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[flint blade]

can someone help we with this problem? thanks

[uncut plank]

I think this is helpful

[flint blade]

thank you so much!! @uncut plank

[uncut plank]

You're welcome @flint blade

[flint blade]

.close

[lone heart]

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[midnight atlas]

hey, can someone please help me to prove both of this by the definition of limit?

[midnight atlas]

I just cant figure out what is the delta that I need to set every time

<@&286206848099549185>

[tacit arch]

you're supposed to work backwards to find delta

[midnight atlas]

I know, i have done a few of this, also in sequence, i just cant get the inequalitiy right

[tacit arch]

show where you're stuck

[midnight atlas]

this is on the left one

the right one I dont even know where to start

@tacit arch

[lone heart]

@midnight atlas Has your question been resolved?

[lone heart]

@midnight atlas Has your question been resolved?

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[wet spindle]

Ray bought 2 bags of fruit, he bought 1 bag of oranges for $10 and another bag of apples for $12. He's gonna sell the fruit per bag mixed with a 2:3 ratio for 1 bag, if he wants to get a 25% profit, how much should he sell per bag?

[wet spindle]

I'm confusion, how does 2:3 look like in a bag?

[ember dust]

2:3 ratio means
2/5 parts orange which is $4 worth of oranges
3/5 parts apple which is $7.2 worth of apples
one bag now costs $11.2
add on 25% profit

i got the prices of the fruits by going (2/5)*$10

and (3/5)*$12

[wet spindle]

alright you're just telling me the answer

[ember dust]

okay myb

[wet spindle]

how did you get 2/5 and 3/5?

[ember dust]

what do you need to understand

so 2:3 can be split into two fractions

[wet spindle]

yeah

[ember dust]

in general a ration of a:b can be split into two fractions, that being
a/(a+b)
and b/(a+b)

[wet spindle]

the 2 corresponds to the oranges and the 3 corresponds to the apples right?

[ember dust]

correct

that means if we are trying to figure out how many oranges there are in the bag, we have to understand that the 2 parts oranges is the same as 2/5, since there are 5 total parts, and 2 of what we are looking for

[wet spindle]

so far so good?

[ember dust]

correct. Maybe specify apples and oranges tho

[wet spindle]

why are there 5 total parts?

where did you get 5 from?

[ember dust]

2:3 ratio can be read as
2 oranges for every 3 apples

[wet spindle]

alright

ahhh

"total"

get it

[ember dust]

oranges are the orange ones and apples are red

that is what a 2:3 ratio looks like

[wet spindle]

alright

[ember dust]

is there anything else you dont understand?

[wet spindle]

wait

[ember dust]

...

[lone heart]

@wet spindle Has your question been resolved?

[lone heart]

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[woeful ridge]

Are c and b just 44degrees and 43?

[floral pawn]

no

[woeful ridge]

How would I start? I made a right angle across and did 180-90-44 to get half of the O angle

[floral pawn]

HLJ and HKJ have common chord

[woeful ridge]

Okay what next? Cause I thought I split the triangle up into two right angles to find the missing one

[floral pawn]

do you know this

[woeful ridge]

So A and C are the same?

As would B and D be if we were looking?

[floral pawn]

yes

[woeful ridge]

So for the original question b would be 43 and c 44 right?

[floral pawn]

no, look closely, which segment does angle b share

[woeful ridge]

LHK?

So b would be 44 degree?

[glossy pasture]

can anyone help me with this please?

[wet spindle]

@glossy pasture #❓how-to-get-help

[lone heart]

@woeful ridge Has your question been resolved?

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[sullen shell]

I don't know if I did this correctly

[lone heart]

@sullen shell Has your question been resolved?

[sullen shell]

<@&286206848099549185> May I get some assistance please.

[naive crystal]

Ok

Let me help

And ye

As I expected

Hey

You take common out

From denominator and numerator

[sullen shell]

Remove the common variable from each?

[naive crystal]

Ye like

$\frac{2d(10k^2x^3+4b^4d^2y^2}{2d(16b^3d^3k^2)}$

[ocean seal]

! बाशुदेव

[naive crystal]

Now cancel out

[sullen shell]

So remove the d?

[naive crystal]

And 2

$\frac{\cancel{2d}(10k^2x^3+4b^4d^2y^2}{\cancel{2d}(16b^3d^3k^2)}$

[ocean seal]

! बाशुदेव

[sullen shell]

Thank you

[naive crystal]

It can also be

Further

Simplified

[sullen shell]

I'm listening

[naive crystal]

$\frac{2(5k^2x^3+4b^2d^2y^2}{2(8b^3d^3k^2)}$

[ocean seal]

! बाशुदेव

[sullen shell]

5k^2x^3+4~~

Yee

[naive crystal]

Ye

Ok

You got it

[sullen shell]

Thanks a lot

[naive crystal]

Ok

[sullen shell]

.close

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[tight mantle]

I haven't done systems of equations in a while so I can solve them but I need help making the equations the problem is

Each morning, Jerry delivers the Times to one neighborhood and then the Star to a different neighborhood.  While delivering the Times, Jerry delivers 2 papers per minute.  However, since the Star is so heavy, he can only deliver 1 Star paper per minute.  If he delivers a total of 91 papers and takes exactly an hour to deliver all papers, how many of each type of paper does he deliver?

