help-0

[near turtle]

okay so this in dutch i will give you the translation: Find DE with help of other lengths. DF = 5,4 BD = 9,9. We cant use pythagoras because this is a parallellogram.

I understand how to find BD but I don't get how to find DE

[lone heart]

@near turtle Has your question been resolved?

[waxen flame]

Out of curiosity, how did you find the length of BD without using the Pythagorean Theorem?

[near turtle]

i used fractions, 5,4 x 11/6 = 9,9

[waxen flame]

Did you try using Pythagoreans Theorem to verify your answer?

[near turtle]

Pythagoreas cant be used here, its an parallellogram

[waxen flame]

Ahh

My apologies, I assumed I was looking at a three-dimensional image.

[near turtle]

@hoary sphinx

[waxen flame]

If they are similar parellellograms, can't you use the length of the side you know and the same ratio method?

[near turtle]

ohh it works

thanks bro

❤️

damn bro

everyone thought it was so hard so they started using cosinus and all that

.close

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[trail cairn]

If a sum of $800 were to be shared among a group of people in the following ratios,
how much would each person receive?
a 4:6 b 1:4 c 2:3:5 d 2:2:4

[long axle]

For each ratio, add up the total amount, for example 4:6, 4+6=10

Then do 800/10

Ur answer multiplied to each part of the ratio will be the amount each person gets

#❓how-to-get-help @alpine sable

[ocean seal]

FriedrichDN

[alpine sable]

Ok

My bad

[trail cairn]

so would i do that for the rest

[long axle]

Yea, what’d u get for the first one tho

[trail cairn]

4:6=10, so we do 800/10=80

[long axle]

Right, and then calculate how much each person gets

[trail cairn]

how

do you mean like for b,c,d

[long axle]

One person gets 80* 4 and the other gets 80* 6

[trail cairn]

80x40=320, 80x6=480

[long axle]

Good

That means person 1 gets 320 and person 2 gets 480

[trail cairn]

do i do that for b too

[long axle]

Yes

And the rest of them

[trail cairn]

what about c. 2:3:5 d. 2:2:4

[long axle]

Yea same proces

[trail cairn]

for b is it 160:640

[long axle]

Yes

[trail cairn]

can you help me with c

c 2:3:5

=10

800 divide 10=80

do i do 80x2

80x3

80x5

[long axle]

Ye

[trail cairn]

kk

so 160:240:400

then d = 16:16:32

can we do this question

The scale on a map is 1 : 1000. Find the actual distance (in metres) between two
markers if the distance between the two markers on a map is:
a 2.7 cm b 140 mm

[long axle]

No

[trail cairn]

why

[long axle]

What’s 2+2+4

[weary wyvern]

||8||

[trail cairn]

8

isnt it

[long axle]

Yes

What’s 800/8

[trail cairn]

oh 100

my bad

[long axle]

Some1 else can help u w that map problem, I gtg

[trail cairn]

um do i wait or does someone come

or do i close

[long axle]

U can do either

[trail cairn]

close

.close

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[alpine sable]

I need to get the intersection of 2 plans, I found a solution, is there a website to check if it's correct ?

[keen pasture]

Maybe geogebra?

[alpine sable]

Would it give me the parametric representation ?

of the line

of intersection

[weary wyvern]

Search up "plane intersection calculator" or smth

[keen pasture]

You can also plug in the line equation in the plane equations. If it holds for both planes (no matter for which lampta) it is right

[prime sluice]

You can do 3d in geogebra??

[weary wyvern]

Yes

[alpine sable]

lambta ?

I didn't see any lambta in geometry yet

[prime sluice]

The 2d and 3d are separate apps I didn't know my bad

[keen pasture]

I don't know how you write the line equations. The line needs to be in both planes though

[alpine sable]

I found this one
In the exercice the plane are given in this formula :
(P1) : x-y+2z-3=0
(P2) : x+2y-z=0

how do I write it in general form ?

@keen pasture

[keen pasture]

Sorry, I don't know what you would consider the "general form"

[alpine sable]

Oh okay

maybe standard form ?

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@alpine sable Has your question been resolved?

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[real kernel]

Amani can wash a car twice as fast as Sydney. If it takes both of them, working together, 88 minutes to wash a car, how long would it take each of them, working alone?

completely stumped on this one lol. don't know where to start with it

[thorny root]

let's say Amani alone can finish that job in A minutes and Sydney in S minutes

and set a whole finished job to be 1 or 100%

so firstly, how much work do Amani and Sydney do per minute respectively

use the fact that (Amount of minutes worked) × (Job done per minute) = 1 whole job

[real kernel]

would a = 2s

or i mean s/2

[thorny root]

s/2, yes

[real kernel]

because faster time would be less

ok

s + s/2 = 88 so far

[thorny root]

not really

[real kernel]

that's where i'm confused lol

[thorny root]

s is the time for Sydney to finish one job

s/2 is the time for Amani to finish one job

so adding those two directly doesn't really help

[real kernel]

idk how to find the time sydney would take

[thorny root]

well starting with these will help us progress

[real kernel]

1 minute and 0.5 minute?

