help-0

[strong furnace]

what this tells me

I think you have already derived the general equation for simple harmonic motion

in your course

[silver bay]

oh

i have no clue

[strong furnace]

and all you need to do is show that sin(theta) approximation to theta is accurate in this case

after that they have already established the equation of motion

and they just use the equation of motion for SHM

so you should technically be allowed to use the formulae for motion and time period etc.

[silver bay]

oh okay

how would that work for #2 though

because i did that for #1 i just used the shm equation

i got 38, could you check if that makes sense

sorry im asking for so much help and thank you so much youre really patient

[strong furnace]

approximation gives 39

[silver bay]

oh

yeah its like 38.98

i just said 38 because i floored it

since it doesnt click the 39th time

[strong furnace]

oh wait that actually makes more sense

yeah I am really tired today lol

that is correct yes

[silver bay]

hahaha youre fine thank you so much for helping

sooo for #2

i just say

theta'' = -(g/0.6) theta

does that make sense or should i do something with it

[strong furnace]

it does make sense

[silver bay]

oh okay so thats it for my answer?

[strong furnace]

it is correct

but I think they are expecting

a normal equation

not a differential equation

like in your workbook

they do the same work

equation for motion would be something that describes theta as a parameter of t

so for every t you would know theta

[dawn epoch]

Hello everyone. Im having trouble with my Ti 84 plus calculator. I am doing normal distributions (idk how its called in English hopefully thats correct) and when I go to the NormalCDF thing it gives me the screen as in box number 2. I would want it to show me box number 1, because there it says what information to put where, while in box 2 I have to know the right order. How do I go from box 2 to box 1? Any ideas?

[silver bay]

ah okay

[strong furnace]

the differential equation just does not take initial condition into consideration

[silver bay]

so like the equation we came up with earlier?

[strong furnace]

@dawn epoch channel busy

[strong furnace]

yeah but avoid all that mess

[silver bay]

oh

[dawn epoch]

Do i have to go somewhere else?

[silver bay]

how so?

[silver bay]

try any of the other questions channels ig

[strong furnace]

there are 9 channels find 1 that is not busy

[strong furnace]

the way they did it in your workbook

[dawn epoch]

Oh okay i didnt know every channel was for one thing sorry guys

[strong furnace]

they just proved sin(theta)=theta for 0<theta<15

[silver bay]

this thing?

[strong furnace]

yeah

[silver bay]

i have no clue how they got this or what it means though

[timid flint]

Heyo everyone! i have a exam in Two days, and can use my notes on part two. My exam has geogebra, excel, geometry, algebra etc..
So my question is:
What is most important for me to note down as i can use during my exam?

[ocean hearth]

where can u get help from this server ?

[silver bay]

any of the questions channels which aren't busy

or any of the topic channels

[strong furnace]

you know the arbitrary constants we had in our solution?

[silver bay]

yeah

[ocean hearth]

oh any of u busy?

[silver bay]

we're working on smth in this channel so yes

[ocean hearth]

ight

[strong furnace]

so the phase shift due to those arbitrary constants is arctan(c2/c1)

which is E(symbol for pound) in their expression

and the amplitude due to these arbitrary constants would be sqrt(c2^2+c1^2)

which is theta(naught) in their case

[silver bay]

ah okay

[strong furnace]

they probably did all that we did

already

as a proof for simple harmonic motion

in your class or as an assignment maybe

[silver bay]

they didnt

this is the only assignment on this topic

and the thing i sent is the only material we were given on it

[strong furnace]

weird considering this is differential equation and not introductory mechanics course

anyway that is how we get that equation of motion

we actually got it so hopefully that helps you in understanding it

now according to the workbook you have to use this result I think

[silver bay]

it does for the most part, i just dont know what the vertical and phase shifts are

[alpine sable]

do you find z score first?

[strong furnace]

idk what you're referring to with vertical but phase shift is just the change in input for sinusoidal function so for R-method/Auxillary angle method we get Asin(Wt)+Bcos(Wt)=Csin(Wt+D) A, B and C are amplitude(if this is what you mean by vertical) and D is the phase shift for the resultant sinuosoid from the given sinusoids this is also called auxillary angle

[silver bay]

yeah i meant amplitude sorry

[strong furnace]

phase is the input for sinusoidal function

and amplitude is the coefficient

[silver bay]

yeah

[strong furnace]

since it corresponds to maximum displacement/angle in SHm we call it amplitude

[silver bay]

i just didnt know how that correlated to what i had

[strong furnace]

you do now?

[silver bay]

yeah

thats the r method you were talking aobut right

thats how we get the values from the constants in my old equation with cos and sine

hmm

[strong furnace]

yes

[silver bay]

im gonna try to find out what they mean by motion equation

in the other parts of the textbook

but i dont really have a clue

[strong furnace]

they just mean equation of this form x=Asin(wt+P)

which is the result you get from differential equation

but you have to find the values of A and P

using the given condition

[silver bay]

oh

i asked the class discord whether we're supposed to actually solve for it and i got that 😭

so i guess i just leave it in that format

[strong furnace]

what he probably means is

you don't need to solve the differential equation

which we did earlier

using the characteristic equation

instead use the result Asin(wt+P)

[silver bay]

how do we find A and P though

and what even is w

😭

[strong furnace]

they have actually given the definition of w

but since we actually solved the differential equation

remember we had 4.(something) in our solution?

[silver bay]

yeah

sqrt(g/L)

it says what it is

[strong furnace]

to find A and P as I said

[silver bay]

but i dont know what the meaning of itis

w is angular velocity usually right

what is it in this case

[strong furnace]

mathematically

it means nothing

but in physics

there is something called standard circle

since sinusoids are projections on circle

we represent the variable point of displacement of a point as the projection of a different variable point that goes in a circle

and the angular velocity of this different point

is w

[silver bay]

oh ok so it is angular velocity?

