help-0

[crude kraken]

he used the fact that A=B/C implies CA=B , with C = (cost)^2=1-(x^2)

well i think the bracket must have ended after the first dt/dx (i use t for theta) ..

no worries

[lone heart]

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[hollow sparrow]

[lone heart]

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[charred heron]

,rotate

[charred heron]

how to integrate the x part

[limpid turret]

Factor 1-x^2

[charred heron]

wdym

[limpid turret]

Factorise it

[charred heron]

(1+x)(1-x)

[limpid turret]

Break the polynomial down into root factors

[charred heron]

✅

what do i do after that

partial fractions>

[wild trail]

(1+x) should cancel right?

[charred heron]

done

thanks

.close

[lone heart]

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[worn fox]

What's your question

If what is right?

And what is Nq supposed to represent?

Use a calculator

Not my intention, first i had to extract information out of you to figure out what you actually wanted. This is something you can and should check on a calculator

If you've tried to do it on a calculator then show what you tried to do

[vague coral]

what is Nq tho

?
of what

://///////////////////////////

[limpid turret]

Then you need to learn how to find the result

What is that first thing after e?

[worn fox]

Think we're expected to guess

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[scenic crescent]

pls help

[scenic crescent]

apparently it's just b according to symbolab

but it's not gone thru it so idk y

[tidal crystal]

yeah it's just b, because e^(x) and ln(x) are inverse functions

so those functions cancel each other out

[scenic crescent]

OH RIGHT

ty so much it's clear now

[gentle jackal]

same for any positive value of $t$ for $t^{\log_t(x)}$

[tidal crystal]

[ocean seal]

please request a new nickname

[gentle jackal]

also where t≠1

[tidal crystal]

yep

[lone heart]

@scenic crescent Has your question been resolved?

[lone heart]

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[rich elm]

Hey, I have trouble resolving this system for b:

[rich elm]

can someone help me?

the second line leads me to b>0

oh i forgot to say that b \in R* and x\in[0;1]

[limpid turret]

What is R*?

[rich elm]

sorry it's french maths, it's R without zero

real numbers

set of real numbers actually

[carmine raft]

hi

[hollow sparrow]

real numbers different then 0

[tacit arch]

what do you mean resolving?

[carmine raft]

i need help with a problem

[limpid turret]

So, all reals or all reals except 0?

[tacit arch]

!help

[lone heart]

Please read #❓how-to-get-help

[limpid turret]

!help

[lone heart]

Please read #❓how-to-get-help

[carmine raft]

!help

[lone heart]

Please read #❓how-to-get-help

[rich elm]

i have to find a value for b so that it satisfies the system of inequations

[rich elm]

Yep

all reals except zero

[tacit arch]

comes from rings

[rich elm]

if differs from a language to another i think.. x)

[tacit arch]

show your work for this

[rich elm]

Yeah ofc let me take a pic

On the third picture it's written "but x(x-1)<= 0 when x \in [0;1] because x-1\in[-1;0], so necessarily:"

so i think i managed to solve correctly the first line of the system (even tho i inverted them in the middle but nevermind) but i can't find a way to solve the second one

according to geogebra i should find that 0 < b <= 2 but damn i don't get to it

[lone heart]

@rich elm Has your question been resolved?

[rich elm]

no one? :(

[tacit arch]

your work's just hard to follow

where does the 2nd eqn come from

[rich elm]

the derivative must be positive

I just put b/(x+1)^2 to the other side

[tacit arch]

where does b/(x+1)^2 come from?

oh that's just the derivative inequality

it looks like it followed from the previous eqn

[rich elm]

oh no, they're both different

nevermind guys i think i finally got it

thanks for your help tho!

.close

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[pseudo ice]

,rccw

[lone heart]

@pseudo loom Has your question been resolved?

[pseudo loom]

just need b 🙏

nvm i got it

[serene junco]

I think you want to double check part c as well

it's not some amount of time that's decreasing

[pseudo loom]

what would i put

[serene junco]

Since the function for D has a negative slope, that means D is decreasing

And what does D represent?

[pseudo loom]

distance

[serene junco]

right, the distance from safety

She's getting closer to the safe spot

meaning her distance from the safe spot is decreasing

[pseudo loom]

yea

but she is losing time as she does that

[serene junco]

I suppose that's true in a sense

but the fact that D has a negative slope means that D is decreasing

[pseudo loom]

would i put that

[serene junco]

yeah, something like this

[pseudo loom]

ok

thank u

[serene junco]

np 👍

[lone heart]

@pseudo loom Has your question been resolved?

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[alpine sable]

Can someone please help me?

[alpine sable]

,rccw

[alpine sable]

<@&286206848099549185>

[trim valve]

Is a perpendicular bisector

[alpine sable]

can u explain why

if those angles are right angles what makes angle TNU and RNU the same

[trim valve]

Because looking at it UN it acting perpendicularly to TR and it Aslo bisecting TR

[alpine sable]

bisect means to cut into two congruent parts

[trim valve]

Yes they are the same because they are congruent, they have the same shape size and angles .

[alpine sable]

ok

[trim valve]

Yes and when you split it into two parts they are exactly the same no difference

That congruence

Do you understand?

