help-0

[thorn tapir]

$$\sin 15^@ = \sqrt{\frac{1 - \cos (30^@)}{2}}$$

[ocean seal]

rikusp2002

[thorn tapir]

@alpine sable

[sudden jacinth]

I need help with a probability problem:
Pick 2 random numbers between 0 and 99 (no duplicate). Then we pick a random number between 0 and 99 27 times (there can be duplicate), what's the probability that we found 2 numbers (from the start) in those 27 numbers?

[strong furnace]

what have you tried?

[sudden jacinth]

27*(1/100)(1/99)((1/100)^2)

[strong furnace]

just describe the idea

numbers will match up

[sudden jacinth]

27* since we do it 27 times, (1/100)(1/99) for two random numbers (no duplicate), then (1/100)^2 because we pick 2 random numbers (can be duplitcate) from 0 to 99 two times. But I'm not sure if im correct

[strong furnace]

why would the probability of choosing the 2 numbers matter here?

multiplying by 27 is when you have 27 equivalent cases

this is binomial probability distribution

you will need to figure out the different cases and equivalent amounts using that

@sudden jacinth have you realized where you went wrong?

[sudden jacinth]

I'm still thinking, I don't understand how we can treat 27 cases differently and match with the 2 initial random number

[strong furnace]

ok I will do a rundown for you

think of it this way from the principle of counting you multiply the probability by the amount of equivalent cases you have for the same probability

you multiplying 27 here (and only 1 term) implies there are 27 different ways of getting those 2 numbers and the probability of all these ways is (1/100)^2

which is just false

[sudden jacinth]

alright I see my mistake, but then how can I tackle the problem differently, I might have to look up for binomial probability distribution since I'm unfamiliar with the method

[strong furnace]

look it up that would be good

I would tackle this by taking the conjugate

[sudden jacinth]

thank you for the head start, I'll try to figure this out

[tribal geyser]

Anyone free to explain 16 for me pls, don’t understand how to show that the line is normal to the curve

I’ve found the points

just don’t understand the second part

[strong furnace]

what don't you understand about the second part?

[tribal geyser]

Idk how to show

like I know that the normal is perpendicular to the tangent

but I don’t understand how to show from the points

[strong furnace]

can you find the slope of tangent at those points?

[tribal geyser]

if u know what I mean

[topaz scaffold]

What's the relationship between the slopes of 2 perpendicular lines?

[tribal geyser]

gradients multiply to be -1

Reciprocals

[topaz scaffold]

Negative reciprocal

[tribal geyser]

yes

[topaz scaffold]

So to show that they are perpendicular, just show that the slopes are negative reciprocals of each other

[tribal geyser]

no I get that but I don’t understand the part when it says show that the line is the normal to the curve at One of these points

so do I have to find the tangent of these two points

and see which one is perpendicular to the curve?

[topaz scaffold]

Yep

[tribal geyser]

wait um those two points that I find, which equation do I sub in to find tangent

the curve?

[topaz scaffold]

You don't need the equation for the tangent

You just need the slope of that tangent at that point

[tribal geyser]

The slope of those two points?

[topaz scaffold]

Yep

[tribal geyser]

how about 18? How do I show that it’s a tangent

[topaz scaffold]

A tangent touches the function at a point, and also has the same slope as the function at that point

[tribal geyser]

wait but when i calculate the derivative of the curve and subbed in the gradient of the line it doesn’t equal

becoz u said it has the same slope as the function at that point

@topaz scaffold

[topaz scaffold]

The derivative tells you the slope of the function at the point you subbed in

[tribal geyser]

yes

so how could I show it

because the gradient of the line is -1

[topaz scaffold]

And what's the gradient of y + x + 2 = 0?

[tribal geyser]

I said -1

[topaz scaffold]

Oh sorry

[tribal geyser]

it’s okay

[topaz scaffold]

Ig you need to find where y = x^3 - 4x has a derivative of -1

[tribal geyser]

wait so after I find where it equals -1 what do I do

@topaz scaffold

[topaz scaffold]

See if those two lines intersect at those points

[tribal geyser]

The curve and the line? Intersecting at the two points

[topaz scaffold]

See where y + x + 2 = 0 and y = x^3 - 4x intersects

[tribal geyser]

Yes

[alpine sable]

help

question 7

6 not 7 sorry

@silver shoal sorry for the ping but can you help

im just a middleschooler dont go too deep

[topaz scaffold]

Just use distance formula ig

Find one that has a distance of d from one point and 2d from another point

[alpine sable]

thanks

i was trying to do so

i probably messed up eqs

can i use section formula

nvm i was being dumb got it

im done with it so time to leave the server

[topaz scaffold]

Oof bye

[small holly]

why is the answer for this ±3

i just got 3

just saying i needed to solve for x

[topaz scaffold]

When you put in a square root you need to remember to put the plus or minus

[teal epoch]

When you're solving equations like these, it usually includes the plus-minus sign

[ocean seal]

Nonexisty

[teal epoch]

But when you are asked to calculate the square root of 4, the answer is just +2

[ocean seal]

Nonexisty

[small holly]

oh so whenever i involve rooting in these equations then i have to add the plus minus symbol

[teal epoch]

Yes, usually
Don't forget to check

[gleaming bolt]

This is a quadratic equation, thus, x has 2 values

[fallow pagoda]

quick question it might be dumb but how to i get the x by itself in
13/sin(x) = 16/sin47

like find x basically

[topaz scaffold]

You'll need to use the inverse sin function

[strong furnace]

cross multiply sin(x) both sides and you have a trigonometric equation

principal solutions via the arcsin() function

[fallow pagoda]

wait huh

so 13 = 16sinx/sin47?

im confused lmao

[strong furnace]

sin(x)=13/(16(sin(47)) ) would be better

to start

but its not any different

[fallow pagoda]

wait why does the 16 mulitply with the sin47 now

[strong furnace]

n(pi)+(-1)^n*(primary solution) woud be the general solution

[fallow pagoda]

im sorry im still confused

idk what that emans

[strong furnace]

Look up "trigonometric equation"and their solution

[ivory otter]

Would it work if he multiplied lhs with sin(x), then divide rhs with 16sin(47) and just inverse sin(x) when its alone?

