help-13

[fair nymph]

Yh i get it now

.close

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[granite hare]

You don't need a tan-based unit circle for it btw

cos(θ) and sin(θ) correspond to x and y coordinates in the unit circle

and sin(θ) / cos(θ) = tan(θ)

so divide the values, and simplify to get - 1/root 3

:)

[cedar kiln]

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[frigid sinew]

for question f im not sure what to do

[cedar kiln]

@frigid sinew Has your question been resolved?

[brazen kestrel]

to start, what's the value of the expression inside the sum in terms of n and k

[frigid sinew]

I did 27n + 42 I’m just not certain about it 😅

I’ll redo the calculations just to be sure

[brazen kestrel]

it should be in terms of both n and k

[frigid sinew]

i transformed the k

into n(n+1)/2

[brazen kestrel]

why exactly....?

[frigid sinew]

for f i have to determine

in terms of n

[brazen kestrel]

we will get to that part but for the thing inside the sum it should be n and k

i'm looking at your answers and you seem to have d onward wrong

so let's go back to d

for d you can't use x_k in your answer; it wants you to evaluate f(x) using your answer for c

[frigid sinew]

oh yes they are my old answers

i ahgev corrected

heres rthe new ones

And here is what I did for f

[brazen kestrel]

your mistake was that you didn't put parentheses around the whole f(x_k) term

[frigid sinew]

yup

[brazen kestrel]

the +5 should also be multiplied by 3/n

[frigid sinew]

yes so nwo it should be right i tjink

[frigid sinew]

by this logic g should be

42 right

[brazen kestrel]

yeah that should be right

something doesn't seem right in your work but that's the integral value

you must be doing it a bit differently than i would but you do have it right

¯_(ツ)_/¯

[frigid sinew]

okay tysm!

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[frigid sinew]

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[frigid sinew]

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[cedar kiln]

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[thick urchin]

how do I solve (ii)

(i) is 2<= f <=4

[humble karma]

This is asking you to solve f(x) = 2.5 for x.

[grim badge]

hi

[thick urchin]

it's not working out

[thick urchin]

hello

[humble karma]

How so?

[thick urchin]

3-cos5

[humble karma]

No.

f(x) = 3-cos(2x)

You want to find x such that 2.5 = f(x).

So you must solve 2.5 = 3 - cos(2x)

[thick urchin]

3-cos2x=2.5?

oh

cos2y=0.5

2y=0.5/cos

[cedar kiln]

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[fair copper]

can someone help m,e with this

[wispy talon]

Find the zeroes of the equation and then integrate it from those limits

[fair copper]

like null factor law?

wym by zeroes

[wispy talon]

Yeah so for what x does y become 0

[fair copper]

oh okay

how do u get from the first line to the second

[coral jewel]

multiplication in the integral

[wispy talon]

They opened the brackets by multiplying the stuff inside
x(x+2)(x-3)
= x(x^2 -3x+2x-6)
= x^3 - x^2 -6x

[fair copper]

oh so u multiply the ones in the brackets first and then by the x

[coral jewel]

yes

[fair copper]

do u need to do it in two steps or is thjere a way ot just do it in one

[wispy talon]

You can directly integrate from -2 to 3 instead of splitting it
But only for this question, it depends on equation to equation

[fair copper]

why can we do it for this question and not others

[pliant bear]

you acn't just combine these two integrals either

bcause there's a - before the second one

the rule is int from a to b plus int from b to c is int from a to c

int from a to b minus int from b to c can sometimes be reduced, but it's more complicated

[wispy talon]

Ah yes, mb
Thanks for catching it

[cedar kiln]

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[languid pine]

Solve 6x4 + 5x3 − 24x2 − 15x + 18 = 0 if the sum of 2 of its roots is zero.

[languid pine]

For this one do I sub them into each one of the formulas

[bold vine]

Try associating things with variable names

let x = a be one root

Then x = -a is the other

[languid pine]

Yeah h+v+c+d= -b/a

[bold vine]

h and v?

[languid pine]

Random

I’m just using as an example

To say that would I sub

[bold vine]

i don't think you necessarily need to sub in anything tbh

[languid pine]

Well I got alpha= -beta

As one

And 5/6= two other variable sum

How would I proceed

[bold vine]

i'm really not sure what you're doing - what are alpha and beta?

[bold vine]

i see

[languid pine]

Do you know what to do?

[bold vine]

I would have used this approach

[languid pine]

He would I solve the other 4 riots via that approach

[bold vine]

If x = a, -a are roots of a polynomial, then (x-a), (x + a) are factors of the polynomial

[languid pine]

Yeah

But there’s 4 roots

[bold vine]

You can use polynomial long division

[languid pine]

The whole excercise is about using the theorem

[cedar kiln]

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[pearl vigil]

Quick question

[pearl vigil]

Why on wolframalpha

The cube root of x function has the domain [0,inf)

[idle tusk]

,w domain cbrt(x)

[wraith dagger]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by arte_m_etra

[idle tusk]

you sure?

