help-0

[kindred lion]

We haven't been taught telescopic sum yet so can you like do it in a simpler way if possible?

[true crystal]

Have you seen fraction decomposition ?

[kindred lion]

Yeah

[true crystal]

Decompose 1/((2k+1)*(2k+3))

[kindred lion]

Okk

[true crystal]

then you'll notice something

Which is really nice if this is the first time you see it

[kindred lion]

I got 1/2(2k+1)- 1/2(2k+3)?

[true crystal]

Yeah that is right

[kindred lion]

Yeah okk

[true crystal]

Now explicit the first terms

[kindred lion]

1/4k+2 and 1/4k+6?

[true crystal]

No I mean replace k by 0, 1 etc

[kindred lion]

Oh ok got it

Ok what after it? Replaced by 0 got 1/6, with 1 got 1/10

[alpine sable]

GP i see

[true crystal]

by 0 you get 1/2 * (1 - 1/3) by 1 1/2 * (1/3 - 1/5) by 2 1/2 (1/5 - 1/7) etc

If you sum all these terms what happens ?

[alpine sable]

answer = 20 ²⁰⁄₂₁

is this correct if u have the anwer key?

[kindred lion]

Cancellation right?

[kindred lion]

Yeah it is

[alpine sable]

hi all am i missing something here

[kindred lion]

Thanks for the help!

[ancient bear]

https://cdn.discordapp.com/attachments/751114204307783798/867471170097512468/20210721_202026.jpg

What am I doing wrong?

the problem

the answer

I get a 1/2 in front of that

[true crystal]

@kindred lion are you sure the answer is not 40 / 21 instead ?

[kindred lion]

No the answer key shows 440/21

[true crystal]

400 / 21 is a pretty big number for the sum

and I got 40 / 21

[kindred lion]

It's not in the options

[true crystal]

Yeah but to be sure it is 2 times 2 /3 etc

[kindred lion]

Hm yes

[true crystal]

Wolfram gives this too

[alpine sable]

$test$

[kindred lion]

Should the number be 22 instead?

Shouldn't**

[true crystal]

Why ?

[kindred lion]

Number of terms are 10 so basically should be 22 rather sorry

[proper ibex]

Is there an elegant way of making an area drawer given some equation that can give true/false if you pass it a position?
While one can just go through every single point out there, i'd assume theres a better way

My assumption was first randomly select a point that is "in" the shape that the function would create, and then go in one direction until you hit a border, at which point go along the border until you come back where you started, but this happens to ignore "islands of false" inside the shape

(This is all talking about a solution by code btw)

[ionic jewel]

look up monte carlo simulation, specifically monte carlo definite integrals

its basically just passing in all the points, but theres some clever approaches

[proper ibex]

So theres no way of avoiding passing all points

[ionic jewel]

like I said, theres tricks

you can do a uniform grid of point checking over the entire area, then guess based on that for example

or spread out around each one in the area to get more accuracy

its how they calculate definite integrals sometimes, look up the techniques, its plenty fast

[proper ibex]

Also the wiki seems to be talking about getting an area from it

I simply want to check integer positions

Its not for getting the shapes area, its about getting a polygon (set of points describing said shape)

Well i suppose i could use said algorithm of random points and look for a spot inside the known shape where the function is dangerously close to being false, and investigate a small area around that point

Anyway, thanks

[light quartz]

how do i find the derivative of log(secX/2)

the uh udv - vdu rule?

[alpine sable]

For derivatives use the chain rule

[light quartz]

is it same as the quotient rule?

I'm not getting the answer for this one

[glass lichen]

It's chain rule...

[light quartz]

[glass lichen]

look at your notes or google it if you dont know it

[alpine sable]

Yeah it’s fairly basic

If you meant integral instead, it looks like a really difficult one

[acoustic swift]

f(g(x)) = f(g(x))' * g(x)'

[alpine sable]

It’s more like f(g(x))’ = f’(g(x)) * g’(x)

[light quartz]

maybe I'm wrong but I dont recall my teacher teaching that one

[acoustic swift]

Learn it, it's useful but more important, very necessary

and easy

[proper ibex]

Arent some integrals straight up impossible or something

You end up in loops

[alpine sable]

Yeah, i just checked that one on wolfram alpha and it looks intense

[alpine sable]

Anyway, for your question the differential is equal to 1/(sec x) * tan x sec x

Oops i missed the /2

[proper ibex]

Huh the integral curve doesnt freak out

Must be the work of the log

[light quartz]

Why am i getting Tan x

as the answer

just tanx

[alpine sable]

Yes my thing above simplifies to tan x

[light quartz]

oh

[alpine sable]

I got my math confused

Soz

[light quartz]

Oh it's fine

I'm getting it as

[glass lichen]

some dont have elementary primitives, yes

[alpine sable]

It’s 1/(sec x /2) * 1/2 tan x sec x

So tan x

[light quartz]

2/secx X (secxtanx - 0)/4 now

[glass lichen]

$\dv{x}\ln(\frac{\sec(x)}{2})=\dv{x}\ln(\sec(x))$

[ocean seal]

Mosh

[glass lichen]

the 1/2 is irrelevant

[light quartz]

lemme see

[alpine sable]

Right you do the log thing mb

[light quartz]

now i'm getting 2 tan x

[alpine sable]

Wait how

Just delete the 2 it’s irrelevant

[light quartz]

I definetly made a mistake here

[light quartz]

but you take the derivative of log right

which is 1/x

in this case 1/(secx/2)

[alpine sable]

If you didn’t get it, ln (x/2) = ln x - ln 2

[glass lichen]

$\dv{x}\ln(\sec(x))=\tan(x)\sec(x)\frac{1}{\sec(x)}$

[ocean seal]

Mosh

[alpine sable]

And ln 2 is a constant

So you ignore the denominator

[light quartz]

but it's a part of the log function

[alpine sable]

But you can rewrite it to remove it

[glass lichen]

$\ln(\frac{x}{2})=\ln(x)-\ln(2)$ so differentiating will get rid of the constant term

[ocean seal]

Mosh

[light quartz]

Sec x/2 tho

[alpine sable]

It’s (sec x) / 2

[glass lichen]

unless you fucked up writing it out originally...

