help-0

[static pasture]

OH

AB?

[ionic jewel]

yes

[static pasture]

ohhh ok

[ionic jewel]

now we have

$\tan(26^{\circ}) = \frac{{AB}}{6}$

do you see where I got this?

[ocean seal]

bunny

[static pasture]

I think so. So tan is the angle BC? so it would be 6(26)= 63/27?

[ionic jewel]

no

i have no idea hwere you got 63 or 27 but you misunderstand tan

tan(x) is a function

it evaulates to a number

,w tan(26 degrees)

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

specifically this number

[static pasture]

oh

[ionic jewel]

you want to solve for AB in the equation you have

but honestly you need to watch an introduction to trig video on khan academy or something

looks like you missed it in class

[static pasture]

yea... I should

thank you

[pastel mauve]

how do i find answer

<@&286206848099549185>

nobody knows?

[elder viper]

eh.... I get 8 but it's not available as an answer...

[pastel mauve]

?

@elder viper how about this

[pallid horizon]

?

Anyone know how to do this?

[alpine sable]

My guess is 4, I’m saying that because it cannot be negative, and 2^x is 1 when x=0 so it’s been moved up by 4 I think? @pastel mauve

[supple elm]

what does d(10) represent in the situation? does anyone know how to solve it using my function

[alpine sable]

HOW DO O SOLVE ALGEBRA

[muted raft]

what does the function d mean?

[vale wigeon]

by (a) not yelling, and (b) being a lot more specific about your troubles/doubts/whatever than just "solve algebra"

[alpine sable]

Help

[vale wigeon]

what's troubling you?

@alpine sable

[umbral folio]

whats the gradient vector for the function f(x, y) − z = 0

[vale wigeon]

oh for fucks sake.

[alpine sable]

Like

How do i do this

[vale wigeon]

jeez, why doesn't EVERYONE pile up in this channel. god.

@alpine sable let's move to #geometry-and-trigonometry, otherwise we'll just get shouted over

[alpine sable]

Ok

[blissful pilot]

what is thisssss

<@&286206848099549185>

<@&286206848099549185>

@acoustic sable

[ionic jewel]

not only did you not wait to ping helpers

you pinged them twice

[blissful pilot]

yup

[ionic jewel]

combine like terms

and dont spam ping again

read #❓how-to-get-help

[blissful pilot]

what dose that mean

[ionic jewel]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:combine-like-terms/v/combining-like-terms

heres a good introduction

[blissful pilot]

thanks

[edgy breach]

Where have I gone wrong here or what should I continue with? Am I being completely brain dead and just not seeing what I’ve done wrong ?

[alpine sable]

Can u help me expanding this pls?

$\sum_{n=-\infty}^\infty \frac{t^n}{n}$

[ocean seal]

nosequepasa

[alpine sable]

Q.Q

[muted raft]

What does it mean to divide?

[ionic jewel]

1 + $\sum_{n=-\infty}^{-1} \frac{t^n}{n} + $\sum_{n=1}^\infty \frac{t^n}{n}$

[ocean seal]

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

[alpine sable]

ye, ty

t = e^i*theta

so, how can i expand this?

this is

1 + ... -log(1-t)

right?

[glass lichen]

you assumed f(k+1) was true

[lilac kestrel]

can anyone help with c 🙏

[exotic canyon]

Can someone help please

[edgy breach]

No I assumed f(k) was true

[glass lichen]

$2^k+6^k=8N, N\in\mathbb{Z}$

[ocean seal]

moshill1

[edgy breach]

I’ve seen that method used on YouTube and I want to use it too, but idk if my spec will allow it

In the textbook it shows only the method I used

Making me think I can’t use that 1

[glass lichen]

what other method is there...?

[alpine sable]

try doing f(k+1)-2f(k) and you'll get 4(6)^k which is divisible by 8 for all integers k>0

[glass lichen]

Or just make a strong hypothesis, namely that f(k)=8N and f(k-1)=8M, N and M are in Z

$2^{k+1}+6^{k+1}=2(2^k)+6(6^k)=2(8N-6^k)+6(8N-2^k)$

[ocean seal]

moshill1

[simple fjord]

i need help

[zealous marsh]

hi

[tacit mortar]

hi

ok

im gonna post my question

Write in rational form and then evaluate. Express your answers using only positive exponents. No decimals. Show work.

the answer i got is

[glass lichen]

yes

[tacit mortar]

ok good is that correct

[glass lichen]

I said yes...

[tacit mortar]

so is it right?

[glass lichen]

I already said yes

[alpine sable]

hello

i need help with a question

[glass lichen]

do you know your exponent rules?

[tacit mortar]

ty

[alpine sable]

not really

[glass lichen]

Ok so look at your notes or google them

[alpine sable]

okay i just did

[glass lichen]

and what's the answer to your question?

[alpine sable]

6^6

thank you so much

[glass lichen]

yes

[glossy brook]

not sure how to do this

i tried using ftc but i get different answer than wolfram

[glass lichen]

$\int_{\sin{x}}^{\cos{x}}=\int_{\sin{x}}^0+\int_0^{\cos{x}}$

[ocean seal]

moshill1

[glass lichen]

each of which can be differentiated with chain rule and FTC

[glossy brook]

yes I did the splitting, but I still get a different answer

[glass lichen]

what do you get?

