help-0

[calm willow]

<@&286206848099549185>

[lone heart]

@calm willow Has your question been resolved?

[night wing]

Let's say for a moment that you are not thinking about the surface but the force itself. The force that the water applies to anything increases with the depth

Because in deeper regions there is more water applying its weight

[gusty gorge]

well the surface is infinitely thin probably, so there's no buoyancy or stuff like that

so it's probably referring to the force the water exerts on one side (that's balanced by the same force on the other side)

and given the context that it's one of those weird calculus problems, it's probably just asking for the force caused by the pressure at depth

[calm willow]

Yes

Thats exactly what its asking

[gusty gorge]

so like

where are you stuck

this isn't true given what I said

[calm willow]

Oh

[calm willow]

I dont know how to model the equation

[gusty gorge]

model what equation

[lone heart]

@calm willow Has your question been resolved?

[lone heart]

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[wind jolt]

i am trying to write the approximation of sin x using macalurian series using summation notation

[wind jolt]

but i cant get the signs correct

i am trying to use -1^n to solve this but i have to get + + - - + + - - + + - - + + - -

but -1^n gives - + - + - + - +

[mortal trellis]

well +- is correct. once you account for half the terms being 0

[wind jolt]

but how would that go under summation notation

as the powers and factorials are going by 2n so it goes 2 4 6 8

[mortal trellis]

well, 1,3,5,7 and so on for sin

consider 2n+1

[wind jolt]

so what should be the power for -1

[mortal trellis]

n

[wind jolt]

for n = 0 initally

[mortal trellis]

(-1)^0=1

and 2*0+1=1

[wind jolt]

this is the series

[mortal trellis]

then for n=1 you have (-1)^1=-1 and 2*1+1=3

yes I know

n=2 has (-1)^2=1 and 2*2+1=5

[wind jolt]

but if i am using summation notation it is more like x + 0 + x^3/3! + 0 - x^5/5!

[mortal trellis]

no

you dont even write those 0s

[wind jolt]

i know

oh i get it

i can do summation of -1^(n) * x^2+1/(2n+1)!

[mortal trellis]

yes

ignoring all the missing brackets

[wind jolt]

thanks for your help!

.close

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[late token]

can a number be proved irrational without using the contradiction theory?

[alpine sable]

it depends what that number is

[marsh rapids]

It's possible

[torn elk]

For example, you can prove that sqrt(2) is irration by infinite descense (i don't know if I used the correct word in English)

[marsh rapids]

Or by noticing that X^2 - 2 is irreducible over Q thanks to Eisenstein's criterion

[alpine sable]

(infinite descent is a contradiction proof)

[marsh rapids]

Can easily be adapted to work for any number btw

[torn elk]

I just realized as soon as I said lol

I confused absurd with contradiction

[median oar]

Hey those are words I’ve seen before

[marsh rapids]

Not minding that this criterion is usually proved by contradiction though

It seems that wikipedia's advanced explanation doesn't prove it by contradiction, but the theory is beyond my knowledge

Just embrace proof by contradiction really

[lone heart]

@late token Has your question been resolved?

[lone heart]

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[wet nest]

lim x->0 (e^-1/x^2)/x

[ocean seal]

Toby

$\lim_{x\to0}\frac{\exp({-\frac{1}{x^2}})}x$

[molten pivot]

,w plot exp(-1/x²)

[ocean seal]

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[wet nest]

<@&286206848099549185>

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[molten pivot]

Use lhopital

[wet nest]

It only messes it up

x^3 in denominator

<@&286206848099549185>

[keen plinth]

substitute y=1/x

[wet nest]

Get out of here bro

[primal lance]

wtf

[ocean hawk]

<@&268886789983436800>

[wet nest]

What to do after that??

.close

[lone heart]

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[alpine sable]

I need help with a problem -- I need to use optimization in order to solve it and I'm not sure how.

[alpine sable]

A cone will be inscribed in a sphere of radius 9 in.

Part A: Find the exact dimensions of the cone of largest volume that will fit inside the sphere. (20 points)

Part B: Find the maximum volume cone to the nearest tenth. (20 points)

[alpine nacelle]

Choose a parameter that describes the shape of the cone in such a sphere, and then express the volume as a function of this parameter

The way I would do it is to think like this: if the cone is of the largest volume, its tip touch the sphere, otherwise you still have room for some cone volume

So the only decision to take is where to put the circle-base, and the radius of this base

(position which only depends on the said radius)

[alpine sable]

I mean i figured that the maximum radius of the cone would be 9 since it's inscribed in the sphere with radius 9

but i'm not sure how to solve for h

[alpine nacelle]

It is not 9, it is smaller than that

A cone inscribed in a sphere can't fill the full sphere

[alpine sable]

right. i might be a little stupid

[alpine nacelle]

like if you take radius = 9

oh wait

no I misunderstand what you were saying my bad

[alpine sable]

oh no problem!