[alpine sable]

Yea lmao

[light quartz]

,w derivative Log ( (Secx)/2)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Π I K#4100

[light quartz]

[glass lichen]

yeah..

[light quartz]

i am so sorry

i messed that up

[alpine sable]

That’s how you learn

Please, can anyone help with this?

It’s the least common multiple

What else am I supposed to add?

ASA?

[spice canyon]

For a I think you also have you say they have AD in common

[alpine sable]

Hm, okay

[spice canyon]

b I don't Know ,did'nt even Know sides could be congruent

[alpine sable]

yeah i’m not sure

been trying to complete this for a while now

[jovial ether]

hey

is this channel in use

or can i ask my question

[alpine sable]

Just try another, easier

my question wasn’t completely answered so i’m not sure if someone else can

so i believe yes it is

@alpine sable Maybe you can mention that the kite is symmetric

Or that AD and BC are perpendicular

[jovial ether]

because the kite is symetrical

he can use the angle bisector

thing

and he gets two angles from those

and they share a side

so he gets his last from there

so its SAA right?

[alpine sable]

Is it SAA or ASA

How do I solve for x

27x + 2 = 180-70

assuming the lines are parallel

[celest anvil]

how do you find the transition point?

[alpine sable]

by transition point do you mean the points where it switches from decreasing to increasing and viceversa?

[sand mica]

I assume it means finding the vertex of maximum / minimum point(s), so yeah

[alpine sable]

Yeah you're right, I don't know what else it could mean

[celest anvil]

idk either

so it's max and min points?

[sand mica]

your's sounds more right because I realized it's a cubic

[alpine sable]

I guess how you find them depends on how you've been taught to

[celest anvil]

Transition points are points where the basic shape changes due to a sign change in either 𝑓′ (local minimum or maximum) or 𝑓″ (point of inflection).

[alpine sable]

Oh you have differentials

Just find their roots

[celest anvil]

roots of the original function?

[alpine sable]

of the derivatives

[celest anvil]

1st and 2nd?

[alpine sable]

yes

[celest anvil]

ok thanks

[cursive sorrel]

Does anyone know the rules for reflection like for reflecting points over a line?

[alpine sable]

https://martin-thoma.com/reflecting-a-point-over-a-line/

If you don't get that you can ask again

[cursive sorrel]

No that's the advanced version of what I am learning

I have started with the basics

I just need to know the rules

There are like 4 or 5 of them

[alpine sable]

I don't really know how you're learning it

You got any notes?

[cursive sorrel]

Here's an example of one of the assigments I have to do

[alpine sable]

oh I guess you're doing it graphically

[cursive sorrel]

I need to know the rules

[cursive sorrel]

Ye

[alpine sable]

to reflect a point over a line, draw another line from the point perpendicular to the first line

then extend it past the line by the same distance it took to get from the point to the line

I'll draw you an image

[cursive sorrel]

I think it is easier knowing the rules

[alpine sable]

haha these esoteric rules of yours intrigue me

But this is the best I could come up with without an appeal to formulae

[cursive sorrel]

Ok thanks

[cursive sorrel]

It's like if you are doing across y axis (x,y) turns to (-x,y)

It's some really basic rules to follow in order to make solving these kinds of problems easier

I was introduced to them in class

I should have noted them down somewhere

[alpine sable]

Sorry this is in use

Oh I thought it was finished, apologies.

Np

[true crystal]

btw Pazerx it is correct

[alpine sable]

In that case you also have that reflecting across the x axis turns (x,y) to (x,-y)

[alpine sable]

Thank you for verifying.

[cursive sorrel]

Yeah, see what are the rule?

That is one of the rukes

[alpine sable]

And across the diagonal (-x,-y)

But I’m just deriving these from what you’re telling me

[cursive sorrel]

Yes I believe those are correct

[alpine sable]

You should ask about the rules in class next time, i imagine they’ll be more helpful

[cursive sorrel]

but before I go and loose points, lemme confirm with my teacher tommrowo and then submit the assigment

Alright?

[alpine sable]

Yea go for it

[cursive sorrel]

Yes they will be

Thanks for your help doe

[alpine sable]

Anytime

[marsh valley]

$x^3 + 4x > 5x^2$

[ocean seal]

BAAPA|INDIAN ELITES

[marsh valley]

so we got that it has to be greater than 4 but idk the other answers

We first factored out x

then factored and got

x(x-4)(x-1)>0

and we know x>4

but idk what to do next

<@&286206848099549185>

[alpine sable]

don't ping helpers before 15 minutes

[marsh valley]

oh shoot

sorry

[alpine sable]

dw

anyway, figure out the roots and see what sign the equation takes between them

[noble sinew]

Either all terms need to be positive or two terms negative and one positive for product to be positive

All positive is the x>4 part

[marsh valley]

Thank 😄 , ill let u know what i get

But I already knew that and now I am stuck again

[noble sinew]

Find when two of them are negative and 1 positive

[marsh valley]

How would you find them?

