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[median pulsar]

I dont know what to do when i get 4y-3

:/

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[thin ginkgo]

<@&286206848099549185>

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[vocal dragon]

hey, if i have an even permutation matrix does that mean i can get to that by only rotating the $\mathbf{e}_i$'s in space? it's true in 3D but does it hold in higher dimensions

[glossy valve]

Ꭿmong

[fathom saddle]

eis?

Rotate in space?

[vocal dragon]

$\mathbf{e}_2 = \begin{bmatrix} 0 \ 1 \ 0 \end{bmatrix}$ for 3D

rotate in space as in, you know, how we rotate the co-ordinate system about an axis

[glossy valve]

Ꭿmong

[fathom saddle]

Get to that?

[vocal dragon]

is it possible to convert the identity matrix into an even permutation matrix by using only rotation matrices

maybe better way to frame that idk

[fathom saddle]

Oh I see hmm

Well, you can easily cycle the basis vectors

Giving
0 0 1
1 0 0
0 1 0

And yeah, that's even

Sure enough,
(123) = (23)(13)

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[vocal dragon]

right sorry i went afk

[vocal dragon]

i mean yeah obv in 3d
but can we do that in higher dimensions

if i have a general even 6x6 permutation matrix, can i get to it by cycling rows 3 at a time

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[simple cipher]

Can someone teach me how to find the equation to this table?

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[lusty warren]

Find the area between |x + 1|, x asis and the lines x = -2 and x = 1

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[lusty jacinth]

An airplane has economy and first class seating. There are s seats on each row in economy, there are t seats in first class.

There are 9 rows in first class and 24 in economy .
Write down an expression in of s and t for the number of sweets in the airplane

please help!

[little helm]

youre still on this lol

9 rows in first class, t seats in each row

its like

---

---

---

here there are 3 rows and 4 dashes in each of these rows

how many of those dashes are there?

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@torn jolt Has your question been resolved?

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[torn jolt]

@river gate

do you think you could help me with this

[river gate]

What have u done so far?

[torn jolt]

well

I kinda made some variables to make a system of equations

16x=2(24y)

x + y = 200

but idek if they are correct cause I couldn't go anywhere with them

[river gate]

Oh sorry

So we know x the number of gallons in city driving

[torn jolt]

yes

and y is the number of galloons in highway

;-

[river gate]

That seem to be right.

[torn jolt]

so y = 50?

[river gate]

16x+24y=0

And x+y=200 Try that

[torn jolt]

why = 0

what does that represent

[river gate]

Since we don't know total miles I assume it's zero at the beginning.

[torn jolt]

oh

[river gate]

We know x represent driving city street and y represent high way

[torn jolt]

I got x = 600 and y = -400

which makes little sense

[river gate]

No that's incorrect.

[torn jolt]

how

[river gate]

That's right

i forget twice

[torn jolt]

so

[river gate]

16x+24y=200 2y-x=0.

[torn jolt]

oh ok

[river gate]

I forget to read twice

[torn jolt]

x = 50/7 and y = 25/7

they aren't integers however

[river gate]

There must be something else is missing since it's not correct.

[warm abyss]

Oh, sorry. English isn't my native language so I interpretated the text wrong. In my calculation I'm assuming that the car needs 16 gallons per mile

[warm abyss]

I think it works to replace the 16 by 1/16 and 24 by 1/24

[river gate]

Try 16x+24y =200 and 2y+x=0

[river gate]

I got it

Finally

It's 16x+24y=200 and 2y+x=0

Yup it makes sense

That's 100 percent correct

Sorry it takes way too long

I wasn't thinking right

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[river gate]

Anyways I am going to bed @torn jolt . That should be correct equation. Now you should able to figure total mile.

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[rain nest]

I'm aware I need to use the ML inequality here.
Clearly L = 6pi (the length of the contour, a circle of radius 3).
Hence I need to show that M, the maximum of | (2z̄+1) e^iz | is less than 15/e.
I will post my work so far.

