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[frigid mirage]

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[lone heart]

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[inner bough]

if you have the pattern 1,3,5,8,_ the next number is apparently 13, but i dont get how you get it

[golden canyon]

Are you sure this is the exact pattern

[inner bough]

yes

[golden canyon]

Maybe it should be 1, 2, 3, 5, 8, _

[inner bough]

nope, its 1,3,5,8,_

[golden canyon]

Because in this sequence you get the next term by adding the previous two

It's called the fibonacci sequence

[inner bough]

yea

there's no 2 tho

[golden canyon]

There is a site that recognizes sequences, but it doesn't give any simple results https://oeis.org/search?q=1%2C3%2C5%2C8%2C13&language=english&go=Search

although A080614 is kinda interesting

and the one below is the most simple, but I don't think you are expected to guess that

[royal meadow]

probably a typo

they probably missed 2

[inner bough]

i emailed my teacher, its not a typo, there isnt supposed to be a 2

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[royal meadow]

no clue lol

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[steel phoenix]

There are 2 functions
fx= -1/2 x2 + 3x +1/2
gx= x2

the 2s after the x are square

so how do you have to multiply x and which translation to be in function fx

[steel phoenix]

i tought it was multiply the x axis by -0,5 and then translation (3,5)

Someone pls react i have a test tomorrow

[limpid turret]

x^2 is common plain text notation for exponents

Or, if you are familiar with latex, you can do $x^2$

[ocean seal]

SWR

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[steel phoenix]

i dont see the explanation here

i want to know which translation i do to make gx fx

[limpid turret]

I was just showing you how to write exponents, I hadn't helped with the problem

[steel phoenix]

ohh hahha

oke

[limpid turret]

Do you know how to express f(x) in vertex form?

[steel phoenix]

nope

i dont know vertex

[lone heart]

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[honest flame]

what is this asking

[gleaming granite]

unless [x] is a function, it's asking what's the limit as x tends to 2 for the function x

[honest flame]

the answer key says this

how would i work through this

[gleaming granite]

[x] is probably the greatest integer function then

[honest flame]

i have no idea what ur talking about

[gleaming granite]

,w graph y=floor(x)

[ocean seal]

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[gleaming granite]

it should be this function, but the notation just looks different

[honest flame]

oh i see

floor

ty

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[gray heart]

Wouldn’t a and d both be correct?

[gray heart]

I solved for a but the answer key says it’s d

[exotic citrus]

Can you show your work for when you got a?

[exotic citrus]

I think you forgot to add a +C after intergrating both sides

[gray heart]

What would +C even be in this case?

Wher

[exotic citrus]

it might be under message requests

[lone heart]

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[inner bough]

if you have n points of n different colours with any 2 points having the possibility of being connected by a line, what is the formula for the number of possibilities?
would it not be
$n^n\cdot{n\choose 2}^2$?

[ocean seal]

Chaon

[paper mango]

consider the possibilities for any "first" point

the first point connects to up to n-1 other points

for each of those other points there are two possibilities (connection / no connection)

so for that first point there are 2^(n-1) possible connection options

pick another point

now, you've already considered the connection to the first selected point

so for that point there are 2^(n-2) possible connection options left

2^(n-1) * 2^(n-2) * ...

a pattern emerges

[inner bough]

2^sum(k=1,n,n-k)?

[paper mango]

sum(k=1, n, n-k)?

it'd not be the sum of n-k iterating from k=1 to n

[inner bough]

No?

[paper mango]

2^(n-1) * 2^(n-2) * 2^(n-3) * ... * 2^1 * 2^0

= 2^((n-1) + (n-2) + (n-3) + ... + 1 + 0)

[inner bough]

Yeah

[paper mango]

so you'd get the sum[k=0 to n-1] of k

and you can summarize that sum using a certain formula :3

(Arithmetic Series)

[inner bough]

Right ty

[paper mango]

np 🦇

[inner bough]

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[regal lake]

help me to solve

[regal lake]

$$4p+4q+4r-16 = p\cdot q\cdot r~~~ p,q,r \in \mathbb{N}$$

[ocean seal]

Gilgamesh

[lone heart]

@regal lake Has your question been resolved?

[regal lake]

<@&286206848099549185>

[tardy stag]

do you just need one solution or all solutions?

[regal lake]

all solution

[tardy stag]

hmm

you might have to do some trial and error

[regal lake]

for p=q=2 we have infinity solutions

[tardy stag]

we do?

[regal lake]

yes

[tardy stag]

ah yeah we do

ok what about 1,1 or 1,2?

it seems to me that these numbers can't be very high in most cases

[regal lake]

we can use python to see the solutions firstly

much of the solutions are (2, 2, x)

but i search for the solution like (1, 6, 6) or (1, 5, 8)

can we use modular arithmetic here and how we can use it @tardy stag

[tardy stag]

i'm not sure

[regal lake]

but it must have a trivial way to solve it

[sour shore]

The equation reminds me of the plane that passes through all unit vectors

there's a special name for it, can't remember what

phind.com helped me find it: https://en.wikipedia.org/wiki/Simplex

on the RHS you have a hyperboloid

[regal lake]

and now? 😢

i am to dumb for this task

[real gazelle]

It's a hard task, don't worry you're not dumb

[sour shore]

I'm wondering if you can do something like fix c, consider 4p+4q+4r-16=c and visualize what that looks like (displaced/translated simplex? simplex with different gradient?), as well as pqr=c (hyperbola) and then find the intersection

yep, that gives you a displaced simplex

you can graph the 2d version on desmos

[regal lake]

But I have to show it through elementary number theory and algebra

[sour shore]

lmao I'm dumb I didn't notice the restriction to the nats

Does N include 0?