[alpine nacelle]

it is possible to take a radius of 9 yes, in this case, it means the base of the cone is at half the sphere

so the height would be the radius of the sphere

[alpine sable]

so... 9?

[alpine nacelle]

yeah

but idk if it's the maximum of the volume we can get

[alpine sable]

yeah...

[alpine nacelle]

The volume is 1/3 * h * pi * r² where r is the radius of the circle-base of the cone

[alpine sable]

uh huh

[alpine nacelle]

So if we find a relationship between h and r, we can replace h by r so that's a one variable function and then study it

to find for which r we get the maximum volume

[alpine sable]

ohhhh I think i'm getting it

so if we were to solve for h in terms of r

we could plug it into the volume of the cone formula and solve for r

and then solve for h, correct?

[alpine nacelle]

yeah

[alpine sable]

so we'd have to use slant height of the cone

i think

[alpine nacelle]

we can do some trigonometry too

[alpine sable]

right by using pythagorean

[alpine nacelle]

try a bit and ping me if you don't find

[alpine sable]

alr, ty!!

I got the answer 🙂 thanks for your help @alpine nacelle

.close

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[undone herald]

What’s after this step

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@undone herald Has your question been resolved?

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[keen orbit]

trying to understand what this means

[keen orbit]

a bit more context:

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@keen orbit Has your question been resolved?

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@keen orbit Has your question been resolved?

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[tidal bane]

Does anyone know why this is the case?

[tribal valve]

$b^x = b^y$

[ocean seal]

dabbingpotato

[tribal valve]

b is the same

if these are equal

x and y have to be equal too

[tribal valve]

thats because 3^2 and 3^3 are not equal

[tidal bane]

so both are true in this case ?

[tribal valve]

what do you mean both are true

[tidal bane]

both are ture , that they are both false

both are the correct answer

[tribal valve]

this is not true because if there is a equal sign that means both sides of the equation have to be equal

[tidal bane]

yeah but im saying the solution
1=3 in correct solution
and
2=3 is correct solution

is my assumption correct ?

[tribal valve]

no

you just divided both sides by 9

that doesn't relate in any way to the exponents

[tidal bane]

im not asking if it relates to the exponents , im asking if my first method is mathematically correctly done

[tribal valve]

yes

but 2 = 3 has nothing to do with it

[tidal bane]

what does that mean ?

[lone heart]

@tidal bane Has your question been resolved?

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[wind cloak]

A limit is only said to exist if the left hand and right hand limits are both equal and finite

So yes, if one of the limits is infinity, it formally does not exist

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[cursive root]

I know it used trig identities but what happened here

[cursive root]

inverse tan is cos/sin this I know and sec inverse should be cos/1 wouldn't rewriting it be like this? cos+cos/(1+sin)

[alpine sable]

,tex .wrong recip

[ocean seal]

Toby

[cursive root]

oh so the 2 inverses denominators which are cos and cos aren't a cos + cos? or did am I still misunderstanding something?

[alpine sable]

you should add sec and tan first before reciprocating

dont reciprocate before adding

[cursive root]

oh this didn't occur to me

yup it worked thank you so much

.close

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[loud bronze]

can someone help?

[alpine sable]

You can create a proportion

[loud bronze]

how?

and also why

what proofs they are propotional

[alpine sable]

They are both goalposts. I assumed these 2 goalposts were proportional

Without that assumption I can't help you

[loud bronze]

youre correct

ok another question

why am i wrong

[alpine sable]

Did you draw the diagram?

[loud bronze]

yes

[alpine sable]

Angle DBC is a right angle. BE bisects that angle. Bisect means to cut in half.

[loud bronze]

this is the diagram

yes

so DBE = DBF

right?

[alpine sable]

Before you can say that you have to draw the diagram correctly

Here's the first one

Wait

That's wrong

Okay so "BE bisects angle DBC". DBC is 100°, and bisecting it makes each side 50°.

[loud bronze]

yes

and its bisected again

so 25 25

[alpine sable]

You're finding angle DBF

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@loud bronze Has your question been resolved?

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[noble onyx]

Use mathematical induction to prove that shows the following:

1 + 3 + 5 + ... + (2n-1) ≡ n^2 for all integers n ≥ 1.

[noble onyx]

Base Step: (1) ^ 2 = 1

Inductive Step:
k ^ 2

Prove k + 1:
(k + 1) ^ 2

Am I allowed to leave my work for k + 1 as is?

