help-43

[boreal girder]

Flatus

[icy nymph]

$x = 3$

[boreal girder]

Flatus

[icy nymph]

are you still following or

need help

[last willow]

Oh most certainly still with ya on this. Currently doing graphing and its frustrating because when you are trying to find the points on a line and you have neither x or y, as long as the equation is satisfied it will work. However I keep getting everything wrong even when the math checks out so i sought this place out to see where i might be going wrong

[icy nymph]

sorry im confused

why are you graphing this?

[last willow]

College lol

[icy nymph]

hm?

[last willow]

Graphing Linear equations in two variables

[icy nymph]

i'm kinda getting more confused 😭

but anyways

do u still need help

[last willow]

Thats exactly how i feel

Because if i do it the way the "Tutor" says to do it, i get the wrong answer and if i do it how you do it, its not negative, either way the math isnt mathing for this one lol

[icy nymph]

can you show me

the question

and how your tutor did it

[last willow]

Im using Hawkeslearning if that helps any

the equation that i need to find X and Y for is y=-2/-3x -2. Now i know that you can multiply the fraction by 0 to get y. then getting X is where i keep getting tripped up. The tutor explained to multiply the fraction on both sides being the fraction and the whole number to get -3

[icy nymph]

can you

send the question

take a screenshot

a photo

[compact pewter]

@last willow Has your question been resolved?

[strange pendant]

its the equation of a line, just find two points in the line and make a line that passes through them

find two points (x1,y1) and another point (x2,y2) and draw a straight line through them

just, pick two random Xs and find those Ys,

simplest scenario is when x = 0, thats the y-intercept, then second simplest is when x = 3

[compact pewter]

@last willow Has your question been resolved?

[compact pewter]

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[terse gale]

I did a problem just like this and i’m very confused. i understand the similarities between the triangles and understand someway along the problem i need to use special right triangle ratios but i don’t know where to start

[terse gale]

Not homework btw this is practice exercides

I know angle LJM~angle JMK~ angle LMK

<@&286206848099549185>

[unkempt epoch]

Solve wrt area of the whole triangle

[terse gale]

area is 30

[tulip spear]

write eqns of pythogoras in the blue and red triangle seperately and find relations b/w t and other sides of triangle to continue solving the problem

[dusky kindle]

use the area method

[odd pine]

The area method is much cleaner.

[terse gale]

what is area method??

[dusky kindle]

do you know the area of a triangle is 1/2 bh

[terse gale]

^

[tulip spear]

true

[dusky kindle]

exactly, we can express the areas in too different ways.

[tulip spear]

pythogora would me more rigorous

[terse gale]

i think pythagoras is better because this class is heavy on proofs and theron’s

[dusky kindle]

lets use LJ as the base. Now we can form an equation

[terse gale]

thereomz

[dusky kindle]

ooh ok

[terse gale]

if LJ is a base

then the height is x

[dusky kindle]

yes, so 30 = 1/2 * 13 * x

[terse gale]

wait wait

ohh nevermind yeah

I think i have to solve using right triangle similarity and stuff

[odd pine]

The area method is still valid in this instance. (1/2)bh is well-known enough to be used.

[dusky kindle]

can you find 3 similar triangles?

[terse gale]

Yeah

LJM~JMK~LMK

no?

[tulip spear]

it would fail if the angle wasnt $90^{\circ}$

[boreal girder]

Dhairya

[odd pine]

Well yes, but it is.

[dusky kindle]

yep! we can derive some equations from it and find x

[terse gale]

that’s where i’m confused

deriving equations with similar triangles

[tulip spear]

the orange one

[dusky kindle]

ok so refer to this:

let KL = y. then JK = 13-y.

[tulip spear]

$\Delta=\frac{1}{2}ab \sin{\theta}$

[boreal girder]

Dhairya

[dusky kindle]

yep!

provided they learn trigonometry, tho

[tulip spear]

[odd pine]

-# I'm stepping out of this one, y'all got it.

[terse gale]

yeah but we haven’t gotten to trig yet

[tulip spear]

🥀 thats a matter of fact.

[terse gale]

we do triangles then trig

[tulip spear]

bye sir

[tulip spear]

10th cbse?

[terse gale]

bye jay

[terse gale]

what?

[tulip spear]

are you from grade 10

[terse gale]

no

[tulip spear]

mb

[terse gale]

😭

what grade do you think i’m in

[tulip spear]

10

[terse gale]

nope

[tulip spear]

@dusky kindle continue on mate

i intterupted mid discussion'

[terse gale]

Guys?

Alright guys i’m gonna go to sleep school in 2 hours

[compact pewter]

@terse gale Has your question been resolved?

[vale star]

JMK and JML r similar
JML and MKL r similar

The ratio of sides opposite to thee equal angles r equal

Let's consider triangle JMK and JML
,here in JMK ,thee side opposite to 90° is 12 and in JML the side opposite to 90° is 13

So ere we get a ratio 12/13

Similarly in JMK the side opposite to <J is x and jn JML the side opposite to <J is 9

So we get another ratio, x/9

Since we know that the ratio of sides of similar triangles r equal so we can say that
$\frac{x}{9}=\frac{12}{13}$

[boreal girder]

Victimizer

[vale star]

Now i think u can determine x

@terse gale

[compact pewter]

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[wheat badger]

Can someone help walk me through these questions? I had a really hard time understanding my teachers lesson 😭 I’m gonna go insane
(Just 1-4)

[frigid kiln]

Try to reduce the equations to just powers, no roots, no brackets

[tired rock]

also a reminder that a root can be converted into an exponent

[wheat badger]

Looking at number 1 - right
So how would I go about removing the 3 root

[thorny urchin]

do you know the link between roots and fractional exponents?