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@regal lake Has your question been resolved?

[regal lake]

No

[lone heart]

@regal lake Has your question been resolved?

[small ice]

i need help

[tacit arch]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[livid sage]

in my opinion, the most important thing about this problem is that p, q, and r are symmetric relative with each other

which means that for example, if (2, 2, 3) is a solution, then so are (2, 3, 2) and (3, 2, 2)

then, without loss of generality, you can vary one variable, claim it is the lowest-valued, and solve for the rest

for example, you can start with: "i will say that of the 3 variables, p is the smallest (or tied for the smallest), and p = 1"

then, this becomes a casework problem featuring simon's favorite factoring trick (if you don't know what that is, it's basically factoring equations in the form xy - px - qy + C)

(as an extra note, it's good that you noticed p = q = 2 has infinitely many solutions)

(okay i admit this is a bit of a long/convoluted way of explaining my general thought process, but i hope the idea is still there)

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[brazen slate]

is this correct

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[dusk granite]

What mean this "to"?

[dusk granite]

2i0 to π

From 2i0 to π?

But 2i0 it`s just 2i0=i0=0

[vale wigeon]

this is WA's output

it sometimes tries to say something beyond a mere "DNE" when a limit doesn't exist.

here what it's trying to say is that x^i, a.k.a. e^(i ln(x)), spins around endlessly along the unit circle.

[dusk granite]

okay

so, 2i0 it`s just 0(in imaginary) right?

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[alpine sable]

i need help

[lethal belfry]

[alpine sable]

i have an exam tomorrow and i dont know how to solve this

[raw jetty]

um but they wont intersect? is there like an option to say that they dont have a solution

[alpine sable]

theyre parrell right? cause they are going n the same direction

[lilac bough]

yeah

[alpine sable]

my teacher created this not me

what about this questiom?

if anyone could help

<@&286206848099549185>

[normal spade]

What grade??

[alpine sable]

9th

[normal spade]

What grade

[alpine sable]

9th grade

[alpine sable]

I assume you have to mark the points on the graph/plot points on the graph
So
hint: value of y and $$ y = -\frac{5}{2}x +4 = -1$$ , find the value of x
after you get the value of x then plot (x,y) co-ordinates on the plane

[ocean seal]

Snow

[alpine sable]

thanks

is the answer(2,-1)?

<@&286206848099549185>

[alpine sable]

..

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[whole flame]

i need help factoring cubic trinomials

[whole flame]

2x^3-7x+2 and such

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@whole flame Has your question been resolved?

[median oar]

I’d say it’s just trial and error

,w factorise 2x^3-7x+2

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[lusty sigil]

How did this turn into cosec cot 😭

[storm ridge]

,rccw

[alpine sable]

whats $\ds \f{\m{\sec^2}\theta}{\m\sec\theta}$

[lusty sigil]

I don’t understand what is going on

[exotic canopy]

simplify that part

[lusty sigil]

Ooooooh okay it has smth to do with leaving one sin down

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[hidden wind]

$$\text{Let }(1+x+x^2)^{30} = \Sigma_{r=0}^{60} a_rx^r$$
$$\text{if }Pa_{21}=Qa_{20}+Ra_{19}$$
$$\text{Find } P+Q+R$$

[ocean seal]

xd_senBugha

[hidden wind]

how would i solve this?

[lone heart]

@hidden wind Has your question been resolved?

[hidden wind]

<@&286206848099549185> help please

[ocean seal]

Snöwdinger

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

[hidden wind]

i got that but the number of cases would just be insane for me to find out the coefficients of x^21, x^20, x^19

is there any shorter way?

[hidden wind]

<@&286206848099549185> help please

[lone heart]

@hidden wind Has your question been resolved?

[lone heart]

@hidden wind Has your question been resolved?

[hidden wind]

<@&286206848099549185> please

[real gazelle]

Please don't talk in other people's help channels if you can't help

All of them, please don't talk in other people's help channels if you can't help them

[hidden wind]

<@&286206848099549185> sorry for the 4th ping but I really need help on it, I gotta submit in for an assignment tomorrow

[alpine sable]

What are the P, Q and R?

Like what is the relationship between P and P_(a_21)

[hidden wind]

That's all we know

There's no more info

[hidden wind]

a_21 is the coefficient of x^21

We don't know p,q,r

[alpine sable]

Yeah I know

But what is P_a21

P = value of a at 21th term

[alpine sable]

This is the only way ik to solve a trinomial eq using binomial expansion 🤷
If u want a shorter way then I can't really help u w that

Btw finding co-efficients of this expansion is not that hard

[exotic belfry]

if you write it as ((x+1)x+1)^30 it makes it easier (maybe) to count the terms which results in an x^19, x^20, x^21.