[thorny root]

there really isn't a numerical answer for this, at least not yet

[real kernel]

idk then lol

[thorny root]

well

if Amani takes A minutes to complete one job and we assume she is working consistently and continously

we would need to work 1/A job per minute for that to happen

so A minutes time 1/A job per minute = 1 job

same logic applies to Sydney

do you get it so far

[real kernel]

idk

how do you put sydney in

[thorny root]

well she does 1/S job(s) per minute right

[real kernel]

1/a and 1/s

and s would be a/2

[thorny root]

in these types of question we assume the worker working together doesn't affect their individual workpower

so together they do (1/A + 1/S) jobs per minute

and the question gives us as a fact that they took 88 minutes to finish one job

so 88×(1/A + 1/S) = 1

you can now substitute (2a for s) or (s/2 for a) to solve for them

remember Amani washes a car twice as fast

not takes twice as much time to wash it

you can point out where you got stuck

or several points

[real kernel]

i did 88x(1/a + 1/[a/2])=1 and got a = 264

[thorny root]

seems right

[real kernel]

so a would be syndey's time

[thorny root]

no

we defined it as Amani's

[real kernel]

oh

well i put it in as sydney's and it was right lol

i might of confused the names

[thorny root]

hmm

[real kernel]

amani is 132 and syndey is 264

[thorny root]

maybe

[real kernel]

minutes

[thorny root]

yup

that should work

[real kernel]

thanks for the help

.close

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[thorny root]

glad to help

[lone heart]

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[pastel schooner]

So the answer is suppose to be 2 sqrt(3) but I didn't get that

[ocean flower]

1/2absinc is the formula for a triangle essentially, and since you know it's equilateral:

$\frac{1}{2}a^2sin(\frac{\pi}{3})$

[ocean seal]

spicygreenpeppers

[ocean flower]

now to find a, a is our f(x) for some particular x

[pastel schooner]

Woah

[ocean flower]

so instead of adding up our f(x)

we add up that ^^

a is just f(x)

so our integral is no longer $\int{f(x)}$

[ocean seal]

spicygreenpeppers

[ocean flower]

oof

sorry that took me so long to format

LaTeX is hell

[pastel schooner]

Is that pi * 3

[ocean flower]

pi/3

shit still not formatted lol

[pastel schooner]

Lol

[pastel schooner]

This is the first time in my life

That I heard 1/2 * ab* sin c

Is formula

[ocean flower]

it is now $\frac{\int{(f(x))^2sin(\frac{\pi}{3})dx}}{2}

[ocean flower]

okay it is not too hard to prove

have a go making a line on a triangle so that there is a 90 degree angle between base and tip

[pastel schooner]

Like a trianfle inside a triangle?

[ocean flower]

like thisd

one second

because the vertical line can be worked out using trigonometry in terms of c

we can use the normal base * height / 2 formula to work out the area of the triangle

[pastel schooner]

why not just use our triangle given?

instead of using angle c

we could do a^2 * 1/2

being that a = b

[ocean flower]

it isn't the height

it's the diagonal side length

pythagoras

[pastel schooner]

I am dumb

I thought it was a right angle for a second

and thought side a = b because it is equilateral

but equilateral is not what I thought it was

ah makes sense now lol

[ocean flower]

no worries

[pastel schooner]

So what were you saying after we find the area?

It was a weird equation and we dont use the normal integral

Why not?

Isnt it just integral of A(x) * dx

to find volume

[lone heart]

@pastel schooner Has your question been resolved?

[pastel schooner]

$\frac{\int{(f(x))^2sin(\frac{\pi}{3})dx}}{2}

teXit

$\frac{\int{(f(x))^2sin(\frac{\pi}{3})dx}}{2}

.close

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[worn fox]

use the substitution to find x' in terms of y'

yeah

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[cedar field]

Am I right I remember there was some rule for no.2 but I can’t remember what it was please tell me?

[cedar field]

Like I think there was some rule for negatives

[tacit arch]

Plot the points on a number line

[cedar field]

Ok

[tacit arch]

https://youtu.be/NdMs2YuZLQo

[cedar field]

This is like grade 5 lol

[tacit arch]

So is this

[cedar field]

Sry I’m on a ferry

So umm… -2.34 is bigger?

[cedar field]

I need to go soon wifi is running out

[tacit arch]

Feel free not to ping me just to tell me you're leaving

[cedar field]

Ok

[tacit arch]

That's something a fifth grader would do

[cedar field]

Sorry

[tacit arch]

just kidding

[cedar field]

😝

[tacit arch]

It's fine

[cedar field]

Ok

C ya

Thanks

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[keen orchid]

please help, even trying to vizualise doesn't make sense to me. I'm guessing I have to find q in order to find c but they ll just have such different coordinates that they don't really line up to make a rectangle, from what i can see

[keen orchid]

it doesnt really make sense to look at

am i supposed to find the parallel by using the cross product?

[lone heart]

@keen orchid Has your question been resolved?

[lone heart]

@keen orchid Has your question been resolved?

