help-0

[alpine sable]

yes

it'd be

another similar problem. it'd be reflection

not rotation

because if I rotated it, the labels would be different

[gray isle]

i mean based on this set of questions

they probably are drawn to scale

[wary stream]

It wouldn't be dilation, the size change would be noticeable

[gray isle]

yeh. i guess for dilation they'd extend legs

you should probs just ignore that "not drawn to scale" because, they it really feels like they are

[wary stream]

Like the shapes are still similar in size that it's barely noticeable for dilation

[alpine sable]

what's the difference between < and nothing at all (AB ~= BC)

[gray isle]

between what and what

[wary stream]

One is angle symbol

[alpine sable]

<J and <T

[wary stream]

The other is just the side

[alpine sable]

oh

[wary stream]

No symbol = side

[gray isle]

two letters refer to lengths of a segment

[wary stream]

So JI is a side/segment

<J is angle J

[mortal remnant]

Anyone know how to do this

[wary stream]

Apply alternate interior angle to find angle A, and sum of angles in triangle to find angle ACB

[mortal remnant]

So a would be 49 but I'm just not sure what put for ACB

180-49-49

[wary stream]

Why would A be 49?

[mortal remnant]

Aren't they the same angle

[wary stream]

As B? No

[mortal remnant]

I'm lost then

[wary stream]

Alternate interior angle

That angle 149 is useful information

[mortal remnant]

Would you subtract 180-149 to find E

[chrome plinth]

how do you determine what coordinates are x1 y1, and x2 y2 when determining the slope?

[wary stream]

Yes

[mortal remnant]

So then e and D would be 31?

[wary stream]

You can label how you want, just as long as x1 is still paired y1 and x2 with y2

[wary stream]

You don't need D

[mortal remnant]

But to find C wouldn't we need E and D

[wary stream]

And angle $$E \neq D$$

[ocean seal]

dldh06

[wary stream]

Find A using alternate interior angles

Do you know what that is?

[mortal remnant]

Nope

[wary stream]

My suggestion, review that part

Because using that, you can find A

[gaunt coyote]

hello

anyone here is good at excel and math?

i have a very complicated question

tryd now like 4 ppl here they tryd it but no succes so far

best would be when u are a trader

[cedar wave]

Have you tried one of the more advanced math channels? I don't know what your problem would best fit in, but maybe #computing-software for example?

[broken oak]

how would i get x?

[gaunt coyote]

i will give it a try thanks

[wary stream]

Apply this concept

You can find y which helps find x

[broken oak]

if i find y then im done

[cedar wave]

you shouldn't even need to find y

[broken oak]

with y i can subtract 37 with it

[cedar wave]

You can find z by realising all angles of a triangle sum to 180 degrees, then use that and the image dldh06 just sent

[wary stream]

You don't but it would make it easier because sum of angles in a triangle is 180

[broken oak]

i already know z

31

[cedar wave]

Ok so what is the total angle of the bottom left corner?

[wary stream]

Plus angle Z = Y

[cedar wave]

that works too

[broken oak]

then y = 68

[wary stream]

No

[cedar wave]

No, y = z

[wary stream]

Y = Z

[broken oak]

31

kkkk

[wary stream]

Now find X

[broken oak]

112

respect to you

[devout tundra]

[wary stream]

Respect Google, because all that information I used was from Google, meaning you can Google the info first and if you get stuck, you can ask for more assistance

[trail zinc]

anyone know what inequality ∣r∣>6 means?

[alpine sable]

Like you asking about what the vertical bar on each end mean?

Just the modulus of r is greater than 6

[ionic jewel]

absolute value of r is greater than 6

don't you need two operators for modulus

[trail zinc]

i just dont get what ∣r∣ is tbh

[alpine sable]

thought modulus was a synonym ¯_(ツ)_/¯

[ionic jewel]

no

modulus is like

11=1 (mod 5)

[ionic jewel]

whatever r is, but positive

|-5| = |5| = 5

[trail zinc]

oh i see thanks

[alpine sable]

In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. - Wikipedia

[agile kayak]

can someone help me?

[alpine sable]

and plus most of the time I see people use "modulus" for abs val

[ionic jewel]

well on that case works for me, but I've used abs for that, and modulus for... modulus

[alpine sable]

seen it in books so I started calling it modulus

[ionic jewel]

but fair

[alpine sable]

Not talking about modular arithmetic

[ionic jewel]

maybe different countries

[alpine sable]

Plus isn't that called Modulo

[ionic jewel]

either way it's the positive value, and i have to go

idk

i shorten it to mod

lmao

[alpine sable]

well then suite yourself

bye then

[agile kayak]

can someone help me ?

[tiny rampart]

Go on

[agile kayak]

I have a excel sheet with a bunch of approvals from people. There are 2 sets of age ranges. 18-34 and 35-45

my statistical question is how many over these people approved compared to the other age range

and i need to find out the probability of all of it

in other words i need to calculate the probability of 1 age range having more approval than the other

[tiny rampart]

Oh dang. I sucked at stats, hopefully someone will be able to help you on this. 😩

[agile kayak]

its okay thanks anyway 🙂

[alpine sable]

a plane is at an altitude of 822m trying to land. The angle of depression towards the airstrip is 8 degrees. since there are too many planes on the first runway, the aircraft must land on the next runway which is triggered at a 7 ° depression angle to the aircraft. What is the distance between the two airstrips

[trail zinc]

Rhiannon is making punch for a picnic. She wants to make enough for each person to have at least 1 1/2 cups of punch. There are 8 people coming to the picnic. Write an inequality for the number of cups of punch, c, that Rhiannon can make for the picnic. Use a number line to find your inequality

[junior thorn]

Is this channel busy?

Rn

Anyways
Why do math love e so much ?

