help-33

[still temple]

But even if you dont get some different method, from the student or teacher. It will surely strengthen your concepts

Clever guy..

[marsh citrus]

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[fierce belfry]

hi can someone tell me how to continue pls

[glass silo]

Separate variables and partial fractions?

[fierce belfry]

uhh

how would I make use of N = 1 and t = 0 though

[glass silo]

After you do the integration

[fierce belfry]

hmm the ans key kinda recommended me to do it first lol but i cant see how to use it

[glass silo]

Do what first, the N=1 stuff or the integration?

[fierce belfry]

n = 1

[glass silo]

Ah yeah I was gonna say I think that would help you find k

Could do that now I guess, in any case we’d need to keep that differential in mind

[fierce belfry]

alright

but how do i find k lol

[glass silo]

dN/dt= what they said, N=1

[fierce belfry]

yea

[glass silo]

Substitute that and solve it

[fierce belfry]

uh how do i sub n = 1?

like its dN not N

or am i missing something

[fierce belfry]

OHHHHH

j = 1/40

wtf

sorry keyboard hanged

its k = 1/10

okay now i will integrate both sides

[glass silo]

Now you know k at least, makes your like chill

[fierce belfry]

yesh

[fierce belfry]

should I have left the 1/10 on the right

[glass silo]

RHS should be 1

[fierce belfry]

oh right

[glass silo]

Could have, doesn’t really matter

[fierce belfry]

alrite

[glass silo]

Integral of 1 *

[fierce belfry]

then now partial equations the left and integrate both sides?

[fierce belfry]

liek this?

is my partial fractions wrong

[glass silo]

Should be something like B/N + C/(P-N)

Then find B and C

[fierce belfry]

hmm when is it Bx + c

[glass silo]

When the denom has degree 2

[fierce belfry]

wait but the N is degree 2

[glass silo]

Here the denom is linear

I mean as in the factors

P-N is linear

Degree 1

[fierce belfry]

oh so one of them needs to be N^2

for me to use Bx + C

ohh

i kinda forgot how to solve for the numerators

nvm got it

both A and B are 1/P i think

[glass silo]

Sounds right I think

[fierce belfry]

yay

[glass silo]

,w 1/N + 1/(P-N) common denominator

[elfin berry]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by chartbit#3171

[glass silo]

Why you no understand me OP

[fierce belfry]

ah yes my algorithm is flawed

i am the wolfram alpha

i kinda set wolfram alpha as my name as a joke and now i cant change it

apparently the server removed permissions to change names

[glass silo]

Think the second ln one is - in front?

Cause

[fierce belfry]

OH yea i ened to diff the insides

a ha

okay

now ill combine the lns

[glass silo]

Oh yea one tiny thing

You don’t need two integration constants on both sides

[fierce belfry]

oh that makes sense

[glass silo]

Having an integration constant on one side (ideally the rhs) is fine

Yep, absorbing constants and all

[fierce belfry]

hmmm now

[glass silo]

May be a good idea to create a new constant on the RHS using rules of powers

[fierce belfry]

wait where do i spawn in the A from

oh u answerde me

[glass silo]

Then find it with the values they give

[fierce belfry]

hmm how do i use the rules of powers

do i let A = e^pc or somethng

cuz pc is missing in the final result

[glass silo]

$e^{a+b} = e^a e^b$

[elfin berry]

chartbit

[fierce belfry]

yesh

[glass silo]

Set “a”=tp/10, “b”= the other shit

All good?

[fierce belfry]

something like this?

[glass silo]

Yep like that

[fierce belfry]

yay

ok now hmm

i need to isolate N

[glass silo]

Yep, might help to reciprocal it

But first, might be good to use the initial condition again?

[glass silo]

Actually first flip it I think tbh

[fierce belfry]

oh i kinda did it differently

kinda close though

[glass silo]

Whichever way works

[fierce belfry]

maybe now ill multiply top and bottom by

1/(e^0.1pt)?

so close yet so far

[glass silo]

⏸️

[fierce belfry]

[fierce belfry]

oh its plus

[glass silo]

Divide through the denom and remember $1/a=a^{-1}$

[elfin berry]

chartbit

[glass silo]

(After you correct the sign)

[fierce belfry]

wait so now ill do this?

uhh what does dividing thru the denom mean lol

[glass silo]

As in do 1/e^(…) + A

[fierce belfry]

so this?

hmm

[fierce belfry]

OHHH

okay i got it

tysm XD

theres actually a part 3 to 5

but my battery is at 3%

would u be alive later

[glass silo]

Maybe maybe if I spot you around I’ll check your q out hahah

[fierce belfry]

yes sir

do u mind if i ping u when i get bacc

[glass silo]

Literally about to get a bit of rest

[fierce belfry]

[glass silo]

That’s all good, I don’t mind, feel free to

[fierce belfry]

rest well

baibai

.close

[marsh citrus]

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[marsh citrus]

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[lucid hinge]

not trollin

in my homework, what can i do

[marsh citrus]

@lucid hinge Has your question been resolved?