[strong furnace]

for the point on standard circle yes

but it is called angular frequency

[silver bay]

oh weird

well

so

[strong furnace]

yes?

[silver bay]

for the motion equation

what form am i even supposed to put it in

[strong furnace]

x=Asin(wt+P)

I will give you the steps

I think that would make it clear for you

can you post the problem again?

[silver bay]

#2

[strong furnace]

I will use your workbook as reference

y''=-(G/L) sin(y) you can write this right?

now sin(y) ~ y for 0<y<15

[silver bay]

yeah

[strong furnace]

y''=(-G/L)y

this is the standard differential equation form of Simple harmonic motion so we get general solution

y=Asin(sqrt(G/L)t+P)

now it is given initially it is at y=0.1

0.1=Asin(P)

and it is also given that it is at rest

so y' = Asqrt(G/L)cos(sqrt(G/L)t+P)

which gives us

[silver bay]

how is this a thing

where did the sqrt(g/L) go

[strong furnace]

initially means

t=0

[silver bay]

ohh theres a t

gotchu

[strong furnace]

similarly we get 0=Asqrt(G/L)cos(P)

A cannot be 0 since that would imply y=0 for every t which is not possible

therefore P = pi/2

0.1=A

replacing these in our equation

we get y=Acos(sqrt(G/L)t)

[devout linden]

I only found that

Theta(t) = Acos w+B sin w

How come it become the actual theta(t)? Did they have some experimental constants??

[strong furnace]

this is the equation of motion

[silver bay]

adding pi/2 makes sine into cosine right

and id replace the A with 0.1

[strong furnace]

you use R-method to convert this to a single sinusoid and the corresponding constants are irrelevant from physics point of view so they just name it accordingly but still 2 constants that we don't know about so nothing changes

[strong furnace]

yes

[strong furnace]

and yes

[devout linden]

So am i still almost right?? Coz i just only using characteristic formula that i learned recently

[strong furnace]

you are right

its the same general solution but in a different form

[devout linden]

Ahhh i see.....soo they using some kind of trigonometric characteristics to convert the equation to become like that??

[silver bay]

yeah

[edgy zealot]

Can I put a question in here or r y’all still talking

[silver bay]

maximum angular speed is when theta=0 right

[silver bay]

we're still talking :/ sorry

[edgy zealot]

Ok it’s fine

[silver bay]

so then i'd plug in 0 for theta and find what the time is then? then plug in time into y'?

[strong furnace]

you don't reaally need to do that

you have the actual function

just take y'

and for sinusoid function the maximum is amplitude

[silver bay]

ohhh

okay

so would it be 0.408

and are the units radians/second?

im so confused

gravity is like linear right

so its not 10

how would i even convert that

[strong furnace]

maximum angular velocity is AW , A was 0.1 radians

w was sqrt(g/l)

yeah 0.408

radians/sec

[silver bay]

thanks

how would that work though?

because the gravity

its 10 m/s^2

but thats linear

and this is rotational

sorry im asking so many questions

[strong furnace]

w is 1/sec

because l is m

g/l is 1/s^2

[silver bay]

oh ok yeah

the meter unit cancels out

[strong furnace]

yh

[silver bay]

makes sense

thank you so much!

i have a bunch more tbh

but like

i took up way too much of your time already 😭

[strong furnace]

if it is the same thing I won't be helping you but if it is something different I can help

[silver bay]

its not hard its just the pendulum shm equtions

not bad at all

[strong furnace]

you should actually re try these because if you can't do these you learned nothing from our interaction

[silver bay]

yeah

i tried it

i got 0.253 meters on #7

[strong furnace]

how did you get 0.253

[silver bay]

shm equations

im allowed to use them i think

[strong furnace]

yeah I am asking about the actual calculations

like what did you put in the calcullator

[silver bay]

i solved the equation for L, so since T = 2pi sqrt(L/g), L = (1/2pi)^2 g

if g is 10 m/s^2 then L is just 0.253 meters

[strong furnace]

yeah that is correct

[silver bay]

thanks

lemme do #8 really quick

ok for 8

i got 0.80 * sqrt(1/0.37) = 1.315 seconds

[lime stirrup]

Quick question what's easier to use here horizontal or vertical strips?

[strong furnace]

yeah correct

@silver bay

[silver bay]

thanks 🙂

[lime stirrup]

<@&286206848099549185>

[final fulcrum]

friends i have a big question!!

how to factor x^9 + 3x^6 + 2x^3 + 1?

the answer im supposed to get is at the top, and i know the internet says to factor by grouping but it makes no sense and seems so arbitrary

[ionic jewel]

dont ping helpers right away, and they both work

[manic quail]

,w x^9 + 3x^6 + 2x^3 + 1

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by veryhappyperson#1152

[manic quail]

huh

[silver bay]

i dont think it factors

[final fulcrum]

it does

[manic quail]

,rotate

[silver bay]

did you type it right

[ionic jewel]

ah yes

he typed it right, the handwritten is wrong

[final fulcrum]

huh

[silver bay]

oh nvm

,w factor ,w x^9 + 3x^6 + 2x^3 + 1

whoops

[final fulcrum]

it’s typed and written right

[silver bay]

,w factor x^9 + 3x^6 + 2x^3 + 1

[ocean seal]

Results provided by WolframAlpha

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

Requested by oreo#0999

[ionic jewel]

ah there we go

[final fulcrum]

but why does it factor like that

[strong furnace]

,w x^3+3x^2+2x+1

[ocean seal]

Results provided by WolframAlpha

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

Requested by nyann#4274

[silver bay]

nah thats wrong lmao

[strong furnace]

x^3= u

[silver bay]

the exponents were right

ohhh

ok

sorry

[final fulcrum]

this here is right but how do we get there

[ionic jewel]

i have no idea how they hand factored that, using wolfram seems like the move here

[silver bay]

^

same

[final fulcrum]

it’s for my brothers math test tomorrow🥲

[strong furnace]

,w factor x^3+3x^2+2x+1

[silver bay]

rip

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by nyann#4274

[strong furnace]

cardano's method>?