[pearl vigil]

I think my wolfram smoked something

[cedar kiln]

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[pearl vigil]

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[valid fiber]

Letters are chosen from the word "CRUSADE" at random to create three letter 'words', where no letter can be selected more than once.
(c) How many 'words' have two vowels next to each other?

what i did was (3 * 2 * 4 * 2 )+ (4 * 3 * 2 * 2) as there are two cases, vowel vowel consonant, consonant vowel vowel- but my answer was wrong and i dont understand how to approach it

[cedar kiln]

@valid fiber Has your question been resolved?

[storm abyss]

what about vowel vowel vowel

that satisfies the given condition

[cedar kiln]

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[valid fiber]

oh yeah

[valid fiber]

.reopen

[storm abyss]

it reopend

[valid fiber]

is it reopened?

hm but its still not quite the answer its 54

[storm abyss]

how did you arrive at 3*2*4*2?

for vowel vowel consonant

[valid fiber]

three vowel choices * two vowel choices * 4 distinct * 2 ways to arrange?

[storm abyss]

when you are multplying by two

you are covering the case of consontant vowel vowel as well

[valid fiber]

oh i see

ur right

then for VVV would it be 3* 2 *1

[storm abyss]

yes

[valid fiber]

oh that works out then

[storm abyss]

nice

[valid fiber]

okay i have another question as well

Four digit numbers are generated from the digits <0, 1, 2, ..., 9\ with each digit being used only once per number. The number may not start with a zero.
How many different numbers are possible if the number must be even

[storm abyss]

well what are you thinking?

[valid fiber]

i thought youd have to do 9 * 8 * 7 * 5 ?

5 being the number of choices for the even digits

[storm abyss]

hm but what if you use the digit before?

repetition is not allowed

[valid fiber]

hm

hmm let me think..

maybe 5 * 8 * 8 * 7 ?

[storm abyss]

looks correct

[valid fiber]

okay ill check the answer fingers crossed

hm is 2296 and i got 2240..

hm i need to think 😭 \

[storm abyss]

oh right

I get the problem

the thing is

from the 5 options for making it even

one is zero

but you have already excluded zero

so its getting excluding twice

isn't it

[valid fiber]

but in the 5 options it also includes the 0?

or does that not work

[storm abyss]

yes

but when you write 8 options

for the first digit

haven't you already removed the zero

[valid fiber]

hang on let me just visualise thisin my head wait 😭

okay wait when i write 8 ooptions its getting rid of the even number its excluding the even number already chosen from the 5 and the 0 for the first digit

but then also

thats why i multiply by 8 again to account for even numbers including 0 that were missed out?

[storm abyss]

you multiply by 8 for the second digit of the number

[valid fiber]

yes

[storm abyss]

out of the 5 numbers

when you have the last digit as zero

you actually have 9 options for the first digit rather than 8

1,2,3,4,5,6,7,8,9

[valid fiber]

hmm

so i should count it as two cases .. ?

[storm abyss]

a different case when zero at the end yes

[valid fiber]

one where 0 isnt 'excluded' and where 0 is at the end

and the second case being.. when 0 is 'excluded' ?

[storm abyss]

uh once when zero not at the end and once when zero at the end

[valid fiber]

okayyy

so

it would be

9* 8 * 7 * 1

for 0 at the end

[storm abyss]

yep

[valid fiber]

and for 0 not at the end

8 * 8 * 7 * 4 ????

[storm abyss]

yep

just add em up

and I think we got the correct answer

@valid fiber you got it?

[valid fiber]

yes sorry slow wifi 😭

thanks u helped a lot !

[storm abyss]

your are welcome

you can .close now

[valid fiber]

.close

[cedar kiln]

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[cedar kiln]

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[tranquil arch]

if $(a_n)$ and $(b_n)$ are two sequences of nonnegative reals then how do i show that $$\limsup a_n\limsup b_n \geq \limsup a_nb_n$$

[wraith dagger]

CoolShot

[tranquil arch]

i tried by using the definition

let $E_a$ be the set of subsequential limits of $a_n$ and $E_b$ be the set of subsequential limits of $b_n$

[wraith dagger]

CoolShot

[tranquil arch]

then $\sup E_a \sup E_b$ is the quantity we need to show it for

[wraith dagger]

CoolShot

[wispy marten]

Is this even true?
What if a_n tends to infinity, b_n tends to 0?

More simply, what if a_n = n and b_n = 1/n ?

@tranquil arch

[hollow minnow]

You need the sequences to be bounded, otherwise it's nonsensical.

[sacred grail]

do you though

[wispy marten]

I don't think you need this assumption

[hollow minnow]

As in, it only makes sense of the product is not 0\cd oo or something of that sort.

[sacred grail]

you do

yeah

[wispy marten]

anyway under this assumption the idea is to first show that

$\sup_{k \geq n} a_k \sup_{k \geq n} b_k \geq \sup_{k \geq n} a_k b_k$

Then you can take n goes to infinity

[wraith dagger]

all matrices are invertible

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[split karma]

Can I use $2<x<5-\epsilon<(x=y)<5<y<b$ to algebraically express the intersection between $(2,5)$ and $(5-\epsilon,b)$? Or maybe when $x=y$ we let them equal $c$ so that we have: $2<x<5-\epsilon<c<5<y<b$?

