help-27

[limber kernel]

what am i doing wrong

[supple knot]

This is something Hayley made custom

Ask her and ping her in #bots

[devout snow]

@limber kernel Has your question been resolved?

[devout snow]

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[limber kernel]

Is this the correct way of presenting this division?

And if so idk how to continue

[devout snow]

@limber kernel Has your question been resolved?

[devout snow]

@limber kernel Has your question been resolved?

[limber kernel]

.solved

[devout snow]

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[devout snow]

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[solid osprey]

use simmilar trianhles

[worldly spade]

i got 58 but im not sure if the answer is right

[restive river]

you know that per 100 feet x axis decreases by 150 ft

[solid osprey]

nope

sadly that is incorrect

[restive river]

so per x axis feet it decreases 150/100=1,5 feet

200*1,5=300

300 + 100 = 400 ft total depth

PR = 300 ft

[worldly spade]

it was 133

[solid osprey]

yeah it is 133

[solid osprey]

this is incorrect, it should be 200/1.5

[solid osprey]

you cant say that lmfao

use better words next time ^_^

[solid osprey]

do the same

[worldly spade]

.solved

[devout snow]

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[solid osprey]

if n is a natural number such that 2n+1 is a square number, prove that n+1 is the sum of 2 consecutive square numbers

[lament kraken]

let 2n+1 = x^2, then might be able to show (x^2+1)/2 = y^2 + z^2 for x, y, z in Z+

[solid osprey]

how tho D:

also that still wont prove its consecutive

[lament kraken]

okay

[junior chasm]

find n+1

[lament kraken]

okay nevermind

[solid osprey]

n+1

[junior chasm]

(by taking 2n+1 = x^2, and finding n, then n+1)

[lament kraken]

💀

[solid osprey]

hmm

n=4

[junior chasm]

what

[solid osprey]

er not sure what you mean

[junior chasm]

2n+1 = x^2 -> n = (x^2-1)/2

[solid osprey]

for all odd number x, n=(x+1)(x-1)/2

[lament kraken]

2n+1 = x^2, n = (x^2-1)/2, n+1= (x^2+1)/2

[junior chasm]

n is natural number

what can you deduce from here

[solid osprey]

rrrr

no clue

[lament kraken]

wait so x is odd let x = 2a+1

[junior chasm]

yes

[lament kraken]

since a=0 is clearly dumb

[junior chasm]

and put it back here

[lament kraken]

then n = a^2+(a+1)^2

which is consecutive so yeah

[junior chasm]

(n+1) is integer so (x^2+1)/2 has to be interger too, which means x^2+1 is even so x^2 is odd which means a is also odd

and an odd number is of form 2a+1

[lament kraken]

pog

[solid osprey]

x^2=(2a+1)^2
x^2=4a^2+4a+1
x^2+1=2(a^2+a^2+2a+1)
x^2+1=a^2+(a+1)^2

[lament kraken]

yes

[solid osprey]

is this enough proof technichally?

[lament kraken]

uh yeah

but you need to say the case when a = 0

[solid osprey]

not possible

n is natural number

[lament kraken]

oh yeah

[junior chasm]

what

how do you have x^2+1 on lhs

[lament kraken]

x^2+1 should be replaced by n

[solid osprey]

rightt

wait what

gold on

[lament kraken]

wait

[junior chasm]

put x = 2a+1 in n+1 = (x^2+1/2

there shouldnt be any x term

[solid osprey]

that means 2n+2 is the sum of a^2+(a+1)^2

[junior chasm]

u did smth wrong

[junior chasm]

.

[solid osprey]

oh im dumdum nvm

[lament kraken]

ya

[solid osprey]

.close i see where i went wrong, ty everyone

[devout snow]

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[solid osprey]

dw i have 6 more questions :3

[devout snow]

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[solid osprey]

if n is a natural number such that 3n+1 is a square number, prove that n+1 is the sum of 3 square numbers

[solid osprey]

im stuck on this

should i have let a be the smallest instead of the middle

[lament kraken]

um okay

[hollow ice]

wut? This is toatlly false. Look up x^2 mod3 for 3 consecutive numbers

squares are 1 or 0 mod3

[dark sable]

I thought it was 2n+1

[solid osprey]

oh wait

its not consecutive

there

[hollow ice]

so 3 consecutive squares are 2mod3

[solid osprey]

no

[hollow ice]

ohh, okay then

[stone stump]

it might be a good idea to instead do a few examples to see if there is a pattern to the squares appearing

[lament kraken]

but its a proof

[stone stump]

and?