[lucid hinge]

<@&286206848099549185>

[marsh citrus]

@lucid hinge Has your question been resolved?

[marsh citrus]

@lucid hinge Has your question been resolved?

[marsh citrus]

@lucid hinge Has your question been resolved?

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[marsh citrus]

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[random burrow]

If there is 8 questions and 4 multiple answers with 1 correct answer. What is the percent chance of getting all questions correct?

[glass silo]

Assuming that you’re randomly guessing them?

Each question you have a 1/4 chance of getting right, and there are 8 of them

[marsh citrus]

@random burrow Has your question been resolved?

[random burrow]

Yes but when there is multiple questions it becomes smaller chance each time

Cuss its harder to get something rigth 2 times in a row than just get it rigth 1 time

[glass silo]

Correct, and we're probably assuming that they're independent too, in that getting one right doesn't affect getting the next one right, yes?

[marsh citrus]

@random burrow Has your question been resolved?

[marsh citrus]

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[vestal pilot]

Hi guys

[vestal pilot]

How to know if a transformation matrix describes a rotation, projection or reflection? I did it by checking the basis vectors change but can't just do it.

The matrix is $ \frac1{13} \begin{bmatrix}-5 & 12 \ 12 & 5 \end{bmatrix}$

[elfin berry]

afeAlway

[vestal pilot]

My drawing is

[marsh citrus]

@vestal pilot Has your question been resolved?

[vestal pilot]

<@&286206848099549185>

[marsh citrus]

@vestal pilot Has your question been resolved?

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[still temple]

<@&286206848099549185> i need help

[still temple]

this goofy ahh question is torturing me

[main idol]

[still temple]

wait

[marble glacier]

goofy ahh person

[still temple]

question 9

<@&286206848099549185>

[sinful skiff]

!15min

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[still temple]

ok sir
my bad

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

<@&286206848099549185>

ong

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

@snow flume Has your question been resolved?

[marsh citrus]

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[marsh citrus]

Please don't occupy multiple help channels.

[main idol]

stick to your other channel

.close

[marsh citrus]

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[covert flume]

Mb

.close

[marsh citrus]

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@uneven delta Has your question been resolved?

[marsh citrus]

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[tardy topaz]

i need multiplication or multi-multiplication questions, please.|| i can do 2 by 2's and 1 by 2's.||

[late geode]

do you have a specific question you're stuck on?

[tardy topaz]

no, i need to do 15 minutes of math, and wanted to get questions i don't make up.

people said to go here,

so.

[late geode]

we generally don't make questions for people,
you come with your own specific question that you're stuck on and we'll try help with that

[tardy topaz]

ok, thanks-

.close

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[naive oasis]

hello!

[naive oasis]

i have good news to share

i did well in my mathematics examination guys!

[glass quiver]

good, but do you have a question?

[naive oasis]

thats kinda rude to be honest mam\sir

[distant peak]

true

but #discussion exists

[dense ocean]

lets gooo well done my man

[tardy topaz]

cg!!! what was your score?? 😄

[naive oasis]

yes i do i got answer for expression: factorize y + sqrt y-20 what answer i got is (y-4) (sqrt y +5) is it correct ?

[naive oasis]

thank you sir

[naive oasis]

maybe i get 18 or 19 out of 20 marks

[tardy topaz]

congratulations! 😄

[naive oasis]

its correct @dense ocean ?

[dense ocean]

yes

[late geode]

no

[tardy topaz]

all of you have a nice day.

[late geode]

$y + \sqrt{y} - 20 \redneq (y-4)(\sqrt{y}+5)$

[elfin berry]

ℝamonov

[naive oasis]

thank you

[naive oasis]

why not

[distant peak]

expand, youll see

[naive oasis]

ramanov says its not right

[late geode]

expand, and you'll see

[naive oasis]

can you plz do it

i took y as x^2

[late geode]

they jumped the gun when responding

since it looks close to right,

but its not

[glass quiver]

substi x = rooty

[glass silo]

,w expand (y-4)(sqrt(y) + 5)

[elfin berry]

Results provided by WolframAlpha

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Requested by chartbit#3171

[dense ocean]

ramanov is right i am wrong

because

there's a square root

which i didn't see

[late geode]

make sure you quadruple check whether what you typed here actually matches what you have

[naive oasis]

wait means i lost marks in exam?

