help-0

[ionic jewel]

no

i just told you it was side length cubed

not LxW

LxW is the area of a rectangle

[errant bear]

oh

trey if a channel already has a question with a conversation your not supposed to make another question

[ionic jewel]

oh i see i misread the question a bit

[errant bear]

you have to read the how to get help

[ionic jewel]

for the first one it asked for a generic formula

which is LxWxH

length times width times height

thats the volume of a cubiod (or a cube)

[errant bear]

so if everything is 10 LxWxH would be 1000

[ionic jewel]

yes

10^3

[errant bear]

ok

[ionic jewel]

thats not the answer for the first one

but it is an answer for one of them

[errant bear]

ok

[alpine sable]

could someone please dm me to help

[ionic jewel]

no

[errant bear]

you have to go to different question and ask for help read the how to get helo

help

[ionic jewel]

no ones going to dm to help anyways

anyways vibe

whats the answer to your first question?

anyways vibe

oops wrong order

i already helped

the triangles are similar

use similar triangle properties

[alpine sable]

how would i do that?

[ionic jewel]

i cant really do much more without literally giving you the answer

[alpine sable]

i mean

[errant bear]

look it up

[alpine sable]

i would appreciate it lmao

[ionic jewel]

hm

lemme give you the setup

$a(QS) = RS$ and $a(SP) = ST$ and $a(PQ) = RT$

[ocean seal]

bunny

[ionic jewel]

where a is some number you have to solve for

@alpine sable

[alpine sable]

ok ty

[south rain]

hello, can someone help me solve the system of equations:
0 = y^2 - 2xy + 9
0 = -x^2 + 2xy - 9

ive been trying different ways

but i keep ending up with y^2 = x^2

but that cant be because the main question is asking me to find critical points

[ionic jewel]

if you add them together you get y^2 = x^2

[south rain]

and there are two of them but y^2 = x^2 makes it infinite

yeah i know but that cant be right

like the answer from my book says the critical points are (-3,-3) and (3,3) from solving this

[ionic jewel]

huh

[south rain]

but that equation implies its infinite

[ionic jewel]

yeah wolfram gives the answers

[south rain]

but how do you end up with that?

y^2 = x^2 implies that there are infinite solutions of x and y, but if you check, the wolfram answer is indeed correct because only those two points satisfy the equations above

i just dont know how you come to that

trial and error? that would take infinite time tho..

[ionic jewel]

oh its probably some factoring

(y-x)(y-3) or osmething?

[south rain]

hmm didnt think of that

[ionic jewel]

no doesnt work

no idea lmao

weird

[south rain]

that does sound better than nothing ill be honest with you

i guess xd

since you have that (y-3) part

i mean honestly if you check the 3d graph of the function, which is f(x,y) = (x-y)(9-xy)

the graph is super super weird

[ionic jewel]

maybe quadratic equation on both

[south rain]

ill try that

[ionic jewel]

[2x \pm sqrt((4x^2)-4(9))]/2

$\frac{2x\pm\sqrt{4x^2-9}}{2}$

[ocean seal]

bunny

[ionic jewel]

nah doesnt simplify either

[south rain]

its fine imma have to ask my prof tbh

[ionic jewel]

yea

[south rain]

thanks for the help

[noble sinew]

Cant you just isolate y for example?

So y=(x^2+9)/2x

sub that in

0 = ((x^2+9)/(2x))^2 - 2x*(x^2+9)/(2x) + 9

solve that

,w 0 = ((x^2+9)/(2x))^2 - 2x*(x^2+9)/(2x) + 9

[ocean seal]

Results provided by WolframAlpha

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

Requested by ScapeProf#9427

[south rain]

where did you get that?

[noble sinew]

Isolated y in 2nd equation you posted

[south rain]

oh right

oh i see now

hmm thanks!

[ionic jewel]

hmm

why does that work but adding them doesnt

[ornate reef]

Could somebody help me with this?

A garden was originally 20 ft by 23 ft. If both dimensions are decreased by the same amount, the area of
the garden will be decreased by 120 ft^2. Find the dimensions of the new garden.

[ionic jewel]

(20-x)(23-x)=(20)(23) - 120

[ornate reef]

tysm

[noble sinew]

All adding them together does is you then get an equation which defines the plane you get will contain your solution

[ionic jewel]

thats the entire plane

not very useful

[noble sinew]

can contain inf many solutions

like here

[ionic jewel]

yea but why does it do that

i was taught that adding them together works

eg that would break linear algebra since its dependent on doing that

[oak chasm]

@ionic jewel The area decreases by 120, so you should have the original area minus 120.

[ionic jewel]

oh yea

guess my intuition for solving equations is off

[tawny lion]

Guys, this isn't as much a question but I really need several props/practice worksheets about geometric proofs including:

The Midpoint Theorem
The Intercept Theorem
The Alternate Segment Theorem
The Intersecting Chords Theorem
The Tangent-Secant Theorem

If anyone may have such Pdfs

or know where to find them

[spring harbor]

Google is probably your best friend

[tawny lion]

yeah,, tried that but to no avail

[alpine sable]

Can someone help me in graphing inequalities

<@&286206848099549185>

[alpine sable]

khan academy?

[tawny lion]

@alpine sable looked through, nothing there regarding practice

found some videos but

[alpine sable]

It had an explanation on it

Can someone help me

https://brilliant.org/wiki/power-of-a-point/

i need help with b

[alpine sable]

please ask in an unoccupied channel

[alpine sable]

some geometry problems in bmo1 use these

ok sorry

[tawny lion]

bmo1?

[alpine sable]

Who knows graphing inequalities?

british maths olympiad round 1

[jovial spear]

can anyone help meout with this??

[alpine sable]

I do

[alpine sable]

Can u help. Me

Sure

[alpine sable]

ask in an unoccupied channel, this one is in use

I have like 10 questions @alpine sable

So dms?

Ye

Who can help me in graphing inequalities

<@&286206848099549185>

Ugh

@pearl wraith

Nope

My hw

[topaz wharf]

Can someone help me with this?