[rain nest]

Let $z = x +i y$. $1\leq y \leq 7$, and $-3 \leq x \leq 3$.
$$|(2\bar{z}+1)e^{iz}| = |(2x-2iy+1)e^{ix-y}| = |2x+1-2iy|e^{-y}$$
$$\leq |2x+1|e^{-y} + |-2iy|e^{-y} = (2x+1+2y)e^{-y}$$

[glossy valve]

Espio

[rain nest]

At this point, my guess was that e^-y is largest when y=1, and (2x+1+2y) is largest when x=3, y=4, which would yield 15 as desired, but a quick Desmos check shows that it's actually around x≈1.5, y≈6. I'm not really sure where to go from here.

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[plush egret]

hmm

i want to try but im new to this so i will probably fail

[gritty rose]

I think the hard part is just finding the max of $(2\overline{z} + 1)e^{iz}$ on the circle $|z - 4i| = 3$

[glossy valve]

riemann

[rain nest]

Well... yes, that was exactly what I was asking how to do

[smoky scroll]

$$|2\bar{z}+1|=|\overline{2z+1}|=|2z+1|=2\left|z+\frac12\right|$$
$$\leq 2|z-4i|+|8i+1|$$
$$=6 + |8i+1| \leq 6 + |8i| + |1|= 15$$

[glossy valve]

Mat

[smoky scroll]

This should work maybe

[rain nest]

Oh! That's excellent, thank you!

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[lime bolt]

umm hi can someone help me plz with 2 math problems plz

[lime bolt]

h and i

cause i need to find x

but idk how

[smoky scroll]

For h, you need to be able to solve

[lime bolt]

?

[smoky scroll]

$x^{\log(x)}=x$

[lime bolt]

yes

[glossy valve]

Mat

[lime bolt]

but what abt the ^2

it will be like (x+9)^2=(x+9)

and x+9=0 x=-9?

@smoky scroll

[smoky scroll]

You gen get the equation in this form, which is the essential part of the problem

For instance, after substituting u=x+9

[lime bolt]

so wdym

[smoky scroll]

Are you familiar with using substitutions for solving equations?

[lime bolt]

kinda but

is sometimes complicated

[smoky scroll]

If we let u=x+9,

[lime bolt]

ok

[smoky scroll]

$10^{(\log(u))^2}=u$

[glossy valve]

Mat

[smoky scroll]

We then want to solve this for u

[lime bolt]

ohh that make much more sens

rn

kinda

so u is x+9

[smoky scroll]

Yes, once we get solutions for u, then we get x by knowing that x=u-9

[lime bolt]

ohhhh thx man

and for

i

can u help me plz

[smoky scroll]

So, though, then you can proceed from here, right?

[lime bolt]

yea i think

but not to be wrong

how much will be x

[smoky scroll]

-8, 1 I think

[lime bolt]

bruh i messed up

can u explain to me

cause i am dumb

at math

[smoky scroll]

Mm let's see

[lime bolt]

ok

so if u is x+9

[lime bolt]

and we do apply that

sth like

[smoky scroll]

$u=10^{(\log(u))^2}=10^{\log(u)\log(u)}=10^{\log(u)\log(u)}=\left(10^{\log(u)}\right)^{\log(u)}$

[glossy valve]

Mat

[lime bolt]

ok

[smoky scroll]

And then?

[lime bolt]

so

wait

oh wait

it will b

u^log (u)

?

@smoky scroll

[smoky scroll]

Sorry, here I am

[lime bolt]

ye is ok

but am i right ?

[smoky scroll]

Right

[lime bolt]

yes

[smoky scroll]

u=u^log(u)

$u=u^{\log(u)}$

[glossy valve]

Mat

[smoky scroll]

Then how would you approach this?

[lime bolt]

yes

ye ik from now

but can u help me at i

plz

[smoky scroll]

Ok

[lime bolt]

.

cause that is kinda hard

[smoky scroll]

I seems very similar

u=x+1

Then convert log base 2 into log base 10

[lime bolt]

umm wait how

mat ?

@smoky scroll

[lime bolt]

ok i know how to do this

but

but the logarithm is at the exponent

[smoky scroll]

You can convert it there

[lime bolt]

ok

and from there ?

it will be like

[smoky scroll]

log_2(u)=log_10(u)/log_10(2) right?