[ionic jewel]

what level of math is this?

ive done a lot of math and ive never learned something that can factor that without guess and check

[silver bay]

thats like the cubic version of the quadratic equation right

[final fulcrum]

he’s in 7th grade LOL

[silver bay]

hmm

weird

this should be Algebra I then

[strong furnace]

its reducing cubic to quadratic

[ionic jewel]

are you sure you have to factor it to solve the problem

[karmic crypt]

We didn’t even factor till 10th grade lol

[strong furnace]

there is probably a typo

[silver bay]

yeah that does not look right

[ionic jewel]

do people know how to do this off the top of their head?

[silver bay]

its really long and convoluted

but i had it memorized at some point

its gross though

[strong furnace]

there is generalized thing with coefficients

I don't know how to do this off the top of my head I always just look it up

but you probably can remember the substitution

[karmic crypt]

Either way I don’t think a grade 7 would know that

[strong furnace]

all you need is to convert your cubic to x^3+px+q=0

[final fulcrum]

he’s a smart kid, he’s in an advanced school

[ionic jewel]

oh no i remember this now

[silver bay]

unless hes like some type of prodigy

[final fulcrum]

wait care to elaborate

[silver bay]

taking algebra 1 in 7th grade is advanced

and that looks like algebra 1

[final fulcrum]

he’s big brain that’s for sure :D

[silver bay]

so it should be like basic factoring

[ionic jewel]

fancy guess and check

[strong furnace]

but in this case

[silent prairie]

someone tryna help me in question-1

[strong furnace]

I am pretty sure its some basic property

related with binomial (a+b)^3

there is probably a typo

no way they expect cardano's method lol

[silver bay]

yeah

thats like

very weird math

[devout linden]

Still confused how to convert into the last form

[final fulcrum]

i hope it was a typo bc my dad and i couldn’t figure it out and my brother is stressed for his test now, it was a question on the review packet

[silver bay]

was it like a bonus

[ionic jewel]

well if it makes you feel better a bunch of probably math majors cant do it without wolfram

[strong furnace]

the substitutions A and tan(phi) are all you need

[silver bay]

because i guess if you had a couple of hours you could sit down and do it

[final fulcrum]

no clue i didn’t ask

[silver bay]

guessing and checking 👍

[strong furnace]

no integral roots

according to wolfram

[final fulcrum]

i doubt it’s a several hour long test it’s prob smth like 40-60 min

[silver bay]

yeah

it factors into like a cubic and a degree 6

[final fulcrum]

yeah it was just supposed to get the thing wolfram got

that was the answer on the packet

but i j don’t know how to get that

again google said factor by grouping but i never learned that

[silver bay]

i dont see how youd do that by grouping

[strong furnace]

I think we are misunderstanding what facorization means

they don't want linear factors

just any polynomial*polynomial

[final fulcrum]

yes^^

[silver bay]

yes

its a cubic times a degree 6

also

wait nvm we're not done w this

ill put it in a different channle

[strong furnace]

I don't understand what the objective of doing this is

[silver bay]

wait nyann

[final fulcrum]

u want a polynomial * a polynomial

[silver bay]

can you help me with a laplace transform

[ionic jewel]

i mean i guess but those are basically all guessing too

[silver bay]

sorry i keep asking for help but it makes a lot of sense when you explin it

[strong furnace]

I have not really learned Laplace transform

[silver bay]

ah rip

its just an integral i guess

[final fulcrum]

ah i was wondering where they got them from

[silver bay]

i figured out what to do as far as getting it into integral form

[ionic jewel]

its doable if you sit down and guess well but if this is a factorization someone knows off the top of their head if be super surprised

[strong furnace]

if its an integral

I can do integrals

[silver bay]

sure lol

ill put it in questions-1

[strong furnace]

idk what the purpose of this problem for his brother was ? like what does this even teach for an advanced class?

[ionic jewel]

how to learn esoteric factoring methods appearently

like $x^9+3x^6+x^3+3$ is something id expect on a test like that

[ocean seal]

bunny

[ionic jewel]

not whatever that is

[alpine sable]

does anyone know what g + b and r * 47 and B / R?

[ionic jewel]

am i supposed to know what those letters mean

@alpine sable delete your question from other channels

[lapis compass]

hi

[ionic jewel]

hi

ahri?

[lapis compass]

$x^9+3x^6+x^3+3$ is

[ocean seal]

jplink

[ionic jewel]

thats an actual factor by grouping problem

[tepid cargo]

Anyone know what it means to represent a relation numerically?

[ionic jewel]

absolutely no idea, you cant describe that graph with a single number

[lapis compass]

its easy

[tepid cargo]

You know what it means to solve it numerically?

[ionic jewel]

might just be asking for the slope?

the "relation" between x and y

[tepid cargo]

oh okay

[lapis compass]

yeah both x and y

[tepid cargo]

And equation means y+mx+b right?

[ionic jewel]

y=mx+b but yes

[tepid cargo]

y=*

What about words?

[lapis compass]

yeah

[ionic jewel]

"this is a line with slope ... that crosses the y axis at ..."

[gusty merlin]

hi is it okay if i can ask my question?

[lapis compass]

yeah tell

[ionic jewel]

sure, i think coconut is done

[tepid cargo]

Yep

[gusty merlin]

uh it’s this problem right here

[lapis compass]

@tepid cargo cute skin

[lapis compass]

what? which?

[gusty merlin]

it’s taking very long to send sorry

i tried different ways to solve for angle BAC but i keep on getting it wrong.

my friend told me she got 60 for BAC but i did it and i got like a whole different number

[thin surge]

Hey

So did you find angle BAC same way as you did for others

[gusty merlin]

i tried to

[main zephyr]

whats the formula for curved surface area of a cone?