[dense ocean]

use hidden quadratics

[distant peak]

[dense ocean]

so y = x^2

[late geode]

if this is what you actually wrote, then you'd be wrong

[naive oasis]

whats the entire answer to the expression ?

[late geode]

show your work

[naive oasis]

same i took y as x^2

[dense ocean]

yeah

so when you get your answers for x

[dry spindle]

do take it step by step

[naive oasis]

i have submitted my papers how can i show you?

[distant peak]

you forgot what you wrote ?

[naive oasis]

x^2 + x - (4) (5)

[naive oasis]

nope how can i forget

[distant peak]

then write it on a paper and show

[naive oasis]

ok @distant peak plz wait

[distant peak]

or use the bot

[dry spindle]

(sqrt y)² + 5sqrt y - 4sqrt y - 20 = (sqrt y)(sqrt y + 5) -4(sqrt y + 5) = (sqrt y - 4)(sqrt y + 5)
not (y-4)(sqrt y + 5)

[naive oasis]

here is the work i done

[dry spindle]

.

[naive oasis]

x^2=y and x = sqrt y

[dense ocean]

yeah thats wrong bud

[naive oasis]

can you do paper work and post pic here i cant understand like that

[dense ocean]

you subbed it in nicely

[dry spindle]

ill latex it

[naive oasis]

whats the correct?

[dense ocean]

but why did you factorise it like that

(x-4)(x+5) = 0

in terms of x

not y

[naive oasis]

yes

oh no

[dense ocean]

so x = 4, x = -5

they x^2 = y

[naive oasis]

no no

[dense ocean]

so y = 16, 25

[naive oasis]

x= -4,x=5

[dry spindle]

$(\sqrt{y})² + 5\sqrt{y} - 4\sqrt{y} - 20 = (\sqrt{y})(\sqrt{y} + 5) -4(\sqrt{y} + 5) = (\sqrt{y} - 4)(\sqrt{y} + 5)$
not $(y-4)(\sqrt{y}+ 5)$

[elfin berry]

Kel.plush

[dry spindle]

there

you factored y instead of sqrt y from the first bit

[naive oasis]

.close

[marsh citrus]

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[marsh citrus]

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[fossil patrol]

any idea why a is true ?

[marsh citrus]

Please don't occupy multiple help channels.

@fossil patrol Has your question been resolved?

[marsh citrus]

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[marsh citrus]

@little folio Has your question been resolved?

[little folio]

.close

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[dire otter]

solve for a

[fathom ridge]

what problem are you facing

[dire otter]

how do i get c out of the denominator

[fathom ridge]

well you'd have to take two cases I suppose

One where c is positive and one where c is negative

is it explicity stated anywhere, anything about the nature of c

[dire otter]

... i want c to be out of the denominator because its a variable

im being asked to solve for a

[fathom ridge]

Do you know about the basics of how inequalities work

[dire otter]

kind of

[fathom ridge]

Because if you multiply a negative quantity on both sides, the inequality sign changes

And if you don't know if c is positive or negative, you need to account for both cases

[dire otter]

.close

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[tired sand]

would this be positive?

[hollow quest]

$u\cdot v=\abs{u}\abs{v}\cos \theta$, what is $\cos\theta$ in this scenario?

[elfin berry]

Duh Hello

[tired sand]

im not sure what to put in for u*v

[hollow quest]

ignore the u and v part

but what sign does cos of the angle between the two vectors have?

[tired sand]

im not sure

[hollow quest]

the easiest intuition for the dot product is just that it measures how aligned the two vectors are. if its positive then they are "positively aligned", meaning they are pointing in a similar direction. if its zero they are completely misaligned (perpendicular). if its negative then they are pointing in opposite directions

[tired sand]

ahh okay

ill watch a video on it to understand it better

thanks!

.close

[marsh citrus]

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[hollow quest]

https://youtu.be/LyGKycYT2v0?t=88 see timestamp

[marsh citrus]

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[hard stratus]

how do i do this

[cobalt sentinel]

do u know how to turn mixed fractions into improper fractions?