[cold roost]

It looks like the question is asking for $ John Lee’s saving account made through interest only

[topaz wharf]

@cold roost How would I approach the question

[cold roost]

Well you’re given the principle ($1566), the interest rate (5.5% / yr), and the amount of time of which that interest will accrue you’re trying to find (3 months, 1/4 of a year)

[topaz wharf]

Is there a formula I should use?

[cold roost]

Trying searching formula for compound interest, but I don’t think you necessarily need it

I’m not trying to be rude, but do you know how interest works? It’ll help you understand the question a lot easier

[topaz wharf]

No I don't really

[cold roost]

So in this case, when you save money, you generally earn money by having it multiplied by a very small percentage.

So if I were out $10,000 in the bank and they gave me a 10% interest per year , I would have $11,000 at the end of the year.

[topaz wharf]

Oh

OH

So since its 3 months

I just take 1556

And try to find the interest rate in 3 months with that percentage?

Or?

[cold roost]

The interest rate is fixed, you can’t change it only the amount of time it’s invested

[hollow crag]

hi

[topaz wharf]

What would the working out look like?

[hollow crag]

ok who speak spanish?

[cold roost]

You would want to find how much it would be for 1 year, and then multiply it by 1/4. Since that would represent 3 months of investing at a 5.5% rate / year.

[lean quarry]

I mean we can think as (x)¹²-(x+0.55)⁹

Or

[hollow crag]

The slope of the line that passes through the points P (3, -9) and Q (5, -2) P (3, −9) and Q (5, −2) is:

oh men i am in an exam xd

[lean quarry]

(1556+5.5/100)³

[hollow crag]

plis help

[lean quarry]

Or

Try

Y2-y1/x2-x1

What what s the rest of the question

@hollow crag

[hollow crag]

is no more question

[cold roost]

Please go to a free channel

[lean quarry]

Did you say to me ?

If it s for me I just gave my opinion

And why

[hollow crag]

The slope of the line that passes through the points P(3, -3) y Q(-7, -9)P(3,−3)yQ(−7,−9) es:

a) y= 3/5

b) y= - 1/3

c) y= - 3/5

d) y= 1/3

help

[cold roost]

I was referring to the other user, but I don’t think your function equation is correct either way. @lean quarry

[swift widget]

Hello! Can someone please explain HOW i find the common denominator here

and how it gets like this

I cant use a calculator

[glass lichen]

well the common denominator is 48 since 3 and 2 are factors of it

[swift widget]

yes

[glass lichen]

3*16 is 48 and 2*24 is 48

so that's why 16 and 24 appear

[swift widget]

OOOOOOOOOOOOOOOOOOOOOOH

xd

hahaha thanks... im tired

[pseudo steeple]

Whats half of 2+2 .-.

[glass lichen]

use a calculator

[pseudo steeple]

Alr

0

[stiff moth]

my question is this graph has two turning points right? So it could be classified as a cubic function if we had to?

[alpine sable]

the function can only be classified as a cubic function if it is of the form ax^3+bx^2+cx+d for constants a b c and d

[glass lichen]

it's not a cubic since the red part is constant

it's a piecewise

[alpine sable]

yeah no polynomial would act like that

[stiff moth]

yeah i know but i have to create a single function to represent all three equations

which im struggling with

[glass lichen]

yeah, so you're gonna need a piecewise function

[stiff moth]

yeah but i cant use that

[glass lichen]

well then you cant make a function

[alpine sable]

can you send the problem?

[stiff moth]

here let me send a ss of what was said when i asked for clarification

yeah

ill send a ss

this is the clarification i recieved

[alpine sable]

it wants you to model the pieces with a polynomial function and determine the degree?

[stiff moth]

yeah basically

[alpine sable]

do you have equations for the red, blue, purple parts?

[stiff moth]

yeah

[alpine sable]

yeah there's a bit of a problem

its impossible to model all of these with one polynomial function

[stiff moth]

well fuck

oh sorry

[alpine sable]

because the second derivative of this piecewise function isn't continous

[stiff moth]

frick*

okay so is it the constant thats a problem?

im not too familiar with derivatives

[stiff moth]

ngl am a likkle confuse d

[alpine sable]

so if you take the derivative you get something that's not differentiable at the point x=8

[stiff moth]

and thats not good?

[alpine sable]

look at the second derivative

[stiff moth]

oh

[alpine sable]

see that jump from y=0 to y=2?

[stiff moth]

yeah

[alpine sable]

if the first bit was a polynomial, then the second derivative would be continuous

but the second derivative has that jump, so the first bit can't be a polynomial

[stiff moth]

so the constant is making it impossible for a single poly to represent the piecewise

if i just skip the constant and use the next three polynomials that i used in the piecewise that shouldnt be an issue right

[alpine sable]

oh wait

they don't want an exact fit

they just want something thats kinda close

its impossible to get an exact fit but you can model a cubic that will be kinda close to that piecewise function

[stiff moth]

and i would do that by using the model of a cubic and plugging points into the graph i already have of the first three parts?

[alpine sable]

yeah just choose 4 points on the graph

cubic regression

[stiff moth]

okay ill try that, could i ping you when i finish to see if i did it right?

[alpine sable]

also you have a bit of a gap in your rollercoaster

[stiff moth]

yeah thats not too safe, thanks ill fix that right now

[alpine sable]

https://www.wolframalpha.com/input/?i=cubic+regression&assumption={"F"%2C+"CubicFitCalculator"%2C+"data"}+->"{20.9%2C+23.2%2C+26.2%2C+26.4%2C+16.3%2C+-12.2%2C+-60.6%2C+-128.9}"&assumption={"FVarOpt"}+->+{{"CubicFitCalculator"%2C+"data2"}}

enter 4 points here to generate a cubic function that goes through all 4 points

[stiff moth]

ideally id put the two turning points plus an x int right?

okay thank you

[alpine sable]

can somone help with that

[glass lichen]

That is a white square

[alpine sable]

rectangle

https://drive.google.com/file/d/1MxWt1jVWEe7RJJBu03pM0x5QwYV0jdwE/view?usp=sharing

[glass lichen]

ok well what do you need help with..?

[alpine sable]

the pattern

[glass lichen]

so you filled out the chart?

[alpine sable]

no

idk what the pattern is

[glass lichen]

Ok so what have you done so far?