[lime bolt]

yes

is right

[smoky scroll]

So,

[lime bolt]

but the other log

is kinda complicated

bcs is ^2

[smoky scroll]

$10^{\frac{\log(u)}{\log(2)}} = \left( 10^{\log(u)}\right)^{\frac1{\log(2)}}$

[glossy valve]

Mat

[lime bolt]

ye

oh wait

ik now

how to do it

[smoky scroll]

And the other like we did before

[lime bolt]

yes

is similar

thx for everything mat

[smoky scroll]

Np!

[lime bolt]

thx man

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[pulsar dragon]

How do you solve this?

[pulsar dragon]

It was fine until I had to figure out what c was equal 2

Because I got like

C=ln|6|-1/2ln|9| and I was like

That’s really messy

[hearty ferry]

Can you simplify that expression for C

Your use of log laws was slightly incorrect in your working

[pulsar dragon]

you mean I can simplify it down to ln(6/9)?

what do I do with the 1/2 btw

[hearty ferry]

Kinda but there is the 1/2 infront of ln(9)

Try to put the 1/2 in the log by using a log law

[pulsar dragon]

mm I can raise 9 to the 1/2?

ln(6/9^(1/2))?

[hearty ferry]

Yea

9^(1/2) should be easy to calculate

Then it simplifies

[pulsar dragon]

ty!

wait so I do just wnds up with ln|2|?

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[halcyon shoal]

is this true or false?

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[lunar hearth]

a:b -> a/a+b

1 = a
3=b

a/4?

1/4?

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[lunar hearth]

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[mild mango]

Try to find y such that y-(-3):4-y = 1:3

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@lunar hearth Has your question been resolved?

[lunar hearth]

steps:
1:3 ratio= a:b-> a/a+b
1:3 = 1/4
Xd: x2-x1
Yd: y2-y1
x1=2 y1=4
x2=-3 y2=-3
-3-2=-5 -3-4=-7
Xmovement= Xd * frac = -5x1/4= -1.25
Ymovement= Yd * frac = -7x1/4= -1.75
points(x1+xm, y1+xm)
2+-1.25=0.75 4+-1.75= 2.25
points(0.75,2.25)

since were looking for segment DF, F is the second coordinate so i believed it was 2.25.

[mild mango]

Calculate y2-ym instead to get -1.25

[lunar hearth]

ye just noticed

whoops

[sonic marlin]

I hope you know what is this formula

[lunar hearth]

i dont use that formula

i use a different one

[sonic marlin]

then use your formula

[amber radish]

it's the section formula

just apply that

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[gleaming fox]

what does the
(n-k
k)
do in this sum?

[dawn fossil]

it's a binomial coefficient

if you're asking why it's there, then you should post more context to this sum

although i am guessing this is some binomial theorem stuff

[gleaming fox]

got it

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[hard kestrel]

how do i prove something like this?

[nova basin]

a and b are in [0, 1] or some other constraint ?

[hard kestrel]

i think a, b > 0?

[nova basin]

I'm saying this because the graph shows it doesn't always work if one of them is bigger than sqrt(2)

[nova basin]

This purely computational. Rearrange and find the minimum of the different functions that appear

[nova basin]

better than I made it look. Should be a matter of like 8 lines

there are convenient simplifications that can be made

[polar mica]

you must be good at maths olympiads

im sure theres a solution by QM-AM or the like

[nova basin]

What's QM-AM ?

here you can just express it as a constant +f(x) +g(x), and it turns out they both have their min at 0.5, and at 0.5 it adds to 12.5

really convenient

[polar mica]

quadratic mean-arithmetic mean inequality

[nova basin]

I used a²+b² = 1-2ab, so in a way I kinda used that

then I did use 2ab >= 0.5

[polar mica]

nah i mean a lot of the time u dont need calc

its nicer that way

[nova basin]

very little calc but I did use calc yes

how would you have done it?

[nova basin]

to say a²+b² >= 2ab ?

[polar mica]

yep

that was the method i was thinking too (sorta)

[nova basin]

something has to be wrong in this because you start with (thing) / 2 >= ... >= 12.5, but thing evaluated at a=b=1/2 yields 12.5

unless I messed something up ?

[polar mica]

yeah op added an extraneous 2 in $2\left(\frac{a+b+\frac{a+b}{ab}}{2}\right)^2$

[glossy valve]

A Fellow Human

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[proper pelican]

How would I solve this?

