help-42

[potent lotus]

A dense set

[calm coral]

@blazing coyote Has your question been resolved?

[blazing coyote]

<@&286206848099549185>

[blazing coyote]

.close

[calm coral]

Channel closed

Closed by @blazing coyote

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[blazing coyote]

How does this proof look

We wish to proceed via induction
\
Base case : $1^2=1^3$
\
Inductive hypothesis : $(\sum_{i=1}^{n}i)^2 = (\sum_{i=1}^{n}i)^3$
\
We wish to prove this implies that $(\sum_{i=1}^{n+1}i)^2 = \sum_{i=1}^{n+1} i^3$
\
We start by adding $(n+1)^3$ to both sides
\
This gives us
\
$(\sum_{i=1}^{n}i)^2 + (n+1)^3 = \sum_{i=1}^{n+1} i^3$
\
Expanding the left hand side we get
\
$ \frac{n^2(n+1)^2}{4} + (n+1)^3 = \frac{(n+1)^2(n^2+4n+4)}{4} = (\frac{ (n+1)(n+2)}{4})^2 = (\sum_{i=1}^{n+1} i)^2 =\sum_{i=1}^{n} i^3$

[potent lotus]

A dense set

[blazing coyote]

Is this proof fine?

[calm coral]

@blazing coyote Has your question been resolved?

[calm coral]

@blazing coyote Has your question been resolved?

[runic jewel]

Looks good to me

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mossy wigeon]

the answer can only be n=1 here right

[calm coral]

@mossy wigeon Has your question been resolved?

[old plume]

Which formula did you use?

[mossy wigeon]

i used this one

[old plume]

Then your answer would be correct if there is no calculation mistake

[mossy wigeon]

its just so weird gpt kept giving me answeres like

3 5 or 6

when n_1 literally cant be smaller than n_2

[old plume]

Did you calculate it?
AI's answer can't be trusted

[calm coral]

@mossy wigeon Has your question been resolved?

Channel closed

Closed by @mossy wigeon

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sonic python]

$\int_0^1 \sqrt{\sum_{i=1}^n (x_i+t(y_i-x_i)-P_i)^2}dt$, solution, Wolfram can't?

[fathom shuttle]

what?

[sonic python]

It is a formula, did it not render?

[fathom shuttle]

whats the context

also no dx, dt, or dy

integrating with respect to what variable

what is this for anyway

[potent lotus]

maybeJosiah

[fathom shuttle]

i dont think this has a nice clean solution

[sonic python]

This is for average of all distances for a line from a point. X E.

If it HAS a solution I am happy. X E.

What would Taylor series be?

Or any other method?

[fathom shuttle]

how did you come up with that formula

[sonic python]

distance squared equals sum of dimension changes each squared. X E.

Before P is a point and P is point to compare with. X E.

Iterate over line all points by t. X E.

[potent igloo]

what is X E?

[fathom shuttle]

All as per one might be maybe or might not be maybe, maybe or maybe not, maybe

[sonic python]

Read bio. X E.

[fathom shuttle]

can you explain what that means

because it looks like word salad to me

i dont see why you need a sum and an integral

the line is a line not a parametric curve right?

[sonic python]

It is a not lying thing, whatever precedes, overall true. X E.

[sonic python]

Yes. Straight. X E.

[fathom shuttle]

ok

so you can describe your point as (x_0,y_0)

[sonic python]

It is 3d+ so I need a sum. X E.

[fathom shuttle]

oh ok i see

so you can describe your point as $(x_0,y_0,z_0)$ right

[potent lotus]

me when the gbf

[fathom shuttle]

average distance is infinite

i just relized

[sonic python]

And w etc. X E.

[fathom shuttle]

ok

do you just want it for a short segment of a line?

[sonic python]

Yes. X E.

[fathom shuttle]

ok

[sonic python]

And I don't want point by point. X E.

[fathom shuttle]

your idea isnt too bad, but we have to fix it a little

do you know what your start and endpoints are?

[sonic python]

Also, divide result by distance of line points. X E.

Yes. X E.

[fathom shuttle]

ok thats good

[sonic python]

And I also know other point to compare with. X E.

[fathom shuttle]

lets say we have our starts at $(x_1,y_1,z_1,...)$ and ends at $(x_2,y_2,z_2)$

[potent lotus]

me when the gbf

[fathom shuttle]

the point can be $(x_P,y_P,z_P,...)$

[potent lotus]

me when the gbf

[sonic python]

You need square root in whatever to use. X E.

[fathom shuttle]

so our line can be written as $(x_1+t(x_2-x_1),y_1+t(y_2-y_1),...)$

[potent lotus]

me when the gbf

[fathom shuttle]

this way the line starts at t=0 and ends at t=1 like you did

[sonic python]

Okay. X E.

[fathom shuttle]

good

now we can do our distance formula

for an arbitrary point on the line we get $\sqrt{(x_1+t(x_2-x_1)-x_P)^2+...}$

[potent lotus]

me when the gbf

[sonic python]

Basically what I started with. X E.