[noble sinew]

For x to be negative x<0, for (x-4) to be negative x<4 for (x-1) to be negative x<1

So the solution is?

[marsh valley]

uh

[noble sinew]

If x>=4 none are negative so that won’t work. If x>=1 only one is negative so that wont work either

If x<1 then two are negative wuhuuu

When does it stop working?

[marsh valley]

Ohh my god

wait wait

[noble sinew]

If x<=0 all three are negative so that doesn’t work

So 0<x<1?

[marsh valley]

but

i thought x<4

[noble sinew]

What?

[marsh valley]

so 0<x<4

[noble sinew]

If x=3 then we have two positive and 1 negative term

Don’t we?

[marsh valley]

yeah

but u need 2 neg

[noble sinew]

So x=3 doesn’t work

[marsh valley]

yeah

[noble sinew]

So 0<x<4 is not a solution

Clearly

[marsh valley]

but 0<x<1 isnt

[noble sinew]

0<x<1 is a solution?

[noble sinew]

Both x>4 and 0<x<1

You said x>4 yourself

[marsh valley]

oh lol

[alpine sable]

Can someone help i dont remember these like the explanations

"If the first differences are the same, the relationship is"

and

"If the first differences are not the same, the relationship is"

[ionic jewel]

arithmetic, non-arithmetic (although the only one of this kind you likely know is geometric, so that might be the answer)

[deep pivot]

Could someone tell me how I can make a plot similar to this one? It should basically be a line but at equal intervals it flattens out for a set width and then continues on its old path

[alpine sable]

is this right?

[deep pivot]

the vertical lines are axually gaps

actually*

[alpine sable]

yup

[alpine sable]

I don't know tbh, only idea I have is to make a big piece wise function lol

but that seems unintuitive

[dark granite]

like @alpine sable said, this is correct. This is because the thing you marked is saying run/rise which isn't the slope

[alpine sable]

hopefully someone can save the day

[deep pivot]

I'm trying to make an sdf for a dashed line

[alpine sable]

sdf?

[deep pivot]

signed distance field

[alpine sable]

yup no idea what that is

sorry

I got a

I just need b and c

Pls

[alpine sable]

just add up all the sides you got to get the perimeter

[ionic jewel]

you add all the side length together for perimeter

yea

[alpine sable]

and do you know the formula for right triangle area?

hint: like taking half the area of a rectangle/square

help?

dependent variable changes because of a change in the independent variable

in this situation what change in smth will affect the other

[dark granite]

You can think about it @alpine sable in terms of cause and effect. The independent variable is the cause, the dependent variable is the effect

[alpine sable]

yea that's a better explanation for it

you got the answer @fathom cosmos?

[fathom cosmos]

um

i have a question

[alpine sable]

yea I saw you deleted it lol

[fathom cosmos]

can we go into dm?

[alpine sable]

uhh I like here better unless it's an emergency

[fathom cosmos]

ok

so how do i check the slope on desmos

i mean

[alpine sable]

you'd need the slope to graph

[fathom cosmos]

does rhombus have slopes?

[alpine sable]

that's a shape

wdym slope?

[fathom cosmos]

so

ok

[alpine sable]

are you graphing a rhombus?

[fathom cosmos]

this is the question

Sammy and Pippa's teacher gives them a homework question to solve. She tells them to plot the points A(5, -1), B(9, 4), C(15, 1) and D(11, -4) on a grid and decide whether the shape is a square or a rhombus. Sammy and Pippa do their slope calculations and Sammy insists the shape is a square whereas Pippa insists the shape is a rhombus. Who is right? Show your calculations in your reasoning!

[fathom cosmos]

i think so

i have to show my works

[alpine sable]

if it was a square then two pair of points would be in the same y coordinate and the other two pairs would have the same x-coordinate

you get what I mean?

[fathom cosmos]

yes

[dense frost]

How

[fathom cosmos]

but its not, so it is rhombus right?

90 degree?

[alpine sable]

yea but how to prove it using math

hmm

[dense frost]

Can’t a shape be a square and be at an angle such that all values are different

So no

[alpine sable]

Yeah

if it had diagonal lines

never thought of that

hmm

[dense frost]

For it to be a square, the distance between all two points must be the same

Maybe you could use that fact

In a rhombus you have one pair which has a shorter length

I dont know why you’d calculate the slope of lines connecting two points

[fathom cosmos]

um

[alpine sable]

I guess by slope calculations they also mean finding the distance between two points? No idea lol

[fathom cosmos]

so what do i have to do?

[alpine sable]

use the formula for finding the distance between two points

[tight locust]

rhombii are equilateral

[dense frost]

And?

[fathom cosmos]

what is it?

[dense frost]

If there is a problem let me know

English isnt my first language

[alpine sable]

that means that it can also have equal distance between all points

[tight locust]

oh were you talking about the diagonal?