[upbeat summit]

@keen orchid

To find the coordinates of point C, we know that the opposite sides of a rectangle are parallel and of equal length. Therefore, if we take the vector AB = <2-(-1), 6-2, -9-3> = <3, 4, -12> and add it to the coordinates of point D (3, q, 8), we will get the coordinates of point C.

So, C = D + AB = (3, q, 8) + (3, 4, -12) = (6, q+4, -4)

To find the angle between the diagonals of the rectangle, we first need to find the vectors that represent the diagonals. The diagonal from A to C can be represented by the vector AC = <6-(-1), q+4-2, -4-3> = <7, q+2, -7> and the diagonal from B to D can be represented by the vector BD = <3-2, q-6, 8-(-9)> = <1, q-12, 17>.

We can use the dot product to find the angle between two vectors. The dot product of two vectors is given by:

AC.BD = |AC| * |BD| * cos(theta)

Where theta is the angle between the two vectors and |AC| and |BD| are the magnitudes of the vectors.

So,
cos(theta) = (AC.BD) / (|AC| * |BD|)

We know that:
|AC| = sqrt((7^2)+(q+2)^2 + (-7)^2)
|BD| = sqrt((1^2)+(q-12)^2 + (17)^2)

So,
cos(theta) = (71 + (q+2)(q-12) + -7*17) / (sqrt((7^2)+(q+2)^2 + (-7)^2) * sqrt((1^2)+(q-12)^2 + (17)^2))

And theta = arccos(cos(theta))

It should be noted that the angle between the diagonals of a rectangle is always 90 degrees.

[keen orchid]

oh wow i was going this direction already, thank you so much ill use this for reference if i get stuck. ill keep this open if i have any questions if you don't mind

[upbeat summit]

Sure ask away

[keen orchid]

when you say d + ab you mean od + ab right

[upbeat summit]

I apologize for the confusion, I meant to say AD and BD. AD and BD are the diagonals of the rectangle, and we can use the dot product formula to find the angle between them.

|u| = sqrt((3-(-1))^2 + (q-2)^2 + (8-3)^2 )
|v| = sqrt((2-(-1))^2 + (6-2)^2 + (-9-3)^2 )

u.v = |u| * |v| * cos(theta)

where theta is the angle between the vectors AD and BD

Then we can use the inverse cosine function to find the angle in radians and then convert it to degree.

[keen orchid]

is there a way to find q?

[keen orchid]

what are you trying to correct here? is it the AC.BD that yo u want to switch with BD.AD?

Also since it is a rectangle that means that the angle of the diagonals are all equal right? so only one calculation is needed to get all of them correct?

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[twilit marsh]

I learned this in class the other day. However, I forgot how to do it.

[twilit marsh]

Wait I didn’t give a clear picture

No. 5

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[twilit marsh]

<@&286206848099549185>

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[twilit marsh]

.reopen

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✅

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[deft mirage]

Hi

The triangles are proportionals

You can use the sum of angles in triangles

I would prefer find YZ measure first

You will find easily by cosine law

Tha angle beetwen RY and RZ is 32 degrees

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[reef dawn]

can someone explain why this was wrong?

[vale wigeon]

you are supposed to actually find m and M.

[reef dawn]

m(3) = 15?

[vale wigeon]

what's the minimum value of x^3-3x+7 on [0,3]?

is it actually 5 as you claim?

[reef dawn]

yea

[vale wigeon]

well then

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[quasi vector]

Hello, my question is not about math but I couldn't figure out where else to ask my question

[quasi vector]

So in an electrical circuit the power dissipated by a circuit is given by the formula
P = VI
but, using Ohm's Law there are actually three formulae:
P=VI=I^2 R = V^2/R
and different versions of this formula are used in different instances. My question is how am I supposed to figure out which version of the formula I need to use?

Because using different versions we also get different proportions. Power can't be both directly and inversely proportional to the resistance can it?

[left trellis]

depends on what you want to find and what you're given

[quasi vector]

how would that work

[left trellis]

say you're given the voltage and current, and want to find the power

you'd use the first equation because it's simpler

(if I understand your question correctly)

[quasi vector]

yeah I figured out that much

but if for example two resistors are connected in parallel

what would i do in that case

[left trellis]

do you know the parallel resistor formula?

[quasi vector]

yep

[left trellis]

so you'd figure out the total resistance, and then use that in one of the equations, like for example, R=P/I^2, as long as you know the power or current as well

[quasi vector]

ahh

thanks

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[zenith compass]

I am proving $-\Bigl(\frac{a}{b}\Bigl)=\frac{(-a)}{b}$ by axioms.

[ocean seal]

Trenton

[zenith compass]

I have tried the following:

$$
\begin{aligned}
\frac{a}{b}+\frac{(-a)}{b}&=a\cdot\frac{1}{b}+(-a)\cdot\frac{1}{b}\
&=(a+(-a))\cdot\frac{1}{b}\
&=0\cdot\frac{1}{b}\
&=0\
\end{aligned}
$$

[vale wigeon]

incomplete latex?

seems like a good start though.