[fathom shuttle]

yeah

you were pretty close, but the notation was just wonky

maybe thats just me

either way, what we can do is expand

[sonic python]

Does area of triangle of from point to line relate?

[fathom shuttle]

$\sqrt{(x_1-x_P)^2+2(x_2-x_1)t+(x_2-x_1)^2t^2+...}$

[potent lotus]

me when the gbf

[fathom shuttle]

i dont think so

you can imagine two triangles with the same base and height, but one of the points makes it isosceles and one makes it extremely obtuse

[sonic python]

I am trying to compare which is drawn before, area of a triangle per angles seems like it should relate. X E.

[fathom shuttle]

e.g. this

[sonic python]

This is for a graphics app. X E.

[fathom shuttle]

are you familiar with law of sines?

ok lets step back

[sonic python]

AC is line, B to compare it with. X E.

[fathom shuttle]

what is your original goal

[fathom shuttle]

actually law of cosines would be more useful, but thats beside the point

[sonic python]

To have a consistent draw order based on distances for a graphics engine. X E.

[fathom shuttle]

what are you trying to do with this?

consistent as in?

[sonic python]

I am comparing with polygons, lines, and points. X E.

[fathom shuttle]

ok but what is the draw order

[sonic python]

Draw order as in if one obscures other then it is one with lesser distance. X E.

[fathom shuttle]

arent there already algorithms for this?

[sonic python]

They are all by point. X E.

I am not doing that. X E.

[fathom shuttle]

ok

i dont know how finding average distance will help

since shapes might cross each other or only partly obscure shapes

[sonic python]

Distance is best and average of all should be most accurate of it. X E.

I would cut to parts either entirely in front or behind. X E.

[fathom shuttle]

im not so sure

[sonic python]

No need to argue over that though. X E.

[fathom shuttle]

ok well

finishing off what we started earlier, the formula would be $$\frac{\int_0^1\sqrt{\sum_{i=1}^n((var_i)_1-(var_i)p)^2+2\sum{i=1}^n((var_i)_1-(var_i)_2)((var_i)_1-(var_i)p)t+\sqrt{\sum{i=1}^n((var_i)_1-(var_i)2)^2}dt}}{\sqrt{\sum{i=1}^n((var_i)_1-(var_i)_2)^2}}$$

hah nice

[potent lotus]

me when the gbf

[fathom shuttle]

the integral is of the form $\int\sqrt{a+bt+ct^2}dt$

[potent lotus]

me when the gbf

[fathom shuttle]

i dont know if that has a proper integral

[sonic python]

Correct. X E.

[fathom shuttle]

i think youre kinda out of luck here

[bronze adder]

it does

very annoying one though

[sonic python]

Area of triangle helps. X E.

So how to do it?

What X about?

So it is unsolvable?

What about sqrt(area of triangle of line and point to compare with)?

I guess I will test that. X E.

Maybe also angles help. X E.

Well anyway, not like I expect you to know now. X E.

.close

[calm coral]

Channel closed

Closed by @sonic python

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[finite dagger]

i need help understanding how to solve this

can anyone help? i know its simple

i havent learned this yet

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[west ermine]

do eigenvalues consist of adding up or substracting up the diagonals, im confused

[glass heart]

neither

the trace is the sum of the eigenvalues of the matrix if that's what you mean

(the trace being the sum of the diagonal elements)

[west ermine]

I don’t get it

[west ermine]

Can I give u a context

On where the diagonal I don’t understand what happens

[glass heart]

yes context please

[west ermine]

Here the context is a perfect economy where it’s 1

Ax=1x

[west ermine]

But then here they just pushed away all the constants to the left and added the diagonals by 1

But in some cases I see that we - the eigen values

Minus the eigen values *

That’s what I mean by adding and subtracting

[glass heart]

Ax=1x is equivalent to (A-I)x=0 where I is the identity matrix

so A-I is A but 1 subtracted on the diagonal

which what is usually done

here they did it the other way around

[west ermine]

but in this case they added it

[glass heart]

(I-A)x=0

note that they also flipped all the other signs

[west ermine]

yes because they shifted everything to the other side of the equality

[west ermine]

so would this have worked either way

and give the same answer

[glass heart]

whether you solve (A-I)x=0 or (I-A)x=0 does not matter

its equivalent

[west ermine]

so youre telling me that i can do this

wait

this is the equivalent

[west ermine]

where i start by L1/-0.9

etc

[glass heart]

I dont know why you have (450,50,4) on the other side

[glass heart]

those are equivalent

[west ermine]

its the context

[glass heart]

if there is another vector on the other side then you also have to flip the signs of that

[west ermine]

but those are the resultants

vector resultant

not sure if thats how we say it in english

[glass heart]

you want to solve x=Ax+y where y=(450,50,4)

[west ermine]

yes

[glass heart]

you can either do that as (I-A)x=y which is what they have done

or (A-I)x=-y

[west ermine]

oh so here it would be

(-450,-50,-4)

[glass heart]

yes

[west ermine]

I see

okay i understand

ty

so in all cases where there is an equality

or a problem similar to this i should always shift it like this (A-I)x=-y or the other way

[glass heart]

its just how you would solve equations with numbers

x=ax+y you would solve either with (1-a)x=y or (a-1)x=-y

[west ermine]

kk

.close

[calm coral]

Channel closed

Closed by @west ermine

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spark coyote]

Did I do this right, I did the beginning in my head

[potent lotus]

faiyrose

[calm coral]

@spark coyote Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[brave moss]

if 3 out of 25 students are left handed, and there are 1050 students, how many possible could be left handed.

i did 3+25=28

1050 / 28 = 37,5

3 * 37,5 = 112,5

[calm coral]

Please don't occupy multiple help channels.