[alpine sable]

kinda

ye

idk why but i was doing my hw and had a brain fart lol

ok imma close this ig

ty

very much

.close

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[keen orchid]

hello im having trouble understanding this question

[hollow sparrow]

some of these equation are wrong

you need to find them

[keen orchid]

im leaning towards d. being incorrect, because from what I understand, the dot product of a vector by itself is its magnitude squared, but im still on the fence about that, because I don't know if any of the others are incorrect

[hollow sparrow]

yes the dot product of two vectors give magnitude

[limpid turret]

Are you familiar with the i, j, and k vectors?

[hollow sparrow]

take a look at b for example
it's dot production but it's give another vector
is that right ?

[limpid turret]

Do you know what those vectors represent?

[keen orchid]

its for r3 right, the i is the x, j is the y and k is the z

[limpid turret]

yes

As long as you know that, you can calculate each equation and see if the result is right

[keen orchid]

sorry but why are d and e different answers

[limpid turret]

Cross product

Dot product

[pseudo ice]

Think you meant b, no? Unless I can't read

[hollow sparrow]

yep yep :

[pseudo ice]

Hahah it happens

[keen orchid]

oh now i get it, so its b because it gives a vector rather than magnitude which is what dot product should give

okok thanks everyone

.close

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[dim coral]

i want to solve this problem myself could someone give me some hints?

[limpid turret]

There's lots of ways to solve this

See if you can describe an approach

Intuition. What would you try

[dim coral]

what im thinking is that they have the same gradient

since they are parallel

so i can find the derivative of x^2+y^2=16 and gradient for the other line which is just y2-y1/x2-x1

then maybe i try to sub the values into y=mx+c? idk

[dim coral]

the answer i got for the two gradients are different tho so idk

[limpid turret]

Derivative is def one approach

You know two points of the other line

So that should get you there easy

[dim coral]

yeah but how does that get me the point R tho

i dont have value for x or y at point R

how do i even get the c in y=mx+c

[dim coral]

where i got stuck is after finding gradient for the first like which got me y=-0.577x+c

.close

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[solid coral]

need help

[zinc bison]

whats your question?

[wary stream]

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

[solid coral]

this

[zinc bison]

,rotate

[solid coral]

can you solve it please

[wary stream]

No

[solid coral]

i need a solution

[zinc bison]

then we can help you reach that solution

[wary stream]

We're not here to do your work for you

[solid coral]

yes thankyou

[alpine sable]

do you know the angle of a straight line?

if you know, try forming an equation using the angles given to find the value of x

[solid coral]

bro i dont know

please help mee

[wary stream]

We are

Use what was stated to you

[solid coral]

thankyou

[wary stream]

EC is a diameter, what is the angle of a straight line?

[solid coral]

bruh i dont know

[wary stream]

You can google if you don't know

[solid coral]

its 180 degrees

i searched it

[wary stream]

Also what is this part suppose to be ?

Is this something you're not suppose to get help on?

[solid coral]

just the circle thingy

[solid coral]

dont mind that

[wary stream]

Now try forming an equation using the angles given to find the value of x

[zinc bison]

• Cheating on tests and exams, as well as other forms of academic dishonesty, will result in an immediate ban.

[solid coral]

bro just can you solve it?

[wary stream]

Nope

That's your job

[solid coral]

i dont know bro help me

[wary stream]

We're not here to do your work for you

Now

Now try forming an equation using the angles given to find the value of x

[solid coral]

wait

[zinc bison]

how do EOA, AOB, BOC, relate to EC

[wary stream]

Honestly EC isn't really needed to do

[solid coral]

i just need the angle eob

[wary stream]

Yes we know, and we aren't giving you answers

[solid coral]

nothing just the angle eob

[wary stream]

Yes we know, and we aren't giving you answers

[solid coral]

why huhu

[wary stream]

When asking for help, do not insist on getting just the answer; we are here to help you learn, not do the work for you.

[solid coral]

can you just teach me how?

[wary stream]

I am

Now try forming an equation using the angles given to find the value of x

[solid coral]

what equation do i form?

[wary stream]

You know the angle of EC

[solid coral]

yes

[wary stream]

Form an equation

[solid coral]

howww

i dont know

[zinc bison]

do you know the definition of the words supplementary and complimentary?

[solid coral]

noo

[zinc bison]

you should find the definition of those words first

[solid coral]

ok

done

[zinc bison]

whats the definition of supplementary

[wary stream]

Technically that really won't help

[solid coral]

Two angles are called supplementary when their measures add up to 180 degrees

that?

[zinc bison]

it might when they look at the angles and EC

what is the angle of EC?

2wilightt

[solid coral]

180??

uhmm

[zinc bison]

in this case its going to be the 3 angles on the one side of EC

[solid coral]

i am so dumb at math u know bro huhu

[solid coral]

yes so?

[wary stream]

Then you should ask your teacher for assistance

[solid coral]

i am not at school

im in home

doing assignment

[wary stream]

Ask friends

[solid coral]

they dont know eiter

either

[wary stream]

I really doubt that

[solid coral]

awww

cant you just help me bro dldh06?