[alpine sable]

so finding the distance between points wont help

[dense frost]

It still can

[pearl solar]

you need to show that atleast one of the angles is not 90 degrees

[alpine sable]

or I don't think so

[dense frost]

But true

Doesnt hold true every time

[tight locust]

to determine if the angles at which they meet are perpendicular

[dense frost]

No

Surely it can

If out if all pairs of points

[alpine sable]

so that's where the slope equations come in

ahha

[dense frost]

Ah whatever

Slopes it is

[alpine sable]

I'll leave you to it then

[fathom cosmos]

um

?

[dense frost]

My definition of rhombus was off I forget square is also one

Again, not my main language I dont learn math in english

My bad

Yeah uh idk red chicken lol

[fathom cosmos]

um is no one able to help me?

[alpine sable]

Uhhhhhhh

[fathom cosmos]

guess not

[alpine sable]

how would i graph this?

[tight locust]

0

[alpine sable]

if two lines are perpendicular

then the slope of one

is the negative recipricol of the other

$m = -\frac{1}{m}$

[fathom cosmos]

?

[ocean seal]

Venti

[fathom cosmos]

whats that formula for?

[alpine sable]

two perpendicular lines

the slope of one

is the negative recipricol of the other

[dense frost]

I think checking for distance is still the best option

The question clearly differentiates between a square and a rhombus

So the diagonal lines must be different lengths if its a rhombus

[pearl solar]

no

[dense frost]

How so

[pearl solar]

a rhombus can have all its sides equal

[alpine sable]

.

[dense frost]

But the question differentiates between a square and a rhombus

If it can be a square then dont answer the question at all

[pearl solar]

if you measure at least 1 angle to be not 90 degrees, then it is a rhombus

if you measure all angles to be 90 degrees, then it is both a rhombus and a square

[fathom cosmos]

Square Rhombus
The diagonal lengths of a square are of the same measure. The diagonal lengths of a rhombus are of different measure.
All the interior angles of square measures 90 degrees (i.e., right angle) In a rhombus, the opposite angles are of the same measure.

[dense frost]

Read the question again

Sammy says square the other says rhombus

Then we will take square as a shape where all points are equal length apart

Whereas rhombus will have diagonals at different lengths

Yes thank you red

[pastel jungle]

anyone know of examples/ practical uses of lissajous curves?

[alpine sable]

$\frac{1}{2}bh$

[ocean seal]

Venti

[alpine sable]

where b = base and h = height

[alpine sable]

Yeah yeah that

[deep pivot]

<@&286206848099549185> I'm still stuck on this, I'm trying to create a signed distance field for a dashed line

[alpine sable]

how would i solve a problome like this

[alpine sable]

Use y = mx + b

Where m is the slope

Since there is no x here, m is 0

[gaunt roost]

Can anyone help me with this?

[true crystal]

The two functions have to be definite

For the first which values of x could make a problem

?

[gaunt roost]

I don't understand

this is the whole question

[true crystal]

What is the domain of square root of x+1 ?

[gaunt roost]

x is greater than or equal to -1

[true crystal]

Yeah

And for the second

[gaunt roost]

x < -1

[true crystal]

yeah

and since you want the domain of f - g you need to consider those two inequalities

Both f and g must be define

[glass lichen]

this is poorly denoted as a fyi

[gaunt roost]

so there's no answer?

undefined?

king1219?

cuz the textbook gives an answer

[true crystal]

What is it ?

[gaunt roost]

XER | -1 is less than or equal to x is less than 1

[alpine sable]

actually if the diagonal lengths are always different then you can just find the distance between two opposite points

for the rhombus I mean

[true crystal]

That is strange cause g(0) is not define

[glacial hedge]

is this channel being used?

[alpine sable]

? help please

[glacial hedge]

what are the slope of the 2 lines?

what heppens when 2 lines have the same slope they are ____

[gaunt roost]

ok, this makes me want to die. It wasn't in the corrected textbook answers, and an answer site gave the same results as the textbook. I spent 30 mins at least on this bs

I believe you tho

[glacial hedge]

@gaunt roost whats the question

[alpine sable]

nonvertical parallel lines?

[glacial hedge]

one word

[glacial hedge]

hint you said it in this

[alpine sable]

negative slope

[glacial hedge]

and its not nonverticle

[alpine sable]

oh

[glacial hedge]

there isnt anything special about a nonverticle line

[gaunt roost]

there it is @glacial hedge

[glacial hedge]

isnt it

just x=-1?

[gaunt roost]

that's what I thought

[true crystal]

no

[glacial hedge]

yes

[alpine sable]

paealell lines

[true crystal]

log 0 ?

[alpine sable]

paralell *

Parallel

[glacial hedge]

oh right

then f - g isnt defined

on real numbers

so domain is {}

[alpine sable]

how would i do this one

[glacial hedge]

😦

ddue

dddddudde

look at the slopes

[alpine sable]

im not good at this stuff its above my grade and i only got a day to learn it soo its still pretty hard for me

[glacial hedge]

ok sorry that was sorta mean

hint

a line with -1/slope of some line is perpendiciular to said line with that slope

[alpine sable]

Ok @alpine sable what are the slopes of the equations

[alpine sable]

Fat hint lmao

[glacial hedge]

xD

[alpine sable]

Anyway you're not going to learn it by just asking for answers to everything

You gotta try to do each one for a while

[glacial hedge]

yes i would suggest reading the textbook or watchign somne videos online

and try drawing both lines

[fickle dock]

Hey, I'm trying to prove by induction that for any positive integer n, 3 divides n^3 - 4n + 6 evenly, am I on the right track here?

Would anyone mind helping me with the next step please?