[hidden wind]

Not exactly

A is the coefficient of the expansion

And p is another constant multiplied to it

[hidden wind]

That's actually clever thank you

I'll try to think on it

But if any of you guys find a better way lmk

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[abstract wadi]

how do i do this?

i know using 45-45-90 triangle that the other sides are also 72 ft

and the hypotenuse must be sqrt(2) but i dont know how to go about getting it from therer

72(sqrt(2))

?

i got 101.8 from that

[wise spruce]

ur meant to use trig functions though, not prior knowledge

[abstract wadi]

oh

we learned trig functions and the triangles

during this lesson

but i get what u mean

not prior sorry

[wise spruce]

do u think ur teacher would care?

[abstract wadi]

i dont believe so

she didnt specify

however i will do it using the trig functions just to be sure

[wise spruce]

do u know sin 45 degrees?

[abstract wadi]

the exact value? no

we only went over using trig functions to find angles inside a triangle or parts outside of a triangle

[wise spruce]

u can use calculators right?

[abstract wadi]

like A, a, B, b, C, c

yeah

i have a ti-nspire with the functions

[wise spruce]

so you know sin is opposite / hypotenuse

[abstract wadi]

yeah

[wise spruce]

now you know the opposite but not the hypotenuse

whats a way you can get the opposite on the bottom and the hypotenuse on top

[abstract wadi]

you can either solve it out like that or just use the opposite or repciprocal of that function

so cosecant

is opposite of sine

[wise spruce]

ye just 1/sin45

then multiply that by the length

[abstract wadi]

i see

i got 101.8 as well

that makes more sense

[wise spruce]

and you are correct

[abstract wadi]

i just didnt see it like that at first

thanks

[wise spruce]

the question specifically says to use trig functions, idk ur teacher but i know some of mine would have been annoyed if i didnt do it the way they asked

its kind of dumb

[abstract wadi]

oh i didnt read that lol

yeah its a little assignment that can be redone like infinite amount of times

nor do we do written tests

however im sure that varies upon teachers

thanks anyways

[wise spruce]

bruh lucky

[abstract wadi]

we get paper and pencils then work from an online quiz

but calculus is all written

however im precal

[wise spruce]

oh. i thought u straight up didnt do tests lol

[abstract wadi]

oh lol

i wish haha

anyways cya thanks

.close

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[mystic nebula]

how do i found out the range/domain of every trig function

i know i can look at a picture that lists all of them

but how do i get to it using math

[jagged cobalt]

well, its the reciprocal of cos right?

[mystic nebula]

yep r/x

[jagged cobalt]

cos is between 1 and -1, so what must the range of sec be

[mystic nebula]

wdym its between 1 and -1

any value can be plugged into r and x

?

[jagged cobalt]

i mean cos has a range of [-1,1]

[mystic nebula]

how do you know that

[jagged cobalt]

that should be standard knowledge

,w graph cos(x)

[ocean seal]

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[mystic nebula]

idk im in pre trig

[jagged cobalt]

cos and sin are bounded by 1 and -1

[mystic nebula]

so im just now learning everything

my only solution is to memorize all 6 domains and ranges?

[jagged cobalt]

id just remember what a sin, cos and tan graph look like, its useful stuff to know

[mystic nebula]

i guess

[mystic nebula]

so far i havent learned this

only like a basic unit circle

[jagged cobalt]

i see, the unit circle also demonstrates cos being bounded by -1 and 1, since it doesnt exceed those values at any point on it (the circle has radius 1 so its impossible)

[mystic nebula]

found this in my textbook

so i use the rules they set to help?

like sin is y/r right

y and r are greater than 0 and less than 0

so isnt it -inf,inf

[jagged cobalt]

not sure what you mean there

[mystic nebula]

yea me neither lol

im just tryning to simplify it for myself

[jagged cobalt]

if you can accept cos having range [-1,1] the question becomes quite simple, the unit circle shows this anyway if youve been using it

[mystic nebula]

so if cos is [-1,1] then secant is also [-1,1]?

[jagged cobalt]

not quite no

say cos was 0.5, what would sec be

[mystic nebula]

1/0.5?

so 2

what does that tell me

[jagged cobalt]

tells you the range of sec cant be [-1,1] as you speculated

what happens if you divide 1 by a number with magnitude less than or equal to 1?

[mystic nebula]

you get infinitely larger?

[jagged cobalt]

yeah, the magnitude of the number cant be less than 1 right

[mystic nebula]

right

[jagged cobalt]

so is this possible

[mystic nebula]

yes..?

since it tells me thats inf

[jagged cobalt]

how so?

might be a different way to look at this

[mystic nebula]

if im getting a solution

then its right

[jagged cobalt]

if sec(x)=-0.333 ~ -1/3

then cos(x)=~-3

which is impossible

[mystic nebula]

by impossible you mean you cant get a solution?