[strong furnace]

It's the same thing

[ivory otter]

Ok

[strong furnace]

That is how you get the primary solution

[ivory otter]

Are you Done?

[fallow pagoda]

yeh sorry guys i figured it out thanks for the help!

[ivory otter]

Ok nice

So i have this

Is this correct?

[strong furnace]

Just input the solution in original to check

[ivory otter]

Ye definetly wrong

[strong furnace]

Although looks incorrect

[ivory otter]

What did i mess up

[strong furnace]

You forget the coefficient of cofactor

[ivory otter]

Where

[strong furnace]

(-1)^(j+I) for a_ij

The top right to bottom left diagonal

Nvm

[ivory otter]

[strong furnace]

You multiplied by 9 instead of divide

You actually have the correct signs in the next step so that's not it

[ivory otter]

Am i not supposed to multiply?

Nopp wait

I see the problem

Its not -9

Its supposed to be 1/-9

Damn

[strong furnace]

So just divide your answer by 81

[ivory otter]

Aha

[strong furnace]

You have another mistake in your matrix multiplication tho

[ivory otter]

And that is?

[strong furnace]

18*13=144

When it should be 234

[ivory otter]

How did i get 144

Thx

[hollow pelican]

Hi just a quick question

What is the maximum point for sin graph and cos graphs?

[strong furnace]

There are infinite maximum points

cos(x) has a maxima at (2npi,1) for all n in Z

[hollow pelican]

ohh ok but for this question how to determine the maximum points though

[strong furnace]

R-method or auxillary angle is the most appropriate

[hollow pelican]

ohh

but i still need to draw this graph?

[strong furnace]

you can use information from the graph of cos(x) or sin(x) but plotting a graph is the same information so whatever works for you

[hollow pelican]

okay

[hollow pelican]

but if i use the r method i still cant get the answer though?

[strong furnace]

what is the problem?

[hollow pelican]

like if i use the r method

then i will be stuck here

[strong furnace]

you have the maximum value as amlitude of sinusoid

[hollow pelican]

then i will be completely cluless how to do alr

[strong furnace]

now the question wants the smalles (positive I assume)

angle

as I said cos(x) has maxima at (2npi,1)

you would want to interpolate here somehow

[hollow pelican]

ohhh

[vale wigeon]

where did you get this from?

these don't seem like anything special. just two linear functions of a complex variable, nothing more.

[alpine sable]

the fuck is that photo lol

[vale wigeon]

looks like a screenshot from a shitty popmath video if you ask me

[lusty topaz]

from a puzzle, it was mentioned that it's used to find a curve but i have no clue

[vale wigeon]

can you link the video this is from?

[lusty topaz]

i don't have the link to the video

just that picture

[vale wigeon]

......okay can you link the puzzle

if you don't share anything else then nobody here has anything to go on

[lusty topaz]

that pic is all i have tho 😐

[silver marsh]

Looks like some random funcs they threw in the bg of a video to look cool ngl

[vale wigeon]

you say it's "from a puzzle"

what puzzle is it

[topaz scaffold]

It could have a use, but we don't know what the use is because we don't know what it's trying to be used for

[shrewd otter]

It could be anything.

[gleaming warren]

$\frac{5}{2} - \frac{5}{2} = 0$ how

[ocean seal]

TheGameBot

[shrewd otter]

By reflexivity.

[gleaming warren]

by what?

[shrewd otter]

By reflexivity.

It's the property that x = x.

[gleaming warren]

so what does this do

[shrewd otter]

Actually, you're right.

We can't use that here.

[glass lichen]

Not fully sure if this is a legit question or a troll question

[vale wigeon]

@gleaming warren anything subtracted from itself gives 0 lol

[gleaming warren]

legit question

[gleaming warren]

oh yeah i'm dumb

[vale wigeon]

5/2 is a number just like any other

[teal epoch]

Guys, what's a natural number?
For some reason some people considered 0 as a natural number

[glass lichen]

either {1,2,3,...} or {0,1,2,3,...}

depends who you ask

[gleaming warren]

a natural number starts from 1 to infinity

[vale wigeon]

@teal epoch whether or not 0 is a natural number is a matter of convention and convenience

sometimes it is more convenient to include 0, other times it is more convenient to exclude 0

@nova sail thank you for this valuable contribution to the conversation at hand.

[glass lichen]

those are their only contributions

[strong furnace]

@nova sail shitpost goes in #chill

[gleaming warren]

what is meaning of respectively

[strong furnace]

order

[vale sapphire]

1+2 and 3*2 are respectively equal to 3 and 6

[gleaming warren]

oh

[vale sapphire]

you just say multiple things and your pair them up in order

[vale sapphire]

depends on the definition >:(

[glass lichen]

you have 2 lists, each item in the list matching with the item in the same position

[vale sapphire]

here we include 0

[teal epoch]

So is 0 a natural number?

Should have asked this instead-

[vale sapphire]

It depends on the definition, I said

In the US, 0 isn't included in the natural numbers

So, by the US definition, no

My point is to be aware that this is not an universal or obvious thing and that it depends on the agreed-upon definition

[gleaming warren]

so if the question says find distance of OB and AB respectively then i should do OB first

??

