help-0

[exotic canopy]

yes

$P(A | B) = \frac{P(A\cap B)}{P(B)} = \frac{P(A)\cdot P(B)}{P(B)} = P(A)$

[ocean seal]

artemetra

[exotic canopy]

like that

the P(B) just cancels out

[strange fractal]

what can i do

im missing 2 values

[exotic canopy]

you also have P(A|B) = 0.4

nvm

[strange fractal]

😔

im finished my test is tomorrow

[exotic canopy]

oh and P(AnB) is P(A)P(B)

and P(A) = 0.4

so you'll have an equation just in terms of P(B)

[strange fractal]

wat

isnt that what i tried to do

in the first one

[exotic canopy]

yes but you sub that into the last line that you have

[strange fractal]

ohh wait

[exotic canopy]

you get $0.64=P(B) + 0.4 - 0.4P(B)$

[ocean seal]

artemetra

[exotic canopy]

1 variable

[strange fractal]

cann i do this

wait............

this is REALLY TESTING ME

[exotic canopy]

for get P(AnB)

it equals to 0.4P(B)

[strange fractal]

oh

ok thank u

that very helped

can u pls help me divide decimals tho..

[lone heart]

@strange fractal Has your question been resolved?

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[safe shuttle]

.reopen

How do I find F1 and F2 when all forces equal to 0

[hard patio]

Resolution of vectors

[safe shuttle]

Can you go further into detail about that

[echo socket]

Start by noticing thatthe sum of F2 and F3 should have the direction opposite to F1, this tells you something about the magnitude of F2

If that's unclear, you may consider drawing F2 + F3 using triangle rule and then noticing that the acute angles in the right triangle can be calculated

[safe shuttle]

But I don't know what F2 is, how do I do the triangle rule without knowing it

[pale lance]

Would you like some help?

[pale lance]

Try to split up your vectors firstly

Let me know if you need help doing that

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[safe shuttle]

I got F3 + F2 = 2F1

[pale lance]

Oh really?

Walk me through it

[pale lance]

I can go over this with you some other time, I have to head out soon.

[lone heart]

@safe shuttle Has your question been resolved?

[safe shuttle]

Since F2 + F3 creates a line double the length of F1 I came to the conclusion that F2 + F3 = -2F1

[lone heart]

@safe shuttle Has your question been resolved?

[safe shuttle]

Idk I give up too difficult

[turbid narwhal]

brooo

my qyestion

what can I use

[lone heart]

@safe shuttle Has your question been resolved?

[lone heart]

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[cinder sundial]

I’m watching a video made by 3B1B and suddenly I’m asked to solve some geometric problem by the creator

[cinder sundial]

It asks to solve the shadow area and express the final answer by R, theta, and dtheta

Then I got these purple underlined as my answer. However, I’m unable to know whether they are true or not, as the creator didn’t put the correct answer in his video.

Can someone check them out for me?

<@&286206848099549185>

Can some Geometrics genius solve this shit out real quick

[daring rover]

Just subtract two circle areas, one with radius Rsinθ and one with radius Rsin(θ+dθ)

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@cinder sundial Has your question been resolved?

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[round comet]

i get 1 as a value of x but idk where 3 came from in the mark scheme

i think i know where -1 comes from too but not 3, would anyone be able to explain how to get that value please?

[echo socket]

Try factoring the polynomial, what do you get?

[round comet]

the only thing i got it is -(x-1)^3(4x+1)

[echo socket]

Doesn't look right, can you show your work?

[round comet]

sorry i meant +4

sure ill send haha but i dont think its right either

[echo socket]

Still not it though

[round comet]

should i expand fully and factorise is what you mean?

and then*

its only 2 marks

[echo socket]

No, don't expand

You can factor without that

[round comet]

which part

oh

lemme try again

i got (x-1)((x-1)^2-4))

[echo socket]

Right, and 4 = 2^2, you may apply difference of squares formula

[round comet]

ahh got it thank you so much!!

.close

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[barren marsh]

Could you help me with q5?

This was my test I did and I am learning this for my upcoming test

<@&286206848099549185>

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[alpine sable]

If a/b+b/c+c/d+d/a=6,a/c+b/d+c/a+d/b=8 then a/b+c/d is

[alpine sable]

someone pls

[lone heart]

@alpine sable Has your question been resolved?