[hard stratus]

yes it’s 9/2

then what

[cobalt sentinel]

correct

[elfin berry]

Stephen

[cobalt sentinel]

now we can do one of two things from here

we can simplify the 9 and the 3, or we can multiply, and simplify later

which would u like to do

[hard stratus]

the easiest one

[ripe bronze]

wait is it 4 times 1/2 or 4+1/2

[cobalt sentinel]

4+1/2 , its a mixed fraction

i think thats the problem

[hard stratus]

mhm

[cobalt sentinel]

alr, so we'll just multiply out

[ripe bronze]

oh ok

[cobalt sentinel]

so do u know how to multiply fractions

[hard stratus]

idk 9x5 and 2x3

[cobalt sentinel]

correct

so what do we end up with

in 1 fraction

[hard stratus]

45/6

[cobalt sentinel]

good, now we can simplify

do u know how to simplify

[hard stratus]

no

[elfin berry]

Stephen

[cobalt sentinel]

do u see any common factors of the two

[hard stratus]

no

[cobalt sentinel]

what are the factors of 6

[hard stratus]

only 2 and 3

[cobalt sentinel]

yea, 1, 2, 3, and 6

are any of those factors of 45, other than 1?

[hard stratus]

6

what are the factors of 45

[cobalt sentinel]

nope

try dividing 45 by each of those numbers

1, 2, 3, and 6 and see which ones result in a whole number answer

[hard stratus]

it’s 3

[cobalt sentinel]

correct

so divide the numerator and denominator by 3

what do we end up with

[hard stratus]

15/2?

[cobalt sentinel]

yea

theres ur answer

[hard stratus]

can i make it to a mixed fraction tho

[cobalt sentinel]

if u want sure

[hard stratus]

so it’s 7 1/2

thx

[cobalt sentinel]

ye

np

[hard stratus]

wait

i have another question

[cobalt sentinel]

ok

[hard stratus]

how do i do 4 1/3 x 1 2/7

[cobalt sentinel]

are those mixed fractions

[hard stratus]

yes

[cobalt sentinel]

so first convert both of them to improper fractions

[hard stratus]

then what

i got 13/3 and 9/7

[cobalt sentinel]

good, now, we could repeat the same process as before, but it'll be a little tough simplifying. instead we can cross simplify right now, do u know how to do that?

[hard stratus]

3 and 9 yea

[cobalt sentinel]

yep, so try that

[hard stratus]

they’re both divideable by 3?

[cobalt sentinel]

yes

so divide each of those by 3

[hard stratus]

it’s 13/1 x 3/7?

[cobalt sentinel]

yep

[elfin berry]

Stephen

[cobalt sentinel]

now just multiply like we did before

[hard stratus]

ok so i can change it into a mixed number now?

fraction

[cobalt sentinel]

after u multiply yes

[hard stratus]

it’s 5 4/7?

???

how do you do 9/2 x 5/3

that’s the last question

[cobalt sentinel]

cross simplify, then mutliply

u alrdy know this stuff

wait we alrdy did that problem...

[hard stratus]

i got 9/1 x 1/3 and it’s 3 0/3?

no we didn’t

[cobalt sentinel]

scroll up

[hard stratus]

where

[cobalt sentinel]

it was literally the first problem we did lol

[hard stratus]

idk wym

so my answer is right?

o guess so

.close

[marsh citrus]

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[lavish warren]

Hello, I am doing some linear algebra review and am stuck on a problem. Can anyone explain when a linear combination of two "3x1" vectors would not exist?

[plain wing]

the two vectors will span a plane and i guess any vector not on that plane would not exist as a linear combination of those two

[lavish warren]

I see

How do I figure out whether one vector is not on the same plane as another?

other than using a graphing utility

[plain wing]

let the two vectors above be a and b and let x and y be scalars you equate xa + yb to the vector youre trying to check

if theres a solution to x and y then the vector is on the plane

i think thats how to check if a vector is an element of a span

[lavish warren]

ok, thank you

.close

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[sturdy hedge]

Yeha so basically I think I’ve forgotten the equation of which one this is

[sturdy hedge]

as u see

i drew the triangke

[burnt abyss]

,rotate

[sturdy hedge]

but im reallly lost

sorry

would

i use the equation

a^2=b^2+c^2-2bccosA

?

and just rearrange?

[next garnet]

for which part?

[sturdy hedge]

for a

[next garnet]

for part a, you would use cosine rule and rearrage

rearrange yes

[sturdy hedge]

oh okay

wait

so quickl

it wouldnt have an "a"

right?

and it would be cos()

then what?

[next garnet]

Actually no

You first use 1/2 absinC

to find out what the angle is

since thats how you calculate the error

[sturdy hedge]

wait

so

[next garnet]

1/2(5)(10) sin(theta) = 15

[sturdy hedge]

yeah that

[next garnet]

and then u can do sin-1 to find out what theta is

[sturdy hedge]

yeah

[next garnet]

and then just sub it in for cos

[sturdy hedge]

then i do the cosine rule?

for part b

[next garnet]

for part b, yes

[sturdy hedge]

oh okay

great

wait

could you list all of the rules

please

like

[next garnet]

what do you mean?

the formulae?