[jagged cobalt]

cos is bounded by -1 and 1, so yeah theres no possible way for cos to be greater than 1 or less than -1 so no solution

itll probably help you to learn the characteristics of the 3 basic trig functions

theres not much to go over really, just range, domain, period for the most part

thatll set you off

[mystic nebula]

so cos is bound by [-1,1] sine is bound by [-1,1] and tan is bound by (-inf,0),(0,inf)

[jagged cobalt]

tan can be 0

[mystic nebula]

and i can apply that to the other functions by just inverting it

just -inf,inf then

[jagged cobalt]

yeah

[mystic nebula]

what do they mean by this

tan isnt related to cos

[jagged cobalt]

it is, tan is the ratio of sin and cos

ie tan=sin/cos

[mystic nebula]

oh right

[jagged cobalt]

if cos is 0 tan is undefined

[mystic nebula]

so most of trig is everything being connected through these basic principles?

[jagged cobalt]

pretty much i suppose, theyre the bare fundamentals

[mystic nebula]

i get it

thanks man

[jagged cobalt]

nw

[mystic nebula]

.close

[lone heart]

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[raw warren]

.close

.ask

.close

<@&268886789983436800> can you close this

[night geyser]

it is closed

it just takes some time to move due to bot rate limits

[raw warren]

ah ok

[night geyser]

give it a few minutes

[raw warren]

ok

[lone heart]

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[candid radish]

In right triangle $ABC$, the length of side $BC$ is $2$ units, the length of side $AC$ is $4$ units and the measure of angle $C$ is $60$ degrees. What is the length of side $AB$, in units? Express your answer in simplest radical form.

[ocean seal]

!ｓａｔｏｒｏ !

[candid radish]

uh, I'm stuck on this question

[uncut torrent]

cosine rule

[candid radish]

uhh

what does the AC, and BC mean?

[upbeat eagle]

side

[uncut torrent]

AC means the line between vertex A and C

[candid radish]

oh

what does that vertex mean

wait I don't really understand

[uncut torrent]

the corner

[candid radish]

ohh

I see now thank you

[uncut torrent]

👍

[candid radish]

wait so do you just use cosine rule?

aight thanks

[upbeat eagle]

Yeah but sine rule also exists
[idk if u can use it for ur question, i havent been reading]

[candid radish]

oh ok

[upbeat eagle]

your ganna have to use both of them at some point

[candid radish]

I did this question on alcumus and it says this

[upbeat eagle]

Its a right angled triangle

Mans burnt you in fire

[upbeat eagle]

That means use a^2 + b^2 = c^2

[candid radish]

oh yeah but idk what the ac and bc mean

[upbeat eagle]

You dont need to know sine/ cos rule, its way to advanced for your level

[upbeat eagle]

side

i draw

[candid radish]

I already know sine rule

[candid radish]

yeah

[upbeat eagle]

Well its not the best drawn right angle triangle

[candid radish]

ohh I see now

[upbeat eagle]

but yeah

[candid radish]

I thought a was the length

because in the previous question it just said side A is this length

now it says a - b

ok I understand now

thank you

.close

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[sharp sage]

is anyone able to help me in a call

[burnt cosmos]

how do you format your messages like this

[sharp sage]

is anyone able to help me in a voice call if i share my screen

[raw warren]

its a bot 💀

[burnt cosmos]

 CAN
 DO 
 IT 
 TOO!!! ```

figured it out

[raw warren]

wow

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@sharp sage Has your question been resolved?

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[dire trout]

can someone help me solve this?

[lofty gorge]

I think it might be 0 based only on some playing around with geogebra

No idea if this is actually true, nor how to prove it

[lone heart]

@dire trout Has your question been resolved?

[dire trout]

wait

[west girder]

I doubt this has a nice geometric solution, best bet is a complex bash

[dire trout]

hmm ok

[dire trout]

does it make it easier that there are no solutions

[west girder]

The midpoint of DE works right?

[dire trout]

i dont think so

[west girder]

Yeah nvm I miscalculated

It’s just D and E that work I think

Ggb seems to say there are more

[dire trout]

geogebra says there are none

wait just D and E right?

@west girder

[west girder]

If G is the intersection of the perpendicular bisector of DE and circumcircle of the hexagon every point on DG and EG works

Maybe there is a nice geometric way

[dire trout]

<@&286206848099549185>

[drifting warren]

Its not rigorous but when P is at D or E it satisfies the equality but not the inequality, meaning it is either a minimum or maximum. If P lies on FE or CD, AP + BP decreases as P approaches F or C respectively. There could be other solutions on DE but none of those matter because it would lie on a line anyways let me know if anything seems wrong because im also unsure. If you wanted to make it more rigorous the area of the solution would be a trapezoid with points at E, D, somewhere on CD and FE. Could probably find an equation relating the distance from E/D to P when it is on FE or DC and confirm

It is also only a trapezoid if midpoint of DE does not work I should add, I didn't check if it does

[dire trout]

the midpoint does not work

[drifting warren]

Then either the perimeter of ABP increases until a certain point along FE/CD then decreases until P = F/D, or it strictly decreases. If its the latter then area is 0. If its the former then youd have to find P' where it starts decreasing, which you could do by making an equation relating the perimeter to the area. BCP's area is constant as you move P along FE and FEP constant for BC, so you could probably try something using that, herons formula, and the bounds of AP + BP + CP + DP + EP + FP

but id be surprised if it even did increase along FE or DC

[true aspen]

Hi

[dire trout]

hi

do u think u can figure this out?