[unique flax]

P = 0.5
S = 1
91P + aS = 60

Idk

[alpine sable]

2p+s=91

P+s=60

[tight mantle]

Tysm that's all I need

So I do .close now right

I'm new to this discord

[unique flax]

Ye i think just close

[tight mantle]

.close

[lone heart]

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[tight mantle]

Uh how do I find an equation (y=a*b to the power of x) using 2 points (2,3) and (5, 1/9)

[alpine sable]

$f(x) = (a*b)^x$
Ur trying to find a and b given that the function passes through (2, 3) and (5, 1/9)

?

[ocean seal]

Frustrated Cat

[tight mantle]

The problem says find the equation of an exponential function in the form of y = ab^x passing through those points

[alpine sable]

(ab)^x or a*b^x ?

[tight mantle]

A*b^x

[alpine sable]

Oh

U need to form a system of equations

$a*b^2=3$

$a*b^5=1/9$

[ocean seal]

Frustrated Cat

[alpine sable]

Btw what have u tried?

[tight mantle]

Uhh I had no idea what to do at all I was too confused

[alpine sable]

Try to solve the system of equations now maybe

[tight mantle]

Ok

.close

[lone heart]

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[pale mauve]

Can someone help me a bit confused what the question is asking

[pale mauve]

<@&286206848099549185>

.close

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[gray brook]

Oop

No no u go first

[jagged imp]

,rotate

[gray brook]

,close

[jagged imp]

no dont close

[gray brook]

Nvm

[jagged imp]

the other person claimed another channel

you dont have to wait for one another

[gray brook]

Oks oks

[jagged imp]

,rotate 180

[gray brook]

I alr answered number 3

Im stuck on number 1

Fuk

See

To get ke

I need tme

To get tme i need ke

[wary stream]

Use the KE formula given

[gray brook]

Yea how

To get tme i need to have ke

[wary stream]

No you don't

[gray brook]

?

How

[wary stream]

Did you read that page?

It gives you the formula for KE

[gray brook]

Yeaaaaaa

It needs tme

[wary stream]

No it does not

[gray brook]

???

It dose

[wary stream]

As I asked, did you read the whole page?

[gray brook]

See KE=TME-PE

[wary stream]

You have other KE equations

[gray brook]

?

[wary stream]

Because you are questioning, I am assuming you did not read that entire page

It gives you at least two different formulas for KE

[gray brook]

Heh?

I dont see any

[wary stream]

One third down the page

In the middle

It's there

[gray brook]

The one above direction?

?

[wary stream]

Is that about 1/3 of the page down?

[gray brook]

KE=½MV^2

?

[wary stream]

Yes

That's the other KE equation

[gray brook]

Whats mv

Mass velocity?

[wary stream]

Yes

[gray brook]

I dont have velocity

Whats the formula

For it

[wary stream]

Velocity is given

Oh wait

[gray brook]

Yea

Its no where to be seen

😭

U there?

[wary stream]

Here is the other thing to note, energy is neither created or destroyed, only changed from one form to another

Have you heard of that?

[gray brook]

Yea thats kinetic energy

Why?

💀

👻

[wary stream]

My assumption is that chart is a sequence of events. Meaning you drop a rock from 10m, and find all the energies then when the rock is at 8m, you determine the energies, etc

So if the TME of the system is 200 J, and as I stated energy is neither created or destroyed, only changed from one form to another, what should that mean for the total energy at 8m?

[gray brook]

So its still the same

[wary stream]

Yes

[gray brook]

Ahhhhh

Alr fam thanks

.close

[lone heart]

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[spiral aspen]

Something I'm trying to do is make it so that if a bullet flies within a certain proximity of a player, it will make certain sound effects and shake their camera. My main issue goes with calculating the distance from a bullet fired as a ray and the character (assume point is center of the character). I assume I will need to have the 3D vector and use some sort of distance formula? Would I need to convert the Vector3 into a 3D line equation to move forward? I'm a bit stuck.
https://cdn.discordapp.com/attachments/165226280118255616/968718850415804436/unknown.png?size=4096

[spiral aspen]

There are no physics affecting the "ray" and it's simply this equation:

position = velocity * t + starting_position

where position, velocity, and starting_position are Vector3's

[spiral aspen]

How would I get the point of intersection?

[lone heart]

@spiral aspen Has your question been resolved?

[elder grail]

could u give a bit more detail into what form u have the velocity/ positions in?

like is there a specific coordinate system?

and is the velocity a pre-known vector?

[lone heart]

@spiral aspen Has your question been resolved?

[spiral aspen]

Ah, apologies. Velocity is a 3D vector, and it is being multiplied by time and the starting position is also a 3D vector

And yes velocity is pre-known

Along with starting position (the place where the bullet/ray is fired)

T is just the variable

Of course

[elder grail]

ok so u have the velocity as a vector with known starting point, and also the player's location?