[wary stream]

I'm not giving you answers

[solid coral]

okay bro xd

[wary stream]

If you want answers, this isn't the server for you

[solid coral]

thankyou for your help guys

i appreciate ur kindnees

bye for now

[wary stream]

Also google is helpful
https://www.youtube.com/watch?v=_I-IxR8VOZk&ab_channel=infinityplusone

[solid coral]

yes thank you

[wary stream]

Bye

Close the channel if you are done

[solid coral]

babye

.close

[lone heart]

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[static kindle]

does this resolve to e raised to the power of a?
if so, why (this may be incredibly obvious, however I'm new to calculus)

if @alpine sable sees this, I didn't get your explanation

[alpine sable]

why not

[static kindle]

because by that logic, it would seem that e could be raised to any power and be equivalent to a/n where a is some other number

I am probably misunderstanding your wording, could be a bit more explicit? 😅

or ideally link somewhere where this is formally shown

[alpine sable]

$\lim_{n \to \infty} \left(1+\frac{1}{n} \right)^n = e$

[ocean seal]

rbit ✨

[alpine sable]

this is still clear yeah?

[static kindle]

yes, I understand that

[alpine sable]

you also understand why we can then take any positive a and replace n by n/a?

[static kindle]

yes

[alpine sable]

because if n goes to infinity, so does n/a

$\lim_{n \to \infty} \left(1+\frac{a}{n} \right)^\frac{n}{a} = e$

[ocean seal]

rbit ✨

[alpine sable]

theres one warning for this step however

[static kindle]

a < 0 I suppose?

[alpine sable]

well take the sequence sin(pi*n) for example, the limit of it is 0 because its always 0 because n is natural, but if we now replace n by something like n/2, it diverges

so we somehow need to justify that this replacement is allowed, well good thing is that the function (1+1/x)^x is monotone rising, and therefore it should be easy to justify, but i wont go into too much detail with it now

$\lim_{n \to \infty} \left(1+\frac{a}{n} \right)^\frac{n}{a} = e$

[ocean seal]

rbit ✨

[alpine sable]

so what if we now raise both sides to the power a?

[static kindle]

well yes a cancels on the left and e is raised to a on the right but

[alpine sable]

$\left( \lim_{n \to \infty} \left(1+\frac{a}{n} \right)^\frac{n}{a} \right) ^a = e^a$

[ocean seal]

rbit ✨

[static kindle]

then the numerator within the limit could be anything

[alpine sable]

which numerator

[static kindle]

a/n

we could replace a with x where x is some value that isn't a

[alpine sable]

we can only replace the n itself, but if we change the one n, it also always changes the other n

[static kindle]

this is what I mean

[alpine sable]

but you cannot just change the a, its a constant

you can only replace n by na/x to achieve that (cancels the a and replaces it by x), but then again you also change the other n

[static kindle]

wait

this is what we're trying to prove but rearranged

this is literally what I didn't understand

could you please link some explanation where they've "proven" this 🥺

[alpine sable]

i dont know, i did it all in my head

[static kindle]

dude to be quite frank your "proof" makes no sense, you use what we were trying to prove in your proof

thanks anyways ig

.close

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[chrome shadow]

Hello so I am doing this attached problem and I am aware I need to use the quadratic formula I have all the variables solved but I don't get what I need to do after I have everything setup I have attached my progress on the question as well

[modern crown]

The quadratic formula is used to determine when a quadratic equals zero. But that's not the only thing you want. You alkso want to know when it equals 60.

[chrome shadow]

oh wait yea

h=60

[whole lance]

Yup, then isolate for t

Did it work?

[chrome shadow]

I wanted to think I got it I understand H = 60

But

The quadratic formula doesnt really contain any variables in it once you input everything so how would I isolate T

without T being there

[whole lance]

You only need the function, not the quadratic formula

[chrome shadow]

wait

oh

i solve for

since I know what H equals

using the equation I could solve for T

[whole lance]

Solve for t and insert 60 on h

[chrome shadow]

yes

ty

[whole lance]

Exactly

Nice

How many seconds did you get?

[chrome shadow]

t=-4

but the time wouldnt be negative

so t=4

is that right

[whole lance]

Yeah, you can not have a negative time. The other solution to the equation would be 0, which is impossible as well

So, it is -4 technically, but the real world result is 4 seconds

[chrome shadow]

Alright thank you needed this fast and the response time and help was great

[whole lance]

No problem, I learnt that like one or two years ago, so, it's good to refresh it haha

[chrome shadow]

How do I close this

[vale remnant]

.close

[chrome shadow]

.close

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[gray isle]

there's no issue with t=0 at h=60, and is actually what you should be using @whole lance @chrome shadow

[whole lance]

But, it's asking how long it takes for the ride to drop from 60 ft to 0 ft.

[gray isle]

yes

[whole lance]

How can it take 0 seconds?

[gray isle]

who said it takes 0 seconds

[whole lance]

We are solving for x which is the time

[gray isle]

t=0 represents the starting point

you then determine the time when h=0,

[whole lance]

Oh

[gray isle]

and the differences in those times will be the duration of the ride/drop

[whole lance]

It would also make sense for it to take less than one second considering the speed of 80 ft/s of the ride

@chrome shadow

You are right, Ramonov

[alpine sable]

i dont see it, i started from the limit definition of e, thats the only thing im using. If we cant assume this particular definition of e (which is the definition most widely used), then the proof gets a little more complicated

[lone heart]

@gray isle Has your question been resolved?