[sturdy hedge]

because i keep forgetting them

yeah ik cosine

but the one u said

i completely forgot it

i wanna take a screenie

of the

formulae

[next garnet]

Area of a non-right angled triangle: 1/2abSin(C) - C is the angle
Sine rule (to find an angle): SinA/a = SinB/b
Sine rule to find a length: a/sinA = b/sinB
Cosine rule: a^2 = b^2 + c^2 - 2bccos(A)

[sturdy hedge]

saved

thanks man

i have some other quesitons

if u wanna help me

[next garnet]

I'm good 😭

[sturdy hedge]

im going through a paper ive don

LMFAO

npnp

wshould i make a new one?

.close

[marsh citrus]

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[still temple]

Why left is wrong?

[cobalt sentinel]

thats not the derivative of arccot

[marsh citrus]

@still temple Has your question been resolved?

[still temple]

What?

[still temple]

Ah shit

Thanks

[cobalt sentinel]

np

[marsh citrus]

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[olive gate]

#help-24 message

[olive gate]

@ionic lava

ok, I'm back from class

how did you place the points on the graph?

[ionic lava]

https://www.geogebra.org/calculator

[olive gate]

yes, I have the formula on the graph

but I can't figure out how you placed the points and dotted lines on it

[ionic lava]

did you draw the equation ?

[olive gate]

I just typed it out

[ionic lava]

click here

[olive gate]

ok

[olive gate]

how about the different colored dotted lines to each point?

which line?

[ionic lava]

create a segement

you will find it in the tools

scroll down

[olive gate]

hmm, yours is dotted and different colors

mine is just straight and only black

[ionic lava]

after you created the line

click on it

[olive gate]

great!

ty

[ionic lava]

anytime

[olive gate]

one more thing

How did you color your formula?

I figured out how to get the formula on the page

but I can't change the color of the text

your text is green, mine is black

nevermind, I figured it out

ty

.close

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[marsh citrus]

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[cunning lantern]

what do i multiply the 2 equations by (i have to solve using the Elimination method

[main idol]

the x coefficient for the first equation is -18 and the 9 for the second. do you know how you can make 9 and -18 add up to zero?

[cunning lantern]

yea

just find the lcm of one of the coefficients

but i tried that and it didn’t work

[late geode]

show work

[marsh citrus]

@cunning lantern Has your question been resolved?

[marsh citrus]

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[rotund walrus]

i(2+i)

[rotund walrus]

how do u solve this

[proven timber]

What have you tried

[rotund walrus]

we learned this today

i dont get it

[proven timber]

Have you tried anything?

[rotund walrus]

ye

substituting i for -1

[proven timber]

You can't replace i with -1

i is i

[rotund walrus]

then what u do

[proven timber]

It's not -1

Distributive rule

[rotund walrus]

teach me

[proven timber]

How would you expand x(2 + x)?

[rotund walrus]

2x+x^2

[proven timber]

So how would you expand i(2 + i)?

[rotund walrus]

2i+i^2

[light frost]

The "i" in here is not an unknown number, so you can't substitute for it because it's a constant

[rotund walrus]

so what u do then

[light frost]

"i" is the sqrt of -1

[rotund walrus]

ohhh

ok whats next

[proven timber]

Remember i² = -1

[rotund walrus]

yea

[proven timber]

That's the definition of i

[rotund walrus]

yea

[proven timber]

So what's 2i + i²

[rotund walrus]

2i-1

[proven timber]

Tada

[light frost]

That's right!

[rotund walrus]

ay

thats ez

thanks guys

.close

[marsh citrus]

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[old totem]

Which expression is another way to write
3 4
125x
?

[proven timber]

#❓how-to-get-help

[old totem]

oh

my bad

[marsh citrus]

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[tardy void]

This is tan right? or cos?

[marsh citrus]

@tardy void Has your question been resolved?

[bitter solstice]

yes some tan stuff

[marsh citrus]

@tardy void Has your question been resolved?

[tardy void]

can anyone help me out please I cant figure this out still

[marsh citrus]

@tardy void Has your question been resolved?

[marsh citrus]

@tardy void Has your question been resolved?

[marsh citrus]

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[worthy relic]

hi i have a statistics related question, for an uniform distribution what is the correct formula to find it's variance?

[worthy relic]

this is the formula found online

but the paper solution is done differently

why are 2 different formulas used?

and when asked which one should I choose when?