[tall shuttle]

No

(k + 1) ^ 2 is not even a statement

[noble onyx]

nvm i need to show left hand side is equal to right hand

[tall shuttle]

yes

[merry depot]

your inductive step should be k ^ 2 = something
your trying to prove (k+1) ^ 2 = something.
so far there's no work here.

[noble onyx]

.close

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[scenic wing]

idk where to start

[hasty hill]

try to get f(theta + pi) in terms of theta

[scenic wing]

idk

f(theta) + f(pi)

[hasty hill]

Do you know All sin tan cos?

heard about it before?

[scenic wing]

yes

[hasty hill]

great

now try to apply that in here

think about it

[scenic wing]

i dont know

[hasty hill]

ok

tell me this

[scenic wing]

theta/pi

[hasty hill]

if f(x) = x^2 then what is f(x+a) ??

[scenic wing]

x^2 +a

[hasty hill]

nah you are wrong

see this is quite easy and simple

[scenic wing]

ok im listening im not going to guess it

[hasty hill]

when I am asking for f(x+a) u just need to replace x with (x+a) everywhere

[scenic wing]

ok

[hasty hill]

now tell what will be f(x+a) given f(x) = x^2

[scenic wing]

so (x+a)^2

[hasty hill]

nice!!

now since f(theta) = cot(theta) then what will be f(theta + pi) ??

[scenic wing]

cot(theta + pi)

[hasty hill]

great

now can you simplify that even more

cot(theta + pi) ??

think about All sin tan cos rule

[scenic wing]

$cot \frac{theta + pi}{1}$

[ocean seal]

putridplanet

[hasty hill]

nope

can you explain me about the All sin tan cos rule?

[scenic wing]

cot = x/y

[scenic wing]

.

[hasty hill]

what?

[ebon sparrow]

,tex .recip trig

[ocean seal]

Akira

[ebon sparrow]

better way just say "sohcahtoa"

[scenic wing]

can you just tell me

[hasty hill]

https://www.mathsisfun.com/algebra/trig-four-quadrants.html

I think you don't know the rule..check this article

but cot(pi + x) = cot(x) always..remember this for now

[scenic wing]

cotangent is cos/sin

i know

[hasty hill]

nah I am not asking for definition

it is something else

was looking for this..

[scenic wing]

ok

[hasty hill]

anyway..do go through the article I shared above..I hope you understand from there

so now since cot(pi + theta) = cot(theta) = 3 which is ur final answer

[scenic wing]

how does cot(pi+theta)=cot(theta) ?

[ebon sparrow]

what

[scenic wing]

can you help me

[ebon sparrow]

$f(\theta + \pi) = \frac{1}{tan(\theta + \pi)}$

[ocean seal]

Akira

[scenic wing]

where did the tan come from

[ebon sparrow]

cot=1/tan(x)

[scenic wing]

if i were to look up a video on this what would i type

[ebon sparrow]

recip trig

Trig Reciprocal Identities

for full name

@scenic wing do you still need help? if not then use .close

[scenic wing]

wait so 3 is a point on the circle

[ebon sparrow]

use desmos

[ebon sparrow]

wait since cot= tan then it should be on tan side

[scenic wing]

why is cot(theta) = 3 + pi = 3 ?

[ebon sparrow]

It cannot be equal to a specific value like 3 + pi or 3

,w calc cot(theta) = 3 + pi = 3

[ocean seal]

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[scenic wing]

holu up

what is the x and what is the y

[ebon sparrow]

wdym?

[scenic wing]

for cot

[ebon sparrow]

^^

[scenic wing]

what is cos and sin here

[ebon sparrow]

you mean what is x and y definition for cot?

[scenic wing]

yes

[scenic wing]

why is this

[ebon sparrow]

there's no x or y in this equation

it's the ratio of the adjacent side to the opposite side

[scenic wing]

why is 3 + pi = 3

[ebon sparrow]

it is not accurate

[scenic wing]

?

[ebon sparrow]

don't you see it says "no solution exits" lol

[ebon sparrow]

If this asking to choice which one is correct then you gotta choice "b" because $cot(\theta) = 3 + \pi = 3$ doesn't not have solution

[ocean seal]

Akira

[ebon sparrow]

,w calc if cot(Θ)=3, find f(Θ+π)

[ocean seal]

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[ebon sparrow]

[scenic wing]

thanks for telling me im wrong

after asking a question

learn 100

[ebon sparrow]

no worries

[scenic wing]

.close

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[wild summit]

how do i find the value of d?

[wild summit]

<@&286206848099549185>

[wintry panther]

d?

