help-26

[formal edge]

And c for cos

[fading zephyr]

we can write this as sin(-(540-A))

[tulip monolith]

You did it quite directly without much steps to understand how you got there.

[fading zephyr]

and we can take the minus symbol out

[formal edge]

Can I send one I did already?

[fading zephyr]

so we get -sin(540 - A)

[fading zephyr]

yes

[tulip monolith]

Sure but if you explain how you got there maybe we can explain where and why you went wrong.

[formal edge]

J is correct

[fading zephyr]

wow

this is one way to solve it

but there is a much simpler way

to do it

[formal edge]

So I use this thing with two axes. And then based on if the angle is added or subtracted I change the actual thing for example if cos (720 + x ) was given I'd simplify it to cos x because in the first quarter all of them are positive

Cos (720 - x) would still be cos x because it's then in the fourth quarter where cos is positive

X is always a sharp angle so less than 90 degrees

Or theta

[formal edge]

This was the recommended one from our school

I'm no prodigy, I just want to get this equation to be equal to zero

[fading zephyr]

well can i tell you the other way? or is this method mandatory

[formal edge]

And understand why

[fading zephyr]

so

[formal edge]

I'd say this is mandatory, because tests are marked according to steps

These steps*

[fading zephyr]

oh

my bad

[formal edge]

Anyways

Back to the actual question

[fading zephyr]

if thats the case you can try expanding the numerator and the denominator

using the identities

[formal edge]

How is it that sin(A-540) can be simplified to -sinA and not sinA

[fading zephyr]

yes so

we can write sin(A - 540) as sin(-(540-A))

and by doing that

[tulip monolith]

sine is an odd function, so f(-x) = -f(x).

[fading zephyr]

we take the negative sign outside

[formal edge]

OHHHHH

You guys are right

[tulip monolith]

\sin(-x) = -\sin(x)

[formal edge]

Yeah this

[tulip monolith]

540 is just 3pi

[fading zephyr]

oh yes this too

[tulip monolith]

So yeah do your axes thing

[fading zephyr]

yeah

[formal edge]

Lmao, I'm just trying to breathe through this exam

[fading zephyr]

and sin 3pi - A is just sinA

[formal edge]

The notation in other countries is so advanced but anyway thanks

[tulip monolith]

Its 3pi - A in this case

[fading zephyr]

np

[formal edge]

Ok, I'll close, cheers

.close

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[magic grail]

Does anyone know how to simplify this trigonometric expression? The resultant is tan(nα).

[magic grail]

Should I use successions or something like that? I haven't studied that yet. This is the first exercise I've seen of this style.

and sen is the same as sin

[cursive patrol]

hint: ||sum to product|| trig identity

[heavy bay]

hot milk:

At the café, the waiter heats 220 mL of milk by injecting water vapor at 120.0°C.

The milk, initially at 18°C, is heated to 60.0°C.

Suppose that heat transfers take place only between milk and water vapor,

and all the injected steam becomes liquid and then cools to 60.0°C.

Compact statement:

• What mass of water vapor should the server inject?

Detailed statement:

1- Calculate the energy received by the milk to heat up from 18.0°C to 60°C.

2- Express, according to the mass m of injected water vapor:

a- The energy released by this steam as it cools to 100.0°C.

b- The energy released by this water vapor when it becomes liquid.

c- The energy released by the liquid water formed by being cooled from 100°C to 60.0°C.

3- Using a balance of energy exchanges, calculate the mass m of steam that the server injected into the milk.

• Data:

• Density of milk:

• ρ milk = 1.00 kg. L-1

• Specific energy of water liquefaction

• Lℓ = – 2257 kJ. kg–1

• Energy transferred during a temperature variation Δθ without change of state,

of the mass m of a body of specific heat capacity c:

-Q = m. vs. Δθ

• water (g) = 1.89 kJ. kg–1 . °C–1

• c lait (ℓ) = water (ℓ) = 4.18 kJ. kg–1 . °C–1

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[magic grail]

hmm

What am I supposed to do with that identity?

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@magic grail Has your question been resolved?

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@magic grail Has your question been resolved?

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[serene flax]

help

[polar laurel]

a+b/2 * h

7 + 14.9 + 6.4 / 2 * 8

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[neon iron]

does

[neon iron]

i mean, im confused on how to proceed with this problem

[worthy storm]

try to get an x - pi/2 in the denominator

[gray harbor]

Have you tried applying lhospital?