[lament kraken]

oh

[twilit comet]

you can gain insights on how to prove it formally

if you just spot a pattern

[lament kraken]

明白

[solid osprey]

sure

1->4
5->16
8->25
16->49

i dont see the pattern

[stone stump]

more examples then

also I meant the pattern with the three squares adding to n+1

[solid osprey]

huh

0 0 1
1 1 4
1 4 4
4 4 9

[hollow ice]

well, you gotta skip 1 4 4

[solid osprey]

er

[twilit comet]

0, 0, 1
1, 1, 2
1, 2, 2
2, 2, 3

etc

[twilit comet]

and... why exactly

[solid osprey]

0 1 1
1 1 2
1 2 2
2 2 3
2 3 3
3 3 4

is the pattern like this

[twilit comet]

probably

[hollow ice]

oh, nvm. I got confused

[solid osprey]

its probably this

[twilit comet]

ahk

[stone stump]

bit early to try to conclude something imo

[twilit comet]

check

just to be sure

[solid osprey]

0 1 1
1 1 2
1 2 2
2 2 3
2 3 3
3 3 4
3 4 4
4 4 5
4 5 5
5 5 6
5 6 6

checked randomly and all worked

[twilit comet]

dude

at least check-

okay good

[solid osprey]

not sure how to write the pattern aritmethically

[hollow ice]

split into case when n is 1mod3 and 2mod3

[solid osprey]

huh

[hollow ice]

if n is 1mod3, it looks like larger one repeats, for 2mod3 the smaller one repeats

at least thats what I see, might be other way round

im numerically a bit lost rn

[solid osprey]

er whar

[hollow ice]

nvm, im so lost in my other work im supposed to be doing

[solid osprey]

where did the a^2+a^2+(a-1)^2 go :(

is this proof valid tho

[junior chasm]

yes

[solid osprey]

ok

thanks

.close

[devout snow]

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[devout snow]

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[grim heron]

Could anyone possibly help me with this quadratic equation?

[junior chasm]

help with what

[grim heron]

Solve the roots of the equation

[junior chasm]

substitute the values of a, b and c in the formula

[novel token]

Rotate cw

Rotate cw

[junior chasm]

solve this further

@grim heron

[grim heron]

Is there an error the way i have solved it?

[junior chasm]

no

its correct

[grim heron]

It would also be correct if the answer is 23-√433 over 8 right?

[junior chasm]

yes

its +/-

[grim heron]

And also 23+√433 over 8

[junior chasm]

yes

[grim heron]

Ohh yeahhh

I was just wondering why it was marked incorrect

thanks alot for the help!!

.close

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[devout snow]

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[flint snow]

factoring 6x^2 -13x-5

[eager nova]

What have you tried?

Check what are the multiples of the leading coefficient and the independent term

@flint snow

[flint snow]

I've tried -5 1 vice versa -1/2 10 vice versa

[eager nova]

Answer this question

[eager nova]

We are gonna do in two parts

[flint snow]

-30

[eager nova]

No no each one

6 = 2 and 3

-5 = -1 and 5

Now we are gonna use the -13x to split and match both

What number is the closest to -13 that has a common factor with -5?

[flint snow]

-6

[eager nova]

-6 does not have common factor with -5

You need to find a number in the form -5k

Being k a positive integer

For example if k=2 we get -10

If k=3 we get -15

-10 and -15 have common factors with -5

Do you follow me?

So the closest number to -13 that has a common factor with -5 is -15

Now you have to rewrite -13x in the form 2x - 15x

Because $-13x=2x-15x$ rigjt?

[woven radish]

Samuel

[flint snow]

yep

[eager nova]

And we said that 2 is common factor of 6 so everything is good here

Now we have

$6x^2+2x-15x-5$

[woven radish]

Samuel

[eager nova]

We separate in two groups and factor them individually

Start with $6x^2+2x$

[woven radish]

Samuel

[eager nova]

How would you factor this?

[devout snow]

@flint snow Has your question been resolved?

[flint snow]

idk

[eager nova]

You dont know how to factor $6x^2+2x$ ?

[woven radish]

Samuel

[flint snow]

I've tried but i just cant

[eager nova]

Do you know what to factor means?

Can you factor $4+2$?

[woven radish]

Samuel

[eager nova]

Assuming you don’t do the sum

[flint snow]

to factor is to put an expression in the form (x,m) (x,n)

[eager nova]

Imagine you have 2(x+y)

And you distribute

2x+2y

Right? @flint snow

[flint snow]

yes

[eager nova]

Ok si when you factor you do the oppoite

You have 2x+2y

Find common factor, in this case 2

And rewrite that as 2(x+y)

Now, having this in mind

Factor 6x^2+2x

First, find the common factor

Which one would be? @flint snow

[flint snow]

2

[eager nova]

2(3x^2+x)

Inside the parenthesis 3x^2 +x

They also have a common factor

Which is @flint snow

[flint snow]

x

[eager nova]

So

2(x(3x+1))

Or

2x(3x+1)

Right?

[flint snow]

yes

[eager nova]

Now so the same with the other two which was

-15x-5

Factor this

[flint snow]

5(-5x-1)

sorry -3x

5(-3x-1)

[eager nova]

Now

Inside

-3x-1

Which common factor they have

@flint snow

[flint snow]

-1

[eager nova]

Ok

So finish the factor there

How would it be

[flint snow]

-1(3x+1)

[eager nova]

And that was multiplying another 5

So the final form would be

We are almost done

[flint snow]

5(-1(3x+1)

[eager nova]

And 5 * (-1) is

[flint snow]

-5

[eager nova]

So -5(3x+1)

Now we add both parts

2x(3x+1) -5(3x+1)

What common factor these two have?

[flint snow]

3x+1

[eager nova]

Ok so factor that

Like you did before

[flint snow]

3(x+1/3)

[eager nova]

What was that

Hold on

Let’s go back

Remember when we had 2x+2y?