[gusty merlin]

but i ended up with like 100

[thin surge]

So I think what answer did you get by finding that way would represent angle subtended at the center

[gusty merlin]

subtended😰😰

what does that mean

[thin surge]

I mean

Angle made by arc at the center

[gusty merlin]

ohhhh

[thin surge]

So like 3x =60 gives you angle at the center

Are you getting what I am trying to say?

[gusty merlin]

wait but isn’t 60 the measure of arc AF

[thin surge]

Yes Arc AF making angle at center O

Is 60

[gusty merlin]

OH

ohhhh okay now i get that

[thin surge]

Look I am not sure but I strongly feel that this is what happening

[gusty merlin]

but then how would i find BAC?

do i add the measure of AB and BC

[thin surge]

Wait a sec

Like by your method how much do you get angle of BAC at center?

[gusty merlin]

i got 260😰

[thin surge]

No.no

It's will be

6x that is

120 right?

[gusty merlin]

yes

and 4x is 80

[thin surge]

Now you know the property

That angle made at center

Is double of what made

By the same arc

[gusty merlin]

so is it 4x + 6x = 360??

[thin surge]

At any other point at the circle

[thin surge]

No no what you have calculated for x is absolutely correct

X= 20 is right

[gusty merlin]

ohhh but like how would i use it to find BAC

Do i just

times it by 3

[thin surge]

Can I dm u?

[gusty merlin]

yes !!

[thin surge]

Ok

[wild bay]

Hi. Someone asked me for help with solving this problem, except they haven't learned at all about the pythagorean theorem, nor about squareroot being the inverse function of exponent2 (^2). Is there a way to solve this without those concepts?

I am completely lost of any way to solve this without those concepts.

@alpine sable Can you go to another channel please

[proud burrow]

@wild bay Split it into figure then find there area and aff

[wild bay]

What's aff and what does it mean to split it into figure

[proud burrow]

Sorry add

[wild bay]

Yeah but actually try it, can you split into known-length figures without pythagorean theorem a^2 + b^2 = c^2

[proud burrow]

Yeah by Pythagorus therom you find third side then area then go for other triangle draw perpendicular from 7in side on 20in

[wild bay]

I'm saying, can you solve this problem without using pythagorus theorem

[proud burrow]

No wait I will show how to do

[wild bay]

Okay

[ionic jewel]

probably but pythag makes it easier

[wild bay]

But how could it have been given to a student who didn't learn pythag

[proud burrow]

@wild bay is the answer 179

[wild bay]

To the whole area of the shape?

[proud burrow]

@wild bay yes

You don't know Pythagorus

[wild bay]

240 - 16 + 12*9/2 so
224 + 54
so 278

So no not 179

And yes I know pythagorus but the person who had this problem given to them didn't

[ionic jewel]

is the 20 the entire bottom side or just the part its under?

[wild bay]

I took it to be the entire bottom side

It's pretty ambiguous, not that the other possibility would make it any more solvable without pythag

[proud burrow]

Then how did you find the area

[ionic jewel]

,w 0.5912+1112-1/24*8

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 兔子#6562

[ionic jewel]

that should be the actual answer

but obviously I used a pytharogean identity

[proud burrow]

Yeah I got its same before it was some calculation mistake so I got 179 now it's 170

Yes without Pythagorus it's not easy

[ionic jewel]

i mean I guess you could use law of sines/cosines and trig as well but that seems a tad overkill

[proud burrow]

For that you need to know angles which are not given

[ionic jewel]

you can use trig to get them tho

its easy enough to get the angle across from 12in, then you can go from there

but lets be real if you dont know pythag thm you dont know law of sines or trig

[wild bay]

The blue area you find with pythag. It's 3 times the pythag identity 3 4 5, so the shortest side is 9. area of triangle is base times height over 2, so 9 * 12 / 2 = 54.
the big rectangle is 20 - 9, which is 11 (or maybe it's 20, ambiguous) times the height which is 12. So 11*12 = 132. minus the green area, aka 20 - 9 - 7, aka 4, times base which is 12-4 so 8, divided by 2. That makes the green triangle be area 16. So 54 + 132 - 16 = 170, or 278 with the 20 being the bottom side of the rectangle and not the whole thing. I am stupid.

[proud burrow]

@ionic jewel yeah understood by using it also we can find 3rd side

[wild bay]

Yeah if they don't know pythag they prolly never heard of trig

[proud burrow]

@wild bay I understood

[wild bay]

depends on what 20 in is, but sinde it's in the middle of the rectangle, it's probably not for the entire side tbh

Which means it's 20 - 7

[ionic jewel]

the simple answer is teach them pythag or at least the 3 4 5 triangle

since not using it is just trolling at this point

[edgy zealot]

Can I type here

[wild bay]

They didn't want to, I'll try again

[proud burrow]

@edgy zealot yes

[edgy zealot]

Thanks

[wild bay]

Thanks though guys this confirms my like thoughts

[ionic jewel]

tell them the alternative choice is not being able to answer the question

[wild bay]

that he really had to learn pythag

[ionic jewel]

this is a pythagorean question, and you have ot learn it

[wild bay]

Yeah okay

[sudden torrent]

I’m kind of new here so I don’t know how to use texit but

[tight locust]

That image really didn't come out okay. I'll type it up if it's too hard to read

[sudden torrent]

You should be able to find it if you know that the angle of CAD is half Arc AD

[proud burrow]

@tight locust what's the function

[tight locust]

The fuel consumption of a car in miles per gallon is modelled by $F(s) = 6\exp(\frac{s}{20} - \frac{s^2}{2400})$, where s is the speed of the car in miles per gallon (mpg).