[wraith dagger]

zenathd

[cedar kiln]

@split karma Has your question been resolved?

[cedar kiln]

@split karma Has your question been resolved?

[cedar kiln]

@split karma Has your question been resolved?

[cedar kiln]

@split karma Has your question been resolved?

[short blade]

@split karma i dont think we really understand your question

do you have an original question that this relates to

for added context

[cedar kiln]

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[sullen spire]

i got 654.552 for the moment

but it was wrong

not sure what the right approach is

[subtle hinge]

!showwork

[cedar kiln]

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

@sullen spire Has your question been resolved?

[cedar kiln]

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[warm coral]

how do I find the expected value again?

[chrome flax]

xP(x)

[warm coral]

-32.5?

the answer

alrightt thankss

.close

[cedar kiln]

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[jaunty charm]

can someone help me with my ap calculus bc homework unit 10 series and sequences

[cedar kiln]

@jaunty charm Has your question been resolved?

[jaunty charm]

asking very soon shoot

gotta finish dinner lol

can someone cal or no

[lofty topaz]

What is the question?

[jaunty charm]

how do i do this

and this:

<@&286206848099549185>

[lofty topaz]

Let $a_1$ be $a_n$

[wraith dagger]

Roman_Garland

[jaunty charm]

yes

[lofty topaz]

@jaunty charm

Plug in that for 9.

[jaunty charm]

plug in n = 9?

[lofty topaz]

For No. 9

[jaunty charm]

yes ok

what do i do next

4/3

[lofty topaz]

$\frac{a_{n + 1}}{a_n} = \frac{1}{10} \rightarrow a_{n+1} = \frac{1(3)}{10}$

[wraith dagger]

Roman_Garland

[jaunty charm]

it keeps changing lmk when its done lol

[lofty topaz]

So here n is 1 right? Because $a_n = a_1$.

[wraith dagger]

Roman_Garland

[lofty topaz]

So $a_2 = \frac{3}{10}$

[wraith dagger]

Roman_Garland

[lofty topaz]

@jaunty charm Do you understand?

[jaunty charm]

uh hold on

pls

so a2 is 3/10

yes

i get it

thank u

[lofty topaz]

Let $a_1$ be $a_n$\
$\frac{a{n + 1}}{a_n} = \frac{1}{10} \rightarrow a{n+1} = \frac{1(a_n)}{10}$\
So here n is 1 right? Because $a_n = a_1$\
So $a_2 = \frac{a_1}{10} \rightarrow a_2 = \frac{3}{10}$

[wraith dagger]

Roman_Garland

[jaunty charm]

yes

[lofty topaz]

No Problem.

Do you know L'Hopital's rule.

[jaunty charm]

yes

[jaunty charm]

ye

[lofty topaz]

So, do you know how to "Find the limit of each of the following sequences"?

[jaunty charm]

kind of

kind of a new topic recently

like it converges or divergfes

[lofty topaz]

How would you do it?

I will point out if you are wrong.

[jaunty charm]

i dotn know what the next step is

[lofty topaz]

$ok$

[jaunty charm]

???

[lofty topaz]

Which one?

[jaunty charm]

how do i do number 9

we didnt finish it lol

[wraith dagger]

Roman_Garland

[lofty topaz]

I thought it was an arithmetic series.

So $r = \frac{a_{n + 1}}{a_n} = \frac{1}{10}$

[wraith dagger]

Roman_Garland

[lofty topaz]

$r = ratio\
a_1$ = first term

[wraith dagger]

Roman_Garland

[lofty topaz]

@jaunty charm

[jaunty charm]

is 9 infinite or finite

[lofty topaz]

@jaunty charm

[jaunty charm]

yes

[lofty topaz]

What is $r$ in geometric sequence?

[wraith dagger]

Roman_Garland

[lofty topaz]

@jaunty charm

Here:
https://youtu.be/zRKZ0-kOUZM?si=VbXjM2Km7CTIoAZc

[cedar kiln]

@jaunty charm Has your question been resolved?

[cedar kiln]

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[cedar kiln]

Please don't occupy multiple help channels.

[brazen geode]

someone help me, im confused

[dire geode]

close one of your channels

[brazen geode]

this one

[dire geode]

.close

[brazen geode]

idk how i can choose one

[cedar kiln]

Channel closed

Closed by @dire geode

Use .reopen if this was a mistake.

[brazen geode]

ok

i closed the other

[dire geode]

instructions here

[dire geode]

.reopen

[cedar kiln]

✅

[brazen geode]

.reopen

so can you help me

ive been stuck for 15 minutes

anyone?

[digital cliff]

15 minutes isnt particularly long, be patient

[brazen geode]

ive been patient

ive tried to solve it myself for 15 mins and failed

and now ive waitijng 30 minutes for someone to assist me

[wicked mantle]

lmao, true

[brazen geode]

nobody can help me?

[wicked mantle]

Which one is your question?