How do you factor that?

@flint snow

[flint snow]

2(x+y)

[eager nova]

Realize the process

Find the common factor , in this case 2

Put 2 in front

Open parenthesis

The two multiplies inside parenthesis

Inide the parenthesis we put what 2 was multiplying before

Before, the 2 in 2x+2y was multiplying x and y

So we put that inside the parenthesis nd get 2(x+y)

Now

2x(3x+1) -5(3x+1)

We know the common factor is (3x+1)

So our first step is… @flint snow

[flint snow]

put 3 in front

[eager nova]

3 is not the common factor

The common factor is (3x+1)

As a whole

I will help you out using a subtitution

Let’s A = 3x+1

So we have

2xA -5A

Right?

[flint snow]

yep

[eager nova]

Now try factoring that with the steps i showd u

[flint snow]

a(2x-5)

[eager nova]

Beautiful

Now remember a=(3x+1)

Replace back

[flint snow]

(3x+1)(2x-5)

[eager nova]

Remember parenthesis

Yes

And there u go

Now, to be sure you did correctly

You only need to distribute that

And if u get the original problem

U did correctly

[flint snow]

Thank you

[eager nova]

Welcome

!done

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[flint snow]

.close

[devout snow]

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[bitter osprey]

Hello

[bitter osprey]

Can someone please explain what i am doing wrong

[devout snow]

@bitter osprey Has your question been resolved?

[devout snow]

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[gilded ocean]

can someone help me

[gilded ocean]

plssss

expand the logarithm please

[restive river]

which one

[gilded ocean]

all

[restive river]

log (ab) = log a + log b

this is a law

so the first one is quite simple

[gilded ocean]

just log(6) + log(11)??

[restive river]

Yes

Similarly log(a/b) = loga - logb

[gilded ocean]

oh okayy

how about if there's a exponent?

[restive river]

As in the third one?

[gilded ocean]

yes

should the exponent go before the word "log"??

[restive river]

log_b x^m = m * log_b x

[restive river]

correct

[gilded ocean]

2log(6) - log(11)

is that it?

[orchid sierra]

you neglected to provide the instructions for this problem set.

[gilded ocean]

.

[restive river]

it's 2(log(6) - log(11))

so 2log6 - 2log11

[gilded ocean]

oh okayyy

[orchid sierra]

ah.

but these are already in your notes

[restive river]

these questions are directly on the laws of logarithms

so revise those laws

[gilded ocean]

i don't really understand them... sometimes i got confused lol

sorry

for number 4
log(3) + 3log(2)??

[restive river]

yeah

nice

[gilded ocean]

thanks

is the parenthesis in the right place?

[restive river]

eah

yeah

[devout snow]

@gilded ocean Has your question been resolved?

[devout snow]

@gilded ocean Has your question been resolved?

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[restive river]

1kg-m is a unit of what?

[restive river]

like N-m is unit of work

no

Mass/Volume = density

you have multiplied them

[frozen stump]

also density

[flint spire]

no, torque is Nm

[drifting sierra]

Why use - instead of .?

[restive river]

it's related to work

[frozen stump]

is kg/m even a thing?

[restive river]

No

kg . m is a thing

[frozen stump]

physics

[drifting sierra]

Linear mass density

[frozen stump]

oh

[restive river]

oh

[drifting sierra]

kg.m is nothing though

AFAIK

[vocal tartan]

https://physics.stackexchange.com/questions/32096/what-exactly-is-a-kilogram-meter

[restive river]

oh as far as I know

it is a thing

my physics teacher told

he was also explaining N.m

[vocal tartan]

freight movement is an interesting place it shows up

[drifting sierra]

Transportation, yeah that makes sense but is very niche

[cinder nova]

maybe they meant kgf m then?
which is torque

[drifting sierra]

Yeah that's just torque

[restive river]

mhm

thanks

[vocal tartan]

It's also a unit of measurement for the amount of mass sitting on a lever (i.e. torque but we measure the mass instead of the force the mass is applying)

[drifting sierra]

Well no, you measure the torque and deduce the mass given the distance

[restive river]

ok UwU

.close

[devout snow]

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[vocal tartan]

As in you scale the value based on the distance of the mass from the fulcrum, not literally the amount of mass in kg

[devout snow]

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[ancient tusk]

Idk if the bot can read images

Use synthetic division to find the result when x^4-8x^3+21x^2-10x-24 is divided by x-3

[faint gorge]

https://youtu.be/FxHWoUOq2iQ?si=fbd37cYkPqg4cMXO

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[twilit cloud]

No idea on what to do on exercise 412

[restive river]

simplify each side first

[soft umbra]

Simplify both sides in the first place

Remember that x cannot be 0, -3, or -1

Or else some of the fractions in the initial inequality will be undefined

Also be aware that you should not multiply both side by unknown variables such as x-1 as well as x, since the multiplication may interfere with the result

[devout snow]

@twilit cloud Has your question been resolved?

[twilit cloud]

This is the most simplification I can do

Idk how to proceed now

[soft umbra]

Combine them

[twilit cloud]

Done

[soft umbra]

Remove these

Because x cannot be zero from your previous statement

Also, if x is negative

It will automatically be transformed into positive after the power of 2 is added to it

[twilit cloud]

Ok removed those two

Multiplied both sides by x^2

[snow raptor]

have you learned about method of intervals (wavy curve method)?