[vale sapphire]

No, it just means find both

[glass lichen]

that just reads "find both the distances of OB and AB"

[gleaming warren]

oh

[vale sapphire]

But when you give the answer, you might say "the distances are 3 and 6 respectively"

where 3 is OB and 6 is AB

[gleaming warren]

ok thankyou

[vale sapphire]

But you're not required to write it like that

[gleaming warren]

oh

kie

[pearl musk]

what does "inserting n geometric means" mean? insert n numbers such that a GP is formed? if so, why so? how is the definition of geometric mean tied to a geometric progression?

[shrewd otter]

What is the geometric mean, and why is it called such?

[vale wigeon]

@pearl musk yes, insert n numbers to make a GP

[pearl musk]

you take the nth root of the product of n numbers. afaik qualitatively, a type of average so mean and geometric because it has to do with taking a product?

[vale wigeon]

it's bad wording imo but yes that is what it means

[shrewd otter]

No, it's called the geometric mean because it relates to the geometric series.

Namely, if you have the n + 1th and n - 1th element of a geometric series, the geometric mean gives you the nth element.

[sacred vigil]

How to do this

[pearl musk]

hmm makes sense that way. thanks 🙂

[sacred vigil]

@shrewd otter @vale wigeon

[shrewd otter]

Use log properties.

Namely log(a / b) = log(a) - log(b).

[teal epoch]

Logarithm Rules.

[alpine sable]

wrong rule lmao

hurubon

[shrewd otter]

Eh?

[alpine sable]

Ig works too

[teal epoch]

$log(a) + log(b) = log(a \cdot b)$

[alpine sable]

but addition makes it cleaner imo

[shrewd otter]

No, it doesn't.

[ocean seal]

Nonexisty

[alpine sable]

yes it does

everything cancels out

its 🔭

[shrewd otter]

How can something cancel out if you have a sum of positive values?

That's nonsense, I feel.

[alpine sable]

ure nonsense

1/2 * 2/3 cancels

[shrewd otter]

Ah, I see.

I was looking at breaking up the logs, not putting them together.

[gleaming warren]

how is $(1.5 - 3)^2 = (1.5)^2$

[shrewd otter]

,w calculate (1.5 - 3)^2

[ocean seal]

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TheGameBot

[shrewd otter]

These are not questions for people.

Because x^2 is an even function.

Meaning f(x) = f(-x).

[alpine sable]

yes.

[gleaming warren]

how

[alpine sable]

wdym how

how much is 1.5 - 3

its -1.5

[gleaming warren]

what

wait

[alpine sable]

what is 2 - 4

[gleaming warren]

2

[alpine sable]

no

[gleaming warren]

-2

[alpine sable]

great

so 1.5 - 3 is -1.5

[gleaming warren]

ok

[alpine sable]

and when you square it the minus sign disappears

[gleaming warren]

oh

[alpine sable]

because (-1)^2 = 1

[glass lichen]

$(-a)^2=(-1)^2a^2=a^2$

[ocean seal]

Mosh

[dawn wraith]

$$ - \cdot - = + $$

[gleaming warren]

i know that

[ocean seal]

Hunnydrips

[gleaming warren]

i also know this

[alpine sable]

ok then u should be done

[gleaming warren]

how is it in positive

[alpine sable]

because it is the same so he skipped it

(-x)^2 = (x)^2

in your case x=1.5

[gleaming warren]

but he cancelled the square with the root

means cancel

[glass lichen]

yeah... sqrt and squaring are inverses

[gleaming warren]

i know

1.5 -3 = -1.5

\sqrt(-1.5)^2= -1.5

[glass lichen]

$\sqrt{(-1.5)^2}=\abs{-1.5}=1.5$

[ocean seal]

Mosh

[gleaming warren]

oh

ok

[vagrant rover]

f(x) = x^3 - 4x

What does f mean here?

And why is it written as f(x) specifically?

I always see equations written like this.

What fundamentally does it mean?

[velvet pelican]

f is a function

f(x) means the function takes one input x

[vagrant rover]

A function just takes input (in this case x) and then gives you an output, right?

[velvet pelican]

yes

[vagrant rover]

And the output is equal to F?

[velvet pelican]

the output is f(x) which = x^3 - 4x here

[vagrant rover]

Ah alright

I see

and x is the same on gboth sides

right?

[velvet pelican]

yes

[vagrant rover]

Also, functions can be used to do many different things, not just one thing, yes?

[velvet pelican]

functions have a lot of uses

[alpine sable]

maybe try thinking about it this way: this f function takes some number, lets say 5, and applies a formula to that number and spits out the result

[vagrant rover]

Like anytime you want to take input and put it into an equation you use a function?

[vagrant rover]

Ah, i see.

Okay I think I get it.

Thanks guys!

[alpine sable]

So for example the easiest function which basically does nothing is f(x) = x - it takes x and spits out the same number x

[vagrant rover]

Can you have a function that is not called f?

[alpine sable]

yes its just a name

do you know/understand the graphs of functions?

[vagrant rover]

Ah alright, it's basically exactly how programming languages use functions then

[alpine sable]

the y and x axis?

[vagrant rover]

Not really

[vagrant rover]

Yeah

I know about graphinh

[alpine sable]

like this

,w graph f(x) = x

[ocean seal]

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[vagrant rover]

Yeah so this is basically like giving x as 1 and then it gives output 1

[alpine sable]

this function f with formula f(x) = x take some x - lets say 0.5 and applies it to y

[vagrant rover]

give it two and it igves 2

etc..

[alpine sable]

yeah

[vagrant rover]

Right?

Yeah yeah, awesome.