[glossy brook]

thats what i get

but the answer is

[frosty zodiac]

if it’s 13m/s, how much would that be in km/h

[glass lichen]

how do you get that?

possible for you to post your work?

[glossy brook]

so I put e^(f(x))^2

[frosty zodiac]

nvm i got it

[glossy brook]

then using chain rule

[glass lichen]

what's f(x)?

[glossy brook]

sin(x) and cos(x)

[glass lichen]

ok so you're doing it in reverse

[glossy brook]

because younhave two integrals

[glass lichen]

you do chain rule then sub in

[glossy brook]

🤨

[glass lichen]

$f(x)=\int_0^x e^{t^2}\dd{t}$ what's $f'(x)$?

[ocean seal]

moshill1

[glossy brook]

$2xe^{x^2}$

[ocean seal]

time

[glass lichen]

no

$\dv{x}\int_a^xf(t)\dd{t}=f(x)$

[ocean seal]

moshill1

[glass lichen]

that's what FTC says

[glossy brook]

so $e^{x^2}$

?

[ocean seal]

time

[glass lichen]

yes

[glossy brook]

hmm

OH

ok

i get it

[glass lichen]

now $\int_0^{\sin{x}}e^{t^2}\dd{t}=f(\sin{x})$

[ocean seal]

moshill1

[glossy brook]

thank you

[latent lance]

hello

where should I ask a question regarding functions between contable and uncontable sets

can I ask here ?

[gray gorge]

Sure

[latent lance]

let S be the powerset of N. Now me and my friend, we are dealing with a function from S to Z.

now my first thought was like

[prime crypt]

[latent lance]

wait

the power set of N is the set of every subset of N right

oohhh I think the problem is there

wait okay so S is defined as the set of every subset of N, perhaps that's not the power set of N

but like

my thought was like

S is uncountable and Z is countable right

so now

by pigeonhole

[frosty zodiac]

A car accelerates from 0 to 100 km / h in 13 seconds.
What is the acceleration a?

[latent lance]

there has to exist at least two elements A and B of S such that f(A) = f(B)

right

(I don't really know much about the terminology used here I'm sorry)

[glass lichen]

is it constant acceleration?

[frosty zodiac]

yes

[glass lichen]

also use an unused channel

[latent lance]

yeah bro pls I'm also looking for help

[gray gorge]

In the pigeonhole principle, one of your objects must be finite

Which is not the case here

[latent lance]

really ?

[gray gorge]

Yes

[latent lance]

I thought there was like a version of pigeonhole that worked for infinite sets

but regardless it's intuitive isn't

like

the cardinality of S is bigger than that of Z right

[gray gorge]

Yes

[latent lance]

but then like

my friend showed me a function

[gray gorge]

the number of "pigeons" can be infinite yes, but then the number of "holes" should be finite

[latent lance]

ohhh

okay I see

but even if the number of holes is infinite, if the number of pigeons is bigger than the number of holes, you can derive what I derive right ?

like

arrive to

but then my friend showed me this function

$$f(A)=\prod_{x\in A}p_x$$

[ocean seal]

Astrolopithecus43

[latent lance]

where p_1p_2...p_n are the first n prime numbers

which is a bijection between the powerset of N and the squarefree numbers ?

and thus it's an injection between S and Z?

what

I can't find the error on here

rip

what's going on

help ?

me ? or the other guy ?

[lilac kestrel]

mb

[latent lance]

oh ty guys

[gray gorge]

no it isn't

what if A has infinite size

your square-free integer would be infinite? That doesn't make sense

[latent lance]

but there're infinitely many prime numbers right

[gray gorge]

Suppose you take set A to be the set of all even numbers

then f(A) = ?

certainly not an element of the naturals, let alone the squarefree integers

[latent lance]

but there's a bijection between the prime numbers and N right

[gray gorge]

Yes, and?

[latent lance]

so for any subset of integers on S, there will be enough primes to construct this product right?

it will be arbitrarily large ?

but mmm

[gray gorge]

There will be an infinite amount of subsets of N for which f is not well defined

And does not map into the square-free integers

[latent lance]

like what subset ?

mmmmm idk I'm not convinced

[gray gorge]

Any infinite subset of the natural numbers like I said

Suppose you take set A to be the set of all even numbers
then f(A) = ?

[latent lance]

but there are infinitely many primes tho?

[latent lance]

infinity ?

wait

[gray gorge]

yeah and now suppose you take A to be the set of all multiples of 3

then f(A) = ?

[latent lance]

okay right

so f is not well defined !

[gray gorge]

You can't convince me that's a bijection

[latent lance]

mmmm

[gray gorge]

yeah precisely

[latent lance]

okay so mmm

what happens if

let's say f maps from S to N

then f({set of natural numbers}) is not well defined either ?

like

cuz for every A in S, we have that f(A) + f(A^c) = f(N)

but then you would need an infinite amount of pairs of integers x + y such that x + y is equal to f(N) right

also so the first reasoning is correct then ?

[gray gorge]

f({1}) = ?

[latent lance]

ohhh wait

this relationship is for disjoint sets

[latent lance]

how can you know ?

[gray gorge]

idk

You're trying to construct this function

not me

[latent lance]

lol mmmm

no like

it's just a condition that defines a set of function

like the set of functions that satisfy the equation

mmmmmmmm

okay but the first thing that we said

[gray gorge]

Ok, so that implies that set contains some functions that you can build explicitly

Can you name one for me?