[ocean seal]

EndTimes

[edgy zealot]

Ok

@sudden torrent I don’t get what u mean

[proud burrow]

@tight locust let me try

[tight locust]

If the car is travelling at 50 mph and its speed is changing at the rate of 20 mph/hour, what is the rate at which its fuel consumption is changing?

[proud burrow]

S is speed

[rapid jewel]

@edgy zealot Your taking up 2 questions....

Whatever, can someone help me with a math project? I'd rlly appreciate it.

I just need help choosing the measurements.

Im a bit confused to what this means.

Its a lot different compared to the homeworks.

I'm creating my own figures, but they have to make sense.

Just found out D means space diagonal

[left robin]

d prob means diameter?

[rapid jewel]

Nope

I got it though.

Question-0 is open.

[fair cove]

How to calculate square root 🙂

[hidden horizon]

do you know what are perfect squares ?? @fair cove

[winter swan]

can someone help?

[fair cove]

nope

[hidden horizon]

learn them first

[leaden ferry]

So, I got a number sequence, 4, 8, 9, 10, 12, 14... What is the next number in the sequence?

This is my solution.

Is my approach correct?

[fair cove]

i dont have enough timee

[hidden horizon]

bruh -___-

u cant understand sq rooots without that concept

[fair cove]

okay but what is that

[hidden horizon]

its like abcd for english

[leaden ferry]

Guys?

[hidden horizon]

search google

[fair cove]

o ok

[ionic jewel]

the best part about sequences is you can say anything is right

[leaden ferry]

I guess it really depends on the answer sheet of the teacher, right?

Mine is explainable tho.

I'm not sure with the 0 on the middle term of the sequence if that is acceptable.

[ionic jewel]

oeis has both 15 and 16 as possible continuations

i mean yours is explainable, not sure if that logic would match the teachers sheet tho

[ionic jewel]

in fact I'd argue it's wrong becuase you are going to have a very hard time continuing past that point

[leaden ferry]

I guess you're right. But other than my method, I am not sure about its pattern tho.

[ionic jewel]

Numbers that are not the product of consecutive primes
Like I said there's no way to know, and you can justify anything. The quote above follows your sequence but is probably not right.

[minor dagger]

Can someone please help me with these 2

[ionic jewel]

delete to go to an unoccupied channel

[minor dagger]

Okay

[ionic jewel]

there's nothing obvious that stands out to me, so yours is probably as good as anything else, but it doesn't strike me as "the right" solution

[leaden ferry]

Hold on, I think I got an alternative approach. But welp, it's late to change my answer from a finished exam. I'm just reviewing it for the best.

[ionic jewel]

that is an awful question

someone put that on an exam?

unless there's more context that's purely a terrible question

your approach seems fine then, you should argue for your points if you don't get them*

• if there's no other context

[soft zodiac]

Is dividing by 9 the same as multiplying by 0.11?

[ionic jewel]

no

[leaden ferry]

Yeah, it was part of an exam.

[ionic jewel]

1/9 is not equal to .11

[leaden ferry]

And sorry about the delayed answer. My PC keeps crashing.

[ionic jewel]

well your exam is poorly written

[hidden horizon]

sad

[ionic jewel]

well "finish the sequence" questions like that are terrible

[leaden ferry]

It is. It has given me a hard time figuring out the sequence. But still, it was a fun experience.

Now, this might be the alternative approach to it. Idk if it's what the teacher's answer sheet looks like:

[ionic jewel]

that's an equally valid solution

[leaden ferry]

Yeah. Eh, it's just 1 wrong mistake if that's the case...

[ionic jewel]

but you could also just day "it's the sequence of "4,8,9,10,12,14, whatever you want" repeated forever

you can contrive an example for any number than follows

19 is not more correct than anything else

no

that's even dumber

-3,0,1,0,3

what kind of pattern is that?

your soln actually made some sense

[leaden ferry]

Lol. Idk tho. I'm just figuring out, unless I extend more to see what's going on deep.

[ionic jewel]

it's a terrible question, you better not lose points on it

[leaden ferry]

Yeah, no use. Unless it's in the deeper... -3, 1, -1, 3,...

Yeah, I'll make sure for it. Idk if the teacher sees it or not. The annwers he inputed are only the basis, so this means that the site checks it and not actually the teacher himself.

I also did with this problem. It's very fun tho:

[ionic jewel]

-1,-1,-2,-3, what is this the Fibonacci sequence?

[hidden horizon]

@leaden ferry this series is the combination of 2 or more series....take the series 1 , 3 , 4 , 7 , 11 , 18 and observe that they hv Fibonacci differences

[ionic jewel]

haha we both see the Fibonacci

[hidden horizon]

xD

[leaden ferry]

Yes. Yes. Also, I already saw your message but got distracted on this channel for my approach showcase. lol.

[hidden horizon]

oki np

[leaden ferry]

I'm sorry for not replying back. 😦

[hidden horizon]

juss want to point it out

[hidden horizon]

aww shucks no matter u guys in this server are the only ones who respond lmao

[leaden ferry]

lol

Just behaving with proper etiquette as said in the rules... because it's an academic server. :"D

[ionic jewel]

you would be surprised how many people ignore that

[leaden ferry]

F. I know. It's the nature of social medias, specially for Discord being depicted in the public as a "gaming chat community."

But otherwise, now, it is for basically every general use.

Schools, studies, interests, movies... you named it.

Aight. Gotta go. I got some titration quiz for ANALAnalytical Chemistry later. It was fun to discuss with you. :"D

[junior thorn]

get the inverse laplace of $F(s) = \frac{1}{s^2} \frac{s-1}{s+1}$

[ocean seal]

William Brown

[finite magnet]

is 36 DNE or positive infinity? if neither, then what is it? also, is 33 also DNE?