[true aspen]

Which question?

[dire trout]

.

[true aspen]

Which math is that? Like calc, trig, algebra?

[dire trout]

geometry

bruh

[true aspen]

What have you tried so far?

[dire trout]

i know that points d and e satisfy it but i think thats it? im not sure how to proceed

[dire trout]

i dont get this lol

[dire trout]

<@&286206848099549185>

can someone

[lone heart]

@dire trout Has your question been resolved?

[lone heart]

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[hybrid aspen]

I need help with this question (6v^3 + 42V^2 - 50V - 20) / v+8

[solemn juniper]

that's just an expression. What's the question?

[lone heart]

@hybrid aspen Has your question been resolved?

[hybrid aspen]

oh

I mean that was the question i was assigned

i think i had to do long division

[solemn juniper]

ok there we go

so what's giving you issue?

[hybrid aspen]

to be honest I might of forgotten how to do it

the long division

[hybrid aspen]

think you could help me out

?

[solemn juniper]

i'm not going to teach you how to do polynomial long division, if that's what you're asking

if you can get started and end up running into a roadblock, then I can help overcome that

[hybrid aspen]

oh alrighty

thanks

.close

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[dapper coral]

how do i solve 6C if they don't give me an equation

[solemn juniper]

you use a linear approximation

[dapper coral]

how do i do that again?

[ocean hawk]

$f(y) \approx f(x) + f'(x) (y - x)$ should work

[ocean seal]

cwatson

[dapper coral]

is that the same as

[solemn juniper]

that's the definition of the derivative

(or a definition if you insist)

[dapper coral]

o

ok thx!

wait what would f(x) be

since only the x value is given

[solemn juniper]

x is the value for which you know f(x)

[dapper coral]

would it just be f(140) + f'(140)(y-140)

[solemn juniper]

it would not

you don't know f(140) (since you're trying to estimate it)

[dapper coral]

the only f(x) thats given is f(135)=120

would i use that in the equation

[solemn juniper]

of course

[dapper coral]

then would the y be 140?

[solemn juniper]

it would

[dapper coral]

so then the equation would be 120 + 2.5(140-135) ??

[solemn juniper]

no

now yes

[dapper coral]

oh ok thx!

[lone heart]

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[buoyant saddle]

how does the combination formula relate to matrices

[buoyant saddle]

the 2x1 matrix for a combination is n!/(n-k)!*x!

how does this relate to a 2x1 matrix

or does it not

because the standard way of writing it looks like

are there formulas like this for other matrices with different dimensions

[solemn juniper]

it's not supposed to be read as a vector/matrix

it's just notation

[tacit arch]

This is correct

[buoyant saddle]

oh so y would they make it look like a matrix

[solemn juniper]

the context should make it clear when it's to be treated as a vector and when as the combination interpretation

[buoyant saddle]

i’d prefer to write it as nCk

[solemn juniper]

the same way (x,y) can either be an open interval or an ordered pair

[buoyant saddle]

true

i just didn’t know if they were related at all

[solemn juniper]

fair enough

[buoyant saddle]

thank you tho

.close

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[signal dust]

I'm wondering when to use long division and synthetic division when dividing polynomials?

[tacit arch]

https://flexbooks.ck12.org/cbook/ck-12-interactive-algebra-2/section/1.4/related/lesson/long-division-and-synthetic-division-alg-i-hnrs/

https://www.splashlearn.com/math-vocabulary/division/long-division#

[vale wigeon]

they accomplish the same thing, do they not

well, ish

[signal dust]

as im looking at what he sent, yeah, i missed last math class and didnt know anything abt the two

[vale wigeon]

synthetic is specialized to linear divisors with leading coeff 1 while long can handle any divisor

[signal dust]

what do i do when im left with a remainder?

[vale wigeon]

so your real question was "what even ARE long division and synthetic division"

[signal dust]

lol yeah

[vale wigeon]

depends on what the problem's asking you for...

[signal dust]

when i do long division, and i end up with a remainder, how do i write it up top, dont i have to write as "remainder/divisor"?

[buoyant saddle]

the same way when you divide numbers you might have it as a mixed number like 3 and a half

3 +1/2

which is really 7/2

but 2 goes in 3 times with a remainder of 1

so u put the remainder over the divisor which is 2

it’s the same principle

just with variables now

[lone heart]

@signal dust Has your question been resolved?

[lone heart]

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[left niche]

at T minutes past 2 pm , the time needed by the minute hand of the clock to show 3 pm was found to be 3 minutes less than T^2 /4 minutes . Find T

[left niche]

Can someone help me with this question ??

[twin nimbus]

!status

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[left niche]

1

[twin nimbus]

Ok, you begin by setting up an equation

So

If it is T minutes past 2, then how many minutes is it until 3?

Hint: 3:00 = 2:60

[left niche]

okay then ?