[nova basin]

When you go through the numbers in order, every third number is divisible by 3. Feels much simpler than doing weird digit sums like that

[proper pelican]

oh got it

thanks

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[latent breach]

.open

[quaint falcon]

hi guys does anyone know how to solve this

[hollow geode]

it's asking for the domain of h

[quaint falcon]

What does domain means tho? I am new to functions

[hollow geode]

Domain is the set of inputs

[quaint falcon]

Ohh

[hollow geode]

You dont need to ping every message btw

[quaint falcon]

Ok

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[worldly jolt]

i dont know how to set this one up

.close

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[grim ravine]

Can someone please help me with this question?

[grim ravine]

I don’t know how to apply the quotient rule to this

[hollow geode]

Like any other quotient

[grim ravine]

But what is the g(x) and g’(x)

[hollow geode]

g is the denominator

Again, like any other quotient rule application

[grim ravine]

This is what I’ve done so far, is this the right direction?

I’m thinking from this point to replace the x with -10 and then solving it through

[tender rain]

,rotate ccw

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[torn jolt]

How do i get "h"

[nova flume]

can someone @ me if there's an answer im curious too

[torn jolt]

and "d=40 cm"

[velvet spoke]

You can construct an equilateral triangle using 3 circles

[kind jay]

yes

[torn jolt]

Does this make sense

[velvet spoke]

@torn jolt what do you get if you sub d=40cm?

[velvet spoke]

this is approx 56.57 which is not correct

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[pallid snow]

guys is radical5 + 2 the same as 2 + radical5

[shy valley]

a+b = b+a

so yes

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[amber radish]

Addition is commutative

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[sick ivy]

Need some help with this question. Not really sure how to approach.

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[sick ivy]

<@&286206848099549185>

.close

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[torn jolt]

How do I make variables in math equations

[torn jolt]

like for example

sec

a ratio of 2 volumes

how can i do this

not what i mean

basically

how can i let people know

these are both volumes

[ivory cairn]

use sentences.

like "where v_1 is the volume of a cube and v_2 is...."

[torn jolt]

yes but

how would i write down the equation

un

um

do i just write it down seperately

[ivory cairn]

yes

[torn jolt]

and also is it correct to do V_1 and V_2

or is there a diff way

im just curious lol

[ivory cairn]

"Let v_1 = whl be the volume of the solid, then .....

[ivory cairn]

there might be, just writing out that they are equal is probably the easiest and most straightforward.

[thin flint]

Let $\frac{V_1}{V_2}$ be the ratio of the two volumes $V_1$ and $V_2$.

[glossy valve]

Katharine

[thin flint]

@torn jolt

[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

well yes but where do i define the v1 and v2

[thin flint]

what do you mean?

Do you want to say

$V_1 = $?

[torn jolt]

ueah

yeha

ysh

yeah

[thin flint]

Let $\frac{V_1}{V_2}$ be the ratio of the two volumes $V_1 = $ and $V_2 = $.

[glossy valve]

Katharine

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[full forum]

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[torn jolt]

Help

[gritty rose]

You getting trolled

[torn jolt]

wdym

[gritty rose]

,w zeta(3)

[glossy valve]

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[torn jolt]

but it doesnt want a approx it wants a fraction like zeta(2)=pi^2/6

[gritty rose]

.

[torn jolt]

i dont get it

[gritty rose]

Where's the problem from

[hollow geode]

Given the Basel Problem took a very long time and one of the greatest mathematicians to live, I highly doubt you're actually expected to derive zeta(3) exactly

[torn jolt]

Solved by Leaonard Eular but today modern computers and mathmatical methods can help derive what zeta(3) percisely is

according to my teacher

he says we probably need an IQ of over 150 but

still

[arctic wedge]

Yeah so type it into wolfram lol

[hollow geode]

well duh, we're not saying it's not doable

we're just saying this isn't the typical problem to encounter as a student

showing convergence of the sum would be more typical

[torn jolt]

well thats easy

[hollow geode]

Im aware

[torn jolt]

but why not this

didnt eular find this easy using taylor and maclaurin formulas

[gritty rose]

"in the form of a fraction" implies the result is some rational number or multiple of some well known irrational number like 1/2 * e