[alpine sable]

There's one issue here

You can't assume that the k+1 expression is equal to 3q

That's what you're proving

You need to derive it from the induction hypothesis

However, the proof itself is done

You simplified the k+1 expression down to the k expression and some terms multiplied by three

Which is trivially divisible by 3 using IH

[glacial hedge]

Question: I think the answer is false because the transformation is 2 * I and the det of that is 4 but not -4 but I am still confused

nvm im stupid

[0 2]

[2 0]

nvm

xD

stoopid

[fickle dock]

so then inside my then statement, what should I be setting it equal to instead?

[alpine sable]

Nothing

[safe pewter]

How come the answer is possible youtube sources says you cant make a sum of unequal root values?

[alpine sable]

Unless you've been taught some specific form these arguments need

[alpine sable]

Sorry channel in use

[fickle dock]

not that I remember, I think that should be ok

[safe pewter]

So should i ask in a diff

[alpine sable]

Yea just try another

[fickle dock]

so I get to the last equation, and now the left side contains the k expression plus some other expressions

[alpine sable]

#❓how-to-get-help

Yes

Then the k expression is equal to 3m

[fickle dock]

but how do you know that that k expression + some other expression is still divisible by 3?

[alpine sable]

Because the other ones are all multiplied by 3

Which you can factor out

[fickle dock]

ohh true

[alpine sable]

So yeah your proof is fine, it's just the method that's a bit confused

[fickle dock]

so then I would end up with k^3 - 4k + 6 + 3(k^2 + k) = 3m(3q + 3)?

the right side is wrong isn't it

[alpine sable]

Forget about the q haha its not a good way of doing induction

[fickle dock]

but k+1 and k cannot have the same multiplier of 3

or might not

[alpine sable]

You end up with 3m + 3k^2 + 3k

Where k and m are natural numbers

This is equal to 3(m + k^2 + k) which is divisible by 3 for any value of m and k

[fickle dock]

ohh it seemed a little weird to me that I could just throw out the right side but it makes sense in the end

[alpine sable]

Yeah, you only get to the right side at the end

I need help

Shoot

[fickle dock]

alright man I got it, thank you so much!

[alpine sable]

Glad to help

For 4 you can calculate ab using the area formula for triangles and the length of AE

Then I think you have a formula for the area of a trapezoid

[alpine sable]

?

(A+B)/2 times height

Yea exactly

Height is given by AE

Which you have to figure out using the area of the triangle

For which the formula is base * height / 2

For this would I use the centroid theorem?

[warped phoenix]

when im calculating an intersection of two graphs, what does it mean when it asks me for first and second curve? one of the graphs is y = x and the other is a parabola

it seems that no matter where i place the "curves" I still get the same answer for my placement of "guess?"

[alpine sable]

<@&286206848099549185> Apologies for the ping.

[alpine sable]

?

[glacial hedge]

How do I do this?

I think its the inverse of A

but not sure

[alpine sable]

can someone help

[glacial hedge]

your supposed to

plug in $\sqrt {x}$ for z

getting

[ocean seal]

Elonmosqito96

[glacial hedge]

$\frac {x} {x^2+9}$

[ocean seal]

Elonmosqito96

[alpine sable]

so that would be the correct answer?

[glacial hedge]

yes....

[alpine sable]

Says its wrong?

[glacial hedge]

?

[glacial hedge]

you forgot

x^2

it should be

[alpine sable]

OH

[glacial hedge]

x/(x^2+9)

[alpine sable]

Damn it's wrong 😔

[glacial hedge]

??

[alpine sable]

It's somehow squaroot of x/2(x^2+9)

Should I debate with my teacher @glacial hedge

[glacial hedge]

wait wut

[alpine sable]

Ikr?

[rough compass]

no

thats correct

[glacial hedge]

yeah i think i messed up somehwere

[rough compass]

when u do that u need to multiply by the derivative of root x

u prob missed that part

[alpine sable]

Bruh

[rough compass]

you get this and then multiply by (1/2 x^(-1/2)

and then rationalize denom

[dire pilot]

can I get help

[alpine sable]

I'm going to tell me teacher

[glacial hedge]

Oh my bad i forgot that it was a composite funciton since its not integral of 1 to x

[rough compass]

??

your teacher had it right

[dire pilot]

so can I get help

im relearning algebra

and I really need help with this question

[rough compass]

A

[shrewd oracle]

Nah his teacher was the square root thingy

[dire pilot]

@rough compass how did you get A

[rough compass]

that was the correct answer

[rough compass]

slope of 0 is horizontal line

[dire pilot]

oh ok

thanks

[shrewd oracle]

Oh thought you were saying it was wrong for a min

[rough compass]

nah its correct

[dire pilot]

thanks

[shrewd oracle]

Yeah im aware

[alpine sable]

Did I do this correctly and if not can someone tell me how

[upper pebble]

isn't CG also parallel to AH

and wouldn't BI also be parallel to DG

[alpine sable]

Thank you @upper pebble

I'm not sure how to figure out the numbers though

Those were complete guesses.