[ocean seal]

Trenton

[zenith compass]

Suppose I know why $0\cdot\frac{1}{b}=0$

[ocean seal]

Trenton

[zenith compass]

but I am not sure whether $\frac{a}{b}=a\cdot\frac{1}{b}$ is just definition or something I have to show.

[ocean seal]

Trenton

[vale wigeon]

it is a definition

[zenith compass]

oh ok thank you

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[kindred anchor]

Have you tried anything?

[trail cairn]

no because i dont know what to do or start with

..

is it 6x2+3

for ai

[wheat isle]

yeah it’s just basic algebra here

[wheat isle]

yes

[trail cairn]

.close

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[cunning depot]

Two hundred students are placed in a circle, each wearing a hat with a real number on it. Two numbers inscribed on two adjacent hats always have a difference between $1$ and $3$ (in absolute value), and the sum of the $200$ numbers inscribed on the hats is $1600$. Find an interval $[a,b]$ with $a$ and $b$ integers such that we are sure that there are $5$ adjacent students whose numbers on the hats have a sum in the interval $[a,b]$. Among all the possible intervals, we will choose the one maximizing $a$ and then, if necessary, the one minimizing $b$. Once this interval is found, give the value of $a⋅b$.

[ocean seal]

Pierre de Fermat

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[alpine sable]

Hello

[alpine sable]

I have a question

This is polar coordinates

How can i do part a)

Making then equal to each other hasn’t worked

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

How can i do 2e^-theta = 1/2e^theta

[ocean seal]

Modus

[alpine sable]

Thanks

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[cinder sundial]

It’s crossed the y-axis how could it be 90 degree?

The question is asking for the cos (the angle between vector AB and positive direction of x axis)

But the diagram that the teacher had made is totally nonsense

[cinder sundial]

I think we lead to a contradiction right here

[lone heart]

@cinder sundial Has your question been resolved?

[cinder sundial]

<@&286206848099549185>

[limpid turret]

What's 90 degrees

[cinder sundial]

the angle that blue arrowed pointed

i think if its crossed the y axis then theres no way its 90 degrees

[limpid turret]

Where are you seeing it's 90 degrees?

[limpid turret]

Oh

[cinder sundial]

the teacher said it is

[limpid turret]

I see it

[cinder sundial]

but if AB is a line crossed the y-axis, then theres impossible its 90 degrees

[limpid turret]

But I have to squint

https://tenor.com/view/smol-gif-18164930

Okay I'm understanding the context a bit more

Let me read it again

Okay so point A is at (1, 0, 0)?

And point B is at (0, -1, sqrt2)?

[cinder sundial]

given that A is (1,2,3) and B is (2,1,3+sqrt2)

[limpid turret]

Okay yeah this image makes no sense

If those are your points then this image is way off

[cinder sundial]

then it leads to my former question

im fine with that cos beta, you can prove it very simply by trigs

but if you wanna apply the same thing to prove that cos alpha is true, then i think we got a problem

[limpid turret]

Why's that

[cinder sundial]

since we can't create a right triangle then i don't think its gonna works on the cos alpha

[limpid turret]

You don't need a right triangle

You are using law of cosine

[cinder sundial]

i think its called the azimuth of vector in space or sth

[limpid turret]

https://en.m.wikipedia.org/wiki/Law_of_cosines

[cinder sundial]

but that form doesn't looks like the result of law of cosines

its more looks like it took sqrt(a^2+b^2+c^2) as the hypotenuse

then the length of a as the adjacent

[olive loom]

its just slightly hard to visualise

[cinder sundial]

It is possible

But AB crossed the y axis

[limpid turret]

Your legs adjacent to alpha are (1, 0, 0) and (a, b, c)

And your opposite leg is (a-1, b, c)

[cinder sundial]

If that is right triangle then AB should be parallel to yaxis

[limpid turret]

Get the lengths of these legs, plug the results into law of cosines, and solve for cos

[olive loom]

maybe try to think with the help of your room
one corner is origin
then you have the x y z axes on the edges
imagine a vector starting from that origin to your eyes and just try to see the angles and triangles

[cinder sundial]

I don’t get it

[cinder sundial]

It’s seems like that will never be a right triangle no matter how I moved that wood stick

[limpid turret]

This is the error in your judgement. The vector is not in the yz plane

[olive loom]

the blue line is supposed to be ur vector (starting from the corner to somewhere floating in the front you)
and the stick that you have put down is supposed to be starting from the end point of that vector and drop perpendicularly on the x axis

[limpid turret]

I like effort you went to tho

[cinder sundial]

Does the line AB that I have drawn earlier crossed the y-axis

[cinder sundial]

This one

[olive loom]

nope

3D is hard to imagine 😢

[cinder sundial]

Then I think I misinterpreted the diagram

[limpid turret]

Don't forget to try this out to answer your other question too

I'm off to bed so good luck

[cinder sundial]

For sure, I will try to prove that formula by law of cosines later

[cinder sundial]

Good night and thank you so much for providing those good ideas

[olive loom]

(dont cringe out)
this will help you visualise
https://youtu.be/Uws4tmZbNtU

[lone heart]

@cinder sundial Has your question been resolved?

