help-23

[timid ridge]

so dA/dt = 0

[zinc panther]

But the geometric intuition of the problem

how would the triangle be arranged

This shouldnt be a problem for me but it is

and its been eating at me all day

[austere forge]

the area is base * height / 2 right

[zinc panther]

Yes

well for a triangle yes

[austere forge]

the sin(theta) just comes from the height, because the height equals one of the sides times sin theta

like

does that make sense?

[zinc panther]

Yes but the thing that keeps messing up MY logic, is that if theres a side with length 20 and another side with length 30, do i have to assume that one of those sides is the hypotenuse?

beacause sin(theta)=hyp/opp

therefore opp*sin(theta)=hyp

sorry

[austere forge]

well no the theta is for the sub-triangle

[zinc panther]

i got hyp and opp confused

should be opp/hyp

[austere forge]

like the right triangle in this image

[zinc panther]

sub triangle is the one with gamma as the angle right?

is that gamma

[austere forge]

yeah

[zinc panther]

okay and how do i form this sub triangle

[austere forge]

you don't really need to, this is just showing where the area formula comes from

see: https://www.google.com/search?q=area+of+triangle+with+two+sides+and+angle

thats where the image i posted is from

[zinc panther]

yes but the issue is that for this problem, I NEED to let A=ab*sin(theta)

and im trying to understand how height can be equal to bsin(theta)

and I know its from that image

but im unsure how that triangle is being formed in such a way that we can say height is bsin(theta)

because the only way i've been able to interpret it (so far) is by letting the base be the larger side (the 30cm one) and making my other side pi/6 radians from that side and making that one (20cm) long

[austere forge]

well you don't need to choose a or b, because you are multiplying them right

it could be h = a sin(theta) or h = b sin(theta)

the area will be the same

because A = bh/2

[zinc panther]

okay, technically, yes, but im trying to understand how this triangle can be formed because this triangle is the key to understanding why i can replace h with b (or whatever constant you want it to be) time sin(theta)

[austere forge]

this works for literally any triangle. if you have any two sides and any angle you have that as the area

[zinc panther]

I can know h=bsin(theta) but I want to understand why

[zinc panther]

Yes I know it seems like common sense

but I want to know the reasoning behind the common sense

[austere forge]

well when you have two sides and one angle, whichever sides and angle those are, you will neccessarily be able to form that sub-triangle and find the height from that

it could be with the a side, or the b side, but since you are multiplying it doesn't matter which

[zinc panther]

Okay yes this is what im asking right here this is on track

so i understand the sub triangle

I think^

but what about the larger triangle that gets formed

where does that come from

[austere forge]

sub triangle gives you the height, because you split the triangle up into two right triangles with it

[austere forge]

thats just the triangle coming from the problem. the sub-triangle is not actually part of the problem, it's simply a way to visualize how you get the area formula

like i said, if you are able to accept this area formula, you can solve the problem without any trouble

[zinc panther]

So the larger triangle is the actual triangle in the problem, but I create a sub triangle within that one in order to find the height so i can do bh/2 to find the area?

and by creating that sub triangle, i form that angle which (in the picture you sent) is gamma, and sides a and b are the ones that form that angle?

and the third side essentially doesnt matter in that case?

[austere forge]

yeah, the problem talks about an arbitrary triangle, and gives you information about two of its sides and its area

your goal is to find the information (rate of change) of the angle

[zinc panther]

when the angle between the two sides is given?

Oh wait that makes so much more sense now.

Rereading the question it was kinda unclear that the angle between them was pi/6

[austere forge]

well you set up the derivative equation, and then you plug in the specific values for that to solve for the rate of change of the angle

[zinc panther]

Yes yes i see now

Yeah I was just having trouble set up the area equation but i understand it nkow

I had to gpt that part and the derivatives and stuff was trivial

but gpt wasnt giving me the explanation that you were able to provide

Thank you

How do i close this

[austere forge]

type ".close"

[zinc panther]

.close

[safe radish]

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[vestal mauve]

im so lost

[vestal mauve]

in the volume formula, they both use the same height. so is y that's shown in the diagram used for the volume of cones as well?

this makes no sense

[strange flint]

They shouldn't be the same

If you look closely, you'll notice that the height of the tank is independent, but the height of the conical top and bottom depend on something

Check for the given information about the conicals

Do you see it?

[vestal mauve]

wdym

wait which qs are u doing

[strange flint]

They gave you 3 pieces of information about the conical top and bottom, 2 of which are the formulae

[strange flint]

You'll find it at the beginning

Before questions

[vestal mauve]

the angle?

[strange flint]

Correct

You reckon you can make use of that to calculate the height?

[vestal mauve]

with ?

[strange flint]

Perfect

[strange flint]

You could use just the tan formula

[vestal mauve]

i'm gonna change the h into y for cylinder

[strange flint]

Since tanθ = opp/adj

[strange flint]

Yeah that'll help clear thing out

[vestal mauve]

i deadass forgot about trig

super duper hell topic

[strange flint]

Lol it's okay

I assume everything's cleared out

[vestal mauve]

so i get 1.19 for my height of cone

[strange flint]

The base radius is 1.25

[vestal mauve]

i'm doing q2

tan(35) = x/1.7

ok what the flick

i got 35.34

but it says rounded i should get 35.4

wait how does rounding work with sig figs

[strange flint]

Yeah in that case ur right

[vestal mauve]

bc it's 35.348 so does that become 35.35 and then 35.4

[strange flint]

Usually you only round the first digits

[vestal mauve]

so did i get it wrong

what the flick

[strange flint]