[upper pebble]

i don't completely understand it either but i think you can use trigonometry

looking at triangle AIC and trying to determine the length of IC, we can recognize that AI is 10 feet and AC is 14 feet, since I is the midpoint of AH and C is the midpoint of AE. maybe that helps

can't use Pythagorean theorem since it's not a right triangle so idk what to do there

but i encourage you to figure out how to do it instead of guessing

[rough compass]

is this channel open

[upper pebble]

i think Pazerx's question kind of still needs an answer

[rough compass]

ok

[alpine sable]

Im so confused on what to do

[timid karma]

To add animation during their soccer season, the team leaders decide to use a mascot for each of the 20 maths. They wonder whether they should buy or rent the costume. Rental rates are $ 10.50 for each game

The seamstress who would make the costume asks for $ 128.00 for the sewing work and the fabric that would be used sells for $ 25.50 / m2

The mascot costume will be a reproduction of a soccer ball. The dimensions will be 4 times larger on the mascot than on the ball

Balloon volume: 4189 cm3

Determine the cheapest option

plz I need help

anything

[warm vine]

what is the difference in magnitude notation between |v| and ||v||

[charred hound]

Hi Gents,
How are you going?

Each node is connected to the other. Connection from Node1 to Node2 is not the same in the cost as connection from Node2 to Node1.
What's the name of this graph?

Is there any solution to find the fastest route between node1 and node2?

[alpine sable]

help

[glacial hedge]

could someone explain this to me?

*this is a t/f question

i think its true

[hybrid parcel]

quick question, is the x and y intercept in a quadratic equation always the same?

im a high school freshmen btw

[glacial hedge]

????

no

[glacial hedge]

you can have

y = (x-1)^2 for example

y intercept is x=1

*x intercept

y intercept is 1

versus y=x^2

with x and y intercept of 0

[hybrid parcel]

alright thank you

[dull lance]

https://cdn.discordapp.com/attachments/409596215697866773/867598855792885800/unknown.png

How to solve x

[tired hamlet]

How is (x-2)^2 =y-12 not the answer? It said I was wrong

[dull lance]

[gaunt magnet]

hi

You are given a polynomial function and two of the known roots.  You must determine the values of m and n and then use polynomial division to determine the other x-intercepts and then write the function in factored form.  Use polynomial division to determine the other x-intercepts.  Show your work!

so for this question
I got n=-42 and m=-11
and then using these value we need to find x intercept using long divison
and then x intercepts i got are x=2, - 1, 3/2

am i correct

[glass field]

theres a few ways you can check your own work... first you can stick 7 and -4 in for x and see that your values for m and n make it so the expression is equal to zero. then i guess you can do the same for the other roots you found or you can expand the factored form to see if it matches with your expanded form

[tired hamlet]

Anyone wanna help me with mine😢

[glass field]

youre supposed to complete the square or something?

everything looks right in your solution except that the last line is not consistent with the 2nd to last

[gaunt magnet]

i think i did it right

[glass field]

i think so too

[robust cradle]

Anyone help?

[clever folio]

For (i) you see how the long side of A is 18 m and the short one is 3m?

@robust cradle

[robust cradle]

Yea

@clever folio

[clever folio]

So then do you know the formula for area of a rectangle?

[robust cradle]

Length x width x height

But I’m trying to find the side

[clever folio]

Nah rectangle

[robust cradle]

Length times width

[clever folio]

Exactly.

[robust cradle]

How do I find the side

[clever folio]

Using the picture

[robust cradle]

18x4 for A?

Correct?

[clever folio]

Like this

Nah 18x4 would give you the area for the bottom and top faces. Do you see?

[robust cradle]

So what do I do for side A

4x3

?

[robust cradle]

Channel taken

[clever folio]

Like I said, you have an 18m side and 4m side for the rectangle which is face A

You see how Ixm seeing that in the pic right?

[robust cradle]

Ye

For B is it 18x4

?

I got the answers

[clever folio]

Yah that's what I was going for lol.

[robust cradle]

what abt this?

[upper pebble]

do you know what the formula for the area of a semicircle is

[robust cradle]

@clever folio

[floral jungle]

anyone able to do this with steps?

[old cobalt]

Can anyone verify I did this right I don’t really know what the question is asking

[clever folio]

Oh this one?

Ah I think aleko was here first tho

[old cobalt]

My bad

[clever folio]

For the two points plug them in for the x and y's of your equation to get two equations in a,b,c. I believe c is the asymptote

So that gives two eqns in two unknowns to solve.

[floral jungle]

would you be able to show how? cause im still confused

[clever folio]

For ex c=-5 so y=ab^x -5

Then we have a pt (0,-8) so -8=a(b^0)-5 so one of the equations is just -8=a(1)-5 which you can solve for a.

[alpine sable]

hi all how can i do this

[floral jungle]

ohh, thank you, i understand a bit now,

[old cobalt]

Is this occupied?

[alpine sable]

wym occupied?

[topaz scaffold]

Nope

[old cobalt]

@topaz scaffold are u able to help me with the question?

[topaz scaffold]

If it's within my tiny window of knowledge

[topaz scaffold]

Oh let's go that's in my tiny window of knowledge

Standard form is $ax^2 + bx + c$

[ocean seal]

RipeOrange

[topaz scaffold]

And all you need to do it to multiply everything out

[old cobalt]

Ok thanks fam

[lofty jasper]

Ooof ripe

[lavish lichen]

Please help me

[topaz scaffold]

Why you stalking me man

[gaunt magnet]

Oi hello

anyone check my work

[dark granite]

huh?

[dire pilot]

can anyone walk me through solving this problem please

[topaz scaffold]

If the circumference is 10π, what is the radius?