[runic jewel]

Why 25+3?

[brave moss]

because ratio 3:25

[runic jewel]

But it’s 3 out of 25

[brave moss]

yes if we have 25 students

in a group

at least 3 of them are left handed

[runic jewel]

Right

[brave moss]

oh yeah

we need to now expand the group to 1050

so 1050 divided by 25

[runic jewel]

Yep

[brave moss]

is

42

and so with 3

expand that by 3

= 126

@runic jewel

omg so easy

[runic jewel]

Correct

[brave moss]

.close

[calm coral]

Channel closed

Closed by @brave moss

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[stone roost]

can length AB be found out with this data?
BD or AD are not given, E or C are not middle point

[remote mural]

mb

[stone roost]

can similar triangles be used in this way?
AB/EC = AD/CD

base ratio= hypotenuse ratio

wait, but that won't help anything

[fringe swan]

why think deeply anyway

js do it the normal route

oh wait no mb

im thinking it wrong

[stone roost]

!helpers

[calm coral]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[stone roost]

<@&286206848099549185>

i actually need to find speed, I have time to cover length AB

[wooden socket]

what is written on the distances?

[stone roost]

same

[wooden socket]

and on the upper row of the table?

[stone roost]

when going and coming, distance is same (trip1 trip2) but going takes double time than coming. so I need to find ratio of speed of both trips

[wooden socket]

isnt the ratio 1:2 ?

[calm coral]

@stone roost Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wheat wyvern]

I tried doing
= 180 (10-0) + 319 (15 - 10) + ... 4151 (125 - 62)
to get 313226

but it was wrong what did I miss

[unkempt drift]

it says approximate using the data

so you need to round that

to the right number of sig figs

[wheat wyvern]

Yes, but it's an early estimate

[unkempt drift]

I'd say 3 sig figs

[wheat wyvern]

do I need to multiple the total by delta t?

I don't think so cause I multiplied each one

[unkempt drift]

no I'm saying to round your answer 313226 to 3 sf

at least try it

[wheat wyvern]

it says enter an exact number

[unkempt drift]

oh okay

[wheat wyvern]

but it didn't like 313000 also

:(

they wanted me to ignore the last data

[unkempt drift]

ohhhh

right yeah I totally missed that
yes cause you are only doing it to 62s

so the last data point for 125s is irrelevant

[wheat wyvern]

why tell me useless data

yeah

[unkempt drift]

read the question moment I guess

[wheat wyvern]

thank you though

.close

[calm coral]

Channel closed

Closed by @wheat wyvern

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tulip herald]

the continued fraction x=<1,1,1,1,...> should be clearly positive and we have that $x=1+1/x$, thus $x$ is a solution to $x^2-x-1=0$

[potent lotus]

somethingwrong

[tulip herald]

solving the quadratic equation then gives us $x=\frac{1\pm \sqrt{5}}{2}$

[potent lotus]

somethingwrong

[tulip herald]

and so the solution must be the positive root but is there anyway to to do without referring back to the original expression?

[vagrant oak]

x = 1 + 1/x has 2 sols

so you have to refer to the original expression

to eliminate one

[viscid zenith]

golden ratio mentioned

[tulip herald]

ah okay wait, its not a very smart question now that i think about it oops, x=1+1/x is just an equation that the continued fraction satisfies, doesn't imply that the solutions must be related to the continued fraction

.close

[calm coral]

Channel closed

Closed by @tulip herald

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[remote mural]

Would the relative acceleration of the block m w.r.t. to the surface it's touching (trolley 1) not be a_1 - a_2?

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

<@&286206848099549185>

[umbral lark]

?

[remote mural]

?

[calm coral]

@remote mural Has your question been resolved?

[remote mural]

.close

[calm coral]

Channel closed

Closed by @honest stream

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[mental tendon]

How did this guy get rid of ln

[mental tendon]

,rccw

[drifting seal]

$\lim_{x \to 0^+} \frac{\ln(\tan 7x)}{\ln(\tan 3x)}$

[potent lotus]

knief

[drifting seal]

this?

[mental tendon]

yes

i feel like what he did is wrong

[drifting seal]

is this your work?