[brazen geode]

all of them

[wicked mantle]

There are multiple questions on it

[brazen geode]

i wasnt here in the term

[wicked mantle]

… I see

Lemme check

[brazen geode]

when my teacher covered it

i was in the hospital

so i litterally dont know anything 😭

i have my ipad and i pen ready to take notes tho

[wicked mantle]

Sorry, I have to head to my class

[brazen geode]

damn

[wicked mantle]

I’ll come back to help if no one helps you in the next 50 minutes

[brazen geode]

okay

thank you

[brazen geode]

they probably wont so ill js wait

at the end of this i might gift you nitro

if you want it

[dire geode]

why can't you just watch lectures on youtube

[brazen geode]

havent got much time

[dire geode]

or read the book

[brazen geode]

• that would take longer than someone teaching me

[dire geode]

?

[brazen geode]

i didnt get given the book

since i was in hospital at the time they learnt this

116k messages 🤣

[dire geode]

you think you're funny?

[brazen geode]

i implied that when?

[dire geode]

.

[brazen geode]

how was that me thinking im funny?

so your ashamed of that

[dire geode]

:rofl:

nah but you using that implies you think you're insulting me

[brazen geode]

so your ashamed of that stat

[brazen geode]

how?

elaborate

[dire geode]

nah you should be doing stats

should use your time better

learning how to find mean and variance

[brazen geode]

retired my dad at 17

ive already used my time well

now im trying to do well for them academically

[dire geode]

.

[dire geode]

.

[brazen geode]

so yea trust me ive already used my time well 🤣

idk about you tho

[dire geode]

<@&268886789983436800> troll

[slim hearth]

you know we can see deleted messages right?

[brazen geode]

what have i said that was wrong tho

lool

check my messages

[slim hearth]

troll is a bit of a stretch, but handled

[short pumice]

Everyone here could have been more focused on the topic

[slim hearth]

anyways I think this was an unproductive comment

[hidden vapor]

msc stands for?

[slim hearth]

.close

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[ivory finch]

is this setup of permutattions in cycle form possible?

[ivory finch]

i think not since there are two 4's in T

unless someone can correct me?

[dire geode]

composition of two permutations is another permutation

[ivory finch]

is "multiplication" same as composition

they call it multiplication here

same process?

[dire geode]

yes there's only one operation in groups

[ivory finch]

one leading to 2 and one lewading to 1

[4->1, 1->4] [4->2, 2->5]

[dire geode]

you just need to make this diagram

[ivory finch]

yup

same thing

[dire geode]

show the diagram

[ivory finch]

basically is it sayign o = (1 4 3) composed with (2 5 7 8) and T = (2 3 6 4) composed with (1 5 7 6 8 4)

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[feral juniper]

do you know a Series that looks close to this, that you know the value of?

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[forest violet]

is there a good way to solve this without a calculator?

[forest violet]

when i solve the system of equations by hand the numbers get very bad

[flint plinth]

well you can use the quadratic formula but the numbers are indeed grungy

[forest violet]

ok ty

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[thick girder]

Need help understanding some geometry formulas

[ruby abyss]

can someone help me fine the limit with this one? the limit exists (some how)

<@&286206848099549185>

[pseudo merlin]

is it broken it says this channel is available

[lofty topaz]

$\lim_{n\to\infty} \frac{\sqrt[n]{(2n)!}{n}$

[ruby abyss]

yes broken

[wraith dagger]

Roman_Garland
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[lofty topaz]

$\lim_{n\to\infty} \frac{\sqrt[n]{(2n)!}}{n^n}$

[ruby abyss]

i know what u try to do

still didnt figure it out

[wraith dagger]

Roman_Garland

[ruby abyss]

( ((2n)!)/(n^n) )1/n

<@&286206848099549185>

[lofty topaz]

$\lim_{n\to\infty} \sqrt[n]{\frac{{(2n)!}}{n^n}}$

[wraith dagger]

Roman_Garland

[hot patio]

.

guys, im sorry but i dont really get it

for the first time, ive never understand a math, especially like these

[cinder shard]

You need to take your question to an empty help channel, this one is being used. The quadrilateral should have the labels M A T and H on the four corners as a starting point. It’s then a mixed geometry (angle sums) and presumably cosine/sine rule question. Just took a glance tho. Like I said go empty channel and someone can help in full

[cinder shard]

If you don’t know sine/cosine it could also be a similar/congruence question

[cedar kiln]

@cinder shard Has your question been resolved?

[hot crag]

@cinder shard

you accidentally claimed this channel

do .close

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[hot patio]

this was available earlier...???

[cedar kiln]

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[proper mesa]

is anyone able to check if this is correct?

[upper laurel]

there is some magic happening here for sure

first:

this is saying $\frac{2^7}{2^3}=\frac73$

[wraith dagger]

mtt07734

[proper mesa]

how should i tbe simplified?

