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[junior geode]

okay it seems the row 2 got affected before row 1 was subtracted from row 3

but it's hard to visualize so i guess matrix multiplication would be the way to go

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[golden shore]

AYY

[golden shore]

How to simplify this

How to turn off the calculator

[paper acorn]

shift + AC

[paper acorn]

you really can't... unless you have specific form in your mind

[golden shore]

Thank you

[golden shore]

I see

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[quasi hamlet]

I tried answering this but when n=1, the series would have 1/0. What should I do?

[quasi hamlet]

I solved it using partial fractions

[stiff musk]

you are right

they should start at n=2

[quasi hamlet]

is it a typo? or does it mean it diverges

[stiff musk]

it's hard to be sure but i assume it was a mistake by the author

and they didn't intend to have the first term be infinite

i would solve it assuming it starts at n=2 and maybe write a sentence explaining why

but that's just me

[quasi hamlet]

Okay thanks!

[stiff musk]

sure, cheers

[quasi hamlet]

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[static ore]

I think I did a mistake,

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[hybrid skiff]

why does this hold?

[paper acorn]

it is from Chebyshev's inequality

[hybrid skiff]

yes i know. Im trying to understand the proof. By using this equality and Markov one can get Chebyshev. However why does this equality hold?

[paper acorn]

transformation of random variable. Notice that |X|^2 = X^2

[hybrid skiff]

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[torpid perch]

,, \int \frac{dx}{(x^2-4x+3)(x^2+4x+5)}

[glossy valve]

938c2cc0dcc05f2b68c4287040cfcf71

[torpid perch]

@wicked seal

[zealous rose]

<@&286206848099549185>

[restive veldt]

Use partial fraction decomposition https://en.wikipedia.org/wiki/Partial_fraction_decomposition

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[nova bloom]

I have to express c & y, while including the side a and an angle function of Alpha in the formula

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[thick token]

try calculating sin and cos of alpha

that way you can express c (or y) in terms of alpha and h

h is not what theyre asking for but its one step closer

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[north creek]

so the question was:
"What percentage of total contributed income including donated objects was accounted for by the National Flora Museum in Year 3?"

[north creek]

i dont even know where to start. okay got it

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[wicked zephyr]

Hey there, i have a problem here at part (ii)

Is there any technique to solve inverse function of cubic ??

[hot herald]

no nice way to solve most cubics, but for these types of questions
they usually give something that's identifiable by inspection

[spiral vigil]

I don't think it was helpful to do the x-5 stuff first

[prime crystal]

whats the answer of (ii)?

[hot herald]

doing stuff with x-5 is fine, but just leave it as is, instead of expanding

but you can just work with the given equation as is.

for f^-1(8), consider when x^3 + 7x + 8 will have the value of 8

[wicked zephyr]

5

[wicked zephyr]

first part (i) did i do well ?

<@&286206848099549185>

[median marten]

yes

[sullen hinge]

you didnt need to do the y = x + 5 stuff, you should just set x = 3 because that wouldve given you f(x + 5) = f(3 + 5) = f(8) = ...

[wicked zephyr]

oh you're right

[wicked zephyr]

then how bout the inverse part in (ii) ?

[sullen hinge]

its also easier in (ii) if you didnt do the y = x + 5 stuff

[hot herald]

for f^-1(8), consider when x^3 + 7x + 8 will have the value of 8

[sullen hinge]

^^

basically you want to solve x^3 + 7x + 8 = 8

[wicked zephyr]

why cuh i dont get it

[sullen hinge]

well you want to know when f(a) = 8

we have that f(x + 5) = x^3 + 7x + 8

so if we solve x^3 + 7x + 8 = 8

then we get a value for x

lastly we add 5 to that value to find our a

[wicked zephyr]

x(x^2+7)=0

x = 0 or 7i ?

[sullen hinge]

+- 7i yes

but it says that f is a function R -> R so we discard the complex solutions

[wicked zephyr]

then my x = 0 sub into f(x + 5) = x^3 + 7x + 8 again ?

[hot herald]

yes

[wicked zephyr]

but the outcome is 168

[hot herald]

how are you getting 168...

[sullen hinge]

i think from when they did the y = x + 5 stuff

[sullen hinge]

if you sub x in this

you get 8

specifically f(5) = 8

[hot herald]

how exactly are you doing this substitution

then my x = 0 sub into f(x + 5) = x^3 + 7x + 8 again

[wicked zephyr]

owh i found it my mistake

How bout this part ? @sullen hinge

[sullen hinge]

f is decreasing which tells that when x < y we have f(x) > f(y)

can you think of another way of writing f(x) + f(2 - x)

[wicked zephyr]

use the value as previous ?