So 35.348, you directly look at 35.34, since 4 < 5, then 35.3

[vestal mauve]

did u get the same thing i did

[strange flint]

I didn't calculate for myself ngl

Lemme check

[vestal mauve]

oh allr

[strange flint]

Yeah checks out

35.3504

Rounded to 35.4

[vestal mauve]

how did i get 35.348

i bricked it yo

i have no clue what i did wrong

i keep getting the same answer

pi * 1.7^2 * 3.1 + 2/3 * pi * 1.7^2 * 1.19

ai got the same answer as me

[vestal mauve]

how

[strange flint]

Try with tan(35)*3.1 instead of 1.19

[vestal mauve]

and then i lowk chuck it in radians 👿

oh wow

41.284

hmmm

[gaunt belfry]

Uhh...bro, your answers that are written in the sheet are wrong😅

[vestal mauve]

yeah prolly

the start is wrong

i think

[gaunt belfry]

Uhm not prolly, it's wrong 😅

[vestal mauve]

actually all is wrong

lmao

[hollow oxide]

how to interract in a math server, can someone enlighten me on this?

[gaunt belfry]

y is actually denoting the height of the cylinder, you have to figure out the height of the cones using the radius and the angle given separately

[vestal mauve]

yeah i figured that out

so when doing questions, instead of the h being h i put y

[hollow oxide]

how to add mathematical equation in powerpoint?

[vestal mauve]

what is happening

[hollow oxide]

ur house gives me nostalgia, nice design!

[empty gate]

Thanks

[vestal mauve]

but idk how i'm off by 0.0024

[gaunt belfry]

Depends if it's the h for cylinder or the cones, if it's cylinder then y and if it's cone then r×tan(35°)

[vestal mauve]

yeah that's what i'm doing

i changed the front already

[vestal mauve]

and then slant height is just use this and pythagaros right

[strange flint]

This does work btw

[strange flint]

Yup

[gaunt belfry]

They are probably trolling you, avoid them

Or you can tag the mods

[vestal mauve]

but my paper says it's 35.4

and he got it

[gaunt belfry]

What is this you are calculating again?

[vestal mauve]

show that the volume of a tank with base radius of 1.7m and height of 3.1m is 35.4m^3

(3 s.f.)

[hollow oxide]

Can anyone tell me there any fast and swift method of solving this without trial and error? I am in urgent need of enlightment

[gaunt belfry]

Okay let me see

[vestal mauve]

bro go somewhere else

#help-36

go there

[hollow oxide]

thanks

[gaunt belfry]

Please go to #❓how-to-get-help

[vestal mauve]

what'd u get

[vestal mauve]

pmo bro

[gaunt belfry]

I used desmos scientific calculator

[vestal mauve]

wow i got it !!!

i have no clue why that and what i did is different

but oh well

bc i also copied like 1.19 to like 7 d.p

and got same ans

[gaunt belfry]

Well it would come close to 35.4, I think your question setter has rounded it up to that value

[strange flint]

Just use a physical calculator

Or use parentheses

[vestal mauve]

so i just get screwed over bc i'm off by 0.0024

but lowk does it even matter

i coulda just wrote i got 35.4

since it says i should get it

[strange flint]

Usually you want to show the answer before you round it

= 35.3504 ≈ 35.4

[gaunt belfry]

Technically 35.3504983 will round up to 35.4 if you want one value after the decimal point

[vestal mauve]

can u lot look at this

idk how this works

[strange flint]

y = Ar, find the expression A

[vestal mauve]

am i supposed to make y back into h

and factorise it

pi r^2 h (1 + 2/3) = V

is that even allowed

[strange flint]

That's a formula for volume

Also h is the height of the cones

The height of the silo is y

[vestal mauve]

yeah

[gaunt belfry]

[
15 = \pi \cdot 1.25^2 \cdot y + \frac{2}{3}\pi \cdot 1.25^2 \cdot \left(1.25 \tan(35^\circ)\right)
]

[flat frigate]

K.D

[vestal mauve]

is it not asking for like y and r is x

[strange flint]

Yeah

[gaunt belfry]

Oh

[strange flint]

You just use this and separate the y

[vestal mauve]

y= = V / Pi r^2

and then V is 15

[strange flint]

Now idk how in depth ur required to go

[vestal mauve]

so y = 15 / pi r^2

[gaunt belfry]

[
15 = \pi r^2 y + \frac{2}{3}\pi r^3 \tan(35^\circ)
]

[flat frigate]

K.D

[vestal mauve]

can't u just ignore

the cones

[strange flint]

It's probably this

[vestal mauve]

how is there an r^3

[strange flint]

Cuz the height is tan * r

That's ur third r

[vestal mauve]

ohh

but doesn't it want

y on the 15 side

[gaunt belfry]

Just separate y from this and you will get your expression of y in r

[gaunt belfry]

Yeah you have to rearrange it now lol

You do know how to separate a variable from an equation and form the formula, right? 😅

[strange flint]

That question feels very weird ngl

Oh nvm

[strange flint]

This is false btw

[vestal mauve]

yeah

i bricked

[vestal mauve]

wait er

doesn't it get kinda weird

bc they're like

2 things

[cunning plank]

Anyone, resources for pre-university physics?

[vestal mauve]

oh wait nvm

it's kinda nice actually

[gaunt belfry]

I'm just going to post the answer man, it's simple you just have to do some manipulation on both sides to make equation like
y = f(r)

[
y = \frac{15}{\pi r^2} - \frac{2}{3}r \tan(35^\circ)
]

[flat frigate]

K.D

[vestal mauve]

yeah i got that

[gaunt belfry]

You may join the physics server, go to #old-network

[vestal mauve]

is domain of the height differentiate that

and find maximum ?