[lone heart]

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[alpine sable]

Can you show the region in exercise 33? And what did you try?

[tacit arch]

Show exercise 33

[lone heart]

@lethal berry Has your question been resolved?

[lethal berry]

Not sure but i think p's lower limit will be 0?

Upper limit ,hmmm
Not sure

[lone heart]

@lethal berry Has your question been resolved?

[lone heart]

@lethal berry Has your question been resolved?

[lone heart]

@lethal berry Has your question been resolved?

[lone heart]

@lethal berry Has your question been resolved?

[slender marten]

#multivariable-calculus

[alpine sable]

@lethal berry

are you here

i just totally missed it earlier sorry haha

[alpine sable]

thats what you're looking for right?

have you tried anything?

[lethal berry]

👍

[lethal berry]

Np

[lethal berry]

Yea

[lethal berry]

Nope

.close

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[steep ember]

What is happening in the last part

[wary stream]

$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \cdot \frac{d}{c}$

[ocean seal]

dldh06

[wary stream]

Dividing by a fraction, keep, change, flip, concept

Keep the numerator, change the sign (division to multiply), flip the denominator

[steep ember]

how did my teacher get from the second to the thrid part

[wary stream]

Dividing by a fraction, keep, change, flip, concept
Keep the numerator, change the sign (division to multiply), flip the denominator

With that

If you have $\frac{a}{\frac{b}{c}} = a \cdot \frac{c}{b}$

[ocean seal]

dldh06

[wary stream]

Except, you have fraction in the numerator, in that problem

[steep ember]

so for now he just flipped it and multiplicated everything

[wary stream]

Keep the numerator, change the sign (division to multiply), flip the denominator

That is what you do when you divide by fractions, or with any number

[steep ember]

what sign do u mean

[wary stream]

It says it in the text

(division to multiply)

Division sign to multiplication sign

[steep ember]

Ah

It confused me that he put the 2 fractions on top of each other

Was there any reason for that

[wary stream]

Because that's how the problem was

Literally this part

[steep ember]

why didnt he just flip it like me

[wary stream]

The stuff on the left was the numerator, the : represents division, right side is denominator

[wary stream]

It did

Literally right here

[steep ember]

yeah but why would you put those 2 fractions on top of each other

[wary stream]

You just did one more step

[wary stream]

Because that's how the problem was

The stuff on the left was the numerator, the : represents division, right side is denominator

[steep ember]

left top u mean

[wary stream]

No

[steep ember]

oohh

the whole fraction is numerator

on the left

[wary stream]

Yes, that's what I said

The stuff on the left was the numerator, the : represents division, right side is denominator

[steep ember]

well thats confusing

[wary stream]

Literally like that

[steep ember]

is there multiple solutions to these type of tasks

[wary stream]

Not sure what you mean

[steep ember]

is it possible that my solution looks different to his

or is there always only 1 solution

[wary stream]

What do you mean it looks different?

Those two definitely look the same to me

[steep ember]

no i mean at the end

there are further steps

[wary stream]

Then what do you have vs what the solution has?

[steep ember]

nvm but how he got that

[wary stream]

Can you post the full work of everything?

[wary stream]

It is hard to tell without context

[wary stream]

Like your full work and the solution?

[steep ember]

what happened here

ah no i mean here

[wary stream]

Factor out the GCF from both the numerator and denominator

[wary stream]

That's just factoring

Factor the denominator

Using whatever methods you know, ideally factor by grouping first

[steep ember]

hmm i dont really get how he factored that

like how did he manage to put it into these 3

[wary stream]

That's just factoring
Factor the denominator
Using whatever methods you know, ideally factor by grouping first

Are you even reading what I'm saying?

[steep ember]

yeah but i dont understand what u mean

[wary stream]

If you factor by grouping, a factoring method, what would the denominator result in?

[steep ember]

i dont know any methods where suddenly those 3 brackets pop out

[wary stream]

Do you know what factor by grouping is?

[steep ember]

not really

[wary stream]

Well, when you factor by grouping, which I suggest you look up if you don't know what that is, you'll result in (x - 1)(x^2 - 25)

Then you can factor again, using difference of squares

If you don't recognize those terms, I suggest looking them up

[steep ember]

ok i will thank you

/close

[wary stream]

.close

[steep ember]

.close

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[steep ember]

Is this correct

Like is it possible to factor -25

And just swap the signs

[tacit arch]

Your notation is confusing

Looks like you're subtracting 25(x-1)

[prime anchor]

The last one looks like a difference of two squares, you can factorise it too in (x -5) (x + 5) and divide it with the one on the top

Try to write it by hand and then send us a pic

[steep ember]

Like this?

[prime anchor]

Yes

[steep ember]

kk thx

.close

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[hexed eagle]

i know there is a formula for this and i just need to know what the name of it but if i have a complex number z how do i find all solutions to the equation

[hexed eagle]

z^n = a + bi

where i is sqrt(-1)

i know it will have n solutions

[alpine sable]

https://en.wikipedia.org/wiki/Nth_root#nth_roots

taking nth roots?