[lavish cave]

!status

[lone heart]

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

[alpine sable]

I asked gpt it is so bad at maths

[lavish cave]

a^2 cd + b^2 ad + c^2 ab + d^2 bc = 6abcd
a^2 db + b^2 ac + c^2 bd + d^2 ac = 8abcd

By multiplying both sides by abcd

https://math.stackexchange.com/questions/3911548/sum-of-all-possible-valuse-of-fracab-fraccd?noredirect=1

Ah this question is the same but the numbers 6 and 8 are just different

[alpine sable]

Yess

[lavish cave]

https://approach0.xyz

[alpine sable]

I will try to understand from there

[lavish cave]

If you want to search competition problems I recommend this website

No worries

[alpine sable]

Ok

[lavish cave]

Knew it would be easier to just search it

nw

[alpine sable]

Thanks buddy

[alpine sable]

.close

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[shy stream]

determine the equation of the circle that touches both coordinate axes and passes through A(-9,-2)

[shy stream]

I don't know how to solve this

[cinder sundial]

Draw it

So you can have a grasp on the graph

Let me try it

[old brook]

the fact that it touches the coordinate axes should be a big help

think of how the centre’s coordinates could relate to the radius of the circle

[shy stream]

but how do I find out the center or the radius

[old brook]

one sec

ok back

hi

so

imma try solving it

and get back to u

[shy stream]

okayy

thank youu

[old brook]

ok i am back

so

basically

[old brook]

this thing

ill show u one sec

sorry for the poor circle

but u get the idea hopefully

[shy stream]

yeah yeah

[old brook]

since A is in the third quadrant

[hot hatch]

U are searching for equation ryt

[old brook]

it would make sense for the centre to lie in the third quad too

so the centre

is (-r,-r)

now you know the centre

[old brook]

and the radius = r

so form the equation

[hot hatch]

This is wrong

[cinder sundial]

You can assume (r,s)= point A or B

[hot hatch]

Passing through (-9,-2)

[cinder sundial]

Then you put the other point to find the radius and it should be done

[old brook]

hm

so you couldnt write the circle as

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

?

then just sub A's coordinates

and get r

then youre done

[old brook]

^is this right?

the steps ive mentioned

[hot hatch]

Hmm, yeah

[old brook]

then where was i wrong?

[hot hatch]

It's correct

[hot hatch]

U took -9,-2 as centre

[old brook]

i didnt?

[hot hatch]

That was wrong

Oh wait

[old brook]

ive clearly put a dot and named it A

[hot hatch]

My bad

[old brook]

yeah

[hot hatch]

Sry abt that

[old brook]

np

[shy stream]

pkay so I got this

[old brook]

@shy stream do these steps make sense?

[shy stream]

but like

i dont get

what after that

[old brook]

right

so x and y

you know that

A passes through this circle

so it must satisfy this eqn

so plug in the x and y coordinates of A

into that equation

that way you could find r

[shy stream]

okay okay,

I think I got it

[old brook]

let me know if it works for u

[shy stream]

Okay I understood it and got the right answer

Can I just ask another question?

Why does this task have two answers?

[old brook]

because

when you solve for the radius

like when u sub the valuesof A

you get a quadratic

for r

and using the quadratic formula

youd get r = 5

or r =17

so our circle could have two different answers

[shy stream]

oo

okayyy

thank you soo much

.close

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[tired trout]

does anyone know how to calculate this with a calculator

[keen pasture]

Apply log rules

[tired trout]

i dont remember of the log rules haha >.<

[keen pasture]

ln(a^b) = ln(a)*b

[shrewd prism]

What do you know about logarithmic functions

[tired trout]

you use logaritmic if the exponent is unkown?

i don't know much about logaritmic functions >.<

[keen pasture]

Can you apply this one?

[tired trout]

hmm, i'll try

[ancient temple]

The natural logarithm is the inverse function of e^x.

[tired trout]

if we have to use log, why did we use ln for e?

i heard ln always comes with e

[gray isle]

ln is log with base e

its being used since the base of your exponent is e

allowing you to apply the inverse relation

[tired trout]

thank you guys:)

.close

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[sleek topaz]

Hmm I'm not sure if I've made an error or Idk how to proceed

[sleek topaz]

.close

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[limpid turret]

did you receive help?