[frigid kiln]

Yes, recall that relation between them

[wheat badger]

Is it like that root 3 is 1/3 if there was no exponent next to a number

Just an example

[thorny urchin]

wdym no exponent next to a number

[wheat badger]

Like let’s say there was no exponent

To a number

Just the root 3

It would be 1/3

Exponent

[thorny urchin]

poor wording.
that would be described as cube root or 3rd root

$\sqrt[3]{x} = x^{\frac 13}$

[boreal girder]

ℝαμOmeganato5

[thorny urchin]

root 3 means $\sqrt{3}$

[boreal girder]

ℝαμOmeganato5

[wheat badger]

This is what I was saying

[wheat badger]

OH

ok so I was just wording it wrong ok

So what would I do with that 2nd part in the equation

Distribute the 1/3?

Or is there something else I should do

[strange ermine]

The root of a product is the product of the single roots, first of all

Then, for each of those three terms you can write ^⅓ instead of the ³√

[strange ermine]

But first do this

[wheat badger]

Can you elaborate

[wheat badger]

yeah ok this makes sense to me

[strange ermine]

Do you know the words "root" and "product"?

[wheat badger]

Yes 😭

Am I going on the right track here?

[strange ermine]

Then I just meant what I wrote...
Hence, this:

$$\sqrt[3]{ABC} = \sqrt[3]{A}\cdot\sqrt[3]{B}\cdot\sqrt[3]{C}$$

[boreal girder]

Alberto Z.

[wheat badger]

yeah ok I understand this

[thorny urchin]

cube root of 9 isn't 3

[strange ermine]

I don't get this 3

[wheat badger]

Yeah that’s wrong so just move that to the inside of the root

Not the outside

The 9

[strange ermine]

Yep

[wheat badger]

Got it alright

[strange ermine]

It has to stay under the root, unfortunately

[wheat badger]

How do I proceed here now

Something with multiplying the 2 equations right

Apply what?

[strange ermine]

Start by multiplying these two together

Wait wait

Where does that 2 come from?

[wheat badger]

I corrected the 3 btw

[wheat badger]

Mistake I made

That’s also on the inside still

[strange ermine]

Oh ok

[wheat badger]

Right?

[strange ermine]

Yup

(the 6)

[wheat badger]

Here’s what it looks like doing that

[strange ermine]

y⁴ not y³

In the front

[wheat badger]

Alright

[strange ermine]

Because you have y•y³

[wheat badger]

1+3

Yep alright

Now the other part

Do I multiply those too?

[strange ermine]

Of course

[wheat badger]

Ignore the cube root for now

Right

[strange ermine]

$$\sqrt[3]{A}\cdot \sqrt[3]{B} = \sqrt[3]{A\cdot B}$$

[boreal girder]

Alberto Z.

[strange ermine]

Just use this

[wheat badger]

So write everything out like that

[strange ermine]

You should have just one big cube root

[strange ermine]

As this suggests

[wheat badger]

Just combine the two big cube roots into a big one

?

[strange ermine]

Indeed!

[wheat badger]

Got it and then combine like terms right

[strange ermine]

This is what's written here, isn't it??

[strange ermine]

Yup

[wheat badger]

Final answer I think

[strange ermine]

Very good job

Just s minor hint: you can write 54 as 2•27

So that you can simplify $\sqrt[3]{54}$

[boreal girder]

Alberto Z.

[wheat badger]

Got it

[wheat badger]

So move the 27 to the outside

Right?

[strange ermine]

Exactly

So that it becomes 3, since 3³ = 27

[wheat badger]

Lmk if that’s what you mean

[strange ermine]

You forgot the ⁷ on the z

[wheat badger]

OH oops okay thank you for noticing that

[strange ermine]

And also inside the root there should be 2xy, not 3xy

Because 54 was 2•3³

[wheat badger]

Alright

All good after that

?

[strange ermine]

Yes

[wheat badger]

So I started setting up the next one

I think I messed up with the 2nd part

[strange ermine]

So far everything is correct

[wheat badger]

Really okay

[strange ermine]

But I suggest you to write the second bit as $\sqrt[3]{{(9x^2y^4)}^2}$

[boreal girder]

Alberto Z.

[wheat badger]

Should I tackle that ^2 first

[wheat badger]

K

Does that look correct?

[strange ermine]

(y⁴)² is y ⁸, not y⁶

[strange ermine]

Here, I mean

[wheat badger]

Got it

Anything else

[strange ermine]

Correct that mistake, so then we can go on with correct things

[wheat badger]

I’m doing this really early in the morning so I’m making sorta stupid mistakes

[wheat badger]

I went on to fix all the errors that caused

[strange ermine]

Very well, you're almost done

You can still simplify something inside that cube root

Such as y⁴ = y•y³

And the x³

[wheat badger]

Btw I went on to setup the other 2 problems

[wheat badger]

got it

[strange ermine]

I have to go afk for some time

Feel free to tag helpers

[wheat badger]

Okay thanks for your help

[strange ermine]

You're welcome, you've done very well

[wheat badger]

Thank you :) also is the very cool people the helper role?

[strange ermine]

Wdym?

[wheat badger]

Like who do I tag 😭

The “helpful role” users

?

[compact pewter]

@wheat badger Has your question been resolved?

[wheat badger]

I just wanna make sure I setup these two up right

[wheat badger]

Did I?

[vale star]

R u stuck here?