[hexed eagle]

maybe let me seee

[minor needle]

or I used to use this one also

but trig form required

[hexed eagle]

maybe thats the formula yea

trig form is fine

thank you

.close

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[bright charm]

https://gyazo.com/de993dcd47669a28dbac667bb17d1c9c

[lone heart]

Please don't occupy multiple help channels.

[rocky grove]

Please don't occupy multiple channels

I'll close this one

.close

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[rigid tundra]

stuck on this hard limit

[rigid tundra]

feedback/hint said to use Null limits rule and sandwich theorem

but i cant get this function bounded by somthing that converges to same number

[tacit arch]

Divide all terms by x^3

[rigid tundra]

ok

[ruby current]

also note -1 <= sin x <= 1 and -pi/2 <= arctan <= pi/2

[plain flame]

recall which functions are bounded

[ruby current]

you can choose one pair of values to replace each function for an upper bound and lower bound respectively

[rigid tundra]

the upper and lower bound limits dont agree so cant use sandwich theorem in this manner

[ruby current]

why don't they agree?

i haven't checked it, but it seems to me like they should

just intuitively speaking

because sin and arctan are upper and lower bounded by constants

so should be bounded above and below by limits to -3/8

,w limit x to infinity (3x^3+x^2+sin(e^x))/(5x-8x^3+arctan(log(x)))

[ocean seal]

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Requested by tushar#0942

[ruby current]

looks right

maybe send what you have for your lower and upper limits

[rigid tundra]

fair enough enough i looked at pi/2 and -pi/2 and thought limits wont agree but you added theyre bounded by other constants and so would work , ill try this , Thanks

[lone heart]

@rigid tundra Has your question been resolved?

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[tulip violet]

Is anyone able to get the answer for this? I’m unable to get the required answer after finding dy/dx

[tulip violet]

I got dy/dx = 3costheta/ -5sintheta

[rocky grove]

That's dy/dx

That's the tangent

[keen mason]

U want the normal

[rocky grove]

And remember that the normal line is

$\frac{-dx}{dy}$

[ocean seal]

VulcanOne

[rocky grove]

From straight line equation

[keen mason]

Negative reciprocal

[rocky grove]

Because perpendicular slope equals negative reciprocal of the slope

[tulip violet]

thank you

.close

[lone heart]

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[rocky grove]

Good luck ya abood

[haughty gulch]

hello

[rocky grove]

👍

[rocky grove]

Hey

If you want help

!help

[lone heart]

Please read #❓how-to-get-help

[haughty gulch]

i put noncoplanar, got it wrong

oh

sorry

[lone heart]

✅

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[tulip violet]

I get (y - 3Sintheta)(5sintheta) = 3Costheta (x-5costheta)

is anyone able to get the answer to this question

[keen mason]

Is that for the gradient of the normal?

[tulip violet]

Ohh wait

I forgot to switch

[keen mason]

:/

[tulip violet]

no that’s wrong

[keen mason]

Ok now u got the gradient

[tulip violet]

@keen mason i got the answer but it’s-16SinthetaCostheta

gradient of normal is 5sintheta/3costheta

.reopen

[lone heart]

✅

[keen mason]

Ok now u have a gradient

U have an x and y cord

[tulip violet]

I did that

[keen mason]

(y-y1) = m(x-x1)

And get eqaution

[tulip violet]

I got the answer but it’s-16Sinthetacostheta instead of 16Sinthetacostheta

would you be able to try it? maybe printing error?

[keen mason]

I can’t try rn I’m in bed and tired sorry, but try using a calculator

[tulip violet]

no problem ty

<@&286206848099549185> would someone be able to try this and let me know if they got the same answer

[rocky grove]

I verified the equation in the picture

It is indeed 5xsin(theta) - 3ycos(theta) = 16sin(theta)cos(theta)

[tulip violet]

hmm okay I’ll try it again

[rocky grove]

$5x\sin(\theta) - 3y\cos(\theta) = 16 \sin(\theta) \cos(\theta)$

[ocean seal]

VulcanOne

[rocky grove]

You got the gradient as -3cos(theta)/5sin(theta)?

[tulip violet]

also how would one find the y intercept of the line? substitute x=0?

[rocky grove]

Yeah

[tulip violet]

no. 5Sintheta/3sintheta

[rocky grove]

Okay before subbing point P?

[tulip violet]

I took it using chain rule

so there’s no before subbing P I think in this method

[rocky grove]

Hmm

I got the gradient before subbing as -9x/25y

[tulip violet]

I’ll try it again

[rocky grove]

Make sure that you simplify the expression early

[tulip violet]

@rocky grove I got it

it was just a simplification error

for the second part of the question do I have to find the equation of the tangent to the new point all over again or is there any easier method for that?