[twin nimbus]

What do you mean? I asked a question and am awaiting a response from you.

[twin nimbus]

This one.

[left niche]

we could take that as a variable maybe ?

[twin nimbus]

Well, you're correct that we don't know it; however, we don't need to introduce a new variable, we can describe this in terms of T

[left niche]

yes

[twin nimbus]

There are 60 minutes in an hour

If T minutes have already elapsed in this hour, how many minutes are left out of the 60 total?

[left niche]

60 minus T

[twin nimbus]

Ok cool.

[twin nimbus]

Just bringing this down for me

So we have "the time needed by the minute hand of the clock to show 3 pm", which we just figured out to be 60 - T

[left niche]

yes

[twin nimbus]

"was found to be" (e.g. equal to), "3 minutes less than T^2/4 minutes"

So what's this last part in equation form?

[left niche]

3 minus T^2 / 4

[twin nimbus]

Not quite

(T^2 / 4) - 3

[left niche]

ooh okay

[twin nimbus]

Just like 3 less than 20 is 17 or 20-3

[left niche]

yes you are right

[twin nimbus]

So now we have both halves of the equation, let's put them together.

[left niche]

from the first we can take value of T equals to 60

[twin nimbus]

No

60-T is found to be (T^2/4) - 3

What is that as an equation?

[left niche]

I am solving that right now just give me a few minutes

[twin nimbus]

This is kind of a mean equation, because it really punishes you if you just use the quadratic equation. If you attempt to complete the square it is much nicer

[left niche]

I have got the value of T 14

[twin nimbus]

That is correct.

[left niche]

the other one is negative 18 hence ,that would be rejected

[twin nimbus]

Also -18, but that's not an allowed value.

Yup

[left niche]

yess

so thank you for helping me

[twin nimbus]

Have a nice one

[left niche]

BTW where are you from ??

[twin nimbus]

Originally from Louisiana, currently living in the Midwest.

[left niche]

okay nice

are you a teacher ??

[twin nimbus]

Nope

This is just a hobby

[lone heart]

@left niche Has your question been resolved?

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[hidden pier]

do you know how the graph looks in the plane?

[pulsar lynx]

Yes

yes

[hidden pier]

then what aspect of the graph do you see represented in the equation

wait what are the answer choices?

just I, II, or III?

or can there be a combination of 2

[pulsar lynx]

I don't know what is 'constant or coefficient' means? When question ask about this for what I have to look?

[open compass]

constant would be some number or scalar

not a variable

so like 1,2, 2.3, pi, 1/9

[pulsar lynx]

So here that is slope form right?

x = 0 and y = -9

[lavish rapids]

But are those constants or coefficients?

Or rather is x

[pulsar lynx]

constants mean not changing so vertex always remains -9 in y it doesn't change?

[pulsar lynx]

yes

[hidden pier]

so what does the -9 represent in the equation?

[pulsar lynx]

it represent that y coordinate in vertex is -9

[hidden pier]

what else, for this graph specifically?

[pulsar lynx]

-9 peak ?

It is down parabola looks like -9 is highest point of it

[hidden pier]

what's the y-intercept

[pulsar lynx]

y intercept is -9?

[hidden pier]

yeah

[pulsar lynx]

so y intercept is displayed as constant or coefficient?

[hidden pier]

yeah

in this case

[pulsar lynx]

or both y cordinate or vertex

[hidden pier]

if it was like (x-2)^2-9 then it wouldn't be

[hidden pier]

both

[pulsar lynx]

Yes so II and III

[hidden pier]

i believe so

[pulsar lynx]

what about this

how can I create a form of it that display constant or coefficient

x intercept of parabola

[hidden pier]

factor

[pulsar lynx]

I have to factorize it

[hidden pier]

yep

roots of a polynomial are where y=0

i.e., the x intercept

[pulsar lynx]

(x-3)(x+7)

[hidden pier]

so what are the roots

[pulsar lynx]

So this is the answer?

[hidden pier]

i think so

[pulsar lynx]

x = 3 and x = -7

[hidden pier]

yeah

well wait

i think it should be the answer but idk if it wants you to have 3 and -7 in the polynomial

that'd be kinda silly though

[pulsar lynx]

okay so when y intercept is displayed as constant or coefficient the form is vertex form however, incase of x intercept is the factored form?

[hidden pier]

the x part is right

the y-intercept is not always the y value of the vertex though, as i said earlier

[pulsar lynx]

.close

[lone heart]

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[clear tulip]

for this one, i dont really understand how they found out it was continuous

(i dont get the explanation)

[hidden pier]

do you know what ⋂ means

[clear tulip]

nooo

[hidden pier]

"U" basically means anything that's in set A or B
"⋂" means anything that is in both set A and B

$f(x)=g(x)+h(x)$ where $g(x)=(x-4)^3-\frac{3x}{2}$ and $h(x)=9\log_4(x)$

[ocean seal]

Vѳrtєx-

[hidden pier]

we know that the polynomial is continuous across $(-\infty,+\infty)$

[ocean seal]

Vѳrtєx-

[hidden pier]

however, $9\log_4(x)$ is only defined on the positive interval $(0,+\infty)$

[ocean seal]

Vѳrtєx-

[hidden pier]

adding two continuous functions gives you a continuous function

i can elaborate on this if needed

but basically over the interval $(0,+\infty),$ you know it's continuous because both $g(x)$ and $h(x)$ are continuous on that interval

[ocean seal]

Vѳrtєx-

[clear tulip]

oh so because, basically there are two ranges, for the polynomial and the log
$(infty, -infty)$
then
$(0, infty)$ for the log cause $4^a=x$ can not have any negative x

[ocean seal]

adumb

[clear tulip]

oh okay i get it

also for all log, there ranges are 0,infty?