[twilit cloud]

Uhhhhhhhh no

These exercises are fractional inequalities

Wait lemme check what's a wavy curve method

i dont know whats that but i think i did it

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

but i cant apply it yet with -4x^3

and the other side not being 0

lemme get it to zero

ok removed a - and fixing some stuff

This is the current situation

[soft umbra]

Make the two fractions have the same denominator

And deduct the left side to the right

[twilit cloud]

Messed the exercise up ong. I wrote the wrong items.

Thanks for the help I'll reopen if i re encounter issues

.close

[devout snow]

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[jolly nebula]

hey there guys could anyone walk me through a question?

[winged bluff]

sure thing!
but you should get a channel first

[jolly nebula]

yeah i just read over the rules, sorry! fixing it now

[winged bluff]

its fine dw

[devout snow]

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[mild lagoon]

How can I solve this limit?

[mild lagoon]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[mild lagoon]

$\lim_{x \to 0}\frac{sin(x^2+\frac{1}{x})-sin(\frac{1}{x})}{x}$

[woven radish]

Douglas Fanucchi

[mild lagoon]

that is all i could do

[woven radish]

Douglas Fanucchi

[eager nova]

Have you tried ignoring the denominator?

@mild lagoon

[mild lagoon]

I didnt know this is possible

[eager nova]

If you split the fraction and you compare the two limits without de denominator

If you get limit = a for a=0 then the limit will be infinity

Of u get a=0

That would mean both limits in the numerator are the same s

So the limit will be 0

Do you follow my reasoning?

[mild lagoon]

Not much

[eager nova]

(a-b)x = a/x - b/x

If we ignore the denominator and compare numerators

If a-b=0 that means a=b

[mild lagoon]

yes

[eager nova]

So that would mean a/x - b/x is also 0

If a-b=c

Being c a real number

Then c/x would be infinity or minus infinity

[mild lagoon]

because x goes to 0, right?

[eager nova]

Yes, i mean u still have to do the limit

But u dont deal with denomintor until the end

[mild lagoon]

I think i got what you said

But why c/x would be +- infinity?

we had a - b = c, right?

and the x was the denominator

oh

i think i got it now

[eager nova]

Lets say u find a-b = 3

[mild lagoon]

yeah, because that is a constant divided by x that goes to 0

[eager nova]

Have in mind that

U will only have a limit if the limit is 0

Eitherway the DNE

[wanton prawn]

fk

[devout snow]

@mild lagoon Has your question been resolved?

[devout snow]

@mild lagoon Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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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!

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[soft umbra]

I need some hints for breakdowns on this question

[soft umbra]

I'm programming on c, and I'm not used to 2D array

I hope to proceed with for and while loop

[faint gorge]

that's actually interesting

You would go the first entire row
then the last entire column
then backwards the last entire row
then backwards the 1st column

Then you would stop at the pre last element and do the same but with one element less

[soft umbra]

how do I proceed with this notion?

[faint gorge]

maybe you can do this with recursion

[soft umbra]

I did come up with something like giving those numbers coordinates

and print them orderly by coordinates

[uncut crow]

what exactly are you supposed to do though. what is this chatgpt response

nvm, that answers

[soft umbra]

If you enter 3, you're supposed to get the result like that

4, 5, and so on

[faint gorge]

I have an idea

[dry geyser]

I mean you have 4 directions, and once you’ve finished one direction you have one row/column less (the matrix becomes smaller)

[soft umbra]

that's a breakdown

but the problem is, the compiler print the numbers from left to the right

I need a place to store every integer before printing

[faint gorge]

I thought of something like this as a blueprint

Basically introduce a counter variable that counts up for each iteration, so that then you for one element less each time

[dry geyser]

Oh you want to print out the matrix from a given spiral order?

[soft umbra]

yeah, but how do I put that in practice?

[soft umbra]

yes

[uncut crow]

here is one possible way. write a function that takes in a matrix and 4 indices a b c d (think of these like corners) and prints the path going from a to b, b to c, c to d. you can assume that e.g. a[0] = b[0], b[1] = c[1] etc. say your matrix is M. first pass M and the corner indices through M. can you see what to do next?

[dry geyser]

Got it, i was somehow thinking the other way around before

[uncut crow]

oh..

[uncut crow]

well you could reverse this idea then

[soft umbra]

alr I'll give those a try

ty to you all

.close

[devout snow]

Channel closed

Closed by @soft umbra

Use .reopen if this was a mistake.

[devout snow]

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.

[stable orchid]

I need help with this question

[stable orchid]

All 3

[faint gorge]

The first one has 3 extreme values, what would that mean for f'(x)

[stable orchid]

I'm not sure

Idk where u get those 3 extreme values

[faint gorge]

ups and downs

max and min

[stable orchid]

3 turning points

Oh ok

[faint gorge]

this means your first derivative has 3 roots

which implies a polynomial of 3rd degree

so your primal function should be of 4th

[stable orchid]

So what would I write down?

As the answer

[faint gorge]

use the hints

[stable orchid]

Idk honestly

I don't see any hints

Never heard of derivative

[azure dew]

4, just take the turning points and add 1

[stable orchid]

Just the number 4?