[alpine sable]

wait

nvrm

just found it

im a fricken bumbas

but i need help with the equation

[glass lichen]

Ok so every increase in ticket is an increase of how many dollars?

[alpine sable]

x9

[glass lichen]

yes, so the slope of the relationship is 9

[daring chasm]

i mean you could do it approximately

[glass lichen]

so c=9t+a, but a is clearly 0 since 9=9(1)+a

[alpine sable]

so its c=tx9

or c=9t

[daring chasm]

you'd want to choose your points carefully tho - in a uniform point distribution the polynomial will oscillate more and more towards its edges

[stiff moth]

yeah thats what im trying, i just plucked some points from the graph that i had and plugged it into a cubic formula ,, am now just using system of equations to solve. most pieces i think should be represented??? minus the constant portion ofc

the points specifically are two points that i believe are the turning point and i unrestricted the last equation to find the x - int, the 4th point was just a random one

[daring chasm]

the way to fix it is to make the points nearer the edge of the range closer together - more specifically, the chosen points should be $\frac{a+b}{2}+\frac{b-a}{2}\cos(\frac{\pi{k}}{n})$ where $k \in {0,1,2,...n}$

agh im shit at latex lol

[finite valve]

ive become... kind of addicted to it

[stiff moth]

lmao thats okay, i was bound to be confused either way

[ocean seal]

Deleted User

[stiff moth]

latex notation is too much for my single braincell

[finite valve]

i mean...

[daring chasm]

you can just look at the formatted output lol

[finite valve]

once you can memorize certain parts you get a rhythm almost

[sly mantle]

\{\} @daring chasm

${x}$

[ocean seal]

RokabeJintaro

$\{x\}$

[stiff moth]

lol im confused about what you just outputted ngl

[finite valve]

like at the start it took me half an hour to get this correct

now i can quite easily do stuff like this

[sly mantle]

$\left(\frac{z_{\alpha/2}\sigma}E\right)^2$

[stiff moth]

bruh yeah, i think ive used texit once in my life and it was for straight up text and i still messed up

[ocean seal]

RokabeJintaro

$\left(\frac{z_{\alpha/2}\sigma}E\right)^2$

[finite valve]

$$n = (\frac{(z_{\alpha/2})(\sigma)}{E})^2$$

[ocean seal]

GameSkipper

[finite valve]

i mean

[sly mantle]

you left out left/right

[finite valve]

i was way too lazy to do that

but i can do it sure

[daring chasm]

this is how you should choose the points: $\frac{a+b}{2}+\frac{b-a}{2}\cos(\frac{\pi{k}}{n})$ where $k \in {0,1,2,...n}$\linebreak
a and b are the left and right limits\linebreak
n is how many points you want (the more points, the more accurate itll be)

gah

[sly mantle]

they adjust brackets depending on size of inside stuff

[finite valve]

$$n = \left( \frac{(z_{\alpha/2})(\sigma)}{E} \right)^2$$

[ocean seal]

GameSkipper

$$n = \left( \frac{(z_{\alpha/2})(\sigma)}{E} \right)^2$$

[finite valve]

ye

[ocean seal]

Deleted User

[daring chasm]

:V

[sly mantle]

ono

[finite valve]

ope

what happened there

[daring chasm]

justified alignment

[finite valve]

ah yea

[prime grove]

can someone explain xor

[finite valve]

the gate?

[daring chasm]

exclusive or - outputs 1 if they're different, but if they're both the same, that is, 0,0 or 1,1, it outputs 0

yeah that

[finite valve]

truth tables!

[stiff moth]

yeah they are

[oak chasm]

@prime grove If there are an odd number of trues, it's true. If there are an even number, it's false. With only two inputs, it's true if the inputs are different.

[prime grove]

oh i get it ty

[oak chasm]

No problem.

[stiff moth]

the truth table just brought up blocked memories from robotics, i cant 😔

[alpine sable]

6. During a movie the film projector broke. The manager refunded the money to the people watching. Each ticket costs $6.00. Let p represent the number of people watching. Let r represent the total amount of money refunded. Write an equation that relates p to r.

[prime grove]

6p =r ?

whats the difference between negation and converse

[charred flint]

negation is negating both clauses

converse is reversing them

[alpine sable]

?

[prime grove]

6 * p(number of ppl watching )= r(total money refunded)

unless the problem isnt what i think it is

[alpine sable]

yes

[prime grove]

do u understand y

[alpine sable]

no

[prime grove]

each person paid 6$ to watch the movie. if we represent all of the people who paid to watch the movie with p, then people paid p x 6 dollars to the theatre. while the people were watching the movie, the projector broke and the manager had to refund the people. we know that each ticket costs 6 dollars so we know that 6p or p x 6 represents how much p paid and it also represents the money refunded (r). since 6p = r it's the relation between p and r

that's an overkill explanation but some parts might be confusing

[alpine sable]

i get it

so its 6p=r

[prime grove]

ye

would this be e and 7?

[charred flint]

uh oh

[pseudo steeple]

Wat is a fee 😫

[prime grove]

e confirms the statement and 7 confirms the contrapositive?

well not confirm but idk the right word

if the card is not an even number, then it wont have a vowel on the other side

[charred flint]

this is a little tricky because you have to try to disprove it

if (false statement) then (statement) means nothing

er yea you're right, E and 7

[prime grove]

why is it 7 though

my reaosning was using the contrapositive

also idk why this still confuses me 🤦‍♂️

[charred flint]

because 7 on one side vowel on the other would disprove it

yea the P implies Q chart is really weird

[alpine sable]

does this look correct so far

[charred flint]

post the image lol

[alpine sable]

https://drive.google.com/file/d/1ey2UUpTaAyKSIqQQ51hUTkJ0q3C3W6XI/view?usp=sharing

press the image

[charred flint]

oh you want it as y=...

[alpine sable]

like this y=x-3

[charred flint]

yea

[alpine sable]

ok thats what i had at first but than i changed it

thank you for clarifying

[sly mantle]

a usual way to give intuition is, when i say 'if P then Q', the only case where i'm a liar is if P is true but Q is false

[alpine sable]

• looks like a biology problem
• you sure this isn't a test?