[mental tendon]

this is what my friend did

[drifting seal]

🤔

[mental tendon]

idk how he got rid of ln

[drifting seal]

first, please tell them to write clearer and not write 7s like that

[mental tendon]

and idk where the -1 cmae from

[drifting seal]

oh wait

[mental tendon]

is it lhopital

[drifting seal]

yea i’d just use lhopital here you have inf/inf

[mental tendon]

ok

[drifting seal]

$\lim_{x \to 0+} \frac{\frac{7\sec^2 7x}{\tan 7x}}{\frac{3\sec^2 3x}{\tan 3x}}$

[potent lotus]

knief

[mental tendon]

so i got 7cos(3x)sin(3x)/3cos(7x)sin(7x)

do i lhopital again

[drifting seal]

yea that looks good

[drifting seal]

no you don’t need to

split the limit

[mental tendon]

how do i do that

[drifting seal]

$\lim_{x \to 0^+} \frac{7\cos 3x}{3\cos 7x} \cdot \lim_{x \to 0^+} \frac{\sin 3x}{\sin 7x}$

[potent lotus]

knief

[drifting seal]

the left limit is just substitution

[mental tendon]

oh

[drifting seal]

and the right limit is a common trig limit

$\lim_{x \to 0} \frac{\sin ax}{\sin bx} = \frac{a}{b}$

[potent lotus]

knief

[drifting seal]

you can use lhopital to verify that

if you’d like

[mental tendon]

does it matter if its 0+ or 0-

[drifting seal]

for this?

no

because for the limit to exist in the first place the right hand and left hand limits have to be equal

[mental tendon]

ok

then it would just be 1

[drifting seal]

yea (7/3)(3/7) = 1

[mental tendon]

ok

thank u so much

[drifting seal]

you’re welcome

[mental tendon]

.close

[calm coral]

Channel closed

Closed by @mental tendon

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[junior zodiac]

iii

[junior zodiac]

Is this correct

Or is this better

[calm coral]

@junior zodiac Has your question been resolved?

[calm coral]

@junior zodiac Has your question been resolved?

[calm coral]

@junior zodiac Has your question been resolved?

[calm coral]

@junior zodiac Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[smoky igloo]

Can someone help me start this?

[calm coral]

@smoky igloo Has your question been resolved?

[clear delta]

see if you can find a formula involving dy/dx

[smoky igloo]

Should I treat c as a constant or make it 1/2rootc

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[smoky igloo]

.reopen

[calm coral]

✅

[smoky igloo]

<@&286206848099549185>

[remote mural]

what?

@smoky igloo

[smoky igloo]

The above problem

I found dy/dx

But I'm not sure what to do next

[cursive bane]

After that , just write the equation in point of contact form
Let's take ( x1 , y1 ) as point of contact of tangent
From the equation calculate x and y intercept
Add them up and it should be solvable using the first equation

[remote mural]

x = 0 or y = 0

x ,y >= 0

so x = 0, y = c
y = 0, x = c

x + y = c

are you ok?

understand?

@smoky igloo

?

[cursive bane]

U calculated this from the main equation , not the tangent

[remote mural]

yah

[cursive bane]

Why tho

[remote mural]

my failure

[calm coral]

@smoky igloo Has your question been resolved?

[remote mural]

derivative:

The slope of the tangent line at a point (x0, y0) is:

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[blazing coyote]

$y'=3cx^2+e^x$
\
$y"=6cx+e^x$
\
for the double derivative to change signs, $6cx+e^x=0$ must have a solution.
\
thus $y=cx^3+e^x$ has inflection points for all those $c$ for which $6cx+e^x=0$ has a solution

[potent lotus]

A dense set

[blazing coyote]

How does this look

hmm

I could find a maxima of $-e^x/x$, on $x>0$

It would be -2

[potent lotus]

A dense set

[calm coral]

@blazing coyote Has your question been resolved?

Channel closed

Closed by @blazing coyote

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[sick owl]

for q12 am i doing something wrong?

[sick owl]

i wrote this in system of equations

[true rover]

Erm

[sick owl]

y2' = -1/16 y
y' = y2

and then i found the eigenvalues so got

so i am getting eigenvalues as 1/16 and 1

but the solution is a circle so i guess it has to be complex?

[calm coral]

@sick owl Has your question been resolved?

[calm coral]

@sick owl Has your question been resolved?

[runic nest]

@sharp cargo

[sharp cargo]

try in an empty one

this one has someone already

[runic nest]

like what

[sharp cargo]

help-40

at the very top of the helps

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[calm coral]

Please don't occupy multiple help channels.

[slate field]

.close

[calm coral]

Channel closed

Closed by @slate field

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ocean bough]

Is there a formula to count the number of integers by skipping certain steps

[ocean bough]

For example let a and b be any 2 integers
b>a

Number of integers in [a,b]=b-a+1

That's if I skip only one step

Now let a=2 b=6

Now if I skip 2 steps in [a,b] we have 2,4,6 so 3 numbers

Any formula or a good way to visualise would be appreciated

[fringe swan]

u take the higher bound and divide it by 2

if its even

if its odd tho, add one then divide it by 2

[ocean bough]

What's a bound

[fringe swan]

say we have thenfollowing inequality: a < b

a is considered the lower bound of the inequality

and b is the higher bound

[ocean bough]

Hmm

But what if we're skipping say 19 steps

[fringe swan]

now this is between us as a formula, tho its not an internationally recognized one

[fringe swan]

hm

[ocean bough]

Like what if a=-183 and b= 298 and we are skipping 19 steps

Find number of integers in (a,b)

[fringe swan]

open interval?