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[ocean seal]

y0shi

[subtle light]

that’s implying that they are equal

while they are not

you’re just using 1/n^2 for comparison

you should also write out what comparison test you used

no they’re not

you’re saying that a sum that converges to a number or diverges to infinity is EQUAL to 1/n^2

a finite number or infinity doesn’t equal a variable

it isn’t up there

you have to say that

cuz the summation doesnt include everything after the equal sign

also you should be comparing it to the sum of 1/n^2

[modern sedge]

essentially equal doesnt justify the use of equal sign

[subtle light]

not saying that it is equal to it

[modern sedge]

wait this isnt sufficient

it actually is

im stupid

$\sum_{n=1}^{\infty}\frac{1}{n^{2}+4}\le\sum_{n=1}^{\infty}\frac{1}{n^{2}}$

[ocean seal]

MethIsAlwaysRight

[modern sedge]

yeah, this is how i'd write it

the series on right converges

[subtle light]

yeah

and this is by the direct comparison test

[modern sedge]

oh my god

[subtle light]

you have to state this

oh my

don’t ever write infinity

in an expression like that

you can only approach infinity

no they definitely do care

[modern sedge]

if its physics or engineering, then it's fine

if its math then its ugly

and incorrect

[subtle light]

is it graded by a teacher?

or just for practice

okay

but still i wouldn’t recommend developing the habit of writing that

[modern sedge]

^

[subtle light]

so you can choose to do either the limit comparison or direct comparison

[modern sedge]

1/(n^2+4) < 1/n^2

for each n

same for their absolute values

0 <= 1/(n^2+4) <= 1/n^2

hence if sum of 1/n^2 converges, then sum of 1/(n^2+4) converges

so whats left is proving that sum of 1/n^2 converges

which is done on the next line

[modern sedge]

This is called direct comparison test btw

[subtle light]

also works

doing the limit comparison doesn’t require you to write out an inequality like we did up there

you just need to prove that the limit equals a finite positive number

it doesn’t matter which one you choose as a_n or b_n

it’ll still work

so we got the limit to be 1

which is a finite positive number

[subtle light]

so the above conditions will be met

yep

i don’t believe you’ll deal with imaginary numbers in infinite series

i’m not quite sure on that bit

can you post it?

yeah seems right to me

yep

either by p-series or integral test

[ocean seal]

y0shi

[subtle light]

basically just replace infinity with a dummy variable

and just evaluate the limit without ever putting in infinity as the work

[ocean seal]

y0shi

[subtle light]

plug in b instead of infinity when using the fundamental theorem of calculus

and just simply say that the limit goes to infinity

for limits, no work really needs to be shown

you’ll usually get away with just saying that the limit equals a certain value

yeah since the integral diverges

so we would have to compare that

|sin(n)| cannot exceed 1

since we know sine oscillates between -1 and 1 but now it’s absolute valued

so it can only go between 0 and 1

okay so we can just use the direct comparison here

mm we can’t really use the divergence test

you took the limit to infinity so i suppose you used that

you kinda have it up there

[ocean seal]

y0shi

[subtle light]

yep

mm i would say direct comparison is easier

mm not exactly

did you do the integral test or

yep

exactly

it’s more so i haven’t really seen much of that

well let’s list out a few terms

if we had n=1

we would just have |i|=1

as for n=2, |-1|=1

n=3, |-i|=1

so it’s basically always 1

all of the absolute values evaluate to 1 regardless

yep

it should just be |n^3-1| btw

the original question was like that

oh

damn i see

so we can just convert using pythagorean theorem

setting the real component as n^3

and imaginary as -1

yeah

resend the text

[ocean seal]

snow

[subtle light]

oh i meant like Re(n^3-i) and Im(n^3-i) mb

[ocean seal]

y0shi

[subtle light]

yep

so now just use one of the comparison tests

either would work

yep

[ocean seal]

snow

[subtle light]

exactly

and sqrt(n^6) is just n^3

yep looks good

and just state that the original series is absolutely convergent

yep

is that all it asked for?

cuz usually when something doesn’t converge absolutely

we might need to find whether it is conditional convergent or divergent

oh

then yeah i think your answer is fine

ohh i see

alright

yw!

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[gray heart]

Why is 2 multiplied by the first derivative in the second derivative

[fervent ferry]

i think it's because it's implicit differentiation of y

it's taking the derivative of the original equation

[gray heart]

So i use implicit differentiation whenever x and y are on the same side?

[gray heart]

But then why is dy/dx multiplied by 2 instead of 8?

[fervent ferry]

i don't feel i'm the right person to ask this

[fervent ferry]

cause the original equation is 8x-2y

if you take the derivative with respect to x you get
8 - 2y'

y is secretly y(x), so you write ok i'll take the derivative of that but i don't know what is exactly the function y(x), so i'll just write y'

and then they realize, oh y' is the original function. so let's substitute back the original function in there.

