help-0

[pearl marlin]

Yes

Uncountable

[tough hatch]

why so? i'm curious

[harsh swallow]

you can make an infinite amount of numbers from the numbers you already have

thats why it's uncountable infinite between 0 and 1

[ripe osprey]

They are uncountable (or infinnite), and hence cannot be compared directly

[tough hatch]

so the amount of numbers between 0 and 1 is equal to the amount of numbers between 0 and 10?

[harsh swallow]

pobla just said no

not comparable

[pearl marlin]

Yes

[median tendon]

Think of it this way, any number between 0 and 10 can be divided by 10 to be between 0 and 1

[pearl marlin]

It is uncountable

https://math.stackexchange.com/questions/2283065/prove-that-the-intervals-0-1-and-0-infty-have-the-same-cardinality

[harsh swallow]

@ripe osprey They are then still in the same class of infinite right

even though not comparable?

[tough hatch]

i see

[harsh swallow]

not directly

[ripe osprey]

Yes. they are in same class
but we cannot say that they are equal

[pearl marlin]

Or continum

[ripe osprey]

there are different kinds of infinity
and this one class in one of them

[tough hatch]

so any subset of the set of real numbers has same cardinality as the set of reals

[harsh swallow]

But if they are in the same class wouldn't that mean that as far as infinities go they would be equal?

[pearl marlin]

Nop take Z

[harsh swallow]

or is that entire idea wrong?

[tough hatch]

i meant uncountable ofc

uncountable subset.

[shrewd blade]

someone help wit dis plz

im confused

[median tendon]

Make the gradients equal

[shrewd blade]

how

[harsh swallow]

grad(functions) = itself

[tough hatch]

you can write both as y=

[harsh swallow]

that's much easier

[celest arch]

set of natural numbers has cardanility alph null and real numbers has continum, c

[harsh swallow]

special case

[pearl marlin]

Use rule of parallel

[ripe osprey]

there are different types of uncountability
which can be also said as, there are different kinds of infinity

The number of natural numbers is infinity
the number of real numbers between 0 to 1 is infinity

but, it can be proved that the second type of infinity is bigger than first one, and hence both of them as different types of infinity

[harsh swallow]

i thought they were multiple variable equations

[median tendon]

Get them into a form of y=mx+c and them make the m terms equal for both eqn

[shrewd blade]

ik the slope is same for parellel lines but how do you do it?

[pearl marlin]

You can saY that

[shrewd blade]

so the answer is 5?

[pearl marlin]

Or a1/a2=B1/b2

[shrewd blade]

?

[tough hatch]

oh right the RHS of one equation should be the other's RHS + a constant

not equal.

[harsh swallow]

@ripe osprey Yes but because the numbers between 0 and 31/985, and 31/985 and 1 are the same uncountable infinity would they not, as much as infinities can be equal, be equal?

[shrewd blade]

I still didnt get it

lmao

[tough hatch]

when you say sets are equal

every member of one set is in the other

[median tendon]

Im confused, wouldn't the amount of numbers between 0 and 1 be equal to the amount of numbers between 0 and 10 because there is a direct mapping between them (1/10)

[tough hatch]

and vice versa.

but 32/985 is not even in (0,31/985)

[tough hatch]

just write both as y= first

and what do you get?

[shrewd blade]

I did that

[ripe osprey]

No

both of them are infinite
both of them are same "type" of infinite

as per the defination of infinity, we cannot "count" them, and hence it cannot be said to be equal to something (as equal means that count in both of things we are saying is defined in some way, which here is not)

[shrewd blade]

-4y=-5x+10

2y=-5x-4

[harsh swallow]

ok so this was right?

[tough hatch]

yes, basically what i said here lmao

[tough hatch]

not finished

write it exactly as y=

[ripe osprey]

true

[tough hatch]

so no coefficients for y

[shrewd blade]

oh kk

[tough hatch]

what do u have now

[tough hatch]

also u forgot that this was 2y=kx-4

[shrewd blade]

so -4y=-5x + 10 is

y= -5x+10/-4

[tough hatch]

nope

[median tendon]

U need to divide each term

[tough hatch]

careful with how you divide.

[shrewd blade]

by -4?

[tough hatch]

yep

[shrewd blade]

so write as decimals

[tough hatch]

no need

just write them in fractions

[shrewd blade]

kk

y=5/4x+10/-4

thats what I got

[tough hatch]

u mean (5/4)x

[shrewd blade]

yes

and - 10/4

[tough hatch]

what about the other eq.

[shrewd blade]

right>

the other one is

[tough hatch]

yes

[shrewd blade]

the other one is

y=k/2x-2

[median tendon]

What part of that equation do u think is the gradient?

[shrewd blade]

the blank times x

[median tendon]

Ok, now u want to choose k so that the gradient of both equations are equal, right?

[shrewd blade]

yes

I still didnt get it plz help

@median tendon

thx

bro

[median tendon]

Which value of k would make the following expression correct
K/2==5/4

[shrewd blade]

2k/4

?

k=2.5

[median tendon]

Yes

[shrewd blade]

so the answer for this is 2.5

?

[median tendon]

You should try and convince yourself that is correct, try plotting both equations on an online graphing tool like desmos

[shrewd blade]

its wrong

@median tendon

[median tendon]

Could u please show me a ss

[tough hatch]

k/2

not k

wrong slope for red line

[shrewd blade]

no its right I did 5/2

and got 2.5

[tough hatch]

.....

[shrewd blade]

?

srry im dumb

[tough hatch]

if u insist it's right u should be getting parallel lines

[shrewd blade]

ya ur right

so wut should I put?

[tough hatch]

but you're not

k/2

not k

u divided the second eq. by 2.

so divide k by 2.

[shrewd blade]

so 2.5/2?