[spiral aspen]

Correct

I think what I need to do is find the perpendicular line to the ray

But I have no clue how to do that

[elder grail]

i'll get back in a moment?

[spiral aspen]

Sure man

Thanks

[lone heart]

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[brave granite]

Got a quick triq question-

[brave granite]

"Explain how you could use a protractor and a ruler to find the height of a building?"

[limpid spade]

shadow

Pythagoras

[brave granite]

we be doing sin cos tan

[limpid spade]

yes

[brave granite]

kinda stuff

[limpid spade]

shadow

Pythagoras

[brave granite]

we dont know that

[limpid spade]

wait no Pythagoras

[brave granite]

havent learned it

[limpid spade]

huh

learning sin cos and tan before Pythagoras?

[brave granite]

atleast idk what it is

[limpid spade]

I mean realistically you wouldn't see the angle of the shadow by the building

mhh

[brave granite]

I was thinking you look at the protracter

or something

find the angle

and the distance from u to the building with the ruiler

[limpid spade]

well if somehow u know the angle, and u find the distance of the shadow

[brave granite]

but idk how u can find a angle with a protracter when you are looking at it head on and not sideways

thats all i got with the question

[limpid spade]

u can use tan to find height

[brave granite]

ok i actually figuired it out

[lone heart]

@brave granite Has your question been resolved?

[lone heart]

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[vital bay]

im not sure how to find the zeroes

when i put p(x) into desmos there is only one zero

i feel like im missing something here but idk what it is

[alpine sable]

there is no equation to find the zeros of this polynomial

unless u use newtons method

[quartz oxide]

Instead of finding the roots directly, interpret them with their Vieta’s formulas
This helps you find the answer

[vital bay]

oh ok

[alpine sable]

i am pretty sure there is another way to get round it

[vital bay]

thanks i will have a go!

[quartz oxide]

Yeah

[sweet vault]

vegeta's what?

[alpine sable]

veitas ig

[quartz oxide]

Go look it up

[sweet vault]

what grade is this

[alpine sable]

oh man quadratic formula

is that what u mean?

i googled it up

[quartz oxide]

No

[alpine sable]

oh ok

[blazing saffron]

https://en.m.wikipedia.org/wiki/Vieta's_formulas

[limpid spade]

Elon musk unban me from 5witter

[quartz oxide]

Lol

[alpine sable]

lol

[alpine sable]

oh ty

[vital bay]

im still not sure how to do the question :/

[floral pawn]

you still need help?

[vital bay]

yes please

[floral pawn]

so you need to find $(r_1^2-2)(r_2^2-2)(r_3^2-2)(r_4^2-2)(r_5^2-2)$, right?

[ocean seal]

R31_

[vital bay]

yep

[floral pawn]

since the roots of $P(x)=x^5+x^2+1$ are $r_1,r_2,r_3,r_4,r_5$

[ocean seal]

R31_

[floral pawn]

means $x^5+x^2+1=(x-r_1)(x-r_2)(x-r_3)(x-r_4)(x-r_5)$ right?

[ocean seal]

R31_

[vital bay]

yep

[floral pawn]

now plug in $x=\sqrt{2}$ and see what you get

[ocean seal]

R31_

[floral pawn]

write it in here

after you get that, plug in $x=-\sqrt{2}$

[ocean seal]

R31_

[merry depot]

oh sh*t that's clever 🤦

[floral pawn]

and then multiply the 2 together

[vital bay]

yoo that is so smart

thank u

[elder grail]

yeah this smort

[vital bay]

i still dont know how to type latex so im just gonna do it on paper

tysm

[floral pawn]

thats aight

np

you might have to do some work with like the plus and minus signs, but I think this is the best way to do it

(to not have to expand out the entire (r_1^2-2) terms)

[vital bay]

oh yeah u just have to multiply by -1 once

thank u very much!!

.close

[lone heart]

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[merry fiber]

How to make a function which shape is a d***

[limpid spade]

pls

delete

. close

.close

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[soft cosmos]

hello

[soft cosmos]

i know how to get the amount of preys in 11 weeks

and the population

but how exactly do i get the rate

[torpid barn]

f(g(11)) is the predator population at 11 weeks right? then u can do f(g(12)) and find the rate

@soft cosmos

[soft cosmos]

wdym?

[blazing saffron]

I don't know about that

I would just take the derivative of the composite function

And evaluate at 11

[soft cosmos]

which composite function?

[blazing saffron]

f(g(t))

[soft cosmos]

oh well

after doing that, how do i find the rate

[blazing saffron]

I said it

That is the rate

[blazing saffron]

.

If you view t as being time d/dt f(g(t)) is the rate of change of the predator population with respect to time

Which is what you are looking for

Specifically the time being 11 weeks

[soft cosmos]

ah yes

thank you

[blazing saffron]

Yup

[soft cosmos]

.close

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[waxen owl]

How do you evaluate this?