[alpine sable]

so as you can see in this case its a line

[vagrant rover]

THanks 😄

[alpine sable]

y is basically the result f(x)

ure welcome

the one you sent has a weirder graph

,w graph f(x) = x^3 - 4x

[ocean seal]

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[vagrant rover]

Interesting

[sacred vigil]

w, graph f(x) = tanx + x^3 - 4x

[alpine sable]

,w graph f(x) = tanx + x^3 -4x

[ocean seal]

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[sacred vigil]

[alpine sable]

,w graph weierstrass function

[sacred vigil]

,w graph weirstrass

[strong furnace]

bruh

[ocean seal]

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[sacred vigil]

,w graph weirstrass

,w graph 7x+89+x^100

,w graph x^100

[alpine sable]

,w graph sinx/x

[sacred vigil]

,w graph x>45x+102-x^15

[alpine sable]

,w graph sinx/x^2

[ocean seal]

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[sacred vigil]

,w graph x<1

[ocean seal]

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[alpine sable]

,w graph f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a)

[sacred vigil]

,w graph loga*logb

[ocean seal]

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[sacred vigil]

,w graph (x-y)*(x+y)

[ocean seal]

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[sacred vigil]

,w log 1.125

,w log_10(1.125)

[ocean seal]

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[sacred vigil]

,w log_10(-12)

[ocean seal]

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[teal epoch]

Any tips on how to solve functional problems in general?

[sacred vigil]

,w log_1(1)

[ocean seal]

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[sacred vigil]

,w log_2(1)

[ocean seal]

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[sacred vigil]

Kbyethx

[wind lily]

$find x if 4^x - 4^x * 4^-^1 = 24$

[ocean seal]

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

[wind lily]

can someone help me with this?

[ocean seal]

Nonexisty

[teal epoch]

is this what you meant?

likely not tbh

[wind lily]

4^-1 isn’t in the exponent

but otherwise yeah

[teal epoch]

Find $x$ if $4^x-4^x\cdot4^{-1}=24$.

[ocean seal]

Nonexisty

[coral cosmos]

x = 5/2

take 4^x common

you get 4^x ( 1 - 1/4) = 24
4^x = 32
2^2x = 2^5

2x = 5
x = 5/2

[teal epoch]

Binomial Theorem?

[wind lily]

ty

[coral cosmos]

Yes

[coral cosmos]

welcome : )

[lime rain]

how do i add 45 degrees in a point of a circunfere?

[vale wigeon]

what's a "circunfere"?

[lime rain]

any point in the circle limit

[vale wigeon]

no idea what you're talking about...

[lime rain]

for example

the orange point is where i am

i want to go to the green one

[vale wigeon]

so you want to rotate by 45 degrees around some center point?

[lime rain]

i think so

but orange can be anywhere in the circunference

the radius is 25

[vale wigeon]

circle. the word you're looking for is circle.

[lime rain]

no

circle is the geometry form

cincunference is the limit point

[vale wigeon]

you keep saying "circumference" when you mean circle

if you mean the difference between the curve and what's inside the curve,

the inside is called a disk

[lime rain]

whatever

anyway

[vale wigeon]

anyway

[shrewd otter]

What are functional problems?

[vale wigeon]

is the center arbitrary or is it at the origin?

if it's at the origin the formula will be a little bit simpler

[lime rain]

center is 0,0

[vale wigeon]

okay so it's at the origin great

[lime rain]

yeah

[shrewd otter]

This isn't so weird. I know my language makes a distinction between the "circumference" and the circle.

[vale wigeon]

so if you start at the point $\bmqty{x \ y}$ then rotating it by an angle of $\theta$ around the origin will take it to $\bmqty{x \cos(\theta) - y \sin(\theta) \ y \cos(\theta) + x \sin(\theta)}$

[ocean seal]

Ann

[vale wigeon]

in your case θ = 45°

[shrewd otter]

Namely:

kružnica := { (x, y) : x^2 + y^2 = 1 }
krug     := { (x, y) : x^2 + y^2 <= 1 }

[lime rain]

wtf

[vale wigeon]

yeah, that's circle vs disk.

[lime rain]

translate that to me

pls

[vale wigeon]

i'm using $\bmqty{x \ y}$ to write $(x,y)$ purely for aesthetic value

[ocean seal]

Ann

[vale wigeon]

the coordinates of your point

[shrewd otter]

Is is actually great, because it taps into linear algebra.

You have a vector [x, y].

And you want to apply a linear operation to it.

Namely, rotation.

[teal epoch]

Can we talk to another channel?

[lime rain]

yes

[shrewd otter]

Yes.

[lime rain]

?

[vale wigeon]

you could also write it like this: $\begin{cases} x' = x \cos(\theta) - y \sin(\theta) \ y' = y \cos(\theta) + x \sin(\theta) \end{cases}$, where $(x,y)$ is the old point, $(x', y')$ is the new point and $\theta$ is your rotation angle

[shrewd otter]

You simply need to find the matrix which describes a rotation operator.

[ocean seal]

Ann

[vale wigeon]

don't overload kusterzin with info they don't need.

[lime rain]

i am lost guys

[vale wigeon]

you asked for the formula, you got the formula

[lime rain]

ah i see

what is this

[vale wigeon]

i even did you one better

instead of giving you just the formula for rotation by 45 degrees, i gave you one that can let you rotate by ANY angle

[lime rain]

what is that 0 in the parenthres

[vale wigeon]

that's not a zero

that's the greek letter theta

and here i am using it to denote the angle by which you want to rotate (even though i already wrote that, but apparently it needs to be said again)

which in your case is 45°

[lime rain]

can u gimme the formula by 45

pls

i dont know hot to use that formula above

[vale wigeon]

wait so you don't know any trigonometry??

you can't calculate cos(45°) and sin(45°)?

[lime rain]

the 0 is where i put 45?