[gaunt belfry]

As you can see, there's r^2 on the denominator so r cannot be equal to 0

[vestal mauve]

so just r can't = 0?

is that it

[gaunt belfry]

No, now you differentiate both sides and let dy/dr = 0 and find the values of r where y is maxima/minima

[vestal mauve]

how does differentiating trig work ..

[gaunt belfry]

tan 35 degree is a constant bro

[vestal mauve]

x = - 2.73, 1.37 - 2.37i, 1.37 + 2.37i

what the flip

[gaunt belfry]

....

[gaunt belfry]

Show me what you did right now

[vestal mauve]

chucked it in my calculator

diff( ( 15/(pix^2) - 2/3 x tan(35)

[gaunt belfry]

Not everything can be done in the calculator bro 💀

[vestal mauve]

it's a classpad

(-(2x^3 x pi x tan(35)+90)/3x^3 x pi)

x is *

but it makes italics so

[gaunt belfry]

Do the differentiation by your hand carefully

[vestal mauve]

what's tan(35)

[strange flint]

Just write it as is

It's just a constant

[vestal mauve]

how do i differentiate that

bro

[gaunt belfry]

You don't really need that value right now just treat the whole thing like a number

[gaunt belfry]

Do you know derivatives?

Calculus?

[vestal mauve]

yeah

so do i just do quotient rule

[gaunt belfry]

Then just do the derivative of both sides

[vestal mauve]

on both?

[gaunt belfry]

💀

[gaunt belfry]

Help me here dude

[strange flint]

Let a = tan(35)

Treat it as if it was
$$y = \frac{15}{ \pi r^2} - \frac{2ar}{3}$$

[flat frigate]

ScoobySnacks

[safe radish]

@vestal mauve Has your question been resolved?

[gaunt belfry]

i'm just showing you the intuition here, as you can see from the graph,
as r = 2.17071, y = 0
and as r approaches 0, y goes to infinity
and we know that r cannot less than or equal to 0

so the domain of r is: 0 < r <= 2.17071
and the range of y is: 0 <= y < infinity

[safe radish]

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[safe radish]

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[primal onyx]

Can someone help with this?

[frank widget]

what is a marginal cost funcn?

[primal onyx]

C’(x)?

[frank widget]

ah i think i wont know, i dont know the definitions 🙏

[primal onyx]

oh okey thanks still

[idle anvil]

I mean think what exactly the marginal cost function means then follow the graph and see if some point would lead to a logical error

[primal onyx]

Isnt it the cost if you make 1 more unit?

[idle anvil]

Or you can also imagine that if this were the derivative how the original function looks like, ud quickly find an error there

[idle anvil]

yeah

[primal onyx]

Is it because it goes down? So technically producing another one makes it cheaper?

[idle anvil]

I mean its supposed to go down but the issue is that it becomes negative

So if u produce 100 phones then producing each phone on average should be cheaper when producing only a total of 10 phones but producing 200 phones shouldnt be cheaper then producing 100 phones

So the graph says that a certain point u get moeny for producing one more unit

[primal onyx]

Mhhh got it

So how could I formulate this in a sentence?

[idle anvil]

come on u'll be able to figure that one out on ur own

[primal onyx]

I came up with: It cant because it becomes negative, meaning we would get MORE money for producing an extra Unit.

[idle anvil]

Itll definitely give some points but maybe not full marks as the question specifically mentions to explain why it makes no sense via the law of diminishing returns

[safe radish]

@primal onyx Has your question been resolved?

[primal onyx]

• This contradicts the law of deminishing returns which states that at a certain point additional production becomes less efficient

[idle anvil]

I believe u googled what the law of diminishing returns is and then simply wrote the definition here down not?

[primal onyx]

Basically shahah

[idle anvil]

I mean what u just wrote is that it becomes less efficient this isnt the same as the contradiction u notes earlier that u would get maoney for producing an extra unit

or the one doesnt imply the other per se

[primal onyx]

okey thanks

.close

[safe radish]

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[radiant canopy]

what is the remaining area

[signal crane]

for same heights, areas are in the same ratio as the bases

18 or sm

[radiant canopy]

what height

from the right point

[signal crane]

the two triangles below for example

7,7

[radiant canopy]

yes

[signal crane]

so the corresponding triangles above it

(you can divide the unknown area in two with a line to end up with two triangles)

they'll be equal in area

because of the common base

[radiant canopy]

can u show by drawing

I'm on mobile so i cant

so as far as I get it a line horizontally in the unshaded area

so bases are same

[signal crane]

a+3 and b are the same

7:7 ratio

[radiant canopy]

oh tea

[drifting sierra]

Oh that's a direct isi pyq

[radiant canopy]

what's isi

[radiant canopy]

y

[drifting sierra]

Entrance test

[signal crane]

and similarly a, b+7 are 3:7

[signal crane]

7:7 base ratio from the two 7 triangles

and using the same ratio for a+3 and b

[radiant canopy]

oh so when a triangle is divided into 2 parts one half's ratio would be same to the another half. eg
a+3:b =7:7?

[signal crane]

the two 7 triangles have the same height

therefore the ratio of the areas is the ratio of rhe bases

and conversely the ratio of rhe bases i the ratio of rhe areas

7:7 or 1:1

a+3 and b have those same bases so there areas are also 1:1

[radiant canopy]

how
from the right most point to the middle?

[signal crane]

do u see the intersection line of the 3 and 7 triangle

[radiant canopy]

that goes to North East?