[torn jolt]

modern students can 2

he did it at age 20 why cant modern higher iqs find it at age 15

[hollow geode]

cause Euler was niche case

[torn jolt]

he was not

[gritty rose]

This is getting philosophical. Take it to #math-discussion or somewhere else

[hollow geode]

If you're going to sit there and say the average person is as smart as Euler, then you're unfortunately wrong

[arctic wedge]

IQ doesnt mean shit, also euler was one of the best to ever do it

[hollow geode]

There was also a massive historical significance on ones ability to do mathematics that didn't translate well into the modern world

[torn jolt]

well thats cuz he had the tutor known as bernoulli

[hollow geode]

Ok, and Bernoulli was also a genius

[gritty rose]

@hollow geode please stop feeding trolls

[gritty rose]

.

[torn jolt]

yes

.close

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[vivid finch]

.

[vivid finch]

is am2=am1

yes or no

if so why

[hollow zephyr]

No, one of them has 2 congruent marks, while the other has 1 mark

For them to be equal that means angles a1 and a2 have to also be congruent

Which we cannot say they are

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[unreal flax]

why do i not get the same answer?

[gritty rose]

The real parts are different

[unreal flax]

where did i do smth wrong?

[gritty rose]

No wait it's the same

Distribute the minus sign

[unreal flax]

$\frac{-\sqrt{3}+3i}{2}=-\frac{\sqrt{3}-3i}{2}$

[glossy valve]

AuHasard

[unreal flax]

oh okay.

i see

thanks

.close

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[torn jolt]

@ivory cairn woukd it be possible to check if i got this right?

@fathom saddle

[ivory cairn]

,w taylor series cos x at x=2pi

[glossy valve]

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[ivory cairn]

you have (-1)^2n which is always 1.

[torn jolt]

oh oops

that means I could've used direction substitution on this formula, correct?

is that the standard procedure for finding Taylor series at a = something questions?

[ivory cairn]

looks like it, which makes sense because cos(x) = cos(x+2pi)

[torn jolt]

in which situations do you think the above strategy becomes invalid?

[gritty rose]

What question are you even solving

[torn jolt]

This

[gritty rose]

I don't see a question here

[torn jolt]

oh, I need to find the taylor series for cos x at a = 2pi

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[coral ermine]

How do i do this

[vapid barn]

find what?

[coral ermine]

volume

[vapid barn]

b*h

[coral ermine]

h is 44?

[vapid barn]

yep

[coral ermine]

ok ty

do you guys know what this shape is

[vapid barn]

i don't think it has a particular name

[coral ermine]

ok

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[torn jolt]

how can I write this differently

so I can see the x intercepts

@torn jolt

ty daddy

.close

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[torn jolt]

this is worth 5 marks did i show everything i need to

[little helm]

the answer isnt right

why is there a closed interval ?

[torn jolt]

(5,infinite) part?

[little helm]

both

it should be open everywhere

[torn jolt]

what do you mean?

[little helm]

since, at -5, 0, 5; the expression evaluates to 0

you want it to be less than 0

not ≤ 0

[torn jolt]

oh so 5 doesnt count

[little helm]

yea

[torn jolt]

[ means closed

{ means open

right?

[little helm]

Not really sure if youve been taught that

but () definitely means open

[torn jolt]

im learning on the spot

[little helm]

oh ok

Ig use ()

[torn jolt]

teacher doesn’t actually teach

but would I include 5?

or do i have to put 4.9

[little helm]

No

you would say (5, inf)

and (-5, 0)

[torn jolt]

oh so the problem was with the brackets

[little helm]

yes

[little helm]

this cant really work because between 5 and 4.9 there an infinite number of real numbers except 5 that are valid solutions

dont use {} btw

[torn jolt]

ok I understand now

.close

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[tepid mortar]

just wanted someone to check my work

[ivory cairn]

assuming [x] is the floor function, looks good

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[honest wind]

Ik m too dumb. Not able to solve even ez qstns.

I tried to complete the square but it's not getting right

[umbral viper]

whoa

wait @kind jay don't go

[honest wind]

Lemme try substitution w8

[umbral viper]

alrite

[honest wind]

How can someone be that dumb 😭

Is it ok

Took x common and put it into square root

Multiplying inside fn by x², it becomes derivative of the outside fn

Is it fine?