Why is it everywhere uf its just a number

I understand pi because that's the coefficient of circles and we have nothing to do with it

It experimental

But e HUGHHHH WhY?

[alpine sable]

Search it up

Works like pi but different usage

Euler's Constant is usually used for compound interest

or just works with exponential growth

; exponential relationships

[junior thorn]

Oh

Compound interest makes sense

Whenever there is money I'm in

Thank you I like e now

[sinful night]

It's got interesting unique basic properties

[junior thorn]

Other than compound interest?

[sinful night]

If you add all the reciprocals of factorials, you get e

1/0!+1/1!+1/2!+...

[junior thorn]

Yeah yeah you reminded me

Really interesting actually

[sinful night]

It's also the solution to the differential equation y'=y

[junior thorn]

That the addition of those happen to be the value of many other things

Omg really?

[sinful night]

e^x

[junior thorn]

This one blow my head

[sinful night]

The function whose derivative is same as itself

[junior thorn]

Yeah your right

Omg things add up now

Math is super interesting guys

My mind have just clicked

Does it have more surprises ?

[sinful night]

Also you can write all the trigonomic functions using e and imaginary number i

And of course the famous euler's identity

[junior thorn]

How come !!

Yeah

[celest ledge]

I posted a question on math stack exchange yesterday can i post a link here?

[junior thorn]

I'm just trying to understand why the same number happen to be in really broad things

Ukwim?

Like these things have a relation somehow

[sinful night]

Also e can also be written as this repeated fraction

Which is pretty cool

e is also a trancendental number

[junior thorn]

This one is new to me

Does it have a name?

Transcendental?

Now you r touching the limitations of my knowledge

Lmao

[sinful night]

e is also the base of the natural log

Which has deep connections with prime numbers

And also e is essential in statistics

[junior thorn]

Blow my mind

Omg

Math is so connected

[alpine sable]

Damn you're really going into Euler's Constant

[junior thorn]

That's crazy

Yeah he is

I'm impressed

[sinful night]

Also for the function $x^{\frac{1}{x}}$

[ocean seal]

Pybro

[sinful night]

The maximum is at x=e

[junior thorn]

Smh

If you went in a date with e you wouldn't know that much

[sinful night]

Lol

There's a reason why e and pi are so infamous

[thin stag]

gonna post a question in the next 2 mins, hope its okay w you

copied from #linear-algebra

i was having trouble understanding this passage in lax's linear algebra book , about the transpose of a matrix:

namely the sentence '...we see the matrix T acting from the right on row vectors is the same as the transpose of the matrix T acting from the left on column vectors'. isnt the transpose of the matrix T acting from the left on the row vector l?

for context, l is a row vector representing an element of the dual vector space, and the transpose is defined with dual vector spaces as shown in the picture

[alpine sable]

Found this funny but dark intuition for AM-GM on math.se, but I am not super well practiced with probability stuff so I have a few misunderstandings/questions

If we're getting the probability of survival, why multiply (AND for independent events) the probabilities of death p_i instead of the product of (1-p_i)? (strategy 1)

Hi John 😳

hope you're well grandma pinch

[rotund steeple]

hey

yeah thats like, probably a mistake on their parts

changing p_i with 1-p_i doesnt change the arguement

[alpine sable]

ah ok that means strategy 1 makes complete sense for me then

but I am confused about 2 even if the typo is fixed, wouldn't you put Binom(n, p_i) instead of p_i^n?

[rotund steeple]

well binom(n,1-p_i), and notice how thats precisely (1-p_i)^n

(although it is better to think of it directly, each one has ntimes you need probability 1-p_i to survive)

[alpine sable]

with 0 successes right

those are equal

[rotund steeple]

sure 0 successes in hitting the lethal electricity ig lol

but yeah basically change each instance of p_i with 1-p_i and the arguement remains unchanged basically

[alpine sable]

yeet

[tight locust]

this is more of a CS question, but consider this: you have a function fib(n) that returns fib(n-1)+fib(n-2) for n>2

how many times is the function called?

[alpine sable]

@proud fractal me or someone else can just help here

[proud fractal]

Okie

Please I just have 3 of these to do to bring my grade up to a 80 sumthin

And I dont wanna fail it

But I dont understand

It says givin the rational function of graphing form y=a/x-b+c , complete the information requested.

[alpine sable]

okay, a rational function has x in the denominator

so for the area of the rectangle, we know that the rectangle has to touch the curve at a certain point

[proud fractal]

Mhm

[alpine sable]

if we plug in $x=4$, we solve for $y: \frac{6}{4-3}$ and get $\y=6$

[proud fractal]

?

How did u get 4

[ocean seal]

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

[proud fractal]

I only have 32 minutes left

I'm gonna cry

[alpine sable]

ok, we'll hurry

[proud fractal]

But I dont understand is at all and my adhd is going crazy

I dont want to fail it or not be able to finsih is

[alpine sable]

I got four because you'll notice that y is positive, if x < 3 then Y is negative, if x = 3, y DNE

[clever herald]

hey guys i'm learning inequalities in 7th grade and i still don't understand this boundary thing

like for example

[alpine sable]

the channel is busy go read #❓how-to-get-help

[proud fractal]

I really just need to know how the a b and c transform the graph like does it make it go left or right or up and down

[clever herald]

"Now figure out if the boundary, x = 33.75, is a solution to the inequality."

sorry about that

[proud fractal]

Pingu it sound a bit nicer if yall said please just a tip I'm not trying to judge or anything

[alpine sable]

the area of the rectangle is 12, not 6

[proud fractal]

I didnt put 6

Its plugged in

The teacher put it there

I dont fill in that one

[alpine sable]

what are your options for transformation of a?