[azure dew]

well for the first one min degree would be 4

[stable orchid]

What about the degree?

[azure dew]

you know it's even because the two ends go in the same direction

and negative coefficient because they both go downwards

[stable orchid]

Wait so the degree is always the turning points + 1?

[azure dew]

yeah afaik

uhhhhh sounds about right less i'm tweaking

[stable orchid]

😭

[azure dew]

which is possible

lmao yes

[stable orchid]

I'm buggin

Hmm alr

So the min deg is 4

What about the leading coefficient

3?

[azure dew]

uh huh

[stable orchid]

3⁴?

[azure dew]

wait what

[stable orchid]

Idk

[azure dew]

oh it just wants the sign

the sign of the first is negative

[stable orchid]

Oh

[azure dew]

look at the end behavior to find the sign

[stable orchid]

So -4?

yeye

[azure dew]

and to see if the degree is even or odd

[stable orchid]

Degree is even

[azure dew]

well not -4

yes it is

-x^4

degree referring to the exponent

[stable orchid]

Makes sense

[azure dew]

and the negative is referring to the coefficient

[stable orchid]

What about the other 2?

[azure dew]

so just say -4 & negative

well

[stable orchid]

2 turning points

• 1

= 3

[azure dew]

how many turning points in b

yeah

u got it

[stable orchid]

Min deg is 3

What about the sin

±infinity

[azure dew]

well

do yk what x^3 looks like

in ur head

[stable orchid]

no 💀

[azure dew]

alright it's good to memorize hold on

[stable orchid]

Alr

[azure dew]

https://i.e-z.host/l3sc1j56.png

this is positive x^3

https://i.e-z.host/e0vk6f4k.png

this is negative x^3

what difference do you see?

[stable orchid]

Flipped

[azure dew]

yeah what about the ends tho

[stable orchid]

Infinity

[azure dew]

riiiiiiight but which infinity

[stable orchid]

wym which

X and y?

Both

[azure dew]

https://i.e-z.host/5rjzy5j3.png

compare the other two graphs to this one

[stable orchid]

They're not the same

Oh shi

[azure dew]

right

but the ends are

[stable orchid]

This one has 2 turning points

[azure dew]

you just gotta care about the ends

[stable orchid]

The others don't

Oh

But the ends are the same

[azure dew]

well not quite

[stable orchid]

Expect

[azure dew]

so basically

[stable orchid]

The left one doesn't go above the x axis

Yk?

[azure dew]

on b)

as x goes in the negative direction, y goes to -infinity

and as x goes positive, y goes to +infinity

agreed?

[stable orchid]

Yep

[azure dew]

so as a general rule of thumb, you just gotta memorize this (or think about similar functions)

if -x has y going to -inf & +x has y going to +x, the function has a positive coefficient

[stable orchid]

Understood

[azure dew]

OR if -x has y going to +inf & +x has y going to +inf it's a positive coefficient

so in B) for example, you can see as x goes to -infinity, y goes to -infinity, and as x goes to infinity, y goes to infinity

so you know there's a positive coefficient

[stable orchid]

Yea

Soo it's

x³?

[azure dew]

and if you wanna know quickly if the degree is odd or even, you can also use the ends as reference; if y goes to +inf on one side of the graph but -inf on the other, it's odd

[stable orchid]

The degree is odd

[azure dew]

well the minimum degree is 3 yes

and it has a positive coefficient

[stable orchid]

So...

[azure dew]

well that's ur answer

min degree is 3 and coefficient is positive

[stable orchid]

x³

?

[azure dew]

well the MINIMUM degree is 3, but technically it could be something else

[stable orchid]

After this section I only got one more question to ask if that's fine

[stable orchid]

Max is idk

[azure dew]

so just write "minimum degree is 3" and "leading coefficient is positive"

[stable orchid]

Alr

[azure dew]

yea idm

[azure dew]

sure if i can help

[stable orchid]

I wrote that down

Yea ur smart

[azure dew]

lowkey i only remember some of this so we'll see

[stable orchid]

c)?

[azure dew]

god no

alr what's the degree of c

[stable orchid]

6 degrees

And it's positive on both sides

[azure dew]

yes the min is 6

and yes positive on both sides

[stable orchid]

Positive leading coefficient

[azure dew]

yup

[stable orchid]

So that's it?

[azure dew]

you got it

[stable orchid]

Okok

Ok last question

This part right here

I got 4 of them correct (I think)

I'm stuck on the last 2

e and f

[azure dew]

ohhh alright

hold on lemme read it

[stable orchid]

Yea take ur time

[azure dew]

ok so looking at iv

what can you tell me about the sign of the coefficient

[stable orchid]

It's -

[azure dew]

yup

[stable orchid]

• x and y

[azure dew]

and what about the leading degree?

[stable orchid]

2?

None?

[azure dew]

yup!

2

[stable orchid]

Wait wait

2

Ok

[azure dew]

one turning point, so the leading degree has a minimum of 2

yeah

[stable orchid]

Yep

[azure dew]

so ur between e and f

which of those is negative

leading coefficient

[stable orchid]

e

-3x²

[azure dew]

yup u got it

[stable orchid]

Ohhhh

OHHHHHH

X²

[azure dew]

make sense?