[latent lance]

f(A) = cardinality of A

yes

this one works ?

[barren jacinth]

can someone help me with this, thank u so much

[gray gorge]

ok so what is it about this f that is so special?

That it's not a surjection?

[latent lance]

mmmmm

wdym especial

oh

[gray gorge]

What are you even trying to do now

[latent lance]

okay so look

wait can I dm you the original question?

cuz like we are going to use it on an olympiad

in a month or smth

[gray gorge]

#competition-math

[latent lance]

yes but

the original problem is related to all this questions

and it has to be kept secret

lol

is it okay ?

if I dm it to you?

[gray gorge]

How is it a secret then

[latent lance]

cuz then you won't share it with ppl on the math oly word ?

lol

idk

[gray gorge]

Maybe I will participate in the same olympiad

Who knows

[latent lance]

lol

it's a spanish speaking olympiad

[gray gorge]

No hablo castellano muy bien, amigo

[latent lance]

well then there's no problem ?

🥺

lol

[nova nebula]

Hi good night guys

[gray gorge]

gn

[nova nebula]

I have a question

[latent lance]

idk I thank you a lot for your help bro

[gray gorge]

good luck anyway

[latent lance]

ty

[atomic dune]

I need help with identifying what shape it is

[latent lance]

like the main problem was that my friend sent me that construction for an inyection and we couldn't figure out what was up

but ty

tytytyty

[gray gorge]

is this an exam question?

[nova nebula]

1/3 = 0.333...

1/3×3=1

0.333...×3=0.9999..

Why is that so why is 1/3×3 = 1 and not 0.99999999999

Just for my own interest in not an math person really but I want to know

I'm

[gray gorge]

https://www.youtube.com/watch?v=G_gUE74YVos

[atomic dune]

no,its for my Homework I just learned the concept yesterday

[gray gorge]

ok

[nova nebula]

Thx Ill have a look

[gray gorge]

it looks like a triangular prism to me

[atomic dune]

Thank you👍

[tacit mortar]

hello

can someone check if i did this right

Determine the equation of the following exponential functions, in the form f(x) = ab x + c.

<@&286206848099549185>

is that correct

[glass lichen]

get them both with base 3

[nova nebula]

I get it ok but I don't understand fully. 0.999 / 2 is not 0.5

[tacit mortar]

yes and i got 1

[nova nebula]

It is 0.49999995 somethink

[glass lichen]

,w solve 2x=-2(x-10)

[ocean seal]

Results provided by WolframAlpha

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

Requested by moshill1#9771

[glass lichen]

x=1 isnt correct @tacit mortar

[tacit mortar]

oh

[glass lichen]

$\frac{1}{9}=3^{-2} \ 3^{2x}=3^{-2(x-10)}$

[ocean seal]

moshill1

[tacit mortar]

so what i did was wrong or was the last part wrong

[glass lichen]

I mean you stopped half way through solving at that point

but everything was right

[tacit mortar]

ok so i had to do more?

ty

Determine the equation of the following exponential functions, in the form f(x) = ab x + c.

For this question the slope intercept would be (0, -1) (1, 2)
and the answer would be y= 3x-1

[alpine sable]

Yo

If my trampoline is 14 feet across both ways

How many feet is it around

[limpid spade]

y=3x-1 isn't an exponential function

[alpine sable]

Could you answer my question

[limpid spade]

No

[tacit mortar]

oh so thats wrong

[alpine sable]

Ugh

[barren jacinth]

14 feet as in diameter?

[dire spindle]

I don’t know how to do approach this

[alpine sable]

can someone help me with this?

[foggy ginkgo]

If x, y, z are positive numbers below 10 and
(100x + 10y + z)^2 = (x + y + z)^5

Extract the value of x^2 + y^2 + z^2

Help?

[muted raft]

trigonometric substitution.

[dire spindle]

which function

do i substitute

ive tried both

[muted raft]

whichever you prefer, but try something along the lines of sin(x)^2 + cos(x)^2 = 1

[dire spindle]

okay let me try

[mellow acorn]

can someone help me

[dire spindle]

that was funny

[loud barn]

This channel was already occupied by the way

[dire spindle]

I’m not getting anywhere

[tacit mortar]

Amy makes an initial investment of $5000. The investment loses 13.5% each year.
a) Determine an equation that can be used to model the amount of the investment.
b) How much will the investment be worth after 4 years?
c) How long will it take for the investment to triple?

<@&286206848099549185>

?av

[fierce saddle]

I need help with my elevation and Depression hw

<@&286206848099549185>

[alpine sable]

,w 54+36=100

[ocean seal]

Results provided by WolframAlpha

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

Requested by Taken#9251

[alpine sable]

,w 54+36=

[ocean seal]

Results provided by WolframAlpha

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

Requested by Taken#9251

[alpine sable]

,w 64+36=100

[ocean seal]

Results provided by WolframAlpha

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

Requested by Taken#9251

[glass lichen]

@alpine sable #bots

[jade eagle]

I can help

[wispy urchin]

I’m so mad! This keeps happening to me. Sometimes I use PEMDAS on an equation when I can just move all the terms to the left and factor it!

[glass lichen]

ok..?

do you need help or just ranting in a help channel for some reason

[wispy urchin]

Sorry! I have a question

Give me a sec...

