help-0

[magic terrace]

$\frac{2 + tan^2(x)}{sec^2(x)} - 1 = g(x)$

[ocean seal]

Eyesonjune

[untold knot]

What’s it asking for?

[magic terrace]

Reduce into terms of sin and cos

how do you turn tan into sin or cos

[strong zinc]

tan = sin/cos

[magic terrace]

and what does the squared part do to it

[untold knot]

Tan= sin/cos

[magic terrace]

tan = sin/cos

how does tan get modified by the square

[strong zinc]

tan²=sin²/cos²?

pretty much just using trig identities to simplify that fraction

[magic terrace]

hmm

so

[untold knot]

I’m confused by the question, why is it asking to simplify in terms of sin and cos

[magic terrace]

$\frac{2 + \frac{sin^2(x)}{cos^2(x)}}{\frac{1}{cos^2(x)}} - 1 = g(x)$

[ocean seal]

Eyesonjune

[magic terrace]

First try baby lesgoooo

[untold knot]

Is that right?

[magic terrace]

that is a good question

no clue

they just want us to learn this

[untold knot]

I guess you can go either way

[magic terrace]

I like this one

$\frac{cos(u)sec(u)}{tan(u)}$

[ocean seal]

Eyesonjune

[magic terrace]

Turns into tan(u)

[strong zinc]

I do not know how much they want you to simplify this, but if you know that $\frac{a}{\frac{b}{c}}=\frac{ac}{{b}}$ you can simplify this way more.

[ocean seal]

Jojotes

[magic terrace]

hmm

let's see

so it turns into

$(2cos^2(x)sin^2(x)) - 1 = g(x)$

[ocean seal]

Eyesonjune

[magic terrace]

no i meant

$(2cos^2(x) + sin^2(x)) - 1 = g(x)$

[ocean seal]

Eyesonjune

[strong zinc]

Yes

[magic terrace]

Can it be simplified further

[strong zinc]

Yes. Do you know of any identities using sin² and cos² ?

[magic terrace]

No

[strong zinc]

Well then, here you go for a new one, quite simple : cos²x + sin² x = 1, for all real numbers x.

[magic terrace]

so it goes to

$cos^2(x) - 1$

[ocean seal]

Eyesonjune

[strong zinc]

Hmm, that -1 should go away, as you had +1 before

[magic terrace]

ohhh

so literally just

$cos^2(x)$

[ocean seal]

Eyesonjune

[strong zinc]

Yes

[magic terrace]

very fancy

so I have it like this

$\frac{\frac{1}{cos(t)} - cos(t)}{\frac{1}{cos(t)}} = (f(t))^2$

[ocean seal]

Eyesonjune

[magic terrace]

And I can multiply the top by cos(t)

which gets uhh

1-cos^2(t)?

[strong zinc]

Yes!

[magic terrace]

but how do i turn that into f(t)

[strong zinc]

Well, are you allowed to take the square root of the lhs ?

ie, is the LHS always positive

[magic terrace]

nope

It says that the answer is sin(t)

OHHHH

that one property

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

so 1 - cos^2(x) = sin^2(x)

sqrt(sin^2(x)) = sin(x)

[strong zinc]

Well that works too

(The LHS was always positive, because cos²x has a minimum value of 0 and a maximum value of 1)

And to be precise, it should be $f(t) = \pm sin(t)$ because we don't know if it's positive or negative when we take the square root.

[ocean seal]

Jojotes

[magic terrace]

what does lhs mean

[strong zinc]

left hand side

[magic terrace]

oh

.close

[lone heart]

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[sturdy holly]

4(1+0.5m)=7m

[sturdy holly]

Does this not equal

oh

FUCK

[sleek lance]

huh

[sturdy holly]

.close

[lone heart]

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[sturdy holly]

.reopen

[lone heart]

✅

[sleek lance]

lmao

[sturdy holly]

sighs

[magic terrace]

the borat pfp makes it so much funnier

[sturdy holly]

4(1+0.5m)=7m

Does this not equal:
-5m=-4

[sleek lance]

i am unable to understand the question

[sturdy holly]

4+2m = 7m
-5m = -4

[sturdy holly]

Does 4(1+0.5m)=7m equal -5m = -4

Are they the same equation.

I got to the step of:
4+2m = 7m

[sleek lance]

m= 4/5

[sturdy holly]

2m-7m=(-4)?

is that wrong?

[sleek lance]

youd rather wanna keep m positive

easy to work that way

[sturdy holly]

frick -4/-5 = 0.8

two negatives equal a positive

oh no

oh god

[sleek lance]

keep m on right side of equation?