[elfin snow]

36 is +∞ because it goes all the way up and will keep going all the way up

33 is like -3.2 or something

because it's defined at x=14

[finite magnet]

i see, so it doesn’t matter that the rightmost line stops?

for 36

[elfin snow]

no because it has an arrow

if it has an arrow it will keep going in that direction indefinitely

if there is just a point at the end of the line then it just stops

[finite magnet]

i see what you’re saying, what i was thinking was that since the limit is for x approaching infinity, it would stop at the rightmost line

that one^

right at 14

so therefore it wouldn’t be able to go forward after that

[elfin snow]

but that's as x approaches positive infinity

in #36 it is asking about negative infinity

[finite magnet]

ohhhhhh

i thought it was

[elfin snow]

lol

[finite magnet]

infinity with the negative after

[elfin snow]

nono

that doesn't exist

youre never gonna see like $∞^-$ or $∞^+$

[ocean seal]

gmod

[elfin snow]

so yeah just make sure to read the question carefully

[finite magnet]

yup

thank you so much

🙂

[elfin snow]

mhm

:)

[tepid cargo]

Hello. How am i suppose to represent the relation with words?

[elfin snow]

Either direct or inverse

In this case it is inverse because as x increases, y decreases

if both increased or both decreased it would be direct

[tepid cargo]

Oh, so basically I'm suppose to describe the trend in the graph right

[elfin snow]

yes

[tepid cargo]

Ok, thank you for the help.

[elfin snow]

no problem :)

[finite magnet]

wait for 33 is it still -3.5 even though the graph stops @elfin snow ?

sorry to ask again

[serene jolt]

eyo anyone exist

homeskillet

wewewewew

[noble needle]

Guys need help with these 2 questions

[proud burrow]

@noble needle what we have to find in first

[alpine sable]

in the first one, isolate x first, Asrar

[proud burrow]

So we have to find equation in x

@noble needle you know partial differentiation

@noble needle the second question is linear differential equation

[noble needle]

Can anyone provide me the solutions

[noble needle]

Little bit

[proud burrow]

@noble needle I'd know what to do in first but I can provide second solution

[noble needle]

Ok

[noble needle]

In the first one you need to solve for the value of x

[proud burrow]

We have to just find value of x

[noble needle]

Ya

[proud burrow]

Is this the answer for 1st

[oak wigeon]

Strawberry

[noble needle]

Thnx

[finite magnet]

i got the same

[sand pine]

3^x+4^x+5^x-6^x=0, how do i find the roots without graphing it

[proud burrow]

@noble needle sorry second one is bit long taking time

[sand pine]

$3^x+4^x+5^x-6^x=0$

[normal lance]

What

[hidden horizon]

4 is 2^2

[normal lance]

But it is in multiply

So it will not cancle out

[hidden horizon]

oof yeah

sorry

[normal lance]

Total power = 0

???

[hidden horizon]

wait dude im thinkng

[normal lance]

Take whole power x

They have same

[hidden horizon]

how can u take that lol

[normal lance]

Lol

[proud burrow]

@normal lance it's not possible

[normal lance]

RHS Power = LHS power

[hidden horizon]

lol its not possible lmao

[sand pine]

oh naw

[proud burrow]

@normal lance yes it's not possible

[normal lance]

Let's think

What to do

[proud burrow]

@normal lance if they were in multiplication then we could take common power not in addition

[normal lance]

I know

[hidden horizon]

Consider 3x5^x as compared to 6^x.

6^x will be greater than 3*5^x for x>=7 .

Since 3*5^x > 5^x + 4^x +3^x, we know there must be solution for 3^x+4^x+5^x = 6^x between 0,7.

[normal lance]

Hey yup

[hidden horizon]

Do some trial and error

[sand pine]

$(2^x)^2 -2^x.3^x +5^x+3^x=0$

[proud burrow]

@hidden horizon but we want exact value

[sand pine]

seems to be quadratic in 2^x

[normal lance]

6^x = LHS

[hidden horizon]

lol do trial and error with x between 0 and 7

[proud burrow]

@sand pine but wbu 5^x

[sand pine]

lets say its the c in quadratic equation maybe

[hidden horizon]

lol i did trial and error and for only 3 this works

[normal lance]

$3^x+4^x+5^x-6^x=0$

[ocean seal]

Mad dron Matrix

$3^x+4^x+5^x-6^x=0$

[sand pine]

is this correct?

[hidden horizon]

how wud u simplify it

[sand pine]

yeah, real question

[normal lance]

$3^x+2^2x+5^x-2^x.3^x=0$

[ocean seal]

Mad dron Matrix

[sand pine]

yeah, that's exactly what i rendered before

[normal lance]

It's wrong

[sand pine]

wait a min

[proud burrow]

@normal lance x should be in power

[sand pine]

$2^2x?$

[normal lance]

Yup

What

[hidden horizon]

bruh wut

[normal lance]

$2^2^x$

[hidden horizon]

3 IS THE ANSWER GUYS

ITS 3

x is 3

[normal lance]

You put the value of x as 1,2,3 and see

[sand pine]

no, it has only 1 root

[hidden horizon]

no

Consider 3x5^x as compared to 6^x.

6^x will be greater than 3*5^x for x>=7 .

Since 3*5^x > 5^x + 4^x +3^x, we know there must be solution for 3^x+4^x+5^x = 6^x between 0,7. After some hit & trials you can further narrow it down. In this case solution is x=3

[fading jay]

Axis simmetry -B/(2*A)

A=2

[lethal vortex]

3 = -b/4

oh

@fading jay thank you

[deep walrus]

square root of 2340 in decimals

pls help

<@&286206848099549185> can anyone of you help in this

[hidden horizon]

i think ull get approx...

48.37

[deep walrus]

ohh

[hidden horizon]

,w square root of 2340

[ocean seal]

Results provided by WolframAlpha

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

Requested by IamRDT#8608

[deep walrus]

are you sure ?

ohh ok

thnx

[hidden horizon]

np

[deep walrus]

,w cube root of 357

nice

[tight locust]

,w cube root of 69

[ocean seal]

Results provided by WolframAlpha

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

Requested by EndTimes#8053

[tight locust]

LOL!