[neon iron]

this is what i came up with

[twilit nimbus]

Where did the y come from if you are applying l’hoptial

[neon iron]

i was just trying to make the denominator the same with the numerator

[twilit nimbus]

Oh

Ok

[neon iron]

i guess it's wrong OuO

[twilit nimbus]

Use lhoptial if you learned it

[neon iron]

i will try it

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[neon iron]

thanks in advance!

by the way just pretend h was positive

i dont understand why these methods are yielding different results, they are in correct form, and correct evaluation of expressions

and i took a screenshot of the method provided by the book, but i cant seem to make it work, the picture above shows my work

ty

[flat kindle]

It's a bit messy can you explain what you've done in words?

[neon iron]

yeah

sorry

i took an equation f(x)=x^2

then i made up a transformaiton, f(2x-3)

then i also represented it in the form on f(2(x-3/2))

and following the transformation guidelines on the book screenshot, i applied the method to each of the transformations in the way it said to for the form they are in

-3 -2 -1 0 1 2 3 for each one

got different answers, but they are the same expression

hm... does that make sense?

<@&286206848099549185>

[radiant marlin]

is it this?

[neon iron]

dang no

well

yes

wair

wait

haha

yeah

i agree

but its hard to say the book made an error

ya know?

.close

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[patent dome]

Can you please help me with 1.2

[nova relic]

think of how you can make it so that the denominator has no square root

Hint: sqrt(x)*sqrt(x)=x

[patent dome]

This is what I got

[patent dome]

Hello?

Is it right?

[nova relic]

yes it is

[patent dome]

Thanks

. close

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[velvet pecan]

can anyone help me with this?

[spare monolith]

$x+\frac{a}{b} = \frac{bx+a}{b}$

[thorny flame]

Good

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[fervent bane]

Why plus

[digital river]

Integration by parts

[fervent bane]

I know

Why + h/i f'

(f)* is complex conjugate btw

[digital river]

Yeah

[fervent bane]

Why not -

[digital river]

Oh, because you moved the h/i inside the conjugate

i* = -i

Normally it would be $-\int_{-\infty}^{\infty}\frac{h}{i}\left(\frac{df}{dx}\right)^*gdx$

[thorny flame]

MSC2020 47A15

[digital river]

but you can bring h/i in, but that becomes h/-i

so you bring the - out to cancel

[fervent bane]

Right

Thanks

[digital river]

👍

[fervent bane]

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[severe jackal]

I'm trying to solve this related rates problem. I tried creating the formula first and then plugging in the rate of change (2m^3 /min ) for dh/dt and I got 8pi converting that to decimals since achieve won't let me put a Pi in the answer box. My work is on the left and the problem is on the right

[ruby mural]

V= pi/3 (r²h), if you wanna differentiate it wrt t then you're gonna have to use the product rule

[severe jackal]

Oh ok, So I just took the wrong deriivative

So would dh/dt at h=1.9 be 31.8348?

@ruby mural

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@severe jackal Has your question been resolved?

[severe jackal]

<@&286206848099549185> Any help?

[jolly totem]

WSP

[jolly totem]

use this

[severe jackal]

I did but I don't think I did it right

[jolly totem]

show

[jolly totem]

i cant see very well

but what i will say is try get r in terms of h

<@&286206848099549185>

can someone else jump in i gotta do smth

[severe jackal]

.CLOSE

.close

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[ivory cipher]

How can I express x from this equation

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[worthy storm]

what is $a$, and what do $a[k]$ and $a\lceil k\rceil$ mean?

[thorny flame]

Bungo

[ivory cipher]

its a set

of numbers

and a[k] is just a and index k

its a screenshot from desmos

[worthy storm]

and x is just some number that is not equal to any of the a[k]'s?

[ivory cipher]

ye I took the derivate of the function and I am just finding the local minimum

its only a[k]

[worthy storm]

well you can simplify by observing that $\frac{a[k]-x}{|a[k]-x|}$ is $1$ or $-1$ depending on whether $a[k] - x >0$ or $<0$

[thorny flame]

Bungo

[ivory cipher]

I know but

not quite sure how would that help

[odd pagoda]

!original

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[ivory cipher]

okeoke

I was trying to find the local minimum of this function

so I easily took the derivative of the fist part:

which is:

and then the second part

(I am missing 1/2 in this images)

(I just forgot to put it there but I did use it for the calcualtions)

(and there shoudln't be that minus sign)

so I got this equation to find the local minimum

and then tried to simplify it

[ivory cipher]

and arrived at this expression

[ivory cipher]

it should be

well

desmos has some truble rendering '['

there's no ceil of k

its only a[k]

but it just gets rendered incorrectly

[odd pagoda]

there is a problem with this approach. the function isnt differentiable everywhere. which means the derivative might not be zero at the min, it might not even exist

[ivory cipher]

Do you mean the second part of it?