[waxen owl]

i know the answer if n=1 but idk how to do it cus n=5

[alpine sable]

$\sum_{n=5}^{\infty} \frac{6^n}{7^n}$

[ocean seal]

Frustrated Cat

[inland ridge]

if you know the answer for n = 1 then just substract the numbers for n from 1 to 4

[alpine sable]

$\sum_{n=1}^{\infty} \frac{6^n}{7^n} - $\sum_{n=1}^{4} \frac{6^n}{7^n}$

[inland ridge]

yeah, just like that ^

[alpine sable]

Lol I don't really need to solve the warning

It wrote the thing I wanted

[waxen owl]

So I have the one on the left side

[alpine sable]

@waxen owl this two expressions should be equal

[inland ridge]

an the one on the right is easy to calculate

[ocean seal]

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

[inland ridge]

then just substract and done

[alpine sable]

Ya final bit of editing

[blazing saffron]

\[\sum_{n=1}^{\infty} \frac{6^n}{7^n} - \sum_{n=1}^{4} \frac{6^n}{7^n} /]

[waxen owl]

so to find the one on the right side

[blazing saffron]

Sadge

[waxen owl]

I just plug in n=1,2,3,4?

[inland ridge]

yeah

[ocean seal]

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

[waxen owl]

no need to do up to 5?

[inland ridge]

no

[waxen owl]

Ok!

Thanks

[inland ridge]

here it's starts from 5

so it's included

you don't substract it

so only up to 4

[waxen owl]

Okok

I have one more quick question

How do I reformat this question

[alpine sable]

Reformat?

Solve the sum?

[waxen owl]

Ya Idk how to start it

[alpine sable]

Well dw

[waxen owl]

I can't do (2/4)^n

[alpine sable]

Do you know power series?

First?

[waxen owl]

I'm looking at my notes and I don't see any similar problems

[inland ridge]

but you can do it with 2/8

ah

no

2/16

my bad

[waxen owl]

Oh so I can just do (2/16)^n I see

[alpine sable]

$\frac {2^n}{4^{2n+1}}=\frac {2^n}{4^{2n} * 4}=\frac {2^n}{(4^2)^ n * 4}$

[inland ridge]

and the + 1 you can just change into * 4

yes

just as above

[waxen owl]

Sweet makes sense

[ocean seal]

Frustrated Cat

[alpine sable]

The rest is pretty simple I hope

[waxen owl]

Yaya I know how to do it now thanks

Adios

.close

[lone heart]

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[lament root]

Can someone help with finding the remainder? I was able to find the values of a and b but I am stuck on how to solve the remainder when p(x) is divided by them

[lone heart]

@lament root Has your question been resolved?

[sudden hinge]

First also solve for "a" @lament root

[lament root]

Yeah it's done

It's at the top of the pahe

Page*

[sudden hinge]

"a" should be in terms of x, though

[lament root]

So it should be x=-5/2

[sudden hinge]

no, when dividing $P(x)$ by $x-3$ you should get
$$P(x) = (x-3) \qty[(x+1)Q(x)] + \underbrace{a(x+1) + b}_{\mathrm{Remainder}}$$

[ocean seal]

nvx

[sudden hinge]

$$\implies a(x+1) + b = 1$$

[ocean seal]

nvx

[lament root]

Ohhh sorry I misunderstood

Yeah

And then i substitute 3 in

[sudden hinge]

b = -11

solve for "a" then

[lament root]

Yeah I got that

-5/2

[sudden hinge]

$a = \frac{12}{x+1}$

[ocean seal]

nvx

[sudden hinge]

I don't see how you got -5/2

[lament root]

Well

Okay one second

I'm using the remainder theorom

This is done by substituting the dividend in

Since there is a -3

That all becomes 0

Then (3+1)+11

=1

Or am i using that theorom wrong

[sudden hinge]

imo you don't even need it

[lament root]

Oh haha

[sudden hinge]

just plain division gives this

then if you sub in a and b into the original P(x)

the x+1 cancels and youre left with
$$P(x) = (x+1)(x-3)Q(x) + 12 - 11 = (x+1)(x-3)Q(x) + 1$$

[ocean seal]

nvx

[lament root]

So I'm left with 12-11=1

[sudden hinge]

And dividing this now by (x+1)(x-3) the remainder should be easy to spot

[lament root]

Q(x)+1?

[sudden hinge]

only 1

[lament root]

Oh

Thank you

I feel so dumb now haha

Can you tell me how you got 12?

Don't worry

Have a good day!

.close

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[zenith marsh]

Does non continuous function in Xo that is differential in Xo exist?

I know that continuous function in Xo that is not differential in Xo can exist
Example is f(x)=|x|, but what about that statement?

[zenith marsh]

Non continuous function in Xo that is differential on the left in Xo exists i think
e^1/x

[bitter vault]

What is $Xo$? Note that if a function $f$ is differentiable at $a$, then it is continous at $a$. The contrapositive says if $f$ is not continous at $a$, then it is not differentiable at $a$.

[ocean seal]

1345631

[zenith marsh]

Basically Xo is a

Let me just read what you wrote and try to grasp it, my brain need 20 seconds

[uncut plank]

$X_0?$

[ocean seal]

Si Arya

[zenith marsh]

So what about e^1/x

Isn't it differential from the left?