[deep walrus]

,w cube 23

[ocean seal]

Results provided by WolframAlpha

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

Requested by XaNdEr#2579

[deep walrus]

thnx

[tight locust]

i said the funny number.

you may now laugh.

[deep walrus]

ooh

what is ti ?

it*

[tight locust]

69

lol

[hidden horizon]

lmao

[open hamlet]

Could I get help on this?

Would love an explanation

[deep walrus]

,w compound intrest on 10,800 for 3 years at 12 1/2% per annum compounded annually

:/

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by XaNdEr#2579

[deep walrus]

oof

,w compound intrest on 10800 for 3 years at 12.5%

[ocean seal]

Results provided by WolframAlpha

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

Requested by XaNdEr#2579

[deep walrus]

nice

[hidden horizon]

lol bot wont tell ans to everything lmao

[deep walrus]

lel

[hidden horizon]

do it urself lmao

[deep walrus]

i already did it, just checking my answers

[hidden horizon]

oh okay

[deep walrus]

¯_(ツ)_/¯

[ocean seal]

Results provided by WolframAlpha

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

Requested by XaNdEr#2579

[crystal quest]

can someone help me ? do you know how to solve this?

[ionic jewel]

do you know what the m and b are supposed to be?

not the numerical value, just what they mean

[crystal quest]

ye the slope im i right?

[ionic jewel]

m is the slope, b is the y intercept

Slope is rise/run, or the change in y divided by the change in x

so whats the change in y between the two points

and then whats the change in x between the two points?

[hidden horizon]

u can use two point slope form

[ionic jewel]

thats what we are doing with extra steps

[crystal quest]

oHHH okayy tysm

[ionic jewel]

well use algebra once you get it like that to go to the other form

[crystal quest]

[strong moat]

Let x and y be any real numbers such that x-y=10 and xy=-24. What is the exact value of x+y?

can someone help me w this

[hidden horizon]

square x-y=10

[left robin]

just use substitution

[ionic jewel]

isolate either x or y in the first equation, then plug it into the second one

[strong moat]

thats what i did

[ionic jewel]

does this even work

[strong moat]

but i get 2 answers

[hidden horizon]

yes

we will get x^2 + y^2 = 148

v know dat (x+y)^2 = x^2 + y^2 + 2xy

substitute values and boom

[left robin]

does he need to square it though

[hidden horizon]

anyways hell get same answer

[strong moat]

Solve the equation (2^2x)(5^x)=cuberoot(400)

does any1 know how

[gray isle]

$2^2x5^x = \cbrt{400}$?

[ocean seal]

ℝamonov

[strong moat]

anyone know how?

[ionic jewel]

why are choices b and c the same

either way I can go through this

first letter can be either X or Y, 2 choices
second letter can be anything, 26 choices
third letter is the other of X or Y, 1 choice
second letter can be anything, 26 choices

[alpine sable]

what is a dot product good for

[strong moat]

its B?

[ionic jewel]

B and C are literally the same answer

[ionic jewel]

find the angle between two vectors, which can extend to other applications such as projections, or checking if things are orthogonal

[strong moat]

is the right answer B?

[ionic jewel]

B and C are literally the same answer how am I supposed to know which one it is

[strong moat]

i guess you can take it as one?

so like 3 choices left xD

[ionic jewel]

$26^2\cdot2$ is correct but i dont know which answer choice they want

[ocean seal]

bunny

[alpine sable]

yep, thanks. teacher should have shown how it integrates with cosine law earlier

[strong moat]

anyone know?

[ionic jewel]

theres probably some formula

let me look it up

Chord length is $2\sqrt{r^2-d^2}$ where r is the radius, and d is the distance from the center of the chord to the center of the circle

@strong moat

[ocean seal]

bunny

[strong moat]

do i plug is 16 and 24 to r and d?

[ionic jewel]

no

r is the radius

which is what you are solving for

[strong moat]

whats the d?

[ionic jewel]

distance from center of chord to center of circle

which is 16 in your problem

[strong moat]

whats the 24 for?

just to throw me off?

[ionic jewel]

no

its the chord length

did you even read my formula

[strong moat]

ohh

got it!

[alpine sable]

RECTANGLES
A. Sides -4
B. Angles - 90° or 4
C. Diagonals - 2

RHOMBUS
A. Sides - 4
B. Angles - 90° or 4
C. Diagonals -2

SQUARE
A. Sides - 4
B. Angles - 90° or 4
C. Diagonals - 2

is this right??

[gray isle]

what's the original question

and wdym by

Angles - 90° or 4

[ionic jewel]

a rhombus is not all 90 degree angles

[ionic jewel]

what have you done

[strong moat]

im lost bruh

[gray isle]

plug and chug

[ionic jewel]

^

whats f(3-a)?

[strong moat]

i plugg in x^2-1 to where

[ionic jewel]

start with my question

whats f(3-a)?

[strong moat]

oh

[alpine sable]

our Task:

What are the different properties of each special parallelograms?
Provide your answer using the template below:

THE PROPERTIES OF SPECIAL PARALLELOGRAMS

RECTANGLES
A. Sides -
B. Angles -
C. Diagonals -

RHOMBUS
A. Sides -
B. Angles -
C. Diagonals -

SQUARE
A. Sides -
B. Angles -
C. Diagonals -

[strong moat]

im not really sure

[ionic jewel]

whats f(x)?

[strong moat]

y

right?

[ionic jewel]

no

[gray isle]

basic function notation

[ionic jewel]

well

yes

[strong moat]

yeah

[ionic jewel]

but what is it in terms of x?

f(x) = ?

says it in the problem

[strong moat]

x^2-1?

[ionic jewel]

yes

so whats f(3) then?

[strong moat]

thats your x?