[stable orchid]

And 2

Yes

Thank u

[azure dew]

yaw good good

np

[stable orchid]

Are the other ones correct?

I think so

[azure dew]

lemme finish checking 1 and 2 looked good

[stable orchid]

Yea alr

[azure dew]

yup the rest are all right

[stable orchid]

Perfect

I appreciate ur help

Means alot

Have a good one

[azure dew]

yup! u too

anytime

[stable orchid]

.close

[devout snow]

Channel closed

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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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[sterile cairn]

How do I do this? It's hard idk

[small jackal]

Displacement is the velocity ×time

Distance is |velocity|×time

[sterile cairn]

yeah ik that

[sharp root]

with displacement, it would be the area under the curve, but areas under the curve when it's below y=0 are negative

[sterile cairn]

but that's impossible to do on this graph unless i spend hours

[sharp root]

with distance it's always positive

[sterile cairn]

i don't get where my area should be from

could someone draw it

on the image

[small jackal]

You add the magnitude of both areas

For distance

[sharp root]

Displacement is blue-red
Distance is blue +red

[small jackal]

But for displacement you don't omit the sign

It's "-" because velocity and displacement are vectors

[sterile cairn]

ohh

TY

[sterile cairn]

how did you know to choose those two trapazoids?

[sharp root]

blue is above y = 0
red is below

[sterile cairn]

oh

i think i get it

like whatever's "boxed" towards the x axis

[sharp root]

pretty much yeah

[sterile cairn]

for distance I added them all up, but somehow its wrong. 500+625+750

i got the right displacement

with them

but not the right distance

<@&286206848099549185>

@small jackal

[small jackal]

Yeah

[sterile cairn]

this

i dont get y

[small jackal]

Are of trapezoids

[sterile cairn]

?

[small jackal]

What is the 3rd value

[small jackal]

To get the distance

Exclude any minus sign

[sterile cairn]

so the three values I got were +500 then -625 and -750

but even when u add all them up, the answer doesn't match with the one on my sheet

[sterile cairn]

like here

[small jackal]

Solve again

[sterile cairn]

but I think it has to work right? bcuz the correct displacement came out of those values

[small jackal]

I'm about to go though

🥱

[sterile cairn]

oh braa

trust

[small jackal]

Just try again

[sterile cairn]

this is defying the laws of physics fr

[small jackal]

It's almost 12am

[sterile cairn]

DAM

its only 7 pm for me

all-nighter = sigma

[small jackal]

GN

Hopefully another helper comes

<@&286206848099549185>

I'm sleepy

@tranquil iron

[tranquil iron]

Chose the wrong guy to ping buddy 🗿

But just this once

I’ll try to help

[dense badge]

just take the area

[tranquil iron]

For displacement it’s how far it is from its original point

[tranquil iron]

At the end of the blue but it returns back to its original point

So for displacement it’ll only be the area of the red as that’s the only change from the original point as it doesn’t return back

Which would be negative as it’s area under

[devout snow]

@sterile cairn Has your question been resolved?

Channel closed

Closed by @sterile cairn

Use .reopen if this was a mistake.

[sterile cairn]

got it guys ty

[devout snow]

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• Show your work, and if possible, explain where you are stuck.
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[rare merlin]

Question 8

[faint gorge]

@misty crest

wtf

[misty crest]

it says solution

not a quiz

[faint gorge]

but it says marks

[rare merlin]

.close

[devout snow]

Channel closed

Closed by @rare merlin

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[devout snow]

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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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• Be polite and have a nice day!

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[glossy jewel]

l

[glossy jewel]

hi

[kindred agate]

Hi :3

[glossy jewel]

i need help in this math

[hardy yarrow]

What math?

I can try to help

[glossy jewel]

the math is called

trigonometry

[hardy yarrow]

ok

what is the equation?

[glossy jewel]

let me send it

[indigo fossil]

I might be able to help too but I'm not that experienced

[glossy jewel]

ok let me send it rq

If
x
+
y
+
z

π
x+y+z=π prove the trigonometric identity
c
o
t
x
2
+
c
o
t
y
2
+
c
o
t
g
z
2

c
o
t
x
2
c
o
t
y
2
c
o
t
z
2
cot
2
x
​
+cot
2
y
​
+cotg
2
z
​
=cot
2
x
​
cot
2
y
​
cot
2
z
​

please help

i think the answer is

x+y+z=π, so
x
2
+
y
2

π
2
−
z
2
;
z
2

π
2
−
(
x
2
+
y
2
)
2
x
​
+
2
y
​

2
π
​
−
2
z
​
;
2
z
​

2
π
​
−(
2
x
​
+
2
y
​
). Because of
c
o
t
α

1
t
a
n
α
cotα=
tanα
1
​
, we get
c
o
t
α

c
o
s
α
s
i
n
α
cotα=
sinα
cosα
​
. Then
c
o
t
x
2
+
c
o
t
y
2
+
c
o
t
z
2

c
o
s
x
2
s
i
n
x
2
+
c
o
s
y
2
s
i
n
y
2
+
c
o
s
z
2
s
i
n
z
2

c
o
s
x
2
s
i
n
y
2
+
c
o
s
y
2
s
i
n
x
2
s
i
n
x
2
s
i
n
y
2
+
c
o
s
z
2
s
i
n
z
2