Does anyone know how to solve this? I’m stuck

[valid wagon]

What happens as x gets large?

[vast marsh]

When ur free can u help?

[glass lichen]

y=4^x has a HA at y=0

f has been translated left 1 and down 10

[alpine sable]

Anyone free to assist me with this please?

[indigo vine]

could sm1 explain

how they got that

[glass lichen]

@indigo vine @alpine sable in use, read the rules

[indigo vine]

oh shit

my bad

[wispy urchin]

Oh! Thank you! (Sorry it took me so long. I’m kind of slow) I kind of sort of get how to solve this. I think I need to study asymptotes again.

[uneven isle]

Is the channel free rn?

Or is someone still waiting

I just started coordinate geometry so I’m a bit stupid. I was told that the point where the bisector meet is the center of the circle and then I just need to find the radius

But something came out wrong on the Desmos graph when I tried to input the values

school laptop so I can’t use discord

Sorry for bad image quality, took it with my phoen

<@&286206848099549185>

[carmine stump]

the point N is wrong

[uneven isle]

Wait wot

I am pretty sure point N had the right coordinate

If it is wrong

Would it be possible for u to explain

I am a bit slow to see the problem

[carmine stump]

so l passes through L(-4,0) and M(0,3)

[uneven isle]

Yep

[carmine stump]

so it has a gradient of 3/4

[uneven isle]

Yes

[carmine stump]

and a y intercept of 3

[uneven isle]

Mhm

[carmine stump]

M is midpoint of LN

[uneven isle]

Yeh

[carmine stump]

x and y are independent so (Lx+Nx)/2 = Mx

[uneven isle]

Yeah

N is (4, 6)

[carmine stump]

sub the x in L

wait

nvm im stupid

somehow i got 9 the first time through

[uneven isle]

Oh

All g

Welp dis is awkward

Gonna have to wait for someone else to come

[carmine stump]

yh

[uneven isle]

Struggling with question 13 F

Some thing comes out wrong on the graph when I put the value into a graphing calculator

The points do not line up

And are not all on the circumference of the circle

[carmine stump]

what's the coord for the centre of your circle?

nvm (1.5,3.5)

i'm seeing something

to do with circle theorem

angle LPN is a right angle and L,P & N all lay on the circumference which matches with the angle in a semicircle is 90 degrees theorem

hence LN is the diameter

which makes M the centre

@uneven isle

[uneven isle]

Oh what

How is m the center

I’m stupid

Oh wait nvm I c

Ty

[carmine stump]

np

btw how did you do e

[uneven isle]

Oh

It was easy

[carmine stump]

i know how to do it via dot product

[uneven isle]

Just prove that they are penperdicular

[carmine stump]

oohh

okay

[uneven isle]

I always do it dat way

To prove they are penper just make sure their gradient are the negative reciprocal of each other

Which will always multiply out to -1 as ur result

[carmine stump]

not sure what year are you but i'm in y12 and dot product is just so much easier

[uneven isle]

I’m yr 9

[carmine stump]

that cool man

[uneven isle]

Imma look into dot product

[carmine stump]

sure i think you can learn it pretty easily, but understanding it takes knowledge of linear algebra which i don't think a lot of y9s know

[vernal crown]

anyone know this question?

[glacial pier]

can someone check my answers of this one

<@&286206848099549185>

[vernal crown]

<@&286206848099549185>

[keen wasp]

how do u do this

ive gotten the coordinaates for the vertices & equations for the lines of the triangle but dont know where to go from there

[glass lichen]

pick a point on the line and then find the area of the rectangle from that point in terms of x or y. Then optimize the function

[alpine sable]

Someone help

Pls

[keen wasp]

thanks i figurd it out

[oak chasm]

@proven mortar That's a derivative, right?

@proven mortar Limits can evaluate to infinity.

I think this is an example where a derivative is infinity:

,w D[1/x, x] at x = 0

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

Well, h -> 0 means those limits have to be the same.

No problem.

[nocturne carbon]

Is there a session going on rn

Okay can I get help pls I’m crying

[oak chasm]

No need to ask, just ask your question and people will see if they can help.

[nocturne carbon]

Okay

I can’t understand this pls

I don’t know how to find a slope

[oak chasm]

@nocturne carbon OK, what's the x value in (1, 3)?

[nocturne carbon]

I don’t know 😭

[oak chasm]

OK, x comes first then y.

So, what's x?

[nocturne carbon]

Okay thanks for that

[nocturne carbon]

1

[oak chasm]

Right.

What's the y value in (2, 7)?

[nocturne carbon]

7

[oak chasm]

Good.

[nocturne carbon]

Wait if you can, can we do this in dms so I can find the chat again

[oak chasm]

@nocturne carbon No, sorry, the server rules say it should be done here, but you can copy the chat to Notepad and save it or something.

[nocturne carbon]

Okay let’s continue pls

[oak chasm]

Now, take the two points (5, -3) and (-1, 6).

What are the two y values?

[nocturne carbon]

-3 and 6

[oak chasm]

OK, what's the first minus the second? (-3) - (6)?

[nocturne carbon]

3

[oak chasm]

No, what happens when you start at -3 on the number line and go backwards 6?

[nocturne carbon]

Oh wait I did -3 - -6

-9?

[oak chasm]

Right.