[lone heart]

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[uneven folio]

Solve for x and y:
1.2y = 2x - 5,4
0.8x + 1.4y = 7.8
I tried using the substitution method but Im not comming a long way becasue of the decimals

[vale wigeon]

then multiply both sides of each equation by 5 before proceeding

or by 10 if you do not yet see why 5 would be enough

this will make all the coefficients integers

[uneven folio]

Didint think of that, thank you

.close

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[mellow grail]

if x+y = 4 and xy=-2 then choose the value of (x+x^3/y^2+y^3/x^2+y)

[vale wigeon]

^ for exponents, by the way.

[mellow grail]

Couple questions I have:

• Is the bracket some sort of identity?
• Am I suppose calculate x and y? x = 2+sqrt(2) from my calculations

[vale wigeon]

x^3/y^2, etc.

[mellow grail]

Oops, I didnt know that

[alpine sable]

you can recover what the suitable x's and y's would be

[vale wigeon]

i think you are not supposed to find x and y themselves

[mellow grail]

Yeah I felt that too

[alpine sable]

i don't think 2 + sqrt(2) is correct either by the way

[mellow grail]

...
That is very possible

[vale wigeon]

but instead to, say, rewrite x^3/y^2 + x^2/y^3 as a single fraction and try to express that in terms of the known x+y and xy

the other two terms in your sought quantity are just x+y which you're given

[mellow grail]

Hmm..So then..

[vale wigeon]

er

mistyped the middle things

wouldn't know lmao

[mellow grail]

But I got the trick, thank you so much!

[vale wigeon]

yeah yw

[mellow grail]

Wth..The answers 8 and eights not even in the options

OH WAIT

I am an idiot

its 4+(x^5+y^5)/4..

[mellow grail]

How does one solve x^5+y^5? I googled a factorization but I dont think its of much help

[vale wigeon]

x^5 + y^5 = (x+y)(x^4 - x^3 y + x^2 y^2 - x y^3 + y^4)

[mellow grail]

Yeah exactly, all that gives me is x^4 - x^3 y + x^2 y^2 - x y^3 + y^4 + 4

[vale wigeon]

x^4 + x^2 y^2 + y^4 = (x^2+y^2)^2 - x^2 y^2

x^2 + y^2 = (x+y)^2 - 2xy

[mellow grail]

wait- thats..an eye opener

[vale wigeon]

and -x^3 y - x y^3 = -xy(x^2+y^2)

[mellow grail]

Didnt know this one, thank you su much!

[mellow grail]

This is just taking common right

[vale wigeon]

yes

[mellow grail]

I finally got the answer correct! Thank you SO much!!

.close

[lone heart]

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[slate vigil]

Can someone show steps to solve B C and D?

[desert tusk]

solve A first and show us the working

[slate vigil]

That’s A

Can you show B C and D with steps?

Please

[desert tusk]

Do you have any ideas for B?

Can you tell me the turning point of this quadratic based on the vertex form?

[slate vigil]

the maximum profit be 1953125?

That’s my guess

[desert tusk]

Well, it seems like

Your vertex form is wrong

[slate vigil]

Oh fr?

[desert tusk]

Because your working of finding the vertex form is wrong

Try again

Yeah I’m pretty sure it’s wrong

[slate vigil]

Math away and someone from this server gave me this vertex form

Can u try solve it

And lmk

[desert tusk]

how about you solve it first

And I’ll check

[slate vigil]

I did

[slate vigil]

^

[desert tusk]

Just retry

[desert tusk]

I’ll just try to solve it manually by myself later

give me a few minutes

[slate vigil]

Ok

Lmk

[desert tusk]

Oh it’s correct, sorry

Anyways

[desert tusk]

Can you explain why?

[slate vigil]

Ima be honest I don’t know why

But I just know it is

I think

Can you explain?

[desert tusk]

What does your P represent?

From the equation it has P

[slate vigil]

Profit?

[desert tusk]

Okay

Then

Do you know how to tell the turning point of this qu’oratrice based on the vertex form?

[slate vigil]

I don’t

[desert tusk]

it’s called vertex form for a reason

okay

[slate vigil]

Oh

[desert tusk]

A vertex form would look like this

[slate vigil]

The turning point would be minimum/maximum

[desert tusk]

a(x-h)^2 + k

[slate vigil]

Yeah yeah

[desert tusk]

where h and k are the coordinates of the turning point

h is rhe x coordinate

[slate vigil]

Oh

[desert tusk]

k is the y coordinate

[slate vigil]

Okok

[desert tusk]

so now, can you tell me why 1953125 is the max profit?

[slate vigil]

Because K = Y

And Y is the turning point

[desert tusk]

correct

So your answer is that

1953125$

[slate vigil]

Ok

[desert tusk]

If you’re ready, we can continue the next question

[slate vigil]

I’m ready

[desert tusk]

Now C

How many times do you need to increase the entrance fee to get the max profit

This is the same logic

[slate vigil]

Yeah

[desert tusk]

Look at the vertex form

[slate vigil]

Yeah

[desert tusk]

And give your answer

so your answer should be?