[hidden pier]

domain

range is from -inf to +inf

i could be misinterpreting your meaning when you say "range" though

[hidden pier]

yep

[clear tulip]

oh so

okay wait sorry i meant domain mbmb

[hidden pier]

all g

[clear tulip]

the domain of any log function is 0,infty

then the domain of any polynomial is -infty,infty

[hidden pier]

exclusive

yeah

yeah

[clear tulip]

oh okay nice thank you

.close

[lone heart]

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[warped topaz]

Guys im tripping

[warped topaz]

I cannot factorize sqrt(x) - x^2 = 0

This is the easiest question ever wtf

sqrt(x) = x^2
sqrt(x)/x^2 = x^2/x^2
x^(1/2 - 2) = 1
x^(-3/2) = 1
x^(-3/2) - 1

It says its wrong

[fervent kestrel]

you are getting 1/2 - 2 = -3/2

[warped topaz]

Because its (x^1/2)/x^2, right?

I still dont see whats wrong sry

[fervent kestrel]

1/2 - 2

wait

nvm

[warped topaz]

Oke good haha I was questioning everything

But yeah still dont see what im doing wrong

[gray isle]

you divided by x^2

losing you solutions

[hidden pier]

loses you 0

[warped topaz]

Ohhhhh

Okay I see now

I think I can solve it

Thank you everyone!

❤️

.close

[lone heart]

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[fervent kestrel]

it's almost 4am imma just sit and watch from now on

[lone heart]

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[frosty burrow]

Why does F • Hz = Ω

[loud warren]

How else can you express F Hz and omega?

Btw are you sure your question is correct?

@frosty burrow

Because as far as I know F • Hz = 1/Ω

[frosty burrow]

That sounds right

But why

[glad socket]

context?

farad*hz=ohm?

[loud warren]

Let’s start with the simple one what is a Hz?

[loud warren]

Yes that’s what he means

[glad socket]

do you know about impedance?

[loud warren]

I think that’s too “high level” for the question

[glad socket]

depends on what he is doing

i never found breaking up the units into theor base form and seeing that it does infact equal one another intuitive

[frosty burrow]

Yeah

[loud warren]

Yeah I see what you mean

[glad socket]

then think about a capacitor with some capacitance at high freq AC and low frequency AC/DC

at high frequency its got low impedance

so 1/resistance is high

and at low frequencies its got high impedance so its resistance is high

which to me explains why F*Hz = 1/Ohm

higher frequency-> lower resistance

[frosty burrow]

okay I might get it

.close

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[mellow skiff]

.

3x^2-x-2=0, factorise the function

[mellow skiff]

No

Wait

(X-b)^2 you mean?

yes

we want the expressions to be the same

To multiply with the factors

[ocean seal]

Mycobacterium

[mellow skiff]

Right

We can use

+2bx -x here

[ocean seal]

Mycobacterium

[mellow skiff]

right

Or remove it

No we good

Lets procced

3x^2-x-1

We need a term x for -1

but also

make -2x from *3

-2/3

3x(x-2/3)+(x-1)

Correct?

[hot swallow]

just learn middle term splitting

it is easy and helpful

[mellow skiff]

You got a video for that?

[hot swallow]

no

[sterile turtle]

???

[hot swallow]

put some efforts of your own

[sterile turtle]

Bruh

[mellow skiff]

.close

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[humble salmon]

I have to find the solution to the associated homogeneous equation given that r=1 is a double root of the characteristic equation

[humble salmon]

I've reached an answer but have no means of knowing if I got it right.. is there any online solver for this kind of stuff?

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@humble salmon Has your question been resolved?

[amber nymph]

Use wolfram

[humble salmon]

Got it

.close

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[hollow viper]

Does anyone have a youtube list for these topics?

[hollow viper]

that's discrete math.

[gleaming granite]

Videos: Trevor Bazett Discrete math

Book: Epp Discrete math

Those are my favorite two

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[inland arrow]

Did the author make a mistake here because why is g(b) = f(a) when in reality it's g(b) = f(b - a + b) = f(2b - a)?

[pallid scarab]

it's b+a-x

author's mistake

[pallid scarab]

so yeah happens sometimes xd

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[inland arrow]

Oh

Thanks

.close

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[tidal summit]

Where did i go wrong? the answer is ln(b+1/a+1)

[tidal summit]

I used frullani's integral theorem

<@&286206848099549185>

its supposed to be e^-bu and e^-au in the numerator

.close

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[warm creek]

hi

[little turret]

hello

[warm creek]

hi

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[vale wigeon]

hi, do you have a math question to ask?