[odd pagoda]

yes

[ivory cipher]

yes well the first part simplifies to just the averages of those values in the set

you mean around those sharp edges?

[odd pagoda]

yes

in particular the minimum you dont have derivative 0

[ivory cipher]

or that the in derivative ak can't be equal to x

well

but if I add them put again and only check if those added derivaes are 0 shouldn't that

I mean if I just plug that equation into desmos it will display the correct minimum

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[marsh geyser]

knowing that we have an arithmetic progression with an odd number of terms, and the first term is 3 and the last term is 27. Is there any reason that causes the middle term to be different from 15? (there are no restrictions on whether reason is natural, integer or rational)

[keen matrix]

well the middle term is 15th because 15 is the average of 3 and 27 if that's what you mean

[long stirrup]

always

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[marsh geyser]

ye but is there anyway the midterm is not 15

with an odd number of terms

[marsh geyser]

rlly

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[neon iron]

I want the answer for domain and range of this function

[neon iron]

Do I have to only solve the denominator to find the domain or both numerator and denominator for the domain?

[obtuse garden]

both

[neon iron]

By solving the denominator I am getting this

[obtuse garden]

you also have to keep in mind the fraction has to be +ve

or 0

otherwise itll be a complex root

[neon iron]

What do I do now?

And numerator this

[obtuse garden]

it doenst necessarily have to be lesser than 0

because if both numerator and denominator are negative

then the fraction is +ve so you have to account for that

[neon iron]

So what to do after this

[obtuse garden]

is that a +3x or -3x?

[neon iron]

-3x

[obtuse garden]

you can cancel factors

[neon iron]

K 1 sec

[obtuse garden]

alr

[neon iron]

No I don't think

Cus

[obtuse garden]

cause?

[neon iron]

This can't be solved further

[obtuse garden]

i shouldve clarified what i meant

as in

factorise both of them

[neon iron]

I only need to know what should I do after finding the domain for both denominator and numbnator?

Cus both of these are correct

[obtuse garden]

these are correct but the fraction can be simplified

factorise the numerator and denominatoe separately

[neon iron]

Can you represent it on paper?

[obtuse garden]

do you know how to factorise quadratic polynomials?

[neon iron]

Yes

[obtuse garden]

so factorise the numerator and denominator separately

[neon iron]

Like mid term split right?

[obtuse garden]

yes

[neon iron]

There

[obtuse garden]

now you can simplify the fraction

((x-1)(x-2)/((x-2)(x-3))

you can cancel the (x-2)

and then the fraction will be (x-1)/(x-3)

[neon iron]

So can this be the answer?

[obtuse garden]

can you send it right side up

[neon iron]

Sorry

[obtuse garden]

yeah so try to write x>3 in interval notation

and solve for when both numerator and denominator are negative ie the fraction itself is +ve

ie
x-1<0
x-3<0

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[marble quartz]

Hello

[marble quartz]

I am trying to make it like this.idk what to do?

Like this

The green step idk what to do in my problem

?

[neon iron]

the green section looks like a quadratic

[fallow igloo]

Set a quadratic function and give it an interval

[marble quartz]

I know that but I tried but i am not sure what numbers to give so it connects

[fallow igloo]

Connect with this?

[marble quartz]

One second

Let me try

Honestly it doesnot work not sure why?

It is just too small.

[neon iron]

well the vertex looks like (10, 50)

[fallow igloo]

You can use Newton polynomial to set that

[neon iron]

so use vertex form and drag an A slider until you get a cross

or use lagrange interpolation

[marble quartz]

Could anyone come on a call?

I feel it is easier

[fallow igloo]

y=(x-(the x cord of the spot))(ax+b)+y cord

[marble quartz]

Quick 2 min

[neon iron]

cant srry

[fallow igloo]

Sry, my English isn’t that good

[marble quartz]

Its fine.

[fallow igloo]

I’m afraid that I can’t vc

[marble quartz]

I dont care about english

[fallow igloo]

you sure?

[marble quartz]

Hundred percent

[fallow igloo]

DM

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[fallow igloo]

!done

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[raven cove]

Can someone help explain to me the difference between signed vs signed and magnitude? or do they usually mean the same thing?

[raven cove]

I cant wrap my head around what the difference between signed vs signed magnitude

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[neon iron]

can someone help me with this question

[topaz sinew]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[sudden barn]

.

[neon iron]

3

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[neon iron]

.close

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[main vapor]

I can help

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[pseudo sonnet]

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[hollow rose]

So using sin(x+90) = cos(x)
sin(135) = sin(135-90) = cos(45)
Correct?
Is the middle step valid?

