help-39

[naive musk]

so i found a sum and product for -19 and 90

[peak mist]

alr

[naive musk]

and then wrote that out like (15x^2-10x)-(9x+6)

[peak mist]

you cant factor that

this is the simplist form

[naive musk]

is that 15x^2 - 19x - 6?

i cant factor the entirety of (15x^2-10x)-(9x+6) ymean? or a specific part of it?

but i turn 15x^2-10x-9x+6 into 5x(3x-2)-3(3x+2) which has every part to be turned into (3x-2)(5x-3) except that i was taught i can combine two instances of (3x-2) in an expression but im not sure if i can combine (3x-2) and (3x+2)

or if im messing up somewhere and both of them should be (3x-2)

i found a common factor in 9x+6 and wrote it out as 3(3x+2)

[hybrid dome]

lmao the straight no

[naive musk]

it was an answer to the question i had

anyone able to clarify?

[pearl pond]

@naive musk Has your question been resolved?

[pearl pond]

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[mental sundial]

How do I find the constant?

[mental sundial]

I used u-sub integration to get 1/2sin^2(x) + D

but no idea how to solve for D

[hollow cobalt]

Use the fact that f(pi/2) = 4.5

[mental sundial]

Right, I tried that but i think i did it wrong

I did 1/2sin^2(Pi/2)

1/2(1)^2 = 1/2

I got it

.close

[pearl pond]

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[midnight haven]

100 doors with $1 behind each door. Roll a 100-sided die 100 times and get the money behind the doors with the numbers you roll with the die. How much in expectation do you get?

[cursive fulcrum]

There’s answers on the math stack exchange for this question

[midnight haven]

Why can't Door 1 be opened?

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[tropic saddle]

who says it can't

but door 1 is the same as any other door

the probability that it is not opened is just that we don't pick it in each of the 100 times

[midnight haven]

I don't understand this part

why can't be just calc like this

,w sum from n=1 to 100 of (n/100)

[jolly parrot]

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[tropic saddle]

because that's not how probability works?

what would a probability of 101/2=50.5 even mean

[midnight haven]

Of course I know that the probability has to be under 1!

That would a wrong approach for expected value not the probability.

Because first our success is 100/100 then for a new door its 99/100 and so on

[tropic saddle]

well then but for the third door it could be 98/100 if both the first and second doors are different. or it could be again 99/100 if the first two are the same

and then for the fourth door it could be 97/100 or 98/100 or 99/100 depending on the previous ones

etc

and immediately it gets super complicated

sure you could calculate it that way

but you don't want to

[pearl pond]

@midnight haven Has your question been resolved?

[midnight haven]

ah now I get it, why I got a number much lower than 63.4%
yes you could do this for small examples but for 100 its to much
thanks

[pearl pond]

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[pearl pond]

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[unborn lintel]

I'm just confused

[mild olive]

Hello!

[unborn lintel]

Hi!

[mild olive]

What have you tried so far, or what do you know to start with

[tacit mulch]

It looks like you did something right. What I can see of the work you erased looks correct

[unborn lintel]

Oh really!!!

[mild olive]

ya, I don't trust my vision of erased work tbh, like starting from the beginning

[tacit mulch]

Lol fair enough

[mild olive]

😄

[unborn lintel]

Lol

[mild olive]

alr fish, we want to isolate the variable, in this its X

[heavy lichen]

I concur, the erased parts do look correct, however, it might not hurt to start from the top 🤷‍♂️

[unborn lintel]

K

[mild olive]

so what do u think we should start with

[unborn lintel]

Ok so should I do this

[mild olive]

This is a unique way of writing it, Ill admit

[unborn lintel]

I got rid of the x on one side and since x = 1 then I add 1 to 5 x and get 6x

[mild olive]

but yes thats a good first step!

[unborn lintel]

Niceeeeeee

[mild olive]

now lets get rid of the -5

[unborn lintel]

Wait what

As in like do -5 cross UT out and then do -2 - -5

It*

[mild olive]

You can get rid of -5 by adding 5

and whats done on that side needs to be done on the other, so -2+5

[unborn lintel]

So then it'd 3 =-6x?

Its*

[mild olive]

Yes!

Now we gotta remove the (-6) and get x by itself

[unborn lintel]

Sooo should I do ÷ -6 and then 3 ÷ -6?

[mild olive]

Yup

[unborn lintel]

So then it's-0.5 = x

😄

[mild olive]

Well done!

[unborn lintel]

Nice!!!!