[wild summit]

yes like for the equation a[k(x-d)]+c

for graphing

for the sinusoidal func

[wintry panther]

To be honest, I'm not familiar with this, but I can try to help 😉

Is it a* sin(x - d) + c?

[wild summit]

yes

but theres also k

its the general transformed function formula

[wintry panther]

Oh, I see, so it's a * sin(k(x-d)) + c?

[wild summit]

yes thats it

[ancient saddle]

Hello, what have you got so far?

[wild summit]

hi, i am trying to label the values right now

i just am not sure how to find d

in the theory it says that d = x-coordinate of the starting point of the cycle

im not sure what to make of that

[ancient saddle]

d is also horizontal translation to the right

You want to translate the sinusoid d units to the right so that there's a maximum at 3pi

[wild summit]

okay

[ancient saddle]

Right now where is the maximum of the sinusoid?

without horizontal shift

[wild summit]

i believe it is at (pi/2 , 20) but i am not sure if i am correct

[ancient saddle]

Mmm remember that the period is 9pi now

[wild summit]

um im not sure how to find x but i know that max y value is 20

for 9pi period i forget

[ancient saddle]

Try drawing a sinusoid and see where the maximum is with respect to the period. Remember that when you change the period, the proportions of each part of the sinusoid are still the same

Like the midpoint of one period of normal sine is at pi, which is 2pi/2

[wild summit]

so should i find the midpoint of 9pi period?

[ancient saddle]

Is the maximum of a sinusoid at its midpoint?

[wild summit]

wouldnt the max point be reoccuring though since its a sinusoid, so all periods would have the same max / min point but just at different pi values

wouldnt the period be 2/9 aswell?

[ancient saddle]

Yeah but let's focus on its first period

Otherwise there would be infinite answers

I mean there are, but let's get just the "main" answer

[ancient saddle]

The period is 9pi as stated in the problem

[wild summit]

isnt the theory k = 2pi/k and k is the period

[wild summit]

i think the max would be (pi/2, 20) for the first period and the min is (3pi/2, 4)

[ancient saddle]

Mmm no, maybe check that again 🤔

Or there might be a typo in your class material (?

[wild summit]

this is like the summary for the chapter

period= 2pi/k

[ancient saddle]

Yes

But period is not k

[wild summit]

oh okay

[ancient saddle]

You can call the period T

[wild summit]

is there a way you are checking the graph on a website i am not sure how to check for which x value is max point at

[ancient saddle]

Mmm no I'm not using a website

You can use it if you want

There's a way to find the x value of the maximum of any sinusoid

[wild summit]

how can you do that?

[ancient saddle]

Anyway I thought that I could do the visual explanation

But you can use what you said before

That the maximum occurs at pi/2

So what's inside of sin must be pi/2

2pi/T x = pi/2

[wild summit]

so i was correct of the max being at x=pi/2 or ?

[ancient saddle]

That's not the max for this sinusoid with period 9pi

[ancient saddle]

The point (pi/2, 20) doesn't belong to that sinusoid

pi/2 is the max of a sinusoid with period 2pi

[lone heart]

@wild summit Has your question been resolved?

[wild summit]

so would it be (9pi/2, 20)

[ancient saddle]

No

So far you have
8sin(kx) + 12

Have you found k?

[wild summit]

2/9

[ancient saddle]

Ok great

8sin(2x/9) + 12

It's max when sin is 1

sin(a) = 1 when a=pi/2

[wild summit]

im confused im sorry 😭

[ancient saddle]

How did you get 20 as the max value?

[wild summit]

its the c value + a

so 12 + 8 = max y value

and min would be c - a = 4

[ancient saddle]

And why's that? 🤔

[wild summit]

is it incorrect?

[ancient saddle]

No,no

I mean is it just a formula you're using

Or is it something else you know

[wild summit]

oh no just the y values are affected from the variables outside the brackets

thats what i know

[ancient saddle]

Well when you do that, you assume that sin is 1

8*1 + 12

or -1

8*-1 + 12

sin is 1 when the input is pi/2

[ancient saddle]

What is the input to sin here?

[lone heart]

@wild summit Has your question been resolved?

[wild summit]

the input for sin is 8 >

[lone heart]

@wild summit Has your question been resolved?

[wild summit]

.close

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[opaque radish]

For 2x = - root 3

[opaque radish]

does squaring both sides give u 4x^2 = 3

or is it 4x^2 = -3

[raven rover]

The first

positive on the RHS

[opaque radish]

cos the orinigal question was 2x = tan 120

so 2x = - root 3

4x^2 = 3

x^2 = 3/4

x = +- root 3/2

[raven rover]

Why square both sides?

That's creating issues for you

[opaque radish]

when u just divide by 2 u get - root 3/2

but when u quare both sides u get +_

=-

+-

[raven rover]

Just divide by 2

Why square both sides?