This is classwork

And yes it’s biotechnology

[sly mantle]

@alpine sable don't multipost

[alpine sable]

Sorry

[alpine sable]

Can you help?

[glass lichen]

what's preventing you from asking in the biology disc?

[alpine sable]

google is your best friend

Gotcha

[alpine sable]

Didn’t know about it

[tawny lion]

https://cdn.discordapp.com/attachments/704422075732983871/832707280775806996/Capture.PNG

how do I do this

if anyone couild help id be grateful

[charred flint]

doesn't look possible

[prime grove]

proteomics

thought that was common sense

genome - study of genes
proteonome - study of proteins

wait

ohl dup

[glass lichen]

I mean if you study something then it's common sense. But learning something isnt common sense

[prime grove]

oh specifically proteases

[alpine sable]

Nope it was degradomics

[prime grove]

degradomics i think it is called

[alpine sable]

Yep

I already answered it and got it correct

[prime grove]

lol

what bio class r u takin

[alpine sable]

Intro to biotechnology

[prime grove]

dang ap bio (american college bio in hs) is really washed down man

[alpine sable]

Yea that’s true

I mean I took biology two years ago and now I’m taking biotechnology

does this https://drive.google.com/file/d/1mWNTjnIfRpD3kXWoyy5Y-87yEfIMSExG/view?usp=sharing go with this

[tawny lion]

<@&286206848099549185>

[red sail]

anyone know what the equation would be?

[alpine sable]

would be B

the function starts at 0 like 2sin(x) does

but 2sin(x) starts at 0 and then goes up to 2

we it to go down to -2

so the function would be -2sin(x)

[red sail]

oh okay ty, so here it would be

@alpine sable

[alpine sable]

no, because it starts at 0 and then goes up

would be A

[red sail]

so if it goes down it is cos and if it goes up it is sin?

well ty that's all my questions huge help answering them

[alpine sable]

that's not right

think of (cosx, sinx) as the point on the unit circle you reach after walking x radians counterclockwise on the unit circle starting from the point (1,0)

[abstract sundial]

Is this right

[gray isle]

no

[abstract sundial]

Damn

How do I get the right answer

[gray isle]

sub x=-2

[abstract sundial]

-8?

[frail grove]

How many ways can you store 4 books in 3 drawers?
How is this equal to 3^4?
Can someone explain plz

<@&286206848099549185>

[abstract sundial]

Thanks

[alpine sable]

Books and drawers are all distinct right

So we can put book#1 in drawer number 1, 2 or 3

So we have 3 choices for where to pick book 1

Independently, we have 3 choices for where to put book#2

It can go in drawer 1,2,or 3

3 choices for books #3 and #4 by the same logic

And these are all independent of each other i

In total we have 3*3*3*3=3^4 ways

[frail grove]

But why multiply?

Why not 3+3+3+3

[alpine sable]

Imagine you have 3 choices for what color shoes you wear, 3 choices for what color pants you wear, 3 choices for what color shirt you wear, and 3 choices for what color of hat you wear

You have 3*3*3*3 possible ways to customize your outfit

Does that help?

[frail grove]

Here's what's blocking me, there are 3 drawers each holds up to 4 books so the first drawer can hold 4 books, same for the 2nd and the 3rd so there's 4×4×4 ways

[alpine sable]

The drawers are like the colors

Lets say we have colors red blue and yellow

So having all 4 books in drawer 1 is like an outfit with all 4 pieces that are colored red

4 books and 3 drawers

Each of the 4 books can go into one of the three drawers

[frail grove]

Can it be written like this?

[alpine sable]

No

It splits into 4 then 3 then 2, whats the rationale for that

This diagram is for a different problem

Lets go back to the clothes example, but pretend we have 2 outfit pieces

So the shirt can be red blue or yellow and the hat can be red blue or yellow

Make a table of all the different combinations

The answer is 3*3 not 2*2*2

[frail grove]

Yeah that's a good idea, tysm for your effort 🙏

[alpine sable]

Np

[knotty sleet]

What's the intuition behind matrix determinants being the area of parallelogram/volume of parallelepiped and so on for higher dimensions?

As in why does the particular algorithm for computing determinants result in these areas/volumes?

[alpine sable]

3b1b had a good video on that in his essence of linear algebra series

[knotty sleet]

Yeah I've watched it but

It didn't make the connection with the formula

He basically defined the determinant as that

He showed it for 2D geometrically, but it's not clear how it would generalise

[alpine sable]

Yeah thats true

I can't help you there

I guess you could do a similar geometric proof in 3d, but it'd be kinda messy

and >3d is tough to think about

[knotty sleet]

Yeah :((

[prime grove]

lol the questions here really range from all levels of difficulty 😭

[abstract sundial]

how do I solve this

[alpine sable]

3

i just traced it up

[abstract sundial]

thank you

[alpine sable]

Guys I need too know what I got wrong

On my physics practice

[manic quail]

look at which intervals the slope of the graph is positive.

[alpine sable]

Isn’t it all of them

Except 8to 9

And 9-10

[limpid spade]

'Faster' shouldn't the graph rise when it's faster?

[alpine sable]

No right

[manic quail]

It should rise.

That is what it means for the slope to be positive.

[alpine sable]

So it’s

9-10

4-5

0-3

2*

[manic quail]

0-2, 4-5, 9-10

[alpine sable]

@manic quail

I chose that

On my first attempt

And got 1/3

@manic quail

[manic quail]

That should be right, I might be confused though, @alpine sable

[alpine sable]

How do I do this

It’s a velocity vs time graph

[manic quail]

yes, you are looking when the acceleration is positive, @alpine sable

[limpid spade]

Replace x with 2

[manic quail]

@alpine sable just plug in x=2

[alpine sable]

So how did I get it wrong lol

[alpine sable]

Thanks

[manic quail]

I still think it isn't wrong, but it is nearly 1 am, so what do I know, @alpine sable ...

[ornate hinge]

Remember that velocity is a vector. If i am not mistaken 9 to 10 seconds is technically slowing down as the object is going from a negative velocity (think of a car reversing) to stationary.