[mild olive]

oh I wonder if the bot

,ask -2+x=-5-5x

[jolly parrot]

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Requested by Bestower#6073

[unborn lintel]

Ohh yeahhh the fraction lol

I forgot about that

[mild olive]

cool feature of the bot, can see it come in handy

[unborn lintel]

U gotta convert it

[mild olive]

It can be written as -1/2 or 0.5

[unborn lintel]

Yeahh!!!

[mild olive]

both are the same thing

[unborn lintel]

Tysm!!!!!

[mild olive]

No problem ❤️

[unborn lintel]

This didcord is the best lol

Discord*

U guys never fail

[mild olive]

[unborn lintel]

Ty!!

.close

[pearl pond]

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[unborn lintel]

I'm back again lol

[unborn lintel]

Just confused again lol

Getting rid of the 18 just doesn't feel right.

[tacit mulch]

The 18w is positive, so I don't think we want to add 18w

18+18 isn't 0, we want it to cancel out to 0

[unborn lintel]

So 18-18

[tacit mulch]

Right, subtract 18w from both sides instead

[unborn lintel]

So then it should look like this right?

[tacit mulch]

Almost

You subtracted 18w, not just 18

18w-18w is 0, it shouldn't leave a w behind like that

We should just have -5w+5 = -60

[unborn lintel]

Ok so then after that what would I be doing next? Would I do -60+60 to cancel it out?

[tacit mulch]

Would that get you a step closer to getting the w by itself?

[unborn lintel]

Yes?

[tacit mulch]

We're here right now, right?:

-5w + 5 = -60

[unborn lintel]

Yeah

[tacit mulch]

So far, we gathered all the w's on the left side of the equation

[unborn lintel]

Mhm

[tacit mulch]

Now, we want to get rid of anything else on the left that isn't w

So w will be alone, and we'll have w = whatever

the -60 is on the right, we don't really need to get rid of that

In other words, focus on the side where the w is. Cancel things from that side

[unborn lintel]

So then would I do +5 with the -5w to cancel it out?

So then the -60 turns into a -55?

[tacit mulch]

Hang on, sorry

We have

-5w + 5 = -60

[unborn lintel]

Yeah

[tacit mulch]

Wouldn't the next step be to get rid of the +5?

That -5 is multiplied with the w, we'll get rid of that last, when we divide

[unborn lintel]

O

So then 5-5 to cancel it out and then-60+5 = -55?

[tacit mulch]

You're close

But it looks like you're subtracting on the left and adding on the right

Subtract 5 from both sides

[unborn lintel]

-65?

[tacit mulch]

Yep, -5w = -65

[unborn lintel]

Then we do -5÷-5 that cancels out and then -65 ÷-5 = 13 so w=13? 😄

[tacit mulch]

👍

The steps in general are like

Add/subtract whatever you need to so that all the terms with a variable are on the left (things like -5w, 10w)

Add/subtract whatever you need to so that all the terms without a variable are on the right (things like 10, -60)

Then just divide

[unborn lintel]

Kk tysm!!!!

[tacit mulch]

Sure thing!

[unborn lintel]

I'm back again

0-0

How would I be able to write this out?

.close

[pearl pond]

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[unborn lintel]

.reopen

[pearl pond]

✅

[unborn lintel]

Sorry about that was an accidents

Accident*

[devout zinc]

whaat have you tried?

[unborn lintel]

Nothing

I'm just really confused lol

[devout zinc]

ok so

doo you understaand what the question states?

[unborn lintel]

Well Alice has 8 of the stars and earns one every week and mack has 2 stars and earns to every week and uts asking how much weeks till they have the same amount

And that would be 7 weeks

I just don't know how to write it out to well you know

Like I just did this

[devout zinc]

well

did they ask to write it well?

[unborn lintel]

No

Not really

[devout zinc]

one sec lemme make sure ur right

[unborn lintel]

K

[devout zinc]

I got somethijng different

[unborn lintel]

Huh

Where did I go wrong then

😦

[devout zinc]

what did u do

[unborn lintel]

Well I just did what I showed you in the photo

[devout zinc]

what i would do is I would see, how many starss away is mack from alice rn

[unborn lintel]

6

Stars

Then what I guess

[devout zinc]

so how many more stars is mack earning then alice

per week

[unborn lintel]

1

[devout zinc]

so how many weeks will it take him to get the 6 stars so they have the same amount?

[unborn lintel]

6?

Cause like would I do 6x1?

[devout zinc]

not 6*1

6/1

which is still 6

so I think its 6

[unborn lintel]

Is that 6 divided by 1?