[opaque radish]

idk there might be a question in the future that ask u to square both sides

[raven rover]

Does x = - (something) solve the eqn?

[raven rover]

It's not necessary here

Squaring both sides is "dangerous"

[opaque radish]

why

[raven rover]

Because you introduce extra solns

[sour dove]

you get an erroneous result in that case. tan(120) only has one value, not two

[raven rover]

Does x = root 3 / 2 solve your original eqn?

[opaque radish]

no

alright thanks

.close

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[fair wyvern]

Not sure why I got these wrong (will explain work)

[fair wyvern]

So, I made two different equations

One for the x side, so I said that Bcos(b)=Acos(a)

One for the y side, so Asin(a)+Bsin(b)=25.8

And then I plugged in a=44.4 and b=28.7

And solved for A and B by graphing

[quiet vector]

what do u mean by graphing?

also ur method seems fine to me recheck maybe u messed up a's and alphas or something

[fading moth]

seems like you set up the equations for the x and y components correctly

maybe check your numbers again

[fair wyvern]

Gotcha, ty

I did get a slightly different number

Rounding error perhaps

Fixed it

.close

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[gusty stratus]

Hey I need help on this

[marble coral]

Let's consider that they both left Antrim at time = 0
Belfast bus will leave Antrim at:
time = 0, 36, 36×2, 36×3...
Ballymena bus will leave Antrim at:
time = 0, 45, 45×2, 45×3...

You just have to discover when times are same not considering the 0

36 × n = 45 × k

Least Common Multiple question

[gusty stratus]

So we find the LCM of both and put them in a venn diagram???

[marble coral]

Just find the LCM and that's your answer lol

But convert to time of the day ofc

[gusty stratus]

How tho

Ohh

Acc yh

How

[marble coral]

Tell me the lcm

[marble coral]

My fault, it's 45

[gusty stratus]

Hold up lemme work it out

[marble coral]

36 and 45

[gusty stratus]

2x2x9x3x3x5

Is that how u find it?

1620

@marble coral

Huh?

[marble coral]

Wrong

First number is 2 yeah

You can divide by 2 again sorry

You did other error

[marble coral]

Show me step to step

36, 45 | 2
18, 45 | 2
9, 45 | ...
...

Like this

[subtle birch]

Divide only by factors which can divide both the numbers

Here 2 can divide 18 but no 45

[marble coral]

Don't need to

Answer will be the same anyway

[lone heart]

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[trim tendon]

how did they come up with the first two checks (a) and (b)? !?!?

[trim tendon]

i.e., their claim that for all i and j, f(1, i+j-1) ≤ f(i,j) < f(1, 1+j)

[lone heart]

@trim tendon Has your question been resolved?

[tacit arch]

Plug the given function in for f and verify

[lone heart]

@trim tendon Has your question been resolved?

[steel robin]

i have a question about graphing y= 6sin(2/3x) -3, how do I find the x axis scale numbers

[trim tendon]

I meant like

how did they come up with the formulas in the first place

what motivated their choice of those two "facts"

If I were solving a similar problem on my own in the future

how would I be able to see something like this on my own

because right now, it's a bit like "poof", magic, we claim that "this works" to me

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[dapper lynx]

Hey all

[dapper lynx]

I just want to make sure my path is on point before I proceed with part 2 of this question

[upbeat hornet]

It seems right

Another way you can check your answers is to use a 3d graphing calculator

[dapper lynx]

I did, that's how I knew it formed a long line

Its more the phrasing and interpretation I needed to confirm

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[dapper lynx]

.close

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[rich sigil]

quick question

[rich sigil]

if 2 particles

A and B are going opposite directions

and collide together

[upbeat hornet]

please draw it

[rich sigil]

my problem is part b

from what I got

[upbeat hornet]

You can apply the formula for conservation of momentum directly here

[rich sigil]

in part b?

my problem is interpreting the speed of A and B after the collision

[upbeat hornet]

oh, can you show your work?

[rich sigil]

would B's velocity be greater of less than A's velocity after the collision

yeah sure

it's a little scuffed cause I didn't intend on showing it

[upbeat hornet]

,rotate

[rich sigil]

💀

well part A is just a show that

well my first interpretation was to make v1 swing backwards

but it's not

so do I change the signs for part B

I wrote v1 = 3eu - v2

it might be v1 = v2 - 3eu

instead

and then I'd work out the speed for it and find range for e maybe

but im not sure

[upbeat hornet]

e is the ratio of the final kinetic energy and the initial kinetic energy, just to confirm?