[upper laurel]

second, your choice to use l'hopital of all things instead of just dividing by n

l'hopital is a crutch, avoid using it unless you dont have a choice

[proper mesa]

I see

[upper laurel]

the formatting here isnt quite right

replace n with x

[proper mesa]

oh okok

[upper laurel]

and place those lim n -> ∞ on the left

[proper mesa]

I will revise that

[upper laurel]

anyways to simplify this properly, remember you exponent laws

[proper mesa]

is there a way i can simplify this better?

[upper laurel]

to simplify this properly, remember your exponent laws

[proper mesa]

a^b/a^c = a^b-c?

[upper laurel]

yes

[proper mesa]

okok

[upper laurel]

wait

you dont need to do that

because you have this,

its a bit hard to see but the numerator is:

,,e^{\ln\qty(3^{n/2+6\sqrt n+10})}

(btw do not use the asterisk for multiplication - use a proper \cdot symbol or leave it out, the * symbol is for other purposes)

[proper mesa]

uhm thats a 3

[wraith dagger]

mtt07734

[proper mesa]

yeah

[upper laurel]

you can now use an natural log law to move the exponent down

[proper mesa]

yeah im a bit new to latex

ill do that

[upper laurel]

,,e^{(n/2+6\sqrt n+10)\ln3}

[wraith dagger]

mtt07734

[proper mesa]

okok

[upper laurel]

you do this for the bottom as well

[proper mesa]

then i subtract?

[upper laurel]

yep

[proper mesa]

okok

[upper laurel]

now another thing

reading the text here isnt made nice due to the e forcing it to be an exponent

fortunately this has a workaround

instead of using e^x, use exp(x)

,,\exp(x)

[wraith dagger]

mtt07734

[proper mesa]

ohhh

ok

[upper laurel]

this means the same thing but looks nicer

[proper mesa]

e\exp(x)?

[upper laurel]

\exp

just like for \log or for \sin, all the command does is give you three upright letters

[upper laurel]

since youll move the limit to be inside the exp(), this exp() will remain on the outside throughout the limit

,,\lim_{n\to\infty}\exp(\cdots)=\exp(\lim_{n\to\infty}\cdots)

[wraith dagger]

mtt07734

[proper mesa]

ohh ok

it means the same thing right?

as long as the base is not n?

[upper laurel]

they are both equal

[proper mesa]

oh ok

ill try it out

thank you

[upper laurel]

np

[proper mesa]

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[finite badger]

thermo question hope its okay
how the X1=0.5 was concluded? is it a constant or a equation dependent value in each question of this nature?

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[pale lake]

i need some help underdstanding the solution to this question please

i dont get the answer

i understand everything up to the red dot

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@pale lake Has your question been resolved?

[pale lake]

<@&286206848099549185>

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[austere plume]

For 17c why doesn’t trying to use the discriminate work?

[austere plume]

Sorry my handwriting isn’t great

To explain what I did I the top

I basically turn arg(z+5 into c and y for

I did it again and still got it wrong💀

Is my math wrong or is it the method?

I finally figured out

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[vernal wasp]

Let n be a positive integer. Let S be the set of all subsets of [n] = {1, 2, . . . , n} that
contain the element 1; let T be the set of all subsets of [n] that contain the element n.
Define a bijection between S and T, and find its inverse. So- I've come up with an idea abt the bijection - but I'm unsure abt the inverse portion

[crimson sedge]

nice problem

u solved bijection?

[vernal wasp]

im kinda unsure- but thi is how i went abt it

S is gonna have a cardinality of 2^(n)-2^(n-1) which is basically 2^(n-1). This is becasue the size of all possible sets is 2^n, and the size of all sets without 1 is bascially 2^(n-1).

And for T

since n is also just a single element- with the smae process, we end up wiht the same size of the set

so becasue they have the same number of elements- there's a bijection between them

thats my approach so far

im kinda new to this so yeah if u have a better approach im all ears

<@&286206848099549185>

[vernal wasp]

^^ help pleaseee

[wicked smelt]

Can you solve this

Pls

Article are marked at a price which gives a profit of 25%. After allowing a certain discount,the profit reduces to 12½%. Find the discount percent.

[dusk goblet]

!occupied

[cedar kiln]

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

[vernal wasp]

.close

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[plucky ravine]

This question was on a recent test of mine and i know its simple but it really confused me. I used two separate suvat equations, one for AB and another for BC and did simultaneous equations using the s=ut+1/2at^2 formula, i got 15ms^2 for part a) and 4ms for b)

[floral salmon]

$v(t)=a\cdot t \rightarrow v(2) = 15 \cdot 2 = 30 m/s$

[wraith dagger]

Crystopher

[floral salmon]

I think your acceleration is correct

[upper laurel]

the initial velocity is not 0

the acceleration is not correct

[floral salmon]

well if starting velocity is not 0 then acceleration I got cannot be correct, that's true.

[upper laurel]

were these your two suvat equations?

[plucky ravine]

Yes

[upper laurel]

is the car moving at the same speed at A and at B?

[plucky ravine]

It doesn't specify but i dont think so since it asks at what speed its travelling at A

[upper laurel]

it says constant acceleration

and the car isnt reversing or anything that doesnt make any sense

the car is changing speed at all times

[plucky ravine]

Yes

[upper laurel]

so is the car moving at the same speed at A and at B?