[vale wigeon]

it's not a zero!!!

but yes! in your case, the angle is 45°! θ = 45°!

[lime rain]

i fuck

i m so dumb

u already explain all

in the image

sorry haha

[vale wigeon]

yes.

yes i did.

[lime rain]

what is that above x

?

is just to get the new x

or is a mathf term that i dont know

?

[vale wigeon]

in this case x' just denotes "new x", as i say explicitly

in general, this symbol ' is called a prime and has several different uses

in calculus, the prime symbol can be used to denote derivatives

[lime rain]

got

thanks by the way

[chrome shoal]

ik im supposed to avoid this question, but if i proved that steve can carry 156 million banana's, where do i post it?

[leaden jetty]

is there any mathematical functions if output is known the inputs (must be two or more ) can be predicted ?

[chrome shoal]

but you know 0 inputs?

it depends on the answer tbh

[leaden jetty]

the inputs must be two or more (no zeros)

i meant two inputs or more

[chrome shoal]

hmm, idk im only 13 so im not 100% sure

[thick crater]

I have a question where I'm supposed to find if a person did better on one test compared to the other.

Should I use a coefficient of variation or a z-score?

[lime rain]

and what is this

?

is another mathematics term that i need to use in the equation

?

[leaden jetty]

a)
1 0 1 1 ----> constant
1 0 0 0 xor operation

0 0 1 1

b)
1 0 1 1 ---> constant
1 1 1 0 xor operation

0 1 0 1
so basically if i know only these 0011 and 0101 and is it possible to extract 1011 from that. Is this possible ?

[vale wigeon]

no it's just grouping the equations together @lime rain you can ignore it if you want

[lime rain]

ok

so and how do i find the angle

?

if i have 2 points

in the cicle

[manic glade]

is this eligible? i never know where to put the arrows

[alpine sable]

help me with this please someone

[kind torrent]

If you get whole number then?

For part f you get 7. Something then there you want lb and ub

Are you familiar with lb and ub?

[alpine sable]

nope

i am that one dude in class that doesnt pay attention

[rigid smelt]

too bad you should have

[alpine sable]

ye ik

[kind torrent]

Then first read the definition of lb and ub

[shrewd otter]

This feels like an X Y problem.

Just ask your actual question.

Or state your actual problem.

[alpine sable]

hi everyone

i need help solving a math question

[shrewd otter]

Then ask.

[alpine sable]

i could only find ib

[kind torrent]

If the number is whole number then what’s lower bound and upper bound?

[alpine sable]

?

[kind torrent]

Suppose x=5 then lower bound of x and upper bound x ?

[alpine sable]

not sure 😦

[alpine sable]

is it 10?

[kind torrent]

Nope

57.7
57.7 has been rounded to
1
1 decimal place. Work out the upper and lower bounds (or error interval) of this value.

To calculate the upper and lower bound we need to use the size of the interval which is
1
1 decimal place (
0.1
0.1).

Next we need to divide the size of the interval by
2
2 to get half the interval:

0.1
2

0.05
2
0.1
​
=0.05

Step 1: Calculate the lower bound.

For the lower bound, we subtract half the interval.

Lower bound

57.7
−
0.05

57.65
=57.7−0.05=57.65

Step 2: Calculate the upper bound.

For the upper bound, we add half the interval.

Upper bound

57.7
+
0.05

57.75
=57.7+0.05=57.75

So, we express our error interval for
x
x like

57.65
≤
x
<
57.75
57.65≤x<57.75

Now try to understand how it’s work

[alpine sable]

damn

[kind torrent]

125/15 is around 8. Something right

[void yoke]

8.333333 I think

[kind torrent]

So remove the all the decimal i.e. 8 which is lb

Yes

[noble sinew]

the question is saying each number given is rounded to nearest integer, so 14 could be 13.8 for example

so calculate lower and upper bound of 14 * 20

[alpine sable]

https://tenor.com/view/no-brain-loading-slow-gif-16361840

processing

[noble sinew]

do you know when you round up and when you round down?

[noble sinew]

if I were to round 2.4 to nearest integer what would I get? If I were to round 2.6 what would I get? If I were to round 2.5 what would I get?

oh damn you are so cool

[alpine sable]

lol

sarcasm

thank you @kind torrent

[alpine sable]

4 6 5

[alpine sable]

https://tenor.com/view/squidward-throw-away-brain-spongebob-gif-8612783

[noble sinew]

no

[alpine sable]

me right now

[kind torrent]

No

[noble sinew]

,w number line for 2.4

[ocean seal]

Results provided by WolframAlpha

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

Requested by ScapeProf#9427

[noble sinew]

what is the nearest integer to 2.4?

[alpine sable]

2.2

[noble sinew]

integers are whole numbers like 1,2,3,7,8

[noble sinew]

so not another decimal number

[kind torrent]

Whole numbers are {0,1,2,…}

[alpine sable]

can anyone help me with this please

[alpine sable]

2

[noble sinew]

also negative

[noble sinew]

indeed

[kind torrent]

Whole number

[noble sinew]

what if I were to round 2.6 then?

[alpine sable]

oof

it would be

[alpine sable]

7?

[kind torrent]

3

Not 7

[alpine sable]

dumbness level increases

[kind torrent]

You can do it

[noble sinew]

it can only ever be 2 or 3 if you have 2.(something)

[alpine sable]

o ok

[noble sinew]

,w number line for 2 and 2.4 and 2.6 and 3

[ocean seal]

Results provided by WolframAlpha

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

Requested by ScapeProf#9427

[noble sinew]

notice any number that is 2.(something)

will be between 2 and 3

[alpine sable]

2.6

[noble sinew]

so it can always only be 2 or 3

[alpine sable]

k

[noble sinew]

so if it is 2.0,2.1,2.2,2.3,2.4 we round it down, if it is 2.5,2.6,2.7,2.8,2.9 we round it up

so if the digit just after decimal point is either 0,1,2,3,4 you round it down

otherwise round it up

[alpine sable]

ok

[noble sinew]

so what would 18.3 be?