[tough hatch]

yea

[median tendon]

You have the correct k value, but u are typing the equation wrong, u substituted k incorrectly into the equation

[shrewd blade]

ohhhh ok

[median tendon]

This

[shrewd blade]

its right

nvm

so k = 1.25

[median tendon]

No

[shrewd blade]

thats its tru value

[tough hatch]

[tough hatch]

nope

that is just k/2

[tough hatch]

not k

you gotta be mindful of hoq you manage your equations

[shrewd blade]

ok

ok can we start from the beginning

srry

[tough hatch]

write them first as y=

like you did before

[shrewd blade]

@tough hatch thx for taking ur time I really sppreciste it

appreciate

so

5x=4y+10

that is

y=5/4x-10/4

correct?

now

[alpine sable]

could I get some help?

[shrewd blade]

2y=kx-4

[glass lichen]

what have you tried?

[alpine sable]

i watched some vids didn't find anything helpful just need some sm1 do 1 for me so I can do the other one by myself

[glass lichen]

ok well 2 gives you slope and a point... so just plug it into point-slope formula

[alpine sable]

?

[shrewd blade]

y=k/2x-2

@median tendon

[median tendon]

Yes

[alpine sable]

wdym

[glass lichen]

i mean what I wrote

[alpine sable]

and I don't understand what you wrote

[glass lichen]

ok so you ask a specific question

instead of wdym

[alpine sable]

I asked what do you mean

meaning can you go into detail

[glass lichen]

ok sure, slope is how steep a line is, and a point is a point

[shrewd blade]

so now wut do we do I am confused asfter this

[median tendon]

Do what u did before, remember u need to make the gradients equivalent

Find the value of k

[shrewd blade]

how do you do thst

[shrewd blade]

and dat

?

[median tendon]

Whats the gradient of each of those two equations?

[shrewd blade]

5/4x for the first one

k/2x for the second one

[tough hatch]

gradient is slope in this context btw

[shrewd blade]

yes

[shrewd blade]

this is equal to 2k/4x

[median tendon]

Those aren't the gradients, there should not be the x term

[shrewd blade]

oh yes

5/4

and 2k/4

[median tendon]

Ok good, now u want them equal, which value of k will make them equivalent?

[shrewd blade]

2.5

[median tendon]

Ok

[shrewd blade]

the question asked for k

so the answer is 2.5

[median tendon]

Yes

[shrewd blade]

ok

[median tendon]

But do you know why your equations that you put in desmos were incorrect?

[shrewd blade]

let me try graphing it again

[median tendon]

Write the equations in desmos in terms of k, then after doing that, replace k with 2.5

[shrewd blade]

this is wut I got

[median tendon]

There you go

[shrewd blade]

perfect

so K=2.5

completley

sure

[median tendon]

Before you had typed the equation wrong

[shrewd blade]

100%

[shrewd blade]

yes thx for taking your time to help me. Thats rlly nice of u

[median tendon]

No problem

[shrewd blade]

so 100% correct?

cuz this is rlly important

[alpine sable]

@glass lichen Y - -8 = 6 (x- -1)

smthing like this right?

[glass lichen]

yes

[median tendon]

Yes, it is correct
But you should be confident without me saying anything, you followed logical steps and ended with a graph that you were after

[alpine sable]

and what about the second one

[glass lichen]

find slope, then do the same thing

[alpine sable]

alr ty

[shrewd blade]

yes I am 🙂

k=2.5

u gave me more confidence

thats it

🙂

for this I got d

is that right?

[mystic bobcat]

hi can someone help me with probability calculation

[twin pine]

yes

[tough hatch]

[mystic bobcat]

how can i find a difference between u from union : P(A ᴜ B) = P(2) + P(4) + P(5) + P(6) = 4/6 = 2/3 and the u from OR: P(A ᴜ B) = P(A) + P(B) – P(A ∩ B)
= 0,5 + 0,3 – 0,1 = 0,7

how do i know when i need to use union and when to use OR because they have the same symbol u

[novel siren]

they're the same

[oak chasm]

@mystic bobcat The second one is also union, as A and B are sets of outcomes.

https://en.wikipedia.org/wiki/Event_(probability_theory)

[smoky harness]

Gusy

Guys

Maths puzzle, I have a lot of clues now we are close but need guidance ur ideas

What we know:

The numbers are coefficients

[alpine sable]

major help needed here

[distant otter]

@alpine sable what you need help with

[alpine sable]

|z-5+ 7i | = 5

find the maximum value for arg(z)

i found what z is

but the mark scheme says you must minus it by pi /2

cause i did

2arctan (5/7)

but the mark scheme said you must minus that by pi/2

[distant otter]

i don't get the question

[alpine sable]

oh

[alpine sable]

basically, values of z lie on a circle in the complex plane using the equation you gave

yes

and the centre is in the fourth quadrant

and you have to find the value of z such that the angle made by it is maximum

[alpine sable]

yep

yes

but why must you minus it by pi/2

it said that the answer has to be in the range of (-pi , pi )

[alpine sable]

hmmmmm

so is that a mistake in the book

is answer -pi/2?

no

oof

-0.330 rad

cause to get that

oh yeah its maximum

[smoky harness]

Maths puzzle, I have a lot of clues now we are close but need guidance ur ideas
Hints we got from the creator:

1. "you see the one at the beginning?"
   "It's in it's normal form"
   (Normal form (scientific notation) is a way to write very large or very small numbers in a more compact form. It has two parts:

A number, usually in the range 0 - 10, called the coefficient.
A power of ten to multiply it by called the exponent.)
2. "What defines a polynomial?"
3. hint goes as follows "the numbers are coefficients"

[smoky harness]

1 -454 85767 -8629870 487791388 -14685529320 183977791200

[smoky harness]

Transcript

[alpine sable]

,w arctan(-2/5)

[ocean seal]

Results provided by WolframAlpha

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

Requested by omeganebula#9422

[alpine sable]

close

[dapper vortex]

I have a doubt in maths
Its about compound interest
If I have a rate of interest per annum =6%
And i compound it half yearly
The rate of interest is taken as half the value to do that in that case.
So in calculation we use rate of interest as 3%
why do we do that??
And in the end of doing that calculation we get an overall rate of interest greater than 6%
per annum

[alpine sable]

wait

[alpine sable]

ok so a polynomial is defined by the fact that exponents are positive integers

why is it arctan -2/ 5)

oh its wrong

[alpine sable]

lowest point in the circle (x-5)^2 + (y+7)^2 = 25 is (5, -2)

do u know anyone who can help

[smoky harness]

Ok

[alpine sable]

nope 😅

hmm np

i swear u are advanced

maybe math helpers

oh

[indigo jetty]

can you post the answer scheme here?