[slate vigil]

Uh

How much times do we need to increase the entrance fee to get maximum profit?

[desert tusk]

yes

[slate vigil]

Maximum profit is 1953125

[desert tusk]

what’s your answer

okay so

based on that

what is the answer?

[slate vigil]

35

?

[desert tusk]

Why?

Why is it 35?

[slate vigil]

Uh because

I’m not sure

[desert tusk]

I’ll give you a hint

What does x represent in this equation?

[slate vigil]

How many times u need to increase the price by 0.50

$0.50

[desert tusk]

okay

so do you agree

the profit depends on x?

[slate vigil]

Wasn’t profit P?

[desert tusk]

yeah?

so is P dependent on x?

[slate vigil]

Yeah

[desert tusk]

so that means

If I sub any value as x

The profit will be different

[slate vigil]

Yea

[desert tusk]

I want to sub x so that

[slate vigil]

So if u sub 0.50 in x?

[desert tusk]

I can get the maximum profit

no

[slate vigil]

Oh

[desert tusk]

if I want the maximum profit

[slate vigil]

Yeah

[desert tusk]

I must know what is the exact value of x I must sub

[slate vigil]

Yeah

So u solve for X?

[desert tusk]

so look at the equation again

you can but

if you can read vertex form equations

it’s so much simpler

[slate vigil]

Ok so what would I do

To find the answer

[desert tusk]

your answer is literally 35

the vertex form equation already gave the answer

it’s called vertex form for a reason, remember

[slate vigil]

Yeah

[desert tusk]

the 35 is the x coordinate

[slate vigil]

Yeah

[desert tusk]

the 1953125 is the y coordinate depending on x

so it’s 35

[slate vigil]

So what would I write for my answer

[desert tusk]

Do you understand why now?

[slate vigil]

Under C

[desert tusk]

literally 35

[slate vigil]

I understand the answer but what should I write

[desert tusk]

that’s it

35 times

[slate vigil]

Ok

[desert tusk]

that’s it

now next question

[slate vigil]

And D

Yea

[desert tusk]

This should be easy

[slate vigil]

We sub 35 for x?

[desert tusk]

This does not involve the equation anymore

you must read the question carefully

[slate vigil]

Ok

[desert tusk]

don’t just blindly use the info you got in your previous questions

you must understand what it’s trying to ask

it’s asking what’s the new price now

[slate vigil]

Yep

[desert tusk]

so for every increase, it adds 0.50$ to the price

you increased 35 times

[slate vigil]

Yea

[desert tusk]

to get the maximum profit

Now find what’s the product of 0.50$ adding itself 35 times

[slate vigil]

0.50 x 35?

[desert tusk]

and add the product to the initial price of the entrance fee

and there’s your answer

[slate vigil]

Wait sorry

[slate vigil]

What product gets 0.50 to 35?

[desert tusk]

This should be easy, I’m not going to give you any hints

[desert tusk]

??????

you misinterpreted the question

[slate vigil]

Yeah I didn’t understand lmao mb

[desert tusk]

listen carefully

It asks you what’s the new price

Of the entrance fee

If you want to generate maximum profit

Do you understand what it’s talking now?

Do you understand what it asks now?

[slate vigil]

Yea

[desert tusk]

Okay tell me what is it asking

I need to make sure you fully understand

[slate vigil]

It asking for the new price of entrance fee if you wanna get maximum profit

[desert tusk]

Correct

So how many times you must increase the price worth 0.50$ to get the maximum profit?

You already answered this question in C

So your answer will be how many times?

[slate vigil]

Maximum profit is 1953125

[desert tusk]

And then?

[slate vigil]

So how much times must I increase 0.50 to reach that?

[desert tusk]

…

You already answered that question

In C

Did you not remember?

[slate vigil]

Yeah I do but

I’m confused about D

I understand this part

[slate vigil]

^

Idk how to get there

[desert tusk]

This means

You must add 0.50% to the initial price of the entrance fee

But the problem is

How many times you must add 0.50$

To the entrance fee

So that you can get the max prodit

Is that better?

[slate vigil]

Ok the initial price of the entrance fee

Is

Lemme check

[desert tusk]

45 dolalrs

45$

[slate vigil]

45

Yeh

45 x 50%?

0.50

[desert tusk]

Why?

Why 45 x 0.5?

That would just decrease the price

[slate vigil]

So I can get to maximum profit

[desert tusk]

Wrong

That’s not how it works

[slate vigil]

Oh

[desert tusk]

You can’t do that

That’s all I can explain

[slate vigil]

So what would I do

[desert tusk]

you must increase the price with only 0.50$

Do you understand?

[slate vigil]

Yeah

[desert tusk]

Now

The problem is

How many times

You must add 0.50$ into 45 dollars

So that it generates max profit

Is that better?

Are you clear of what’s the question asking now?

[slate vigil]

Sorta yeah

The questions asks

[desert tusk]

You are going to increment 45 dollars with 0.50 dollars for a certain number of times so that you can generate max profit

Do you understand fully now?