[proud fractal]

I have 15 minutes left actullay

Would a be vertical horizontal or none

[alpine sable]

horizontal dilation

[proud fractal]

Yea I'm just gonna fail it caus ethe next question is longer and harder

[alpine sable]

a is both vertical and horizontal translation

to make another question just do $y=\frac{12}{2x-6}$

[ocean seal]

bleh

[alpine sable]

equation*

[spark ibex]

is my answer for question 8 correct and is the 3d model correct?

[alpine sable]

Why is a^0=1

[wary stream]

Because any number to the power of 0 is 1

[alpine sable]

But why

[wary stream]

It was how math was designed?

Like why is 1/0 undefined?

[barren pawn]

take any number you like a^0= a^4-4= a^4 / a^4 = 1

[barren pawn]

because you cant do the reverse operation

[spark ibex]

can someone answer my question

[proud fractal]

I got a 65

[wary stream]

This was more of an example that defined math, pretty much. It's just something that everyone knows

[barren pawn]

but this makes sense so its not about design, its like 0!

[alpine sable]

Why did you choose 4

[wary stream]

It can be any value

[barren pawn]

any number to prove that it minus itself is zero

[alpine sable]

Shouldn’t you root it with fourth root to get 1 instead of subtraction

[barren pawn]

nope

[alpine sable]

Then I think this is false too

[wary stream]

I believe that @barren pawn wrote it as $$a^{4-4}$$ not $$a^{4} - 4$$
Right, @barren pawn ?

[ocean seal]

dldh06

[barren pawn]

yep

[alpine sable]

Thanks I get it now

[onyx chasm]

how was the gamma function found? $x!\approx \Gamma(x+1)=\int_0^\infty t^x e^{-t}dt$

[ocean seal]

Pedrosso

[onyx chasm]

like how did they find the gamma function as an interpolation of x!

[alpine sable]

At which age do one study these things?

[onyx chasm]

idk

[alpine sable]

So I don’t study these when I’m 16?

[sinful night]

Yes

[alpine sable]

Pls study

Now is the time

otherwise you'll regret all your lyf

[onyx chasm]

I found a random question chat that was empty, yet my question was ignored

why?

[alpine sable]

Whyyyyyyyyyyyy?????????????????

[onyx chasm]

#❓how-to-get-help doesn't say anything bout this

[alpine sable]

https://tenor.com/view/jonah-hill-yay-african-child-screaming-shouting-gif-7212866

[sinful night]

Idk ask euler

He thought about it for a really long fucking time

To come up with the gamma function

[onyx chasm]

he dead

[alpine sable]

So my brain is big enough to understand this even if I’m 15

[onyx chasm]

Correct... I think

anyway but yeah, how was the gamma function made?

[alpine sable]

Ask Euler, talk to his spirit

[onyx chasm]

Since ur being sarcastic in this discord to my question, is there something wrong with my question?

[alpine sable]

No

[sinful night]

What do you mean by how it was made

[alpine sable]

Math doesn’t have answers to everything. I hate that we have to accept things without understanding them fully.

[sinful night]

The history?

The proof?

[onyx chasm]

what I mean is

for finding a function to interpolate x!, how was the gamma function... well.. for the lack of a better word bcuz im stupid, how was it made?

[sinful night]

You didn't clarify a single thing

[onyx chasm]

sry

[tepid otter]

how can i answer this question

[onyx chasm]

this channel is in use

kinda

trying to get it to be

xD

[sinful night]

Euler first came up with the infinite product expression of the gamma function

[onyx chasm]

ok

how?

[sinful night]

Later he came up with the famous integral one

Do you want the proof?

[onyx chasm]

well the proof is just testing if it applies to x!'s rules... right?

[sinful night]

So for this expression

If we find the limit as k approaches infinity

The expression can be changed to this

And the limit of the numerator and the denominator both converge to 1

So it converges to 1

So by multiplying n! this expression holds

No

Not yet

[onyx chasm]

ok

[sinful night]

Because this holds

[onyx chasm]

aight

[sinful night]

The expression can be changed to this

And also this expression can be changed to this

So this holds

And if you divide the last expression by n, that is Euler's infinite product expression of the gamma function

[onyx chasm]

aight, you did what I asked for even I myself didn't even know what I was searching for bcuz dumb

thank you

[alpine sable]

Don’t forget to ask Euler too

[gaunt coyote]

hello
anyone here is good at excel and math?
i have a very complicated question
tryd now like 4 ppl here they tryd it but no succes so far
best would be when u are a trader

[bronze spade]

what's the question ? What's you goal ?

[gaunt coyote]

i want to calculate the total loss

hard to explain

thats a dollar cost average sheet

u know what that is?

[bronze spade]

I don't know the signification of "total loss"

[gaunt coyote]

but u know what a dca sheet is ?

if not i have to start explain this first

[bronze spade]

I don't know but it's too far from the maths I do I guess

[barren pawn]

its a cramer system or you could go on substitution

[celest ledge]

https://math.stackexchange.com/questions/4153688/which-are-the-interior-angles-of-a-crossed-rectangle Ive updated my question with relevant information. Its more of a self documented journey to understanding self intersecting polygons rather than a question.

but id like for people to look.

[radiant bane]

does anyone know how I would solve this? I have literally no idea also kinda urgent

[ionic jewel]

why is it urgent

[alpine sable]

https://tenor.com/view/dance-moves-dancing-singer-groovy-gif-17029825

[ionic jewel]

<@&268886789983436800>

multiple channel rickroll spam from @alpine sable

[radiant bane]

cause its late lol i wanna sleep

I just need an idea of what to do

[sly mantle]

b&

[radiant bane]

nvm i figured it out lmao

[limber ledge]

Hi

is anyone available

can I please get some help with this problem

[carmine lion]

Uhhh

Aren't there 8 faces

[limber ledge]

how?

from what I can tell there are 5\

[wary stream]

It's 2 square pyramids on top of each other on the square base

[limber ledge]

ok

4 edges

then

[wary stream]

2 square pyramids, this value is for one

Actually that value would be the upper/lower pyramid

[carmine lion]

^

[limber ledge]

so 8 edges

?