[honest wind]

.

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[full forum]

@torn jolt Has your question been resolved?

[torn jolt]

<@&286206848099549185>

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@torn jolt Has your question been resolved?

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[raw python]

What’s the formula for circle theorem

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[raw python]

What’s the formula for circle theorem

<@&286206848099549185>

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[raw python]

<@&286206848099549185>

[topaz aspen]

That's a google search away

[dusk inlet]

(x-h)^2 + (x-k)^2 = r^2 where (h, k) is the center of the circle.

r is the radius.

is that what you mean?

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[lapis perch]

<@&286206848099549185>

[meager dew]

ping helpers after 15 minutes only

show work

tell where you’re stuck

[meager dew]

read this

[lapis perch]

sorry

[lapis perch]

just stuck on this

[meager dew]

what have you tried

[lapis perch]

i tried to go to google and use a calculator there but i got 111

but i need to understand how i got it

i get confused easily

[meager dew]

show your work

[lapis perch]

ive been stuck im getting soo confuesed

[meager dew]

perhaps a video or a guide on binary division would help

if you have no idea how to do binary division you shouldn’t start with a problem

start with a video/guide

[lapis perch]

do you have any suggestion

[meager dew]

https://www.google.com/amp/s/www.wikihow.com/Divide-Binary-Numbers%3Famp%3D1

this one seems pretty straight forward

[lapis perch]

hmmm alright thanks il come back if im confused or no thanks

[lapis perch]

sorry i still dont get it being honest

i still get confused

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[carmine shard]

Hello

[carmine shard]

I need help

How to do combinations again?

I just need a quick explanation

[wheat verge]

For part (a), do you know how to count the number of ways to select 5 people from a group of 10?

[carmine shard]

Hi slr im done

Um i need help with rules of probability

[carmine shard]

If that's okay with you

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[torn jolt]

so the question is ratio AB is 3:8 and ratio BC is 6:7

[torn jolt]

wht is ratio ABC

pls help :c

<@&286206848099549185>

[hybrid prawn]

you have to wait 15 mins to ping helpers.

[torn jolt]

oh sorry

[hybrid prawn]

anyways

[torn jolt]

how to close help and make it availible i found answer on yt

[hybrid prawn]

.close

[tender rain]

.close

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[stone tree]

Please let me know what you get, I got 1590.75 cm aquare

<@&286206848099549185>

<@&286206848099549185>

[fossil stump]

Show your work - I doubt others will do a problem for you and check your answer

Help us help you 👍

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[stone tree]

alr

i did show my work but this is like my third time asking tbh

ill do it again

@fossil stump

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[stone tree]

<@&286206848099549185>

https://tenor.com/view/daredevil-daredevil-dog-tough-dog-red-mask-dog-gif-23418245

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[uneven nova]

This question is part of revision for my year 12 topic of trigonometry, and I am unsure where to start.

[wary surge]

So you can first use the sine rule to find the yellow angle, then since you know two angles you can find the red angle and then since angles on a straight line, you can find the green angle and then since angle sum equals 180 degrees you can find theta.

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[hot marlin]

Guys if I have something like int [a -> b] sin(x/2) dx and I wanted to do u-sub, would I change [a->b] to [u(a) -> u(b)] because it

[hot marlin]

's a definite integral

[glossy valve]

abs_0

[neat bay]

@hot marlin with u-sub, you can change the limits of integration in terms of u, it's just annoying

much easier to just say

let u = x/2, so du = dx/2 which means du/2 = dx

[glossy valve]

abs_0

[hot marlin]

uhhhhhhh

ok well I tried that and it didn't work

the full problem is this:

$\int_{0}^{30}\left(82+4\sin\left(\frac{x}{2}\right)\right)dx$

[glossy valve]

SauceBauce

[neat bay]

do you have the solution on hand?

