seal]

Zamarus

[fathom sequoia]

ok

🤦‍♂️

[small pumice]

is it right

[fathom sequoia]

still more 😦

how is this grade 11 math

[alpine sable]

only one thing to work on now

[small pumice]

is it right?

[fathom sequoia]

ok I got it

the answer was

this question took me one hour -_-

[shadow stream]

sorry to not provide much context, but does anyone know how was that derived?

or rather what is the thought process of that?

[fathom sequoia]

how would I simplify this, sorry if it's a stupid question , I am getting stuck on these

the original question was:

i got to this but I dont know how ti simplify this more:

Update, got to this: but I think this is the max I can simplify, but of course it's saying it's not enough -_-

[placid zinc]

Write it with only one c
And one number
Both with an exponent on them

[nimble mulch]

Is this channel free?

[fathom sequoia]

Alright, I got

have i made a mistake

or no?

[frigid hatch]

try $\frac{6c^\frac{4}{5}}{7^\frac{1}{2}}$

[ocean seal]

Thunder7

[frigid hatch]

but do it with roots, I have no idea on how to do it with texit

[fathom sequoia]

what is the explanation behind this conclusion

[frigid hatch]

so you know how $\sqrt{4} = 4^\frac{1}{2}$

[ocean seal]

Thunder7

[fathom sequoia]

Yes

[placid zinc]

After putting the exponents into the brackets on the first step:
6c^(1/2) × 7^(-1/2) c^(3/4)

Add the exponents on the c, and write the numbers in any nice way:
(6/√7)c^(5/4)

[frigid hatch]

yes that

[placid zinc]

The beautiful part here is that there's no need to play with the symbol √. Just add the exponents.

[fathom sequoia]

Ok I will try to understand

how did you get to (6/sqrt(7))

I tried to follow your steps and I got to this

This is very confusing

[alpine sable]

what you have here is equivalent to (6/sqrt(7))c^(5/4), wdym?

[fathom sequoia]

k

it says its not simplified enough

[alpine sable]

you mean the page/website?

[fathom sequoia]

Yes if it is fully simplified I get a green tick

[alpine sable]

that's a bad designed system, there is no set up or fixed defn of "simplified" expression, what you have is already simplified

[fathom sequoia]

well It wants it to be fully simplified

[alpine sable]

you are rather now looking for "how does the website want me to express this in"

[fathom sequoia]

yeah...

[alpine sable]

well, we can't really help on that, i guess you can try with expressing c^(5/4) as a root

[fathom sequoia]

yeah I just did that

still no green tick -_-

[alpine sable]

hm, did you try maybe $\frac{6}{\sqrt{7}}c\sqrt[4]{c}$?

[ocean seal]

Al3dium

[fathom sequoia]

yeah the answer was:

👍

[alpine sable]

glad to hear, but yeah just note that we can't really help with figuring out what the website considers as "simplified", since, as i said, there's no fixed/set up rule on what's simplified and what's not

which isn't really your fault either

[fathom sequoia]

ok, maybe I will give the website feedback to explain better. there are no clear rules

also this is too difficult for grade 11 I think

so I will tell them to make t easier

[alpine sable]

don't know since i'm not familiar with grades/us system, but if you feel like so, then yeah

[fathom sequoia]

well I am not from US, I am from New Zealand so it's 'year 12' here. I just say grades because most pepole are from usa

[modest dragon]

i need help... again D:

[alpine sable]

can anyone help me with algebra ???

[kindred warren]

ok

[fathom sequoia]

whats your question

[alpine sable]

wait

the number 10

[modest dragon]

ok i go to another question text:D

[alpine sable]

i cant find an answer to it

😦

im 7th grade

[gray isle]

you messed up your v and dv

[alpine sable]

my sister wont help me snce she wants me to be independent

[fathom sequoia]

wow... I never learnt set notation

sorry cant help

[alpine sable]

aww ok

[fathom sequoia]

the answer is probably easy just ask anyone who knows set notation

[modest dragon]

so i need to change v and u?

[gray isle]

based on what you started with,
your dv should be
x^2 dx

[kindred warren]

i guess you could just do {red, orange, yellow, green, blue, violet, and indigo}

[fathom sequoia]

also how are you 7th grade and you are learning this? looks a bit complicated for 7th grade

[alpine sable]

idk if its because im in private school

[modest dragon]

why?

[kindred warren]

i gave you an answer

[alpine sable]

ok thank u

👍

[kindred warren]

do you get what i did

[alpine sable]

not rlly

[fathom sequoia]

Ah OK.