[sturdy holly]

i realized my mistake

[sleek lance]

its not a mistake

just an easier way to work

[sturdy holly]

i did a different equation before hand

i mean i divided incorrectly

[sturdy holly]

it is sry

https://tenor.com/view/borat-wawaweewa-sacha-noam-baron-cohen-room-bedroom-gif-15858289

.close

[lone heart]

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[sleek lance]

[magic terrace]

the stuff in the box is just my current step not my answer

how do i simplify this further

[sleek lance]

start new help

[magic terrace]

oh

[sleek lance]

#help-8

[lone heart]

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[tacit arch]

what have you tried?

[lone heart]

@prime pewter Has your question been resolved?

[prime pewter]

im stuck after this

@tacit arch

[lone heart]

@prime pewter Has your question been resolved?

[teal saddle]

-2^2+2 over 2

[lone heart]

@prime pewter Has your question been resolved?

[prime pewter]

huh????

[lone heart]

@prime pewter Has your question been resolved?

[tacit arch]

Did you learn cross products yet?

[prime pewter]

yes

det[3x3]

[tacit arch]

Do you think you could find a way to get two vectors from your problem to calculate a cross product to get an equation for the plane?

[alpine sable]

die

[bright hedge]

read #rules \

[lone heart]

@prime pewter Has your question been resolved?

[lone heart]

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[tepid ravine]

How can i derive the expnential fprmula

[covert agate]

????

there are so many ‘exponential formulae’

which one are you referring to?

[pulsar aspen]

I don't understand what do you mean.

[lone heart]

@tepid ravine Has your question been resolved?

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[lone heart]

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[hazy knoll]

Can anyone help

The only trig identities we've been taught is sin^2 + cos^2 = 1 and sin/cos = tan

[pulsar aspen]

Try to find cos x

[hazy knoll]

What

I don't know what you mean by that

[pale kestrel]

never mind

you should find cos

yes

[woven sphinx]

i mean

the draw a triangle method works

[pale kestrel]

it does?

[woven sphinx]

you just have to then factor in the fact that u have an obtuse angle and use trig identities for that

[hazy knoll]

What do you mean by find cos x

[pale kestrel]

yh yh

maybe confusing

[woven sphinx]

yeah it is

[pale kestrel]

u have sin

u can get cos with one of the identities

[hazy knoll]

I got cos^2 = 8/9

Idk what I'm meant to do next

[woven sphinx]

square root

taking into consideration the fact that cos x should be negative

[hazy knoll]

But how do I get it into the form of tan

[echo socket]

So sine is 1/3 and cosine is -2sqrt2/3 (because cos^2 = 8/9), what would the tangent be?

(We picked negative value of cosine because the angle is obtuse)

[hazy knoll]

I understand that

But I dont know how to get it into the form of tan

[echo socket]

So we have tan(theta) = sin(theta)/cos(theta) = -1/2sqrt(2), right?

We can turn it into the form ksqrt2 like this

[pale kestrel]

if u have sin and cos

[hazy knoll]

Whered you get -1/2sqrt(2) from

[pale kestrel]

tan = sin/cos

[echo socket]

$-\frac{1}{2\sqrt{2}} = -\frac{\sqrt{2}}{2\sqrt{2}\cdot\sqrt{2}}$

[ocean seal]

Beans

[echo socket]

I divided sin by cos

[hazy knoll]

Ok thx

I think I get it

.close

[lone heart]

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[pale kestrel]

the important part is knowing cos is negative

for obtuse

[hazy knoll]

Yeah

[lone heart]

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[nova ivy]

How can I do it without a calculator?

[pale kestrel]

how would a calculator even help?

[pulsar aspen]

Try to factorize the polynomials

[lone heart]

@nova ivy Has your question been resolved?

[nova ivy]

ah thank you

[lone heart]

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[trail crane]

Hello

[trail crane]

You know you can get worse

Cause you are talking in my channel

And that is not allowed

<@&286206848099549185>

?

Man he really needs to study

And I just started

I said hello

And man went like hitler

just shut it and get out man

[sturdy sluice]

[trail crane]

i will use another channel cuz you crying man

.close

[lone heart]

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[dawn lynx]

ABC is an isosceles triangle at A. [BB'] is the height from B.
M is a point of the segment [BC].
H and K are the respective orthogonal projections of M onto (AB) and (AC)
Show that: MH+MK=BB'

[pale kestrel]

similarity

[lone heart]

@dawn lynx Has your question been resolved?

[dawn lynx]

?

i cant see it

[pale kestrel]

3 similar triangles.