[sullen hinge]

wdym ?

[wicked zephyr]

nvm i'd get it how's the another way of f(x) + f(2 - x)

[sullen hinge]

we are given that f(x * y) = f(x) + f(y)

[wicked zephyr]

alright so , f(x) = f(x◦y) - f(y) ?

[sullen hinge]

well yes

but we can apply it directly to f(x) + f(2 - x)

[wicked zephyr]

the f(2-x) got me 💀

[sullen hinge]

wdym

[wicked zephyr]

direct ?

[sullen hinge]

we have that f(x) + f(y) = f(x * y) and we want to say f(x) + f(2 - x) = ...?

[wicked zephyr]

f(x * 2-x) ?

[sullen hinge]

yep

[wicked zephyr]

wait whattt

[sullen hinge]

you just set y = 2 - x

the f(x * y) = f(x) + f(y) is true for any x and y

[wicked zephyr]

okay interesting thing

[sullen hinge]

then we have f(x(2-x)) < 2

[wicked zephyr]

indeed

[sullen hinge]

and in part (i) we found f(1/4) = 2

so we have f(x(2 - x)) < f(1/4)

[sullen hinge]

now we want to use this

[wicked zephyr]

by solving this part can i just cancel out both side the funciton f ?

[wicked zephyr]

i get x < 1 and idk the f(x) > f(y)

[sullen hinge]

if the function was increasing then yes

because that would f(x) < f(y) means x < y

but here its decreasing so we get f(x) < f(y) means x > y

[wicked zephyr]

how do you conclude the range between x and y ? without function equation smtg....

i do understand f(x) < f(y) bcz f(x) is decreasing, but the x > y ?

[sullen hinge]

its the definition of decreasing

[sullen hinge]

imagine a graph

[wicked zephyr]

Look at me prove 😭 my inequalities different as question

[wicked zephyr]

Keep going

[sullen hinge]

yeah you need to flip the inequality at this stage

[sullen hinge]

in words: a decreasing function is one where the further along the x axis we go the lower down the y axis we get

see here, b comes after a

so f(b) is smaller than f(a)

in symbols we say a < b means f(b) < f(a)

a < b means b comes after a

do you see ?

so the way we apply that to this question that we have f(x(2-x)) < f(1/4) which means 1/4 < x(2-x)

i.e. f(x(2-x)) is smaller than f(1/4) we know that x(2-x) must be further along than 1/4

i.e. 1/4 < x(2-x)

[wicked zephyr]

owhh now i understand everything

appreciate it for help @sullen hinge

[sullen hinge]

nws! glad i could help

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[copper dome]

I have to learn a proof for the length of a curve but i don’t understand this part where we take xi in this interval

[copper dome]

That’s the graph

But why can’t xi be equal to di-1 or di

Why do we exclude them from the interval

[topaz valley]

it really shouldn't matter but they're trying to apply MVT

[copper dome]

whats mvt?

[topaz valley]

do you have a better picture of that part

[copper dome]

,rotate

[topaz valley]

yeah so the mean value theorem states that there exists $x_i \in \delims][{d_i, d_{i+1}}$ such that [ f'(x_i) = \f {f(d_{i+1}) - f(d_i)} {d_{i+1} - d_i} ]

[topaz valley]

and it is not true if you include the endpoints

but it really shouldn't matter

it's just an approximation anyway so taking d_i or d_{i+1} is perfectly fine

oh i got the indices off by 1

[copper dome]

but we learnt that for the mvt u can take x [a,b]

[topaz valley]

this isn't true in general

[copper dome]

we learnt it for a convex space tho

and then that its true for [a,b]

[topaz valley]

if you can take x from ]a, b[ you certainly can from [a, b]

but generally the point MVT gives you will lie in ]a, b[

[copper dome]

why is this mvt tho

[topaz valley]

wdym

they get this statement from MVT

[copper dome]

for mvt u want to find a c element of [a,b] for example so that f(c) = r

but why is this r

[topaz valley]

i'm not sure what you mean by r

[copper dome]

just a value

[topaz valley]

the mean value theorem is not for an arbitrary value

[copper dome]

ok why is this mvt

[topaz valley]

[0.7\textwidth]
the full statement of MVT is:

If $f : [a, b] \to \R$ is continuous on $[a, b]$ and differentiable on $\delims][{a,b}$ then there exists $c \in \delims][{a, b}$ such that [ f'(c) = \f {f(b) - f(a)} {b - a} ]