[devout zinc]

ye

[unborn lintel]

Cool

Kk

[devout zinc]

anything else

[unborn lintel]

Ty I don't get it to well tbh but it's helped a little

[devout zinc]

yw

anything else?

but I can try to explain

[unborn lintel]

Pls do ❤️

[devout zinc]

ok

so we want to know how many weeks until they have the same amount right

[unborn lintel]

Ye

[devout zinc]

so we have to find how many more stars maack gets per week, to find how long it will take

right

or else how else would u do it

[unborn lintel]

I guess so

[devout zinc]

you would have too find how many more stars mack needed compared to how many alice needed

to get to a equal amount

[unborn lintel]

K

[devout zinc]

then you have to find how long it will take for mack to catch up

if he gains 1 more star then alice every week, we need to know how many mrooeo stars alice hasa then mack to find how long it will take right?

[unborn lintel]

Ye

Ok so like

Ye I guess I understand it then

Ty

[devout zinc]

yw

[unborn lintel]

But if ur still there could you pls help me out with one more thing and then I'll be out of you hair?

[devout zinc]

sure

[unborn lintel]

Ok so I just started doing this problem and I think I'm doing it correctly but something seems off

[devout zinc]

ur so close

but u mdae 1 mistake

if yoou subtract 7 from both sides youo get -2 = n-7-7 which is -2 = n-14

[unborn lintel]

Sorry my internet is horribme

Ignore that photo lol

[devout zinc]

its fine

sso how woudl you isolate n

n-7 plus what equals n?

[unborn lintel]

7

[devout zinc]

so add 7 to both sides instead off subtracting

[unborn lintel]

So then it's 12=1n

[devout zinc]

ye

and check if it works

[unborn lintel]

And 12 divided by n is 12 right

So 12 = n?

[devout zinc]

yea

good job

[unborn lintel]

Ty that's all then!

Have a great day/night and thanks for all the help!!!!

[devout zinc]

yw!

[pearl pond]

@unborn lintel Has your question been resolved?

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[regal stirrup]

can someone help me

i know how to find them on functions without square root but these quare roots are confusing me

[pearl pond]

@regal stirrup Has your question been resolved?

[pearl pond]

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[carmine fable]

i have an idea but im not sure if its correct

[midnight haven]

what is the idea you have?

[carmine fable]

so i found this formula

and i see it matches up with problem but im not sure how to plug in the sin^5

[pearl pond]

@carmine fable Has your question been resolved?

[wise spade]

good starting point

sin^5(x) = sin(x) * (sin^2(x))^2

[carmine fable]

oh ok

so we do that to break it down?

[wise spade]

yea

sin(x) * ((1-cos(2x)) / 2)^2

I think this could be the answer

[pearl pond]

@carmine fable Has your question been resolved?

[midnight haven]

You need to use Euler's formula

[carmine fable]

?

[midnight haven]

Now use it for sin^5

Then use it again to find cos(x) and sin(x) in your expression

Here is an example for sin^3(x)

[carmine fable]

I've never see that before

[midnight haven]

Sorry it's in french

[carmine fable]

oh that's why

[pearl pond]

@carmine fable Has your question been resolved?

[pearl pond]

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[grim patrol]

i took gamma(1/u) as u goes to inf, idk whats next. btw when they said z=inf im guessing its u=inf

[rustic gate]

what the

there isn't even a z

and there's two arguments

[grim patrol]

what

[rustic gate]

that's kinda dumb

[grim patrol]

??

[rustic gate]

no like

[grim patrol]

z din appear

[rustic gate]

what is the question even saying

[grim patrol]

yes

:c

[rustic gate]

there's no z

and

the beta function has two arguments

[grim patrol]

hb

[rustic gate]

yeah okay

it's

non isolated

[grim patrol]

y

how

[rustic gate]

because gamma has a pole at every integer

negative

[grim patrol]

what about it

[rustic gate]

iirc

so then

[grim patrol]

WOW NO

[rustic gate]

in every neighbourhood of infinity

[grim patrol]

NON POSITIVE

[rustic gate]

same thing

im thinking about the factorial function

[grim patrol]

wait

actually

[rustic gate]

so it's offset

[grim patrol]

does it hv a pole at 0

[rustic gate]

no it's not

it does

[grim patrol]

it does right

yes

[rustic gate]

but i was thinking of z!