s
i
n
(
x
2
+
y
2
)
s
i
n
x
2
s
i
n
y
2
+
c
o
s
z
2
s
i
n
z
2

c
o
s
z
2
s
i
n
x
2
s
i
n
y
2
+
c
o
s
z
2
s
i
n
z
2

c
o
s
z
2
⋅
s
i
n
z
2
+
s
i
n
x
2
s
i
n
y
2
s
i
n
x
2
s
i
n
y
2
s
i
n
z
2

c
o
s
z
2
s
i
n
z
2
⋅
c
o
s
(
x
2
+
y
2
)
+
s
i
n
x
2
s
i
n
y
2
s
i
n
x
2
s
i
n
y
2

c
o
s
z
2
s
i
n
z
2
⋅
c
o
s
x
2
c
o
s
y
2
s
i
n
x
2
s
i
n
y
2

c
o
t
x
2
c
o
t
y
2
c
o
t
z
2
cot
2
x
​
+cot
2
y
​
+cot
2
z
​

sin
2
x
​

cos
2
x
​

​
+
sin
2
y
​

cos
2
y
​

​
+
sin
2
z
​

cos
2
z
​

​

sin
2
x
​
sin
2
y
​

cos
2
x
​
sin
2
y
​
+cos
2
y
​
sin
2
x
​

​
+
sin
2
z
​

cos
2
z
​

​

sin
2
x
​
sin
2
y
​

sin(
2
x
​
+
2
y
​
)
​
+
sin
2
z
​

cos
2
z
​

​

sin
2
x
​
sin
2
y
​

cos
2
z
​

​
+
sin
2
z
​

cos
2
z
​

​
=cos
2
z
​
⋅
sin
2
x
​
sin
2
y
​
sin
2
z
​

sin
2
z
​
+sin
2
x
​
sin
2
y
​

​

sin
2
z
​

cos
2
z
​

​
⋅
sin
2
x
​
sin
2
y
​

cos(
2
x
​
+
2
y
​
)+sin
2
x
​
sin
2
y
​

​

sin
2
z
​

cos
2
z
​

​
⋅
sin
2
x
​
sin
2
y
​

cos
2
x
​
cos
2
y
​

​
=cot
2
x
​
cot
2
y
​
cot
2
z
​
.

x+y+z=π, so
x
2
+
y
2

π
2
−
z
2
;
z
2

π
2
−
(
x
2
+
y
2
)
2
x
​
+
2
y
​

2
π
​
−
2
z
​
;
2
z
​

2
π
​
−(
2
x
​
+
2
y
​
). Because of
c
o
t
α

1
t
a
n
α
cotα=
tanα
1
​
, we get
c
o
t
α

c
o
s
α
s
i
n
α
cotα=
sinα
cosα
​
. Then
c
o
t
x
2
+
c
o
t
y
2
+
c
o
t
z
2

c
o
s
x
2
s
i
n
x
2
+
c
o
s
y
2
s
i
n
y
2
+
c
o
s
z
2
s
i
n
z
2

c
o
s
x
2
s
i
n
y
2
+
c
o
s
y
2
s
i
n
x
2
s
i
n
x
2
s
i
n
y
2
+
c
o
s
z
2
s
i
n
z
2

s
i
n
(
x
2
+
y
2
)
s
i
n
x
2
s
i
n
y
2
+
c
o
s
z
2
s
i
n
z
2

c
o
s
z
2
s
i
n
x
2
s
i
n
y
2
+
c
o
s
z
2
s
i
n
z
2

c
o
s
z
2
⋅
s
i
n
z
2
+
s
i
n
x
2
s
i
n
y
2
s
i
n
x
2
s
i
n
y
2
s
i
n
z
2

c
o
s
z
2
s
i
n
z
2
⋅
c
o
s
(
x
2
+
y
2
)
+
s
i
n
x
2
s
i
n
y
2
s
i
n
x
2
s
i
n
y
2

c
o
s
z
2
s
i
n
z
2
⋅
c
o
s
x
2
c
o
s
y
2
s
i
n
x
2
s
i
n
y
2

c
o
t
x
2
c
o
t
y
2
c
o
t
z
2
cot
2
x
​
+cot
2
y
​
+cot
2
z
​

sin
2
x
​

cos
2
x
​

​
+
sin
2
y
​

cos
2
y
​

​
+
sin
2
z
​

cos
2
z
​

​

sin
2
x
​
sin
2
y
​

cos
2
x
​
sin
2
y
​
+cos
2
y
​
sin
2
x
​

​
+
sin
2
z
​

cos
2
z
​

​

sin
2
x
​
sin
2
y
​

sin(
2
x
​
+
2
y
​
)
​
+
sin
2
z
​

cos
2
z
​

​

sin
2
x
​
sin
2
y
​

cos
2
z
​

​
+
sin
2
z
​

cos
2
z
​

​
=cos
2
z
​
⋅
sin
2
x
​
sin
2
y
​
sin
2
z
​

sin
2
z
​
+sin
2
x
​
sin
2
y
​

​

sin
2
z
​

cos
2
z
​

​
⋅
sin
2
x
​
sin
2
y
​

cos(
2
x
​
+
2
y
​
)+sin
2
x
​
sin
2
y
​

​

sin
2
z
​

cos
2
z
​

​
⋅
sin
2
x
​
sin
2
y
​

cos
2
x
​
cos
2
y
​

​
=cot
2
x
​
cot
2
y
​
cot
2
z
​
.

am i right?