[vale star]

Tag helpers

[vale star]

In these cases try to bring all the terms wihtin same indice
Like u can express all of thwm together within quadratic root

[wheat badger]

I know I just started the problem

[vale star]

Then go on and u can show when u get stuck

[compact pewter]

@wheat badger Has your question been resolved?

[compact pewter]

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[compact pewter]

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[grave sierra]

I have a question about percentages

[compact pewter]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[grave sierra]

Yes I’m forming the question have a moment

[peak talon]

It's alright, take your time

[grave sierra]

So I have 400€ at the start and my bank account rises up to 610€ after 3 years, how do I find out the interest rate of 3 years

[peak talon]

pinned

[cursive harbor]

Simple or compund interest?

Compounded how often

Also fuck it

[compact pewter]

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.

[grave sierra]

Let me pull out my remarkable, one moment

So first I have to find out the interest

And then the amount risen in %

[cursive harbor]

Like I said, unless you answer my questions I can't exactly help here

Is it simple or compound interest

If the latter, how often is it compounded

[grave sierra]

Calculated the interest

Oh oops instead of 400€ = 100% it should be 406€ = 100%

[glad geode]

it will be 407 and 204 becase there is an add so 765

[grave sierra]

I rounded down the number of 1.502…

[glad geode]

765 ans

[grave sierra]

How did you come up with 765 as an answer

[grave sierra]

And 407 isn’t even possible to get a full number when you divide it by 2

Ok did a reverse calculation aka set the 610€ as 100%

[compact pewter]

@grave sierra Has your question been resolved?

[compact pewter]

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[lofty mountain]

i can't create the equation

[vale star]

Let the fraction be x/y

What would be its reciprocal?

[lofty mountain]

y/x

[vale star]

Yes and what would be 175/4 % of x/y

[lofty mountain]

7x/16y

[vale star]

Yes

So it said that the reciprocal is the value u get when u reduce x/y by 175/4 % of x/y

[vale star]

Can u find out the the value of y/x basing on that

[lofty mountain]

didn't understand

[vale star]

By "reduced by",they mean that subtracting 7x/16y from x/y gives u it's reciprocal

[lofty mountain]

(16xy - 7xy)/16y?

[vale star]

Not xy

[vale star]

Can u show ur work on that

[lofty mountain]

wait

[vale star]

It should be something like this

[vale star]

When u do the subtraction u need to divide the denominator of each fraction by the common denominator and then multiply the result with its numerator

Here 16y is common denominator

And for 1st fraction 16y/y=16
And the 16×x=16x

[lofty mountain]

👍 ok

[vale star]

Similarly for 2nd fraction 16y/16y=1 so 7x ×1=7x

[vale star]

U understood?

[lofty mountain]

yes

but not the next step

i mean the upcoming one

what to do now

[vale star]

So here u get 9x/16y

Am i right?

[lofty mountain]

yes

[vale star]

And according to question y/x=9x/16y

[lofty mountain]

4/3

answer?

[vale star]

Yes

[vale star]

This is right

[lofty mountain]

thank you..got it

[vale star]

Np

[lofty mountain]

.close

[compact pewter]

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[trail edge]

$ \text{Let G a group of cardinal $n$ and verifies the condition: } d | n \implies | { x \in G | x^d = e_G } | \leq d$
$\ \text{Prove G is cyclic.}$

[boreal girder]

Ditril

[trail edge]

Trying to prove that there's an element of ord n using proof by contradiction. My current goal is to prove that the set $| A_d = {x \in G | ord(x) = d } | = k_d*\varphi (d)$ I feel like it could help me

[boreal girder]

Ditril

[compact pewter]

@trail edge Has your question been resolved?

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[compact pewter]

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[polar loom]

Hi there I’m really stuck on this question I have managed to get up to the expanded formula but I don’t know how to simplify and factorise it properly, I was just wondering if anyone could explain how this works. I have attached the worked solution and the step id like help on

[kind crane]

do you have an image with higher resolution

[polar loom]

Let me see if I can get one

[kind crane]

did you understand this step

[polar loom]

Yeah I did that and then I expanded all the brackets out on the LHS but I don’t understand the rest of the steps

[kind crane]

gotta be more specific

[polar loom]

This is where I got up to and I’m confused how they factorised it

[kind crane]

factor x out of the 2ax and -4x. what do you get?

[kind crane]

right

you can also factor 2a - 4

and a^2 - 4a + 4

[polar loom]

Okay got it thank you

.close

[compact pewter]

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[compact pewter]

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[opal stirrup]

The total export volume of the metal industry decreased by 7.1% in a certain year, but at the same time the unit price increased by 6.4%. By what percentage did the export value change, if the export value is calculated by multiplying the unit price by the export volume

[opal stirrup]

its not 1.15%

can anyone figure this out

[verbal kiln]

what have you tried?

[opal stirrup]

0,929×1,064=0,988456

0,988456−1=−0,011544≈−1,15%

@verbal kiln

[verbal kiln]

!15min

[compact pewter]

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.

[opal stirrup]

ok

[compact pewter]

@opal stirrup Has your question been resolved?

[compact pewter]

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[low pulsar]

!help

[compact pewter]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[low pulsar]

is the constraint in one of the white dots

[peak talon]

What do you mean by constraint?

[low pulsar]

like the zone

@peak talon

.close

[compact pewter]

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[compact pewter]

Available help channel!

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[low pulsar]

!help

[compact pewter]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[low pulsar]

at least 40 places will be reserved at this diner

reserved places: x walk-ins : y

is at least 40 places x >= 40

[thorny urchin]

There's no need to keep typing that. To claim a channel just ask directly. That command is intended to be directed at those that don't know.