[main idol]

you should use the one in your textbook and not random online resources

[worthy relic]

the thing is that it is there in my text book too, the above formula i mean

the second one is a combination of the general formula to find variance with the found mean

and i dont really have a text book

the second one is from a solved paper from uni

not from textbook

do you know when which could be used?

[main idol]

show the one from your textbook

[main idol]

what

use whatever resource your teacher assigned you

lecture notes, recommended books, etc.

[worthy relic]

ok i understand thanks

[marsh citrus]

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[rapid stream]

Hello, I was just wondering I would go about taking a partial derivative of a vector valued function. the problem I am having trouble on specifically is something along the lines of f(x) = c^T * x where c and x are colomn vectors of the same dimension. I am looking to find df(x)/dx.

[main idol]

do the partial derivative one component at a time

verify your answer here
https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf

[delicate prairie]

f is a scalar in this case

and before computation you may want to label components of c and x, like c_1,..,c_n and x_1,..,x_n

[worn nimbus]

you go to waterloo? 😍

[main idol]

i go to google-oo

[rapid stream]

thank you! that was very helpful!

[proud ice]

google-

[worn nimbus]

probably best not to doxx yourself anyways haha

[marsh citrus]

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[torn gull]

How do I solve this bruh

i did

2t+1 > 17

-1

2t > 16

t > 8

so t has to be greater than 8 so the smallest value it can be is 8

is that not right?

[prime escarp]

Since it’s strictly greater than, 8 will not work since 17 is not greater than 17

[torn gull]

so

8+1?

[prime escarp]

Yes

[torn gull]

so if it was greater or equal

it would be 8

[prime escarp]

Correct

[torn gull]

makes sense now mayne thanks

.close

[marsh citrus]

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[wispy turret]

I don't understand how this gets x=0

I used y=mx+b but can't figure it out

i get y=something not x

[mystic minnow]

the slope of the first line is 0, so it's horizontal.
then the perpendicular line must be a vertical line (has undefined slope)
so the line is of the form x = (some constant)
since you know it passes through (0,5) you know it hits where x = 0, so since the line is vertical that's the equation

the formula y=mx+b requires that the slope, m, be a number. You don't have that here

[marsh citrus]

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[rotund walrus]

how do u find x

[lilac bane]

Angle ABD = 79°

And angle ABD consists of 2 angles

[rotund walrus]

oh i didnt see 79

💀

oops

[marble glacier]

Lol

[rotund walrus]

wait

so u would do

oh wait nvm

i got it

.close

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[grave vortex]

how do i do a

[grave vortex]

i moved the a^-2 up

[brittle vessel]

how did u do that

[grave vortex]

wdym

i moved it up

[wise jackal]

Exponent rules

[grave vortex]

and made it positive

[solid vale]

so if you moved the a up, what is the result?

[grave vortex]

a^2.5/a^4

[solid vale]

correct

[grave vortex]

whats after then

thats where i got stuck

[solid vale]

do they ask you to have it as a positive indice?

so a positive power?

[grave vortex]

it asked simplify and express with positive exponents

[solid vale]

okay

[elfin berry]

Kihei

[solid vale]

a^2.5 ÷ a^4

what happens when they are divided

[grave vortex]

u subtract

[solid vale]

the powers are subtracted correct?

[grave vortex]

ya

[solid vale]

subtract them

[grave vortex]

-1.5

[solid vale]

yes but

They ask for positive exponents

[grave vortex]

1/a-1.5

oh ta

ya

help

what do i do

[solid vale]

so even though a^-1.5 is correct

we need to make it positive

[grave vortex]

yea

[solid vale]

what did you to in the beginning to that a at the bottom which had a negative exponent?

[grave vortex]

move up

[solid vale]

you moved it up right to make it have a positive exponent?

yes

so in this case

[grave vortex]

2/3?

[solid vale]

it’s basically a^-1.5 / 1

so we move a down

[grave vortex]

no

[solid vale]

so then it’s 1 / a^1.5

[grave vortex]

wasent a down alr

[solid vale]

no

[grave vortex]

how

[brittle vessel]

can u paste the whole question?