[rocky gulch]

cos(x) = sin(90-x) not sin(90+x)

if you want sin(135) calculated easily write it as sin(90+45) and use sin(a+b) formula

[hollow rose]

sin(x+90) still equals cosx

[rocky gulch]

yeah but for your exercise you didnt use it right

[hollow rose]

Can you show me how to use it properly then?

[rocky gulch]

sin(135) = cos(135+90) = cos(135-90)

a known value for all these is cos(135-90) which is sqrt(2)/2

[hollow rose]

Yeah

How did we go from cos(135+90) to cos(135-90)?

[rocky gulch]

its the same

[hollow rose]

Oh okay is that because graph transformations inside the bracket appear to do the opposite of what we expect them to?

[rocky gulch]

$\sin(\frac{\pi}{2}+x) = \sin(\frac{\pi}{2}-x)$

[thorny flame]

dqvidutzul

[hollow rose]

Yeah

[rocky gulch]

uhh what

[hollow rose]

Take the a point on f(x)

Now transform to f(x+3)

that point is now

(x-3, y)

So we took away 3 instead of added

Is that the same case here?

[rocky gulch]

i have no idea

sorry 😭

[hollow rose]

Nah dw about it

[rocky gulch]

im not really good with visualizing math inside my head

[hollow rose]

Okay wait

So let's say we are only using sin(x+90) = cosx

and nothing else

Say we want to find the cofunction of sin(135)

x+90=135
x=45

cos(45)

Cool I got it

[rocky gulch]

yuh

[hollow rose]

Thanks for your help

[rocky gulch]

hope you understood

[hollow rose]

Yep, I do now

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[sacred rose]

hi

[topaz sinew]

Please don't occupy multiple help channels.

[sacred rose]

ineed hele

[sacred rose]

a+b

+d

*a

(a+b)

[cinder void]

what

please elaborate

[worthy storm]

appears to be a duplicate of #help-46

please use only one channel

.close

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[timber schooner]

5 six-sided dices are rolled and they have to give you an ascending number (1,2,3,4,5 OR 2,3,4,5,6)

[timber schooner]

order of the numbers given does not matter

so 1,3,2,4,5 is still ascending

how many different ways are there to get ascending

[covert current]

!status

[topaz sinew]

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1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[timber schooner]

ok so

i think the answer is 2 * 10

2 different ways to get ascending

multiplied by 10 because 10 different ways to order each outcome

so 20 / 6^5 is what i think the answer is

i would like my answer checked 👍

[covert current]

How did you get 10

[timber schooner]

10 different ways to order

[covert current]

Yeah what logic did you use

[timber schooner]

uh

one sec

each box represents a dice rolled

first box can be switched into 4 different positions

then i kept going

2nd box can be switched into 3 different positions

3rd box can be swithced into 2 different positions

4th box can be switched into 1 different position

5th box cant be switched (already been counted)

,calc 4+3+2+1

[thorny flame]

Result:

10

[timber schooner]

10

thats how i got 20 different outcomes (2*10)

👍

[covert current]

So

the first number can be 5 different numbers right

[timber schooner]

yes i guess

[covert current]

So how many numbers can the 2nd number be

After I choose the first number

[timber schooner]

5 again

[covert current]

4

[timber schooner]

how

[covert current]

Because I have 4 numbers left

1,2,3,4,5

The first number can be any 5

But after I choose the first number

[timber schooner]

its a six sided dice

[covert current]

no but we are finding combinations of 1,2,3,4,5

[timber schooner]

ohh

right

yes

mb

5 * 4 * 3 * 2?

[covert current]

yeah

[timber schooner]

oh i did it wrong

[covert current]

so its actually 2* 5!

[timber schooner]

yeah

ooo

yeah

you're def right

[covert current]

👍

[timber schooner]

240 / 6^5

,calc 240/6^5

[thorny flame]

Result:

0.030864197530864

[covert current]

3% chance

[timber schooner]

yeah

the cahnces of getting 5 repeated numbers

is

just 6 right?

1,1,1,1,1

2,2,2,2,2

3,3,3,3,3

etc

[covert current]

Yeah

there are 6 ways of 5 consecutive numbers

[timber schooner]

also

how would this look like

using combinatorics/permutation

like the actual letters

is it just 5P5

[covert current]

Yes

2 * 5p5

I have 5 numbers I want to choose 5 with order matters

[timber schooner]

okay

final question

how would we calcultae the chances of getting 2 pairs of repeated numbers

so like

1,1, 2,2, 3

where 1 and 2 are repeated twice

but like every other outcome

does that make sense

[covert current]

Uhhhh

So the chance of 2 pairs after rolling 5 times?

@timber schooner

[timber schooner]

yes

so 2 different numbers are repeated twice

do you know what i mean?