[dawn lynx]

bruh but I need to use something else

[pale kestrel]

idk

im doing geometry in my head, u have it drawn

not much i can do to help

[dawn lynx]

k wait

i'll draw it

@pale kestrel

[pale kestrel]

what can I say

theres a lot of info there

if u draw the perpendicular from A, maybe even more info

[wispy path]

Can someone draw a diagram for this

[alpine sable]

Just a diagram or do you need a solution to

[wispy path]

i am trying to get the answer

but if u can, pls

[alpine sable]

Ok heres my sol

[pale kestrel]

wtf?

why are u channel hijacking

[pale kestrel]

and giving free answers

[alpine sable]

Oh my bad didn't see the other person was hijacking the channel

[wispy path]

thanks, got the same answer

[lone heart]

@dawn lynx Has your question been resolved?

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[dawn lynx]

what?

anyways just forget that

[lone heart]

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[edgy cape]

for 4iii

I did everything correct

except my final answer is ln4+1/2 and the answer is supposed to be ln4-1/2

how?

[gray isle]

show work

[edgy cape]

ok so I figured out where I went wrong sorry

.close

[lone heart]

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[alpine sable]

raw is like cents in currencies

[pale kestrel]

is this exactly the same thing

[arctic harbor]

Hello, I am trying to write a recursive formula for this sequence. The equation I came up with is tn=tn-1 +tn-2

[pale kestrel]

cus then its obvsly 1000???

[alpine sable]

changed xs palace

[pale kestrel]

it was 1e-3 for the other one

[alpine sable]

lets try wait one minute lol

[pale kestrel]

so 1e3 now?

[arctic harbor]

but do I need to state both t1 and t2? Because if I just stated t1, how would t2 have formed?

[alpine sable]

@pale kestrel Thank you so much, contract now works

Want to gift some crypto to you

Can i? lol

[pale kestrel]

don't sweat it lmao

[alpine sable]

Do u know math and crypto is together?

like elliptic curves used for wallets

[pale kestrel]

in aware yh

[alpine sable]

so accept gift lol

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

.close

[lone heart]

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[alpine sable]

can anyone help ?

[bright hedge]

you have to set up a total revenue function

and then maximize it (my guess is that it would be quadratic)

also this isn't a test right?

[alpine sable]

no passed exam questions

[bright hedge]

alright

so we know that total revenue (because they dont talk about costs anywhere) would be the price * the number of cars rented

does that make sense?

[alpine sable]

so it can be

[bright hedge]

?

[tight locust]

Lol

[bright hedge]

@alpine sable if your question is done use .close to close the channel

[alpine sable]

ty

.close

[lone heart]

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[lapis goblet]

I have this function f(x,y) = log(1-x)/clog(1-y) where c is a constant

[lapis goblet]

0<x<1

However the parameters for y is piece wise, and each of the inteverals are the same

And what I want to do in the end is use mean value theorem on it

Should I just break this up into 2 equations for each of the parameters for y?

Then apply mean value to both

Then take average?

Im not sure how to go about this

Please ping me if you have an idea, thank you

[lone heart]

@lapis goblet Has your question been resolved?

[lone heart]

@lapis goblet Has your question been resolved?

[lone heart]

@lapis goblet Has your question been resolved?

[woven matrix]

hello can you please explain this problem

[little drum]

not sure if I should use my brains where I don't even have the full understanding of the context... It'd be help me understand you better if you could just provide the actual question you're working on

[lapis goblet]

That is the question

I don’t know the parameters for y yet

I have to figure it out using this data I have

If I want to take the average value of the initial function from some arbitrary interval would I have to break it up into 2 things because y isn’t smooth

[little drum]

Sure you can do it but I'm not sure about taking average though.. It'd really be better if you could provide a screenshot or a pic of the question

[lapis goblet]

It’s a question bAsed on this data I have

It’s not a hw problem

Also the intervals for Y are of the same length

So I think I can take avg

[little drum]

Idk abt this

[lapis goblet]

well alright

thanks for your help anyway

.close

[lone heart]

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[lone heart]

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[keen spoke]

hi guys, need help with finding eigenvalues using shifting method, thanks

[lone heart]

@keen spoke Has your question been resolved?

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@keen spoke Has your question been resolved?

[lone heart]

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[slow silo]

could someone

help me with B

i dont really get it and i'm new to composition of functions

[wanton junco]

did you do a successfully ?

[slow silo]

yes i got f(0)

[wanton junco]

well b is essentially the same process, except you leave in the variable

except that b invloves an interesting concept

[slow silo]

yes thats what i'm a bit confused on

not quite sure how to solve

[wanton junco]

do you know what g^-1 stands for?

[slow silo]

because its an inverse essentially

[wanton junco]

ok so you do

[slow silo]

so it would be inverse sin?

[wanton junco]

so what confuses you

[slow silo]

just how to solve it

[wanton junco]

yea

[slow silo]

so

f(0)^-1

?

im a bit lost

sin(1/x0?