[ocean bough]

Yeah

[fringe swan]

ill see if i can find smt

[ocean bough]

My idea is to form arithmetic sequence

[fringe swan]

i mean

thats what i tried going for

its the obvious way

[ocean bough]

And find an < b

[fringe swan]

it works

[ocean bough]

Hmm

[fringe swan]

should work

i wonder if there is a way with euclidean division

[ocean bough]

What's Euclidean division

[fringe swan]

for all a,b are natural numbers (b≠0)

there exists (q,r) couple of natural numbers verifying:

a = bq + r

0 =< r < b

this is the definition in natural numbers tho

[ocean bough]

Division theorem

[fringe swan]

well, its euclidean division too ig

[ocean bough]

Oh

[fringe swan]

euclid found it

OH I FOUND IT

[ocean bough]

Some things are so fundamental that I forget it had to be discovered

[fringe swan]

@ocean bough

[ocean bough]

Yes?

[fringe swan]

just do b - a

and divide it by ur 19

u get the answer

i knew some arithmetic had to be involved

[ocean bough]

Let's test

[fringe swan]

ofc round it up if its not a full integer

depends how u round it up

[ocean bough]

(2,4) skipping 2

Answer should be 0

[fringe swan]

oh

[ocean bough]

But we get 1

[fringe swan]

well thats a bummer

it probably has to do with open/closed intervals

wait what it is right

there is an integer between 2 and 4

its 3

[ocean bough]

But we are skipping 2

2 then 4

[fringe swan]

2 is not included

so u cant start from 2

[ocean bough]

2 and 4 not included

[fringe swan]

this is a game of definitions now

[fringe swan]

but 3 is

[ocean bough]

I mean

[fringe swan]

u slhave to start from the first integer

in that set

[ocean bough]

We start from 2 regardless it's included or not

[fringe swan]

are u telling me there exists an integer in (3 ,4)

[ocean bough]

No

[fringe swan]

then u frankly cant start from 3

[ocean bough]

Ok I'm assuming your question is (3,4) right? Skipping 1

[fringe swan]

i wanna modify smt abt ur first statement here

its b >= a to be precise

[fringe swan]

yes

[ocean bough]

Ok so we have we move from 3 to 4 but we reject 3 and 4 it is open interval

[fringe swan]

go on

[ocean bough]

That's it

[fringe swan]

so like

was this an argument or ur trying to understand me

[ocean bough]

Yeah (3,4) is [3,4]-{3,4}

[fringe swan]

true

[ocean bough]

You would start from 3 if it were closed interval, yeah?

[fringe swan]

yes

[ocean bough]

That's what I was trying to say

So we start from a regardless

[fringe swan]

wait wut

[ocean bough]

a as in (a,b)

[fringe swan]

so like

ur with me here?

[ocean bough]

There is a big misunderstanding

[ocean bough]

I was trying to address this

We started from 2 but we have to remove it later

[fringe swan]

in ur (2,4)?

wait

[ocean bough]

Yes

[fringe swan]

u said ur skipping 1 in this interval or 2?

[ocean bough]

2

[fringe swan]

oh 2

[ocean bough]

Yes

I'm pretty sure 'skip' isn't the right term

But thanks for understanding

[fringe swan]

yeah yeah its alright bud

though i found a problem

[ocean bough]

Hmm?

[fringe swan]

skipping 1 in (2,4)

using my method u get 2

so this means theres some conditions

[ocean bough]

Your method?

[fringe swan]

the division thing

[ocean bough]

Yeah we should get 1

[fringe swan]

yeah so there are some conditions non verified

my method sucks too

what if u have [- 2 + sqrt(17) , pi + 12] this method would be absolute horror

[ocean bough]

0 my bad

[fringe swan]

safe to say, js use arithmetic sequence method

to avoid issues

i guess the method i used is certain to be correct if the interval is closed

[ocean bough]

Skipping how much?

[fringe swan]

1

going easy

[ocean bough]

Hold on

[fringe swan]

find as many integers there are

in the interval

[ocean bough]

I think it's possible

For one

[fringe swan]

might have to rely on rounding up

[ocean bough]

Yeah

[fringe swan]

so

would all this

fussin

answer u?

[ocean bough]

If a or b is negative we apply greatest integer function

Otherwise smallest integers function

[fringe swan]

what r u heading for here?