Velocity vs time graphs can be confusing but they way I remember the difference of velocity is that if the line is moving away relative to the x axis the acceleration is increasing (even if the line is moving away in the negative y).

[alpine sable]

@ornate hinge still confused at

So which once’s is it

@ornate hinge so would it be 8-9

Because its moving away from the line

[ornate hinge]

Yes

Think of 5 to 8 seconds as a car slowing down to a halt and 8 to 9 seconds as the car accelerating in reverse.

@alpine sable

[alpine sable]

How do u do this

[sinful pike]

check the slope of the graph (f(4)-f(3))/4-3=-2 and notice that if x=0, y=8. then it's y=8-2x, remember that the general equation it's y=(slope)x+(height at x=0) (one way to do it)

[stiff vortex]

how do i solve this

<@&286206848099549185>

[queen wing]

Don't ping helpers right away please. They don't sign up for that.

[sinful pike]

i have a solution but it's kinda annoying and unpractical to do, you could check the slope every two pairs and see if any of the solutions have two identical slopes as in first triangle

probably there's a better solution

[night sinew]

i'm verifying trig identities. in this problem, i had difficulty verifying from the right side as opposed to the left side, and was told to better start from the left side, which got me the right answer. but i want to understand why start from the left side and not the right? and how to determine which is the best side of an equation to start with when proving it's identity

[queen wing]

You can simply draw those triangles. It's really quick to do.

[wet gorge]

I am trying to show:

$|\frac{-4z^2}{e^z-1}| > 1$

[ocean seal]

dangles

[wet gorge]

for |z| < 1

I expand the bottom out, and break up the top a bit, and end up with this:

$4 |\Sigma_{n=1}^\infty z^{-n+2} n!|$

[ocean seal]

dangles

[wet gorge]

and now I am actually a bit confused, because it looks like this is just trivially > 1 regardless of z, because n! will grow faster than z^n?

But obviously e^z in the denom should take over at some point and make that first fraction less than 1

Have I made a mistake somewhere?

[alpine sable]

what is the equation of a line that passes through (2,2) and (4,8)

anyone know???

<@&286206848099549185> help please

[pearl wraith]

find slope

so m= y2-y1/x2-x1

m= 8-2/4-2

m=6/4 = 3/2

now put that into slope point form

[alpine sable]

thanks

[pearl wraith]

remeber that its y-y1=m(x-x1)

so only use (2,2)

[alpine sable]

so 2,2 is point one and 3,2 is point 2?

[night sinew]

<@&286206848099549185>

[pearl wraith]

yes

(2,2) is x1 and y1

[coral pagoda]

You can go in either direction, but the goal of these exercises is to use identities to get from one side to the other

Often times starting from the RHS is a little trickier because the equation tends to be a little more simplified.

[night sinew]

i see

then, it's possible to start from the right side

it would just be more difficult of course

[coral pagoda]

100%

[night sinew]

is there a way to know which side to start first? some kind of indication? or just try to always start from the lhs

[coral pagoda]

For instance, it's a lot easier to see $\frac{x^2+2x+1}{(x+1)}$ simplifies to $x+1$, but it is a bit less clear that you can write $x+1$ as [ \frac{x^2+2x+1}{x+1}]

[ocean seal]

dackid

[coral pagoda]

If you are using math lab, they tend to always start from the LHS. That's usually a good rule of thumb to work with

[night sinew]

yeah this makes a lot of sense, sometimes you can miss certain things

alright, perfect

thanks alot

[coral pagoda]

You betcha

[vale tundra]

Can anyone help me with this question pls?

[alpine sable]

sketch a picture of a positive decreasing concave down function

decreasing means 1st derivative is negative

concave down means 2nd derivative is negative

simplest example i can think of would be the right half of a downwards-facing parabola

[vale tundra]

Oki let me do that

[alpine sable]

here's an example of such a function

[vale tundra]

So for a i got left> right

Idk how to do the rest

[alpine sable]

@vale tundra so F is the integral of f?

[vale tundra]

Hmm

[woven shuttle]

y is this a spoiler lel

[vale tundra]

So in b both would be =

And the average rate for [6,17] is < than [6,13]

Let me know if i am thinking about this correctly

[true geode]

What does converge to a number mean?
Does it go to that number at infinity or does the sum of the series equal that number?

[ancient pike]

well it depends

[timid quest]

How can i answer this one?

[vale tundra]

This channel is occupied

[ancient pike]

both sums and series can converge

a sum can only converge if a series converges to 0

[vale tundra]

This channel is occupied
@timid quest @ancient pike

@true geode

[ancient pike]

it's been 20 minutes man

[alpine sable]

GUYS HOW TO FIND THE OUTLIERS

[ancient pike]

how long are you gonna keep the channel to yourself

[vale tundra]

This channel is occupied

[alpine sable]

LIKE I WANT A FUCKING FORMULA

oh

sorry

[vale tundra]

I have not gotten my question cleared

[true geode]

@ancient pike where can i show u the question any other channel?

[vale tundra]

<@&286206848099549185> Can anyone help me with b and c

[alpine sable]

Literally use questions-1-9

[prime grove]

if p and q are false, why doesnt q imply p

[oak chasm]

It does. F -> F = T.

[oak chasm]

Yes, that's a mistake there.

[prime grove]

wow

thanks again

🙂

[vernal zealot]

Does anyone know how I should set up this equation?

I thought it would be s + the increase possibly?

sorry if this is a super basic question

[oak chasm]

@prime grove See https://www.wolframalpha.com/input/?i=p+is+false%2C+q+is+false%2C+q+implies+p.

@vernal zealot How do you write something increasing by 2% in algebraic form?

[vernal zealot]

I thought it would be s + x or? but i'm still pretty confused

[oak chasm]

Well, to increase by 2%, you start with 100% and add 2% to get 102%.

[vernal zealot]

or like

[oak chasm]

And 102% in decimal form is 1.02, right?

[vernal zealot]

Yeah so would I add that instead?

[oak chasm]

Nope.

You start out with x*100%. You add x*2%.

You start out with that because 100% of x is x.

Then, you add 2% of x.

[vernal zealot]

so how would I actually write that though into a linear equation?

[oak chasm]

So, you get 102% x.