@signal crane

[signal crane]

these two

green bases

are in a 7:7 ratio

and a+3 and b are thus

again a 7:7 ratio

[radiant canopy]

i saw the ladder theorem lol it was sez

.close

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[stone bane]

for (b) here,
is my reasoning correct?

for the infinite intersection of these sets to have a finite number of elements and since the intersection of the sets J_1 through J_n is always J_n then there must be at least one set in this sequence that has a finite number of elements and all the subsequent sets will also have a finite number of elements and be non empty

but an open interval can never have a finite set of elements.
Let's assume it has a finite set of elements, if we order them a_0 through an
we can always find a newer element in between a(n-1) and a_(n) since we can find a real between any 2 reals

I don't know why but I feel like I am missing something here

[vast obsidian]

It is not correct as it's not true that necessarily one of the J_n only contains finitely many elements

[stone bane]

yes the intersection of sets that are not finite can produce a finite set

my bad

[vast obsidian]

Question resolved?

[stone bane]

yes I found another way to do it

thank you

[vast obsidian]

You're welcome

.close

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[viscid solstice]

Hey i need help to resolve this, i can successfully derivate but im stuck when i want to do the table.

Please do this derivative calculation with a table.

[quiet plume]

What do they mean by table?

[viscid solstice]

This, but im stuck there

i know its false but i dont know why

[quiet plume]

D'une part tu as $4x = 0$ et tu en conclus que $x = -4$ alors que le zéro est à $x=0$.

[flat frigate]

Azyrashacorki

[quiet plume]

Après pour l'autre facteur de la dérivée, tu dis que le facteur est strictement positif parce qu'il y a un carré, mais c'est faux. Le facteur a des zéros

[viscid solstice]

donc en gros je dois utiliser delta?

[quiet plume]

Ou du moins la formule quadratique pour obtenir le(s) zéro(s)

[viscid solstice]

on m'a pas appris ça

[quiet plume]

Tu traites les dérivées sans avoir vu la formule pour résoudre les équations de second degré?

Genre $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

[flat frigate]

Azyrashacorki

[viscid solstice]

oui c'est delta ça

nn

jamais vu cette formule sans te mentir

[quiet plume]

D'emblée j'aurais plutôt cru que delta c'est ce qu'il y a sous la racine.

En général tu fais comment du coup pour trouver les zéros d'une fonction quadratique?

[viscid solstice]

je fais ça sur ma feuille je te l'envoie dans 2minutes

[quiet plume]

Ok!

[viscid solstice]

ca mais apres jss bloque pour les signes

[quiet plume]

T'as encore -4 au lieu de 0

[viscid solstice]

tu peux m’expliquer quel est mon erreur stp?

[quiet plume]

Plus haut ton premier facteur pour la dérivée c'est 4x.
4x = 0 si et seulement si x=0, pas -4

[viscid solstice]

ok c'est la fatigue déso j'avais lu 4 + x

et pour les signes je fait comment stp?

j'galère à ce niveau la

[quiet plume]

En gros le second facteur comme tu viens de déterminer les zéros c'est $2x^2 - 3x + 1 = 2(x-\frac{1}{2})(x-1)}$

[flat frigate]

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

[quiet plume]

Du coup tu peux étudier le signe des trois facteurs, soit $4x$, $x-\frac{1}{2}$ et $x-1$. \
Chacun aura sa ligne dans ton tableau des signes

[flat frigate]

Azyrashacorki

[quiet plume]

Donc pour chacun détermine les signes, et à la fin tu pourras utiliser l'information des trois lignes pour déterminer le signe de la dérivée en dernière ligne

[viscid solstice]

sa j'ai compris

mais comment déterminer le signe de chaque facteur individuellement stp?

je sais jamais si je dois mettre un + ou un -

[quiet plume]

Bah tu peux tester un point

Mais disons (x-1) c’est négatif avant 1 et positif après

C’est similaire pour x-1/2

[viscid solstice]

jsuis désolé js c'est tarpaing chiant pour toi mais jsuis fatigué j'comprend r j'en peux plus

[safe radish]

@viscid solstice Has your question been resolved?

[safe radish]

@viscid solstice Has your question been resolved?

[viscid solstice]

.close

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[tall rain]

I’m doing no. 2.

[tall rain]

So a+b is (-5,3)

But I’m trying to draw it on the coordinate system however the answers are so weird

b is at negative x axis

[unique thicket]

(your diagram is completely correct)

[vague phoenix]

I thought you were doing 1 firsthand and thought it was wrong😂

[tall rain]

But b is up by 4 times…

In y-axis

Not x axis

[unique thicket]

can you voice your confusion clearer?

[tall rain]

bruh kid…

How am I supposed to know that it’s a triangle

OKAY but how do I know where the triangle should be placed dawg

@lean otter

<@&286206848099549185>

[feral onyx]

😂🤣

[compact flame]

Can be placed anywhere

Vectors can be translated

Start with (0,0) though

[tall rain]

Clearly not if that’s the answer

I can have it all start on 0,0 and turn into single lines without a triangle

Tf?

So unhelpful

[tidal imp]

Remember that when adding vectors, each succeeding vector’s tail starts at the head (aka the arrow tip) of the previous one

Then the resultant vector gοes from the first vector’s tail to the last vector’s head

For clarity, the first vector’s tail is usually placed at (0,0) so that when drawing the resultant vector, the coordinates are clear and you don’t have to translate the whole thing

[tidal imp]

Try it out

[tall rain]

Forget it

[tall rain]

Show your steps

[tidal imp]

Well, I can’t do it for you, because we’re supposed to help you do it. I can show you where to start though

so let's graph it on the xy-plane

for vector a, we move 3 units left and 1 unit down, which creates this vector. How will we move for vector b?