[indigo fossil]

Could you remove the newlines?

I can't read it

send a screenshot of the page

[glossy jewel]

sorry i sent the wrong question let me sned another one

Find the minimum value of 5cosA + 12sinA + 12

[hardy yarrow]

The answer is \sin\left(\frac{x}{2} + \frac{y}{2}\right) ]

[glossy jewel]

let me check

[hardy yarrow]

oops

[glossy jewel]

oh

[hardy yarrow]

that was for the first one

my bad

[glossy jewel]

a okay

[hardy yarrow]

-13

is the answer

[glossy jewel]

let me check

you are correct!

you are a new person to this server and you solved a hard question, you should become a big member to this server and help other people to!

.close

[devout snow]

Channel closed

Closed by @glossy jewel

Use .reopen if this was a mistake.

[glossy jewel]

.reopen

[devout snow]

✅

[north roost]

?

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[north roost]

why reopen?

[glossy jewel]

idk

my bad

.close

[devout snow]

Channel closed

Closed by @glossy jewel

Use .reopen if this was a mistake.

[devout snow]

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[white lava]

Hi

[north roost]

Hello :3

):

[white lava]

What does Ip mean? 😅

[north roost]

identity matrix

its the 1 in matrix

$\begin{bmatrix}
1 & 0 & 0\
0 & 1 & 0\
0 & 0 & 1
\end{bmatrix} $

[white lava]

What does it mean?

What am I supposed to do with it

[woven radish]

Average Calc Student

[north roost]

u substitute this as $I_p$

[woven radish]

Average Calc Student

[north roost]

This is an $I_3$

[woven radish]

Average Calc Student

[white lava]

Okay but why

[soft nest]

https://en.wikipedia.org/wiki/Identity_matrix

[north roost]

it wants u to prove whether the two expressions exist, right?

u can only add and subtract matrices if they have the same dimensions, no?

[white lava]

True

[north roost]

so

[white lava]

Oh

So it wants me to see if it's 3x3

[north roost]

or 2x2

or just a square in general

in ur case; they only allow 2x2 or 3x3

[white lava]

Am I on the right track

@north roost

[north roost]

yeah

now what's the dimension of the right matrix

[white lava]

It will be 2 x 2

[north roost]

it's a square, right?

[white lava]

Meaning I have to make it I2

[north roost]

yes

[white lava]

Yo

What did I do wrong lol

@soft nest wanna help 🥹

[soft nest]

Distribute the negative, but other than that, looks good

[white lava]

Wdym

[soft nest]

2-102=-100

[white lava]

They're 2 different numbers

[soft nest]

No, in top left

[white lava]

Thank you for your patience, I don't understand 😅

[white lava]

Ohhhh

I'm so stupid

[soft nest]

Everyone makes silly mistakes sometimes

Did you get b?

[white lava]

Not yet

Pretty sure it's undefined tho

[soft nest]

If you have p=2 yes

If p=3 you should be able to solve it

[white lava]

Im doing another question for now

I'll go back to it

[devout snow]

@white lava Has your question been resolved?

[devout snow]

@white lava Has your question been resolved?

[devout snow]

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Closed due to timeout

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• Show your work, and if possible, explain where you are stuck.
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[vast violet]

what usually gets plugged in

Uk part

becuz like

ik what to put for the deta sign

and g ofc

but what usally gets put in this part

the 0.20?

[acoustic leaf]

$\mu_k$ means coefficient of kinetic friction

[woven radish]

cloud

[acoustic leaf]

so yes

[vast violet]

so deta sign'would be 30

[acoustic leaf]

theta is 30 degrees, yes

[vast violet]

oh perfect

thnx

.close

[devout snow]

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[devout snow]

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[charred pollen]

below i dont know ehere to begin

[charred pollen]

<@&286206848099549185>

[violet raptor]

Try to cut into smaller pieces

[charred pollen]

yeah idek where to start

[violet raptor]

Hold on

[charred pollen]

aight

[charred pollen]

thats. what i did and i got 4 x x + 2 x x-4

[violet raptor]

4x + (2×(x-4))

[charred pollen]

why is it 2x

[violet raptor]

It's because if you take a look at the small rectangle

You would see that the length is 2

And the width is x-4

[charred pollen]

yeah

why is is 2x tho did u mean 2*

[violet raptor]

Why would I use 2 to the power of something?

Or what do you mean exactly

[charred pollen]

no i meant 2 times

[violet raptor]

Oh mb bro

Yes it is two times

[charred pollen]

algds algds

aight i got it and then theres a follow up question could u also help me w that

[violet raptor]

I just have a habit of putting the × as something times something

[charred pollen]

yeah

[violet raptor]

Sure

[charred pollen]

i didnt know how to expand the bracked w x/2

cause it would be x/2(6x-8)=65