[alpine sable]

hmmmm

[dense lynx]

Guys can i text here for any math questions i have with some exercises?

[alpine sable]

18

[noble sinew]

indeed

what would 18.4953213148219231292121913912485402 be?

[alpine sable]

POG

[alpine sable]

0

[noble sinew]

you sure?

[alpine sable]

ye

[noble sinew]

the nearest integer to 18.(something) is 0?

it isn't 18 or 19?

[alpine sable]

i googled for that

question

[noble sinew]

you are wrong then

[alpine sable]

e oof

[noble sinew]

told you the rule right here

why not use it?

[alpine sable]

ok

now what about this

[noble sinew]

if you don't understand how rounding works you can't do it

[alpine sable]

AH

give a problem quick easy one though

[noble sinew]

.

[alpine sable]

19?

[noble sinew]

what is the digit after the decimal point?

[alpine sable]

or 18

49

[noble sinew]

1 digit

not multiple

what is the digit right after?

[alpine sable]

1 digit?

brain is dead

[noble sinew]

"49" is 2 digits is it not?

[alpine sable]

it is

[noble sinew]

so what is the digit right after the decimal point?

[alpine sable]

2 digits?

[noble sinew]

clearly there are like 20 digits after the decimal point

[alpine sable]

brain is dying right now

[noble sinew]

all you need to say is which one is the 1st one

18.(what is this number?)9532....

[alpine sable]

9?

[noble sinew]

what is the first digit after the .?

look to the right of .

of 18.49532

[alpine sable]

4

no wait

[noble sinew]

okay that wasn't so hard was it

[alpine sable]

2?

[noble sinew]

yes it is 4

[alpine sable]

oh

ok

[noble sinew]

18.6319831938198319381831414913931'

the first digit after decimal point is 6

not very hard is it?

[alpine sable]

nope

[noble sinew]

okay so if first digit after decimal point is 4 do we round up or down?

[alpine sable]

down

[noble sinew]

indeed so this rounded is 18

[alpine sable]

ok

[noble sinew]

so when would we round a number to 14?

[alpine sable]

https://tenor.com/view/elmo-shrug-不造-i-dont-know-gif-5094560

[noble sinew]

can you give an example of something that would be rounded to 14?

[alpine sable]

14.0

[topaz palm]

This is sad

[topaz palm]

He legit just t0ld u 😭

[alpine sable]

showed what

[topaz palm]

.

[alpine sable]

oh right

[topaz palm]

Btw, you have to be at least 13 to use discord.

[alpine sable]

i am 13+

[velvet condor]

solve over naturals 3^x+2^y=2^z+1

[alpine sable]

i am just too dumb in maths

[velvet condor]

which mod should i consider

mod 4?

[topaz palm]

Oh fair enough

[alpine sable]

so the answer to your question is 15?

[topaz palm]

What was my q again

[alpine sable]

whats 14.7 rounded

[topaz palm]

Oh noice

[velvet condor]

to how many sf?

[topaz palm]

Yh u got the hang of it :)

[topaz palm]

2

[alpine sable]

nice

[velvet condor]

then 15

[topaz palm]

In this case

Yes

[alpine sable]

[topaz palm]

https://cdn.discordapp.com/emojis/854727480949342258.png?v=1&size=40

[alpine sable]

you used a tiny photo

[topaz palm]

Yws

Yes

https://cdn.discordapp.com/emojis/799284483110993971.png?v=1&size=40

Not a photo but yh

[alpine sable]

now i just need to solve this

theres more questions after that

[topaz palm]

So find the upper bounds for all the multiplication ones to find the upper bound results

Then the lower bounds of each

For division, find the upper bounds of the top and the lower bounds of the bottom to find upper bound results

For lower bounds

Find the lower bound of the top

And the upper bound of the bottom

:)

[alpine sable]

pog

helpful i think

IQ increases 1.00000000000000000000000000000000000000000000000000000000000000000000001

xd

[golden wharf]

a company has 30 members. how many ways are there to select a president, vice president and secretary. Assume that nobody can occupy more than one position

[glass lichen]

pick the people one at a time

[velvet condor]

bro help me./

[velvet condor]

this one

[alpine sable]

so to find upper bounds i have round it up?

[glass lichen]

if you start w/ the president, how many people can you choose from?

[glass lichen]

You posted while the channel was in use.

so no

[velvet condor]

eh ok

[golden wharf]

im assuming that there 30! possible ways of selecting anyone to be the president but assuming i have to subtract out the 3 occupied spots would I do 30!/(30-3)! ?

[glass lichen]

dont give answers

[golden wharf]

cause im kind of confused if I should be using nCr or nPr

[glass lichen]

use logic

[velvet condor]

bro be simple

how many people can choose the first role

[golden wharf]

30

[velvet condor]

yes

we know that 1 person has occupied the first slot

so how many people can choose the second one?

[golden wharf]

so 29?

[velvet condor]

yes 29

and the third....?

[golden wharf]

28

[velvet condor]

so 30x29x28 ways

makes sense?

[golden wharf]

ahh i get it thanks

[alpine sable]

i confused myself again welp

[velvet condor]

<@&286206848099549185> :/

[alpine sable]

<@&286206848099549185>

[gray isle]

what have you tried?

[alpine sable]

i just need to know if i should round the 1st number up or down

[keen blaze]

Hi, I'm new, amm in this group, they help with the homework.