[safe radish]

@tall rain Has your question been resolved?

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[hoary seal]

https://cdn.discordapp.com/attachments/1479648283390382243/1482865356073734356/image.png?ex=69b8817b&is=69b72ffb&hm=e9b4dfa3ba0ec0df0e5f97253d74cec7732f12881bef392361f62b124df5a845&

[hoary seal]

how do we solve this

[tidal imp]

you can try to work backwards here: given $|g(x)-5|<\epsilon$, try to find an inequality where $x$ is greater than something

[flat frigate]

CST (reply ping for help)

[hoary seal]

where x is creating than something?

[wild cape]

you should run through the scratchwork of an epsilon proof of a limit. the scratchwork will give you a suitable M

[hoary seal]

could u send it here I’ve looked around but they seemed irrelevant

[wild cape]

do u know the epsilon definition of limit and how to use it to prove limits?

[hoary seal]

Probably not

[wild cape]

have u seen the epsilon definition of limit at a finite number? u mightve seen it called epsilon delta

[hoary seal]

we didn’t cover the delta

just the epsilon

M is the point where epsilon is within the range

L is the limit

[wild cape]

u only did limits x->infty? not a finite number?

[hoary seal]

|f(x)-L| < epsilon

Let me check

this

[tidal imp]

the question is whether you've done the epsilon-delta definition of a limit for the finite case

[hoary seal]

I don’t think so

[tidal imp]

i.e. $\lim_{x\rightarrow c} f(x)=L$ iff for every $\epsilon>0$ there exists a $\delta>0$ such that if $0<|x-c|<\delta$ then $|f(x)-L|<\epsilon$

[wild cape]

0<|x-c|

[flat frigate]

CST (reply ping for help)

[tidal imp]

ah yes sorry

(since the equals case deals with continuity)

[wild cape]

my question is youve only seen $x\to\infty$ and not $x\to c$?

[flat frigate]

ロケット・ジャンプ

[wild cape]

i ask bc i find it hella weird for ur class to not have done finite yet, and even weirder not teach how to write an epsilon proof

[tidal imp]

Some calculus classes skip the epsilon-delta definition in favor of more colloquial definitions, but no class I've ever seen that uses the epsilon-delta definition starts with the unbounded case

[hoary seal]

we kinda skipped the definition of a limit but I think we will come back to it very soon

[wild cape]

out of all classes that give out problems involving epsilon, do some actually skip the epsilon def?

[tidal imp]

like they just never give the definition. They just say that "as x grows large f(x) approaches this thing"

for example, AP Calculus. Or calculus for non-math majors

[tidal imp]

maybe you

[wild cape]

im well aware that the average calc class totally avoids formal defs

[tidal imp]

are not supposed to answer it yet

[wild cape]

but OP's class gives out problems involving epsilon so i am left to wonder how that can be without them having seen a formal def

[tidal imp]

maybe the teacher just wants to vagueteach it? like some teachers have exercises involving "undoing the derivative" without calling it "antidifferentiation"

[wild cape]

literally all the framing of the def is in the problem yet the def was never stated in lecture?

[tidal imp]

idk it's really weird

[tidal imp]

well @hoary seal if you don't know epsilon-delta scratchwork, start with $|g(x)-5|<\epsilon$, use the formula of $g(x)$ in the problem, and try to isolate $x$ somehow

[flat frigate]

CST (reply ping for help)

[hoary seal]

hmm

[tidal imp]

well let's start. What is $g(x)-5$?

[flat frigate]

CST (reply ping for help)

[hoary seal]

it is5x/(x-8) -5

also im pretty new to proofs ive never computed a proof before but ive seen my lecturers and mathcord do it

[safe radish]

@hoary seal Has your question been resolved?

[tidal imp]

Oh I forgot to answer to this

Yes, but try to combine them into one fraction

[safe radish]

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[hot stone]

I need help with number 7

[hot stone]

Or maybe I’m doing it right

But is this process okay? Or is there a way to show more work?

[winter whale]

you are

[hot stone]

Idk cuz my teacher usually likes it when ppl show alllll their steps

[thin bridge]

looks ok

[winter whale]

good handwriting btw

[thin bridge]

eval/round since thats what the question wants

[hot stone]

Okk

[hot stone]

Lol thx
Ngl I thought it was pretty bad

[hot stone]

Do I need to show how I got to the formula sinB/b = sinA/a ?

[manic patrol]

unless you are not allowed to use that formula directly, no; the sine law is usually considered proven in tests.

[hot stone]

Okay! Thanks

.close

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[mortal thicket]

in this problem in order for me to find the position vector form O to the force components

where do i draw the forces from

as in, do the forces start from point A or? because if so, then i would find distance from point A to O

this is my understandind so far

<@&286206848099549185>

<@&286206848099549185>

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[mortal thicket]

.reopen

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✅ Original question: #help-23 message

[mortal thicket]

<@&286206848099549185>

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[shrewd linden]

Is there easier way than just finding the 3 intersection points

and then using shoelace formula?

[safe radish]

@shrewd linden Has your question been resolved?

[shrewd linden]

<@&286206848099549185>

[safe radish]

@shrewd linden Has your question been resolved?

[safe radish]

@shrewd linden Has your question been resolved?