[wanton junco]

do you know how composition of functions is defined?

given two functions f(x) and g(x)?

[slow silo]

kinda

im a bit new to it just started learning today

[wanton junco]

ok, so how does that go?

[slow silo]

actually i dont know

f of g?

[wanton junco]

well I advise you should go over your notes

but say you have f(x) and g(x) then (fog)(x)=f(g(x))

[slow silo]

yes ik that

f(g(sinx)?

[wanton junco]

okay
what it essentially means is that instead of x, you plug in g(x)

[wanton junco]

This is a composition of 3 functions

g(x) in this case is sinx

[slow silo]

so what would it be once pluged into f(g(x)?

f(sinx)?

[wanton junco]

exactly.

[slow silo]

and then

what to do we after that

oh just sinx?

[wanton junco]

you write out the function you get

[slow silo]

f in this case is cos

so cosx times sinx

cosxsinx

?

[wanton junco]

why multiply?

you composed not multiplied.

those are different operations.

[slow silo]

so what to we do after f(sinx)?

[wanton junco]

f(pi)= cos(pi) correct?

[slow silo]

yes

tahst -1

[wanton junco]

so.. f(y)=cos(y) right?

[slow silo]

yes

[wanton junco]

so... f(sinx)= ?

[slow silo]

cosx?

fsinx?

[wanton junco]

you plugges what's in the parens instead of x so far

so what changes about f(sinx)

[slow silo]

i'm not sure

[wanton junco]

f(sinx)=cos(sinx)

do you see why?

[slow silo]

isnt that essentially what i did?

[wanton junco]

where?

[slow silo]

.\

oh wait

i multiplied

[wanton junco]

[slow silo]

so the final answer is f(sinx)=cos(sinx)?

[wanton junco]

yes

but that is a general form for A

you're doing B now

Now what do you for B?

[slow silo]

you innverse

right?

[wanton junco]

well part of it yea

[slow silo]

wait but i'm confused isnt the answer for part A f(0)

[wanton junco]

it is
but A didn't ask you to show the composed function just the value

[slow silo]

oh

so for b

we know we have

f(sinx)=cos(sinx)

[wanton junco]

Actualy now that I think of it , you didn't determine f(0)

[slow silo]

how?

[wanton junco]

what is f(0)?

[slow silo]

0

[wanton junco]

you're right but it's irrelevant for b

[wanton junco]

0.. ?

are you.. sure ?

I think you're guessing at this point

look at f(x) and plug 0.

[slow silo]

oh no its sinpi

because sinpi is 0

unless i'm wrong

which i think I am

[wanton junco]

Look at your functions.

we've defined the compositions

you know what it's supposed to look like
all that's left is to plug in and understand

[slow silo]

if f(sinx)=cos(sinx)

but thats irrevalant to b

so how can i solve b

[wanton junco]

you still haven't completed a

[slow silo]

a is f(0)

i did f(g(pi))

then i got sin(pi)

and thats zero

[wanton junco]

f(0) is not really determined.

what is f(0)

[slow silo]

idk

[wanton junco]

....

[bright hedge]

deus

[slow silo]

i'm lost

[bright hedge]

what are you asking?

[wanton junco]

the value of F at x=0

[bright hedge]

so goo goo

what is confusing about that?

[wanton junco]

you're correct, but you need to plug in 0 inside f(x)

[slow silo]

f(0)=cos(0)

?

[bright hedge]

yes

and what is cos(0)?

[slow silo]

1

[wanton junco]

that's right

[slow silo]

ok so now

[bright hedge]

so thats ur answer

[wanton junco]

Now you've determined f(0).

[bright hedge]

for a)

how would b be -1?

[slow silo]

so what can we do for b now

b is the inveerse now no

[bright hedge]

yes

[wanton junco]

b is the same process as we did with f(g(x))

[bright hedge]

so what do you get when you have a composition of the function and its inverse?

[slow silo]

pi/2?

[bright hedge]

...

[slow silo]

idk

[bright hedge]

dude

[slow silo]

i havnt really learned about that yet

[bright hedge]

you literally have

$f(f^{-1}(x))$

[ocean seal]

Yottachad

[bright hedge]

you obviously have or ur teacher wouldn't give you this question

[slow silo]

no he didnt teach it

this unit is a self study unit

for us

[bright hedge]

search google for inverse functions

[slow silo]

ik its f^-1

so then it would be f^-1(0)=cos^-1(0)

i think

[bright hedge]

but it says find g(g^-1(x))

not f(f^-1(0))

[slow silo]

sin^-1(0)

[bright hedge]

are you even trying

[slow silo]

i am bro

i just dont get it

[bright hedge]

there is no 0

in part b

at all

so why are you so focused on 0

[slow silo]

f^-1(x)=(sin^-1(x)

[bright hedge]

correct

and we are looking for

f(f^-1(x)) = sin(sin^-1(x))

so what would that be

[slow silo]

not sure

[bright hedge]

so now

i want you to watch a video in inverse functions

[wanton junco]

were you taught what an inverse function does @slow silo ?