[low pulsar]

oh alr

[thorny urchin]

your question isn't clear enough.

[thorny urchin]

wdym by that

[peak talon]

is that the entire question?

[low pulsar]

yeah

[low pulsar]

its the

i indentified the variables

[thorny urchin]

oh, is that meant to be two lines?

[peak talon]

Could you show us the original question?

[low pulsar]

ok

[peak talon]

Appreciate it

[low pulsar]

i cant since its in french

[thorny urchin]

did you mean
reserved places: x
walk-ins : y

[peak talon]

It's alright, just post it here

[low pulsar]

yes

[thorny urchin]

then yes,

[low pulsar]

yes what

[peak talon]

18 Volunteers are reserving a hall that can accommodate from 150 to 250 people in order to organize a fundraising dinner. At least 40 tickets will be reserved for “sponsors.” The number of regular tickets cannot exceed twice the number of sponsor tickets. The price of a sponsor ticket is $85.0, and a regular ticket costs $55.0. The volunteers want to raise at least $15 050 during the dinner. Establish the system of inequalities that represents this situation.

Is the transaltion correct? @low pulsar

[thorny urchin]

yes to your question based on how you defined x

[low pulsar]

yeah

[low pulsar]

oh alr

[low pulsar]

wrong

its 85$

and 55$

15 050$

not 1500

[peak talon]

Done, anything else?

[low pulsar]

should be good

[peak talon]

@low pulsar Do you need someone to verify your work? Since rau have answered your previous question.

[low pulsar]

i didnt work that much

all i found was

z = 80x + 55y

.close

[compact pewter]

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[icy topaz]

If info A implies info B and info B implies info A, does that mean info A is equivalent in info to B?
For example, if someone says that the roots of x^2 + ax + b are c and d and the roots of x^2 + cx + d are a and b, is this statement equivalent to saying that:
-a = c+d
b = cd
-c = a + b
d = ab
?

[kind viper]

sure yeah it is

[icy topaz]

okay

thanks

.close

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[icy topaz]

😄

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[copper sandal]

AC = BC = 12
CF is height, thus AF=FB
MN=?

[copper sandal]

and please, if anyone knows a source for most math rules laws theorems and what not, please send it as i need a refresher for them all

[mild sky]

what are M and N?

just two points?

[copper sandal]

yes

[mild sky]

does the diagram mean <MNB is 90 degrees?

[copper sandal]

yes,

same for CFB

CL = LF too, but that should be expressed with the lines

[mild sky]

Call the intersection of CF and MN by the letter O

what can you say about the triangles CNO and CFA

[copper sandal]

Well

They both share CO, but CFA has it twice as long

and both have a right angle

Oh their angles ACF and OCN should be equal too

[mild sky]

all the angles are the same!

[copper sandal]

and thus the last 2 angles are equal by default, making the difference in the triangles size only and judgjing by the fact OCN shares CF, it means OCN has sides 2x smaller.....

[mild sky]

not 2x

[copper sandal]

Why not

CAF has CF which is CO*2

[mild sky]

because OC is the hypothenus for CNO

but its part of a side in cFA

[copper sandal]

Ohh

The hypothenus in cfa is 12

and i think we can use that to find it for cno but im not sure

the hypothenus for cno is 2x smaller than cfa's side

[mild sky]

I think there is not enough information

you can't really find the ratio

I put this setup in geogebra and its seems like MN can be between 5 and 8.5

and its perfectly valid

[copper sandal]

huh thats weird

i can send the original image but its in another language and im pretty sure i translated it near accurately, with diagram of same accuracy

[mild sky]

am I missing something?

[copper sandal]

pretty sure no

[mild sky]

yeah I can't read that

[copper sandal]

CO=OF btw

thats not helpful though right

[mild sky]

yeah its true in the diagram

you are probably missing something like what is the angle ACB or something

or maybe what is AF

[copper sandal]

AF isnt anything said

but because AC = BC and CF - height, AF = FB

[mild sky]

yeah I was talking about numerical values

I still think we need more info

[copper sandal]

nothing else included

would it be solvable if we knew AB = 12 but didnt know AC and CB's lenght??

[mild sky]

probably not

[copper sandal]

What should i do now?

do i just close this

[mild sky]

is this homework?

[copper sandal]

yes ig

[mild sky]

is it just practice or you are going to get a grade on this

if its for a grade try to talk to classmates

[copper sandal]

honestly im not sure, its summer vacation homework

[mild sky]

you can leave for later and do everything else but this

and if you don't do this just write that you are missing information

[copper sandal]

Welp okay

Ty for explaining to me everything

.close

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[mild sky]

you are welcome

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[south niche]

29

[south niche]

I don’t know how to make it such that I get only theta to solve

ATP I’m here and DK how to go any further

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[south niche]

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[weak glade]

a

[weak glade]

Is this supposed to be rationalisable

[chilly basalt]

Not sure about the question, could you elaborate?

[weak glade]

In a text book it said to rationalise the thing above, and the answer was this

But when rationalising arent u supposed to remove radicals from denominator

[stark marsh]

did it just say rationalize only ?

[weak glade]

rationalise and simplify

[boreal dawn]

Yes it should. Did the problem ask you to rationalize the numerator, by chance?