[frank widget]

i dont think so

i guess this question was made to use shoe

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[mortal thicket]

after you figure out the resultant force vector and total moment at O, how do u get the x and y intercept

[harsh sun]

Use the components of the resultant force

The y component of the force multiplied by the x intercept will give the same total moment you already calculated

You can do the same process for x

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[magic eagle]

can someone pls help me with this

[magic eagle]

and this

[hasty wagon]

First one, what have you tried

[magic eagle]

i just could not figure it out

[hasty wagon]

so, what can you think of when given is x³ and the answer is in x⁶

[magic eagle]

i have no idea

do you double it

[hasty wagon]

we might wanna make x³ become something in x⁶ so what operation

[hasty wagon]

well, you square it

[hasty wagon]

so that's the first hint

[magic eagle]

i think i got it

[hasty wagon]

do tell when you need help with the 2nd one

[magic eagle]

yea i got the first one at the second one i get to splitting the 8 and 18 and taking out the 4 and 9 but i dont know what else i can do

[hasty wagon]

you are doing this, right?

[stoic torrent]

i think he just rewrote 8 as 4x 2 and 18 as 9x2

[hasty wagon]

i see

[hasty wagon]

thanks!

[stoic torrent]

ill let you take this one

[hasty wagon]

?

[stoic torrent]

the help channel?

[hasty wagon]

you can do it if you are free of course

[stoic torrent]

like as in ill back away and let you help

[magic eagle]

no

[hasty wagon]

ah

[stoic torrent]

Oh no your are a good teacher go ahead please

[hasty wagon]

thanks!

[hasty wagon]

do you know what does this mean? @magic eagle

[magic eagle]

i have this now

[magic eagle]

yes

[hasty wagon]

nice, checking

[magic eagle]

but i prefer splitting the stuff

[hasty wagon]

i see no worries, every method has it's own pros and cons

[magic eagle]

do i times them in toghether now

[hasty wagon]

so, next, we can multiply like this
(4)(-8) times √((2a)(2a))

[hasty wagon]

yes

[magic eagle]

oh i understand it now its then -32*2a

thank you for the help

[hasty wagon]

Cheers!

you can type .close when you're done

[magic eagle]

.close

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[copper shadow]

why do we need to choose a different variable for the integrand? I thought that what you called the input doesn't matter since the input you will be inputting the same thing regardless

[summer coral]

<@&268886789983436800>

[plucky elk]

Because x is fixed, like x=3, where as x is not in the integrand and differential

t is a dummy variable that doesn't matter since it gets "integrated out"

[copper shadow]

wait how can t not be in the integrand?

[copper shadow]

wdym integrated out?

[plucky elk]

Typo, fixed

[plucky elk]

https://mathworld.wolfram.com/DummyVariable.html

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[muted mist]

im having problems with (7b^3 c^6)^3 im not good at this but im haiving problems with the first number
and im in algebra I

[native flower]

could you share the specifc question?

[muted mist]

this is what im having problems with

[native flower]

ah okay

okay, so no worries

does it come with a sentence?

i think all its asking for you to do is put in the coefficients and the exponents of the specific variables

[native flower]

ah

nevermind

you have to simplify,

so the ^3 in the whole paranthesis

[muted mist]

im good at the later parts but the first part is my problem

[native flower]

multiplies into the brackets itself

[muted mist]

i tried it alone multiplying

[native flower]

im guessing you dont have perfect knowledge of indices?

[muted mist]

uh

i dont know what indices is

im not good at math

[native flower]

indices are basically a mathematical term for exponents

so bases would be the variables here and 3 would be the exponent

[muted mist]

ok

[native flower]

ill send an image

that will help

[muted mist]

i got the first part done

[native flower]

yeah

so, 3 becomes the new power (exponent) of each of those variables and integers

[muted mist]

so times each number by 3 of its self

[native flower]

sorry on 2nd step it will be 7^3

[native flower]

yeah, since the exponent here is 3, it will multiply each exponent with 3

[muted mist]

kk

[native flower]

since the power of 7 was 1, it multiples it by 3

so 7^ (3x1)

and b ^ (3x3)

c ^ (6x3)

[muted mist]

ok ty i got that one done

[native flower]

yea

make sure to remember

this only stands if each number/varaible inside is multiplying

[muted mist]

i think i can do my other ones my self and i write down how to do stuff on paper so i know how to do them soo ty

[native flower]

if it contains a + or - it wont work this ways

[muted mist]

kk

[native flower]

you will need the expansion formula

[native flower]

alright

[muted mist]

welp ty

[native flower]

no worries mate

[muted mist]

.close

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[plain sage]

i finished up to part a but dont understand what you sub in for t in part b to get the value stated

[plain sage]

my expression for A= sqrt((20t/1+19t)^2)

[timid ridge]

It's an extrema so dA/dt is 0

find t

[plain sage]

i still dont understand? how do i find t? also i thought im finding value for A in part b?

[timid ridge]

dA/dt = 0

solve for t

you know everything else

when dA/dt is 0 there is an extrema

they want you to show that the extrema occurs, at that time and value

[plain sage]

so do i sub in 400/361 as A in the original equation given?

[fresh marsh]

derivation ?

[timid ridge]

no dear if i asked you to find the extrema of x^2 how would you do it the calculus way

besides the obvious it's 0, WHY is it 0?

[plain sage]

bc 2x=0 T-T

[timid ridge]

And x = 0 for that, so at x = 0 there is a minimum of 0 (second derivative test)

so you get the idea

[plain sage]

yea

but im still confused for this question

[timid ridge]

find t such that dA/dt = 0

then prove it's a maximum with second derivative

find the value of A at such t

then you proved the maximum cannot exceed the given value

[plain sage]

okay i kind of get it now but how do i rearrange to find t cuz t is the denominator

[timid ridge]

what

you have A in terms of t as well

if x/7 = 0 what is x

[plain sage]

0

[timid ridge]

ok so

dA/dt = A^1/2 / 10t^2 = 0

or whatever

[plain sage]

i got t=0 idk if its right

[gleaming coral]

||no idea sorry for interrumping||

[plain sage]

me either im still trying to solve it

wait im done and i found a method that works for me

.close

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[versed bone]

just need a sanity check / help understanding what exactly is wrong with my answer here

[tardy mango]

Perhaps I'm being a crank, but I think that this is fine barring the use of the equal sign rather than the isomorphism symbol in the last sentence.