I've never done this types of exercises, so i cannot help on why they are doing that, i'm just trying to unravel what they wrote in there

[topaz grove]

ya, that explanation makes sense

[gray heart]

Ye i can see that now, though i should do more implicit differentiation

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[ocean seal]

Remanlab

[north perch]

yeah correct

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[sharp gust]

is there a formula for finding the area of a shape like this?

[wraith stratus]

you can break it up into smaller shapes to find it yourself

but yes there is

[olive yarrow]

easiest way to do it is to split it up into a bunch of identical isocleses triangles that have their tips at the center

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[steep rover]

kinda confused how to do this

ik i have to take the derivatives of the respective equations

so x'1(t) = x1'''(t)

and x2(t) i figured out is -x1(t)

[lime bobcat]

You have to add incognitas for each derivative that is not first order

[steep rover]

im not familiar with this term, could you explain what incognitas means?

[lime bobcat]

unknown functions

[steep rover]

oh alright

so i can just name x3'(t) as equal to -x3(t)?

[lime bobcat]

I think so

x2 and x3 are not really challenging

x1 tho

[steep rover]

does this look right?

[lime bobcat]

Well

I think it's correct

That's ok I think it works

[steep rover]

ok cool thanks

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[last dagger]

I need to check my answer a little confused on it

[last dagger]

It’s for finance

[vapid shuttle]

How did you arrive at your answer

[last dagger]

I divided the profit by the cost of the original investment

Then multiplied it by 100

Oh wait

No mb I was thinking of another questions

I was thinking of dividing the profit by the 100k

So 80k / 100k

I think I’m right about it but again not to sure

I was assuming it’s asking the return for one of them and not including his dad

Since it’s only talking about his own return investment

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[midnight blade]

Hi, can someone please explain f

[lone heart]

@midnight blade Has your question been resolved?

[midnight blade]

<@&286206848099549185>

like am I just overthinking this

[ocean hawk]

you're given the info in the paragraph at the top

[balmy spear]

I do not got why help

[midnight blade]

.close

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[reef pewter]

Can anyone please help me with my math? It is probability and I am very confused. My teacher did not explain it well. Could anyone Help Me please?

[proven leaf]

how many months have 30 days?

[reef pewter]

I believe four

April june september and november

[proven leaf]

okay and how many months are before August?

[reef pewter]

umm

7 months

January, February, March, April, May, June, July,

[livid sage]

“no later than August” means that August would be included in the sample space

[reef pewter]

oh ok

[livid sage]

how many of these months are in the sample space?

[reef pewter]

So 8 months

And there are two months with thirty days no later than august

So the probability would be 1/4 simplfied right?

[livid sage]

very good yes

[reef pewter]

YES

thank you so much

I just have one more question

This one has me stumped

this is the last one though

This is just really confusing because there are three time frame things

Could someone please help me?

[pseudo ice]

.close

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[random storm]

why was this integral split?

[random storm]

please help i have a final tomorrow 😦

[daring rover]

Because csc(t) has a discontinuity at t=0

[random storm]

is there a definite way to tell when to split an integral? or do I just have to examine case by case and see the function?

[daring rover]

You have to split if the function isnt defined at a point inside the bounds of integration

[random storm]

can you elaborate, I dont get what you are saying to be honest

[daring rover]

You cant integrate a function from a to b if it doesnt exist in a point between a and b

[random storm]

what does it mean for a function to exist or be define at a point inside the bounds?

[daring rover]

Does csc(0) exist

[random storm]

no

[daring rover]

Thats what it means

It doesnt exist so how do you integrate over 0

[twilit veldt]

you dont

[daring rover]

You dont

You split the integral

[random storm]

okay so since the bounds we have 1/x and sqrt(x) can hold any x value including x, then we must split since our function dne at that point

is my understanding correct here?

including 0*

@daring rover

[twilit veldt]

wait ill be honest you dont need to split the integral

but its a more simple

and easier to understand

[random storm]

oh so why was it done if it doesnt need to be split

whats the alternative way?

[twilit veldt]

i mean

is this a model solution?

or ur working

[random storm]

my professor wrote it

so i guess so

[twilit veldt]

yeah would u prefer steps

or just the answer

[random storm]

wdym

[twilit veldt]

like he broke it up

to make it simplier

[random storm]

how would it be more complicated hadnt he split it up?