And is non continous

Does that definition only apply if it is differential on both sides

The one you wrote

[uncut plank]

That? It isn't always continuous. Discontinuity happened at x = 0

[zenith marsh]

^

[bitter vault]

Try to use terms correctly to be clearer. The term is "differentiable", not differential.
The statement I put above says: if f is differentiable at a, then it is continuous at a. The contrapositive is a logically equivalent statement which says: if f is not continuous at a, then it is not differentiable at a.
As mentioned by someone, e^(1/x) is not continuous at 0, so it's not differentiable there

[zenith marsh]

Ah i see

So it does not have f'(a-)

there

[bitter vault]

Not being differentiable means at 0 means $\lim_{h \to 0} \dfrac{f(h)-f(0)}{h}$ does not exist

[ocean seal]

1345631

[zenith marsh]

So that definition you provided applies for all cases

It has to be differentiable on both sides

If it is non continous, it can't be differentiable on either sides alone?

[bitter vault]

It's actually a theorem, not a definition. Differentiability at a point that's not an endpoint of the domain means both left and right derivatives exist and are equal.
So not being differentiable at a point that's not an endpoint means either one or both one-sided derivatives don't exist, or they exist but are not equal

[zenith marsh]

Yeah ,"or they exist but are not equal" this is what interests me, so e^1/x can be differentiable from the left and non continuous?

1.) Function has to be differentiable from both sides in a to be continous
2.) If function is not differentiable at a then it is not continuous
3.) Function can be non continuous but differentiable from left/right side

Are all these statements True?

Now when i concluded it

For the 1.) |X| is not differentiable in x=0 but is continuous right?

So i really don't understand this

Is there a function that is differentiable from the left at some point, and it is not
continuous at that point? This is the question from the practise book

And i thought it is e^1/x

But now i am confused

Is there a function that is continuous at some point and not differentiable
at that point? Is the opposite true? Explain. And this is the other question where i thought that it could be |x|

[bitter vault]

f(x) = |x| is continuous at 0, but the left derivative is -1 and right derivative is +1. These don't agree, so f is not differentiable at 0. You can have continuity but not differentiability at a point.

Please ask one question at a time and wait for a reply. You're asking too many questions at once

[zenith marsh]

But to have differentiability i need continuity?

Sorry

They are all related so i am quite confused

[bitter vault]

Try to use terms correctly to be clearer. The term is "differentiable", not differential.
The statement I put above says: if f is differentiable at a, then it is continuous at a. The contrapositive is a logically equivalent statement which says: if f is not continuous at a, then it is not differentiable at a.
As mentioned by someone, e^(1/x) is not continuous at 0, so it's not differentiable there

From earlier.

[zenith marsh]

You can have continuity but not differentiability at a point, but to have differentiability you need continuity Does this conclude that theorem in common folk language?

[zenith marsh]

Aha understood

Now i reread it few times

Is there a function that is differentiable from the left at some point, and it is not
continuous at that point? So because of that theorem this basically falls off?

So now i guess it can be differentiable from the left?

[bitter vault]

$e^{1/x}$ is not defined at $x = 0$. So if $f(x) = e^{1/x}$, then when you try to compute $\lim_{h \to 0} \dfrac{f(h)-f(0)}{h}$ no matter from which side, it doesn't exist because $f(0)$ does not exist.

[zenith marsh]

So the theorem applies even for the sides seperately

[ocean seal]

1345631

[zenith marsh]

The thing is, i am trying to find out if that question is possible.I may have given a bad example e^1/x which doesn't fullfill that it can be differentiable from the left side and non continuous, but the thing is i am trying to figure out does any function like that even exist

I get that differentiable function in "a" is continous in "a" but that is for both sides

And i also get that continous function in "a" does not have to be differentiable in "a"

But what about just sides seperately can it be differentiable from the left/right somehow and non continuous

Or does if a function is non continuos in "a" then it is not differentiable from any side apply

And the final answer would be No

[bitter vault]

diff in "a" cont in "a"
It's at a, not in a. Continuity and differentiability is a property functions have at points, not in points.

As mentioned before,

It's actually a theorem, not a definition. Differentiability at a point that's not an endpoint of the domain means both left and right derivatives exist and are equal.
So not being differentiable at a point that's not an endpoint means either one or both one-sided derivatives don't exist, or they exist but are not equal

[zenith marsh]

either one or both one-sided So one, in this case left derivative is possible to exist?

[bitter vault]

Possible.

[zenith marsh]

I see, thank you a lot

Sorry for bothering you with this

Can i somehow +rep you or something if that helps with anything

All in all i will close the channel for others to have it available

.close

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[crimson edge]

Could someone please help explain this to me? I know soh cah toa and stuff but im not sure how to find a side using an angle.

[sudden hinge]

So what is tan(A) in terms of the side lengths?

[crimson edge]

1.2?

[sudden hinge]

nah i mean

tan(A) = opp / adj right?

[crimson edge]

oh yeah

[sudden hinge]

what is the opposite side, what is the adj side here

with respect to angle A

[crimson edge]

h is opposite

and 11.4 is adj

[sudden hinge]

right

so tan(A) = h / 11.4

[crimson edge]

ye

ohh

i understand now

11.4x1.2 = h right?

no.