[covert current]

2 different

AACBB AABBC

[timber schooner]

yes

[covert current]

So multiply the chance of AABBC by 2

and AA can be 5 numbers right

[azure panther]

choose three numbers ( c(6,3) ) then c(3,2) are repeated then use repeated places : 5!/2!2!
its a bit complicated => 20 * 3 * 30

[timber schooner]

AA can be 6

[covert current]

Combination problems are complicated

6 yeah I guess

[timber schooner]

6, 6
5,5
4,4
3,3
2,2
1,1

these all can be AA

BB can be anything but AA

so 5

[covert current]

So 6*5*4*2?

That sounds so wrong

[timber schooner]

wait what if the numbers dont have to be right next to each other

so it can be
A B A B C

[covert current]

I don’t think this is right ;-;

[timber schooner]

why not

[covert current]

Idk

[timber schooner]

what makes it sound wrong tho

[covert current]

Gtg

[covert current]

This person sounds more credible

[timber schooner]

can you further explain

im a bit confused

[azure panther]

so do you know how many different ways can we arrange AABBC ?

[timber schooner]

30

[covert current]

I mean AABBC can really be simplified to ABC

so if you had 6 numbers you choose 3 with order matters

[timber schooner]

6P3

[covert current]

6*5*4*2 I don’t really see where the logic falls

[azure panther]

no not really

ABACC is not the same with AABBC

AA is not connected

[covert current]

^

[azure panther]

ik

but dices are different

its permutation with repetition

[timber schooner]

why doesnt 6 * 5 work tho

and also after figuring out theres 30 different ways to arrange it

what now

[azure panther]

its true

but idk how you got 5 * 6

but 30 is true

[timber schooner]

okay so look

rolling 5 dices right?

[timber schooner]

first roll can be any of the 6
second roll has to be whatever the first number was

third roll can be any number but not the one before so 5 different numbers
fourth roll has to be whatever number the third roll was

fifth roll (C) can be any of the 6 numbers since it wont affect anything, having 3 of the same number (AAABB) is still considered winning on twins

this gives us

6 * 5 * 6

^^ this is WITHOUT considering order though

so now i just gotta figure out how many different ways we can arrange this

6 * 5 * 6 * 30 sounds too big

[azure panther]

oh wait

so if AABBA is considered winning on twins

it would get a little bit harder

[timber schooner]

mmmm

okay say C cant be A or B

i still think 6 * 5 * 4

is too big

it doesnt sound right

,calc 6 * 5 * 4 * 30

[thorny flame]

Result:

3600

[timber schooner]

3600 different ways to win on twins sounds wrong

[azure panther]

yeh its 1800

because

you have 2 twins

so you need to divide it by 4

not 2

[azure panther]

.

https://testbook.com/maths/permutation-with-repetition#:~:text=The Permutation with Repetition is,(r times).

i think you need to read this

[timber schooner]

for 5!/2!2!

why is 5! numerator

[azure panther]

because of different ways you can arrange AABBC

[timber schooner]

where did you get 5 from tthough

i know that gives you the number of ways you can rearrange AABBC

5 is 5 dice rolls?

[azure panther]

yeh

[timber schooner]

and then getting 4 repeated

ohh

[azure panther]

yeh yeh

[timber schooner]

mmm ok

30

and how did you calculate the chances of getting AA BB C

C(6,3)

selecting 3 different numbers from 6?

[azure panther]

yeh if c is different

there are 3 differnet numbers

so 3 choices out of 6 available

1 2 3 4 5 6

we need to choose 3 out of 6

[timber schooner]

3 different ones

and then whats 3C2

c(3,2)

[azure panther]

because out of those 3 different numbers that we have chosen

we need 2 of them to be repeated

and 1 to stay normal

[timber schooner]

so c(6,3) * c(3,2) ?

[azure panther]

true

we could further simplify this when solving but i wanted my explanation to be complete

and easier to understand

[timber schooner]

,calc 1800 / 6^5

[thorny flame]

Result:

0.23148148148148

[timber schooner]

23% chance to win

mhmm

[timber schooner]

and how would we go about doing this if C can be A or B

so it can be AA BB A

[azure panther]

idk

i have to think more

since we are counting extra stuff if we consider that

[timber schooner]

yeah cause then it would also affect arrangements

could possibly become 5!/3!2!

right?

to count it, we would probabily need to go through the outcomes themselves

[azure panther]

yeh true

[timber schooner]

so chance of AAABB happening times by two

because AAABB is the same chance of AABBB

and then

[timber schooner]

we add that to this

right?