[grim patrol]

its ok

i got ur bac

[rustic gate]

so every neighbourhood of infinity has a pole

so non isolated

[grim patrol]

ahhhhh

ok

then hb if we think of

f(1/z) as z->0

[rustic gate]

same thing

the poles get shoved into 1/n

so they cluster at 0

[rustic gate]

yes

[grim patrol]

each circle we pick has an X

so we can find treasure in each treasuremap

so the bounty is non isolated

ok cool

Breakthrough

amazing

imma

get gg

thanks

💕

.close

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[gleaming wolf]

$AB$ and $AC$ are two chords of a circle. Let points $D$ and $E$ lie on $AB$ and $AC$ respectively such that $AD$ = $AE$. The perpendicular bisector of $BD$ intersects the circle at points $F$ and $P$, such that $F$ lies on the opposite side of $AB$. Similarly, the perpendicular bisector of $CE$ intersects the circle at points $G$ and $Q$ such that $G$ lies on the opposite side of $AC$. Let $FP$ $\cap$ $GQ = T$, How to prove that $TF = TG$, or is that true?

[jolly parrot]

Epic NPC Man

[gleaming wolf]

can this be proven?

<@&286206848099549185>

[pearl pond]

@gleaming wolf Has your question been resolved?

[pearl pond]

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[midnight haven]

This one please

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[lean pumice]

where are you stuck on this problem? like do you know where to start

[midnight haven]

I just want to know are we finding time or distance

[lean pumice]

we’re trying to find the x that optimises the time that it takes for kevin to reach the swimmer

so neither really

[pearl pond]

@midnight haven Has your question been resolved?

[rancid hearth]

You have to find the function that given the distance x it outputs the time it took to reach the swimmer, then find the minimum of this function

The time running is (80-x)/8 seconds as the speed on land is 8m/s

The time swimming is sqrt(x^2+30^2)/2

,w minimum of sqrt(x^2+30^2)/2+(80-x)/8

[jolly parrot]

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[rancid hearth]

So 2*sqrt(15), and the closes integer to that is 8

@midnight haven

Wait the question says how much does he have to run, not x, that'd be 72m

[pearl pond]

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[midnight haven]

Where does the other negative sign come from here?

I hope it's enough info

Original problem

It's like they're taking a -1/2 constant out and then multiplying it by the evaluation of the positive integral and suddenly the whole thing becomes positive?

Idk how

[potent hedge]

Ok I see

It's because you have to make a u-sub

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[shut matrix]

am i stupid

why is this true

[tacit mulch]

For one thing, it follows from the sum/difference formulas:
sin(a-b) = sin(a)cos(b) + cos(a)sin(b)

But also it's intuitively true if you think about a unit circle

An angle of theta, and an angle of (180 - theta) will correspond to points with the same height on the unit circle

[pulsar lark]

I was about to say unit circle but I'm now curious how you can derive that from the formula

Cool thanks

[tacit mulch]

@shut matrix Does this make it any clearer?

The sine of an angle is the y-coordinate of the point where that angle meets the unit circle. theta and (180 - theta) meet the unit circle at the same y-value, so they have the same sine.

[tacit mulch]

Plug in a=180 deg and b = theta

[pearl pond]

@shut matrix Has your question been resolved?

[pearl pond]

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[elfin stirrup]

can every proof of the Natural numbers be explained with the 5 peano axioms?

[bold ledge]

I think so

real and complex numbers as well I believe

[elfin stirrup]

so math proofs are like a house of cards starting with these 5 axioms?

[bold ledge]

well things like Godel's incompleteness theorem aren't but otherwise yeah

[elfin stirrup]

thanks

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[finite vector]

i dont understand how ot do 5b

[light helm]

differentiate part a) wrt t,

[finite vector]

.close

[pearl pond]

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[primal breach]

hey

[pearl pond]

Please don't occupy multiple help channels.

[primal breach]

🙂

[pearl pond]

@primal breach Has your question been resolved?

[primal breach]

<@&286206848099549185>

[hoary nymph]

What’s ur question

[primal breach]

yay

finally

[pearl pond]

@primal breach Has your question been resolved?

[pearl pond]

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[frozen forge]

hi

[frozen forge]

i got a question

so when u solve for g o f

are u supposed to get a variable as your answer

like for example

[coarse dawn]

Depends on the equations you have

[frozen forge]

f(x)=2x and g(x)=-x+2

find gof

g(2x)

u plug into f

[coarse dawn]

And what did you result in?

[frozen forge]

and u get 0?

not 0 mb

-2x+2

[coarse dawn]

That's fine

[frozen forge]

as a answer?

-2x+2?

[coarse dawn]

Yes

[frozen forge]

oh ok

so thats correct?

right

??

[coarse dawn]

Yes

[flint field]

Ye

[frozen forge]

alr

thx

.close

[pearl pond]

Channel closed

Closed by @frozen forge

Use .reopen if this was a mistake.