[rich sigil]

not in this case no

it's the coefficient of restitution

[rich sigil]

I mean it could be that I'm just not sure

💀

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[alpine sable]

I don’t rlly understand how this works with roots. I’ve tried googling up stuff and it shows up but I don’t understand how they get it

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@alpine sable Has your question been resolved?

[alpine sable]

.close

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[dense scaffold]

yo does sm know how i can find the value of angle GWY

the only angle that is given is HYW that is 75degrees

<@&286206848099549185> 🥺

[gray quiver]

da hail

[gray quiver]

hahahahahahahaha
GYW is an isoceles triangle

[dense scaffold]

yes

how do i find the angle tho?

[gray quiver]

therefore gyw=gwy

[dense scaffold]

yes

and?

[gray quiver]

u r given, hyw= 75

[dense scaffold]

yes

[gray quiver]

hyw= hyg+gyw

[dense scaffold]

ok

[gray quiver]

give me a moment

If we join hw as well, we get a right angled triangle of hyw.

[dense scaffold]

how is that a right angled triangle?

[gray quiver]

SrySry a typing error

[dense scaffold]

all good

[gray quiver]

but

[dense scaffold]

please take ur time

[gray quiver]

if we join hw

[dense scaffold]

yea

id assume thatd be another isoceles triangle?

[gray quiver]

ee get hgy+ygw+wgh = 360degrees

[dense scaffold]

ok

[gray quiver]

in that case, hgy is congruent to hgw

[dense scaffold]

ok

[gray quiver]

WhiWhichWhiWhich grade r u in?

[dense scaffold]

imimimim im in 12th grade

[gray quiver]

😂alright

country?

[dense scaffold]

Canada

[gray quiver]

dammit

no wonder u have illegal questions

[dense scaffold]

whats ur country?

[gray quiver]

dude i am asian

[dense scaffold]

china?

[gray quiver]

ahem ahem therthere are other countries in asia other than china...

[dense scaffold]

ik im from pakistan

[gray quiver]

lol

[dense scaffold]

the assignment is canadian tho

[gray quiver]

oh

360/3

Ok
+

soo... Hyw= hwy

hwy = 75 degrees

now eequate them

[dense scaffold]

?

what do i equate them with?

[gray quiver]

Hyg+gyw=7and hwg+geygwy=7

75

[dense scaffold]

ok

what do i do after that?

[gray quiver]

ok stop
i git the answer

got

[dense scaffold]

✊

🫡

[gray quiver]

360/3= 120

[dense scaffold]

how ? how do u know they are equal

[gray quiver]

considering triangle gyw

180=120+2gwy

bcoz its an isosceles triangle

[dense scaffold]

wait

[gray quiver]

what?

[dense scaffold]

how is that angle 120? howd u get that?

how are those 3 angles equal?

[gray quiver]

herhere

its an assumption

[dense scaffold]

i get it 2 of them might be through congurency

[gray quiver]

the answer will tell us whether its right or not

the answer is 30

[dense scaffold]

oh ok

[gray quiver]

now if u evaluate u will get to know what the correct answer it

is

[dense scaffold]

thanks

.close

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[safe tartan]

Quick question, how do you prove three points are colinear in a vectors problem

[safe tartan]

For ABC line, would you just say AB + BC = AC ?

[fallen verge]

That doesnt prove they are collinear

Usually you would use dot products

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[cerulean talon]

<@&286206848099549185>

<@&286206848099549185>

[lone heart]

Show your work, and if possible, explain where you are stuck.

[cerulean talon]

I just need to know the answer cause when I worked through it, didn’t seem right

Basically

I used y=a(x-h)+k

And then I subbed in vertex for h and k

Solved for a which was -1

And I ended up getting y=-0.91x^2-1.82x+34.54…

Which is wrong

Here I wrote my steps

All messy, not all is relevant and it’s just spare paper I had from something else, ignore the question

Yeah, I need help basically

Where I went wrong or whatever

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

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[keen portal]

how do i start

[alpine sable]

thats tan x right

[keen portal]

yes

tan^2x and tanx

[alpine sable]

1 + tan^2 is sec^2

[keen portal]

yep

[alpine sable]

hold on lemme think about how to solve this

[keen portal]

derivative of sec^2x is tanx right

right

okay i got it

thanks @alpine sable

.close

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[orchid perch]

every human studies a profession only if they love it

[orchid perch]

does only if mean if and only if?

so if a human loves a profession does it mean they study it?

hmmm guess not

its one directional implication

[split valve]

yup same thoughts here

[orchid perch]

ight ty

.close

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[balmy hedge]

Need help

[alpine sable]

how can u find the (width+length) using perimeter

???