[azure panther]

no not really

[timber schooner]

oh wait no

[azure panther]

since we can count extra stuff

actually maybe not

yeh i think we can calculate that and add it

im not sure tho

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[hollow meteor]

I am trying to show this

linear regression model

[hollow meteor]

should be this instead

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[raven plank]

Hi I want some clarification regarding limits of sequences. If I have a convergent sequence a_n then is the limit of a_(n+1) always equal to a_n?

[raven plank]

this sequence for example

with a1=0

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[cinder void]

<@&268886789983436800> ?

[twilit nimbus]

Scam

[ivory sorrel]

!nogpt

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Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

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[topaz sinew]

@neon iron Has your question been resolved?

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[graceful smelt]

can someone help me with this question? i'm not quite sure where to start.

i tried finding the height of the trough (sqrt3) and tried setting dW/dt = 2 but i have no idea where to proceed from there, or if i'm even considering the problem correctly

can someone help guide me through this problem?

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@graceful smelt Has your question been resolved?

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@graceful smelt Has your question been resolved?

[rose thorn]

I think your sqrt(3) might not be quite correct, try redoing that calculation, I'm coming out at total height = 1

Note that isosceles =/= equilateral, maybe that was your mistake? Not sure

[graceful smelt]

the side lengths of the triangle is 2, sqrt(2), sqrt(2), is it not?

[rose thorn]

hmmm good chance that I'm also just bad at math

one sec

Yeah, but then how did you get the height sqrt(3) from that?

[graceful smelt]

i drew the altitude from the base of length 2 which is the height, and i used pythag's

[rose thorn]

Yea, and then the equation is 1^2 + h^2 = 2, right?

[graceful smelt]

i am stupid ahhh i did it with the wrong sides haha

[rose thorn]

😄 happens

[graceful smelt]

yeah you would be correct h would be 1

[rose thorn]

okay, good start! now, the way that this problem works is that you have the amount of volume flowing in, and you want to understand the height

First thing to try: if the water is at height h, what is the volume of water in the trough? That's just an easy geometry thing, and will probably help us

Lemme know if you're able to calculate that

[graceful smelt]

the volume is 9 right?

[rose thorn]

Yea the total volume is 9

How does that scale when your water is not at the total height, but somewhere lower?

[graceful smelt]

i'm not quite sure, it's 9 * the area of the triangle formed by the water but i don't know how to represent that with numbers

since the base of the triangle (assuming the base is the top side of the triangle) changes with the height of the water

[rose thorn]

It does, yeah! Can you express the base of the triangle in terms of the height?

[graceful smelt]

yeah that's where i'm stuck 😭 i'mma give it another shot really quick tho

[rose thorn]

There's many ways to calculate that, have a look and lemme know if you've gotten somewhere!

[graceful smelt]

oh wait isn't the base just the same as (1-w) * 2 (w = height of water)

[rose thorn]

that equation would be wrong when w = 1

'cus we already know the base length then

Unless you're writing the height upside down?

[graceful smelt]

uh i'm not sure

this is my work, i tried using similar triangles but after the screw up with pythag i don't even know if i'm able to do basic math anymore lmao

and you're right, if h = 1 then the base would be 0 which doesn't make sense

omg

wait i know where i went wrong 🤦‍♀️

base = 2 * water height?

so the volume of the trough would be 9h^2, where h is the height of the water

[rose thorn]

ayyyye that's right

Okay, so now you have the volume in dependence of the height. But you're actually interested in the inverse relation, the height in terms of the volume

because the volume is what you have information about, so how much volume of water flows in every minute

Does that give you some inspiration?

[graceful smelt]

well i'm given that the volume of water flows in at a rate of 2 ft^3/min (so dV/dt = 2???)

h=sqrt(V)/3, would deriving that in relation to t do anything?

doing that gives me dh/dt = 1 / (3 * sqrt(V)), or 1/9h
not sure what to do with that

i'm confused on how to incorporate the 2 minutes after the water begins to flow

i understand i have to calculate dh/dt but not sure how to go about that

[rose thorn]

If you know that dV/dt = 2, what is V as a function of t then?

You wanna make every unknown as explicit as possible, so let's try to get an explicit function for V(t)

[graceful smelt]

2V...?

[rose thorn]

2t 😄

[graceful smelt]

oh right

really caught me in a bad time of the day 😭

[rose thorn]

It's assumed that the rate of flow is constant, so every minute you're getting 2 minutes of water in -> 2t

it happens to the best of us hahaha

but you're really close now

[rose thorn]

go back to this with the explicit formula for V(t)

[graceful smelt]

so that would give dh/dt = 1/6?