[slate vigil]

Yeeaahhh

[desert tusk]

Now

[slate vigil]

Increase 45 $ with 0.50 how much times

[desert tusk]

Yes

That

[slate vigil]

How much times tho

[desert tusk]

Tell me the coordinate of the turning point of this quadratic vertex form

first

[desert tusk]

Answer this

This should be easy

[slate vigil]

1953125

[desert tusk]

I already taught you how to read vertex form

[desert tusk]

Wrong

[slate vigil]

WHAT

[desert tusk]

That’s only the y coordinate

[slate vigil]

35?

[desert tusk]

That’s x coordinate, but that’s what I want you to find

now

Do you understand why it’s 35?

[slate vigil]

(35, 1953125)

Turning point

[desert tusk]

yes that’ll

[desert tusk]

Answer this

why is it 35?

[slate vigil]

Increase 45 $ with 0.50, 35 times?

[desert tusk]

congrats

you finally understood

now do the math

and tell me your final answer

[slate vigil]

Yeah but how do I

[desert tusk]

What do you mean how?

[slate vigil]

Oh

[desert tusk]

You just answered your own question

[slate vigil]

So I gotta press 45 + 0.50, 35 times

On my calculator

[desert tusk]

no

There’s a quicker way

Literally just find 35 x 0.5

[slate vigil]

17.5

[desert tusk]

Now add that

[slate vigil]

Add 45?

[desert tusk]

Yes

so what’s your final answer?

[slate vigil]

21.5

[desert tusk]

Wrong

Why is it lower?

[slate vigil]

Wrong

[desert tusk]

It should be bigger

[slate vigil]

???

[desert tusk]

not smaller

[slate vigil]

Wait

I’m stupid

[desert tusk]

You’re decreasing the price.

[slate vigil]

62.5

[desert tusk]

Congrats

you solved it

Now my main concern is

do you understand how to solve this question now

[slate vigil]

Yea I do

Thanks sm

[desert tusk]

Okay

[slate vigil]

This server actually a big W

Damn

[desert tusk]

If there’s nothing else close this ticket

[slate vigil]

Are u in university?

[desert tusk]

type .close

[slate vigil]

Ok

[desert tusk]

if there’s nothing else

[slate vigil]

.close

[desert tusk]

Close this ticket

[lone heart]

Channel closed

Closed by @slate vigil

Use .reopen if this was a mistake.

[slate vigil]

Thanks

[lone heart]

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[old patrol]

How do I do this? I know that the factor theorum is somehow involved, but I do not really know where to start

[alpine sable]

u can find x by solving the quadratic eq first

[old patrol]

Yeah okay

Do I just sub in the value for x then

[alpine sable]

and then substitute both values of x

yeah

and then simultaneous equation

[old patrol]

Okay cool thanks :)

.close

[alpine sable]

oki

[lone heart]

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[feral scroll]

how to siimplify it

x belongs to 0 to pi/2

[wild trail]

is it $\sum_{r=1}^n cosec(2^r x)$?

[feral scroll]

yup

[wild trail]

what's the lower limit for r?

[feral scroll]

1

[ocean seal]

numbpy

[wild trail]

0 and pi/2 are included or not?

[feral scroll]

not included

$\sum_{r=1}^n \text{cosec}(2^r x)$ where $x \in\left (0 , \frac{\pi}{2}\right)$

[ocean seal]

Garuda

[wild trail]

I thought of converting into sin and then expanding but got stuck

[feral scroll]

same

[wild trail]

$\frac{1}{\sin 2x} + \frac{1}{\sin 4x} + \frac{1}{\sin 8x} + ... = \frac{2 \cos 2x}{\sin 4x} + \frac{1}{\sin 4x} + \frac{1}{\sin 8x} + ...$

but then 1 + 2 cos2x doesn't give anything

[feral scroll]

remove the extra 2 from denominator

[ocean seal]

numbpy

[feral scroll]

yup not reaching anywhere

<@&286206848099549185>

[feral scroll]

does cosec$(2^nx)+\cot(2^nx)$ simplify some how

[ocean seal]

Garuda

[wild trail]

I don't think so

[feral scroll]

i got tan$(2^{n-1}x)$

[ocean seal]

Garuda

[feral scroll]

on simplifying it

just convert them into cos and sin and then they will factor out and cancel out @wild trail

[wild trail]

Yeah but is there cosec(2^r x) + cot(2^r x) ?

[feral scroll]

complete question goes like this @wild trail

so in next step we have it.

but still it is not completely simplifying

[wild trail]

ohhh, I see

[feral scroll]

are you attempting it

[wild trail]

nah, it seems too tricky for me. I hope someone else can help

<@&286206848099549185>

[low quartz]

KGF

[feral scroll]

wdym

[low quartz]

nvm

[feral scroll]

please write full form

[low quartz]

looking for your ques

[feral scroll]

.

see this

[low quartz]

ohh

conitnuity

where you got stuck

[feral scroll]

.

unable to simplify it @low quartz

[low quartz]

ok

i am eating right now

just wait

a little bit

you solve another question until then

[unique saddle]

help :))

[low quartz]

bro

open new channel

[unique saddle]

cool cool

sry

[low quartz]

#❓how-to-get-help

[unique saddle]

y'all

[low quartz]

see this

[slow hound]

GARUDA

[feral scroll]

?