[upbeat hornet]

write out the formulas for perimeter and diagonal

and please try your best to ignore my username, but my username is a hint for one of the steps in the solution

[balmy hedge]

The formula for the perimeter is a+a+b+b or 2(a+b). a and b being the the sides

[alpine sable]

yes

so what is a+b

[balmy hedge]

But they only gave so little

[balmy hedge]

Thats two lines

19?

Idk

[alpine sable]

do you know pythagorean theorem

[balmy hedge]

Yes

a²+b²=c²

[alpine sable]

in this context what is c

[balmy hedge]

Or so i remember

Thats 15 cm

Or no?

[alpine sable]

so you have (a+b) and c right

[alpine sable]

yes

[balmy hedge]

Yes I do

[alpine sable]

how do you get a^2 + b^2 from (a+b)

[balmy hedge]

a+b is 19?

[alpine sable]

yes

[balmy hedge]

How

I dont know that part

You cant divide since its a rectangle

[alpine sable]

just square (a+b)

only like 3 more steps

[balmy hedge]

Ohh

Then whats next

[alpine sable]

how do you square (a+b)

[upbeat hornet]

(a + b)^2 = ?

[alpine sable]

hint its not his username

[balmy hedge]

Hmm

Just 19² no?

[alpine sable]

no i mean the algebraic formula with the a and b

[balmy hedge]

I dont know that

Show me

[alpine sable]

literal square of (a+b)

so add up all those terms what do you get

[balmy hedge]

Wait so we used pytha theorem right

[alpine sable]

not yet

this is just multiplying

[balmy hedge]

What are we using

Oh

[alpine sable]

algebra

[balmy hedge]

a²b²?

You said just square it

[alpine sable]

i said add the terms

[alpine sable]

look at the picture i sent

[balmy hedge]

a²+b²?

[alpine sable]

theres the two ab terms

where do they go

[alpine sable]

^

[upbeat hornet]

you fell for it

[balmy hedge]

I dont know bro

The triangle stuffs messed me up

[upbeat hornet]

the square has side length (a+b), so its area is (a+b)^2

You can also see from the diagram that it is made out of four rectangles, two of which are squares

What are the areas of the four rectangles?

[balmy hedge]

All of them together?

[alpine sable]

yes

[balmy hedge]

Not your name??

His*

[alpine sable]

(insert pronoun here)'s name is to confuse people on purpose

[balmy hedge]

Ah

[alpine sable]

so what are the areas

[balmy hedge]

Idk really

Just tell me

2(a+b) but that the perimeter (ab)2 is area??

[alpine sable]

dont bother with that just yet

[alpine sable]

well if you insist

[balmy hedge]

Yes

[alpine sable]

(a+b)^2 = a^2 + b^2 + 2ab

[balmy hedge]

Ohh i get it now

[alpine sable]

you know that the a2 + b2 = c2 and c = 15 right

[balmy hedge]

Yes

[alpine sable]

replace the a2 +b2 with 15^2

and replace (a+b)^2 with 19^2

[balmy hedge]

(a+b)²=15²+2ab

19²=15²+2ab

[alpine sable]

now what is 19^2 and 15^2

[balmy hedge]

361 atd 225

[alpine sable]

so what is 2ab

[balmy hedge]

361-225?

[alpine sable]

yes

[balmy hedge]

136 it

[alpine sable]

correct

u want to find the area right

the area is ab

so find ab

[balmy hedge]

68?

[alpine sable]

yes

thats ur answer

[balmy hedge]

68 is the area?

[alpine sable]

yes

[balmy hedge]

Ohh thanks

[alpine sable]

.close

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[summer stratus]

sry just a quick one

is this line smooth?pls be precise and honest

<@&286206848099549185>

[upbeat hornet]

smooth enough

[fluid venture]

looks pretty smooth to me

[summer stratus]

line connecting point 3 and 4 looks a little weird?

[fluid venture]

the function seems analytic which means it's as smooth as it can get

btw all exponential and trigonometric functions are analytic

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[fresh arch]

Can this be done by pythagoras theorem and BPT instead of trigonometry(If yes then how)?

[fresh arch]

<@&286206848099549185>

[upbeat hornet]

what’s bpt

do you know what AB is?

[fresh arch]

Basic proportionality theorem

[upbeat hornet]

is that like intercept theorem

can you state it?

[fresh arch]

If a straight line is drawn parallel to one side of a triangle then it divides the other two sides proportionally

[tardy stag]

mayybe? (try it!) you don't know how long the midline of the triangle is though (the point's not even labeled) so you'll have to figure that out

[fresh arch]

Yes the place where I saw the solution said it could be done by pythagoras theorem but i can't figure out how

The hard part is finding CD in terms of AB

After that I know what to do

[tardy stag]

the fact that it's equilateral is definitely important

what i'd probably do is start by assigning AB a variable and seeing what else I can write in terms of it

[fresh arch]

Yeah that's what I did

AB= AC =BC =l

Angle CAD =30

And angle DCA = 60

[lone heart]

@fresh arch Has your question been resolved?