How do you write 102% in decimal form?

[vernal zealot]

1.02 but they want me to write the equation not just the single value?

[oak chasm]

Right, so it's 1.02 times whatever.

Now, let's look at your instructions.

[vernal zealot]

1.02 * s?

[oak chasm]

Yes, that would be last year's salary increased by 2%.

But we want an equation. What goes on the other side?

What's the amount of last year's salary increased by 2% in dollars?

[vernal zealot]

I don't know I think s was just suppose to represent that right

[oak chasm]

s is last year's salary, right?

What do you know about this year's salary?

[vernal zealot]

I think so and that it was increased by 2*

2%*

[oak chasm]

Well, check.

What is s defined as in the problem?

[vernal zealot]

so do you put 1.02 on the other side?

[oak chasm]

Guessing isn't going to solve this.

[vernal zealot]

It's defined as the last year's salary right?

[oak chasm]

Right.

What do we know about this year's salary, looking at the problem?

[vernal zealot]

that it increased the first salary by 2%?

[oak chasm]

Right. What else?

[vernal zealot]

that it's a part of 100%?

[oak chasm]

Where does it say that in the problem?

[vernal zealot]

Oh I thought you said that

[oak chasm]

That doesn't say anything about this year.

I asked what the problem says.

It says it's 2% more than last year's salary, which you said already.

What else does the problem say?

[vernal zealot]

to model the change with an equation?

[oak chasm]

That's not about this year's salary.

What else does it say about this year's salary in the problem?

[vernal zealot]

that it's annual?

[oak chasm]

Right. What else?

[vernal zealot]

that its 39,780.00?

[oak chasm]

Right.

So, it's 2% more than last year's salary and it's also $39780.

What's the variable for last year's salary?

[vernal zealot]

S

[oak chasm]

And how do we write 2% more than s?

[vernal zealot]

by subtracting the orginal amount to find the last amount than add the 2%?

but I don't think that's very linear actually

[oak chasm]

No, first you write an equation, then you solve it.

How do we write 2% more than s?

[vernal zealot]

oh 2% > s ?

[oak chasm]

No, different "more than".

What's 2% more than 1?

[vernal zealot]

3?

[vale tundra]

Oh well

[oak chasm]

You think that 2% is the same as 2?

[vernal zealot]

well no sorry its 0.2 so that would be 0.3?

[oak chasm]

No, it isn't.

[vernal zealot]

oh okay? what is it then? sorry i've barely had math classes my entire life so

[oak chasm]

Percent means per one hundred, which means divide the percentage by 100.

So, what's 2% in decimal form?

[vernal zealot]

0.02?

[oak chasm]

Right.

Now, when you say 2% more than something, you start out with that something, which is 100% of what you started out with, plus 2% of what you started out with.

100% of something is 1 times something, which is that something.

[vernal zealot]

oooh I see so it always start's with three digits because your starting from 100%?

or maybe I don't see

[oak chasm]

Sorry?

[vernal zealot]

So do you start it with 0.00 if your thinking 0% then if adding a another 1% go up to 0.01 percent?

[oak chasm]

Not when you're increasing something by a percentage.

To do that, you start out with something, which is 1 times something, which is 100% of something.

100% of a cake is the entire cake.

[vernal zealot]

oh so the 100% is determined by the item?

and not like a fixed scale?

[oak chasm]

It's a multiplier.

[vernal zealot]

like a half of a water bottle would be 50%?

[oak chasm]

100% of whatever is the whole thing.

It would be 50% of the water bottle, which means multiplication.

0.5 times the water bottle.

[vernal zealot]

can you show that in equation form?

[oak chasm]

Sorry?

[vernal zealot]

I guess you kinda did but with words? maybe that will help

[oak chasm]

It's a quantity, not an equation.

50% of a water bottle is a quantity, it's not really an equation.

[vernal zealot]

oh you can't put the quantity into an equation? but like there has to be a 0% to the water bottle right?

or how would it decrease?

[oak chasm]

You can use it as part of an equation, but it's like saying turn 1 into an equation.

What would that mean?

How would you turn the number 1 into an equation?

It's not an equation, it's a number.

[vernal zealot]

so it's just a value and so does that mean it has to be in a type of variablist enviroment to be considered an equation?

like if I wanted to add half to the water bottle I would display that in equation form?

[oak chasm]

No, you need something to be equal to something else to have an equation.

A number is just a number, not a statement that two things are equal.

[vernal zealot]

kind of like the problem I have now where it has the 2% increasing the s?

[oak chasm]

With that, you have an equation.

[vernal zealot]

That's what I meant

[oak chasm]

Look again at what you know about the current year's salary.

[vernal zealot]

adding to the water bottle

[oak chasm]

You know that it's 2% higher than the previous year's salary. You know that it's also 39780.

So, those numbers will both be the present year's salary, so they're equal.

Since you have two things equal to each other, you have an equation.

[vernal zealot]

How would I display that then?

[oak chasm]

Well, to increase something by 2%, you start off with 100% of that something, then you add 2% of that something.

100% s + 2% s

Added together, that's 102% s.

And how do we write 102% in decimal form?

[vernal zealot]

1.02

[oak chasm]

So, we have this year's salary as 1.02 s and as $39780.

So, those two expressions are equal.

Does it make sense how we increase something by 2%?

Starting with 100% of that something and adding 2% of that something?

[vernal zealot]

so do you have have the 100% of that something to add?

[oak chasm]

Sorry?

[vernal zealot]

Oh wait I think I might be getting it what your saying i think that s is already at 100%?

[oak chasm]

You're increasing a value by 2%.

That means to start with 100% of that something and then add 2% of that something.

[vernal zealot]

would that mean that like a 1 would be 100% of itself?

[oak chasm]

Yes, something is 100% of itself.

[vernal zealot]

ooo okay

[oak chasm]

100% is equal to 1 in decimal.

[vernal zealot]

wow that makes me feel whole inside realizing that

[oak chasm]

And when you multiply something by one, you get that something.

So 100% x = 1 x = x.

100% of a cake is that cake.

[vernal zealot]

what if you chop it?

and it's a super tasty angel cake

[oak chasm]

Then the pieces will be less than 100%.