[wary stream]

Yes

[limber ledge]

ok

8 faces and 8 edges

what about verticies

@wary stream

[wary stream]

There are more than 8 edges

[limber ledge]

..

[wary stream]

What do you know about vertices?

[limber ledge]

let us clear up the edges first

[wary stream]

I thought you were saying this for the amount of faces, which is 8

[limber ledge]

yes

what about edges

16

[wary stream]

Nope

Just count the amount of lines there are

Also 16 isn't an answer choice

[limber ledge]

12 egdes?

@wary stream

[wary stream]

Yes

[limber ledge]

ok

now for vertices

how many are their

[wary stream]

Sum of angles in a trapezoid and triangle

[wary stream]

What's are vertices?

And the concept of supplementary angles

[limber ledge]

not sure

[wary stream]

Find the missing angle in the trapezoid, apply supplementary angles to find z, when you get z, supplementary angle with y, then find the missing angle in the triangle, then supplementary angle with x @night scarab

[wary stream]

It's when two or more edges meet at a point, correct?

[night scarab]

so what would the answer be?

@wary stream

[wary stream]

I don't tell answers, but I will help you understand the concept

So step one, find the missing angle in the trapezoid @night scarab

[alpine sable]

Did I do it correct for question 8?

[wary stream]

This channel is currently busy

[wary stream]

I'm not sure sure about combinations/permutations, sorry

[alpine sable]

Ok

No worries

Can someone help with 4b

[wary stream]

For this, would you multiply the possibilities together? So the first blank would be 4, then 5, and then 4?

[alpine sable]

Isnt it 4 x 5 x 4

Yeah

Ok can u help me now

Wait yeah

It’s 4 4 3

Cuz i should do the middle one last

Go ahead homies

I got it

[wary stream]

Use the quadratic equation to find the solutions of each equation. I don't recall the general solution but that could easily be looked up

[alpine sable]

What do you mean by general solutions

[wary stream]

It would be 4, 4, 4. First space is limited to 4 values, then the last is limited to 4, and the middle limit to 4 because no repeats

[wary stream]

That general form

[alpine sable]

Whats general form

[ocean seal]

dldh06

[alpine sable]

Can you please go through the questiom step by step

[wary stream]

Find the solutions of each quadratic equation

[alpine sable]

What what

But e^lamdax is not a constant

[wary stream]

Do you know how to find a solution to a quadratic equation?

[alpine sable]

Yesss

[wary stream]

Find the solutions of that

[timid wind]

Is there a calculator for matrices

[wary stream]

https://tutorial.math.lamar.edu/classes/de/SecondOrderConcepts.aspx
Look at that link, it'll help

[wary stream]

You can look up matrix calculators on Google

[alpine sable]

So im screwed

Im gonna fail

Or worse

🙃

<@&286206848099549185>

[strange lagoon]

Can anyone help me with this question -->

We just had a massive trial of Farkonicus, I’m sure you saw the trial on the Probastream this
morning, everyone was tuned in. As you know, there were exactly two witnesses: Kantonimus and Rambicitus.
They both have a long history of not being fully accurate. Kantonimus has a probability of 13 of telling the 14
truth and Rambicitus has a probability of 14 of telling the truth. Both Kantonimus and Rambicitus stated
15 that Farkonicus was guilty! We know that statistically, Farkonicus is guilty with probability 300 . I’m not good
at probability, but I heard you are! I was wondering if you could tell me what the probability that Farkonicus is actually guilty? (We can assume that Kantonimus and Rambicitus telling the truth are independent events.)

[sand lichen]

<@&286206848099549185> how would i get 2 fractions with unlike denominator for 3/5

[remote heron]

huh?

[sand lichen]

i got a but not b

thers another question like this too

[remote heron]

i would try like

so you want them to sum to 3/5

then 1/5 + 2/5 seems like the intuitive choice

but theres a lot of ways we can express 3/5

say like

6/10

9/15

there are equally intuitive ways for choosing how to split these up

[sand lichen]

so i can use 6/10 + 9/15

right?

[remote heron]

well 6/10 = 3/5

and 9/15 = 3/5

so 6/10 + 9/15 = 6/5

not a sum of 3/5

idk you can do the cheating way if you want

which IDK will get you full credit

but if 1/5+2/5=3/5

then 2/10 + 2/5 = 3/5

[sand lichen]

is 2/5+1/5 = 3/5 right

[remote heron]

yea

it is

[sand lichen]

ok

[elfin snow]

well how about this

3/5=6/10

you could take two numbers that add up to 6

for example 1 and 5

1/10+5/10

but 5/10 reduces to 1/2

so 1/10+1/2 works

[sand lichen]

B has to have a different denominator

[remote heron]

it does

[elfin snow]

exactly

[remote heron]

these are the two ways to go about doing this problem i think

[sand lichen]

so 1/10+1/2 works

[elfin snow]

yes

[remote heron]

do you see why

[sand lichen]

ok

[elfin snow]

it's all about splitting the fraction

[remote heron]

its a little weird since its like

its like adding two fractions with dissimilar denominator

but backwards

[elfin snow]

you said there's a similar problem so try it on that

[sand lichen]

ok

thx

[ocean gust]

i need to know what this graph shows

[remote heron]

?

its a graph

whats the context

[ocean gust]

yeah but is it like something specific? like a phenomenon in maths or something? there's no question, i just need to find what this graph might be about

[sand lichen]

Using a model, explain how dividing a number with a fraction is the same as multiplying the number with the fraction’s reciprocal?

how do use a model

https://apps.mathlearningcenter.org/fractions/ You can use models in this website to show me

[remote heron]

idk how youre supposed to figure that out

without more context

it kind of looks like x=1 -> f(x)=pi/2

so something like arcsinx? idk

its not shaped like arc sin though

maybe someone smarter than me

[remote heron]

this site doesnt work for me

[sand lichen]

oh but can you explain

[remote heron]

for what class?

you could use algebra

[sand lichen]

math fractions

or i have another question

[remote heron]

okay

[sand lichen]

u can help me-with

[remote heron]

can the denominator be 20

like in the result?