[rocky grove]

Find when x = 5/2 using 5cos(theta) and when y = 3root3/2 using 3sin(theta)

Wait

Don't do that no

[tulip violet]

there has to be an easy method I guess. because in our syllabus they rarely expect you to do something over and over again

[rocky grove]

I think you find the theta for x = 5/2 and y = 3root3/2

[tulip violet]

we don’t get to use calculators @rocky grove

[rocky grove]

I am aware

You refer to the unit circle

[tulip violet]

I’m unable to understand sorry

[tulip violet]

oh I just noticed how I could find it

i was like wait 5/2 is 2.5 how am I supposed to get sin for that

[rocky grove]

No they are the same angle

pi/3 or 60degree

[tulip violet]

5Cos60,3sin60

[rocky grove]

Yep yep

[tulip violet]

ty

[rocky grove]

Should give you your equation in x and y only

[tulip violet]

yeah and then sub 0 for x

?

[rocky grove]

For the y-intercept yeah

[lone heart]

@tulip violet Has your question been resolved?

[lone heart]

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[fringe fable]

hello

[fringe fable]

is here anyone to help me

[rancid trail]

Yes?

Give your question @fringe fable

[fringe fable]

the product of 9 consecutive numbers is divisible by 1111. What is the minimum arithmetic mean of 9 numbers

idk this question

could u help me :)))

[rancid trail]

9 numbers right?
And they are consecutive

Assume the terms to be

a-4 ,a-3, a-2, a-1, a, a+1, a+2, a+3, a+4

[fringe fable]

yes

[rancid trail]

Now take arithmetic mean

It will be a

[gray isle]

have you tried anything yet

[rancid trail]

Or the central most term

[fringe fable]

a

[fringe fable]

tried

[rancid trail]

Lmao i completely forgot

[gray isle]

tried what exactly,

[fringe fable]

i typed

this is maybe hard problem

can u try my geometry?

[gray isle]

whut

what I'm trying to ask you is whether you've attempted this progress and whether you've made any progress even it it may be little (and if you have show what you've done)

[fringe fable]

lemme show the picture

this is what i tried

[gray isle]

hint: consider the prime factorisation of 1111

[fringe fable]

what is it

like 101?

[gray isle]

something for you to do

[fringe fable]

11

[gray isle]

1111 = 11 * 101

[fringe fable]

yeah

[gray isle]

that's a huge hint,
you don't want to deal with a 9th degree polynomial

[fringe fable]

okay

[gray isle]

have a think about what you can do with that

[fringe fable]

nah

but

101 is prime number

11 couldnt be the arithmetic mean

oh oh

i got it

thx

[fringe fable]

ok now the geometry?

[gray isle]

what geometry

[fringe fable]

should i give the question?

[gray isle]

how are people supposed to help without knowing the question

[fringe fable]

haha

ok

ABCDE is right triangle . IN AE there is K point, in CD there is a L point.

LAE + KCD = 108°

AK: KE = 3:7

CL:AB =?

[gray isle]

is this the original question? is there a pic that comes with this

[fringe fable]

nah

oh

it is not triangle

it is pentagon

[serene junco]

a regular pentagon? or is that not given

[fringe fable]

right pentagon

[serene junco]

meaning what? a pentagon with a right angle?

are you sure?

[lone heart]

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[cedar field]

Please find where I went wrong in my working

[rustic ruin]

do you have the final answer to cross-verify?

[cedar field]

first create a triangle using one of the four cables that stabilize the flag pole to solve for the opp side you subtract the top part of the flagpole from the whole flagpole, and to solve for hyp, all the cable used to stabilise the flagpole is l and there is for segments.

.close

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[fleet geode]

I need help with 19

[fleet geode]

.close

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[spare fern]

hey guys

[spare fern]

could anyone help me out with these questions?

[pliant cedar]

u have y in terms of x, replace the y in other equation with that

[lone heart]

@spare fern Has your question been resolved?

[spare fern]

I did that then solved for the quadratic and got

x = 0 and x = -39

is this correct?

[pseudo ice]

,w solve 2x + 2 = x^2 + 5x - 2

[ocean seal]

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[pseudo ice]

,w solve x^2 + (3x - 5)^2 = 25

[ocean seal]

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Requested by chartbit#3171

[pseudo ice]

Which one did you get that for?

[spare fern]

oh my bad I think I did -3x - 5 instead of 3x - 5

.close

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[strong rain]

hello

[strong rain]

can someone help me understand the red circled area?

how it was factored :/

i don't understand where the ^2 went and how x turned into 1/x

if u multiply and de-factor them dont u get x + x/x^2 ?

[molten pivot]

sqrt(x²+x)
= sqrt(x² ( 1 + 1/x))

= sqrt(x²) × sqrt(1+1/x)

[strong rain]

ahh

so its just a mathematical thing that the sqrt(x²+x) is the same as sqrt(x² ( 1 + 1/x))

[molten pivot]

Tell me this:
What is 6²

[strong rain]

36

[molten pivot]

Now what is 2² × 3²

[strong rain]

4 x 9 so 36

[strong rain]

and yeah so this is a factor of 6 sq

[molten pivot]

6² = (2×3)² = (2×3)×(2×3) = 2² × 3²
Basically we can say that exponents distribute over multiplication in the same way that multiplication distributes over addition

[strong rain]

ahhhh right!

but how does it correspond to the previous circled expression?

sq root of ( x sq + x)

[molten pivot]

Do you agree that:
x² + x = x²(1 + 1/x)

[strong rain]

actually thats the part i didnt get xd

ah!

yes

i do

ohhhhh

[molten pivot]

Do you agree that
25 + 5 = 25(1+1/5)

[strong rain]

yeah yeah

okay think i get it now!

we extract x^2 from the expression

and make it 1+ 1/x inside the bracket

and then the sq root of x^2 is just x

thank u so much!!

actually

is there a reason why the extract didnt just factor 25 + 5 = 5 ( 5 + 1 ) ?