[ocean seal]

Chai T. Rex

[nocturne carbon]

y minus -9 hmmm

[ocean seal]

Chai T. Rex

[nocturne carbon]

Didn’t I just subtract both the y’s

[oak chasm]

Yes.

[ocean seal]

Chai T. Rex

[nocturne carbon]

Okay

I only have to do after 4 but

The y’s are 4,9

[oak chasm]

OK, let's look at how your worksheet wants you to do it.

[nocturne carbon]

Should I send it again

[oak chasm]

Look at the top. We'll do that and then you can apply it to problem 4.

No, I've got it.

[nocturne carbon]

Okay let me try the worksheet now

The proper way

OH

[shell karma]

hey

can someone help me with this?

[oak chasm]

@shell karma Sorry, channel busy.

[shell karma]

ah ok

dm me later if you can though, im stuck $$

[oak chasm]

@shell karma You can ask in #help-9 if you hurry.

[nocturne carbon]

Is the answer for 4

5/8

Did I do it right

Ugh online school is much harder

[oak chasm]

Yes, that's the slope.

[nocturne carbon]

THANKS

[ocean seal]

Chai T. Rex

[nocturne carbon]

IVE BEEN STUCK FOR AN HOUR

[nocturne carbon]

For the y I got 5 and for the x I got 8

[oak chasm]

OK, good. You went the second one minus the first one, which is how they wanted it.

You're welcome.

[nocturne carbon]

Wiat

Wait

Can I do another one and can you check it

[oak chasm]

OK.

[nocturne carbon]

I got 3/11

[oak chasm]

For which one?

[nocturne carbon]

5

[oak chasm]

Yes, that's right.

[nocturne carbon]

Okay thank you so much I can’t thank you enough

[oak chasm]

You're welcome.

[brave canopy]

Hey guys I’m stuck on this question, anyone know how to start ?

How many subsets of {1,2,3,4,5,6,7,8,9,10,11,12} contain at least 8 elements ?

I know there’s a formula n! / ((n-m)!m!) but the “at least 8 elements” part is throwing me off

[ocean seal]

Chai T. Rex

[oak chasm]

Does that part make sense?

[brave canopy]

Ok so that’s for exactly 8

[oak chasm]

12C8 + 12C9 for exactly 8 or 9 elements.

Does that make sense?

[tacit mortar]

Hello is this channel free

[oak chasm]

@tacit mortar No, sorry.

[brave canopy]

Yes it makes sense

[tacit mortar]

ok ill wait

[oak chasm]

@brave canopy So, what counts are 8 or more?

[brave canopy]

Hahaha uhhhhh

I mean like both 8 9 10 11 12 are 8 or more

[oak chasm]

Right.

[brave canopy]

So do I add it all up ??

[oak chasm]

Yes.

[brave canopy]

Oooooooh

So do I do the formula 4 times for each one

And then add them together ?

[oak chasm]

You do the formula once for each one.

[brave canopy]

Yeah that’s what I meant

Ahhh thanks man

[oak chasm]

12C8 + 12C9 + 12C10 + ... + 12C12

You're welcome.

[brave canopy]

Thanks !!!! I was getting confused

[gaunt magnet]

ok is this free now

[tacit mortar]

i was here first

[charred flint]

POST QUESTIONS GOGO

[tacit mortar]

ok

Determine the equation of the following exponential functions, in the form f(x) = ab x + c.

[ocean seal]

Chai T. Rex

[oak chasm]

@vernal crown Sorry, channel busy.

[vernal crown]

i asked at 8:30

[tacit mortar]

would the slope intercept be (0, -1) (1, 2)
and y= 3x-1

[oak chasm]

Yes, that's the equation of the line that joins the two marked points.

[crude flame]

relate hypothesis testing in a specific situation you experienced or you observed. how important is to follow step by step process? (can anyone help me to answer this question) <@&286206848099549185>

[tacit mortar]

so did i do that correct?

[oak chasm]

@crude flame Sorry, channel busy.

@tacit mortar What question were you answering?

[tacit mortar]

this one

[ocean seal]

Chai T. Rex

[tacit mortar]

yes

it should be in the form f(x_= abx +c

[ocean seal]

Chai T. Rex

[tacit mortar]

oh

what am i doing wrong

[ocean seal]

Chai T. Rex

[oak chasm]

Do you see how I got these?

[tacit mortar]

are those the slope intercepts (0, -1) (1, 2)

[ocean seal]

Chai T. Rex

[tacit mortar]

oh

[ocean seal]

Chai T. Rex

[tacit mortar]

yes

[oak chasm]

OK, how did I get the -1?

[tacit mortar]

from the graph

[ocean seal]

Chai T. Rex

[tacit mortar]

uhh

[sullen nova]

,w int x(x+1)^1/2 dx

[ocean seal]

Results provided by WolframAlpha

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

Requested by Le Vorn#7624

[oak chasm]

@sullen nova Please use #bots for that.

Or just use the Wolfram Alpha website directly.

@tacit mortar Stuck?

[tacit mortar]

yes

[foggy onyx]

What is an arithmetic series

[ocean seal]

Chai T. Rex

[oak chasm]

@foggy onyx Sorry, channel is busy.

[foggy onyx]

oops

Sorry lmao

[tacit mortar]

yes

[ocean seal]

Chai T. Rex

[tacit mortar]

1?

[oak chasm]

No, in terms of the formula.