[sudden hinge]

tan(A) = h / 11.4 = 1.2

h = 1.2 * 11.4

correct

[crimson edge]

oh okay thanks

got it thank you

.close

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[scenic anchor]

hello everyone, i would like to wkow where star to study math to win competitions

[worn fox]

Have you tried looking at past Olympiad questions?

[oak perch]

Download lots of questions along with solutions then train yourself

[scenic anchor]

yes, i tried to do it but I would also like to study something more. Can you suggest some resources to deepen some things?

[oak perch]

Just read some textbooks

[sudden hinge]

There are also various youtube channels solving and showing strategies for olympiad problems

michael penn, letsthinkcritically, letssolvemathproblems etc.

[oak perch]

Idk, something like this

Too many textbooks, just read one at least

[scenic anchor]

Ok thak u a lot!!

I'll follow your hints!!

[lone heart]

@scenic anchor Has your question been resolved?

[lone heart]

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[visual plinth]

Would this be fine for this?

[real glen]

that should work since 137/3 is not integer

[visual plinth]

ok so I should divide by 3?

to show that

[vale wigeon]

you have it the wrong way around

it's not "137 is not a factor of 3" it's "3 is not a factor of 137"

[visual plinth]

oh yeah ...

ok thanks people

.close

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[obsidian lodge]

i dont know how to solve this

[obsidian lodge]

im stuck here

<@&286206848099549185>

hello??

[marsh rapids]

Remember that sin x / x -> 1

With a bit of rearranging it works out this way

[obsidian lodge]

uhm ok

can u show me??

[real glen]

use $\cos^2(x)=\frac{1}{2}(1+\cos(2x))$ to simplify denominator first

[ocean seal]

jixana

[marsh rapids]

Not needed

[real glen]

hmm, my way used it so i suggested it

what is your way

I wanted to bring it to $\frac{2\sin(x)\cos(x)}{x \cos(x)}$ and calculate limit like this

[ocean seal]

jixana

[marsh rapids]

Since both limits are well defined, you cut the product into sin^2(2x)/x^2 and 1/(1+cos(2x)), and the limit will be the limit of the products = the product of the limits

[real glen]

thats true nice

[obsidian lodge]

oh okok

thanks

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[past dagger]

i made the probability of 6 1/4

and all the others 0.15

but this is the answer

whoops

.close

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Channel closed

Closed due to the original message being deleted

[alpine sable]

H

[lone heart]

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[fickle plinth]

for factoring expressions, if the equation is 14m^2+m-3 and when I get the 2 factors that add up to the middle number, the middle number is 1

[fickle plinth]

what do i do

<@&286206848099549185>

[worn fox]

either one should work

what two did you find?

[alpine sable]

Ping helpers after 15 min

[alpine sable]

Read this

[fickle plinth]

oh ok

sry

but the steps

i times 14x-3

which is -42

[alpine sable]

$14m^2+m-3$

[ocean seal]

Frustrated Cat

[fickle plinth]

but now i have to get the 2 factors that add up to the middle number

[alpine sable]

U want to factor this right?

[fickle plinth]

yes

[alpine sable]

Can you tell what two numbers add upto the middle term and their product is -14*3?

[fickle plinth]

so the middle term is 1 right?

[hollow shale]

14*3?

[alpine sable]

Ya

The coefficient of m if that sounds clearer

[fickle plinth]

1, 2, 3, 6, 7, 14, 21, 42

so um

idk

this is blowing my brains

[uncut plank]

Dont forget negative factor of -14*3

[alpine sable]

Ya i edited it rn

It should be -14*3

Mb

[fickle plinth]

uhhh

i can't seem to find the

2 numbers

[alpine sable]

$xy=-14*3$

$x+y=1$

Can you really guess the values of x and y

[ocean seal]

Frustrated Cat

[fickle plinth]

is there like a equation to find the 2 numbers or something

[alpine sable]

There is

But I don't think u will understand it

[fickle plinth]

what is it

oh

[alpine sable]

Ur in class 8 ig?

[fickle plinth]

grade 8 yeah

i think this stuff is algebra 1

[alpine sable]

You need to know the quadratic equation to get a systematic way so you can't understand now!

[fickle plinth]

oh ok ok

wait so what is the 2 numbers that add up to 1 and mutiply by -42?

[alpine sable]

Multiply to

[worn fox]

use this list you found

[alpine sable]

-42

Not multiply by

[fickle plinth]

-6 and 7

right?

[worn fox]

yep!

[alpine sable]

Yup

Now just break down the 1 like that

[uncut plank]

Yup. Now what to we do?

[alpine sable]

Middle term factor it

[fickle plinth]

(9m-6)(9m+7)

[alpine sable]

Straight forward

[fickle plinth]

is the answer?

[uncut plank]

Nope

[alpine sable]

Just a sec

[fickle plinth]

ok

[alpine sable]

$14m^2-6m+7m-3$

[ocean seal]

Frustrated Cat

[fickle plinth]

oh wait shoot

[alpine sable]

I am pretty sure you made a mistake

[fickle plinth]

i looked at the wrong question

mbb

hold on

[alpine sable]

U looked at the last one

U asked

Ig lol

[fickle plinth]

(14m-6)(14m+7)

?