[dire pilot]

5?

so the distance from p to o is 5

[topaz scaffold]

Yep

And P to R is 10

And since PQR is an isosceles triangle, we can conclude that QO is perpendicular to PR

Which means we can use those 2 lines as our base and height

[dire pilot]

oh ok

so 5 x 5 x .5

would be the math to get the area right?

[topaz scaffold]

No

[dire pilot]

why

the heigh and base would both be 5 right>?

[topaz scaffold]

PR has a length of 10

[dire pilot]

so thats are base

so

10 x 5 x .5?

[topaz scaffold]

Mhmm

[topaz scaffold]

Correct

[dire pilot]

25sq ft

[topaz scaffold]

Where you get the feet from?

[dire pilot]

oop

meters

[topaz scaffold]

Just square units

[dire pilot]

units

**8

to tired for this sht

trying to learn all of algebra 1 in 1 nght

[sharp sail]

The number of ordered pairs (x,y) such that 2^x + 3^y = 5^(xy) is

Can someone help me with this

[ionic jewel]

im pretty sure theres just the one solution

[topaz scaffold]

Wolfram? 👀

You lying to me?

[ionic jewel]

uh lemme check wolfram

,w solve 2^x + 3^y = 5^(xy)

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

[floral jungle]

anyone able to do this?

[topaz scaffold]

1 integer solution

Many non integer solutions

[sharp sail]

So 1 integer sol. and infinite real solutions

[dire pilot]

can anyone help me through this

[topaz scaffold]

Use exponent rules

[sharp sail]

m³ will be 8 and m=³√8

So the answer is 8 ofc

[dire pilot]

wait so

what

[sharp sail]

umm the question and the given condition simplifies to the same thig...

[dire pilot]

im to dumb rn

its like 2 am

[topaz scaffold]

Using the rule $$\frac{c^a}{c^b} = c^{a-b}$$

[ocean seal]

RipeOrange

[dire pilot]

so

9 - 6 = 8???????

or what

or is it

[alpine sable]

Its 8

[floral jungle]

what is-

[topaz scaffold]

Where in the world

[alpine sable]

Oops

[alpine sable]

Not urs mate sry

[dire pilot]

https://cdn.discordapp.com/attachments/490557019623915520/867633430160998410/unknown.png

so

[sharp sail]

This guy broke maths

[alpine sable]

C

[dire pilot]

im to fucking dumb for this man

[topaz scaffold]

$\frac{m^9}{m^6} = m^{9-6} = m^{3} = 8$

[dire pilot]

but how does that equal 8

[alpine sable]

M to the power 3

[ocean seal]

RipeOrange

[topaz scaffold]

You find a number for m that makes it equal to 8

[dire pilot]

and how is 3 equal to 8

[alpine sable]

2 to the power 3

[dire pilot]

ok

[sharp sail]

In a triangle ABC, point D is chosen on BC such that BD:DC = 2:5 . Let P be a point on the circumcircle ABC such that angle PDB = angle BAC . Then PD:PC is?

Anyone?

[true nebula]

Someone can help me in a problem of mats?

Its to examen please

I dont know how resolve it

√121

Well, it is not for exam but it is for an assignment for which they give points for the exam

[brittle grove]

what is the problem?

√121=11 if that is what you are asking for

[true nebula]

i dont know how resolve it

thx you very much

[brittle grove]

np

[true nebula]

You can teach me

how to resolve it?

please

You are pana walter 😮

[brittle grove]

it is not really a simple formula for finding square roots

you just need to find a number that when multiplied by itself gives the number inside

[topaz scaffold]

I think there is tho

[brittle grove]

11*11=121

[alpine sable]

There are a few algorithms

[topaz scaffold]

Saw one by some Indian guy as always

[brittle grove]

i didn't know

[alpine sable]

You could reasonably use newton's method

[true nebula]

thx

[brittle grove]

true

[alpine sable]

Tho would you want to ahaha

[topaz scaffold]

This is like nuking a house to kill a fly

[brittle grove]

yeah

[true nebula]

i dont speak english, i speak spanish srry if i write wrongly a word

[brittle grove]

yeah its fine

[topaz scaffold]

We're not talking about √121 anymore are we?

Just general case?

Oh

[brittle grove]

yeah

[true nebula]

Its ilegal use mayus?

[brittle grove]

in general you just memorize what numbers are perfect squares

[topaz scaffold]

What

[brittle grove]

mayus?

[true nebula]

Mayus = mayusculas

mmh

Mayus = IERNMCEUEQWIAAAAAAAAAA

[topaz scaffold]

I do not know what that is

[true nebula]

No mayus = iernmceuqwiaaaaaaaaaaa

Mayus = HIIII

No mayus = hiiii

[alpine sable]

I'm really sorry, but i'm not really understanding
its not your fault

[true nebula]

😦

Mayusculas

MAYUSCULAS

[brittle grove]

i google transalated and Mayusculas = Capital letters

[true nebula]

mmh

I do not know how to explain it to you

Mayus = ARBOLITO ARBOLITO ARBOLITO

No mayus = arbolito arbolito arbolito

When you write in big print

[brittle grove]

k, i think i understand

maybe

[true nebula]

yes

HAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA = mayus

haaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa = no mayus

:(.

[brittle grove]

yeah, but you asked if it was illegal to use them

when?

[true nebula]

mmh

in

algunos

servers its are ilegal

On some servers it is illegal

[alpine sable]

I dont think its a problem

[true nebula]

idk why but they can mute me in the server

When you divide a negative number, is the result positive or negative?