[slow silo]

it undoes another function

[bright hedge]

he said it was a self study unit

[bright hedge]

wait u know how it works?

then what is confusing about

[slow silo]

it would be x

[bright hedge]

yes

correct

(for all x in the domain of arcsin)

[slow silo]

so f(f^-1(x)) = sin(sin^-1(x))=x

[bright hedge]

which is x in -1 to 1

correct

[slow silo]

just to clarify this is the final answer

[bright hedge]

yes correct

does it say anything what x values it works for?

cuz in this case it would only work for

[wanton junco]

it is correct but b asks for the other way around

[bright hedge]

$-1 \leq x \leq 1$

[slow silo]

wait what

[bright hedge]

?

[wanton junco]

g^-1 (g(x))

[bright hedge]

oh ur right

then it works for everything

nah

for all x in btwn -pi/2 and pi/2

anyways that doesnt matter

goo goo it would ook like this

$g^{-1}(g(x)) = x$

[slow silo]

oh

[ocean seal]

Yottachad

[slow silo]

thats the final answer?

[wanton junco]

huh?

why would x be bounded?

[bright hedge]

cuz arcsin can only return values between -pi/2 and pi/2

so if it was above it

then it would return the fractional part of x + (the integer part of x mod 2pi)

i think

mod something else anyways

you get what i mean

[slow silo]

is this final answer?

[bright hedge]

yes

[wanton junco]

thus y is bounded not x tho

[slow silo]

so i dont put this

[bright hedge]

deus

what if x was 3pi/2

then it would give us back -pi/2

[wanton junco]

you're right

that's what im saying

[bright hedge]

oh

[wanton junco]

x is defined (-inf,inf)

but y is bounded

[bright hedge]

oohhhh

yeah that makes sense

[wanton junco]

since its composition

if it were g^-1(x) then yea you'd be right

[bright hedge]

yep

domain of sin is all reals

[slow silo]

so could someone walk me through the steps one more time so i fully understand

[bright hedge]

commposition of g and its inverse is just x

that's all

[slow silo]

f(f^-1(x)) = sin(sin^-1(x))

so this is wrong then?

cause its asking for the other way around?

[bright hedge]

yes

also f(x) = cos(x)

g(x) = sin(x)

so it would be:

g^-1(g(x)) = sin^-1(sin(x)) = x

[slow silo]

so far the steps i write g(x)=sinx

then g(x) = sin(x)

g^-1(g(x)) = sin^-1(sin(x)) = x

[bright hedge]

yes

[slow silo]

if you guys would be willing too

theres last question

i need help with

this

f(g(2/x)

[vague coral]

you determine the domain of g, then the domain of f, and you take the intersection

[wanton junco]

I think you should sharpen your understanding a bit more on compositions, maybe watch a couple vids before tackling it

[lone heart]

@slow silo Has your question been resolved?

[lone heart]

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[opal dock]

can anyone tell me what this problem is asking for

like net income per square meter?

.close

[lone heart]

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[placid zinc]

See the rules on helper pings

Yeah yeah it's done already haha. Just for the future

So by conservation of energy,
879 = 0.5mv² + mgh

v, h, g are known, so we solve for m

m = 879 / (0.5v² + gh)

Done by factoring out m, and dividing

Conservation of energy

Initial energy = final energy

[buoyant kayak]

you're solving for m

getting it as a denominator will do nothing for you

in fact it sets you back

solve for m

no it's not

algebra

algebra?

you're just solving for a variable

no different than if i asked you to solve for x in the equation x(5y-2)=2

[tacit arch]

,rotate

[buoyant kayak]

uhh

by factoring it lmao

it's a common term

x(y+z)=xy+xz

if you don't know algebra you definitely shouldn't be doing physics

i'm not gonna teach you algebra

someone already did, appreciate the name though

big words tough guy

i'll make sure i live by em

[sacred flax]

tf is happenming here

[alpine sable]

[sly mantle]

@fading quest knock it off. come back in 24h

[tacit arch]

[sly mantle]

.close

[lone heart]

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[alpine sable]

Hello I need help with this

[alpine sable]

Is this even possible to write that discrete sum as an integral

[frigid geyser]

ehh.. not really

[alpine sable]