[grave vortex]

ya

[solid vale]

we moved everything up remember? including a^-2 and a^4, which resulted in a^-1.5

[solid vale]

it’s all in the numerator

there’s nothing left in the denominator

[grave vortex]

we did 2.5-4

so remainder is in denominator

right

[solid vale]

yes?

no

[bright jay]

This makes it not a fraction anymore that's why it's not in the denominator anymore

[solid vale]

everything is gone

you added 2 , because of a^-2

[grave vortex]

why is it up and not down

[bright jay]

This makes it not a fraction anymore that's why it's not in the denominator anymore

[solid vale]

then you subtracted 2 , because of a^4

[bright jay]

If it's not a fraction, there is no denominator

[solid vale]

let’s do it another way then perhaps…

[grave vortex]

sure

[solid vale]

ok so let’s deal with the denominator first

a^-2 times a^4

what happens to the exponents if they have the same base

they are added

[grave vortex]

yuo

[solid vale]

so it becomes a ^ -2+4

what does it become

[grave vortex]

2

[solid vale]

do now the denominator is a^2

[grave vortex]

yes

[solid vale]

so this is what our problem looks like now

[grave vortex]

yea

[solid vale]

what should we do now to ensure there is a positive exponent

move the a^2 up or… move a^0.5 down?

[grave vortex]

0.5 down

[solid vale]

correct

[grave vortex]

1/a3/2

[solid vale]

yes

[grave vortex]

ohhh

omg

thank u sm

🤲🤲🙏🙏🙏🤲🤲

[solid vale]

np :)

[marsh citrus]

@grave vortex Has your question been resolved?

[grave vortex]

.close

[marsh citrus]

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[jagged prairie]

hi i still havent figured this out, this time im asking someone to simplify it rather than to walk me through it, could we reword it? its been some hours and im still strugglin

[jagged prairie]

we thought it mightve been (-5,4,6) for the range, but the ordered pairs part confuses me

[dusky wing]

You are correct, the range is {-5, 4, 6}. When it is asked to write the function as ordered pairs, you write it as (x, f(x))

[brittle coral]

Ordered pair is basically (x,y)

[dusky wing]

So it'll look like {(-1, -5), (2, 4), (?, ?)}

[jagged prairie]

oh wait, is it meant to include more than what we have or?

wait

wouldnt it be 4,6 next

since those arw the next numbers?

[dusky wing]

Yes that is correct

[jagged prairie]

alright thank you! this one was honestly so confusing

.close

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[timber flax]

Ok so really quick, i have this task right here, i understand how it's supposed to be done but what i don't understand is how can i pick an arbitrary point from this straight line equation L
in the answer for this one(as shown in the second picture) he substituted the y in the equation with 9 and i've no clue why specifically 9 and not any other random number

[timber flax]

i tried it with a different number(in particular 0) and the final answer still came out wrong according to the site

ok nvm i figured it out im dumb

kekw

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[rotund yacht]

$$
sin
165
∘

√
A
(
√
B
−
1
)
4
.$$

[elfin berry]

ology

[rotund yacht]

$$sin(45∘)cos(120∘) + sin(120∘)cos(45∘)$$

[elfin berry]

ology

[main idol]

pain

#latex-testing

[rotund yacht]

$$rad2/2 -1/2 + rad3/2 rad2/2$$

[elfin berry]

ology

[rotund yacht]

i get

$$-rad2 rad6/ 4$$

[elfin berry]

ology

[rotund yacht]

and how do they get 3

[still temple]

What is this notation...

[rotund yacht]

i got the 2 right

but how do they get a 3

[still temple]

$\sin(45\degree)\cos(120\degree) + \sin(120\degree)\cos(45\degree)$

[elfin berry]

♡A(lex)♡

[rotund yacht]

yup

[still temple]

Oh weren't you doing this a few hours ago or something

[rotund yacht]

yesterday

but i figure most of it out

i just want to see how someone else does it

[still temple]

I mean not much different

You can also say like
$\sin(30\degree)\cos(135\degree) +\sin(135\degree) \cos(30\degree)$

[elfin berry]

♡A(lex)♡

[still temple]

Does it matter? no

[rotund yacht]

yes

bcuz i got a 6

and the answe was 3

[still temple]

Yeah factor it

$\f{-\sqrt{2}+\sqrt{6}}{4} = \f{-\sqrt{2}+\sqrt{3}\cdot\sqrt{2}}{4} = \f{\sqrt{2}(\sqrt{3}-1)}{4}$

[elfin berry]

♡A(lex)♡

[rotund yacht]

ty

cornflakes

.close

[marsh citrus]

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[restive night]

How many five-element subsets of {1,2,3,4…12} are there that do not contain the pair of elements 1 and 2

I know that there are C5(12) = 792 five-element subsets but how do I find out how many five-element subsets are there that do not contain 1 and 2?

[proper zodiac]

Perhaps compute how many do

[restive night]

And how do I do that?

[marsh citrus]

@restive night Has your question been resolved?

[marsh citrus]

@restive night Has your question been resolved?