[alpine sable]

i soooooo cant help you

i need help in the 1st problem

[gray isle]

you'd consider both cases

[velvet condor]

i guess+-0.5?

never heard of upper and lower bounds

[glass lichen]

#rules #❓how-to-get-help

[alpine sable]

i confused myself so i should round the number up then upper bound it?

[gray isle]

i confused myself so i should round the number up then upper bound it?
no, you the values given are already rounded.

[alpine sable]

oh

[gray isle]

you should consider the potential values of the original numbers

and using those consider the smallest and largest values that could've been possible

[alpine sable]

btw this

[alpine sable]

but i dont see how i can do in this

[gray isle]

lets look at a)

[alpine sable]

14*20

[gray isle]

for the lower bound,

since you're dealing with the product of two numbers,

you'd want to consider the smallest number that would round to 14

and the smallest number that would round to 20
(when rounding to the nearest integer)

[alpine sable]

HMMMMMMMMMMM

[gray isle]

fk typo

edited

[alpine sable]

wait but i gotta multiply upper bound into upperbound

[gray isle]

wdym

[alpine sable]

the first one is multiplication

[velvet condor]

the heck is bound thingy

i wonder

[alpine sable]

its 9th grade stuff

[velvet condor]

eh

so thats what u study in ur syllabus

[alpine sable]

honestly i dont wanna

[gray isle]

The lower bound is the smallest value that would round up to the estimated value.
The upper bound is the smallest value that would round up to the next estimated value.

[velvet condor]

i studied stuffs like am gm

logarithm

[alpine sable]

i gotta find the closest numbers to 14 so i can multiply with 20 @gray isle ?

[gray isle]

no

[glass lichen]

so you've never seen an inequality..?

[alpine sable]

https://tenor.com/view/headache-migraine-ugh-sick-explode-gif-4610831

[velvet condor]

i have

:v

alot

[glass lichen]

so then you know what bounding something is

[gray isle]

what's the smallest number that would round to 14 (when rounding to the nearest integer)?

[velvet condor]

the vietnamese syllabus doesnt have it sorry

not everything is perfect smh

[alpine sable]

how do i see the line thing from the bor

[sleek elbow]

I have seen an inequality and have no idea what bounding is lol

[alpine sable]

bot

[gray isle]

what line thing?

[alpine sable]

,w

[velvet condor]

i studied very weird ways to solve an inequality

for example using dirichlet.....

[alpine sable]

the bot that shows you stuff

[sleek elbow]

$5+5$

[ocean seal]

Ladan

[sleek elbow]

like that

[gray isle]

dollar signs at the start and end if you know what you're doing

look up how to tex in your spare time

[alpine sable]

ye

[gray isle]

otherwise communicate with plain text instead of exprimenting blindly

[alpine sable]

how can i use it for bounding

[gray isle]

or draw + pics

how can i use it for bounding
wdym

[sleek elbow]

only thing you need for basic texit

fractions: \frac{numerator}{denominator}

[alpine sable]

i need to see the closest integer from the bot

[sleek elbow]

the bot doesnt solve stuff for you i think

[gray isle]

14 is the closest integer of some unspecified number

[full cypress]

can someone explain fractional exponents pls

[velvet condor]

it's easy

[gray isle]

20 is the closest integer of a different unspecified number

[velvet condor]

for example

a^(1/2)= square root a

[alpine sable]

damn

it

[gray isle]

you'd want to consider the upper and lower bounds of those (given that they were rounded to the nearest integer)
and hence determine the upper and lower bounds of their product

[full cypress]

ok but i want to know how to solve for it without knowing the root

[velvet condor]

wdym

[gray isle]

The lower bound is the smallest value that would round up to the estimated value.
The upper bound is the smallest value that would round up to the next estimated value.

[glass lichen]

the channel is in use, dont help someone else as it can be annoying

[gray isle]

since you're dealing with the product of two numbers,
you'd want to consider the smallest number that would round to 14
and the smallest number that would round to 20
(when rounding to the nearest integer)

[full cypress]

like how do i solve 3^1/3 without knowing its root

[gray isle]

do you know how to normally round to the nearest integer?

[alpine sable]

no

wait

14.7 is 15

[gray isle]

14.7 would round to 15 yes

for now I chose to focus on the lower bounds first

you'd want to consider the smallest number that would round to 14

[alpine sable]

can it be like 14.15 or something?

[gray isle]

14.15 would round to 14, but it isn't the smallest value that wound round to 14

[muted lark]

can someone look at the question I send at #help-7｜zen1thxyz

[sleek elbow]

||shouldnt that be $14.0000000..01$ or something?|| for @gray isle

[ocean seal]

Ladan

[sleek elbow]

oof

:/

[alpine sable]

pog

[sleek elbow]

dont look

[alpine sable]

i looked

[sleek elbow]

probably wrong tho

as you cant put something after an infinite amount of numbers

[gray isle]

no

similar to 14.15, 14.000000...1 would round to 14, but it isn't the smallest number that would round to 14

[sleek elbow]

wut

okay I have no idea 😄

[alpine sable]

,w numberline 14 to 20

[gray isle]

do you think that numbers below 14 don't exist or something?

[sleek elbow]

im dumb

lol

LMAO

got it

[alpine sable]

I GOT IT

nvm

i tried to do 14.199

[gray isle]

do you think that numbers below 14 don't exist or something?

[alpine sable]

15 16 17 18 19 20

[glass lichen]

numbers below 14

[gray isle]

why are you listing integers between 14 and 20

[alpine sable]

idk

i am cluless

[gray isle]

what types of numbers round to 14?