[vernal zealot]

what if they started out without the rest of the 100%

[oak chasm]

Not sure what you mean by the rest of the 100%.

[vernal zealot]

If the pieces were just made without the chopped at the start of there existence would it be still less than 100%?

then if it was chopped be less than 100% since it reverts the base percentage?

[oak chasm]

If part of the whole cake is missing, yes.

If the pieces add up to the whole cake, you still have 100% of the cake there.

[vernal zealot]

Oh okay cool so does that mean like conjoined twins where clashed together use to be only 100%s of themselves but then when the other was added 200%?

[oak chasm]

No idea.

[vernal zealot]

I mean if it stems from that idea maybe sorry very interesting every time I learn a basic thing in math my mind starts spinning in off directions

[oak chasm]

Oh, OK. Let's go back to your problem.

You know what 100% of something means, I think. The next part is what it means to increase by 2%.

It means you add 2% of that thing.

You have 100% of something plus 2% of something.

[vernal zealot]

oh so like 2% of the first cake

[oak chasm]

Right.

[vernal zealot]

lil tiny piece placed on top

[oak chasm]

So, you have 102% of the cake.

In decimal, that's 1.02 cakes.

Which is 1.02 times a cake.

[vernal zealot]

oooOOOh i see it better now because its one cake that's why the 1 in the front is there

[oak chasm]

Right. You have the 100% because you're not losing any of the original cake.

You're increasing it.

[vernal zealot]

1.02 * 1.02? since were increasing it by a whole cake?

[oak chasm]

No, 1.02 times a cake.

[vernal zealot]

like the 2% of the cake?

[oak chasm]

We're only increasing it by 2% of the cake.

Not by a whole cake.

[vernal zealot]

okay

so 1.02 * 0.02?

[oak chasm]

Nope, 1.02 times cake.

[vernal zealot]

times cake?

[oak chasm]

Right. Take a cake, add 2% of another cake, you get 1.02 times a cake.

Also known as 1.02 cakes.

[vernal zealot]

okay so that is the way to display the process then?

[oak chasm]

Yes, so we have last year's salary increased by 2%.

So that's 1.02s.

We also have $39780.

[vernal zealot]

100% s + 2% s ?

[oak chasm]

They're both this year's salary, so they're equal.

Yes, that's right.

[vernal zealot]

or 1.00 + 0.02 ?

[oak chasm]

Right, times s.

[vernal zealot]

1.00s + 0.02s?

[oak chasm]

Right, which is 1.02s.

So, that's this year's salary, right?

[vernal zealot]

Yeah it's the result of the increase from the past salary

[oak chasm]

I'd recommend simplifying it by combining like terms.

OK, and $39780 is also this year's salary, right?

[vernal zealot]

oh so just 1.02s?

[oak chasm]

Right.

[vernal zealot]

yeah I think so I don't think they would have s display as the past salary if it wasn't

[oak chasm]

Well, it says the salary "is" $39780, which is present tense.

[vernal zealot]

cause than we would already have the value to substitue i think

[oak chasm]

So, since it's present tense, it's the current salary.

[vernal zealot]

Yea!

[oak chasm]

So, we have 1.02s = $39780.

[oak chasm]

Since both sides are the same number (this year's salary), they're equal.

[oak chasm]

Yes, it doesn't like commas.

Try $39780 or 39780 on the right.

[vernal zealot]

yay!

Thanks for your patience with me Chai

[oak chasm]

You're welcome.

[vernal zealot]

and also helping me learn basic things about existence

[alpine sable]

For any x>0 theres an y such that y^2 = x

is this true?

[oak chasm]

@alpine sable Well, solve for y.

[alpine sable]

My conclusion is that it always true, is this correct?

[oak chasm]

Yes.

[alpine sable]

Thanks

[oak chasm]

No problem.

[alpine sable]

If T is the transpose function for all real 2 by 2 matrices then what would be the eigenvalues and characteristic polynomial

For T

T just does transpose for any 2 by 2 matrix u give it

Should I just put a,b,c,d for the entries, transpose, and find the eigenvalues for that?

[woeful pulsar]

yeah you can do that

[alpine sable]

I feel like I'm overcomplicating this problem

[ionic jewel]

no that's the right approach

the characterisric polynomial is

(a-t)(d-t)-bc

you can solve for eigenvalues by multiplying out then using quadratic formula

[alpine sable]

Wouldn't A^T = lambda * A

So the entries would be a_ij = lambda * a_ji

[ionic jewel]

what

[alpine sable]

And a_ji = lambda * a_ij

It would just give lambda^2 = 1

[ionic jewel]

i have no idea what's up with the lambdas, but this part is right

what's the transposed matrix?

a_ij=a_ji

[carmine ermine]

Hey can anyone help me with the concept of derivatives?

I don't get how we could find how much a function is increasing at an instant

like at one point

how could we know how much a function is increasing

[vale wigeon]

the gist is that we never do that directly

are you familiar with the concept of average rate of change?

like, over an interval

[carmine ermine]

Yes

[vale wigeon]

yeah so when you evaluate the derivative of a function at a point

[carmine ermine]

Average rates of change actually have a difference that we can visualize

Like for ex, 3 to 6

[vale wigeon]

what you're really doing (in a sense) is taking the average rates of change over progressively shrinking intervals

[carmine ermine]

we can visualize the distance and length

[vale wigeon]

and looking at what those approach, if indeed they approach anything

[carmine ermine]

Hm

OHHHHHH

[vale wigeon]

that's what the formula $$f'(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x) - f(x)}{\Delta x}$$ is saying --- the expression in the limit is actually just the average rate of change of $f$ over $[x, x+\Delta x]$

[ocean seal]

Ann

[carmine ermine]

so technically

we're not actually finding the rate of change at one instant

but rather finding what the average rate of change of shrinking intervals are leading to

[vale wigeon]

essentially yeah

[carmine ermine]

Ahh alright

Tysm

One more question...

what do they mean by in respect to x?

I once got the meaning years ago

But I heard it being used in a way that confused me

[vale wigeon]

with respect to x

anyway you usually hear that in multivariable calculus when the function has two or more variables as input

and you need to say which one we think of as changing

[carmine ermine]

Oh

But like

if an algebraic problem says

solve in respect to x

Then..?