[ocean seal]

Chai T. Rex

[tacit mortar]

Nope

[ocean seal]

Chai T. Rex

[alpine sable]

can someone help me with this problem?

[oak chasm]

@alpine sable Sorry, channel busy.

[alpine sable]

ah

mb

[tacit mortar]

yes

[ocean seal]

Chai T. Rex

[tacit mortar]

ohh

[ocean seal]

Chai T. Rex

[tacit mortar]

so x will be replaced by 0?

[ocean seal]

Chai T. Rex

[oak chasm]

Yeah, like that.

Does that make sense?

[tacit mortar]

yes it is making sense but how did u get 2 and 3

[oak chasm]

I made them up as an example.

[tacit mortar]

oh

[ocean seal]

Chai T. Rex

Chai T. Rex

Chai T. Rex

[oak chasm]

Does that make sense?

[tacit mortar]

f(0) would be f(x)

[ocean seal]

Chai T. Rex

[tacit mortar]

yes

[ocean seal]

Chai T. Rex

[tacit mortar]

yup that we have to write it in for f(x) = ab x + c

form

[ocean seal]

Chai T. Rex

[tacit mortar]

x can be replaced in the formula for f (x)
f(0) means to replace it with 0

[ocean seal]

Chai T. Rex

[tacit mortar]

yes

[ocean seal]

Chai T. Rex

So,
$$f(0) = -1 = ab^0 + c$$
$$f(1) = 2 = ab^1 + c$$

[oak chasm]

We get the middle part from the graph.

[ocean seal]

Chai T. Rex

[tacit mortar]

-1, 2 are from the graph?

[oak chasm]

Yes, that's right.

[tacit mortar]

ok

[oak chasm]

So, we simplify the right sides. What's a number to the zero power?

[tacit mortar]

number 1

[oak chasm]

Right.

[coral pagoda]

Hey Chai! Hope you're having a great night/day!
Carry on 😁

[oak chasm]

What's a number to the first power?

Thanks 🙂

You too.

@pine lake Sorry, channel busy.

[pine lake]

Oh ok

[oak chasm]

@pine lake #help-3 looks open if you hurry.

[tacit mortar]

any number raised to the power of 1 will be the number

[ocean seal]

Chai T. Rex

[tacit mortar]

yes

[oak chasm]

OK, so what happens if we subtract the first equation from the second?

[pine lake]

I posted the question

If ur free pls help

[oak chasm]

Oh, I'm not ready yet, sorry.

[tacit mortar]

it will become 1

[ocean seal]

Chai T. Rex

[oak chasm]

See how I subtracted the left side of the first one from the left side of the second one?

[tacit mortar]

oh

yes

[oak chasm]

And the same with the right side?

[tacit mortar]

oh

[ocean seal]

Chai T. Rex

Chai T. Rex

[tacit mortar]

oh so now we need a and b?

@oak chasm

[oak chasm]

@tacit mortar OK, now what y value is it asymptotically approaching as it goes to the right?

[tacit mortar]

on the graph

[oak chasm]

Yes.

[tacit mortar]

3?

[oak chasm]

Right.

[tacit mortar]

yes

[oak chasm]

So, what kind of exponential graph starts going up and then levels off as it starts to go right?

[tacit mortar]

yes

[oak chasm]

That's not a yes or no question.

,w plot 1^x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

See, with 1 as the base, it's a flat line.

,w plot 2^x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

With something greater than 1 as the base, it swoops up like that.

[tacit mortar]

oh

[oak chasm]

,w plot (1/2)^x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[tacit mortar]

oh

[oak chasm]

With less than one as a base, it swoops down and then levels off.

[tacit mortar]

yea

[oak chasm]

We want it to level off, but to swoop up, so:

,w plot -(1/2)^x

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

That's something like our graph.

That graph approaches y = 0 as it goes to the right.

[tacit mortar]

yup

[oak chasm]

So, to get it to approach y = 3 as it goes to the right, we need to add 3.

,plot w -(1/2)^x + 3

,w plot -(1/2)^x + 3

[tacit mortar]

yes

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

So, c = 3.

[tacit mortar]

yea

[vestal hollow]

Is this channel free now?

[oak chasm]

@vestal hollow No, sorry.

[vestal hollow]

Gotchya

If you'd like to help out after, could you ping me once it's free?

[gaunt magnet]

am next

im waiting for 1 hour

https://tenor.com/view/king-kong-chest-pound-angry-rage-furious-gif-13202471

[tacit mortar]

ok

[ocean seal]

Chai T. Rex

Chai T. Rex

[tacit mortar]

so it would be
3= a (-4 -1)

[ocean seal]

Chai T. Rex

[tacit mortar]

oh

wasnt -4 a?

[oak chasm]

Yes.

[ocean seal]

Chai T. Rex

[tacit mortar]

yes

[ocean seal]

Chai T. Rex

[tacit mortar]

so -4(b-1)=3?
and i have to solve for b?

[gaunt magnet]

yes

b would be -5 i think

[tacit mortar]

ok

[oak chasm]

@tacit mortar Yes, you're right, but it's not -5.

[gaunt magnet]

oops

[tacit mortar]

would it be 5?

[ocean seal]

Chai T. Rex

[gaunt magnet]

finding b and would b 1

[tacit mortar]

is b 5

[oak chasm]

@tacit mortar No.