[uncut plank]

Nope

[alpine sable]

No

[fickle plinth]

huhh

how

why

[alpine sable]

First how (14m-6) (14m+7)

[fickle plinth]

um

idk it's was just like a formula that my teacher gave me

[alpine sable]

Take it slowly factor $14m^2-6m$

[ocean seal]

Frustrated Cat

[fickle plinth]

$7m^2-3m$

[ocean seal]

zeim

[uncut plank]

Factor 14m² + 7m that's another way to solve it

[fickle plinth]

that would be

$2m^2+m$

[ocean seal]

zeim

[fickle plinth]

so now what do i do from there?

[uncut plank]

It can be factored even further

[fickle plinth]

the m?

2^2

4

just 4?

[uncut plank]

Yes. the m

[fickle plinth]

yeah and all there left would be 4

because the 2^2

[uncut plank]

What? Can you explain how

[alpine sable]

Srry i was afk

Ya

[uncut plank]

I apologize that it doesn't make any better. But let's put that aside

[fickle plinth]

2m^2+m and the m's go away so 2^2+nothing

[alpine sable]

U can factor $7m^2-3m$ furthee

[ocean seal]

Frustrated Cat

[alpine sable]

Take m as common factor

[fickle plinth]

7^2-3

[alpine sable]

$(14m^2-6m) = 2m(7m-3)$

[ocean seal]

Frustrated Cat

[alpine sable]

Get it?

[fickle plinth]

hmm

[alpine sable]

Now $14m^2-6m+7m-3=2m(7m-3) + (7m-3)$

[ocean seal]

Frustrated Cat

[alpine sable]

again do common factor

My keyboard lagging brb

[fickle plinth]

why is that so long

[uncut plank]

Don't forget to use distribution property.
A(B + C) = AB + AC

[alpine sable]

Why do we need it here?

It's just one more common factor

[uncut plank]

In this case, A = (7m - 3), B = 2m, and C = 1

[fickle plinth]

ahhhh

[alpine sable]

C=-3

How 1?

[alpine sable]

Wdym?

[fickle plinth]

nvm

[uncut plank]

Because,
(7m - 3)(2m + 1) = 2m(7m - 3) + (7m - 3)

[alpine sable]

Am i being clear ;-;

[fickle plinth]

yeah

it's just my dumb brain that can't process it

[alpine sable]

Nice now take the common factor @uncut plank just showed

[alpine sable]

All are equal as per me tho

[fickle plinth]

so i get rid of the m's

or do i distribute it?

[alpine sable]

Do you know common factor?

[fickle plinth]

yeah

[alpine sable]

ab+a=a(b+1)

Know this?

[fickle plinth]

uh

thats not the common factor i know

isn't common factor just like a factor that can be both divisable by both numbers?

[hollow shale]

I think you mean a factor that can divide both numbers/terms

[fickle plinth]

yeah

[worn fox]

$a$ is a factor of both $ab$ and $a$, in other words it is common to both of them, a.k.a a common factor

[ocean seal]

iCaird

[lone heart]

@fickle plinth Has your question been resolved?

[lone heart]

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[mint oracle]

how would one approach to finding the value of this sum on undergraduate level assuming no knowledge of hypergeometric function?
i performed partial fraction decomposition, etc... myself

[lone heart]

@mint oracle Has your question been resolved?

[tacit arch]

show what you've tried.

[mint oracle]

the original problem looked like this. i got stuck on this stage above and i need some hints

[noble sinew]

,w sum from n=1 to inf of 1/((2n+1)(3n+1)*2^n)

[ocean seal]

Results provided by WolframAlpha

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

Requested by ScapeProf#9427

[tacit arch]

F

[noble sinew]

Notice it can’t give an answer not involing hypergeometric dist

So why would you be able to find the sum?

[mint oracle]

i already checked and these two are the same

[noble sinew]

I’m saying you aren’t gonna be able to find an answer

[mint oracle]

it was a problem on one of my exams a week ago and i've been discussing it with a friend today.

i didn't solve this problem and left it out

and now i was wondering how to even solve it

[tacit arch]

did you learn the definition of hypergeometric?

[mint oracle]

the task was to just "compute the sum of this series"

[mint oracle]

I know of the hypergeometric function, yes, but i learned it on my own (not in the curriculum just yet) and assumed it won't be required for this problem.

a friend suggested me that there's a trick involving power series(?) and an integral, but i'm not seeing it

[tacit arch]

are you sure you remembered the problem correctly?

[tacit arch]

this is your work, right?

i.e. not a screenshot taken from an exam

[mint oracle]

the exam was on paper

i copied the problem to a sheet and brought it home

then i attempted to solve it again

the other problems were fairly simple (multivariate optimisation, etc...)

[noble sinew]

There isn’t a closed form solution

[mint oracle]

the screenshot was taken in wolframalpha of course

[tacit arch]

fwiw, i think the sequence of your series can be written as $1/a_k$ for integers $k\ge 1$.