[alpine sable]

hmm ill try

i cant sorry cause my phone broke and im on a trash laptop

but i can type it out

[indigo jetty]

ok

[alpine sable]

2arctan(5/7) -pi /2 = -0.330 rad.

[indigo jetty]

how did you get 2arctan(5/7)?

[alpine sable]

so i drew the circle on an argand diagram

with the centre 5 ,-7

i drew a tangent on the right hand side of the circle

split it into two congruent triangles

used tan rule

to find one angle

and times it by

2

[smoky harness]

Anyone can help me in #help-3 pls

This is a common technique for hiding messages in cryptography
You find the zeroes
You find the roots
When does P(x)=0?
Those numbers are coefficients
That should be enough info to form P(x)
Once you've got P
you find the zeroes
you translate into letters
That's the answer

[smoky harness]

The Rational Zeros Theorem states: If P(x) is a polynomial with integer coefficients and if is a zero of P(x) (P( ) = 0), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

[minor heath]

wait can you use calculators for this

cuz thats the major problem here

[smoky harness]

Yes anything

U can use anything

[minor heath]

oh

ok

[smoky harness]

absolutely anything except hacks

[minor heath]

is wolframalpha acceptable

[smoky harness]

Yes idk what is ia

[minor heath]

cuz thats the only thing you can do to find the answer

[smoky harness]

u can use it

We have been doing this for like 12hrs

[minor heath]

wait what

[smoky harness]

sendhelp

We have discord group

[minor heath]

you havent thought of wolframalpha at all?

[smoky harness]

No can u help us

[minor heath]

ok uh theres 6 numbers in there, so its probably that its a 5th degree polynomial

[smoky harness]

Check ur dms

[indigo jetty]

@alpine sable ok I got it, the angle you found 2arctan(5/7) is the angle between the two tangents that mark the min and max of arg(z) respectively. However, arg(z) is the angle that complements 2arctan(5/7) in the pi/2 frame, so in other words, arg(z) is a displacement of 2arctan(5/7) from the min angle, which is -pi/2, so your final answer is -pi/2 + 2arctan(5/7). You can check this diagram for clarity (ignore the numbers or whatever as i just used a diagram found as an example, just see what arg(z) is supposed look like)

[alpine sable]

oh i see

thx

[indigo jetty]

👍

[median flint]

Can someone help me with this?

[tough hatch]

you can also do it by trial and error

i.e. plug in the same set of values into each equation

[median flint]

How would I do that?

[shrewd blade]

need help with a

plz

I did it and got 3.60555127

[pearl marlin]

for lenght use distance formula

for b use two point form

[shrewd blade]

I did

can you plz solve it quickly

[gray isle]

dont use a calculator

leave the answer in exact form

[pearl marlin]

$\sqrt{13}$

[ocean seal]

learn4math

[shrewd blade]

ok I got it right than

thx!!!

[sonic kayak]

regarding mathematical roots, can i say "6 to the root of 2" to mean the same thing as "square root of 6"

[vale wigeon]

you can certainly try, but it's very likely you won't be understood.

[gray isle]

6 to the root of 2 would be interpreted as $6^{\sqrt{2}}$

[ocean seal]

ℝamonov

[sonic kayak]

right, cause i'm making a simple 4 function calculator, and I don't know how to say roots like you would say 5 "times" 3

how would you say a root in terms of x and y?

[vale wigeon]

what are x and y?

[sonic kayak]

ah im bad with mathematical notations

let me think of an example

[vale wigeon]

do you mean how to express roots in terms of exponents?

[sonic kayak]

like this

[vale wigeon]

$\sqrt[y]{x} = x^{1/y}$

[ocean seal]

Ann

[sonic kayak]

how would I say that in english?

thats my main question

just x to the power of 1 over y?

[gray isle]

y-th root of x

or x to the power of (1/y)

[alpine sable]

soory to disturb again

but can someone explain to me on how to get the maximum and minium value for arg(z) for a circle with the centre ( -3 , 2 sqrt 3)

[full cypress]

how does 0.9^2 = 0.81 and not 8.1?

[gray isle]

why do you think its 8.1?

[harsh swallow]

0.9^2 = (9/10)^2 = 9^2/10^2 = 81/100 = 0.81

[full cypress]

9 x 9 = 81 then move it 1 place to the left

[harsh swallow]

2 places

[full cypress]

oh ok

why tho?

[harsh swallow]

because you have 2 0.9

[full cypress]

two 0

yee

[harsh swallow]

if you did 0.9 * 9

it would be 1 place

0.9 * 0.9 is 9 * 9 but move 2 places to the left

[alpine sable]

katharine are u good with complex anlyasis

[full cypress]

alright thanks

[harsh swallow]

i don't think so

[alpine sable]

oh no worries

[minor elbow]

someone help me with the next part plz

[vapid smelt]

Hey how are you supposed to do this?

|x    2x-3| = 0
|4      x |

You are required to find the value of x.
but when we multiply (cause its determinant) we get a factorize form.