[topaz valley]

and in your notes, it's directly applied to f on the interval [d_(i-1), d_i]

[copper dome]

and why cant c be a or b

[topaz valley]

MVT is stated for the open interval

the c is guaranteed to exist inside the open interval

maybe it also works for the endpoints

but MVT usually doesn't assert this

[copper dome]

is that because if its not in a convex space

[topaz valley]

no

[copper dome]

😭

why do i see that it is closed intervals then for mvt

[topaz valley]

MVT doesn't assume that f'(a) or f'(b) even exist

but again, in your case it doesn't matter

you're just doing this to derive an expression for an integral

via riemann sums

it doesn't matter where you pick x_i

it can be chosen to be the endpoints

[copper dome]

ok so its basically because you're not sure if the derivative in those two endpoints exist?

@topaz valley

[topaz valley]

in your case it should

[copper dome]

but generally you're not sure

[topaz valley]

yeah

but still like

in MVT you don't get to choose the c

it just exists

and maybe the endpoints work

who knows

depends on your function

[copper dome]

okay

thanks

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[midnight niche]

I don’t know how to find all the hits

[torn jolt]

“include a sketch”

draw a graph of sin x

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[lilac dagger]

How i can do this limit, im triyng but i can't, i need to variable change

[echo marsh]

differentiate both num and den

[hallow walrus]

$\lim_{x\to -1}\left(1+\frac1{x+1}\right)^{\frac{3}{e^{x^2-1}}}$

[glossy valve]

kheerii

[hallow walrus]

wait, the question seems wrong to me

ah wait is it just a product

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[next quartz]

This is from a study guide for an upcoming exam.
1: how much is sin(a) if tan(a/2)= -0.75
2: transform equation into multiplication
3: Prove that the left side = the right side
Those are the ones i need help with

[next quartz]

<@&286206848099549185> please i am desperate

[thick hedge]

sure

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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

[next quartz]

so i solved number 1

but on 2 i have no idea how to approach it

[sacred yarrow]

alr, do you know how to state sin2x,sin3x, and sin4x with sinx and cosx?

[next quartz]

sin2x yes

its 2sinxcosx

but 3x and 4x im not sure

[sacred yarrow]

sin3x=sin(x+2x)

[next quartz]

ah ok

so sincos+cossin

damn thats gonna be a long one

[sacred yarrow]

Just use the result you got from sin2x on sin3x and 4x

Or you can just apply triple angle formula

[next quartz]

so this is the result?

[sacred yarrow]

3x?

[next quartz]

i used the formula for sin(a+b)

where a is 2x and b is x

sin(a)cos(b)+sin(b)cos(a)

[hallow walrus]

it is right,

but I suppose they want you to write it completely in terms of sin and cos

which is tedious

[next quartz]

yeah

they want me to write it as a multiplication

[hallow walrus]

I'm not sure what that means

you have to factor it?

[sacred yarrow]

Proceed

[next quartz]

so just expand what i wrote here

what should i write cos2x as?

[sacred yarrow]

ye, you have to expand it

[next quartz]

cos^2-sin^2 maybe?

[sacred yarrow]

In the terms of sin

[next quartz]

ok so 1-2sin^2

damn ok ill struggle with it real quick

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[slim bay]

May, I ask
If i have this logarithmic equation. (for example)

[slim bay]

And i need to solve the Y
Do I just multiply A until i found out the Y?

[next quartz]

you can express 81 as 3^4

[viral jasper]

that's right

[slim bay]

thanks

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✅

[slim bay]

How can express 81 without knowing A and Y?

[barren fiber]

Log 3^4

Or 4log3

A is 10

If not written it’s always 10

[slim bay]

Could be log 9^2?

[barren fiber]

Prefer simplest

[rain dragon]

in the end you will have to simplify it for simplicity ofc

[slim bay]

make sense
thank you

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[torn jolt]

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[leaden yarrow]

How do I go from the equation of the line as the intersection of two planes to the equation of the parametric line?

[leaden yarrow]

This is the way the book goes trough

And i understood it BUT what if the equation of the line is :

I would do like:
x = k
r: { k + z = 1
y = 2

And so the vector of r would be:
v(1; -1; 0)
right?

Yes, it's right.

Thx

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[heady marlin]

I’m confused why is the phase shift not pi/3???? The answer key says the phase shift is -pi/6

[gentle aurora]

phase shift (x-a)

you have 2x

2x-c = 2(x-c/2)

shift : c/2

[heady marlin]

So the a is flipped? If it’s positive it’s really negative and if it’s negative it’s actually positive?