Ikr

This need to be solved using other methods

[tacit arch]

isn't this from someone else

[hasty elk]

yes

[tacit arch]

if you want to be a pedant, you can use the counting lebesgue measure

[hasty elk]

didn't i answer this

[alpine sable]

Oh

[frigid geyser]

i mean it's not exactly the same but it works as an approximate

[alpine sable]

What’s that

[hasty elk]

something that transforms an integral into a sum, don't worry about it

[tacit arch]

https://math.stackexchange.com/questions/764076/integration-with-respect-to-counting-measure

[alpine sable]

Ok

[tacit arch]

has nothing to do with the problem, just me being a pedant

[hasty elk]

anyway, it's like maybe twelve hours ago in the competition math channel

[tacit arch]

listen to camill

[hasty elk]

that i answered this

[alpine sable]

Oh ok

So I don’t need to bother with this

[frigid geyser]

wait does that actually work??

[alpine sable]

Like it’s out of my syllabus

[hasty elk]

it works as an approximation

and a pretty tight one for this particular function and range

[alpine sable]

Hmmm

[frigid geyser]

oh wow this is REALLY tight

[alpine sable]

I see

[frigid geyser]

i mean ofc it works as an approximate but i thought it would be terrible

but it's surprisingly good

[alpine sable]

@hasty elk so is this by any chance out of the scope of my studies

[hasty elk]

depends on your level

[tacit arch]

you can calculate the delta to see why. essentially, the series grows incredibly slowly so every rectangle approximating the integral is close

[alpine sable]

I just got out of high school

[hasty elk]

if you're doing calculus at a university year 1 level, not a chance

[pale kestrel]

sum 4 to 10e6 of n^(-1/3)

[alpine sable]

Guess that answers my question

[pale kestrel]

are u tryna calculate this

in closed form?

or what

[alpine sable]

@hasty elk are u in masters

Cause this lebesgue thing seems super advanced

[hasty elk]

good luck lol

[pale kestrel]

what even is the question

[alpine sable]

This

[pale kestrel]

i dont get it

[hasty elk]

the original question yesterday was find the floor of that sum, i

[pale kestrel]

you have 2 expressions written down

[hasty elk]

i think

it's equivalent anyhow

[alpine sable]

So umm

[pale kestrel]

floor[sum 4 to 10e6 of n^(-1/3)]

[alpine sable]

Dayum

Should I close anyway

[pale kestrel]

is there no elementary solving technique? @hasty elk

[alpine sable]

People said Jensen inequality or something

[frigid geyser]

if youre a math major i believe baby rudin covers like a liiittle bit of measure theory

in case youre interested in that \epsilon_0

[alpine sable]

Uhh nope

[pale kestrel]

yh no, i dont remember jensen lol

[alpine sable]

I’m not atm

[alpine sable]

Me neither kek

[hasty elk]

there is

i just found the calculus one first

but there is a telescoping argument i believe, though i'm not the one who came up with it

[alpine sable]

What is a telescoping argument

[pale kestrel]

i wanna do log idk

🏳️

[alpine sable]

.close

[lone heart]

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[lethal bronze]

Can someone help me, I need to know how much 14% of 5 seconds, and if possible how to calculate that so I can do it myself in the future. Thank you.

[glass lichen]

what's 14% as a decimal?

[lethal bronze]

.14 I believe.

[glass lichen]

so just do 5*.14

[frigid geyser]

$x$% of $y$ is $\frac{x}{100} \times y$

[ocean seal]

xdk1235

[wary stream]

You can also do 5% of 14, if that makes the math easier

[frigid geyser]

^

[lethal bronze]

It might seem silly, but it confused me becase it's time. where my 5 seconds are like only worth 60 and not 100 (I assume its not the case, but you can see where it confused me)

[glass lichen]

,calc 5*.14

[ocean seal]

Result:

0.7

[glass lichen]

so 0.7 seconds

[frigid geyser]

just keep the unit and it's gonna be right

i see what you mean tho

[edgy sail]

u mean minutes are worth 60

[lethal bronze]

Thank you, appreciate it.

Yaaa it's the fact it was time that through me off. sorry to bother with simpleness. Have a great one.

[wary stream]

If you're done with the channel, close using .close

[lone heart]

@lethal bronze Has your question been resolved?

[lone heart]

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[tacit arch]

what's your f(x+h) ?

[wary stream]

What did you try?

[cursive geode]

i have no idea what i messed up on 😭

[wary stream]

Your signs for -f(x) are all wrong

They should all be the opposite

Because -(9x^2 -8x +3)

[cursive geode]

oh shit

so the signs should be oppoiste of what i have

[wary stream]

Yes

[cursive geode]

does -8x become positive

and the 3 becomse negative 3 right

[wary stream]

Follow this, -(9x^2 -8x +3)

Distribute the negative

[cursive geode]

ok i shall redo this with the correct signs and see now

.close

[lone heart]

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[inner sky]

confused abt how the range came into existence. my notes say to calculate max/min but that doesnt tell me the range

[lone heart]

@inner sky Has your question been resolved?