Please do happen to ping me if you do know

[gray isle]

what's your determinant?

you should have quadratic equation

[vapid smelt]

the determinant is 0

[gray isle]

what's the algebraic expression you get when you take the determinant of the matrix

[ocean seal]

Inheritanc-e ♦
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vapid smelt]

i got x = 4 somehow

i think its right

[glass lichen]

it isnt

[vapid smelt]

oh

[glass lichen]

$x^2-4(2x-3)=0$ is what you're solving

[ocean seal]

Mosh

[gray isle]

well apart from that tex fk up

[vapid smelt]

ye

[gray isle]

you did seem to get the correct determinant

[vapid smelt]

can you understand that

[gray isle]

you should have no issue with solving quadratic equations by the time you're doing linear algebra

[vapid smelt]

ye i think just got confused a lil bit

thx though

[gray isle]

the second half of your work is trash

[glass lichen]

you got to $(x-2)(x-6)=0$ then did nonsense

[ocean seal]

Mosh

[vapid smelt]

oh

right

cause its in multiply

[glass lichen]

yes, not addition

[vapid smelt]

so how exactly am i supposed to continue to get a value of x

or does (either or) work

[glass lichen]

.

[vapid smelt]

right

[glass lichen]

so how would you solve $(x-2)(x-6)=0$?

[ocean seal]

Mosh

[vapid smelt]

either or?

[glass lichen]

??

what either? there's 1 equation

[vapid smelt]

right

hmm

i kinda don't know

[smoky harness]

https://cdn.discordapp.com/attachments/866290319808266241/866715116464635904/unknown.png

cryptograph

anyone got ideas

[velvet condor]

bro do you know quadratic formula:)))

[smoky harness]

twa

yes

[vapid smelt]

the one which is derived from x2 + bx + c = 0?

[velvet condor]

uhhh

if $ax^2+bx+c=0{for some a} \ne 0~then ~x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

[ocean seal]

Minh Baka

[velvet condor]

no more testing

but yeah

you should know how this formula is derived

:))) just kidding

cant u solve (x-2)(x-6)=0

[vapid smelt]

uh i am confused

i do know the formula

[velvet condor]

you memorize it like a robot?

[vapid smelt]

uh no?

but if we are to use the formula then its supposed to be x^2- 8x + 12, right?

[gray isle]

apply the zero product property

[velvet condor]

yes

so how will you apply it?

[vapid smelt]

ok ima try

[velvet condor]

bruh.......

[gray isle]

you already have the correct factored form

[velvet condor]

ok-

[gray isle]

don't overthink it

[smoky harness]

RRRRRRRUUUUUUULLLLLLLLLLLLLLLLLLLLDUDUDU

decipher

[gray isle]

if
mn = 0
what does that tell you about m and/or n?

[vapid smelt]

that one of them is 0?

[gray isle]

if at least one of m and n is 0, mn will be 0

[vapid smelt]

right

[gray isle]

and apply that principle to
(x-2)(x-6)=0

[vapid smelt]

i got it in my head now need to put it on paper

[gray isle]

try not to overthink it

[vapid smelt]

right

thankyou

i apprecieate it

[high wolf]

$10=1.05^x$ how can i solve for $x$?

[ocean seal]

plain

[glass lichen]

log

[fathom cosmos]

Calculate the equation of the line if two points are (2,6) and (5,0)

Hint, you will have to find the slope of the line and then sub it into the equation y=mx+b

what is y,x,b in this equation

[high wolf]

thank you

[glass lichen]

y and x are the variables, b is the y intercept

[fathom cosmos]

ya

[high wolf]

the answer is in the form of e.g. y = 2x + 5

[fathom cosmos]

do i leave x y b as variables?

[glass lichen]

ok ignore what I said

[high wolf]

you have to find m and b

[fathom cosmos]

ok

i know how to get b, but idk how if i dont have y and x

[gray isle]

i know how to get b, but idk how if i dont have y and x
what does that even mean...

so do you or don't you know how to get b?

[fathom cosmos]

i dont know how because i dont have y and x

[gray isle]

you are given points

[high wolf]

the slope is $m=\frac {y_2-y_1} {x_2-x_1}$

[ocean seal]

plain

[fathom cosmos]

ya

m=-2

(0-6)/(5-2)

-6/3

so -2 right?

[gray isle]

m will be -2

[fathom cosmos]

ok, now how do i get y and x

[gray isle]

if you were to follow their hint, you would have
$$y = -2x + b$$
at this point

[smoky harness]

RRRRRRRUUUUUUULLLLLLLLLLLLLLLLLLLLDUDUDU

[ocean seal]

ℝamonov

[fathom cosmos]

ya

[gray isle]

your answer/equation at the end will have both x and y in it

[fathom cosmos]

oh

[gray isle]

sub in either point into the equation to determine b

[fathom cosmos]

how do i get b?

[gray isle]

https://discordapp.com/channels/268882317391429632/490557019623915520/866725733819482162

[fathom cosmos]

what does it mean?

[gray isle]

choose one of the points you're given

substitute the respective x and y values into the equation

then isolate b to get your value of b

[fathom cosmos]

ok

y=6 x=2?

[high wolf]

you can plug those values in to find b

[fathom cosmos]

ok

[high wolf]

btw you can plug in either point, both works

you'll get the same answer

[smoky harness]

help

pls i work on this for 6hrs

if anyone can just solve it in like 5mins

[fathom cosmos]

6=-2(2)+b
6=-4+b
10=b

[high wolf]

ya dat correct

do you know the next step?

[distant otter]

with what bro

you ain't saying much

[fathom cosmos]

y=-2x+10

[high wolf]

that's your answer!

[fathom cosmos]

ok thanks!

do i thanks someone or

[high wolf]

nope, that's it

[fathom cosmos]

ok

thank u for helping me

[high wolf]

np haha i need help with a lot of stuff too

[smoky harness]

RRRRRRRUUUUUUULLLLLLLLLLLLLLLLLLLLDUDUDU

this is a cipher

anyone got a clue?