[weak glade]

no

[stark marsh]

i'd suppose the square root on the numerator is the only thing that can be rationalized here

[boreal dawn]

Odd

[weak glade]

my guess is there might be somethign to do with limits

[stark marsh]

but still it's vague to know especially since a has square roots in both the numerators and denominators

[weak glade]

even tho its not referenced

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[low pulsar]

i finished but i dont know what equation is it to find minimize production cost

A company specializing in lawn fertilizer offers a spring fertilizer and a summer fertilizer.
The fertilizers are made up of nitrogen, potassium, and phosphorus. There is a maximum of 4650 kg of nitrogen,
3000 kg of potassium, and 3100 kg of phosphorus available to prepare the fertilizers.

Contents per bag of fertilizer

Spring Fertilizer	Summer Fertilizer
Amount of nitrogen (kg)	10
Amount of potassium (kg)	8
Amount of phosphorus (kg)	4
Production cost ($)	6

Given that the company wants to produce at least 490 bags of fertilizer, how many bags of each type should it produce to minimize its production cost?

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[ornate cipher]

Hey guys. I'm writing my IB math IA right now, and I wanted to compare three different attempts to model caffeine in the body using the Akaike information criterion. Namely, the michaelis menten equation (given by v = (Vmax*[s]) / (Km +[s]) where Vmax and Km remain constant), a first-order one-compartment model ( given by C(t) = (D*Ka) / (Vd(Ka-Ke)) * e^(−ke​(t))−e^(−ka(​t)). Where every parameter(?) is a constant ) and finally a polynomial regression model ( as y=β0​+β1​x+β2​x2+β3​x3+⋯+βn​xn+ε ). I'm learning stats and modelling basics for the very first time so please forgive me if im forgetting important information or giving unimportant ones. However, I read on the math stack exchange that if I'm comparing non-nested models like these, I shouldn't be using the AIC in Ripley's school of thought. Is he right in stating that, or for my purposes am I safe to use the AIC to determine the best fitting model?

https://mathoverflow.net/questions/249448/use-of-akaike-information-criterion-with-nonnested-models/249753#249753

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[somber rivet]

can someone explain how to solve part d for me

[somber rivet]

if part c the total energy is 12.25j

because i think my answer key is wrong but ai multiple ai have been giving me different answers

[peak talon]

Could you show your work?

[wooden crag]

How did you get that as 12.25 ?

Ok nvm

I approximately got it

[somber rivet]

okay wait

uh my phones charging

but for part c is just a + b combined

A) Is 0.5x0.005x12^2
B) is 250x0.005x9.8
C) is A+B

[wooden crag]

You just did the P.E formula

[somber rivet]

ye which is mgh

but what is my gpe value to find the h

[wooden crag]

Yup

[kind gate]

Yo yo 🤟

[wooden crag]

Wait let me do the question myself

[somber rivet]

okay

[wooden crag]

If kinetic energy is 6 J in the last one

[kind gate]

Silly boy

[wooden crag]

Given

[kind gate]

Bro mgh is 6J

[wooden crag]

Ye

[somber rivet]

wait how

[wooden crag]

I can't explain everything in one sentence

[somber rivet]

isnt ke 6j why is that mgh

[kind gate]

Wait

Listen

[somber rivet]

yes

[wooden crag]

Delta K.E = 6 - 0.36 j = 5.64J

[somber rivet]

where did u get delta from what

[kind gate]

When the bird dropped it
The worm had the same v as the bird
So worm had both U AND KE
And now you can find h from U

[wooden crag]

It's just the initial that's it I am from physics major

[somber rivet]

whats U

[wooden crag]

So I use it anywhere

[kind gate]

Potential energy

[somber rivet]

okay so im learning quit simple physics rn

i though that u would subtract the total energy from the ke which is 6j

[wicked osprey]

dhruv bhai wtf

[somber rivet]

why is it the same

[kind gate]

Hehe ayush

[wicked osprey]

lol epxlain the ques first

[kind gate]

Potential energy difference

[wooden crag]

P.E = 5.64
0.005 × 9.8 × h(drop) = 5.64

[somber rivet]

wait so my thinking for this was likee form part c the answer is 12.61J so i subtract that from 6J of the worm's KE to find the remaining GPE right

[wooden crag]

Solve this last equation you get your answer in height

[somber rivet]

look at my key rq wait lemme find it

[somber rivet]

i saw the answer of 115 the ai said it but im confused like what is the thinking process

[kind gate]

Bro just use circle to search

[somber rivet]

circle

[kind gate]

Or Google scan

[somber rivet]

ai is giving me all different answers

[kind gate]

Use chat gpt

[wooden crag]

Relation between k.e and p.e

Bruh

[peak talon]

nah, they all suck

[somber rivet]

wym

[somber rivet]

it gives me a different answer every time

wait what is the relationship between k.e and p.e

[wooden crag]

With respect to gravitational potential energy

[somber rivet]

what is p.e and gpe not hte same

in this case

bruh what can u jst explain it from the very start

[wooden crag]

Height probably in what chapter you are in has the formula

[somber rivet]

ive learnt basically all the simple formulas

and like gpe=mgh or ke=1/2mv^2

[wooden crag]

h = mgh/mg

[somber rivet]

ye

[wooden crag]

So by using that we get the answer

[somber rivet]

i havent seen that formula but i can get how u rearange it

wait isnt that just gpe formula?

[somber rivet]

this is my course outline on this part

i dont get where do i start

[wooden crag]

P.E = mgh ?