[vale wigeon]

that's a misnomer

i'd say solve for x

[carmine ermine]

if something says the derivative in respect to x

[carmine ermine]

Ohh alright

Tysm Ann!!!

[vale wigeon]

yw

[sturdy glen]

if i have a parametric equation for a plane

$x + y + 2z = 0$

[ocean seal]

Joseph S

[sturdy glen]

how do I find the normal vector for this plane?

[vale wigeon]

this is not a parametric equation

the normal of a plane whose equation is in this form can be read off the equation

the coefficients on x, y and z are the coordinates of your normal

[late spade]

Is 6 multiplied by root 6 = 0 ?

[vale wigeon]

in your case, [1, 1, 2]

@late spade no.

[sturdy glen]

weird, my lab says it's a parametric equation

[vale wigeon]

are you sure it says that, joseph

[late spade]

Ok thanks

[sturdy glen]

probably just a typo

ok that would make more sense. thank you

[echo pawn]

how would I go about estimating an antiderivative from points?

I've got four points, and one point representing the antiderivative, and I'm supposed to estimate the rest

[ionic jewel]

make a function for the base function then integrate?

i mean you could try estimating the area under the curve but that's kinda sus

[ionic jewel]

.

[echo pawn]

yeah I've got no clue, I'll save it for later and try what you suggested

math makes me so irrationally mad lmao I need a brain breather

[vale wigeon]

[ionic jewel]

my second answer is probably what they are looking for

[vale wigeon]

this looks weird af

[ionic jewel]

^

[vale wigeon]

where did this come from

[echo pawn]

this is part of a calc 2 exercise

[vale wigeon]

great can you show the exercise

in its entirety

[ionic jewel]

hey i was probably right

[vale wigeon]

idk what kind of "reasonable" underestimate they're looking for, but what you can say is:
f(t) ≥ 1 for t ∈ (0,3]
f(t) ≥ -2 for t ∈ (3,6]
and f(x) ≥ -3 for t ∈ (6,9]

these bounds cannot be improved with the problem as-stated

thus we have $\int_0^3 f(t) \dd{t} \geq 3$, $\int_3^6 f(t) \dd{t} \geq -6$ and $\int_6^9 f(t) \dd{t} \geq -9$

[ocean seal]

Ann

[echo pawn]

just processin this in my head

that's the weird part is by "reasonable underestimate"

do they mean within a certain range or

rhetorical question but

yeah

[vale wigeon]

i don't know

for all we know the function could look like this

[alpine sable]

how to solve cos(sinx)≥0

[vale wigeon]

channel busy please move

[echo pawn]

yeah, there's no indication as to what's between the points in the original function/table

there's straight up not enough information imo

[vale wigeon]

there is enough information for a lower bound

[echo pawn]

but not upper

[vale wigeon]

which is what they ask of you

you can make an upper bound too

gimme a moment to sketch it up

you can consider a function like this

no this channel isn't free

[echo pawn]

oh true since the upper limit would be the y value of the point preceding

so how was the upper limit estimated again? since we havent got the original function

[vale wigeon]

well the function is bounded above by 3 on (0,3), by 1 on (3,6) and by -1 on (6,9)

by virtue of f being decreasing

[echo pawn]

ah duh, makes sense

[alpine sable]

i determined the point A and B
but i dunno what to do next

should i apply (x-x1)/(x1-x2)=(y-y1)/(y1-y2) to determine the equation?

[vale wigeon]

if you want?

i mean like

you need the coords of the points 1/3 and 2/3 of the way from A to B

[alpine sable]

no i mean will it be accurate?

oooh yeah im so frekin dumb

didnt notice the word trisection until now lol

anyways thanks

[quiet lantern]

can someone help me with this

[quiet lantern]

<@&286206848099549185>

[noble sinew]

Where are you stuck?

[vale wigeon]

may i suggest considering sum (n+1)x^n instead?

may be a bit more suggestive

[quiet lantern]

@noble sinew I did

(k-1)x^k - x^k-1 - x^k-2 - ...... -x^2 - x

[turbid narwhal]

occupied?

[quiet lantern]

@turbid narwhal oui

i guess the question is a bit difficult

[alpine sable]

is there an easy way with which i can solve these equations to find A,B,C,D?

[vale wigeon]

well this is a linear system, so yeah it will be easy-ish

[noble sinew]

Would recommend induction on k

[quiet lantern]

idk how to use the bot here 🤔 @ocean seal

[finite valve]

the TeXit i can help with, at least, enough. 😄

[river minnow]

Can anyone help me with this one question

I don’t know the area

[quiet lantern]

is there problem with the answer i gave 🤔

@river minnow occupied

[finite valve]

no no

[noble sinew]

You are missing some (k-2),(k-3)... terms in 1st line? And why would x+x^2+...+x^k=0?

[alpine sable]

i might be late but divide the nonagon into other shapes and calculate

2 triangles and 2 trapeziums are possible

[stuck veldt]

"If a function f is continuous in [a,b] and f(x)/=0 for all xε[a,b], prove that it takes only positive or only negative values"

I suppose it needs Bolzano's theorem? Its a theoretical exercise under that chapter but it doesn't include an answer. Thanks in advance

[rigid smelt]

yes, also known as intermediate value theorem

[lethal vortex]

can anyone give me a hint on how to solve this

[gray isle]

what topic is this supposed to be?

that notation is a bit ambiguous

[lethal vortex]

its composite functions

i am doing some exercise books and tryna

get used to this

[gray isle]

ahk

$g(g(x)) = 4x - 15$

[lethal vortex]

any idea where i can start with that

[ocean seal]

ℝamonov

[vale wigeon]

||calculate g(g(x)) in terms of a and b||

[lethal vortex]

i understand that but talking about the ggx

[fading zephyr]

a poly is equal to another if each term is equal

[vale wigeon]

expand and simplify a(ax+b)+b

[fading zephyr]

so the composition gives you two equations

and you have 2 variables

[lethal vortex]

so i need to do (ax + b)^2 ?

[fading zephyr]

not at all