[fathom cosmos]

do i have to find y and x or no?

i think that will be final question

[high wolf]

the question asks for the equation of the line

you got the equation of the line

[fathom cosmos]

this?

[high wolf]

yea

[fathom cosmos]

ok so i dont have to find y and x right?

[high wolf]

you don't have to uhm

[fathom cosmos]

uhm is...?

[high wolf]

https://www.desmos.com/calculator/03jwi7rvyh

the equation represents the relationship between the y and the x value

[fathom cosmos]

ok

omg best server ever

[high wolf]

hahah

[fathom cosmos]

thank you a lot

[high wolf]

i love this server too!

np

[fathom cosmos]

wait

plain, last question

@high wolf

[high wolf]

don't ask to ask, just ask

[fathom cosmos]

Which equation is in standard form?
Question 2 options:

a) 3x - 4y - 2 = 0

b) y = -2x - 3

c) 3x + 7y = 4

d) y = 2

is it b?

[gray isle]

no

[fathom cosmos]

standard form

no?

[high wolf]

nope

[gray isle]

b would be the slope-intercept form

[fathom cosmos]

then

is it a?

[gray isle]

no

[fathom cosmos]

?

c?

[high wolf]

yea it's c 😂

[gray isle]

are you just guessiong?

[high wolf]

HAHAHAH

[fathom cosmos]

i mean

i knew that d wasnt

so

ya sorry

[ionic jewel]

technically c and d are the same form

[karmic scarab]

perhaps more absurdly technically it'd be 0x + y = 2

[ionic jewel]

u really get me up there

perhaps even more absurdly technically it's be 0x + 1y = 2

i had to do it

[high wolf]

i was just waiting for that to happen

you have to find the hypoteneus

$a^2 + b^2 = c^2$

[ocean seal]

plain

[high wolf]

2.1 and 1.7

wait

how did you get 7.3?

okay now you have $7.3 = c^2$

[ocean seal]

plain

[high wolf]

you have 1 more step

it makes the fancy thing pop up

nope, $\sqrt {7.3}$

[ocean seal]

plain

[high wolf]

yup

i hope you learned something 😂

[copper wedge]

i have a question, and i want to confirm its as simple as i think it is. i have to write an algebraic expression of -19 divided by the quantity of g plus h

and i just -19 / g + h

[topaz scaffold]

Physics?

[sleek elbow]

#❓how-to-get-help @ornate peak

[ornate peak]

i get it

[sleek elbow]

good

[tawny venture]

What would be the procedure for this

[mellow canyon]

hey all! so I have a trig textbook that wants me to learn all the numbers/values excluded from the domain of all 6 trig functions, which seems utterly pointless to me. I suppose you could check to see if your answers are right, but other than that what is the benefit of knowing that a tangent function doesn't accept 90* or similar facts?

[glass lichen]

work through it while understanding how floor, ceiling and mod work

[alpine sable]

Uhmmm

Please

Help me

😭😭😭 other people tried explaining to me but

I can't do itt 😭😭😭😭

I looked at my text book and tried it's method but it still doesn't work

Find the value of a in eag of the following values

3 : 4 = a : 12

Please 😭

I don't get itt 😭

[twin pine]

okay calm down

why are you multiplying with 2?

[alpine sable]

Sorry, Im actually having a breakdown about this question.

[alpine sable]

Idk I'm trying to do the format someone gave me

I don't get it am I doing it wrong

Im doing method 2 LCM

I don't know

[stark pebble]

It's right in my opnion

Just sayin

[alpine sable]

😭😭😭 it's wrong I just know something is wrong about jt

[stark pebble]

Is it because of the decimal?

[alpine sable]

I can't figure out what it is

[alpine sable]

No?😭😭😭

[stark pebble]

Err

It's correct

:)

[alpine sable]

Do it your way and let's compare the answers 😭

[stark pebble]

The way you did it is my method tho

[twin pine]

What?

[stark pebble]

:>

[twin pine]

a=9

[alpine sable]

^^^^^

[stark pebble]

Ha?

[alpine sable]

That's what so many people said to me

I just don't know what I did wrong 😭

[stark pebble]

Me neithet

R*

[alpine sable]

Learning is about knowing what you did wrong and learning from it

[stark pebble]

I dont understand?

[alpine sable]

Not to be rude but are you qualified 😭😭😭

To be here.

[twin pine]

ok look, the method you are using, I have never seen before and it looks kinda unnecessary

[alpine sable]

The way you are typing it seems really naive 😭

[twin pine]

but let me explain what your friend is trying to do

[alpine sable]

Okie

Actually let me just re try it

And see if I get it correct this time

Oh I made a mistake

The denominator

I forgot that it should be the same 😭

HAHHAHAA IM so sorry if I was being really troublesome

[twin pine]

yes that is what your friend is doing but it just seems very stupid to me

[alpine sable]

[twin pine]

@alpine sable The rule is you multiply the numerator of the one side with the denominator of the other side and vice versa

[ocean seal]

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

andreask

andreask

[minor elbow]

need help with this plz

my answer was this

wait

but apparently its wrong

[little comet]

[minor elbow]

yes

[hybrid sparrow]

@alpine sable
Well,

you could think of two line segments that are connected at a jointed point B:

(Sorry for the horrible writing)

What would happen to the distance between A and C if you were to "fold" this line?

Also, flipped the numbers around, my bad

Well, you can't really halve the line,

but like... Move the line around,

y'know?

Like the hand of a clock, basically

What would happen to the distance between A and C?

That's if you made the lines intersect,

but they could also be like this:

Right?

Man, I need to work on my sketches XD

Well, either way, the distance would be shorter, right?