[frozen forge]

.reopen

[pearl pond]

✅

[frozen forge]

im ocnfused on (gof)(2)

so u get the answer for g?

then multiply by 2?

[coarse dawn]

No

Do you know what f(2) means?

[frozen forge]

ye

look

Number 39

What would that be

[coarse dawn]

This means plug in 2 for x, in the function f(x), right?

[frozen forge]

no

thats why im asking

[coarse dawn]

What do you mean no?

[frozen forge]

dont u solve for gof

then multipy by 2?

[coarse dawn]

No

[frozen forge]

?

[coarse dawn]

First, I'm asking you if you know what f(2) means because it relates to (g o f)(2)

[frozen forge]

nope

[coarse dawn]

You don't know what f(2) means?

[frozen forge]

i do

f of x=2

f of 2 basically

[coarse dawn]

And (g o f)(2) is related to that

[frozen forge]

so what would u do

[coarse dawn]

Except you are doing g composed f of 2

[frozen forge]

can you go step by step

so first

[coarse dawn]

Find g o f

[frozen forge]

i did

[coarse dawn]

Then plug in 2

That's what that is

[frozen forge]

bruh

plug in 2 for x?

cuz i got -12x-21

for gof

[coarse dawn]

f(2) is the same idea as (g o f)(2) except you doing it with composite functions

[frozen forge]

simple terms?

[coarse dawn]

That's as simple as it is

[frozen forge]

but

[coarse dawn]

Literally f(2) means f of 2, (g o f)(2) means (g of f) of 2

[frozen forge]

isnt it also g(2)

wym by composite

[coarse dawn]

g o f is a composite function

[frozen forge]

ye

[coarse dawn]

How about that

(g of f) of 2

[frozen forge]

what do u do with the 2

i found gof

then what

[coarse dawn]

(g of f) of 2

[frozen forge]

so multiply

by 2

[coarse dawn]

If you know what f(2), which means f of 2, meaning plug in 2 for x, it's the same idea for (g of f) of 2

[frozen forge]

ohh

can u check my answer

with the functions i gave u

[coarse dawn]

What did you get?

[frozen forge]

i got -45

[coarse dawn]

Sounds right

[frozen forge]

what grade u in?

your smart

[coarse dawn]

Grade doesn't really matter, experience does

[frozen forge]

ye

but

what grade?

im just curious

[coarse dawn]

Uni

[frozen forge]

oh dang

uh will u be here if i have anymore questions

i dont wana close it

[coarse dawn]

You can close it and open a new channel if you need to

[frozen forge]

oh alr

sounds good

[coarse dawn]

And no, I'll be lingering around, but there are other people here that can help

[frozen forge]

ok

.close

[pearl pond]

Channel closed

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[pearl pond]

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[zealous igloo]

a lot of the functions i have been working with have their inflection points at the midpoint between the min(s) and max(s). is there some sort of trick that would allow me to know whether this rule holds or not without having to solve for the inflection point directly through finding the second derivative and setting it equal to 0?

[bold ledge]

I think that's just because a parabola has it's min/max at the midpoint of the two x-intercepts

so if you integrate that you get the scenario that yo umentioned

but there isn't really any other reason for that to be true

tl;dr no

[zealous igloo]

damn

arlight

thanks

.close

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[lethal thicket]

I just have no clue where to even start and how to even get x

[small spruce]

straight line adds up to 180

[slim geode]

use these 2 rules:

1. Sum of internal angles of a triangle is 180
2. Sum of angles on a line is 180, i.e. the interior + exterior angle at any vertex is 180

[small spruce]

so you can write the angle TUS as 180-(12x+17)

[lethal thicket]

Ik and that’s 12x-163

[small spruce]

then angles in a triangle add up to 180 so the sum of TUS UST and STU = 180

solve for x

[lethal thicket]

I did but I got a decimal last time and ion know if we’re supposed to get decimals because it’s basic geometry

[small spruce]

oh this is meant to be 163-12x

thats probably where u went wrong im guessing?

[lethal thicket]

How did the 12x become negative??

[small spruce]

its 180 - it

180-(12x+17)

you gotta be careful with expanding brackets

[lethal thicket]

That doesn’t make sense

[small spruce]

what

[lethal thicket]

163-12x is the same as -12x+163

[small spruce]

yes ?

[lethal thicket]

How did the variable become negative if you’re subtracting the whole numbers

??

[small spruce]

the variable isnt negative (or well we dont know if it is or isnt), its the coefficient which is negative.

[lethal thicket]

Well then how did the coefficient get negative

[small spruce]

because we subtracted

do u know how to expand brackets

like

-1(10x+10)

that sorta thing?