[ocean bough]

You said if a or b is decimal

[fringe swan]

yes

[ocean bough]

Pi+12 or something

[fringe swan]

yds

yes

[ocean bough]

Yeah then we apply greatest integer function for positive

[fringe swan]

oh wait i kept thinking

GCD

im sorry

greatest function wouldnt work

only works for the higher/upper bound

but the lower bound no

[ocean bough]

Oh ok

How about this

Always smallest integer function for lower bound

Greatest for higher bound

That should work

[-2.1 ,3.1]

Then we get [-2,3]

So 6

[fringe swan]

greatest integer for lower bound

smallest integer for upper bound

cause we wanna keep everything in the interval

dont get them out of it

and this technique

suprisingly works

im impressed damn

[ocean bough]

When I mean greatest integer I mean greatest integer LESS than or equal to that number

That's how it is in my country

[fringe swan]

oh shit

no u have a point

im wrong here

i forgot the definition

[ocean bough]

👍

[fringe swan]

yeah u resolved it bud

im amazed

i didnt think of it

[ocean bough]

I was wondering all this because I was amazed that there were formulae for counting numbers

10/10 would recommend

[fringe swan]

which formula?

[fringe swan]

theres always an answer to everything

[ocean bough]

[a,b] has b-a+1 integers
(a,b] or [a,b) Has b-a integers
( a,b) Has b-a -1 integers

All these are for skipping 1

Made my life easier

[fringe swan]

ohhh

yeah they do

[ocean bough]

I got greedy and I was wondering for skipping 2 or more hehe

[fringe swan]

there is no formula

so u js have to prove it

[ocean bough]

I guess I'll never need it, if I do, I'll use arithmetic mean

[fringe swan]

oh yeah

definetly

[ocean bough]

We can solve for an < b

[fringe swan]

yes

ur method works

i verified it

[ocean bough]

Ok wait

What

[fringe swan]

what what

[ocean bough]

Let's do arithmetic mean

(a,b)

So a+(n-1)d<b

N is an integer

[fringe swan]

woah woah

aye

a is not included

dont start with it

[ocean bough]

?

Nth term of an ap is a+(n-1)d

I wrote it as an

an=a+(n-1)d

[fringe swan]

u used a

ur saying a is the first term?

[ocean bough]

It should be the first term

Because we are starting with a

But we will -1

[fringe swan]

but a is excluded

[ocean bough]

Yeah

[fringe swan]

ok ill let u finish

well

unless u have nothing to finish

sparkling?

[ocean bough]

Ok

So we get for (a,b)

Ok lets start again shall we?

[fringe swan]

as u please

[ocean bough]

(a,b)

We're skipping 1

so d= 1

An=a+(n-1)d= a+n-1

And An<b

a+n-1<b

n<b-a+1

Now n is the maximum number of terms between b and a

[fringe swan]

yes

[ocean bough]

So n should be the closest integer to b-a+1

But not greater

(assuming b and a are integers)

[fringe swan]

well ur reasoning is correct

[ocean bough]

So the closest number to that is b-a

And finally we remove 1

b-a-1

[fringe swan]

uh

[ocean bough]

We needed a number lesser than b-a+1

[fringe swan]

oh wait ur demonstrating the formulas u had?

ohhh

[ocean bough]

That's b-a

[fringe swan]

i was lost

no no

i got it

[ocean bough]

Yeah

So now assuming b-a is not integral

[fringe swan]

what does this mean

[ocean bough]

Not an integer

[fringe swan]

oh

okay

[ocean bough]

We just apply greatest integer function to (b-a)

[fringe swan]

sure

sounds right

[ocean bough]

(-pi, pi)

Should get 5

No

[fringe swan]

yes

[ocean bough]

6

[fringe swan]

what

[ocean bough]

-3 included

3 also included

Hmm

[fringe swan]

then....

[ocean bough]

So 7 😭

[fringe swan]

its 7

LMAO

[ocean bough]

Yeah

[fringe swan]

YOOO

[ocean bough]

Let's just apply formula and check

[fringe swan]

smts not right

[ocean bough]

Yeah we get 6 in formula

[fringe swan]

well actually

the formula works for a,b are integers

for our case, greatest integer(a) - smallest integer(b) + 1

is the way to go

because they become included

[ocean bough]

Yeah...

[fringe swan]

so it turns into

closed interval

so we go back to the other formula

[ocean bough]

-1

[fringe swan]

+1

[ocean bough]

For open it's -1

[fringe swan]

thats for open

when the bounds

are integers

in our case, (a,b) where a and b are irrational

the amount of integers in (-pi, pi) is the same as the amlunt of integers in [-3, 3]

we turned it closed, u see?

[ocean bough]

Ohhh

Correct

[fringe swan]

soooo

3 -(-3) + 1

is 7

yep

[ocean bough]

I think it's best not to just try to find a formula for everything 😭

Some things we have to do in steps

[fringe swan]

no this one has a formula actually

[ocean bough]

And do what we know

Like we did for (-pi,pi)

We converted it into a problem we know

[fringe swan]

to find the amount of integers in (a,b) where a and b are not integers, we do greatest integer(b) - smallest integer(a) + 1

this is actually a formula

[ocean bough]

Let me check it

[fringe swan]

works for (a,b) or [a,b) or (a, b] or [a,b]

[ocean bough]

Oh

Yeah

Makes total sense

As it becomes some sort of closed bracket problem

[fringe swan]

yuppers

[ocean bough]

Good point to remember

[fringe swan]

is this all for ur questions?