[somber rivet]

ye

[wooden crag]

Ye

[somber rivet]

wait so ik the ke is 6J

what do i do from there

jst tell me like a simply way on how to solve it

[wooden crag]

Subtract the initial K.E when the bird drops it from 6 J

You get 5.64

[somber rivet]

ye rq why do we subtract it from the initial

[wooden crag]

Increase in k.e

[somber rivet]

and so basically this answer is wrong

[somber rivet]

yes

[wooden crag]

What tf is this solution

So complex to understand

[wooden crag]

Scrap that

[somber rivet]

idk bruh

[wooden crag]

Therefore we get mgh(drop) as 5.64

[somber rivet]

yes

[wooden crag]

h=mgh/mg

h=5.64/0.005×9.8

[somber rivet]

wait does gpe not equal to ke cuz of like total mechanical energy?

cuz like pe turns into ke as it falls right so that would mean the pe is 6J?

[wooden crag]

Nah

[somber rivet]

so we subtract from the start

bruhh ts is so confusing

[wooden crag]

P.e and k.e are different

[wooden crag]

Later

[somber rivet]

but doesnt potential at start equal to kenetic at end because like

when an object falls

its being converted no?

[wooden crag]

Bruh i just said k.e and p.e are different concepts

[somber rivet]

ye but when an object is falling

does it not convert

cuz thats what we;ve been learning at school

[wooden crag]

Why are you making it complicated for yourself?

[somber rivet]

cuz i dont get it

im tryna understand it

[wooden crag]

Also why are you discussing physics in the math server

🗣️

[somber rivet]

cuz its a math kinda question

idk where else to ask

[wooden crag]

There's a particular physics server like this one

[somber rivet]

can u send me the link

[wooden crag]

I came over to solve cuz this is basic physics

[somber rivet]

i dont get this bruh

[wooden crag]

https://discord.gg/physics

[somber rivet]

ty

.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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[kind viper]

thats a lot of different problems

which one(s) do you need help with? if more than one, which one do you want to start with? what's your progress on the problem(s)?

[true lava]

i need a couple help here

mainly the top section then the limit notation stuff

but like question 2 would be a good start

[kind viper]

ok

have you learned about holes and vertical asymptotes in class yet?

[true lava]

yes

but i dont remember everything

[hot parrot]

When does it happen?

[true lava]

wdym when does it happen?

[hot parrot]

Like when does f(x)/g(x) has a hole or a asymptote when f(x) and g(x) does not.

[kind viper]

https://www.youtube.com/watch?v=XE-Z2-F3oWw

heres a big ass video to remind you of various things here

[true lava]

oki doki

[wooden crag]

It's a chemistry tutor ?

[kind viper]

organic chemistry tutor has a LOT of videos specifically about math

[true lava]

ik what a hole is on a function but does number 2 even have any holes? because none of the factors are the same so no canceling for a hole

[wooden crag]

I'm a physics major so I got no issues in math mainly

Unless it's something very complicated

[kind viper]

you're right, there are no matching pairs of factors.

so indeed there are no holes.

[hot parrot]

Good for you not the place to say it.

[true lava]

but for 4 there is a hole at x=-2?

[kind viper]

yup

[wooden crag]

I'm here if anyone has a doubt in a match problem

Math*

[kind viper]

your enthusiasm is appreciated, but i (and @hot parrot) can handle ourselves in this channel specifically.

you're best off looking for a different help channel or #1021175428326633542 thread to help in.

but obviously keep #❓how-to-get-help in mind

[true lava]

now number 5 is where im getting a lil stuck idk how to factor the bottom part

[wooden crag]

Ok

[kind viper]

biggest thing is do not feed answers

@true lava this one, yeah?

[true lava]

yuh

[kind viper]

theres one factor you can pull out easily from x^3 - 4x

[hot parrot]

Try to look for components that both have it.

[true lava]

i did

but i cant do it without the factor

[kind viper]

ok let's be a bit more direct

these terms, x^3 and -4x, have a common factor that you can pull out

what is this common factor

[true lava]

x

[kind viper]

right

so do it

[hot parrot]

Yes.

[kind viper]

x^3 - 4x = x(???)

[true lava]

so x(x^2-4)?

[kind viper]

yes

do you see how to factor further?

[hot parrot]

For x^2 - 4

[kind viper]

hold

[hot parrot]

Ok

[true lava]

huh

[kind viper]

you've factorized x^3 - 4x so far as x(x^2 - 4). this is correct but you're not done yet.

do you see how to factorize it further?

[true lava]

x(x-2)(x+2)?

[kind viper]

wonderful

[true lava]

so hole at x=2

[kind viper]

so it seems, yes.

[true lava]

number 6 is also where i get stuck

[kind viper]

kinda blurry, this one

does it say $p(x) = \frac{x^2-1}{x^2+1}$?

[boreal girder]

Ann

[true lava]

yes

[kind viper]

right

what's troubling you about this one?

[true lava]

im not sure where to start

[kind viper]

where would you normally start

[hot parrot]

Again when does it happen?

[kind viper]

the running theme so far has been looking at where the denominator equals 0, yes?

(and in service of that, we factorized the denominator)

[true lava]

yeah?

[hot parrot]

Can it be 0? And where?

[kind viper]

yes, so what happens when you try to do it in this one?

[true lava]

i dont know

[kind viper]

can you at least write down the equation x^2 + 1 = 0 and stare at it

[true lava]

move 1 over then root?

which is 1?

[kind viper]

careful there.

[hot parrot]

First move it yes. But...

[true lava]

what

[kind viper]

i will recommend against using words like "move" until you're grown up enough to be fully fluent in algebra.

[kind viper]

when you subtract 1 from both sides (which is your "move 1 over" but said properly),

what happens?

[true lava]

you get x^2=-1

[hot parrot]

Now when does x^2 = -1?

[true lava]

it cant

its imaginary

[hot parrot]

Yes.