[lethal thicket]

Yes that’s distribution

[small spruce]

yeah

so

when we have

180-(the angle)

the angle is what

12x+17

so its

180-(12x+17)

both things are being subtracted

-1(12x+17) you distribute the negative sign

then add like terms

[lethal thicket]

Ohh

[small spruce]

163-12x

[lethal thicket]

Ok hold up

So this is the answer?

And you want to find TSU so you’d just plug 10 into the x spot?

[small spruce]

ur lemme see

[small spruce]

yup

so 59

[lethal thicket]

Yessir I got that

Thank you so much 😭

[small spruce]

no worries

[pearl pond]

@lethal thicket Has your question been resolved?

[pearl pond]

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[short nexus]

is this correct?

[shrewd basin]

Don’t think second one is necessary true

||e||

[short nexus]

Howcome?

[shrewd basin]

Take f = g = x and lim as x-> inf

[short nexus]

Ah ok, so just first and third?

<@&286206848099549185>

.close

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[fair dawn]

So um i suppose its possible right?

Cz im like stuck at the last step

[pulsar lark]

,rccw

[fair dawn]

Oh lol sorry i took it diagonally

[foggy mason]

should be a crime

[fair dawn]

Tho it isnt haha

[foggy mason]

anyways you know that for the last step you need to show that the sum from k=1 to n+1 of 1/sqrt(k) >= sqrt(n+1) right ?

[fair dawn]

Yep

[foggy mason]

you first assumed that its true at the rank n right ?

[fair dawn]

Yep

Then i should put

The sigma of n+1

Or uh

Ye out of ideas

[foggy mason]

then you have :
$\sum_{k=1}^n \frac{1}{\sqrt{k}} \geq \sqrt{n}$

[jolly parrot]

Ｈｅｒｅｌｓ

[foggy mason]

add 1/sqrt(n+1) on both sides I guess

[fair dawn]

Oh

Oh demn

Wait hang on ill check if i understood

Like this?

[foggy mason]

yes

now work on the right side

[fair dawn]

So ur saying this is all i had to write at the finale phase?

No way

[foggy mason]

well yea but you are not done yet

[fair dawn]

Yeah figured it out

[foggy mason]

gg

[fair dawn]

So i must have it without the 1/sqrt(n+1)

[foggy mason]

you should have sqrt(n+1) on the right

[fair dawn]

Oh

I mean

Sure i get it ig

[foggy mason]

did you find out how ?

[fair dawn]

Still trying

Wbu?

Oh wait

Buh im dum

So like u can go the hard way but

The first part of question had this

[foggy mason]

ah

[fair dawn]

So like instead of adding it to both sides

We just add sqrt(n+1) on left side

And the other one leaves only sqrt(n+1)

:D

[foggy mason]

with this,
$$\sqrt{n} + \frac{1}{\sqrt{n+1}} \geq \sqrt{n+1}$$

ez

[jolly parrot]

Ｈｅｒｅｌｓ

[fair dawn]

Hehe

Yep

Welp was ez i was dum

Didnt think it was to be used

Aight ty

[foggy mason]

np

[fair dawn]

Ill probably need more help later xd

Aight we're done here

.close

[pearl pond]

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[opaque cairn]

Why 28C4?

[pearl pond]

@opaque cairn Has your question been resolved?

[scarlet gulch]

@opaque cairn because theyre doing all the scenarios where you pick 3 green balloons, multiplied by all the 4 other balloons scenarios because u have to pick 7, then divided by ALL DIFFERENT scenarios

so theyre doing
3 green balloon possible scenarios / different scenarios of 7 balloons

40-12 = 28 other balloons to pick from

28c4 = all possible ways of getting 4 balloons from a lot of 28 unique balloons

ping me if u need me so i can see the channel

[opaque cairn]

Ohh yeah u still have to pick 7

.close

[pearl pond]

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[fallow epoch]

Make r the subject of the formula

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

@midnight haven Has your question been resolved?

[pearl pond]

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[gloomy osprey]

how to do this using remainder theorem

[grim patrol]

do uk how remainder theorem works

[gloomy osprey]

a little bit

just learned it like today

so yes i know the theorem but not fluent at it

[grim patrol]

so

apply it here

[gloomy osprey]

but here we're not dividing by x-a though

and idk how to simplify 2x^3 + cx^2 - 11x + 30 into x-a

[grim patrol]

eh

same

x-a

2x+7 = 2(x-(-3.5))

[gloomy osprey]

isnt that 2x^3 + cx^2 - 11x + 30 divided by 2x+7 instead of 2x + 7 divided by 2x^3 + cx^2 - 11x + 30?