[marsh citrus]

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[marsh citrus]

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[smoky sail]

given ABCD is a square, AD // EF and AB // GH
if CHIF is twice of AEIG (area), find angle FAH

[smoky sail]

cannot find a way to somehow utilize area values in calculating angles

[still temple]

No idea - I'm just thinking out aloud here:
Let the square be 1 x 1
Let AG = x, and AE = y

So we have 2xy = (1-x)(1-y)

[smoky sail]

didnt get anywhere with that

[still temple]

FH^2 = (1-x)^2 + (1-y)^2

AF^2 = 1^2 + y^2

AH^2 = 1^2 + x^2

Using these, you should be able to get the angle using trigonometric functions, right?
Doesn't look nice at all, but some trig bashing should work, however ugly

[smoky sail]

dont know how id do that though

probably isnt intended to brute force with law of cos and a 4th degree poly

nevermind i got it

[still temple]

How?

[smoky sail]

im incredibly blind

ok so from earlier

2xy = (1-x)(1-y)

we get x+y = 1-xy

and from pytha we get fh^2 = (1-x)^2+(1-y)^2 = 1-2x+x^2+1-2y+y^2

= x^2+y^2+2-2(x+y)

subbing in x+y with xy-1 results in FH = (x+y)^2

[still temple]

2xy = 1 - x - y + xy
xy -1 = - x - y
You've got a sign wrong

[smoky sail]

oh yeah

[still temple]

Oh cool, ok

[smoky sail]

and then once you get FH = x+y you can translate triangle ABH by rotating it 90 degrees clockwise around point A

call translated point H H'

we get that AH' = AH

resulting in 2 similiar triangles (AFH' and AHF)

angle H'AF = FAH so FAH = 90/2 = 45

[still temple]

I lost you in the last few steps, but cool if you've got it 👍

[smoky sail]

ty

mistake ignore AF it isnt actually equal to AH or AH'
v

^ mistake ignore AF it isnt actually equal to AH' or AH

.close

[marsh citrus]

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[still temple]

Yeah, that was the step which didn't make sense to me at all..

[still temple]

.close

[marsh citrus]

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[smoky sail]

ignore AF it isnt actually equal to AH it was an error
and AHB being beta lmao
its similar by side-side-side

[still temple]

ok

Ah your edited msg makes sense

That's a very cute solution 🙂 Nice

.close

[marsh citrus]

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[celest silo]

Hey.

[celest silo]

Determine whether the following series are blocked from above and below:

Need help with those, thanks!

[glass silo]

Bounded from above and below?

[glass silo]

Think about whether sin and cos are bounded between something to work out bounds (which can be a little bit wide if you'd like)

[celest silo]

Yes, bounded sorry

I study it in a different language

We call it blocked haha

[glass silo]

Looks convergent to me

[glass silo]

Hahah fair enough, makes sense anyway

As long as we get you

[celest silo]

[glass silo]

do my hints help much btw?

[celest silo]

i'm not quite sure lol

[glass silo]

You know what sin and cos have to be between right?

[ionic lava]

sin(n) and cos(n) are always between ||1 and -1||

[celest silo]

ye

[glass silo]

Can you use those to form a "wide" bound for sin(n) - cos(n)?

Spoiled

[marsh citrus]

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[marsh citrus]

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[marsh citrus]

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[wise pine]

hi

[wise pine]

i need some help solving this question

I dont know where to begin

[late geode]

i suppose based on the wording that they want you to differentiate

(and apply the relevant rules like quotient and chain when doing so)

[wise pine]

wow

this is gonna be a first for me

[marsh citrus]

@wise pine Has your question been resolved?

[wise pine]

am not sure i follow,

do you mean i use both rules?

or just one of them

[late geode]

whatever rules are relevant in the process

[wise pine]

so i can use more than one rule 🙂

I didnt know that

[marsh citrus]

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[marsh citrus]

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[quaint jungle]

The question asks to write this in a + bi from

[quaint jungle]

how should i do that?

its a cubic, and im thinking of using the factor theorem

any ideas?

[whole linden]

yep

[quaint jungle]

ive got z = 1 as a solution

then using the synthetic division i've got myself z^2 + z + 2

is this correct?

[whole linden]

yea proceed with solving the quadratic

[quaint jungle]

i've now got myself
(-1 +- sqrt(7) * i) / 2

[whole linden]

yep

and don't forget the 1

[quaint jungle]

from the solution?

how do i apply it here?

[whole linden]

the question asks you to solve for z and express as a + bi, I assume?

[quaint jungle]

yes

[whole linden]

you've got your 3 solutions, right?

[quaint jungle]

is this considered 2 solutions?