[sand lichen]

yes

[remote heron]

idk if theyre implying that it can be reduced

[sand lichen]

the answer for the 2 fractions

[remote heron]

if it can be reduced after you multiply then yes

[sand lichen]

i was away when we learned this

[tawny lion]

hi

[remote heron]

say you wanna find two numbers

whole numbers

take 8

multiply it by one of the numbers

then divide it by the other

you want it to equal 20

thats sort of the core of this, youll have some additional weirdness since the 8 is inside of another fraction

or you can try uhh

try rewriting 2/8 in lower terms

thats probably the easier way

$\frac{2}{8} = \frac{1}{?}$

[ocean seal]

jan Niku

[remote heron]

@sand lichen make sense?

[scarlet spire]

i think it implies it cant be reduced. thats just my input tho

[remote heron]

or uhh

start at 1/?

reduce this first

this makes the problem much easier

[sand lichen]

yes i think i get it

[plain summit]

Free channel?

[shut tartan]

Ally goes to the store to purchase 5 Middle Eastern country flags.

Which counting method would be used to determine the number of 5-flag possibilities Ally could purchase? Explain.
How many 5-flag possibilities does Ally have?

can anyone help

[remote heron]

how many middle eastern countries are there

i guess it doesnt matter

counting method?

sounds like a combination to me, idk if thats what its asking

[remote heron]

most of the other channels are super dead atm

[plain summit]

Yeah but I asked in #help-4 and no one replied...

[shut tartan]

there are 20 countries in the image

so do i just do 5!=120

[remote heron]

idk i think its way higher

think you have 20 flags to choose from

assuming you can get duplicates

[shut tartan]

i think i use the combination formula then

[remote heron]

since a flag store probable has more flags than just one of each

[shut tartan]

so i do 20 nCr 5 = 15504

[shut tartan]

The number of 3-digit numbers less than 500 that can be formed if the last digit is a 7, 8 or 9 is ________. Assume that a 3 digit number cannot start with a '0'.

what about this

[remote heron]

this seems like something you could just enumerate

its a proportion right

[summer quiver]

$3 \cdot 10^2$

[ocean seal]

iateawalrus

[summer quiver]

right

[remote heron]

try counting

[summer quiver]

Because the two numbers that aren't 7 each have 10 possibilities

Then we do the same for 8 and 9, which gives us the same number

so $3 \cdot 10 \cdot 10 = 300$

I think

[ocean seal]

iateawalrus

[shut tartan]

idk how to do it you have to use the fundamental counting principle

[remote heron]

i mean i would just say like

some set of ten numbers

3/10 of them meet that criteria

so for every 10 numbers you get 3

for every 100 you get 30

[shut tartan]

The game of Kaiser is a 4-player card game that involves some of the cards from a standard deck. The cards included are:

All of the 12 face cards
All of the Aces
One card that is the 5 of hearts
One card that is the 3 of spades
One card that is the 7 of clubs
One card that is the 7 of diamonds
All the 8s, 9s and 10s
Each player is dealt 8 cards. How many 8 card hands have:

1. no restrictions
2. Five face cards and 3 Tens
3. Six spades
4. there are at least 3 Aces

@remote heron

how about this

[random crypt]

Can someone check if I’m right

<@&286206848099549185>

<@&286206848099549185>

[plain summit]

Read rules #❓how-to-get-help .. dont ping helpers right away..

[random crypt]

Sorry

[quiet crown]

How can i solve this simultaneous equation using elimination?

[late tundra]

multiply one equation with a the other with b

[quiet crown]

Ok

[late tundra]

then subtract one equation from the other

then solve for x

[sand lichen]

Using a model, explain how dividing a number with a fraction is the same as multiplying the number with the fractions reciprocal? How do i do it with a model been stuck on this for a very long time

[quiet crown]

So I get $abx - abx + 2by - 2ay = ca - cb$

[ocean seal]

Vex

[late tundra]

yes

[quiet crown]

Which i think is then 0 + 2aby = ab

I think that is wrong

[late tundra]

no

2by-2ay= ?

2y(b-a) right ?

[quiet crown]

yeah

[late tundra]

now 2y(b-a)=c(a-b)

b-a cancels

2y(b-a)=-c(b-a)

2y~~(b-a)=-c(b-a)~~

2y=-c

y=-c/2

got it ?

[tight yew]

I am struggling with this question, I am not really sure how to get a bijection from a set of functions to a set of ordered partitions

Any chance of some help?

[charred flint]

@tight yew have you tried a small example, like with the set {a,b} and k=2?

[tight yew]

in that case the ordered partions of X of length k = ({a,b},{}) , ({a},{b}) and ({},{a,b}) and the functions are f1 and f2 where f1 = a->1, b->2 and f2 = a->2, b->1

maybe the partions of X of length k only have the first or last one, but I still don't know how to generalise a bijection from them to the functions anyway

[quiet crown]

If anyone understands this feel free to help me lol. Still don't get it

[charred flint]

@tight yew you're missing some, each should have 4 possibilities

maybe this way of defining a function will make you see it (n=4, k=3)

[snow sand]

Hi just introducing myself.I am sam. amateur guy looking around what this server is about. cheers!!