[alpine sable]

[kindred warren]

well the colours of the rainbow are red, orange, yellow, green, blue, indigo and violet

so i just replaced them with the colours

[alpine sable]

OHH

oke

thankz

[kindred warren]

np

[fathom sequoia]

oh yeah make sense 👍

[modest dragon]

i dont get it, why dv should be x^2dx?

[gray isle]

Because then your
int u dv
would actually be your original integral

if you're going to use that form for ibp,
you'd start with
u and dv

and get du and v from that

[modest dragon]

i dont understand :/

[glass lichen]

$\int u\dd{v}=uv-\int v\dd{u}$

[ocean seal]

Mosh

[glass lichen]

in IBP, you pick one part to be u which you differentiate to get du, and the other to be dv which you integrate to get v

[alpine sable]

is math notation hard to learn?

[glass lichen]

so for $\int x^2\ln(x)\dd{x}$, $$u=\ln(x)$$ and $$\dd{v}=x^2\dd{x}$$

[ocean seal]

Mosh

[glass lichen]

since you can easily differentiate ln(x) and easily integrate x^2

[glass lichen]

no.

[alpine sable]

how do u simplify it

so only 2 methods

[glass lichen]

simplify what?

[modest dragon]

ohh thanks!!!

[alpine sable]

math notation

[glass lichen]

...

[alpine sable]

[glass lichen]

you dont unless you opt to define notation for the problem

ex $\dv{x}{t}=\dot{x}$

[ocean seal]

Mosh

[alpine sable]

i still dont get it but yes ok

ill just learn it

[lime sequoia]

someone can help me with this problem? I use u = e ^ x but I can't keep solving

[woeful pulsar]

hmm what happened after u=e^x substitution? maybe you need further substitutions?

[fervent patrol]

someone please help im struggling

[alpine sable]

famous finance question but how would u solve this?

  headed. Pick a coin at random, and toss it 10 times. Given
  that you see 10 heads, what is the probability that the next
  toss of that coin is also a head?```

[lime sequoia]

I don't know what i did but i did this

[woeful pulsar]

but you shouldn't have e^(2x) leftover, everything should be u

[woeful pulsar]

just keep doing the same thing to both sides

[fervent patrol]

ik but at the end its 9=16x

[woeful pulsar]

what can you do to both sides to isolate x?

[fervent patrol]

divide

but they dotn have a common multiple

[woeful pulsar]

just divide then, you can still divide 9 by 16 to get another number, right?

[fervent patrol]

hm

ive never been good at division

[woeful pulsar]

write as fraction?

[fervent patrol]

its 0.5625

[woeful pulsar]

are you supposed to express as decimal or fraction?

[fervent patrol]

fraction i think

[woeful pulsar]

try drawing a tree diagram for all the possibilities

[woeful pulsar]

what fraction do you get when you divide 9 by 16

[fervent patrol]

idk

[woeful pulsar]

what fraction do you get when you divide 2 by 3

[fervent patrol]

6 repeated

0.6*

[woeful pulsar]

that's a decimal, not a fraction

[fervent patrol]

oh

2/3?

[woeful pulsar]

do you know what fractions are

yeah

2/3

[fervent patrol]

OH

9/16

[woeful pulsar]

^^

[fervent patrol]

soo

[woeful pulsar]

fraction division is way easier than decimals

[fervent patrol]

x=9/16?

ok i think i got it now ty

[lime sequoia]

oh yeah sorry i mistook it for another problem i got this "answer"

[alpine sable]

i got this!

i have one more question

how could i do bullet point 1

i did bullet point 2 through bayes theore m

[tawdry spindle]

what does this equal to?

[fringe spindle]

for each baker, multiply the proportion of cookies they make by the proportion of their cookies which contain hair, and add them all up

[alpine sable]

like when u say proportion

is it .05*.65 for baker A for example

or just .05

[fringe spindle]

yes, exactly that

[alpine sable]

ok ok cool i did

[fringe spindle]

oh nice

[alpine sable]

(.05 * .65 ) + (.15 * .25) + (.1 * .5) = .12

[fringe spindle]

that's the answer i got as well

[alpine sable]

awesome, thank you!

[fringe spindle]

np

[loud blade]

One question could someone explain

X intercepts

How do I solve for them if I’m not given an equation? Like For example this sheet ?

[jade birch]

But this sheet does give you the equation.