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[true sandal]

P(t > 2.03, Degrees of Freedom = 29) = 0.0258

[true sandal]

how'd they get this from a table?

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[alpine sable]

hi

[clear tulip]

oh sorry

[alpine sable]

How do i create a help

[clear tulip]

just chat here

then send ur problem

[alpine sable]

istg i need the clean solution for this

[pine gazelle]

first find the distance

[alpine sable]

oopsie i got it now

thank you

;-;

what abt this? ^^

[pine gazelle]

50 minutes + (time taken to do the 2 km) gives 17:35

[alpine sable]

so the ans is 17:35

?

[pine gazelle]

wait nvm i read it wrong

she travels from home to gym and reaches at 17:35

you can find the time taken from home to gym using the 2 km and 10 km/h

idk how the 50 minutes from school to home is relevant

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

Austin and Brian started running at constant speeds from the point in opposite directions. After running 10 minutes, they were 2,500 m apart. Austin ran at a speed of 150 m/min.

This is easy but like how

Wait ill get the ques

Find the total distance that Austin ran

Find Brian’s speed.

[lone heart]

@alpine sable Has your question been resolved?

[fervent kestrel]

@alpine sable after 10mins austin ran x amount of distance. He ran 150 m/min. First try to set up an equation

Hint in the units how can you cancel out the time?

in m/mins

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[alpine sable]

I need help understanding this I'm in 9th grade I don't really remember this all it has An= an-1 + b I need help understanding that and how to graph it? I dont even understand this at all honestly all of it so I do need some help?

[alpine sable]

feel free to ping me

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[alpine sable]

<@&286206848099549185>

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[alpine sable]

!close

.close

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[frosty burrow]

A transmitter system has a power of 13 W, no line loss and an antenna gain of 39.0 dBi. Assume that the transmitting antenna is replaced with an isotropic antenna and that the line is still lossless. What must the transmitter power be for the signal to be as strong as it was along the previous main lobe? Give the answer in watts.

[frosty burrow]

I thought that dBi meant that you had an isotrooic antenna

But the gain is in dBi before we switch to the isotropic antenna

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[frosty burrow]

<@&286206848099549185>

[frosty burrow]

.close

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[lavish crypt]

Question 1 is solved and idk how to do Question 2

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[vocal hawk]

not sure if that's the correct place to ask

but what is the center of rotation here

considering the points as the top left of each square

[cinder tundra]

Looks like the center is the middle one isn’t it?

[raw stream]

Yeah

[cinder tundra]

Try doing it with a different coloring and rotate it

Si you can visualize it

[raw stream]

the middle square

[vocal hawk]

what middle square

[cinder tundra]

The figures are created by four squares each one

The one in the middle is the one that doesn’t move from his position

Only moves his direction

[stark crater]

the middle square changes from 2 to 3

[cinder tundra]

Where?

[stark crater]

the one in the 3rd box is the middle right one in the 2nd box

[cinder tundra]

I think it’s rotated the other way

[vocal hawk]

yeah, each rotation here is 90 degrees

[cinder tundra]

Mmm

[vocal hawk]

so the 3 is rotated 180 degrees

[cinder tundra]

Now I am the one doing the colour thing xd

[vocal hawk]

I feel like this rotation is impossible

because for it to be symmetric after a 180, means that it should be in the middle vertically

[cinder tundra]

No

[vocal hawk]

and the fact that 90 degrees rotation = 270 rotation, means that it should be in the middle horizontally

[cinder tundra]

What I see is a rotation in a different direction

First rotates to second one direction

Then goes back to the first by doing the opposite rotation

[vocal hawk]

no

[cinder tundra]

Then keeps that kind of rotation

[vocal hawk]

first -> second -> third -> fourth -> first and so on

[cinder tundra]

To get third

I know that

I’m saying what’s happening

First and third is the same position of the figure

And fourth is third + Same rotation from 2 to 3

So I still see the center of rotation in the middle square in all the secuencies

[vocal hawk]

can you tell me what you mean by middle square?

because there are two above and two below

which one is middle

[cinder tundra]

It’s a 3x3 matrix

The middle is the position 2x2

[vocal hawk]

ahh, right

I represent each point of the 3x3 matrix by it's top left

so would it be the top left of the 2x2 or the middle of 2x2?

[cinder tundra]

I’m trying to make something so u can see but I’m not sure I will be able cause I’m in the mobile in my bed but

[vocal hawk]

gray is center of rotation

[cinder tundra]

But the second image doesn’t correspond right?

The second would be the 4th

[vocal hawk]

all of them are wrong

[cinder tundra]

The center is the other one

“Also”

With the bottom right of the 2x2

Both: top left + bottom right

[vocal hawk]

what do you mean

[cinder tundra]

One sec, I think I will be able to show in a moment

My programming skills are not very good, I’m still trying xd

[vocal hawk]

lol

if you only draw on the picture and I'll program it

[cinder tundra]

I can’t draw in mobile I am very bad with mobiles lol

[cinder tundra]

Is that thing you showed me where u work?