[alpine sable]

i cant find

13.5

YE THAT GO TO 14

@gray isle

[warm granite]

Can someone please help me with this

[gray isle]

ok good, you've found the

The lower bound is the smallest value that would round up to the estimated value.

the lower bound for 14 is 13.5

similarly, what will the lower bound be for 20?

[alpine sable]

19.5

[gray isle]

and hence according to your info sheet,
the lower bound for 14 * 20 (given that values were rounded to the nearest integer)
will be 13.5 * 19.5

[alpine sable]

what about upper bound

@gray isle

[gray isle]

The upper bound is the smallest value that would round up to the next estimated value.

[alpine sable]

example

[gray isle]

whats the next integer after 14?

this isn't supposed to be a trick question

[alpine sable]

15

[gray isle]

and similarly what's the smallest number that would round to that?

[alpine sable]

14.7

[gray isle]

no

[alpine sable]

wait

[gray isle]

are you saying that anything smaller than 14.7 won't round to 15?

[alpine sable]

14.5 14.6 14.7 can round to 15

[gray isle]

what's the "smallest" possible value?

[alpine sable]

14.5

[gray isle]

yes

that will be your upper bound for 14

similarly what will be the upper bound for 20?

[alpine sable]

19.5

[gray isle]

no

that's the lower bound for 20

[alpine sable]

oh

[alpine sable]

19.9

[gray isle]

No

[alpine sable]

oof

[gray isle]

at this point I should probably ask you to explain the basic rules of rounding

[alpine sable]

lower bounding i can do i forgot how to do upper bound

[gray isle]

same process outlined for upper bound of 14

what did I ask you to do there?

apply the same process for 20

[alpine sable]

find the lowest number

[gray isle]

read the logs

[alpine sable]

that can bound to 14

[gray isle]

no, that's not exactly what I said

[alpine sable]

let see logs

the lower bound of the number thats close to it

[gray isle]

that's not what I said

Let's walk through the process again

What's the next integer after 20

[alpine sable]

21

[gray isle]

and what's the smallest number that will round to that?

[alpine sable]

19.5

[gray isle]

No

by "that", seeing it was immediately following the response of 21 is in reference to 21

what is the smallest number that will round to 21

(this is the lower bound of 21 which will also be the upper bound of 20)

[alpine sable]

20.5 maybe?

[gray isle]

why maybe?

how sure are you?

[alpine sable]

50 50

[gray isle]

20.5 is indeed the smallest number that rounds to 21

20.5 will be you upper bound for 20

[alpine sable]

ok

[gray isle]

and as per the rules you posted

the upper bound of your product will be
14.5 * 20.5

[alpine sable]

the next one is super hard

[gray isle]

how so?

[alpine sable]

3 digits

[gray isle]

exact same idea

number of digits changes nothing

If you know your round rules

are you implying you don't know how to round to the nearest integer for numbers greater or equal to 100?

[alpine sable]

k

135 lower bound is 134.5

[gray isle]

yes

[alpine sable]

25 is 24.5

[gray isle]

yes

for simplicity, since the numbers have been rounded to the nearest integer,
-0.5 for the lower bound, +0.5 for the upper bound

[alpine sable]

ok

[gray isle]

And that's all I have time for

[alpine sable]

ok

[mystic bobcat]

does someone here speak german and can help me with economy math ?

[boreal musk]

❓

[alpine sable]

u slow

kidding

use photo math for that lol

[topaz scaffold]

Parentheses first then go from left to right

[glass lichen]

dont comment if you're not going to actually help

[wild nova]

i think the question is broken, it doesnt work out

[topaz scaffold]

Oh yea

[tawdry flicker]

are the dots multiplication

or decimal values

if its multiplication

its 3

[boreal musk]

3² + 2⁴ – (6 . 5 + 3 . 4 – 5 . 8) + √49 – 4² + 25⁰ - √225

[tawdry flicker]

oh

[topaz scaffold]

,w 3 + (52) - (48 + 32) + 47

[wild nova]

the dots are meant to be multiplication

not decimals, formatted absolutely horribly

[topaz scaffold]

Hehhh

[wild nova]

its 3. this aint on bedmas

[boreal musk]

15?

[topaz scaffold]

Oh I typed it in wrong

[wild nova]

work it out with the decimals being multiplication, and put brackets around them

[ocean seal]

Results provided by WolframAlpha

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

Requested by RipeOrange#4907

[boreal musk]

thx!

Guys my math test and jaja can you help me?

[topaz scaffold]

Can't help with tests

[pearl marlin]

In these type of questions use BODMAS

[whole prairie]

Hey I have a super quick question

Is the answer to this 24?

It’s what I got

[pearl marlin]

You can check by simple integrating

[whole prairie]

Okay

[pearl marlin]

,w \int_{1}^{3}(x^2+3)

[ocean seal]

Results provided by WolframAlpha

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

Requested by learn4math#9125

[vagrant hatch]

Hey y'all! I am a college student taking Calc for business rn and was wondering if someone could help me find the correct answer to this problem with the given conditions.

[ionic jewel]

take the derivative of it while thing

4xy requires the product rule

the rest is power rule (or constant rule if you call it that(

then sub in the values given

[vagrant hatch]

ah, I see it wasn't the worst to do, just with all the conditions was making it seem harder than I thought. Thank you!

[alpine sable]

ok is 135.5 and 25.5 the upper bound

[ripe crypt]

Trying to figure out all the 4:3 aspect ratios on a graph as I am trying to print a canvas with an abnormal aspect ratio and want to find the closest one I can use and then crop. Basically need a graph showing x/y=1.3333 and all combinations up until 2000. so like, 4x,3y; 8x,6y; 12x,9y;... etc Not sure how to write an equation for this to plot into WolframAlpha

4/3 = (x + 4)/(y + 3), something like that

I think I answered my own question...

[pliant crater]

anyone?