[twilit veldt]

have you tried doing the integration without spliting it

[random storm]

no

[twilit veldt]

see if there is a differnce

thatll answer ur question

[random storm]

can you just tell me if you have the time pls, i have my final tmrw and im rlly tight on time

[twilit veldt]

i dont know

but i couldnt see why not

[random storm]

alright thank you

.close

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[tiny iron]

Im having trouble with partial fractions the ones that are like (x-1)² also dont know when to use things like Cx+D and after i need to get the values i can't do that either.
I got the problem which i could not even start
(2x-1)/(9x²-x)

[lone heart]

@tiny iron Has your question been resolved?

[tiny iron]

<@&286206848099549185>

[lapis jungle]

I aint gonna hold u

Im bricked rn

Js letting yk

[lapis jungle]

Photo ref might help

[tiny iron]

Also what is bricked? Like high?

[hot hatch]

Hey

It's A/X - B/9x-1

Now take LCM and find A and B

[hot hatch]

As for (x-1)^2 you should split it as $ A/(x-1) + B/(x-1)^2 $

[tiny iron]

Why is it -B here?

[hot hatch]

Mb it's +

But it's not important

If u get 3 for +, you'll get -3 if you take -

@tiny iron

[tiny iron]

Does the thing up the division matter?

i mean this

[hot hatch]

? Wdym

P and Q are given variabls

[tiny iron]

If i have like a 1 up there

i dont have to use partial fractions?

[hot hatch]

Suppose if the numerator is 17x+ 14 then when taking LCM and finding a and b

You should get numerator 17x+14

[hot hatch]

See the right hand side

A and B

Now take LCM

[tiny iron]

i dont know whats LCM

[hot hatch]

You'll get numerator in terms of A and B

[hot hatch]

A/X +B/9x-1 , you get till this?

[tiny iron]

yeah

i got rn

2x-1=A(9x-1)+Bx

[hot hatch]

Yep

[tiny iron]

so i just solve rn right?

[hot hatch]

Now take X coefficient as 2

[hot hatch]

Yeah

Just solve for a and b

And u can. Integrate easily

[tiny iron]

i got

A=1 B=-7

how can i tell if this is right?

[hot hatch]

Now try taking LCM

With 1/X -7/9x-1

If you get numerator same

It's correct

[tiny iron]

ah so from there i gotta get 2x-1?

[hot hatch]

Yep

You'll get it if you didn't mess up finding a and b

[tiny iron]

Yeah it is!

So the integral is Ln |x| - 7/9 Ln |9x-1| + C?

i just checked it, it is ty very much!

If u dont mind i still have doubts with the Ax+B problems
i cant find an integral like that tho only the (x-1) squared

[hot hatch]

Which one

[hot hatch]

.

Also ping me

[tiny iron]

@hot hatch i found this one

should i use C or Cx+D for this one?

i just dont get when to use which

oh wait this is Cx+D

Is there an easier way to solve this without having to use Gauss Jordan?

@hot hatch

[lone heart]

@tiny iron Has your question been resolved?

[hot hatch]

Hwy

[hot hatch]

CX+D

[hot hatch]

U mean partial fraction? I don't there is a easier method

[tiny iron]

Yeah like to solve this

How do i solve it w/o blowing my mind xd

How would u solve it?

[tiny iron]

@hot hatch

[hot hatch]

The way you do only

It takes a bit of time

But substitution techniques doesn't work here

Even if they do, it'll take even more time

[tiny iron]

i c alr

[tiny iron]

i got it @hot hatch ty very much

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[alpine sable]

i

[lone heart]

Please don't occupy multiple help channels.

[raw jetty]

close this

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[mint flare]

how do I find the exact value of Tan 210

[mint flare]

is it - (tan 30)

[alpine sable]

$\tan(\pi+\theta)=\tan(\theta)$

[harsh lion]

it is tan 30 I guess

[ocean seal]

yajat

[mint flare]

oh yeah 210 is in third quadrant and tan is positive in third quadrant

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[unreal cipher]

can someone help me with g) please

[subtle birch]

can you individually calculate y^2 and x^3?

[unreal cipher]

y^2 shoudl be 54

x^3 is 24root3 from my calculations

but i maybe wrong

[subtle birch]

yes, that's correct

now can you divide them?