[ocean seal]

Chai T. Rex

[tacit mortar]

-4 -3 = b

[oak chasm]

No.

What's the last thing you do in calculating the left side?

@alpine sable Sorry, channel is busy.

@alpine sable Please read #❓how-to-get-help.

[tacit mortar]

uh

add

[oak chasm]

Is there any addition on the left side?

[tacit mortar]

would u move the -4 over

[oak chasm]

How?

[tacit mortar]

nvm

[oak chasm]

You need practice in basic algebra.

You shouldn't be doing these problems if you have trouble in it.

There's Khan Academy online if you want to learn how to solve equations like this.

[tacit mortar]

oh

[gaunt magnet]

LOL

XDDDDD

😂

[oak chasm]

There's also the "Elementary Algebra" Schaum's Outline if you want a workbook with short explanations and lots of problems and answers.

[tacit mortar]

oh

[gaunt magnet]

whats ur grade idkwhat

[tacit mortar]

11

[gaunt magnet]

fat cap

[oak chasm]

Yeah, you need to review solving basic algebra equations quick.

All your classwork will expect you to know how.

So, to get better grades and stuff, please study up.

[gaunt magnet]

and where are u getting the questions from

[tacit mortar]

oh

[tacit mortar]

its home work

[oak chasm]

@tacit mortar Here's a course online: https://www.khanacademy.org/math/algebra. It'll show you how to do stuff like what you were stuck on.

[tacit mortar]

ok thanks

[gaunt magnet]

ok can i get help now

idk if this channel free now or what

ok ima post

[oak chasm]

@tacit mortar Here's the workbook if you like that better: https://www.mhprofessional.com/9780071611633-usa-schaums-outline-of-elementary-algebra-3ed-group.

[gaunt magnet]

isnt he in high school

i was here first

bro u werent even here

ive been waiting for 1 hour

[oak chasm]

@pine lake Your addition/subtraction at the end was wrong, I think.

[gaunt magnet]

i

[pine lake]

@oak chasm #help-3

[gaunt magnet]

i got the answer 4 for this

correct?

[oak chasm]

@gaunt magnet What was the question?

[gaunt magnet]

this i just wanted to make sure i did it correct

[gaunt magnet]

.

[oak chasm]

,calc (-8)^(2/3)

[ocean seal]

Result:

-2 + 3.4641016151378i

[oak chasm]

Blah.

,w (-8)^(2/3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

@gaunt magnet What course is this for?

[gaunt magnet]

11

[oak chasm]

Yeah, but algebra, geometry, precalculus, what?

[gaunt magnet]

its grade 11 functions

[oak chasm]

OK, have you learned how to get complex numbers as answers to powers?

[gaunt magnet]

yes

[oak chasm]

OK, 4 is an answer.

[gaunt magnet]

ty

for this i got

[oak chasm]

,w (-8)^(2/3) real

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[gaunt magnet]

8x ^4/9y ^5

[oak chasm]

Looks good, though you should practice putting the denominator in parentheses on here.

[gaunt magnet]

ok alr last question

[oak chasm]

,w 8x^4/9y^5

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

Chai T. Rex

[oak chasm]

Yes, looks good.

[gaunt magnet]

and i got -5

for this

you had to solve for x

[sullen nova]

is is right?

[ocean seal]

Chai T. Rex

[gaunt magnet]

would it be 5 or -5

[oak chasm]

,w 3^(2x) = (1/9)^(x - 10)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

@gaunt magnet 5

[gaunt magnet]

ok ty

[sullen nova]

it's 5 + (ipi)/2log(3)

[oak chasm]

No problem.

[gaunt magnet]

for this question i got 1 + 10 = 11

i think i did this wrong

[gray isle]

1 + 10 = 11
is true but you haven't finished the problem / found x

[gaunt magnet]

would it be 11=11

[gray isle]

is true but you haven't finished the problem / found x

[gaunt magnet]

ok the final answer would be 1?

[gray isle]

no

ideally you'd want to manipulate your equation and isolate x (which will tell you what x is)

i.e. first isolate 4^x
and then apply log/exponent laws (or intuition) to determine the value of x

[gaunt magnet]

ok would it be 0?

[gray isle]

yes

[gaunt magnet]

so i was correct but

i didnt finish

[gray isle]

the process is bad

[gaunt magnet]

oh

[tacit mortar]

hello

[gray isle]

1 + 10 = 11
by itself tells you nothing about what x is

[gaunt magnet]

yea

[gray isle]

and if you plan to compare 4^x to the 1,
then you're much better off starting with your original equation and subtract 10 from both sides to get:
4^x = 1 directly

which you can then use to deduce x=0

(or apply log_4 to both sides to get the same result)

[gaunt magnet]

ok ty

[tacit mortar]

Determine the equation of the following exponential functions, in the form f(x) = ab x + c.

the answer i got for this

was

5

,w solve 2x=-2(x-10)

[ocean seal]

Results provided by WolframAlpha

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

Requested by idkwhattoputhere#2004

[tacit mortar]

right?

[gray isle]

no

5 is not an equation

nor does x=5 satisfy any of those properties

[tacit mortar]

then

[alpine sable]

is it supposed to f'(g(x)) on the right?

[tacit mortar]

@gray isle

[gray isle]

i have no idea how what you're doing is relevant the the question

@alpine sable what's written in the image is correct

[alpine sable]

oh

so it's sort of different from chain rule one

[gray isle]

not different. chain rule is applied there.