[grim patrol]

wot

im confused

yes?

im just simplifying that 2x+7 thing

[grim patrol]

into some const * this

[gloomy osprey]

wait

so we apply the remainder theorem for x+3.5 and then times the result by 2?

[grim patrol]

errr

idt we can just * the result by 2

idk feels weird

just try it with some sample polynomial lol

idk i wld just

divide the whole polynomial by 2 first

hm wait no diff i still dk whats the thing

[grim patrol]

do it for some

ax+b lol

[gloomy osprey]

hmm ok

[grim patrol]

but idt it matters

just use x+3.5

n u get the result i think

without any * or /2

[rustic gate]

the remainder will be different

but

you can find the remainder when dividing by x + 7/2 first

and then divide by 2 again

to get the result of dividing by 2x + 7

[gloomy osprey]

I think I got the answer

c=1

thank you guys so much

[pearl pond]

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[weak surge]

What are these colons called? :

a:b

I’m not sure how to read that

[wild fable]

It’s not a ratio?

[weak surge]

Colon is ratio?

[wild fable]

well sometimes it’s used to denote ratios

[weak surge]

Oh

[wild fable]

I would read it as a to b

[weak surge]

OK

[wild fable]

I could be wrong but I’m pretty sure

[weak surge]

What if it’s 2/1 = 4/2

a:b = unit ratio?

Not just ratio

Because unit ratio is per only one unit in the denominator right?

[weak surge]

So for this it would be unit ratio = ratio

Simplified they would both be unit ratios

But how would I make both sides equal 4/2? If the left side is already 2/1

If I multiply one side don’t I need to multiply the other side too?

[pearl pond]

@weak surge Has your question been resolved?

[pearl pond]

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[ebon cedar]

I need some help with L'hopital's rule. Basically, I'm trying to find the derivative of (x-10)^-2 using limit notation and l'hopital's rule. Here's what I have so far.

[ebon cedar]

Then, I take the derivative of both the numerator and denominator to get

How do I proceed from this?

Won't evaluating it give me 0/1 as the two terms in the numerator and denominator will equal each other as h approaches 0?

[toxic lichen]

l'hôpital's rule????

l'hôpital's rule literally INVOLVES derivatives.

it's literally fucking circular

but also (x-10)^-2 is constant in h so its derivative wrt h would be 0.

[ebon cedar]

yeah idk why i have to do this problem but it whats the book says

[ebon cedar]

wait but why are you taking the derivative with respect to h

[rustic gate]

because the limit is as h->0

[pearl pond]

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[ebon cedar]

thank you so much!

.reopen

[pearl pond]

✅

[ebon cedar]

.close

[pearl pond]

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[pearl pond]

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[shell oxide]

Wasap

[shell oxide]

Oops sorry, can u repost after the bot says “available help channel”?

.close

[pearl pond]

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[glossy wave]

ln(x)-ln(x)=ln($\frac{x}{x}$)

[jolly parrot]

Lambda

[glossy wave]

=ln1=0

But wait

[halcyon parrot]

thsi is not true

[glossy wave]

What is ln(x) -1/x

ln(x) times (-1/x)?

[light helm]

how are you getting from
ln(x) - 1/x
to
ln(x) - ln(x)

doesn't answer my question

can you show the original problem

and not use = signs inappropriately

[halcyon parrot]

well it's definitely not true if you write it like this

[pearl pond]

@low oar Has your question been resolved?

[pearl pond]

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[silent rivet]

i would like some help with this one

<@&286206848099549185>

[pearl pond]

@silent rivet Has your question been resolved?

[silent rivet]

<@&286206848099549185>

any <@&286206848099549185>

an hour

big

[pearl pond]

@silent rivet Has your question been resolved?

[pearl pond]

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[pearl pond]

@analog wave Has your question been resolved?

[pearl pond]

@analog wave Has your question been resolved?

[pearl pond]

@analog wave Has your question been resolved?

[pearl pond]

@analog wave Has your question been resolved?

[pearl pond]

@analog wave Has your question been resolved?

[autumn narwhal]

@analog wave What exactly do they mean by the largest diameter? What you found is the y value of the vertex.

[pearl pond]

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[silent rivet]

for this function: for all x\in R is H continious? and What does this say about the possibilities of choosing a value c = h(0,0), such that h is continuous throughout R2?

[silent rivet]

i answered that H is discontinious hence (image) and then if x=0 then its undefined?

i hope that is correct, and then what does this say about the possibilities of choosing a value c = h(0,0), such that h is continuous throughout R2?