So, the thing we can conclude is that the maximum distance between A and C is when the line is straight, right?

The full 5 + 4 miles

Anything between 1 and 9 (including those numbers) is a valid distance between the two points,

but 10 doesn't really fit in that range

Hopefully the answer made sense!

Sure thing!

[little comet]

[warm wren]

First calculate the sixth derivative evaluated at 1 over 6 factorial. The sixth derivative is just -120/x^6, the 120 simplifies with the 6! in the denominator to 1/6 so you're left with -(1/6)*x^6 evaluated at 1. So just -1/6. Then we want (x-1)^6

So the result is just P6 = P5 + -(1/6)(x-1)^6
which is basically just this divided by 6 I think:

[minor elbow]

wait wha?

6!=720

how does 120/720 cancel out??

[warm wren]

oh yeah scratch that nvm xD one sec

[minor elbow]

lol yeah

i was thinking like whaaa

oh frick

i realised my silly mistake

[warm wren]

yeah my bad there's a 1/6 still left there

[minor elbow]

i put (x-1)^5 on the calculator

my badddddd

[warm wren]

oh...

[minor elbow]

i found my silly mistake lol

it should be ^6

bruh moment

yeah

i just did a silly mistake lol

@warm wren thx for the help tho

[warm wren]

no worries, it's good practice

[minor elbow]

can you help me with another thing plz

[minor elbow]

yeah

[warm wren]

I think the correct answer is just what you had times -1, the inverse, you probably lost a -1 somewhere in the calculations

so -t^3+12t^2+9t-220

[minor elbow]

omg thankyou

[minor elbow]

how willing are you to do like 5 more of these types of questions?

[warm wren]

uhm, idk, it usually depends on the problem, whether it's interesting or not 😄 or sometimes I just feel like practicing a bit as well, you can keep posting them around and someone might answer them, also I hope these aren't for an exam... 🤔

[minor elbow]

nah dw

just practicing

i have a lot to catch up on lol

i dont think a test would tell you its correct straight away lol

[minor elbow]

or give 10hrs time limit XD

[warm wren]

true, although i've seen some strange ass exams in my life :p

[minor elbow]

well damn

the closest im getting is an 8hr comp sci exam

in like 2-3 weeks

[fathom cosmos]

how do i change the original equations to that one

[minor elbow]

so sort them from steepest?

[fathom cosmos]

ya

[minor elbow]

i think the higher the gradient

the more steeper it is

[fathom cosmos]

what does gradient mean

[hybrid sparrow]

The number next to the x variable

[minor elbow]

cause gradient is legit the slope of a line

rise/run

[hybrid sparrow]

Multiplying it

[fathom cosmos]

ok

[fathom cosmos]

15*x

[minor elbow]

?

no the 15 next to the x is the gradient in y= 15x +5

[fathom cosmos]

oh so

if the number before x represent the steepness?

[minor elbow]

yes

[fathom cosmos]

ok

then

[fathom cosmos]

y=x+100 < y=0.15x-1 < y=4x < y=15x+5

is that it?

[fathom cosmos]

@minor elbow

[minor elbow]

uhhh

other way

the higher the gradient

the steeper it is

wait nvm

yeah thats right

good job

[fathom cosmos]

ok thanks

is it because increasing way?

[minor elbow]

i pulled an all nighter so my brain in a mess lol

[minor elbow]

yeah

[fathom cosmos]

oh

thank u for helping me

[minor elbow]

no worries

[fathom cosmos]

do helpers get paid?

[minor elbow]

im not sure

we'll need to ask a helper

probs not

[fathom cosmos]

ok

[grave hazel]

a friend of mine is having trouble with these two probability problems
we're both bulgarian, she's not articulate in english but she understands it well

if the channel's not in use that is

actually nvm, it's in #help-7｜zen1thxyz

[alpine sable]

Helpers are volunteers, they do not get paid.

[fathom cosmos]

ok thanks. I was just wondering how the systems work

[cerulean junco]

help .... the solution is given....but i can't understand it .Can someone EXPLAIN this ...PLEASE

[warm wren]

have you figured it out?

[minor elbow]

noooo idea

7hrs in and im about to die of sleepiness

[warm wren]

I think the matrix is ((0,-1), (-1,0)) and the polynomial is just λ^2 -1

it just inverts and swaps the coordinates

or rather, according to the problem t^2 - 1

[glad iris]

oof

[minor elbow]

nope

apparently not

i got it

wooooooo

its -1,0 and 0,-1

this one and

this one

the last ones

then i sleep for a week

[warm wren]

wait, didn't you find that one? that's the one i was referring to before

[minor elbow]

idk how to do a taylor problem backwards

oh lol

i was doing a different question

my bad

[warm wren]

oh, so is it this "((0,-1), (-1,0)) and the polynomial is just λ^2 -1"?

[minor elbow]

yeah

thank youuuu

[warm wren]

no worries, yeah that got me weirded out for a second there xD cuz if it was "-1,0 and 0,-1" none of it made sense anymore 😄

[minor elbow]

lol

yeah i'd be confused too

i have no idea how to do the last one

how do we work backwards for these?

[warm wren]

assume you have a third degree polynomial of the form ax^3+bx^2+cx+d and look for a, b, c, d

as we proved earlier p2(x) = p1(x) + smth
so we find smth
we take the 2nd derivative and evaluate at x = 0, and we find 2b, we divide by 2! and find b, then we multiply by (x-0)^2, so we have bx^2

So P2(x) = P1(x) + bx^2

next we have P1(x) = P0(x) + smth1
we try to find smth1
we take the first derivative and evaluate at x = 0, and we find c, we divide by 1! and still have c, we then multiply by (x-0), so we have cx

So P1(x) = P0(x) + cx

Next we calculate P0(x) which is just d*(x-0)^0 so just d

So now we have P2(x) = bx^2 + cx + d
and we also know that P2(x) = 4x^2 + 3

So b must be 4, c must be 0 and d must be 3

Therefore we go back to our original polynomial

f(x) = ax^3+4x^2+3 for all a in R

All polynomials of this form will have that P2(x) taylor polynomial.