[honest rover]

hi

[wanton fable]

Could I please get some help

[gray isle]

getting crowded here

[alpine sable]

but chainrule is f'(g(x)) * g'(x)?

[gray isle]

consider that you're taking the derivative of an integral

[alpine sable]

alr, i'll just remember it's different that way lol

[gray isle]

you could go through the long way

let F be the antiderivative of f

=d/dx( F(g(x)) - F(k))

and applying chain rule
= F'(g(x)) * g'(x)
= f(g(x)) * g'(x)

[gray isle]

is the base supposed to be a square?

[wanton fable]

Yes

[gray isle]

how did you get 75.6?

[wanton fable]

I applied the formula but it keeps coming wrong

Let me show you the formula I used

Not sure if it’s the right formula

11= height 3= side length/ base

[gray isle]

that's not the correct fomula to apply here

at a glance the h in that formula represents the altitude of the square pyramid
however in this question you're given the slant height

here, you can calculate the areas of your faces directly (simple formulae of areas of triangle and square)
and add them all up

[wanton fable]

Could you help work it out or provide an example

[gray isle]

do you know how to calculate the area of a triangle?
do you know how to count the number of triangles?
do you know how to calculate the area of a square?
do you know how to add stuff?

[sullen nova]

no weh ma mans

[gaunt magnet]

ok?

[gaunt magnet]

ayo someone can help me id appreciate it

[rigid zenith]

<@&286206848099549185>

I am done with that I need help with this do

<@&286206848099549185>

[ionic jewel]

multiply both sides times 7 @rigid zenith

[coral pagoda]

<@&268886789983436800> they are getting a bit ping heavy.

[sly mantle]

@rigid zenith familiarize yourself with the rules in #❓how-to-get-help. in particular wait 15min before pinging helpers, and only ping once

[gaunt magnet]

ok

hi

[gaunt magnet]

can anyone help

[ionic jewel]

hey rokaba how do u get the bot to quote the rule

the embed for rule 4 or whatever

[lone heart]

From

#❓how-to-get-help

Rule 4

If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[sly mantle]

!r4

[lone heart]

From

#❓how-to-get-help

Rule 4

If your question has not been answered for a minimum of 15 minutes, you may use the Helpers tag once. Please do not try to bump your question using this ping unnecessarily. Do not abuse this ping. Do not individually ping users with the Helpers tag without their express permission.

[ionic jewel]

ah

ty

[sly mantle]

generally !r# for rule #

[coral pagoda]

Thank you as well.

[gaunt magnet]

can i get help with this

[tacit mortar]

Determine the equation of the following exponential functions, in the form f(x) = ab x + c.

the answer i got is -4(1/4-1)=3?

[gray isle]

-4(1/4-1)=3
is true but is not an equation for an exponential function

[tacit mortar]

is the 1/4 what makes it wrong?

[gray isle]

firstly i don't know where the 1/4 is coming from
and what makes it wrong is that

is not an equation for an exponential function

has no x present

is not in the form
f(x) = ab^x + c

[tacit mortar]

oops sorry i posted the wrong question it was this

-4(1/4-1)=3

[gray isle]

what's the question asking for?

[tacit mortar]

Determine the equation of the following exponential functions, in the form f(x) = ab x + c.

-4 is the a value

1/4 is the b

[gray isle]

and your c value?

[tacit mortar]

3

[gray isle]

,w graph y = -4*(1/4)^x + 3

when x=1, you should get 2
however according to your values, you'll have 1

[tacit mortar]

yes

is the a, b and c value correct?

[gray isle]

your c value is correct, your a and b are wrong

[gaunt magnet]

oh

hello

can i get help

[tacit mortar]

oh

[gray isle]

what do you need help with

[vale wigeon]

you can do it very cleanly here

1/(x+3)^4 ≥ M iff |x+3| ≤ M^(-1/4)

[alpine sable]

Thanks, yeah I realised I was being silly as soon as I clicked post.

[harsh acorn]

2,5,17,71,?,2159

find the "?"

[vale wigeon]

19

malicious compliance with underspecification

[harsh acorn]

how did u find can u explain me

[vale wigeon]

malicious compliance with underspecification

the missing number could be literally anything you want

because you don't give NEARLY enough information

[vestal needle]

is this correct for (c)?

[vale wigeon]

dont think so

you need to be more explicit and use part a

to get that A_ij = (A^T)_ij for i, j in 1:n

[vestal needle]

ohhhhh right

yep got ot

it

thanks ann!!!

[worthy badger]

Men, I must make an announcement... today this very fine man has passed away... may god bless his soul

[high furnace]

hi

I've been breaking my head over an algebraic problem

I'm trying to figure out the phase and amplitude of a sinusoid from two samples. The frequency is know, and y zero is known

An approximation is my case is good enough

This is what i came up with until now

http://notepadcalculator.com/s/d6b9ccc8ac3474adb58207af84109b7f0a9f85fe

at the end there are two equations

with just two unknowns

so i substitute

but then i don't know how to solve for amplitude nor for phase

[high furnace]

it's for the MiSTer project, for the simulation of some sinusoid/noise analog sounds that are used in atari arcades

if it's unsolvable I'd love to hear it too, then I will approximate with squared error optimisation