[alpine sable]

we;l

[charred flint]

@quiet crown multiply the first by b and the second by a

[alpine sable]

welcome SamTitusMenacherry

[charred flint]

that'll match up the x terms so you can subtract them

[tight yew]

oh, would the other 2 functions for first ones be f3 = a->1, b->1 and f4 = a->2, b->2

and the other partition would be ({b},{a})

and then the bijection would be, when the partition is ({a,b},{}) it would translate to the function where a->1 and b->1, when the partion is ({a},{b}) would translate to the function a->1 and b->2

that now makes sense, but not sure how to word it for a generalised version

[limpid stone]

how to do q6

idk how to find the modulus

[quiet crown]

Yeah did that

[tight yew]

modulus is just the absolute value

[charred flint]

yea scott that's right

[tight yew]

the modulus of -2+3i is sqrt((-2)^2+3^2)

as example

[charred flint]

concisely A_j = f^-1(j)

[limpid stone]

i know that but for this question tho

[tight yew]

idk, maybe NA maths is different

thanks for making me understand @charred flint

I got it now

[verbal tundra]

Hello, so, I need some help in an exercise of non-homogeneous differential equations. So, I'll show my exercise

It's the last one of the bunch

I have managed to do the first 4 ones

Since all 5 start the same, here's the solution I git for that first part

But I can't seem to solve the exponential part

And I can't find where I went wrong

Btw, I think this channel was free, if it wasn't I'll delete and move to another

Ah wait

Crossed the parts that I didn't use

Supposedly, for yp, I'm supposed to get: (1/2)*(e^(2x)*x)

[carmine lion]

How to eliminate theta

$x=2+\cos{X} \$ $y=1+\sin{X}$

[ocean seal]

abe

[ionic jewel]

theres literally no theta here

[carmine lion]

Sorry

[carmine lion]

X

Can you help

[ionic jewel]

i mean

[gray isle]

consider Pythagorean trig identities

[ionic jewel]

this is a circle

if that helps?

i believe its

oh no its not

its an ellipse

[gray isle]

(if you want to use a plain text substitute for theta, better off using t)

[late tundra]

multiplying eq1 with b and eq2 with a
we get
abx+b²y=cb.............1
abx+a²y=ca.............2
subtracting 2 from 1
y(b²-a²)=c(b-a)
y(b-a)(b+a)=c(b-a)
y(b+a)=c
y=c/(a+b)

[carmine lion]

I'm confused @gray isle

Do I do 1^2 + 2^2

[quiet crown]

But that’s incorrect according to my textbook

[late tundra]

it's a circle

[late tundra]

the textbook is wrong

[quiet crown]

apparently y = a-b/2b

[ionic jewel]

oh

yeah it is

im kinda dumb

$(x-2)^2 + (y-1)^2 = 1$

[ocean seal]

bunny

[carmine lion]

Omfg

[ionic jewel]

who needs algebra when you know common parameterizations

[carmine lion]

How did I not...

See that

[late tundra]

see the answer on ur textbook does not have a "c" that proves the textbook answer is wrong if you still doubt try substituting it back in the equation

[late tundra]

the correct answer is
x= c/(a+b)
y=c/(a+b)

[vagrant jetty]

Did i do it right guys

[gray isle]

no

[verbal tundra]

You gotta uh...

[hidden horizon]

2nd line (-6)^2 is 36 not -36
and (-21)(-8) = 168 not -168

[gray isle]

why put an extra - sign like that

[hidden horizon]

ok i changed

[gray isle]

the -4ac part was fine

[vagrant jetty]

i put -6 squared ona calculator and it says -36

[hidden horizon]

its +36 , moreover -6^2 is different from (-6)^2

[ionic jewel]

$-6^2 \neq (-6)^2$

[ocean seal]

bunny

[verbal tundra]

The calculator works in funny ways

[gray isle]

-6^2 is not the square of -6

[verbal tundra]

You have to include the negative sign inskde the parenthesis

(-6)^2

[vagrant jetty]

ohhhhhhhh

im dumb

[gray isle]

is also something you shouldn't be using a calc for

[vagrant jetty]

welp time to do this all over again

[hidden horizon]

ya dont start using calc from young ages it will seriously deteriorate ur calculating ability

[ionic jewel]

meirl

WA was a mistake

[verbal tundra]

WA?

Ah

Ye

[wary stream]

People should start using abacuses again to do math

[ionic jewel]

factual

im pretty sure i would be really good at mental math if abacuses were the only choices

[hidden horizon]

maybe.....

u can learn vedic math

[ionic jewel]

i basically plug everything into wa at this point

[hidden horizon]

ITS OSSUM

[ionic jewel]

i know what to type into wolfram thats the important part of math :^)

/s

[gray isle]

it's apparently the principle being used by genius kids to quickly add large amounts of numbers

[ionic jewel]

not really related, but i learned how computers do large multiplications, karatsubas algorithm is pretty cool

now i need to learn what ramonov just said

[wary stream]

Hold up, it's always been /s to denote sarcasm, \s?

[ionic jewel]

/s is sarcasm

never seen \s

cant tell if that was a meta-message

[verbal tundra]

So, does anyone know what I'm doing wrong here?

[real loom]

Send original q

Or yh

[verbal tundra]

I did

It's further up

Here it is

Last one

[vagrant jetty]

Pretty sure i did it right now

2nd coming of albert einstein plz check

[ionic jewel]

,w roots of 2p^2-6p-21

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

this is correct

[vagrant jetty]

thx sir

[verbal tundra]

Wooo

Nice

[proud axle]

Its been a while since i did triangles so give me a sec

wait

QTS is an isosceles triangle?