[rose thorn]

idk maybe i didn't do the calculation

but if you took the derivative right then probably

[graceful smelt]

it's one of the options in the mcq so hopefully haha

i'm going to double check it i don't trust myself anymore

but that does help a ton, thank you so much for your time

[rose thorn]

don't forget adding units btw

[graceful smelt]

👍

.close

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[rose thorn]

ye 1/6 is good

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[neon iron]

If reading of spring balance= (force on spring)/g. Does the reading change when I have g_eff instead of g?

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[radiant marlin]

@neon iron it would because it's measuring mass, g_eff would change but so would the force in equal amounts

[neon iron]

Don’t understand what you mean

[radiant marlin]

like I assume you mean using a balance on the moon or whatever, there g is 1/6 of earth but the force of gravity is 1/6 too

so like F/g = (1/6F)/(1/6g) is fine

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[neon iron]

Sorry for my poor wording but I meant like say along an incline with angle theta. The effective gravity acting is mgsin(theta).

[radiant marlin]

yea that'd change because the reading is using normal g but the force gets a sin(theta) factor

like clearly pushing a balance at an angle changes it

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[trim owl]

Qs 5 c

I could solve it with arithmetical by gp sum but I didn't understand intuition behind

This is solution given

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[trim owl]

<@&286206848099549185>

[trim owl]

<@&286206848099549185> I just need to understand who we land 2 out every 7 numbers

No one to help me 😦 <@&286206848099549185>

[radiant marlin]

they do 1/x on 7/2 to get 1/(7/2)=2/7 of the numbers

it makes more sense with easier numbers, like if I keep adding 3 like 1->4->7->10->..., I'm basically hitting 1/3 of all the numbers

so adding 7/2 would be like adding 1/(7/2) of all the numbers

[trim owl]

I didn't get u

I don't even understand why we are taking reverse and what that signifies

I understood that expected value will 7/2

[trim owl]

Of every roll

[radiant marlin]

yea so 7/2 is the distance between rolls, and we want the density of those numbers on the number line

like for every stretch of 7/2, there'll be 1 landing

the longer the rolls the thinner all the landings on the number line will be right?

[trim owl]

Yes landings will start to concentrate towards center of the stretch

3.5/1 we break into stretch

So for every sum probability is 1/3.5

What is this topic called?

How were we able to treat expect value this way

[radiant marlin]

hmm I'm not sure, sometimes there's something called recurrence in probability where and expected value evens out over everything

[trim owl]

Aah okay got it

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[vivid berry]

When taking a derivative, is d/dx = 0/0 a critical value?

[acoustic pecan]

whats the definition of a critical point/value

[vivid berry]

A min/max point

[covert current]

0/0 is undefined

[wary tulip]

!original

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[acoustic pecan]

that all?

[outer portal]

speak up bro
did you get 0/0 from the limit definition of the derivative?

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[timber schooner]

$x^2+y^2= 117 \ x-y=3 \ \ \text{Solve for x & y}$

[thorny flame]

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

[verbal crater]

isolate x or y from the linear equation

put it into the first equation

solve

[timber schooner]

do i need to square root the first equation

or na

[verbal crater]

no

you have x - y = 3

then just isolate x or y

then put it in the first

you should have a quadratic eq

[timber schooner]

one sec

expanding (y+3)^2

that should give

$y^2+6y+9$

[thorny flame]

pixel

[rocky gulch]

yup

all that + y^2 = 117

[timber schooner]

$2y^2+6y+9=117$

[thorny flame]

pixel

[timber schooner]

null factor law now

solve for y

sub back into equation

to find x

boom done

[verbal crater]

yes

[rocky gulch]

nice

[timber schooner]

,calc 9-117

[thorny flame]

Result:

-108

[timber schooner]

i got two y values

which one is correct

[verbal crater]

both are correct

[timber schooner]

i got 6 and -9

oh

[verbal crater]

you should have 2 x values and 2 y values corresponding to them

[timber schooner]

oh

so when y = 6

x = 9

when y = -9

x = -6

[verbal crater]

yes

[timber schooner]

oh

so both values work

lemme test

$y = -9 \ x = -6 \ \ x-y=3 \ \ -6--9 = 3 \text{works}$

[thorny flame]

pixel

[timber schooner]

$y=6 \ x = 9 \ \ x-y = 3 \ \ 9 - 6 = 3 \text{works}$

[thorny flame]

pixel

[timber schooner]

ohhh

mm

ok

so x can be 9 or -6

and y can be 6 or -9

[verbal crater]

heres the graphical representation if you're wondering why there's two

[timber schooner]

yes yes thank you

.close

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[proven finch]

If lim (n -> inf) an = 0 and lim (n -> inf) an+1 = 0 (where an a sequence,
does lim (n -> inf) an+1/an = 1?