[plucky ravine]

No because its accelerating no?

[upper laurel]

then dont use the same variable for the "initial speed" part of the suvat equation

[plucky ravine]

Ahh ok

[upper laurel]

what you do instead is

[plucky ravine]

Makes sense my bad sorry

[upper laurel]

you consider the suvat for AB and for AC

[plucky ravine]

Yeah Ac instead of BC

Oh ok that makes sense

[upper laurel]

sounds good

[plucky ravine]

My bad im aorry

[upper laurel]

dw

[plucky ravine]

Thanks a lot 🙏🙏

[upper laurel]

np

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[glacial steppe]

Ok so like net displacement from positive Y axis is that angle right?

Am I missing some or am I just like looking for the wrong angle?

[livid hound]

they want angle with the y-axis

draw in the xy axis

[glacial steppe]

Yeah that was correct

[livid hound]

and it should be clearer what you messedup

[glacial steppe]

I thought since it said net displacement it meant from the origin

[livid hound]

you're just looking at the wrong angle

draw in the xy axis

(centred at the starting point)

[glacial steppe]

How do I look at an angle like this though? Since it’s mixed between m/s and m/s^2

I could just be looking at the wrong angle again

Better question

What’s the formula to find the magnitude of a 3D particle with respect to time?

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[winged grail]

!status

[cedar kiln]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[winged grail]

1

[warm mica]

Just try to simplify it and get all the perfect squares out

Like root(48) is 4xroot(3) and root(12) is 2xroot(3)

After cancellation you'll get the answer

[cedar kiln]

@winged grail Has your question been resolved?

[winged grail]

Is the answer 10

[winged grail]

<@&286206848099549185>

[real tree]

No its not

[winged grail]

I mean 20

[real tree]

its not 20 either

could u shwo me ur calculation

I could probably tell u where u went wrong

[winged grail]

@real tree

[real tree]

where did the 2^2 come from

its only 2

when u seperate root 48

u get root (12*4)

that is 2root12

[winged grail]

@real tree like this?

[real tree]

Right

44root5

thats correct

[winged grail]

Ayy

Thanks

What about this question

[real tree]

try to get same number

in the root

so u can take common

[winged grail]

I don't get it

[real tree]

like

u can modify 6root75 as

6 into root(25*3)

so u get 6*5root3

= 30root3

[winged grail]

Alr

10 radical 48 is 10 radical 6×8 which is 10 radical 2×3×2²×2 20 radical 12

[real tree]

root12 is again root(4*3) = 2root3

[winged grail]

So 40 root 3?

[real tree]

yes

[winged grail]

What do I do for -5 root 300 tho

[real tree]

5root300

try taking out root3

and then see whta u get

[winged grail]

What?

[real tree]

5root300 = 5root(100*3) = 50root3

u get what I did

ok then u take root3 common fromall 3

u get root3 (30+40-50)

u can do the rest

Im gonna go sleep gn

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[winged grail]

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[winged grail]

Ty gn

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[crimson sedge]

how many 10 digit numbers have the sum of their digits equal to 4.

[crimson sedge]

let me show my solution and you tell me if I its good.

[digital cliff]

sure

[crimson sedge]

yes. i changed the problem. it was the sum of their difference it was*** sum of their digits***

so my logic here is this. for the sum to be equal to 4, only 4 digits need to be used.

0,1,2,3,4

if the first digit is 4, then there is 1 possible combination

if the first digit is 3, then we need to choose 1 digit (being 1) to fill in 1 of 9 places. the rest will be filled with zeroes

if the first digit is 2, we can either fill 1 of 9 places with digit 2, or 2 of 9 places with digit 1.

and if the digit is 1, we can either fill 3 of 9 places with 1s, fill 1 of 9 places with 3s or fill 1 of 9 places with a 2 and then 1 of 8 places with a 1.

add them all up together and you get the expression i wrote

[cedar kiln]

@crimson sedge Has your question been resolved?

[stiff vigil]

this should be correct

[cedar kiln]

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[crimson sedge]

Is this allowed?

[cedar kiln]

Please don't occupy multiple help channels.

[coral jewel]

!1c

[cedar kiln]

Please stick to your channel.

[crimson sedge]

.close

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[plush wharf]

Which is wrong?

Is A and F rational?

[drowsy sage]

What is a rational function?

That's the first question...

[plush wharf]

Polynomial

[drowsy sage]

Nope

[plush wharf]

Yes

Fraction

[drowsy sage]

No... you need a whole number in the numerator and the denominator of a fractional representation

There's no pair of whole numbers we can use to express pi

3.1415....

or sqrt(2)

or e

[plush wharf]

This video says that

[drowsy sage]

reading

[plush wharf]

Ok so which ones in my problem are rationals

[drowsy sage]

So... try subbing in 1 for x and see which ones produce decimated numerators or denominators

decimal... decimated... simply means "divided by 10"

hint - prime numbers can not be expressed as a fraction of two whole numbers

[plush wharf]

Isn’t there a faster way

[plush wharf]

Like this

I don’t get which is wrong

[drowsy sage]

1/2 = .5

1/3 = .3333333..