[unreal cipher]

so then i get 9/4root3

[subtle birch]

yes

you can simplify it further

[unreal cipher]

i dont think so

[subtle birch]

yes you can

9=3*3

and 3 can be written as sqrt(3)*sqrt(3)

in general, we do not leave surds in the denominator

[unreal cipher]

OHHH

[subtle birch]

and instead change it to numerator

[unreal cipher]

so

ohh and then

raitionalize?

[subtle birch]

yep

that's rationaliszation only

[unreal cipher]

wait im a bit confused

what does 9 simplify to?

if 9 is 3x3

and 3 is sqrt(3)*sqrt(3)

would that make the numerator 4root3?

@subtle birch

[subtle birch]

$\frac{9}{4\sqrt{3}}=\frac{3\cdot3}{4\sqrt{3}}=\frac{3\sqrt{3}\sqrt{3}}{4\sqrt{3}}=\frac{3\sqrt{3}}{4}$

[ocean seal]

B-eard

[unreal cipher]

ohhh in understand now

ty

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[velvet orbit]

I need help evaluating these integrals real quick

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[unreal cipher]

can someone help me with this

2nd numerator is a 5 btw

nvm i solved it

.close

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[lethal anchor]

The volume of a cylindrical can is 54π cubic units. Get the least amount of metal used.

[lethal anchor]

where should I start and what are the steps.

[alpine sable]

can you send the original question?

as it it is shown

[lethal anchor]

I translated it . and it is the full question nothing more given.

[alpine sable]

you can send it to me in Russian

I'm Russian too

translation often omit details

[lethal anchor]

oh Im not russian my name is slavic

[alpine sable]

Oh okay

[slender gull]

With the given context, I think you're trying to minimise the surface area of the cylinder. And the cylinder will be hollow or something. But that's just how it looks the way you presented the problem.

[lethal anchor]

Im currently studying Optimization and I have the answer

But it is not understandable

[slender gull]

Can you minimise the surface area

[lethal anchor]

well in the answer it said (The surface of the metal used in the can is equal to the diameter of the entire cylinder)

so it first find height of the can (piR^2h=54pi so h= 54/R^2 ) then S(R)=2piR^2 + 2piR . (54/R^2) ...

[earnest rapids]

S(R) = 2piR^2 + 2piR(54/R^2)

unless the cylinder is open on top

[lethal anchor]

yes I missed a 2

[earnest rapids]

so u just have to minimise S(R) for R>0 since we are talking about a radius

[lethal anchor]

well put it that way yes but my question wasn't about what is the answer it's about how we get there

[earnest rapids]

S(R) = 2piR^2 + 108piR^(-1)

to find the minimum you can find the turning points

by setting the derivative to zero

and checking whether it is a min or max with the second derivative or testing values

[lethal anchor]

yes I miss this step. and the answer would be 54π . tnx

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[little swan]

need help to solve for 'a'

[earnest rapids]

parallel means that they have the same gradient

so equate the gradients of both lines

[little swan]

yes and different y-int

[earnest rapids]

ye

[little swan]

ok

x(2a-3)= 3x-4

[earnest rapids]

no

what is the gradient of y=(2a-3)x+1

[little swan]

-3

not too sure

[earnest rapids]

the gradient is the entire coefficient of x

[little swan]

y=2ax-3x+1

[earnest rapids]

u know y = mx + b?

[little swan]

yes ofc I do

[earnest rapids]

so m is the gradient

[little swan]

the only coefficent of x is '-3'

[earnest rapids]

in y=(2a-3)x+1
m=2a-3
b=1

[little swan]

wait

OH

right

gradient for second line is 3

[earnest rapids]

ye

now equate the gradients and solve for a

[little swan]

ohhh

a=3

[earnest rapids]

ye

[little swan]

.close

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[alpine sable]

Uh can someone help with critical numbers

[alpine sable]

I think this is right but cengage is saying im wrong?

[earnest rapids]

it should be 6(x-2)(x+1)

[alpine sable]

Bruh

Salam brother

And thank you

🙏🏾

Wait but why does it have to be that way

[earnest rapids]

waalaikum assalam

try expanding your one

[alpine sable]

Oh im dumbbb

[earnest rapids]

and you will see it is different

[alpine sable]

😭

Bruh the 1 is supposed to be negative

Im cooked bruh

[earnest rapids]

ye

[alpine sable]

Thanks

[earnest rapids]

np

[alpine sable]

.close

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[velvet copper]

hi

[velvet copper]

how do u do this

ik this is prob really easy but my math teacher told me that this is gonna be in my assesment (angle stuff in general) even tho he never taught me

[whole nexus]

whats the total angle in a quadrilateral

[velvet copper]

Erm

Idk

[whole nexus]

a quadrilaterals angles always add up to 360

[velvet copper]

ohh

so basically like

a shape with 4 sides?