[versed bone]

Oh yeah definitely messed up on that

okay so the groups I chose do work

thanks I thought I was going insane lol

.close

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[white basalt]

How to do 3 and 8

For 8, do I just assume c is 0 and the t value is positive for any given k?

Cuz ds/dt=ks
ln|s|=kt
s=e^(kt)

[stoic torrent]

oh for 8 you can just differentiate each side wrt time

[white basalt]

But answer is B

[stoic torrent]

yeah and you would het that right?

[white basalt]

I was thinking like finding double derivstive and then use substitution

[white basalt]

Uh

[stoic torrent]

um not required

[white basalt]

So I need find ds/dt?

[stoic torrent]

see, after dofferentiating both sides by time, we get dv/dt

which is just a

and ds /dt is just v right?

and we already know that v = ks

so we can put it back in after differentiating wrt time

[white basalt]

Yes

[stoic torrent]

so we would get a = k (v) = k(ks) = k^2 s

does this make sense?

[white basalt]

I don't get the a=k(v) part

[stoic torrent]

ah okay

so v= ks

[white basalt]

Ohhh I get it

S is position

[stoic torrent]

try differntisting this eqn wrt to time

[white basalt]

And the derivstive of that is v

So kv

[stoic torrent]

yeah sorry i explained it badly😭

[white basalt]

Lmaoo dww

So smart

Wb 3 tho

[versed bone]

I think a way to look at it is just realizing v = ds/dt so we have ds/dt = ks

[white basalt]

I think I setted up correctly

Yeah that's what I did lol

[stoic torrent]

for 3 is there any other data which you may have cropped out?

[white basalt]

I just got confused for the c

[white basalt]

Uh

No

[stoic torrent]

well okay

so for starters lets assume some parameters

[white basalt]

I assume h is height

And 2r is width for rectangle

So r is radius

[stoic torrent]

So the assumptions that we need to make our -
Radius
side of rectangle

yeaup!!

[white basalt]

Yes

[stoic torrent]

now lets find the area

[white basalt]

And pir^2+2rh=100

[stoic torrent]

okay!!

[white basalt]

And perimeter is uh

[stoic torrent]

now whats the formula for

[stoic torrent]

yeah you jst read my mind😭

[white basalt]

Wait sorry that weong

[white basalt]

😭 😭

[stoic torrent]

why.

[white basalt]

It's semi circle

[stoic torrent]

oh shoot😭😭

[white basalt]

Sooo pir^2/2+2rh=100

[stoic torrent]

what am i doing😓😓

[white basalt]

Loll all good

[stoic torrent]

yeah

[white basalt]

And P=2r+2h+2pir/2

[white basalt]

And then u solve h in terms of r?

[stoic torrent]

okay now we wish to minimise this

[white basalt]

Yes

Wait uh can we just divide r out

[stoic torrent]

yeah b

[white basalt]

Ohhh alrr lemme tryna do it sec

[stoic torrent]

yes!! but not directly right?

[stoic torrent]

.

[white basalt]

Uh 😭 my answer is wrong

I'm finding the y value right

I'm doing this right

Then I turn r into x and p into y

[spiral bison]

im trying to look at context what math is this

it loooks like related rates

[white basalt]

I dont gotta find first drrivative cuz I can just graph it

[white basalt]

It's optimization

[spiral bison]

yea

[white basalt]

Optimization harder than related rates in my opinion lol

[spiral bison]

really?

[white basalt]

Yeah

[spiral bison]

i feel they are both about the same low difficulty

[white basalt]

Cuz optimization is basically the same thing over and over

[spiral bison]

i mean to each their own

[white basalt]

Ohh hmm

I find it the most difficult part lol tbh

[spiral bison]

i cant read that so ill let the other guy help you

[white basalt]

Lmao

Can u help me tho🙏

If u were to type it out

[spiral bison]

oh

hi

uhm

whats the question

[white basalt]

Number 3

[spiral bison]

the area of the whole figure right

is 100

[white basalt]

I thought it's 100 but it's a bit ambiguous

[spiral bison]

yeah

[white basalt]

But just assume it's 100

[spiral bison]

aight

let me work it out rq

[white basalt]

Alrr tyy

[stoic torrent]

this looks find actuasky

[white basalt]

But it's wrong lmao

😭

The correct answer is c

Oh my I have a test this Friday anyone of u guys wanna help me study in dm 😭

[spiral bison]

i might

im working on this rn tho gime a ssec

[white basalt]

Yay ty🙏

Alrr

I'm basically free all week

[stoic torrent]

yo whatd you get r as

[white basalt]

Uh

For the min?

Lemme chdck

[stoic torrent]

the radius suchtht perimeter is minm

[white basalt]

I got 7

7.071

[spiral bison]

@white basalt i demed you

dmed

[white basalt]

Alrr

[stoic torrent]

wait what.