So an example of it would be f(x)= x^3 + 4x^2 +3

[minor elbow]

damn

thats

quite something

[warm wren]

@minor elbow The other exercise below is the exact same logic as this one so it's left as an exercise to you xD Just follow the same steps. although you'll have to expand 3+8(x-1)^2 to 8x^2 - 16x - 5

[minor elbow]

oh thank you

[wheat radish]

Can someone help me with us?

[minor elbow]

bro thank you so much for all the help today

im gonna go to sleep so cya

[warm wren]

no problem, glad to help, rest well 👋

[warped phoenix]

Here, they're trying to find which two have the greater avg. rate of change

between the word problem and table

for the table, why did they find the avg. rate of change only for values 1-3? shouldnt it be of the whole table?

<@&286206848099549185>

anyone?

[warm wren]

What's θ here? the angle from the positive x-axis to the vector (-5,-12)? If yes:
First calculate the hypotenuse, which is 13, since sqrt(12^2 + 5^2) = 13 (which is basically the distance of the point from the origin)
Calculate the sine if the angle was only from the negative x-axis to the vector.
So sinθ = 12/13, cosθ = 5/13 and tanθ = 12/5
But these are from the negative x axis, you want from the positive. So the cosine and the tangent is the inverse.
So sinθ = 12/13, cosθ = -5/13, and tanθ = -12/5.

So since we know the angle is in the 3rd quadrant, and we know the trig numbers, we find that the angle is about 247.38 degrees.

For the second question I assume you can figure it out yourself. Just remember the basic trigonometric numbers:
sin0 = 0 cos0 = 1
sin30 = 1/2 cos30 = sqrt(3)/2
sin45 = sqrt(2)/2 cos45 = sqrt(2)/2
sin60 = sqrt(3)/2 cos60 = 1/2
sin90 = 1 cos90 = 0

From these you can calculate the tangent as well.
When you go from +x-axis to -x-axis the cosine inverts
when you go from +y-axis to -y-axis the sine inverts.

[wheat radish]

Ok thank you. That helps me understand a lot more 😁

[warm wren]

This makes no sense at all. Is this from a book??
The legend says "for each value of x, the value of the function is found by multiplying by 2 and then squaring"
So f(0) should be 2*0^2 = 0
f(1) should be 2^2 = 4
f(2) should be 4^2 = 16
f(3) should be 6^2 = 36 etc. etc.

Then the average rate of change is the average from all the rates of change so:
4-3=1
11-4=7
30-11=19
67-30 = 37
and then you take the average out of these
so (37+19+7+1)/4 so 64/4= 16

This seems like a very weird problem? 🤔

[warm wren]

no problem, glad to help

[warped phoenix]

yeah its from a pearson algebra II book

i regret taking the course

[random pelican]

sorry for interrupting, but a quick question, what is a³ - a?

[warped phoenix]

they're teaching things in the wrong order, they have, (worse than typos), entire problems wrong, they're teaching bits of calc, none of it makes sense

its dumb

[past sundial]

i THINK a and the small 2 because a x a x a - a = a x a
forgive me if I’m wrong

Like the small 2 I can’t type it like uh
2
a

But the 2 is smaller

[warped phoenix]

assuming you're factoring, it's $a\left(a+1\right)\left(a-1\right)$ i believe

[ocean seal]

TheMane3

[warm wren]

Damn, that's really unfortunate man :/ I hope it doesn't chase you away from math though :p just a bad experience is all

[warped phoenix]

it would be $a^2$ if he was dividing $a^3$ by a, not subtracting btw

[ocean seal]

TheMane3

[warped phoenix]

its all good, it just sucks because i want to take precalc in the upcoming school year which is why i took this summer course, but if the course itself is in shambles im afraid i wont pass the test to test out of alg 2 which would allow me to enter precalc

praying for the best tho hahha 🤞

[warm wren]

that's the spirit 😄

[warped phoenix]

$g(x) = -2\left|x+1\right|-2$

[ocean seal]

TheMane3

[warped phoenix]

The vertex of this is (1, 2), right?

[woven pollen]

-1

[warped phoenix]

?

[woven pollen]

graph it

[warped phoenix]

i see that it's -1, -2

but that doesnt make sense

a vertex is (+h, +k), isn't it?

[woven pollen]

you can't see something that doesn't make sense 😸

[warped phoenix]

it doesnt make sense because i dont understand why that's the vertex when a vertex is meant to be (+h, +k)

[woven pollen]

seriously, grah it.

[warped phoenix]

i did.

[woven pollen]

I don't want to go around in circles. But either your graph is wrong or your belief the vertex is (+h,+k) is wrong? pick one.

[warped phoenix]

(h, k), according to vertex form, h is within the absolute value signs and the k is to the right of it

according to that, the vertex should be (1, -2)

h is 1

k is -2

how is h negative

i can clearly see

that the graph shows it as such

why is that

[woven pollen]

maybe the general form is (x - h, ... ) and not (x + h, ...) ?

if it is x - h then x - (-1) agrees with your graph AND the equation (question)

[warped phoenix]

so h is normally negative?

[woven pollen]

usually. yes.

[warped phoenix]

that i was unaware of

so its (-h, k)?