Also wait 15min then ping helpers

[loud blade]

Oh my bad

Sorry I just joined

My name is ironic

Lol

[jade birch]

And the graph for f(x)=x is wrong

You drew f(x)=|x| instead

[loud blade]

Ohhh

[jade birch]

channel occupied

[woven sparrow]

oof

[jade birch]

Moving on to answer your question about x-intercepts

[loud blade]

How would I determine the x intercept tho for the others in having the biggest issue with that? Do I make an equation?

[jade birch]

The x intercept is the place where the graph touches or passes through the x-axis

[loud blade]

Ohhhhh

So for a parabola it doesn’t exist

[jade birch]

At the x-axis, the y value is 0

or namely, f(x)=0

So you'd want to solve for x when f(x)=0

[jade birch]

It does exist

[loud blade]

Ohh

[jade birch]

f(x) = x^2 right?

[loud blade]

The y intercept doesn’t tho

Right

[loud blade]

Yea

[jade birch]

The y value for x intercepts is 0, as I said f(x) =0,so you can say that

0=x^2

[loud blade]

Ohh

I see

So for most

Functions

It’s 0

Basic

[jade birch]

don' think of it like that

There are infinitely many functions

[loud blade]

I see since it could also be like 5 units down

So it wouldn’t apply to that

Yea

[jade birch]

wdym by 5 units down

x intercepts are located on the x axis, where y=0

[loud blade]

Like say the the x intercept 0,-5

I mean

The

Vertex

[jade birch]

if the vertex is at (0,-5) then the x intercept is not at 0

, w graph x^2-5=0

[ocean seal]

Results provided by WolframAlpha

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Requested by .itsjustnai#9187

[loud blade]

I see

[jade birch]

Also you mentioned the y intercept

To find the y intercept you set x=0 and find f(0)

[loud blade]

Ohhh

[loud blade]

Your a goat bro

I see now!

[jade birch]

In this equation our y intercept is the same as the vertex

,w graph (x-1)^2-5

[ocean seal]

Results provided by WolframAlpha

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

Requested by .itsjustnai#9187

[jade birch]

But say you have this quadratic

[loud blade]

Yea

[jade birch]

our vertex is at (1, -5) but our y intercept is at (0, -4)

Any questions?

[loud blade]

Ohhhh

Thanks a lot, i just started school today so this helped

Thank you @jade birch

[jade birch]

Your cubic is incorrect though

The interval of increase/decrease

[kind crest]

Can someone please help me?

[alpine sable]

so, if you divide 100 by 3 you get 3.3333... and if you multiply 3.33333 by 3 you don't get 100 you get 99.9999... wheres the 0.000001?

[loud blade]

Ohh yea I kind of winged it

[alpine sable]

anyone?

[jade birch]

The range for the quartic as well

[woeful pulsar]

0.000..... = 0

[alpine sable]

well no brcause there is still a 1 at the end. Right?

because

[woeful pulsar]

what end?

[alpine sable]

now i get it

[jade birch]

3.33333 does not equal 3.3333...

[alpine sable]

what you are saying that infinit has no end therefor if the one is at the end it do not exist because infinit has no end

that makes sence

[jade birch]

What

[alpine sable]

no?

u dont get it?

[jade birch]

I don't know what you mean

[alpine sable]

infinit has no end right?

[jade birch]

3.3333... goes repeats infinitely, there is no last 3

[alpine sable]

just lkie the missing 0.0000000000001....

since the one is at the end

but the number is infinit

and infinit has no end

so the 0.0001 is not there

[jade birch]

Can I point a few things that are incorrect here?

[alpine sable]

yes

pls

that what is want

i

1/3=1/3 pas 0.33333 qui est une approximation

[jade birch]

If you divide 100 by 3, you get 3.3333... False, you get 33.3333...

[alpine sable]

daccord

yes

[alpine sable]

sorry thats what i meant

[jade birch]

If you multiply 3.33333 by 3 you get 99.9999... False, you get 9.99999

Also

[alpine sable]

i got it

its a writing mistake

[jade birch]

9.9999... does not equal 9.9999

[alpine sable]

wow

[jade birch]

9.9999... =10
9.9999= 9.9999

[alpine sable]

oh yes

let me put it this way then

100 / 3 = 33.3333..., 33.33333... * 3 = 99.99999..., 99.9999... != 100

[jade birch]

Almost

99.9999... does equal 100

however

[alpine sable]

yes tthat what i wrote

[jade birch]

99.9999 does not equal 100

[alpine sable]

!=

yessss

[jade birch]

!= is does not equal

[alpine sable]

!= is not equal in python

so i used it in math too

[jade birch]

Yes, I'am aware

[alpine sable]

poco

[jade birch]

But look

[alpine sable]

yes?