<@&286206848099549185> 🙂

[pearl pond]

@silent rivet Has your question been resolved?

[silent rivet]

<@&286206848099549185>

[silent rivet]

@marble siren

[silent rivet]

<@&286206848099549185>

<@&286206848099549185>

.close

[pearl pond]

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[wanton roost]

Hello

[wanton roost]

i tried to do the answer this is what i got

<@&286206848099549185>

[unborn zephyr]

what is ur question

3225.52 / 8?

[wanton roost]

yeah

[unborn zephyr]

just use a calculator......

[wanton roost]

cant

im blocked from using one

[unborn zephyr]

then use brains

this is grade 5 mathematics

[wanton roost]

still strugling man

[unborn zephyr]

do more training

[wanton roost]

its a big number

[unborn zephyr]

[unborn zephyr]

it really isnt

by the time ur replying my msg ur probably done

[wanton roost]

alr alr

let me try to solve this again

FINALY GOT IT

damn i need t odo some practice

.close

[pearl pond]

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Remember:
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[coarse sage]

$P(X+Y \leq \frac{1}{3})= \frac{\frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{3}}{\frac{1}{2} \cdot 1 \cdot 1}=\frac{1}{9}$

[jolly parrot]

QuantumBee

[coarse sage]

Similarly, $P(X+Y \leq \frac{1}{5}) = \frac{1}{25}$

[jolly parrot]

QuantumBee

[coarse sage]

But, the answer is incorrect.

Where am I going wrong?

[manic kite]

The density function is not a constant so the probability is not area ratio.

[wind wigeon]

sounds like you need to integrate

[coarse sage]

Hahn, so do I have to plug in values for x and y to find out that?

Ok, I'll try integrating.

[wind wigeon]

yes\

such that X + Y <= 1/3

[coarse sage]

$\iint_{Y \leq \frac{1}{3}-x} 24xy \dd{y} \dd{x}=\int_{0}^1 \int_{0}^{\frac{1}{3}-x} 24xy \dd{y} \dd{x}$

[jolly parrot]

QuantumBee

[coarse sage]

@manic kite @wind wigeon, Is that right?

[wind wigeon]

x goes from 0 to 1/3 i would imagine

[coarse sage]

No

Why not from 1/3 to 1?

[wind wigeon]

because you integrate over a triangle right

[wind wigeon]

you integrate that blue part i think

[coarse sage]

,calc 1/3

[jolly parrot]

Result:

0.33333333333333

[coarse sage]

Alright. I get it.

Thanks I got the answers.

[coarse sage]

Could you elaborate on why this is true?

[manic kite]

Since the integral of the constant is a multiple of the area, the area ratio can be used when density function is a constant

[coarse sage]

That constant defined for particular conditions must be unique, right?

@manic kite

[manic kite]

yes， it's uniformly distributed

[coarse sage]

Thank you!

.close

[pearl pond]

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[pearl pond]

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[zinc grove]

Hi, do we only need to check for n = 0 to 8 because past 8, youd be restarting because 9 mod 9 is the same as 0 mod 9? Like its comes full circle right? Thsnk

[wind wigeon]

exactly

[zinc grove]

Awesome! --thanks

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[near moat]

whats the answer for this i wanna check my pleasee

[ember cloak]

What is your answer? 😄

[near moat]

ok idk how to write certain bits of keyboard but

wait let me draw it

[wind wigeon]

yes good

[ember cloak]

Yes, that is correct

[wind wigeon]

you can always just evaluate h(h^-1(x))

it should equal x

[near moat]

yaya

[near moat]

ok yeah

ty

.close

[pearl pond]

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[pearl pond]

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

[pearl pond]

Please don't occupy multiple help channels.

[willow lake]

How to solve

43

44

46

47

48

[broken mason]

Hello! Am I allowed to help you?

[willow lake]

Yess

Sure

[broken mason]

I'll do my best 🙂

[willow lake]

Thnx

[broken mason]

Which one do you need help with?

[willow lake]

43,44,46,47,48

[broken mason]

Okay..what grade level is this supposed to be?

I only know how to solve #44, I suck...

[willow lake]

10th

[willow lake]

Same

Can u check if the answer is 62

[broken mason]

Okay.

Wait- 62?

[willow lake]

Yes

[broken mason]

That's not an answer on there....

[willow lake]

A part?

[broken mason]

What?

I don't get it...

[willow lake]

44th question

A option

<@&286206848099549185>

[broken mason]

Your options are 50, 51, 54, and 55.

You selected 50.