[ocean bough]

Yeah, thanks a ton, Youssef

[fringe swan]

no needa mention it bud

[ocean bough]

👍

[calm coral]

If you are done with this channel, please mark your problem as solved by typing .close

@ocean bough Has your question been resolved?

Channel closed

Closed by @ocean bough

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[swift laurel]

id:customize

try pressing the "subscribe me to pings" button twice

you can also customize roles in #info

or use ,iamnot Helpers

[potent igloo]

@raven nest if all else fails

[swift laurel]

it seems to be gone now

[potent igloo]

Congrats. You are now deaf to <@&286206848099549185>

Blue for active and very active. Green for helpful (not to be confused with the helpers role), and purple for donor

[swift laurel]

color roles are determined by activity level. so you get a blue role for being active, another blue role for being very active, a green role for helping a lot in help channels/forum, and purple for server boosting

[eternal shard]

the pre last is a lie

[hollow totem]

Yeah they actually only give out the green role to people who are really hot

[remote mural]

[limpid nebula]

Wait can I get a role

Helpful maybe

[potent igloo]

It needs to be earned

Display a consistently helpful nature. Guiding people with their homework problems and help them understand concepts

[limpid nebula]

I have thousands of msgs of me helping ppl

[eternal shard]

i am top 3 and look at me

[limpid nebula]

Damn

Wait so what’s the min msgs for helpful

Also how do ik my rank

[potent igloo]

Its not a message count

[eternal shard]

I will just say to stay careful, cause there are people who won't like you for who you are

It is not a matter of earn

They pick specific people who fit in their world view

[calm coral]

@fathom ivy Has your question been resolved?

[potent igloo]

You need to have a noticeably positive impact on the community. You need to be actively helping in a way that is

1. Effective. Your help must be useful and actually providing guidance
2. In conformance with the server rules. You need to display an openness to helping and generally should offer a positive attitude. Being hostile or simply sharing solutions will not get you the role. The idea of the helpful role is that you are basically a mentor for people
3. Reasonably advanced. At minimum, a strong understanding of calculus is when you start to get noticed. But this rule is extremely subjective. I’m sure there are helpful here who don’t know calculus

The exact way to become helpful is an internal process. If you want it, just keep putting in quality work and you’ll be noticed.

I was never seeking the helpful role. I didn’t even know it was a thing. I just want we to help people learn. That’s kind of the mentality you need to earn it

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[drowsy sand]

guys please help its 1am and i have a test tomorrow

[ocean bough]

Translate?

[drowsy sand]

almost everything inside the brackets translated wrongly

[ocean bough]

Cap means 'and' right?

[drowsy sand]

where do you see cap

[ocean bough]

Upside down V

[drowsy sand]

ahh

yeah

[ocean bough]

What does Y|8 even mean

[drowsy sand]

thats what i dont know

[ocean bough]

Y such that 8?

[drowsy sand]

i have no clue tbh

[ocean bough]

Is this a homework question or you're practicing?

[drowsy sand]

practice

[ocean bough]

For the test

Okay

Wait

[drowsy sand]

i was supposed to have the test a long time ago but some kids were sending bomb threats to school and its been delayed till tomorrow

[ocean bough]

Kids? That's crazy

Anyways

,rotate

[ocean bough]

Does this make sense?

A is a subset of P

So AUP is P

[drowsy sand]

wait

[ocean bough]

A intersection P is P

[drowsy sand]

yeah thats right

but how to get b

[ocean bough]

I have no idea, you better worry about other questions

[drowsy sand]

i went through everything else

[ocean bough]

You ought to ask your teacher before the test

[drowsy sand]

nah not possible

is this right

[carmine sorrel]

x|8 means x divides 8

so x is a factor of 8

[drowsy sand]

so

wait

1, 2, 4, 8,

[ocean bough]

Then B= {1,2,4,8}

[drowsy sand]

yeah

thanks

also i forgot how to do this

[ocean bough]

B\A is difference?

[drowsy sand]

yes

what does 'x' do

[ocean bough]

Cross product I would assume

That's how it is usually in sets

Doesn't make much sense tho

[calm coral]

@drowsy sand Has your question been resolved?

[drowsy sand]

i just got it

for example A={a,b,c}, B={1,2}
AxB={(a,1), (a,2), (b,1), (b,2), (c,1), (c,2)}

ok im set for my test tomorrow

thanks

[ocean bough]

Gl

[drowsy sand]

https://tenor.com/view/flight-does-he-know-faded-gif-11697106329231392146

thanks

.close

[calm coral]

Channel closed

Closed by @drowsy sand

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tough star]

A bag contains 6 red and 4 green marbles. Three are drawn randomly without replacement. What is the probability that the third is green given that at least one of the first two is green?

Cases (GRG, RGG, GGG)

((4/10)(6/9)(3/8)) + ((6/10)(4/9)(3/8)) + ((4/10)(3/9)(2/8))

Why is this not the answer?

[tough star]

anyone?

[mental tendon]

draw a tree diagram

[tough star]

the highlighted ones r the good cases

[mental tendon]

yes

and label the probability

for each case

[tough star]

case of GRG
((4/10)(6/9)(3/8))

case of RGG
((6/10)(4/9)(3/8))

case of GGG
((4/10)(3/9)(2/8))

right?