[jade birch]

You have written
99.9999...!= 100

[alpine sable]

!= = not equal

[jade birch]

That means that 99.9999... does not equal 100

[alpine sable]

yes

[jade birch]

But it does equal 100

[alpine sable]

what

99.9999...

not 100

[jade birch]

https://en.m.wikipedia.org/wiki/0.999...#:~:text=This%20repeating%20decimal%20represents%20the,number%20is%20equal%20to%201.&text=There%20are%20many%20ways%20of,arguments%20to%20mathematically%20rigorous%20proofs.

[alpine sable]

If you just extend that infinitely

it does equal to 100

[alpine sable]

ok

[jade birch]

I'll show you something as well

[warped phoenix]

is this channel taken?

[alpine sable]

euuuu yes well mmhm

i understand the spanish but not the math😂

nvrm

i thnk i got it

mmhm

i get the graph but what r u suppose to do

[tight locust]

in a sampling distribution, what happens as n increases?

[alpine sable]

oh

[jade birch]

3.33333... = x
33.3333... = 10x

subtract left from left, right from right

33.3333...-3.3333...=10x-x
30=9x
x=30/9
x=10/3
@alpine sable

[alpine sable]

ok

kinda makes sence

[jade birch]

If you apply this to any number with repeating 9 in the decimal, for example 99.9999.... you get 100
3.9999... you get 4 and so on

[alpine sable]

mmhm yes

but

ok

[jade birch]

Do you know when a limit exists? @fringe shuttle

[alpine sable]

and what is f(x)

how do you calculate

[jade birch]

@alpine sable he is given a graph

[alpine sable]

f * x (i think)

[jade birch]

f(x) is another notation for a function

y=3x+2 is the same as saying f(x) =3x+2

[alpine sable]

its -1

[jade birch]

No it's not?

[alpine sable]

whats the arrow for?

[alpine sable]

yes it is

what class are you in 😂

it is not continuous at 5 but the limit is -1 as it approaches 5

[jade birch]

the left limit is not the same as the right limit

[alpine sable]

this is getting complicated

and x approaches 5 from the left only I believe here?

yes

[jade birch]

No

NO

[alpine sable]

there one arrow

oh yes

no limit

or

one mf*king arow

[jade birch]

No.

[alpine sable]

There are 2 things

where the second then?

one approaches from left

another from the right

I didnt see it sorry

[jade birch]

👍

[alpine sable]

i stiill dont see it 😂

there is no limit, yes.

[jade birch]

Look

[alpine sable]

yes im looking

can someone resend the formula i dont want to scrool

[jade birch]

A limit exists at point c only if the left limit is equal to the right limit at point c. $\newline$ The left limit notation is:
$\ \lim_{x\to c^-} f(x) \$
The right limit notation is:
$\ \lim_{x\to c^+} f(x)$

[alpine sable]

mmhm

[ocean seal]

.itsjustnai

[jade birch]

@fringe shuttle

[alpine sable]

hey, I mean its already evident that since the limits from left and right are different there is no limit, but from what I see, there is something continuous at x=5

does it contribute anything to the limit

sorry, I learnt limits about a day ago

go on

pls

[jade birch]

For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point.

It's defined on the interval (5-a,5+a) where a is a small real number however it is not continuous

@alpine sable

[alpine sable]

what about this,

[jade birch]

What about this?

[alpine sable]

yes

i need help

[jade birch]

Regarding?

[alpine sable]

oh god

this

[dapper kernel]

there it is, our beloved

what about him?

[alpine sable]

sarcasme?

[jade birch]

But what is your question?

[dapper kernel]

no.

[jade birch]

@fringe shuttle Do you understand why?

[alpine sable]

you need to continue on the three little dot

[jade birch]

I need to?

[alpine sable]

no

[jade birch]

No I don't :)

[alpine sable]

i mean

u know what i mean

[jade birch]

I still don't understand what your question is... Where are you stuck/what don't you understand?

Do you know what the big sigma means?

[alpine sable]

i dont know what is the fractionis suppose to be

fraction

[jade birch]

It's an infinite sum where the fractions are all positive integers brought up to the power of whatever s is

[alpine sable]

oh

that...

makes sence

[shadow edge]

How many ways can you store a biography on a shelf?
and 4 novels chosen from 3 biographies and 7 novels if we want the
biography always at the center?