[lone heart]

@fresh arch Has your question been resolved?

[alpine sable]

can anyone help me with math

[lone heart]

@fresh arch Has your question been resolved?

[lone heart]

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[alpine sable]

yoyo i need assisstance

[cinder thicket]

Yoyo

What is it

[alpine sable]

can you help with this stuff

[cinder thicket]

What did you try?

[alpine sable]

umm so the spheres volume is 4/3 pi r^3

so i applied it

1.2 * 1.2 * 1.2

i ended up with 1.728

then multiplied with 3.14

5.42592

then multiply by 4/3

correct?

[coral thorn]

that'll give you the volume

[alpine sable]

yup

[coral thorn]

what did you do after that

[cinder thicket]

Convert mm into cm

[alpine sable]

wait deadass?

convert?

[coral thorn]

yes

[alpine sable]

umm give ne a sex

sedx

sec

sec i mean sec

1.2 * 10^-5

right?

[cinder thicket]

My guy

What?

[coral thorn]

millimeters into centimeters

[cinder thicket]

You tripping bro

[coral thorn]

divide the value by 10

[alpine sable]

very much

[alpine sable]

bro i converted to meter then tocenti

1.2* 10^-1

there we go

[cinder thicket]

Yes

[alpine sable]

then what?

[cinder thicket]

M=vd

[alpine sable]

huh?

[cinder thicket]

V is volume

D is density

M is mass

[alpine sable]

oh nvm i get it

ok continue

[cinder thicket]

Multiply v with d

That's it

[alpine sable]

we still havent founf v

[cinder thicket]

?

[coral thorn]

v is volume

[alpine sable]

we only have the radius

[coral thorn]

you just calculated the volume

[alpine sable]

havent done no squaring

[coral thorn]

.

[cinder thicket]

Blud what is the drop shape?

Sphere

[alpine sable]

we didnt do tgat

[coral thorn]

[alpine sable]

THATS ME

[coral thorn]

real

[alpine sable]

IM WAY TO HIGH FOR THIS

science got me fucked

[coral thorn]

[alpine sable]

pls yall

[cinder thicket]

Me when chemistry

[alpine sable]

we only converted 1.2 to cm

[coral thorn]

bruh

[cinder thicket]

Ok

[coral thorn]

use the volume formula again

your radius is in cm now

[alpine sable]

ok

[coral thorn]

then just use this to get the mass

[alpine sable]

so (1.2 * 10^-1) ^2

[cinder thicket]

Bro has a feud with parentheses

[coral thorn]

just use 0.12 to make your life easier

[alpine sable]

ok

[cinder thicket]

Nah

[coral thorn]

and cube it

[alpine sable]

i was gonna say we addd the powers

cause thats a thing now

[coral thorn]

$\frac {4}{3} \pi r^{3}$

[ocean seal]

__saad

[alpine sable]

0.001728

correct?

[coral thorn]

0.00724

[alpine sable]

the we multiply by 3.14 to get 0.00542592

[alpine sable]

heh?

[coral thorn]

after using the volume formula

[alpine sable]

so after everything its that

[coral thorn]

yes

[alpine sable]

ok much faster

so then we multiply by d

[coral thorn]

yes

[alpine sable]

which is 13.6

[coral thorn]

yes

[alpine sable]

0.098464

[coral thorn]

looks right

[alpine sable]

then into scientific notation

with only 3 sig. figures

[coral thorn]

that should be easy for you

[alpine sable]

9.85 * 10^-2

thats not the answer tho

[coral thorn]

what is the answer

[alpine sable]

it is what is written in the pic

that is i believe the right answer from the practice quiz

[coral thorn]

oh

i used pi instead of 3.14

[alpine sable]

oh cmon man

[coral thorn]

sorry

[alpine sable]

0.00542592

here it is

[coral thorn]

no

[alpine sable]

bro ive been using a calculator

tf u mean no?

[coral thorn]

wtf

wait

did you cube 0.12

[alpine sable]

yes

[coral thorn]

impossible

[alpine sable]

i got that answer in the end

what i wrote was before 4/3

after all of the calculations

u get 0.098390016

which goes to 9.84 *10^-2

still not correct

u know what im sorry but i gotta go

i gotta sleep tomorrow is my final

see ya saad

.close

[lone heart]

Channel closed

Closed by @cursive musk

Use .reopen if this was a mistake.