[mental tendon]

yes

[tough star]

when i add them up

i get 7/30

but thats not the correct answer

its 7/20

[calm coral]

@tough star Has your question been resolved?

[calm coral]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[raven crest]

@calm coral

[raven crest]

I need help on the following number theory question:

<@&286206848099549185>

[calm coral]

@raven crest Has your question been resolved?

[rapid cliff]

hint: y = 1/x <=> x y = k n (mod n)

The inverse of 3 (mod m) is the number x such that 3x = km for some interger k.

what have you tried?

[amber bolt]

yeah it bascially jumps at you

something times 3 is 1 more than some multiple of 6n+2

shuba misspoke

[calm coral]

Channel closed

Closed by @raven crest

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[abstract wasp]

solve for a

I cant get a clear answer online

[eternal shard]

Factor a

[abstract wasp]

ah

right

...

.close

[calm coral]

Channel closed

Closed by @abstract wasp

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[whole shuttle]

hello guys

[whole shuttle]

lets say i have a bunch of points on a cartesian plane

and together those points look like a quadratic

how can i get the equation for this curve

[unkempt drift]

how many points are there?

[whole shuttle]

like a lot

[unkempt drift]

okay is using technology fine then?

like you can find the best-fit quadratic on Desmos

[whole shuttle]

those points won't fit perfectly into a quadratic equation

yes

[unkempt drift]

https://www.desmos.com/calculator/bmzpdtieov

here's an example

of course your case is probably messier

[whole shuttle]

are there any other ways of doing this

without using technology

[unkempt drift]

yes but if you are in high school this is beyond your knowledge

[whole shuttle]

crap

[unkempt drift]

is this for an internal assessment?

[whole shuttle]

i'm working on a math project which is modelling the trajectory of tennis serves

[whole shuttle]

yes

[unkempt drift]

okay then

[unkempt drift]

basically you should just pick three points from your data

and fit a unique quadratic between these three points

[whole shuttle]

i don't get it

[unkempt drift]

you don't get how to do that?

[whole shuttle]

wdym three points

[unkempt drift]

yeah, choose 3 points from your data

3 (x, y) values

[whole shuttle]

do they have to be consecutive

[unkempt drift]

no

[whole shuttle]

or can they just be three random ponts

ok

[unkempt drift]

yeah like you should graph your points first

look at the graph and choose 3 points that look like they will fit well

[whole shuttle]

what should i do after this

[unkempt drift]

then sub in each of these (x, y) values into y = ax^2 + bx + c

you will get 3 linear equations in a, b, c

[whole shuttle]

whats the next step

hang on

[whole shuttle]

wdym 3 linear equations

oh wait

never mind

[unkempt drift]

a + 2b + 3c = 4 and so on

[whole shuttle]

and how can i turn this into a quadratic

[unkempt drift]

if you solve for a, b, c, you know the quadratic cause it's just y = ax^2 + bx + c

[whole shuttle]

oh right

[unkempt drift]

https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_1e_(OpenStax)/07%3A_Systems_of_Equations_and_Inequalities/703%3A_Systems_of_Linear_Equations_with_Three_Variables

here are some examples

[whole shuttle]

so i just solve a b and c with the simultaneous equation

[unkempt drift]

yes

[whole shuttle]

is there a name for this method?

[unkempt drift]

I'm not sure if there's an exact name but it's super common

tons of places do maths investigations and so a lot of people will have done an investigation on quadratics

https://sites.math.washington.edu/~conroy/m120-general/quadraticFunctionAlgebra.pdf

[whole shuttle]

what about cubics

[unkempt drift]

oh this is a special case of Lagrange interpolation

works for all polynomials

[unkempt drift]

now you sub in 4 points, then you will have 4 linear simultaneous equations in a, b, c, d

[whole shuttle]

oooohhhh

yeah i get it

[unkempt drift]

for y = ax^3 + bx^2 + cx + d

then for a degree n polynomial it's (n + 1) points

you get the idea

[whole shuttle]

yep

[unkempt drift]

cause a cubic has 4 free variables

[whole shuttle]

can i use this method for this curve?

rn i'm using a piecewise function

[unkempt drift]

you have to use two polynomials

yeah cause it's piecewise

[whole shuttle]

ok

[unkempt drift]

it can't be expressed as a single polynomial cause of the sharp turning point

[whole shuttle]

ok

thank u so much

this is very helpful

.close

[calm coral]

Channel closed

Closed by @whole shuttle

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ripe mountain]

is there a reason they did it in this order? multiplying the middle and second last one first?

[ripe mountain]

i multiplied the first two, then multiplied that by the last one

got a diferent answer but not sure if i messed something up or if i'm just missing something

[ancient thistle]

the order shouldn't matter

you'll get the same answer either way

so at least one of you have made a mistake

[ripe mountain]

gotcha

thank you

.close

[calm coral]

Channel closed

Closed by @ripe mountain

Use .reopen if this was a mistake.

[calm coral]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.