[ionic jewel]

do you know this function notation?

we sub in the 3 for x

[strong moat]

yes

[ionic jewel]

in the equation

yes, so what is f(3) for your problem?

[strong moat]

im lsot

im lost

[ionic jewel]

if f(x) = x^2 -1, what is f(3)?

if you havent seen this before thats fine

[strong moat]

3^2-1

?

[ionic jewel]

yes

so now

if f(x) = x^2-1, what is f(3-a)?

[strong moat]

(3-a)^2-1

[ionic jewel]

perfect

now reread your question and see if you can do it now

[strong moat]

ohh

[alpine sable]

Find the area of a square if its perimeter is 52 cm.

Select one:

-121 cm2

-169 cm2

-144 cm2

-196 cm2

[ionic jewel]

go to an unoccupied channel kuri

#help-1

[alpine sable]

can you really just cancel the squares like this?

[fading zephyr]

i mean, it's doing something like saying

x^2 + a = x^2 + 2x + b

the x^2 can be subtracted from both sides

[alpine sable]

yeah but in $(u_{123}^2) + (v_{123}^2) = 2uv*cos\theta$, if you wanna get rid of the squares you have to sqrt both sides, no?

[ocean seal]

Betelguse

[fading zephyr]

but that's not what it's doing

[warped ember]

Hello, please can someone tell me what is difference between radicle and square root?

[alpine sable]

sqrt is second radical

[fading zephyr]

it's cancelling the squares from the two circled expressions by subtracting them

[warped ember]

Please elaborate.

[fading zephyr]

you don't just have the cosine term on the right

[ionic jewel]

$\sqrt{x} = \sqrt[2]{x}$

[ocean seal]

bunny

[ionic jewel]

other radicals would be anything thats not a 2 there

[warped ember]

So are they the same thing?

[fading zephyr]

square root is one particular radical

[alpine sable]

shit that took a long time for me to see. i just considered right side and not considered left as well. thanks

[fading zephyr]

no prob

[warped ember]

So are radicals all different types of square root

[fading zephyr]

no

there are many types of radical expressions

sqrt is one of them

you can use radical and root interchangeably

square root is the 2nd root

[ionic jewel]

$\sqrt[3]{x}$ is called a cube root, and it is also a radical, but it is not a square root

[ocean seal]

bunny

[fading zephyr]

but there are more roots

there's 1st root, 2nd root, 3rd, etc.

the 2nd root is one of many roots

[ionic jewel]

do they have complex roots

[fading zephyr]

aight

[ionic jewel]

never seen these but i cant imagine the field doesnt exist

[fading zephyr]

i think that's beyond the point right now

[ionic jewel]

it was an unrelated question

I cant find anything to search that finds results

[fading zephyr]

this goes in the direction of the fundamental theorem of algebra

roots are related to polynomials and lie on the complex plane

is that what you meant?

or do you meant like a complex radical? like the ith root

[ionic jewel]

the latter

[fading zephyr]

cuz one can certainly raise to a complex power

[ionic jewel]

$\sqrt[a+bi]{n}$

[ocean seal]

bunny

[ionic jewel]

yeah thats a very good point

not sure why i didnt see that

[fading zephyr]

that would be a companion to x^{a + bi} = n

[ionic jewel]

they should never have introduced radical notation, just give me my n^(1/b)

[fading zephyr]

this quite a... radical take

[ionic jewel]

i cant believe youve done this

[glossy nymph]

Free?

"a polynomial of even degree will always be an into function." Why? Also any examples?

[north hemlock]

Quadratic: (-x)^2=x^2

And then an odd degree function would be -x vs x

Where it’s symmetric

[glossy nymph]

Okay but please reason with me: The way I see the definition of into, there'll be atleast one value in the codomain that does not belong to the range.

But we say the range of quadratic polynomials is always all real numbers.

So what am I missing?

[north hemlock]

Well it’s more simple really

Think of it like

If I have x and I make it negative, will I get the same y-value? If so then it’s into

[stark lantern]

This is not true for all quadratics, consider a quadratic like y = x^2. Will y ever be negative?

[glossy nymph]

Isn't that how we define many-one functions?

[glossy nymph]

Yes but I was talking of polynomials of the form ax^2+bx+c, won't they be even degree too?

[north hemlock]

Imagine c =-5 and b=0

and a=1

[glossy nymph]

Yes

[north hemlock]

It’s just x^2 shifted down

So there will be negative y values

But not all negative y values

[glossy nymph]

Ahh I understand

And for odd degree, x distinguished with -x can cover all values in its codomain, right?

Thank you!

[hybrid patio]

Could someone help me with this

[north hemlock]

Plug in x and and y and see if the left and right are the same

[hybrid patio]

Don't get it

[north hemlock]

That point is (x, y)

You’re line is y=5-2x

[quaint trout]

That you cannot answer this question indicates a serious lack of conceptual understanding. So I will explain that instead of answering the question.

[north hemlock]

If we plug in x and y

They should be the same on both ends

If it is the same then it’s true

If not then it’s false

[quaint trout]

The plane consisting of a y axis and an x axis is a collection of ordered pairs (x,y) where x gives you the x coordinate and y gives you a y coordinate. When we have an equation that describes a graph on the plane, what that means is that the graph consists of all the points that satisfy the equation. For example take

y = 5x + 1.

Is the point (0,2) on the graph? That's the same as asking if (0,2) satisfies the equation. Now y = 2, but 5x+1 = 5(0)+1 = 1. So it does not satisfy the equation, so it is not on the graph.

Now consider the point (0,1). y = 1 and 5x+1 = 5(0)+1 = 1. So it does satisfy the equation, so (0,1) is on the graph.

@hybrid patio read and tell me if you don't understand and what you don't understand

[hybrid patio]

Yep

[quaint trout]

To emphasize, because I didn't say so. For (0,2) we had y ≠ 5x+1 and for (0,1) we had y = 5x+1.