[white basalt]

For r

[stoic torrent]

i got 5.921

[white basalt]

Uh😭

Wait what's ur equation for P

[stoic torrent]

P = 2r + 2h + pi r

[white basalt]

I meant after u sub in h

[astral holly]

screw that what is that calc

its so cool

[white basalt]

Numeorks

[white basalt]

Yea that's what I got too

Uhh

[astral holly]

161$ 😭

[white basalt]

So 2r+2(100-pir^2/2)/2r+pir=P

[white basalt]

Nah it's 100

Wist the price raised what the heck

I swear it's 100 but now its 125 rn somehow

[white basalt]

😭 uhh what's ur y value

When u graph the function when u sub in h

[stoic torrent]

@white basalt

idts your radius is correct

it should be 5.291

oh wow is india already up

[feral onyx]

?

Wdym

[stoic torrent]

oh soeey i thought ur indian😭

[feral onyx]

I am

[stoic torrent]

oh so i was expecting it to be sunrise a little later in india

[feral onyx]

I live in the US

[stoic torrent]

anyhow @white basalt getting the exact answer with r = 5.291

[white basalt]

Hmm

Wait u use the first derivative?

I was thinking like

The min value of the function is the answer

So then

[stoic torrent]

yeah i am i find it more reliable and errorless

[white basalt]

Ohh

[stoic torrent]

um

you forgot to put 1/2 in pi x^2 term

[white basalt]

Oh crap

😭 😭 😭

TYY

[stoic torrent]

aw anytime

okey i gtg now

byee

[white basalt]

Alrr tyty byebye

[safe radish]

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[peak pecan]

x/a + y/b = 1

I know how to derive this formula but i dont know how this formula makes a straight line.

Just like the distance formula can be imagined like we find length of the line in both x axis and y axis component by x2 - x1 and y2 - y1 respectively and find the length of the actual line by using Pythagoras theorem. We can easily visualize how this formula works.
But how to visualize x/a + y/b = 1 just like that.

[safe radish]

@peak pecan Has your question been resolved?

[peak pecan]

not yet

[tardy mango]

,w solve for y if x/a + y/b = 1

[flat frigate]

Results provided by WolframAlpha

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

Requested by civil_service_pigeon

[tardy mango]

Note that this is simply a line with slope $-b/a$ and $y$-intercept $b$ (assuming that $a,b \neq 0$)

[flat frigate]

Civil Service Pigeon

[peak pecan]

.close

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[peak pecan]

thanks

[tardy mango]

[safe radish]

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[sleek hornet]

A palm reader claims that one of your palms predicts your future but they cannot know
which one. They say your left palm predicts that you will be rich and happy and that
your right palm predicts that you will be happy. Use the absorption laws to simplify
what they are saying

[sleek hornet]

Am I doing correctly

oops

.close

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[buoyant shadow]

no that's not the intent

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[pale bone]

i dont see how

to do it

i dont get how that therom is seen

[delicate shore]

are you confused because in this diagram the lines don't intersect

you can imagine dragging the top point on the circle and moving it around to the left and then you will get the right picture

[pale bone]

how should i see or notice it during

and exam

Also another question how does b ( 1-2a)=0

[vague phoenix]

If an angle A from the centre is subtending an arc, and an angle B on the circle also subtend this arc, then B =A/2

Just use angle theorem in the circle

[pale bone]

oh i see it

[vague phoenix]

Then for angle b i dont see anymore information given

[pale bone]

how aboutt thiss one

[vague phoenix]

Ahh i completelt forgot

[vague phoenix]

Yeah the sides are radius

So isoceles

Is this a multiply b? The symbol circle i only see it in composite functions

[pale bone]

whatt

[vague phoenix]

Proving a.b = a+b+2ab here

What is this dot a.b meaning can you recall

[pale bone]

an order of operation?

[vague phoenix]

Just identify e is a real where e . a = a.e = a

Oh nevermind you used b

Yeah thats correct it should be 0

[pale bone]

oh i didnt write that, the teacher did, but i dont get how b(1-2a)=0

and b=0

[vague phoenix]

We have b real and assume if b.a=a.b=a

Now use the rhs equation to remove a

This means for any values of a, there exists a value of b such that this equation correct both side

[pale bone]

whatt

OH NVM I GOTIT

[vague phoenix]

Ye ye

[pale bone]

.close

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[rich dune]

I need help on how to continue

[stoic torrent]

Well i see you have reached the multiplicity of the root step correct?

so now we can say that General solution y§ of the homogeneous equation is a linear combination of particular solutions yi corresponding to roots lambda i

So simply put,

and for this, we have the general solution

Is all clear till now?
If so then we will move on to finding the undetermined constants

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[vague rain]

Help

[vague rain]

How i can get 1/4integral(sec^3(x)

[burnt notch]

Mmh there's something off, I believe, in those calculations

[honest idol]

No

It’s correct

[burnt notch]

But where does the 1/4 come from?

[honest idol]

3/4∫sec^3x dx - ∫sec^3x dx

[burnt notch]

Not there, at the beginning I meant

[honest idol]

but OP is asking about the secant right

The one on irs own

Its*

[vague rain]

How?

[vague rain]

I dint see

[safe radish]

@vague rain Has your question been resolved?

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[twin prawn]

I need help with 1

[frozen marlin]

check the differences

[twin prawn]

What I did so far:

1. added the terms by 1 so we have
   6, 12, 30, 84

2. factored it out
   6 = 2 x 3
   12 = 2 x 2 x 3
   30 = 2 x 3 x 5
   84 = 2 x 2 x 3 x 7

3. checked their differences
   84 - 30 = 54; 30 - 12 = 18

the most i have rn is

(a_[n - 1]) + 6(n + 1) but this only works for 12 and 30 (where n starts at 0)

[hasty wagon]

hint: ||you can try minus 2 too||