[low quartz]

?

[slow hound]

why are you all questioning me

[low quartz]

do u got the garuda question?

[carmine reef]

Oh this is cool

nvm

not that easy

csc(2x)=2csc(x)sec(x)

[low quartz]

yeah

we are stucked in

sigma equation

[carmine reef]

2 * sum csc(x)sec(x), this time from 0 to inf but idk what I'd do after that

[feral scroll]

have you seen the complete question @carmine reef, one posted above

[carmine reef]

This?

[feral scroll]

this one

[carmine reef]

what is n for g?

[feral scroll]

same for all

[carmine reef]

Oh, n is fixed but unknown?

ok

seems like the <0 limit would be easier

though to prove continuity you'd need them both

What's the backwards N thing in the denominator of that

is that "x"?

[feral scroll]

x \sin x one ?

[carmine reef]

yeah ok

L'hopitals twice gives 0 for that

or no

forgot a minus sign

gives 4?

[low quartz]

how you use l hospital in x>0

[lone heart]

@feral scroll Has your question been resolved?

[carmine reef]

doubt you can

but now we know the lower limit is 4

so p has to be 4

H is continuous => p=4, maybe that counts as solved?

we don't have the inverse implication

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[alpine sable]

Can someone help me understand this formula

[tacit arch]

Do the worked examples on wiki
https://en.wikipedia.org/wiki/Hypergeometric_distribution

[alpine sable]

We haven't got to the hypergeometric distribution

or any distribution for tha tmatter

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[summer seal]

anyone knows who to solve this demostration?

[mortal trellis]

I assume this notation here refers to the gcd?

[carmine reef]

yeah

[mortal trellis]

how would you know

[carmine reef]

i've seen it before

and its obvious from context

[mortal trellis]

well yes same but still that doesn't mean it has to be the case here

[summer seal]

ues

yes*

[carmine reef]

the question is a relation for greatest common factors

hmm

you could try proving separately (ac,bc) <= |c|(a,b) and (ac,bc) >= |c|(a,b)

[summer seal]

i dont know what properties i could use to go one way to the other

[carmine reef]

if (ac,bc) > |c|(a,b)

[summer seal]

i was thinking is seperate the ac and bc in their primes and then saying that the gcd is the multiplication of the primes that repeat

[carmine reef]

that could work

[summer seal]

if you do that it is obvious that it is the case that (ac,bc) is iqual to c(a,b)

but i dont know if that is a formal property or just a general rule

[carmine reef]

yeah this might be overkill

could you prove that (ac,bc) is divisible by c

(a,b) divides both a and b

so |c|(a,b) will divide ac and bc

since that makes it a common divisor, |c|(a,b) <= (ac,bc)

[summer seal]

mmm

[carmine reef]

you can do the other way if you know you're allowed to divide (ac,bc) by |c|

so we need to know c|(ac,bc)

[summer seal]

yeah i think it work

thanks

[carmine reef]

np

[summer seal]

how do i close the channel?

[carmine reef]

.close

[lone heart]

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[carmine reef]

assuming you wanted to

[summer seal]

no

like

[carmine reef]

.reopen

[lone heart]

✅

[carmine reef]

ah well that's how anyways

[summer seal]

making the channel help avaliable to others

[carmine reef]

oh yeah that'll happen after some time

[summer seal]

ok

[carmine reef]

you can do .close too

after a minute or so of being closed it'll get recirculated as an open channel

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[tall trout]

I got up to the part where the initials are 10 cats : 25 dogs

[surreal meadow]

i would increment 5:3 into 10:6, 15:9, 20:12… until you get a ratio where the left number is a multiple of 10 and the right a multiple of 25

there are less janky and more algebraic ways to do this, but idk if the extra work is warranted

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[wary ingot]

yo

[wary ingot]

i am just starting calculus 3

and hw problem asks to find equidistant equation

i realize its plane and found midpoint

but how do i create a plane perpendicular to a and b?

[alpine sable]

if the plane (through C) is perpendicular to A, its already perp to B (since ACB are colinear)

you can use the normal form of a plane: http://mathonline.wikidot.com/point-normal-form-of-a-plane

[modern topaz]

No

[wary ingot]

i havent learned this yet but i will give formula try

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[lost steeple]

I'm not sure how to appraoch this

do I factor?

[ivory pivot]

tan^-1 is monotonous so you have only to view if the argument goes to infty or -infty

[lost steeple]

alr

.close

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[chilly dove]

I only need help on (ii)

[quaint star]

what are you answers for a, b and c

and what were you resoning for ii), what's troubling you

[chilly dove]

A) n=7
B) $12
(i) 17 apples

i just dont know where to start for (ii)

[quaint star]

alright so you have 3 mangoes at 1.60