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

in here @molten pivot so sorry for ping!

wouldn't it have been the same ?

they just wanted to be fancy?

[molten pivot]

Because then we get the sqrt(x)

Instead of sqrt(x²)

[strong rain]

ohhhh

okay yeah yeah

so couldnt become a normal x

haha

[molten pivot]

Which doesn't really let us simplify

[strong rain]

yeah okay i see ! thank u so much again !!

.close

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[lethal berry]

https://media.discordapp.net/attachments/1061135993706664006/1061135993836671066/Screenshot_20230107_094203_WPS_Office.jpg

[molten pivot]

Whats your question

[high bridge]

You could start a by considering the fact that the volume of a sphere with radius 2 can be represented as the triple integral of a function $f(r,\theta,\varphi)$ over the region R in three-dimensional space. which I write as:

$\iiint f(r,\theta,\varphi) , dV = \iiint f(r,\theta,\varphi) , r^2 \sin(\theta) , dr , d\theta , d\varphi$

It would be more helpful if you explained what you're stuck with.

@lethal berry?

[ocean seal]

UnknownGenius

[lethal berry]

The limits, idk how to figure out just with rho =2

[lethal berry]

Wait isnt spherical coordinates
Dp dphi dtheta?

[lethal berry]

Stuck with figuring out the limits for the integral

Idk how to do this with just rho =2 ,for spherical ,rectangular and cylindrical coordinates

[high bridge]

To determine the limits for the triple integral in spherical coordinates, you should consider the region that we want to integrate over and how it is represented in spherical coordinates.

[lone heart]

@lethal berry Has your question been resolved?

[lethal berry]

Um, for spherical i think its ez, roh will be 0 to 2 , phi will be 0 to pi/2,theta will be 0 to 2pi

But how do i find other limits for other coordinates using the only info i have which rho =2

[lone heart]

@lethal berry Has your question been resolved?

[lone heart]

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[brittle sleet]

.close

||.close||

[shell widget]

.close

[lone heart]

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[rare swift]

if A power of 2 minus B power of 2 = 8]and AB = 2 , find A power of 4 plus B power of 4

[median oar]

that question doesn't make much sense

[rare swift]

sorry its from my tuition paper

[median oar]

$A^2 - B^2$ and $A\cdot B=2$

[ocean seal]

Frosst

[median oar]

what's the connection for A^2 and B^2?

[rare swift]

minus

[median oar]

yeah but what about it

what about A^2 - B^2

[rare swift]

= 8

[median oar]

oh

you didn't write that

so we have

[rare swift]

sorry

[median oar]

$A^2 - B^2 = 8$ and $A\cdot B=2$

[ocean seal]

Frosst

[median oar]

find $A^4 + B^4$

[ocean seal]

Frosst

[median oar]

so im thinking it's some sort of (A+B)^4 expansion

[alpine sable]

i think you should expand (a^2-b^2)^2 first

[median oar]

but that results in a bunch of odd powers that we can't really deal with

[median oar]

man im getting there >.>

[alpine sable]

ah lol

sowwya

[median oar]

it's about the thought process not straight to the answer

[median oar]

when we expand this we get things like AB^3 and A^3B and we can't really solve those

so the other way would be some sort of (A^2+B^2)^2

plus or minus it doesn't really matter all that much at this point

[lone heart]

@rare swift Has your question been resolved?

[rare swift]

wait resolved?

[alpine sable]

it does matter, you don't know the value of A^2+B^2, but only A^2-B^2

you can know that (A^2-B^2)^2 = (8)^2

you can't know the value of (A^2+B^2)^2

[median oar]

well my point is you wanna expand it out first

then figure out what you need

[boreal verge]

A^2-B^2 = 8 => A^4-2A^2B^2+B^4=64
AB=2 => A^2B^2=4 => 2A^2B^2 = 8

=> A^4+B^4 = 64 + 8 = 72

[lone heart]

@rare swift Has your question been resolved?

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[tardy charm]

my brain lagged

[vivid relic]

i

[tardy charm]

i thought of that but i got lagged again

[molten pivot]

don't we need a0

[tardy charm]

i solved it

[alpine sable]

Use a general (x-a) as your additional factor

[tardy charm]

thx

[molten pivot]

Yes but none of the answers are in terms of a, and the higher degree terms depend on the lower degree terms, therefore not enough info

[tardy charm]

its enough

.close

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[neon smelt]

could someone explain to me the steps in section b why was the values pi/6 and 3pi/2 chosen

[supple cobalt]

they are solutions to sin theta = 0.5 and -1 respectively

plus they are also the smallest positive solutions

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@neon smelt Has your question been resolved?