[brittle grove]

depends

[alpine sable]

If the number you are dividing is positive then dividing by negative gives negative

[dark granite]

@true nebula If it's illegal some servers, why are you saying it lol?

[true nebula]

In others servers

they mute me

for use mayus

:(.

[dark granite]

why? doesn't seem like a bad word

[true nebula]

no

i only say

[alpine sable]

By mayus he means to use all caps

[true nebula]

IDK WHAT YOU ARE SAYING

I say it

and

they mute me

[dark granite]

oh gotcha

[true nebula]

5h

[alpine sable]

Because Mayus means capital in spanish ye

[dark granite]

ah gotcha

[true nebula]

B(

I speak spanish 😄

:D.

[dark granite]

They prolly mute you cuz it looks like you're yelling at them

[alpine sable]

^^ bump

[true nebula]

yes

prolly...

or they hate trees

...

[alpine sable]

Logician i was wondering if you could help me out with a combinatorics question

[true nebula]

yes

[true nebula]

ehm

[alpine sable]

I've tried case bashing, but it does not seem to work

[true nebula]

i have bad english

wait i use traductor

[alpine sable]

Thats completely fine

[dark granite]

why me lol? Let me see your question

[true nebula]

Hes have a dog

And the dog

Move it

[dark granite]

huh?

[true nebula]

eh

[dark granite]

what dog?

I'm so confused

[true nebula]

Bob is dog?

[brittle grove]

is this even math anymore?

[true nebula]

eh

[alpine sable]

Philosophy now

[true nebula]

yes

[dark granite]

@alpine sable What was your question?

[alpine sable]

Sorry I think it got lost in the thread

[dark granite]

okay, what have you tried so far

[alpine sable]

I've tried to case bash

But thats been pretty fruitless

I've also tried to draw a tree diagram but that hasnt worked either

[dark granite]

yeah I'm not surprised the tree diagram hasn't worked because there's some serious dependency here

I'd count the complement and subtract from the total

[alpine sable]

Thats problematic

I've been thinking about that

[true nebula]

what

[alpine sable]

but when I try grouping shirts together, i cant stop double counting

[true nebula]

I do not understand much of your method to solve

[dark granite]

You need to use something called the PIE

the Principle of Inclusion and Exclusion

[alpine sable]

Ok

I'm unfamiliar with that ideo

I remember hearing that in derangements?

[dark granite]

yeah it comes up in combinatorics from time to time (quite often actually) For instance let's say I asked you to find the number of 5-digit codes that have start with 5 or end with 2.

[alpine sable]

start with 5 or end with 2

Ok

then i can do two cases

[dark granite]

three actually

[alpine sable]

oh ye

both

[dark granite]

because PIE

right

so what'd the answer be?

to the question I asked

[alpine sable]

i dont understand what you mean by PIE

but i can do the question

like its just 10^4 or 10^3 for your cases (right?)

[dark granite]

if all you do is take 2*10^4 as the answer, you'll overcount because you'll have counted the codes that look like 5....2 exactly twice, but we only want to count those exactly once so you'd need to subtract off the number of codes that look like 5...2

[dark granite]

codes starting with 5 would be 10^4. Same with codes ending with 2.

[alpine sable]

aah i see

its like adding two sets together

with an intersection

[dark granite]

exactly taking their union

[alpine sable]

ok

[dark granite]

if the sets are disjoint (i.e., if the 'or' is exclusive) all you need to do is add. However, if the intersection of the sets is nonempty, then you need to do some subtracting

[alpine sable]

That makes sense yes

And here there is definitely some intersection

[dark granite]

yes

[alpine sable]

yo

[dark granite]

so the answer to my question should be $2\cdot10^4-10^3$

[ocean seal]

logician_pdx

[alpine sable]

can anyone help me with geometry

Ok

[dark granite]

This channel is busy

[alpine sable]

sure

Ok that sounds fair to me

Tho... I'm kinda unsure how to apply it to this instance

[dark granite]

well so that was just to give you an idea about an instance when you need to use PIE

[alpine sable]

ok

[dark granite]

Now looking at your question....

[alpine sable]

I can put it here again

[dark granite]

All good, I got it open in a new tab

[alpine sable]

ok

[dark granite]

So you've probably tried counting this directly. I bet that was pretty hard if not impossible

[alpine sable]

yep

[dark granite]

so let's count the total, then the complement.

[alpine sable]

Sure

[dark granite]

What would the total be?

[alpine sable]

I found the total to be 8! / (2!)^4

[dark granite]

yes

okay, now let's count the number of ways in which some two shirts are next to each other.

[alpine sable]

Some two shirts are next to each other

[dark granite]

there's going to be some casework

[alpine sable]

Ok. Are we going to try and group two idnetical shirts together ?

[dark granite]

yes

[alpine sable]

that would be (7!)/(2!)^3 for each shirt right

[dark granite]

I'd recommend having this picture in the back of your mind:

$AABBCCDD$

[ocean seal]

logician_pdx

[dark granite]

each letter represents a type of shirt

[alpine sable]

Ok

[dark granite]

explain

[alpine sable]

yep I'm already using that notation lol

Well i was thinking

if we group AA together

[dark granite]

okay

[alpine sable]

Then it would be 7 objects

and 7! x 2! / (2!)^4 ?

[dark granite]

yes

yes

[alpine sable]

and do we repeat that for B,C , D (so we multiply by 4) ?

[dark granite]

yes

[alpine sable]

OK