[hot marlin]

$which can be automatically written as 2460+4\int_{0}^{30}\left(\sin\left(\frac{x}{2}\right)\right)dx$

[glossy valve]

SauceBauce

[hot marlin]

uh it's about 2474

but its the $4\int_{0}^{30}\left(\sin\left(\frac{x}{2}\right)\right)dx$ I can't get

[glossy valve]

SauceBauce

[hot marlin]

for what ever reason

[neat bay]

,w 2460 + 2(-cos(15.0) + 1)

[glossy valve]

Results provided by WolframAlpha

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Requested by abs_0#8527

[neat bay]

2474?

that's weirdly close

wait @hot marlin something is wrong here

[hot marlin]

uhhhh

[neat bay]

2460 + something = 2474

[hot marlin]

yeah so what's going on with the limit changing?

[neat bay]

oh

instead of actually doing u-sub

they just applied it to the limit

-cos(u(x)) applied at 30 and 0 = -cos(u(30)) - -cos(u(0))

[glossy valve]

abs_0

[hot marlin]

ahhh

ok Imma do that

that's really weird tho I've never had to change the limits before

[neat bay]

so r u good?

[neat bay]

honestly i don't get how this is wrong

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@hot marlin Has your question been resolved?

[oak basin]

if you did u-sub for a definite integral, the bounds had to be changed so that it is in terms of u, because simply you are integrating wrt u

[neat bay]

couldn't you keep the bounds the same and substitute u back later

[oak basin]

of course if you didnt want to change the bounds, you have to denote it as x=a, x=b and in the end, you have to substitute x back into the result to evaluate

[oak basin]

yes

but again, if you wrote the bounds without inplying that it is in terms of x, then the integral is not the same thing

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[upper magnet]

hell o

[upper magnet]

a commitee of 7 hast to be formed from 9 boys and 4 girls . in how many ways a commitee can be formed by selecting atleast 3 girls

this is my question i want to know how to do it

[north forum]

prove it's equal to (number of ways you can form a committee with 9 boys and 4-3=1 girl) * (number of ways you can choose those 3 girls)

[upper magnet]

ahhh

say me answer itself i am so dum

4c3 * 9c3+4c4 *4c3 is this the answer

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[quasi oriole]

Show your working, or what you've done till now

First customer didn't buy 10n

Re-read that part

1/10 of what

Remaining stock

n is the number of customers

Yeah, now find the same for second customer

To get a pattern

You've also been given that any 2 customers bought the same amount of stock

So you can equate them

1/10 of remaining stock

One min lol

I think that should give you the answer

Equating the first 2 customers

Did you try it, assume the initial stock to be 'x'

Try the steps that I told you

So it's 1/10th of remaining stock

Everytime someone buys, the stock should be reduced by that amount

Initially stock x
then after first guy buys it's x-10
Then he buys 1/10 of (x-10)

Now remaining stock is x-(1/10 of (x-10))

Second guy bought 20
Then he bought 1/10 of (x-(1/10) of (x-10) -20)

Let me know if you followed this^

You there? @torn jolt

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[main scaffold]

Yo

[main scaffold]

Help

anyone hmu

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[kind jay]

posting a whole screeenshot of 11 exercises with 'help'

doing great ben shapiro

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[main scaffold]

K bud

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[open isle]

i am having a hard time with this

do we use a chain rule?

even if we do chain rule on this

it would be like this

derivatice of f(1) is 0

0 * it doesnt even matter

and i dont quite think 0 is the answer

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@open isle Has your question been resolved?

[vestal stag]

really you should take the derivative before you plug in x=1: take the derivative of f(x^2) using the chain rule

[open isle]

well

f'(x^2) * 2x

do we plug in x now?

x = 1?

ohh wait

i think i see it

it would be f'(1) + 2

which becomes 2

so its C?

[vestal stag]

shouldn't it be f'(1)*2?

[open isle]

oh ye thats what i mean

wait

it would be 0 * 2 ;-;

so the answer is 0?

[vestal stag]

yes

[open isle]

oh okay

i see it now

idk why i thought 0 wasnt the right answer

[vestal stag]

in this case, plugging in and then differentiating got the right answer, but it could give the wrong answer elsewhere. If you plug in first, you get a number, and then the derivative of any number is 0, even if 0 isn't the correct answer. Just be careful about what order you do things in basically.