[kind viper]

that's right

this also means x^2 + 1 is unfactorable

(and it never equals 0)

what can you conclude about this function's holes and VAs?

[hot parrot]

For the reals at least.

[kind viper]

this is precalc, of course we're in reals.

[true lava]

there isnt any

[kind viper]

correct.

[true lava]

oki for number 7 i know hown to write the notation

[kind viper]

so do you know how to calculate limits in general

and what your first line of attack should be for a function like this

[true lava]

calculate?

[kind viper]

solve. find. work out. whichever other word you wanna use.

[true lava]

oh ok you made it sound like i had to do some calculations

[kind viper]

i mean you would have had to do some calculations anyway. this is math homework.

[hot parrot]

We are going to.

[kind viper]

calculations are going to happen regardless.

[true lava]

yeah

[hot parrot]

I recommend trying to find how does the function behave around 3.

[true lava]

how do i do that

[kind viper]

think about what happens to each factor as x -> 3

[true lava]

i dont need to graph this do i ?

[kind viper]

x-3 will approach 0, so for that one it'll be important whether it's positive or negative

no, no graph needed.

[hot parrot]

You need to do it in your mind a little.

See where it goes.

Ok then.

Continue.

[true lava]

well thats positive

[kind viper]

it's only going to be positive for x -> 3+

for x -> 3-, x-3 will instead be negative

[true lava]

yeah ok

so its postivie infitity and negative infitity

[kind viper]

for stuff approaching a nonzero number, sign matters a bit less.

[kind viper]

infinity, and you have to say which limit is which!

[true lava]

when its approching 3 from the right its going to f(x)=+infinity

[kind viper]

you sure?

[true lava]

is it now?

is it not*

[kind viper]

i think you may have skimped out on doing what i said

do you want me to take you through this step by step to ensure you didnt miss anything?

[true lava]

yeah i think that would help alot

[kind viper]

ok

$f(x) = \frac{(x+2)(x-6)}{x-3}$

[boreal girder]

Ann

[true lava]

ok

[kind viper]

we will be examining the behavior of f(x) as x → 3+, i.e. x approaches 3 from the right.

we do this by examining what happens to each factor in f(x) separately.

[true lava]

yes

[kind viper]

i will name the factors one by one, and you will have to tell me what the factor approaches, and if it approaches zero, from what side it does so.

this means that i will not accept just "0" as an answer; it will have to be "0 from above" or "0 from below".

[hot parrot]

We want the sign.

[kind viper]

(nonzero limits, such as "6", can be stated without a "from above/below" qualifier)

are we clear? @true lava

[true lava]

yeah

[kind viper]

cool

first, x + 2.

as x → 3+, what does x+2 approach?

$\lim_{x \to 3^+} (x+2)$

[boreal girder]

Ann

[kind viper]

@hot parrot i think i'd like to continue this myself btw.

[true lava]

well its approaching x=2

[kind viper]

bad wording and also wrong answer anyway

[true lava]

oh well

[hot parrot]

Alright then I'll check again later.

[true lava]

is this based off the end behavior

if so

i think i know what to do

[kind viper]

no, not end behavior

[true lava]

ok then im lost

[kind viper]

have you done problems about limits before?

like, not necessarily limits at infinity but also at a finite point

[true lava]

i did but im not the best at them and frankly i didnt understand alot of it

[kind viper]

hm.

https://www.youtube.com/watch?v=YNstP0ESndU

ig give this a watch cause its gonna get quite long if i try to explain it over discord char

chat*

[true lava]

ok

wait is this a the sign chart thing?

[kind viper]

no, not really.

for this particular problem, here is what i expected you to produce (with my guidance):

[true lava]

ok

[kind viper]

as x -> 3+,

• x+2 approaches 5
• x-6 approaches -3
• x-3 approaches 0 from above.

so the whole thing ``becomes'' $\frac{5 \cdot (-3)}{0^+} = \frac{-15}{0^+} = -\infty$ actually.

[boreal girder]

Ann

[true lava]

ok

is it helpfull to have a calculator for this to sub in values close to 3?

[kind viper]

i would say no, it's only distracting.

the whole idea of looking at each factor is to break your function down into pieces where you don't have to use a calculator to figure out the behavior near your point.

[true lava]

oh ok

ok

so i watched the video

wait do i just plug in 3

[true lava]

so you sub in 3 here

but how is that negative infinity

[kind viper]

numerator comes out to -15

denominator comes out to what you should think of as a small but POSITIVE number.

-15 (negative) divided by a small number (positive) gives a huge number (negative)

[true lava]

oh ok

[true lava]

but what did you mean by theses other answers

[kind viper]

again,

i broke it down factor by factor

[true lava]

oh so you plugged in the values from the factors into the equation

[kind viper]

thats not how i would've phrased it but i guess i'll take it.

[true lava]

so you subbed in x=-2 x=6 and just x=3

[kind viper]

no

no, i did not.

[true lava]

oh

[kind viper]

the value i subbed in at each stage has been the value that x approaches, which is 3.

not -2, not 6, not 69, not 420, not 0.

[true lava]

funny number

[kind viper]

but 3, because the question says to find the limit as x approaches 3.

[true lava]

yeah i understood that you sub that in where ever x is

[kind viper]

i think i have to go now, sorry.

[true lava]

oh ok.

.close

[compact pewter]

Channel closed

Closed by @true lava

Use .reopen if this was a mistake.

[compact pewter]

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[lofty mountain]

que no. 3
I can't understand it

[kind viper]

you put 1 lakh into compound interest account, in n years you will have 2 lakh, so you will have 4 lakh in?