1/4 = .25

[plush wharf]

Bro what

[drowsy sage]

sqrt(2) = 1.4142135623730950488016887242097.....

1.4142135623730950488016887242097... can not be expressed as a fraction of two whole numbers

ergo

sqrt(2) is irrational

[plush wharf]

Easier way if there is sqrt, absolute value, decimal/fraction exponent then it’s not rational??

Is that correct

[drowsy sage]

There is always a square root... though it may not be rational

There is always an absolute value

[plush wharf]

No it’s only in I

[drowsy sage]

Bud... grab your calculator and find the square root of sqrt(2)

The absolute value is just the positive value of whatever that is

1/2 is a rational number - 1 and 2 are both whole numbers

3/4 is a rational number - 3 and 4 are both whole numbers

3.14159..../1 is not a rational number... 3.14159 is not a whole number

that's not to say that every decimal number is irrational

.25 is rational... it's 1/4 - where 1 and 4 are both whole numbers

0.14285714285714285714285714285714... is rational - it is 1/7

You need to understand rational numbers vs. irrational numbers before you can answer this question

[cedar kiln]

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[crimson sedge]

for this i dont think my parameterizations are differentiable

[crimson sedge]

like if this is the case, this is going to be HORRIBE

<@&286206848099549185>

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[heady spindle]

I'm trying to show (or give a counterexample) that the complex functionf: z ---> |z| is bijective, but I don't know how to continuos the proof of injective, I suppose that |z| = |z'|, then I get sqrt(a^2 + b^2) = sqrt(x^2 + y^2), then a^2 + b^2 = x^2 + y^2, and here is I'm stuck, because I don't if can I continuos thinking that b and y are the imaginary part (a + bi and x + yi) after calculate then absolute value :(

[buoyant latch]

How is f(z) = |z| bijective, that doesn’t sound right

[heady spindle]

why doesn't sound right? how do you get that intuition?

[buoyant latch]

f is a function from ℂ to ℝ do you agree?

[wraith dagger]

Frosst

[heady spindle]

Mm I don't understand why R

[buoyant latch]

Well |z| is always real, do you agree?

[heady spindle]

Ooh of course sqrt(a^2 + b^2) will be always real

[buoyant latch]

Yeah?

[buoyant latch]

So do you agree with this

[heady spindle]

Mm since a and b are reals, and they are because z = a +bi, where a and b are reals

[buoyant latch]

Right

[heady spindle]

Yay :D

[buoyant latch]

Ok so can you understand that ℂ is a lot “bigger” than “ℝ”?

[heady spindle]

Yes

[buoyant latch]

So there are no set isomorphisms between ℂ and ℝ

[heady spindle]

So R doesn't have the enough elements for the bunch of elements of C

[buoyant latch]

Yeah

That’s my intuition

And you can see this because there are a lot of complex numbers z you could put into f

That gives the same modulus

Can you think of an example?

[heady spindle]

I think of 1 and -1, but they're real :( an example of complex doesn't came to my mind

[buoyant latch]

That still works

[heady spindle]

how? :0 I need to have a imaginary part, isn't it?

Also a quick question

[heady spindle]

This is the statement of the exercise, so the image and preimage are they, right?

[buoyant latch]

What’s the image of i

Where does f(i) go

[buoyant latch]

Real numbers are Complex numbers

[heady spindle]

1?

[buoyant latch]

Yes

[heady spindle]

I know, sorry :( it's just my first time using them :')

so, a counter example can be 1 and -1, and they imaginary part is 0?

[buoyant latch]

Yes

[heady spindle]

So the pre image will be i and the image is 1?

[buoyant latch]

Do you get i when you put 1 into f?

ie. f(1) = i?

[heady spindle]

ah

I don't understand well the statement, my mistake, english is not my first language

[heady spindle]

f(1) = 1

[buoyant latch]

The preimage of i is all the inputs to give i

What can you put into f to get i?

[heady spindle]

All the solutions of the equation a^2 + b^2 + 1 = 0

[cedar kiln]

@heady spindle Has your question been resolved?

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[sharp oak]

Hello,
While finding the Particular Integral (y sub p) for a DE in the form

sin(ax)/f(D)

if the denominator becomes 0 after putting D^2 = -a^2, we diff the denominator and multiply by x in to numerator so that it becomes

xsin(ax) / f'(D)

Lets say it is

xsin(x) / 2D

Now do we need to integrate xsin(x) or sin(x)?

[mortal grove]

this question isn't very clear. what is D? and do you mean particular solution? it would help if you wrote out the actual Differential equation

[cedar kiln]

@sharp oak Has your question been resolved?

[cedar kiln]

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[south slate]

I don't really understand how to do b.. I'm stuck on starting and what the proof should look like

[flint plinth]

possible hint: notice that (b/a)a = b

[south slate]

i dont understand.. how did you get (b/a)a from the function?

[flint plinth]

i'm saying, notice that every element of the image has the property that the product of the first component and the second component equals the numerator of the first
is that true for an arbitrary element of the codomain?

like for example, is (3/5, 7) contained in the image?