I cant seem to get the answer, can someone help?

[alpine sable]

quick question where does this expansion of binomials end? 0 to 6, right so basically the last term is C(-6, 6) x^6

[shadow edge]

My question:

https://cdn.discordapp.com/emojis/737162069719121921.gif?v=1

[fathom sequoia]

How can I simplify this further

[alpine sable]

your question isnt very clear @shadow edge

[shadow edge]

Its the best i could translate

[alpine sable]

and 4 novels chosen from 3 biographies

this isnt valid

[shadow edge]

thats the part i dont get either

[alpine sable]

then most probably the question is wrong or smth

[fathom sequoia]

Wait nvm I solved it

[shadow edge]

Ok

[alpine sable]

its already simplified, the best you could do is probably

[fathom sequoia]

nah I simplified it more but I forgot the answer

[alpine sable]

sorry i dont know latex

[silver yoke]

How do i solve HOH equations

[fathom sequoia]

Same, I want to learn it

[sharp canyon]

YALL

what's the mathematical name for (#)?

[stoic fable]

please help me

[woeful pulsar]

how is it used

[keen trail]

can anyone help me out on logical equivalences?

[left saffron]

When the power is not a nonnegative integer (eg the power is -6), the binomial expansion is infinite

[keen trail]

how should I start off?

[shadow edge]

How many ways can 4 people share 12 items different items if it is understood that each must have 3?

the teacher says its 369 600 ways

idk how tho

[sharp canyon]

they asked what's the name of the number sign

[frigid hatch]

number sign

[full dome]

How do I determine the slope of my line of best fit and identify the y-intercept?

[kindred hull]

Choose two points on the line and put them into the gradient formula

For the slope

Then you can write out the equation for the line

Then just use algebra to find the y intercept

[surreal lily]

,rotate

[surreal lily]

need help with the first one

the lowest I was able to get was -78 using -9, -6, 6, and -4

[dark granite]

use the fact that (s -> t) is equivalent to (~s v t). and then use distributive law

[dark granite]

can you please post the problem with the exact wording it used because what you stated here^ doesn't make any sense.

[dark granite]

this is because you can think of the arranging the 12 different items in a row as 12! and for each of those arrangements (for instance, abc def ghi jkl) then we can arranged the items abc in 3! ways and still have those three items assigned to person 1, we can have the items def arranged in 3! ways and still have those three items assigned to person 2, and similarly for person 3, and person 4. So the answer is 12!/[(3!)^4].

,w 12!/[(3!)^4]

[ocean seal]

Results provided by WolframAlpha

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

Requested by logician#7452

[dark granite]

which is exactly what your teacher got^

[lusty plaza]

Amazing that it’s represented so simply

[dark granite]

yea I mean there's another way to do this that looks messier. Watch this....

$\binom{12}{3}\binom{9}{3}\binom{6}{3}\binom{3}{3}$

[ocean seal]

logician

[dark granite]

,w (12 choose 3)(9 choose 3)(6 choose 3)

[lusty plaza]

Ow my brain

[ocean seal]

Results provided by WolframAlpha

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

Requested by logician#7452

[dark granite]

see^

(3 choose 3) is just 1, so I left that off

[lusty plaza]

Right

Good stuff

[dark granite]

https://tenor.com/view/thumbs-up-good-great-excellent-like-gif-4987000

[lusty plaza]

That was my original way of thinking about it

12 choose 3 and then so on

[dark granite]

this was my original way of thinking about it^

[lusty plaza]

Intuitively I would have multilplied the whole thing by 4

[dark granite]

no!!!! don't do that!

[lusty plaza]

Which is wrong

[fleet gyro]

need help

[flat vale]

never encountered such q but I'm assuming that you need to use distance formula

and show that the distance from the point to the origin is 1

[jagged sonnet]

can someone help

[small trellis]

Observe a trapezium

[lusty plaza]

.img trapezium

[full dome]

How do I determine the slope of my line of best fit and identify the y-intercept?

Someone answered earlier but they can't elaborate atm.

Urgent help please, it's 3:00 am and I just want to sleep.

[small trellis]

The y intercept is the y coordinate that intercepts the axis

It always intercepts the y axis

Hence the name

If it intercepts the y axis, then it must have the quality X=0

Because the entire y axis is X=0

Then you just read where the line crosses the y axis and find your y coordinate

You can see it

[full dome]

What would the coordinate be for that little dot on the far right?