[uneven isle]

Apparently

Not drawn to scale

[proud axle]

I see

[hidden horizon]

@uneven isle wait i will send sol

[uneven isle]

Ty

I’m but slow

[proud axle]

if thats the case I assume QT=TS

wait..

[hidden horizon]

no need lol

do some angle chasing

[proud axle]

yep

I shall leave it to u lol

now I still got a maths assignment

sigh

[hidden horizon]

@uneven isle tell me if u hv doubt

[ocean seal]

IamRDT

[upper kayak]

channel open?

[proud axle]

think so

[upper kayak]

$\frac{tan \theta + sin \theta}{tan \theta - sin \theta} = \frac{2 + \sqrt{3}}{2 - \sqrt{3}}$

oops

[ocean seal]

gang

[upper kayak]

yeah there you go

i tried solving and ended up with a sixth degree equation in sin theta

[hidden horizon]

what do u need @upper kayak

i mean what u need to find

[upper kayak]

theta

[hidden horizon]

ok

[ocean seal]

IamRDT

[hidden horizon]

ignore this

@upper kayak expand tan theta as sin theta / cos theta

[upper kayak]

ok

[hidden horizon]

what do u get

[upper kayak]

nothing much

[hidden horizon]

wat

[upper kayak]

i mean yeah, now i've subbed tan theta

now what?

[hidden horizon]

there must be an equation that u get

[upper kayak]

yeah, the same equation except tan theta is now sin theta / cos theta

[hidden horizon]

ok

now take lcm

[upper kayak]

alright now i have

$\frac{1+cos \theta}{1-cos \theta} = \frac{2+ \sqrt{3}}{2 - \sqrt{3}}$

[ocean seal]

gang

[hidden horizon]

yes

now u can find theta i guess

[upper kayak]

yeah thanks

[hidden horizon]

cool

[ionic jewel]

@upper kayak put a \ before your trig

$\tan\theta$

[ocean seal]

bunny

[upper kayak]

ok

[ionic jewel]

prob didnt need to ping but ez latex improvmeent

[upper kayak]

thanks

[alpine sable]

what is the answer to this

[ionic jewel]

assume the first one is heads

they are both heads if the second one is heads

[alpine sable]

we dont know if its the first one

[ionic jewel]

50%

okay

assume the second one is heads

they are both heads if the first one is heads

50%

[placid zinc]

Yikes this question

[ionic jewel]

it doesnt matter, you could simply re-order the coins to make the heads come first, so you can assume heads is first

[placid zinc]

EMILY just came here to watch the world burn

[harsh acorn]

How can I solve this question easily?
I always try to find square numbers that divisible by 9 (checking with hand) and after, I check them that they are divisible by 7 or not

are there more easier way?

[alpine sable]

[harsh acorn]

oh

occupied?

[placid zinc]

Google "Boy-Girl paradox" for a best explanation. The answer is 1/3

[upper kayak]

not sure but you can use divisiblity rules and set up equations where you represent BCB as 100B + 10C + B

that's how i do it

[ionic jewel]

oh i got jebaited didnt I

[hidden horizon]

use divisbility rules ig

[placid zinc]

It's a common troll problem haha @ionic jewel

[ionic jewel]

no 1/2 is still a legit answer

as per wikipedia

[harsh acorn]

I don't know how to use rules to this question

Can u show me please?

[hidden horizon]

ok wait

[ionic jewel]

its an ambigious question, now that I read the description, but the 1/2 is a valid interpretation of it

either way I can watch out in the future

[alpine sable]

i still dont know the answer

[gray isle]

consider the sample space

[ionic jewel]

its 1/2 or 1/3, the problem is ambigious

as kaynex said, look up the "boy-girl problem"

it explains both interpretations

the 1/3 would be from knowing that "tails tails" is not an options, and knowing 1 of the remaining 3 options is "heads heads"

[hidden horizon]

@harsh acorn what do they mean by "odd no of factors"

[harsh acorn]

It means it is perfect square

perfect squares have odd number of factors

[hidden horizon]

hmm then u can use ur method itself lol

its more easier ig

[prime badge]

prime squared

not any number squared

[hidden horizon]

no any number squared only

suppose 6^2 = 3^2 x 2^2
therefore total factors 3x3 = 9

[harsh acorn]

All of the perfect squares have odd number of factors

[hidden horizon]

which is odd

[harsh acorn]

it is a rule

[prime badge]

oh

right

thanks

[harsh acorn]

@hidden horizon I found more easier way, I will memorize perfect square numbers that have 2 same digits and check them :d

[hidden horizon]

xD

[gray isle]

you can combine the second and third condition to make checking less tedious

[alpine sable]

alright thanks

[harsh acorn]

How can I combine them

[gray isle]

CBB is divisible by 9, means that C + B + B must also be divisible by 9

[harsh acorn]

yeah that's right but still idk how to combine this with odd factor fact

[gray isle]

and since for #3, you number starts with BB

you'd only need to consider:

117
225
333
441
558
etc

[harsh acorn]

ooh I get it now

So we choose 225 and 441

[gray isle]

determine which of those are actually perfect squares

[harsh acorn]

and answer is 441

Yeah that's easier

[gray isle]

whoops mistake

gotta rearrange the order of the numbers

BBC = 225 → BCB = 252
BBC = 441 → BCB = 414

[harsh acorn]

Oh damn I forgot this

So I just need to memorize perfect squares that has 2 same digits for these type of questions huh

For more faster solution

[gray isle]

could help a bit

but writing out your possible options, it should be relatively easy to identify

[alpine sable]

I am mad :/

I forgot how to do explnents

Like i knew them last year and now i need to know them becuz they are on a review for my exams

[harsh acorn]

Is answer 26?

first example of a+d=16
second example of a+d= 5 or 15
That means a+d=15 and c+b+1=12
c+b=11
11+15=26

[harsh acorn]

How can I factorize this?