[inner sky]

<@&286206848099549185>

.close

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[fallen rapids]

Hello,guys.I am a new member here.Hope y'all are doing good.😊
By the way,I have a very simple math question regarding the rounding rule.Do we round 5.48 up or down?I know it's too absurd,but I have seen many people rounding the number multiple times and rounding it up to 6.That's why I am feeling bemused.

And yes, provide the function supporting your logic,please.

[jagged imp]

if you're rounding 5.48 to the nearest unit, it rounds to 5

[placid zinc]

https://www.factmonster.com/math-science/mathematics/rounding-numbers-rules-examples-for-fractions-sums

[covert agate]

usually, we round 5.48 to 5 because 5 < 5.5 (which from this point, we round to 6)

so for example we round 101.8 to 102 (because 101.8 ≥ 101.5), and 101.49 to 101 (because 101.49 < 101.5)

[placid zinc]

5.48
Digit before our round is 4
And we always round down a 4.

So that rounds to 5

Never to 6

Note the 8 doesn't matter.

[lone heart]

@fallen rapids Has your question been resolved?

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[fallen rapids]

Thanks for your aid,guys.😊

[lone heart]

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[barren nest]

idk how to solve it without any numbers :///

[tacit arch]

start writing some equations from the given information

start easy: circumference of the circle

[barren nest]

uhuh

[tacit arch]

have you found the length of the minor sector in terms of r and theta?

[barren nest]

im not sure how to do that

[tacit arch]

it's just $L_{minor} = r \theta$

https://www.cuemath.com/geometry/arc-length/

[ocean seal]

riemann

[barren nest]

icic

[lone heart]

@barren nest Has your question been resolved?

[lone heart]

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[tardy robin]

help with part c pls

how do i draw it without knowing the exact a value

considering there can either be no x intercepts

or multiple

[pale kestrel]

When there are different shapes due to parameter, usually you would sketch a different graph for each case

But maybe there is no difference between cases here

You have to check

Do you know how to approach this?

[tardy robin]

nope thats what im asking

how do i approach this

since i dont know what the a value is

i can only think of a range of what the graph looks like

[pale kestrel]

well first is algebraic manipulation

Do you recognise what shape that should be

[tardy robin]

yea

its a circle

[pale kestrel]

yh so complete the square

it could be a circle or ellipse

[tardy robin]

okay ill try it

[lone heart]

@tardy robin Has your question been resolved?

[lone heart]

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[alpine sable]

Shubhi bought 6.700L petrol at Rs.45 per litre. How much did she pay for the petrol?

[alpine sable]

can anyone tell answer

hello

[echo socket]

Just divide them maybe?

[alpine sable]

i did it but it is wrong in answer sheet

hello

[echo socket]

What did you get?

[alpine sable]

in answer sheet it is 301.5

do we have to multiply it

[echo socket]

Their product is definitely bigger than 301.5 tho

Did you mean 6.7?

[alpine sable]

yes

[echo socket]

Then yes multiply them

[alpine sable]

beans can you give me explaination

[slender gull]

,calc 6.7*45

[ocean seal]

Result:

301.5

[slender gull]

Correct it is.

[alpine sable]

that means we have to multiply it or what

[slender gull]

We have to multiply.

[alpine sable]

but why

[slender gull]

45 is price for one litre.

We have to find for 6.

If a book is $5 and you have to buy two, you pay 10 right?

[alpine sable]

yes

[slender gull]

So you multiply it.

[alpine sable]

we multiply 5x2

[slender gull]

Yes.

So in this case we multiply 6.7 with 45.

[alpine sable]

thanks

[slender gull]

Yw

[alpine sable]

my question is solved

[slender gull]

@alpine sable .close

[alpine sable]

.close

[lone heart]

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[tired drum]

How would I do this?

[tacit arch]

Contradiction

[tired drum]

What would I have to assume?

[tacit arch]

The contrapositive

[alpine sable]

Assume that there is a sequence with cd

[tired drum]

Mhm

[pale kestrel]

You know what an arithmetic sequence is right?

[alpine sable]

Then prove its contradictory

[tired drum]

I think lol

[pale kestrel]

yh then u should be fine with their advice

[tired drum]

Could someone show working

[pale kestrel]

1. is a bit sus

[tired drum]

Man why can’t anyone just straight up carry in this server lol

[pale kestrel]

???