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[fallen verge]

Split into two cases: x is an integer, x lies between two integers

[molten pivot]

What does a real number look like?

What is a real number

Lol

Nope

Lol

Pi is real

[gray isle]

pi isn't infinite

[fallen verge]

By that definition .3333... wouldnt be real

[alpine sable]

do you know rational numbers?

[wanton pebble]

and irrational?

[surreal meadow]

!(p/q)

not necessarily

[wanton pebble]

hell nah

[surreal meadow]

rationals are numbers of the form p/q where p,q are comprime integers, and q is not 0

[wanton pebble]

22/7 is rational

[molten pivot]

They don't have to be coprime

[surreal meadow]

irrational numbers are numbers that are not rational, that is, they can’t be expressed in the form above

[surreal meadow]

my definition requires so

to be in Q is to have p and q be coprime

[molten pivot]

Doesn't make a huge difference but 2/4 is rational

Even if you don't rewrite it as 1/2

[surreal meadow]

2/4 is not an element of Q for me

1/2 is

[gray isle]

just integers is sufficient with q not being 0

[fallen verge]

Can be expressed as 1/2

[alpine sable]

the actual definition of reals is a bit more complicated but .. looking at the decimal expansion of an irrational you will see that the digits never form any repeating cycle

[fallen verge]

I think thats what max is saying

[surreal meadow]

maybe my Q is not the usual Q…

[wanton pebble]

i think we should focus on question

[surreal meadow]

in which case sorry for the confusion

[alpine sable]

take the maximum integer n such that n ≤ x, then it has to follow that n+1 > x (otherwise our n wouldnt have been the maximum)

then how would you choose epsilon?

right

and then due to
n ≤ x < n+1
we get
n-n ≤ x-n < n+1 - n
0 ≤ epsilon < 1

it at least proves the existance (well for 100% you would also need to prove why such an n even exists, but that should be clear)
you still need to prove the uniqueness

are you confusing rationals with integers?

[fallen verge]

Isolate x

Oh sorry i jumped in and thought you needed help w it

[alpine sable]

see what would happen if there was any other integer n ≠ n' that satisfies

like, what if n < n', then we have n+1 ≤ n', can an epsilon even exist then?
what if n > n', then we have n-1 ≥ n', can an epsilon exist?

(an epsilon with 0 ≤ epsilon < 1)

yeah, to get into more detail
for the first one we already had x < n+1, and then we will get x < n' and for any epsilon ≥ 0 we would just get x < n' + epsilon
for the second we had x ≥ n, we get x ≥ n'+1 and then replacing the 1 with an epsilon < 1, we get x > n' + epsilon

you got this

one tip, you can use the result for the first one and apply that to the second one for a quick proof

[alpine sable]

right
you could take the above statement, and then just take the negative of the equation
-x = -n - epsilon
and then it doesnt matter whether our x is positive or negative, it works for all x
x = -n - epsilon
and then of course we can also just negate our integer (if such an n exists, we just take -n and it will satisfy the below equation)
x = n - epsilon

[lone heart]

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[misty sluice]

guys can you help explain why did it result to raised to negative 5?

[delicate jacinth]

$a^c\times a^b = a^{c+b}$

[ocean seal]

sopinha

[delicate jacinth]

so what would be $2\times 2^{-3}$?

[ocean seal]

sopinha

[misty sluice]

-2?

[delicate jacinth]

$2\times 2^{-3} = -2$?

[ocean seal]

sopinha

[misty sluice]

4^-2

[delicate jacinth]

where did you get 4

$a^c\times a^b = a^{c+b}$

[modest lodge]

2^-2

[ocean seal]

sopinha

[quick karma]

this is just 1/4

[modest lodge]

Or that

[delicate jacinth]

$2\times 2^{-3} = 2^1\times 2^{-3}$

[ocean seal]

sopinha

[misty sluice]

1/4

[delicate jacinth]

Can you elaborate on your tought process?

[misty sluice]

oh mybad its 1/4

[delicate jacinth]

Can you elaborate on your tought process?

[misty sluice]

i solve 2^-3 first then multiply it to 2

[delicate jacinth]

hmm

it works but your teacher probably don't want that

[misty sluice]

i got this but 2 in the numerator

where did i go wrong

[delicate jacinth]

should've been $\dfrac{1}{4}\cdot x^{-6}\cdot 2^2\cdot x$

[ocean seal]

sopinha

[misty sluice]

omg thank youu

[lone heart]

@misty sluice Has your question been resolved?

[lone heart]

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[spiral jay]

I tried solving this question and my brain just can’t comprehend what to do. <@&286206848099549185>

[alpine sable]

!15m

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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.

[minor needle]

you want to find max of F(x,y) within the circle x^2 + y^2 = 64?

[spiral jay]

Yes

And minimum value

And the points of the max and min

[minor needle]

firstly check whether extrema occurs

doing partial derivatives

then check on the border

[spiral jay]

Ok wait let’s ditch this question cause I feel like it was invented by satan himself. I’ve got another question with my workings that I’m stuck on

Where did I go wrong?

[lone heart]

@spiral jay Has your question been resolved?

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