[hidden horizon]

-3 can be wriiten as -4+1
So , this is equal to (x + 1)^2 - (y + 2)^2
i think u can do from here @harsh acorn

[harsh acorn]

ooh damn idk why I didin't see it

Yeah I can solve it now

[harsh acorn]

@hidden horizon Do you know name of this equation ?

What is that called?

[hidden horizon]

this one ?

[harsh acorn]

yeah

[hidden horizon]

umm idk

ive heard of Pell's eqn but its different

well ? what is it called ?

[harsh acorn]

Idk

[grand dust]

Hi can someone explain me how to solve y’(t)=t*y(t)

[vagrant cobalt]

Dy/y=t dt

Lny =t^2+c

[grand dust]

Isnt it for y’(t)=t ? My equation is y’(t)=t*y(t)

[vagrant cobalt]

I dont understand you

[strong furnace]

You asked something similar like a week ago I think , this is the general second degree homogeneous equation which represents the general equation of all the conic sections in a plane , factorizable means it has discriminant=0 which corresponds to pair of straight lines so you will be getting 2 linear terms as factors

[alpine sable]

<@&286206848099549185>

[stark rampart]

This has a general equation (ax + by + c)(dx + ey + f)

You can start with letting y = 0 and then factor

x^2 +2x -3 = (x+3)(x-1)

Let x = 0, to get

-y^2 -4y-3 = (y+3)(-y-1)

We can combine the factors (x+3) and (y+3) to (x+y+3) and (x-1) and (-y-1) to (x-y-1)

it becomes:
x^2-y^2-4x+2x-3 = (x+y+3)(x-y-1)

cheers

oh im new to the server so pls comment on my solutions if it's giving away too much or if it needs more elaborating 😁

[strong furnace]

It's never bad to give away too much

[sly leaf]

How would I solve for x?

[stark rampart]

factor first

u'll get linear factors

(x-2), (x+3), (2x+5), smth like that

then let each factor be zero, where u get a value of x for each

e.g. x(x-5)(x+1) = 0

so x = 0, x-5 = 0, x+1 = 0

and u get x = 0, 5, -1 for each

u do the same for that prob

[sly leaf]

I've done x(x^2+2x-16)=0 but I can't factor x^2+2x-16

[lament flame]

imaginary roots.....b^2 - 4ac < 0

[stark rampart]

u still gotta write it down afaik

[sly leaf]

huh isn't that the discriminant im so confused haha

[stark rampart]

coz it's still a solution

yeah the discriminant "discriminates" the solutions as either real or imaginary

[stark rampart]

since this is true, u gonna expect imaginary solutions

[lament flame]

sry sry

b^ - 4ac > 0

[stark rampart]

oh wait HAHAHHA yeah yeah

use quadratic equation for that one

[sly leaf]

use quadratic to solve x^2 +2x-16?

okie dokie

[lament flame]

i got -1 (+-) root(17)

cross check

[sly leaf]

yep

ay thanks

idk why it didn't occur to me to use the quadratic formula

cheers

[stark rampart]

yep same

[alpine sable]

Step1 = (2)^p/q=7
Step2= (2)^p=(7)^q
How???

[gray isle]

as written, that is false

[alpine sable]

How?

[gray isle]

oh

that's not what you typed

[alpine sable]

My bad

[gray isle]

\verb|2^p/q| is intepreted as $\frac{2^p}{q}$

[ocean seal]

ℝamonov

[gray isle]

raise both sides to the power of q

to correctly represent that exponent you should be writing: $\verb|2^(p/q)|$ \
\verb|(2)^p/q| is no different from \verb|2^p/q|

[ocean seal]

ℝamonov

[raw garnet]

Hi I got a question about integration by parts in Questions-1 if someone got time .)

[lost crane]

Any knows a function to power series calculator?

[tiny oyster]

I seee but i think adding blankets may make less mistakes

[rigid smelt]

firstly, is this a test?

secondly and if its not, what do you need help with?

[lucid ember]

for part a would manipulating the definition of an eigenvalue work

[jagged imp]

wolfram alpha?

,w power series sinx

[ocean seal]

Results provided by WolframAlpha

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

Requested by Sneaky#0928

[jagged imp]

if you go to the site it'll give you the full thing

[upper kayak]

open?

guess so

$\sin 2\theta = \sin \theta$

[ocean seal]

gang

[upper kayak]

i got 0 and 60deg

how do i find the rest of the solutions in $0 \leq \theta \leq 2pi$

[ocean seal]

gang

[jagged imp]

those are the only 2.

what makes you think there's more?

[upper kayak]

the answers list 5

oh no

[jagged imp]

take a screenshot

[jagged imp]

well first off those are in radians

[upper kayak]

yeah

[jagged imp]

and second, they aren't in the specified range

[upper kayak]

oh my

sorry

[jagged imp]

you're sure it says to solve in [0,90] and not [0,360]?

[upper kayak]

i copy pasted from the pdf file

and it got messed up

yeah its 0 <= theta <= 2pi

sorry

[jagged imp]

ok, do you know another way to write sin(2x) that could help?

[upper kayak]

yeah

2sinxcosx

[jagged imp]

great, so 2sinxcosx=sinx

[upper kayak]

yeah

[jagged imp]

then, 2sinxcosx-sinx=0

and we can factor

[upper kayak]

ok

sinx(2cosx - 1) =0

[jagged imp]

close, if you expand that out you'd get 2sinxcosx-2sinx=0

[upper kayak]

oop

edited

[jagged imp]

perfect, so now sinx=0 or 2cosx-1=0 right

[upper kayak]

yeah

got it

thanks

i'm curious, why didn't taking the arcsin of both sides work for the original equation?