[south slate]

no right?

[flint plinth]

are you asking me or telling me? 😁

can you see why it's not contained in the image?

[south slate]

telling LOl sorry im really bad at dicrete math

[south slate]

because 7/3/5 * 7 does not equal to 7

[flint plinth]

right

and no matter how you write 3/5, you can't make (3/5)7 be an integer

[drowsy sage]

then don't start talking in a channel that's outside your sphere of knowledge

[flint plinth]

even if you write it as 6/10 or whatever

[south slate]

yep understood

this means that f is not a surjection correct, since its not true for all arbitrary elements?

[flint plinth]

correct

[spice kraken]

f(7,21/5) = (3/5,7) though

Isn't f surjective?

[flint plinth]

oh crap, i overlooked that b doesn't have to be an integer

yea, scratch what i said

[south slate]

oh okay

can someone explain to me why its surjective then

[spice kraken]

We can choose appropriate a,b such that f(a,b) = c,d for any c,d

It's obvious we need to choose a = d

Now we need c=b/a

And choosing b = ca works

[south slate]

so since b = ca, for all elements in the codomain, f(a,b) = (c,d)?

[spice kraken]

Yes by choose appropriate a,b

[south slate]

ok thanks

.close

[cedar kiln]

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[sharp oak]

.reopen
well it's the differential operator...

(D^2 - 4D + 5)y = e^(2x) sin(x)..... D is the differential operator d/dx

.reopen

[mortal grove]

!status

[cedar kiln]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[delicate yarrow]

whoops i solved it

.close

[cedar kiln]

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[cedar kiln]

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[timid rivet]

How would i solve question 12?

Because 12.4 x 10^-4 isnt scientific notation

[half elk]

How about 12.4/4

[timid rivet]

Oh you mean i need to divide 12.4 by 4?

[half elk]

What you found for 11 in scientific notation?

[timid rivet]

I put 8 x 10^5 as the scientific notation answer

[half elk]

Well how you found that 8?

[timid rivet]

Because the standard answer (at least that i found) was 800,000 so i just moved the decimal over

[half elk]

That's one way to do it

You learnt that

$a^b*a^c = a^{b+c}$

[wraith dagger]

Ñøïr

[half elk]

Right?

[timid rivet]

Yeah

[half elk]

$(210^3)(410^2) = 210^3410^2$

[wraith dagger]

Ñøïr

[half elk]

Yes?

I just removed brackets

[timid rivet]

where did the other numbers come from like 2?

or are you just making an example

[half elk]

I was showing it for 11

[timid rivet]

ohhh

[half elk]

Which equals to $2410^3*10^2$

[wraith dagger]

Ñøïr

[timid rivet]

ohh okay that way makes sense but how does that apply to question 12?

[half elk]

So by that logic we can do rational part and exponentialy part seperately

$\frac{12.410^{-4}}{410^2} = \frac{12.4}{4}*\frac{10^{-4}}{10^2}$

[wraith dagger]

Ñøïr

[timid rivet]

ohh okay so it would be (in scientific notation) 3.1 x 10^6 ?

[half elk]

3.1 yes

$\frac{a^b}{a^c} = a^{b-c}$

[wraith dagger]

Ñøïr

[timid rivet]

and then stabdard form its 31,000,00?

standard*

[half elk]

No

You got the exponent wrong there

[timid rivet]

oh?

[half elk]

Here if we plug in the values we have $\frac{10^{-4}}{10^2} = 10^{-4-2}$

[wraith dagger]

Ñøïr

[timid rivet]

ohh so its -6

[half elk]

Yes

[timid rivet]

okay! i think i've got it now, tysm !

[half elk]

Yw

[timid rivet]

.close

[cedar kiln]

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[vernal kite]

have i done this question correctly so far?

[vernal kite]

i’m proving congruency in 4 triangles first

then seeing if it helps with proving pqrs

[icy mirage]

shudnt u say OS=OQ and PO=PR cus of midpoint

and then its SAS?

Also thats between triangles PSO and PQO

[vernal kite]

so u prove that and sor and qor?

[icy mirage]

yea

[vernal kite]

why can't you do triangle spr and qpr

and triangle spq and srq

[icy mirage]

u cant rly prove that firstly and secondly, u cant say that all the sides r equal cus they're not all congruent to each other

whereas with wat i said, all 4 triangles r congruent

[vernal kite]

true

alr then

wait but then how am i supposedf to prove sro and qro

if the lines are shared

[icy mirage]

exact same reasoning as the first two triangles

[vernal kite]

would i use angle sop is equal to angle qop

cus of angles on a straight line = 180

[icy mirage]

u can say that or u can pr and qs bisect it at right angles

[vernal kite]

ohh

thats probs better then

[icy mirage]

👍

[vernal kite]

and how would i do part d

for question 2

[wicked mantle]

What is BR?

[vernal kite]

ill retake a photo of the triangle

[wicked mantle]

State it with x

[wicked mantle]

No, I’m good with the current graph