[whole nexus]

yeah

[whole nexus]

so then you add the three known angles and subtract the sum from 360

[velvet copper]

ok

i got 220

but my friend somehow got 270

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[alpine sable]

haw many objects in this set - {Φ}?

[fleet crown]

What do you think?

[alpine sable]

hmm 1?

[fleet crown]

What's your reasoning behind that?

[alpine sable]

that if it's void set phi will not be written behind curly brackets

but here phi is written behind brackets so it is taken as an oject

that's ma' thinking

[fleet crown]

Good, this is a set that contains 1 element which happens to be an empty set

[alpine sable]

thanks

[fleet crown]

Here's some visual

[alpine sable]

but in book its written 1

[fleet crown]

hm?

[alpine sable]

Φ is an variable I think if its in the bracket

[fleet crown]

...hmm??

Maybe you missunderstood me...

let me rephrase

Good, this is a set that contains 1 element and that 1 element happens to be an empty set

[alpine sable]

maybe something is wrong with ma' english

[fleet crown]

English is confusing af

[alpine sable]

[alpine sable]

what's ur language

[fleet crown]

german

even more confusing

[wheat isle]

aki are you chartbit's doppelganger

[alpine sable]

destuch

🤓

I use germany as location for my vpn

[fleet crown]

no, I wish I was though

[alpine sable]

I'll think about it

[fleet crown]

Ugh, so let's simplify it

A = { B }

B = Φ

[alpine sable]

there is 1 object in the set and it's null

[fleet crown]

A has 1 element

B has no element

[alpine sable]

understood🗿

[alpine sable]

ok mam

see ya' if I have another problem

bye

aki sensei bye

[tardy stag]

you have a grocery bag containing an empty Ziploc bag

[fleet crown]

But doesn't the bag have air in it?

[tardy stag]

no we're on the moon

[alpine sable]

moon dust

[lone heart]

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[frail sand]

hi can you help me with this question?

[lone heart]

@frail sand Has your question been resolved?

[nimble fern]

what have you tried?

[frail sand]

i thought f(x) and g(x) were linear functions

but i coulndt find the answer

[nimble fern]

i see, well, the question didn't state that they are linear functions

so you might to have start by placing some values of the functions

e.g.
Given
f(x-2)=g(x+5) ---(1)
f o g (6)= g o f (4) ---(2)
g(10)=10 ---(3)
f(0)=2 ---(4)

From (1) we can see that
f(x)=g(x+7)

So let's make a list on what we need (note that we have to find f(2) )
f(0)=g(7)=2
f(3)=g(10)=10
f(g(6))=g(f(4))

so we can take a guess that g(6)=f(4)+7

[nimble fern]

you can start from here @frail sand

[frail sand]

yeah i found that but i dont know what to do next

[nimble fern]

reading

[nimble fern]

from this situation, I was wondering why you've got the idea that f and g are linear function

like if they really are linear functions, then this could be solve?

don't mind me typing, I'm just checking the numbers

from what i haven been thinking, i think we can't conclude what f(2) is without any further information

that's why i was asking if you know if they are linear functions or not 🤔

[frail sand]

probably they are not linear functions because then they don't satisfy the conditions, maybe there is missing information in the question

[nimble fern]

if they are linear, then the question can be solved.
note that we are just "guessing" that g(6)=f(4)+7, but not necessarily is

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[vernal prawn]

Multiply and divide by cos^2(x), take one of the cos(x) inside the square root, and then substiture cos(x) = u

[agile sundial]

is that how they got this?

[vernal prawn]

oh

that is quite smart

[agile sundial]

oh wait i just realised

[vernal prawn]

they multiplied the top and bottom with sqrt(sec x - 1)

and used the identity

[agile sundial]

ty

resolved

.close

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[stone barn]

Yo

[stone barn]

If two letters are randomly selected from AAB will the combinations made be 3 or 2?