[ocean seal]

riemann

[mint oracle]

that's pretty straightforward, yeah

[tacit arch]

the first twenty terms are
[24, 140, 560, 1872, 5632, 15808, 42240, 108800, 272384, 666624, 1601536, 3788800, 8847360, 20430848, 46727168, 105971712, 238551040, 533463040, 1185939456, 2622488576]

and it's not in oeis

https://oeis.org/search?q=24%2C+140%2C+560%2C+1872&language=english&go=Search

[mint oracle]

i've been looking for a trick to get power series here and then turn it into an integral somehow.

[tacit arch]

yea that probably will work. defining $f(z) = \sum \frac{z^n}{(2n+1)(3n+1)}$ and working with that might be useful. and then your series is just $f(1/2)$

[ocean seal]

riemann

[mint oracle]

so if this will probably work why is finding a closed form solution impossible

[tacit arch]

this is a closed form

[mint oracle]

special functions can not appear in closed form expressions

[tacit arch]

there might be an equivalent identity that is "closed form"

[mint oracle]

of course, wolframalpha can't solve every problem

https://dlmf.nist.gov/15.4 this table might be helpful for figuring out some stuff

i'll try figuring it myself since it's a really difficult problem and i doubt anyone wants to solve it

.close

[lone heart]

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[reef rock]

i need help

[naive crystal]

Ask ur question

[lone heart]

@reef rock Has your question been resolved?

[reef rock]

No.

[hard patio]

but what is your question?

[reef rock]

1+1

[hard patio]

???

[reef rock]

whats 1+1?

[hard patio]

please stop

trolling

[reef rock]

so

im asking a math question

and u cant even help

[hard patio]

Nope, cant, sorry mate

[reef rock]

then dont

ask me

what my question is

get help yousrelf tbh

[hard patio]

yessir.

that is why i am here

[reef rock]

lo

lol

lol

well

i actually

awnt to know

why

1+1 is

what it is

[hard patio]

to get myself help sir.

sir, you ever heard of counting?

[reef rock]

what do u think

u think im living

under a concrete rock

heres teh real question

[hard patio]

sir, i make no assumptions

[reef rock]

so

i dont gt this

cn someone help

?

<@&286206848099549185> 7

[round sable]

https://dontasktoask.com

[prime badge]

you can flip two of them over

now it's doable

[reef rock]

dc

[reef rock]

Ok

[round sable]

You should. That's why it took an hour to get an answer to this question which could have been solved in 5 mins

[reef rock]

dc

[reef rock]

still

how do i get my anser

[prime badge]

you have 15 angles total

the unmarked ones add up to 180°

you only need to know what all 15 add up to

[reef rock]

ok

ok

im gonn fail

so hard

im gonna fa

fail

[lone heart]

@reef rock Has your question been resolved?

[reef rock]

no

but idc

rlly

[lone heart]

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[past dagger]

for the second bullet point

i need help making a constraint

linear programming^

[marsh rapids]

letting a and b be the numbers of mp3s of types A and B respectively, you can write a double inequality ... <= a <= ... with simple expressions with a and b

[past dagger]

i have done that, just using x and y

i have

0.4(x+y) >(or equal to) x >(or equal to) 0.1(x+y)

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@past dagger Has your question been resolved?

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@past dagger Has your question been resolved?

[lone heart]

@past dagger Has your question been resolved?

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[lone heart]

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[solemn compass]

Is this how you solve for “h”, if not how do you. Thanks.

[lone heart]

@solemn compass Has your question been resolved?

[cursive crescent]

The middle column looks like the right idea

[solemn compass]

Oh ok

Thanks

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[ember herald]

Hello, how many radius lengths are in 2 revolutions?

[ember herald]

that's pretty much it

[shell widget]

S = r(theta)

in 2 revolutions, you cover an angle of 4pi radians

[ember herald]

interesante

what about half of a revolution?

[worn fox]

If 2 revolutions is 4π, then what do you think 1/2 revolutions is?

[ember herald]

wait

goddam

im a dumbass

thanks

!close

[shell widget]

.close

[lone heart]

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[hasty gale]

I need some help on this middle school arclength question

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@hasty gale Has your question been resolved?

[hasty gale]

<@&286206848099549185>

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@hasty gale Has your question been resolved?

[hasty gale]

<@&286206848099549185>

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[proud lake]

Hi, I'm currently taking an online exam and it would be great if you can help me.

[alpine sable]

Srry but please go through the rules we don't help on exams or tests

[proud lake]

ok

.close

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[waxen owl]

I did the divergence test and ended up with 0-0

[waxen owl]

So it's inconclusive right

[tacit arch]

Show your work

[lone heart]

@waxen owl Has your question been resolved?

[waxen owl]

Well I just ended up with e^infinity - e^-infinity

[last ether]

If it's 0, it's inconclusive and you have to do another test

What I would do is expand $e^{-10(n-1)}$ @waxen owl

[ocean seal]

Umbraleviathan

[last ether]

And then simplify

[waxen owl]

so (e^-10)(e^n)(e^-10)

[last ether]

No

[last ether]

Foil in 10, use exponent properties, and then factor out a common term

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