[fallow igloo]

I wonder how you get lim an = 0 and lim an+1 = 0 simultaneously

[proven finch]

an+1 is an without the first term, so they have the same limit

[fallow igloo]

wdym

[proven finch]

lim an+1 = lim an = L

a(n+1)

not an + 1

[fallow igloo]

I see

Sorry

[proven finch]

For example, let an be a sequence where a1 = -10 and a(n+1) = 1/(3-an)

I found that L = 0 and I need to calculate lim (n -> inf) a(n+1)/an

but if L = 0, we have 0/0

or is it 1 bc a(n+1) and an have the same limit

[fallow igloo]

Same logic applies to other sequence which converges to zero

[proven finch]

ok, thanks

.close

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[frigid token]

prove that √3 is irrational

[shut belfry]

You can prove it by contradiction..

Assume it is rational

[frigid token]

show me the sol.

[shut belfry]

so it will be equal to p/q where q is not equal to zero, p,q are relatively prime

[frigid token]

yes then?

[shut belfry]

square both sides

3q^2 = p^2

u will get this

[frigid token]

root 3 square = (p^2)/(q^2) ?

[shut belfry]

yeah

multiply q^2 on both sides

[frigid token]

okay

then?

[shut belfry]

u can see that 3 divides p^2

so it divides p

lets p = 3c, for some integer c

put this in the equation

[frigid token]

what??

[shut belfry]

look at this

[shut belfry]

3 divides p^2

[frigid token]

but how

q^2 = (p^2)/3 ??

@shut belfry help

<@&286206848099549185>

<@&286206848099549185>

[shut belfry]

look here is an example

[kind rampart]

p² is 3 times a whole number

so 3 is a factor of p²

[shut belfry]

3 times an integer.

@frigid token ?

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@frigid token Has your question been resolved?

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[upbeat tartan]

is 105deg cotermoinal with -435deg

[topaz sinew]

Please don't occupy multiple help channels.

[upbeat tartan]

19584 ppl online and not a single one can answer...

,help

[thorny flame]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[fallow heart]

If I knew what coterminal means I could help 😅

[upbeat tartan]

🤣

the two angles land on the same line

even if they have different angle rioatations

ie the coterminal angle of 225 would be

,calc(225+360)

[thorny flame]

Result:

585

[upbeat tartan]

and

,calc(225-360)

[thorny flame]

Result:

-135

[upbeat tartan]

these two angles have diff roatations but land "togeather" at the same place

wait nvm

I got the answer thgansk for trying!

.close

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Channel closed

Closed by @upbeat tartan

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[upbeat tartan]

,calc(1/2 * 11^2*pi/4)

[thorny flame]

Result:

47.516588885546

[upbeat tartan]

,calc(121pi/4)

[thorny flame]

Result:

95.033177771091

[upbeat tartan]

,calc(121/4pi*pi/180)

[thorny flame]

Result:

1.6586418507386

[upbeat tartan]

.close

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[neon iron]

Im tyring to prove every cubic curve has exactly one point of inflection

Im confused on what they do after, finding x

[azure panther]

you dont know what epsilon is right ?

@neon iron

[neon iron]

Kind of,

I dont rlly know why they included it

tbh

[azure panther]

do you know sign table ?

[neon iron]

no?

[azure panther]

oof

[neon iron]

3= 3XR?

[azure panther]

wth

no sign table

[neon iron]

no

[azure panther]

https://i.ytimg.com/vi/AG_dgnfJBVw/hqdefault.jpg

sth like this

[neon iron]

why would i want that

[azure panther]

then forget about it

[azure panther]

just to prove that it changes from - to +

or vice versa

[neon iron]

This is an example of another inflection question

[azure panther]

do you know what is the definition of inflection point is in a function ?

[neon iron]

d2y/d2x = 0

[azure panther]

yeh exactly that not it

[neon iron]

yes it is tho

[azure panther]

its not defined that way

[neon iron]

Oh

[azure panther]

lemme send it :

[neon iron]

When it changes sign

f''(x)

[azure panther]

yeh exactly

[neon iron]

🙏

either way me no get

[azure panther]

yeh wait

sorry 1 min

trying to find the theorem page

couldnt find it

but it basically says this :

if a continous function changes sign it would be at its roots

in this case

f(x) = ax^3 ....
is continuous

and d2y/d2x is also continuous

so it changes sign at it roots

so the roots are inflection points

[neon iron]

.

[azure panther]

this definition is only acceptable for continuous functions

[neon iron]

hmmm

[azure panther]

and epsilon is just proving that its changing sign

[neon iron]

ok

I think im having the problems with the basics

after hearing this

[azure panther]

you dont