[open isle]

okay

thank you

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[slender lynx]

hi

[slender lynx]

e^(x)+x+1=0

can any one solve this for me

i want to find x

<@&286206848099549185>

[quiet stirrup]

Something like this you would just throw into an online calculator

[slender lynx]

nah i need to find it how

its a quetion

[quiet stirrup]

You can just use newton's method if you want then

[slender lynx]

idk what's that

[quiet stirrup]

Here is a sloppy but fast answer

https://en.wikipedia.org/wiki/Newton's_method

[hollow geode]

there's no analytic way to find the root of e^x+x+1 iirc

you need numerical methods

[slender lynx]

it just poped in a exercice saying find x in g(x)=0

idk what to do

[nova basin]

depends on whether you consider the Lambert W function to be a numerical method or not

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[coral mantle]

This is what I did but the answer key gives the integral of 0.04y^2 dy between 0 and 25

Im not really sure where I went wrong

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[delicate vigil]

I'm trying to find a proof of this:
-a = -1 . a

How could I google this? I swear I tried many things but I can't find anything

[hollow geode]

STS that a+(-1.a)=0

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[delicate vigil]

Ah sorry the delay, was outside. Yea I guessed it was from there. Though I'm not sure what STS means. Google says is "swear to satan" but I doubt it applies to this case lol

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@remote fox Has your question been resolved?

[remote fox]

<@&286206848099549185>

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[proper dune]

I don’t know how to evaluate the limit in the following problem

[stiff musk]

can you write cos(pi/2 - x) in terms of sine?

[proper dune]

Do you mean like this?

[stiff musk]

no, i meant use $\cos(a-b) = \cos(a)\cos(b) + \sin(a)\sin(b)$ to simplify $\cos(\pi/2 - x)$

[glossy valve]

OurBelovedBungo

[proper dune]

Ohhh let me try that

I dont remember my trig properties

I get approx. 1.03

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[proper dune]

am I doing this right?

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[tribal pulsar]

any idea how to do 8?

[tribal pulsar]

i figured out the center is at the origin and c= 2. no idea where to go from there

i have to find the vertices but that’s 2a but idk what a is

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[tribal pulsar]

<@&286206848099549185>

[tribal pulsar]

.close

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[full shore]

a trapezoid cannot have congruent bases because then, it will be a parallelogram right?

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@full shore Has your question been resolved?

[oak basin]

well technically it can, its just a very special trapezoid called a parallelogram, of course if you were asked to draw a trapezoid, it's just not very sensible to draw a parallelogram

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[plush egret]

Need some help with a limit, I'm kind of spinning wheels for maybe 15 minutes

[plush egret]

$\lim \qty( \frac 1 2 + \frac i 4 ) ^n$

[glossy valve]

jan Niku (Shuri for Honorable)

[plush egret]

should I squeeze this?

im not seeing any meaningful way to split

(n to infinity if its not clear by context)

[torn jolt]

good luck 🙏🏻😭

[plush egret]

huh?

through eulers i get to this

it cant be right

i mean i refuse to believe this is the good way of doing it

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[red verge]

I dont understand how to solve these

<@&286206848099549185>

[onyx glen]

have you worked with proportions before in general?

[torn jolt]

Can you think about it for a while?
Like if I say I bought 10 chocolates with $20 dollars and then I buy 20 chocolates of that same kind, how much would it cost me

You would first find out how much 1 chocolate costed right?

Or you would like do
Let $x be the cost of 20 chocolates
$20/10 = $x/20

[onyx glen]

@torn jolt that's not telling the whole story

there's also the relationship between length and volume here

[torn jolt]

wait what

RIP

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[onyx glen]

...

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[chilly mulch]

hey guys i need help

[chilly mulch]

I know how to solve this but i dont know how to get the function

And i need to know the function to solve this

[slate thunder]

I don't think the question is written english Or is it just thr handwriting?

[chilly mulch]

Its not

It just says to decide an close value of the integral

[slate thunder]

I see

and also is that a substraction sumbol

[chilly mulch]

If i can find out the equation for the function i can solve it

[slate thunder]

Or a different integtal

[chilly mulch]

Yea

[slate thunder]

Aight

Uk trapezoidal integrals

I might be saying it wrong

[chilly mulch]

Can you help me find out the equation for the function?

What

[slate thunder]

U don't needd to know it

Tho

[chilly mulch]

Exactly.. so dont tell me

[slate thunder]

If u want an approximate value

[chilly mulch]

Just tell me how to find the equation for the function