We don't give answers

[alpine sable]

Wait giving

[pale kestrel]

No don't.

[tired drum]

Noo pls

[pale kestrel]

Like if you're stuck we can help

[tired drum]

Lol

[pale kestrel]

But can't you read the rules?

[alpine sable]

Ok

[pale kestrel]

This server isn't here to do your homework

[tired drum]

Yeah this isnt my homework tho lol, im doing some study before school starts

[alpine sable]

another hint a+nd|a

ma=nd

I might be wrong tho

[pale kestrel]

I wouldn't say this is easy, but I would start by trying to write some sequences of prime numbers

and see what goes wrong.

3, 5, 7, ... why do I get stuck here?

5, 11, 17, 23, 29, 🤔

[tired drum]

Mhm

Lol done that

Still dont know how I could mathematically show it

[pale kestrel]

hint, write out what an am looks like

lets say we start with p

p, p+d, p+2d, p+3d, p+...

[tacit arch]

Pretty entitled attitude there

[pale kestrel]

Can you see what will eventually happen?

[tired drum]

Why thank you

[alpine sable]

Well this is getting pretty heated

[tired drum]

No not really lol

I’ve self taught myself arithmetic sequences so I’m really good at them

[pale kestrel]

ok let me give u another clue

Let's say we have p = 5 ok?

5, 5+d, 5p+2d, 5+3d, 5+4d, 5+5d, 5+6d, 5+7d,...

@tired drum Any problems with what I've written ^ ?

If they are all prime

[tired drum]

5+5D isn’t prime

ohhhh

I get it now lol

Cheeers

[lone heart]

@tired drum Has your question been resolved?

[lone heart]

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[rich basin]

https://www.youtube.com/watch?v=Tf0jetLbFX4&ab_channel=blackpenredpen

[rich basin]

how did he go from here?

?

[wispy path]

yo

D is an inner point of an equilateral triangle ABC satisfying angle ADC=150 degree. How do you prove that the triangle formed by taking the segments AD, BD, CD as its three sides is a right triangle?

can someone send the solution

without rotation

can we do this problem?

[vale wigeon]

@wispy path this channel is occupied. read #❓how-to-get-help and get your own channel.

[rich basin]

<@&286206848099549185>

[lone heart]

@rich basin Has your question been resolved?

[little drum]

$e^{ix} = \cos x + i \sin x$

[ocean seal]

Ansh

[little drum]

you'll get your expression from that

[rich basin]

forgot about thanks

.close

[lone heart]

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[real night]

i have two doubts

[real night]

first is this one-

ss from my test last week

[tawny orchid]

Do you know the theorem which says that the angle subtended by a chord to a point on on the circle is equal?

So BAC = BDC

[real night]

through that logic would the answer be C?

60 degrees

[tawny orchid]

Yep

[lone heart]

@real night Has your question been resolved?

[real night]

one more question

i am 70% sure it is C

the answer key is not out for this as well

so I can't cross check

[tawny orchid]

It's C

you're correct

[real night]

one final crosscheck-

this was the last question i was having trouble with

[tawny orchid]

It will be half the area of the parallelogram

[real night]

hmm.. how

[real night]

oh yea, i get it now. thanks!

.close

[lone heart]

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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!

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

[floral quail]

How would I do this int by sub?

Not sure how to deal with the ^3

[pale kestrel]

(u - 1)^3

according to your sub?

for a good sub

[floral quail]

tryna get it to du though and get rid of dx

[pale kestrel]

uhhh

ill give it a shot i guess but i never was good at these

[floral quail]

alr ty

[pale kestrel]

$$I=\int\frac{e^{3x}}{1+e^x}\dd{x}$$

[ocean seal]

Shuri2060

[pale kestrel]

why not just u = e^x

du/dx = e^x = u

du = u dx

[pale kestrel]

what.

[floral quail]

required to use u=1+e^x so..rip

[pale kestrel]

ok, let me crash and burn first lmao

$$=\int\frac{u^2}{1+u}\dd{u}$$

[ocean seal]

Shuri2060

[pale kestrel]

pretty sure this is doable but ill try that

$$I=\int\frac{e^{3x}}{1+e^x}\dd{x}$$

[ocean seal]

Shuri2060

[pale kestrel]

u = 1 + e^x

du/dx = e^x

du = e^x dx

[floral quail]

Yeah

[pale kestrel]

$$I=\int\frac{(u-1)^3}{u^2}\dd{u}$$

that right?

then you can multiply top

and divide thru term by term

[floral quail]

One sec, trying to understand it

[pale kestrel]

oh man

mistake

$$I=\int\frac{(u-1)^3}{u}\frac{1}{e^x}\dd{u}$$

[ocean seal]

Shuri2060