[mossy swift]

why don't you write them all out

[stone barn]

It’s AB and AA so it’s 2

Coz BA is same as AB

[mossy swift]

in your context (yes)

[stone barn]

but like how do I account for repetitions when putting it into the calculator

like i gotta input 3C2

but instead of 3 distinct letters I got 2

[mossy swift]

yeah because the 3C2 counts for

,, A_1 A_2 B

[ocean seal]

nyxie9151

[mossy swift]

notice how we treat the A's as distinct

[stone barn]

I see but what if I don’t have it as distinct

[mossy swift]

so technically the 3C2 gives you: {A_1, A_2}, {A_1, B}, and {A_2, B}

[stone barn]

Is there a way to modify my calculation to account for repetitive objects

Like I have A_0, A_0, B

Or is what I’m asking dumb

[mossy swift]

well i mean generally you'd just do casework on it

{A,B} is counted twice because {A_1, B} and {A_2, B} are the same since A's aren't distinct

so in your calculation it's fair to write that?

3C2 gives you all two element subsets such that A's are distinct

you subtract the "1" because you want that A's aren't distinct

[stone barn]

That question above is simply an example I made for a bigger problem

Suppose 5 letters are randomly selected from the word ACTIVATED

I gotta find the total number of selections

So is it just 9C5?

Which is 126

[agile sundial]

no, a is repeated

and t

[stone barn]

And T too

But then how do I find the total number of selections then

[agile sundial]

if you have an element that is reapeted r times you have to divide by r!

[agile sundial]

so here it should be this/(2!x2!)

cuz a and t reapeated 2x

[stone barn]

Isn’t that for permutations with repetition tho

[agile sundial]

yeah the a and t are being repeated

cuz aca and aca are the same word

but you count it 2x

cuz you switched the a

[stone barn]

ye I see

But the thing is this is actually part of a bigger problem

[agile sundial]

dude post the problem

[stone barn]

If 9C5/2!2! Is the total then it won’t make sense

Ok

[mossy swift]

first of all your original problem made no sense too

[mossy swift]

which was this

so you need/want to elaborate on this too

are you looking for (A,B) , (B,A) , (A,A)

or are you looking only for {A,B}?

[stone barn]

Btw the total number of ways where it contains more T’s than A’s is 40

[agile sundial]

is that the ans?

[stone barn]

Nah

So after I got a 40

I gotta divide it by the total number of selections

To find the probability

So I’m trying to find the total number of selections

[mossy swift]

These are your three cases

and your question prior doesn't relate whatsoever but okay

[stone barn]

Mb

[stone barn]

For?

[mossy swift]

Wait i misread

[stone barn]

If it is that then once i do 40/(9C5/(2!*2!) the probability will be higher than 1

[agile sundial]

my bad

you have to use p

try adding all 3 cases

[stone barn]

That’s permutations tho

Questions asking for selections

[agile sundial]

but is the ans correct?

[stone barn]

I mean your first case is Alr 5P5 which is 120

[agile sundial]

abc and cba are different and thus should be counted as 2 separate things

[agile sundial]

what does the ans key say

[mossy swift]

first of all, you should translate your question:

does not contain more T's than A's translates roughly to the count(A) >= count(T)

[stone barn]

The answer asks for probability and that’s 0.683

[mossy swift]

the total 5 letter subwords you can get word from activated is 9C5

,calc 86/126

[ocean seal]

Result:

0.68253968253968

[mossy swift]

yeah checks out

[stone barn]

Hmm why did u divide by 9C5 tho

[mossy swift]

9C5 is the total count of 5 element subsets

all 5 element subsets you can have

that's the "total"

the better question is where the 86 comes from lol

[stone barn]

But there are some repetitive letters so wouldn’t that cause it to decrease total selections?

[stone barn]

Nah I Alr know that that’s fine

[mossy swift]

no?

we consider each letters distinct in this case?

it should be less if not yeah i agree

[stone barn]

So we look at the problem like A_1 and A_2, T_1 and T_2

[mossy swift]

Right

[agile sundial]

wait how does this work

the letters aren't distinct

[stone barn]

Oh I was assuming something like: suppose the 5 random selected letters are ACTIV and another 5 letters letters are ACTIV but this the time the second A and second T

[agile sundial]

yeah this is correct right?

[stone barn]

They should be the same since they both combine to be ACTIV

[agile sundial]

yes

[stone barn]

So I thought there should be less combination than 9C5

[agile sundial]

yeah

[stone barn]

bro

So what do I do

To reduce it

[agile sundial]

i think the question is framed incorrectly

[stone barn]

It’s an official paper tho

I doubt it

I think our thinking is wrong or our answer is

The other dude Alr used 9C5 and got the correct answer

my question now is simply why

[stone barn]

Cause of this

They the same

They don’t even ask us to treat us as distinct