[woven pollen]

no.

the basic form of the equation is a*|x-h|+k

[warped phoenix]

ahhh

right

huh

so why does h become the opposite sign

in abs(x - h), why is h positive, and in abs(x + h), why is h negative

[woven pollen]

if you graph a few dozen of them, you'll "get it"

[warped phoenix]

well im looking at a graph of (x - h) and (x + h), and im not quite sure what im looking at..if it's (h, k), then you should also take the sign of h, just like you do with k, right? in (x - 1) - 2, the vertex should be (-1, -2), but it's not, why do you take the sign of k (-) but not the sign of h?? if you have no clue what i just said, thats fine, regardless, ill just remember that h is going to be the opposite of what the sign inside the parenthesis is, but k wont

[pearl wraith]

guys i dont understand

can someone help me

to find the value of the equation

[old swan]

The figure formed by (−3, 2), (−4, 1), and (−1, −5) is translated 3 units right and 5 units up. What are the coordinates of the new figure?

i serriously have no clue how to do this

[past sundial]

Translate means move. Now equation turns to this:

The figure formed by (−3, 2), (−4, 1), and (−1, −5) is moved 3 units right and 5 units up. What are the coordinates of the new figure?

If you still need help, I can explain more.

[gritty cave]

i forgot how it goes from step 2 into step 3

[smoky harness]

Yo

You have to translate it then decrypt

[barren wasp]

Use the function to find the preimage of w.

T(v1,v2)=(3√2v1−12v2,v1−v2,v2), w = (3–√,2,0)

The preimage of w is [w].

[glass lichen]

what spaces does T act from and to?

also the mapping is very tricky to understand due to lack of notation

[barren wasp]

@glass lichen does that help?

I had got v2=0 and v1 = 2

[glass lichen]

v_2 is clearly not 2

comparing the 3rd components gives v_2=0 IF w is in Im(T)

but yes, v_1 = 2 and v_2 = 0 gives w

[barren wasp]

Sorry I had made a typo

V1= 2
V2 = 0
It had said that was wrong.

[glass lichen]

$T[(2,0)]=(\sqrt{3},2,0)$

[ocean seal]

Mosh

[barren wasp]

Okay so maybe I had formatted it wrong when Answering. I Entered <2, 0>.

[glass lichen]

yeah I cant help w/ formatting how an online submission wants it

[barren wasp]

Im somewhat bland on interpration of things, but just to confirm I am correct?

[glass lichen]

yes,

[barren wasp]

That makes me feel bettter, Ive scratched at this for a few minutes and didnt understand where this simple of a question was went wrong.

For this one, I got it failed scalar and addition. It took me a bit, my question is do you have any tips on how to analyze and answer quickly

[glass lichen]

just go through the conditions

I mean in this instance you can just know it's not linear because the mapping is just the standard parabola

[barren wasp]

Ah

[glass lichen]

/ can be thought of as that

[barren wasp]

That would instant fail Scalar right>

[glass lichen]

yes since c!=c^2 always

[barren wasp]

I forgot about those sneaky tricks

[glass lichen]

$T[(cx,cy)]=(cx,(cy)^2)\neq (cx,cy^2)$

[ocean seal]

Mosh

[glass lichen]

then additivity is just that freshman's dream isnt true always

(x_1+y_1)^2 != x_1^2+y_1^2

[smoky harness]

hi

anyone kknow a constructed languages detector or translator?

or is there a bot?

[old swan]

i just need the answer and an explination on how you got it, my assignment is already late

[arctic glen]

can anyone help me with this

[rich basin]

33 degres

@arctic glen

033 actually

[arctic glen]

how did you get that answer?

:|

[rich basin]

My bad

i thought O was described by the right hand

but O is the actual bearing

[arctic glen]

mmh

mhm

[rich basin]

Lets just say O is a point

and A is another point

You would have to turn 123 degrees clockwise inorder to rotate towards A

if you were facing north on O right?

[arctic glen]

mhm

[rich basin]

anything you missing?

[arctic glen]

would this be followed by the same thing your saying right now

or is this something completely different

[rich basin]

Yeah they are similar

[arctic glen]

ok

[ionic jewel]

combine the logs?

also why is there an equality inside the log?

[vagrant tinsel]

Hello, I got a question relating to financial maths lol.

Idk how to figure this out

[alpine sable]

Are you familiar with the formula $P(1+\frac{r}{n})^{nt}$?

[ocean seal]

Cicopath

[vagrant tinsel]

yes

@alpine sable

[alpine sable]

Alright, so it looks like that formula has to be applied here

[vagrant tinsel]

ok

[alpine sable]

Let P be the initial investment, r is the % rate in decimal, t the time in years, and n the # of times it's compounded per term of t, in this case per year

In summary, replace the variables with their respective values

[vagrant tinsel]

where does the 4 times go then?

[alpine sable]

So, t will be in years. That will be our x

We have the numbers for n and r, r = 0.11 and n = 12, yes?

[vagrant tinsel]

uhhh

I’m not sure

the 4 times confuses me

[alpine sable]

$P(1+\frac{0.11}{12})^{12t}$

[ocean seal]

Cicopath

[alpine sable]

The 4 times comes in when we make it into an equation

$y=P(1+\frac{0.11}{12})^{12t}$

[ocean seal]

Cicopath

[alpine sable]

So now that we have an equation, what exactly is y?

[vagrant tinsel]

I just have to calculate the number shown right?

[alpine sable]

You are asked to find how much time it will take for the initial investment to quadruple

We know the initial investment is P

So, how much is 4 times the initial investment?

4P

Does that make sense?

[vagrant tinsel]

so 4 is the P?

[alpine sable]

Nono, P is the initial investment

[vagrant tinsel]

so 4 is Y?

[alpine sable]

If we want the investment to be 4 times the original

We multiply the initial investment by 4

[vagrant tinsel]

ok

[alpine sable]

Say the initial investment is 500, this is just an example

I put 500 to invest

[vagrant tinsel]

ok

[alpine sable]

I want to figure out how much time it will be for my investment to quadruple

So, I know $500 * 4 is $2000

[vagrant tinsel]

ok

[alpine sable]

$2000=500(1+\frac{0.11}{12})^{12t}$