[lofty mountain]

i don't know how to do this

[kind viper]

when you write "can't understand it", it sounds like "i don't understand something in the question" rather than "i don't understand the approach/method/whatever"

[lofty mountain]

ok

my bad

[kind viper]

growing by 4× means doubling then doubling again

[lofty mountain]

how am i going to double by

how to solve this...i don't know

[kind viper]

you put 1 lakh into compound interest account, in n years you will have 2 lakh, so you will have 4 lakh in?
think about this
growing by 4× means doubling then doubling again
and this also

[lofty mountain]

It's not easy for me

[lofty mountain]

please give me more hints

[kind viper]

i really can't without giving away the answer

[lofty mountain]

i put 1 lakh into C.I. so it becomes 2 lakh in n year..
won't it take less than n year to becpme double

[kind viper]

no

you just said it doubles in n years

yknow

double of 1L is 2L...

[lofty mountain]

can you give me an example

[kind viper]

no

[compact pewter]

@lofty mountain Has your question been resolved?

[mortal apex]

I wanna know the differentiation

[low bramble]

ok tell me the formula you remember for compound interest

[lofty mountain]

I took the help of chatgpt and got the answer 2n..
i also tried to make an example..
can we take easier example than this

[low bramble]

I'm sure you'll be able to understand this. Can you tell me the general compound interest formula, assuming annual comounding?

[lofty mountain]

A = P(1 + r/100)^t

[low bramble]

exactly

so here what they're telling you is that after t=n years, your money doubled

can you try incorporating this information in the formula?

[lofty mountain]

2A= P(1+R/100)^n

[lofty mountain]

^

[low bramble]

thats exactly right!

[lofty mountain]

oh

get it now

if we wanna double the A ,just square the t

for triple

multiply n by 3

right?

[low bramble]

no that's not right

look

each year, your money gets multiplied by (1 + r/100) right? that's why when you keep your money for n years, your money is getting multiplied by (1 + r/100)^n. first tell me if this makes sense to you

[lofty mountain]

ok

yes

[low bramble]

so they've told you that after n years your money doubled, meaning your money got multiplied by 2. meaning (1 + r/100)^n = 2

because (1 + r/100)^n is the money multipler (we just discussed this)

[lofty mountain]

ok

[low bramble]

so you have (1 + r/100)^n = 2, this is just saying that your money doubles after n years. so if you want your money to quadruple, what will change? you need to get 4 on the RHS.

so what do you do

[compact pewter]

@lofty mountain Has your question been resolved?

[lofty mountain]

sorry snooze..i am busy right now

can we continue this later

[compact pewter]

Channel closed

Closed by @lofty mountain

Use .reopen if this was a mistake.

[compact pewter]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wintry knot]

Problem Statement: Design an algorithm to serialize and deserialize a binary tree. There is no restriction on how your serialization/deserialization algorithm should work. You just need to ensure that a binary tree can be serialized to a string and this string can be deserialized to the original tree structure. how do i start with this?

[cursive harbor]

Well are you familiar with DFS

@wintry knot

[wintry knot]

yeah

[cursive harbor]

Well that's basically the idea

You'd need a way to indicate when there's no more children

And you can just do DFS and separate by commas

[wintry knot]

so we can just check if lc and rc are null? for each parent node

[cursive harbor]

And if they're null you use a special character to indicate that

[wintry knot]

how does that help?

[cursive harbor]

Cuz you want a way to indicate when you're done with the left and are going to the right

[wintry knot]

makes sense

i get what i have to do but it is a little complicated for me to code it

i will try to do that now

[cursive harbor]

Good luck

It is essentially DFS

[wintry knot]

yeah, i get it now; thank you!

figured it out

.close

[compact pewter]

Channel closed

Closed by @wintry knot

Use .reopen if this was a mistake.

[cursive harbor]

Yayyyyy

[compact pewter]

Available help channel!

Send your question here to claim the channel.

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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[undone topaz]

prove that the given expression doesn't depend on x

[compact pewter]

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

[undone topaz]

1

[mossy island]

Did u try rationalizing?

[undone topaz]

no because it's that big square root over 4

[mossy island]

Fr

Very chonky expression

[undone topaz]

i really don't know how i should start

[chrome harness]

did u try taking root over 16 - x^2 as a u substitution?

or try taking a trigonometric substitution

[tulip spear]

$E(x)=x \sqrt2 \frac{\sqrt{16-x^{2}}+8}{\sqrt{\sqrt{16-x^{2}}+4}}-(x+4)^{\frac{3}{2}}+(4-x)^{\frac{3}{2}}, \forall x\in [-4,4]$

[boreal girder]

Dhairya

[chrome harness]

oh well yeah i guess a trig substitution will work

let me try it rq

[undone topaz]

that 3/2 is something i haven't learned

it's for fresh 9th grade

im concerned

[chrome harness]

thats perfectly fine!
here, just write (x+4)^3/2 as (x+4)*(x+4)^1/2

and then substitute x = 4costheta

or 4 sintheta

since by observation we can see that x ranges from -4,4 and cos, sin range from -1,1

this shud make the entire equation much easier to solve as you can use trig identities instead of brute force algebra

[undone topaz]

im going to go pray

let me process for a sec

[chrome harness]

alright, let me know if u need further help

[undone topaz]

i got the thing with 3/2, but i have to look further into the trig identities

[chrome harness]

how much trigonometry have you learnt so far?

[undone topaz]

basic

[chrome harness]

like?

have u gotten till half angle identities? you'll need them for this

[undone topaz]

no, no