[gentle aurora]

yeah but it makes sense why its like that

when you subtract the graph shifts to the right

[heady marlin]

Hmm

Okay

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[whole flume]

Help for a function question. I need to know what grade it's from and what unit it is. Even better, can someone give me the answer so I can learn from it later on?

[stuck storm]

this is calculus

[whole flume]

Oh sorry
I thought it was functions

I'm so lost

[verbal mantle]

first of all these are 2 equations

but yeah it is calculus

[whole flume]

Someone gave it to me and told me to learn the math in 2 months. With no contexxt

I was wondering what the unit was

[verbal mantle]

makes no sense to start from this

[whole flume]

and what grade you learn it on

I'm assuming 12?

[stuck storm]

its a college course but many highschoolers (especially those interested in STEM fields) take it in 11th or 12th grade

[whole flume]

Yeah, I understand that

[stuck storm]

the specific topics i guess are limits and integration

but yeah dont start with integration

[verbal mantle]

i took it when i was between 8th and 9th lmao

[stuck storm]

lol your cracked

[verbal mantle]

i should have made them this year

[whole flume]

I'm in 8th. I understand grade 10 math and I'm rapidly learning stuff. (It took me two days just to understand concepts for grade 10. I understand I'm not a master at it and I might be missing parts but I'm just learning a lot right now)

[verbal mantle]

that's good

[stuck storm]

thats great

[verbal mantle]

i learnt mostly from YouTube but you need to know how to use it

[whole flume]

Same, I learn from Organic Chemistry Tutor

[verbal mantle]

id recommend ypu to try and find a full calculus 1 course

[whole flume]

Alright

[stuck storm]

khan academy is great

look at their ap calc course if you wish

[verbal mantle]

bro i follow something like 80 or more math channels

[whole flume]

Do I need to learn all of grade 11 and 12 for this? Or is it just a whole different side part of math? (For example how science units work?)

This question might be dumb, I understand

[blissful condor]

No you don't

[verbal mantle]

no it requires trig and other prior knowledge

[whole flume]

Sure, I'll do that

[whole flume]

Yeah, I used it to learn grade 10 math

[verbal mantle]

you look like me about 3 years ago

i believe in you

[whole flume]

Thank you

[blissful condor]

if you're looking to self study look for mit open courseware math

[stuck storm]

you should be familiar with trig and very familiar with the concepts of functions

[blissful condor]

You also don't want to be learning calc 1 unless you are solid with algebra and pre calc material

[verbal mantle]

you need to have rock hard bases to proceed

[blissful condor]

Calc 1 is not too difficult so you can get by with it but..

for first exposure I'd get good with trig and algebra

[verbal mantle]

ye

[whole flume]

So basically, I should get familliar with the main concepts. Also, I need to udnerstand it very well before I learn calc1?

[blissful condor]

Yeah so actually

[whole flume]

Alright, I'll start doing that

[verbal mantle]

get very very used to normal trig, and stuff like that

once you can work around with those very easily you can start

[blissful condor]

and learn identities

trig identities especially

[verbal mantle]

yep

i know so much stuff by memory you have no idea

also weird angles

[whole flume]

This is honestly helping so much, whenever I'm learning matth, I'm lost. I don't know what to learn.

[verbal mantle]

i recommend some kind of notes with all useful functions and identities ypu might need

[whole flume]

However, I think I know what to learn now

[whole flume]

Yeah, I'll do that for sure

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[heavy lodge]

hey dont spam ping

[sharp sand]

Ok

8 letters each with 8 different placements

[heavy lodge]

it might be 8!

[sharp sand]

idk

clone could be right

[heavy lodge]

$8!$

[glossy valve]

clonesolopros

[sharp sand]

it probably is 8 factorial

because with each combination you would lose an option

[sterile chasm]

8P8 so its 8!

[digital shard]

no duplicates

so 8!

[sharp sand]

might be repeated?

yea 8!

[digital shard]

anytime you se arrange

think of factorial

[rare dock]

‘possible’ is not written in the problem

but anyway surely it’s rearrangements of the letters

not strings you can make out of any number of the letters

yes

[gentle aurora]

multinomial coefficient when using words

you have three 7 left and 51 total cards

[ashen crater]

2/52 for picking a red 7 right

And then you're left with 51 cards total, and three 7s left

So multiply those

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[scenic moon]

I get 25.8 but the answer is supposed to be 28

[scenic moon]

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[modest pumice]

A few minutes after I solved this I realised that cosx can be equal to 1

[granite torrent]

do you have a question about that?

e - e^cosx remains within a constant range while x grows indefinitely, so your conclusion that the limit goes to 0 is correct

[modest pumice]

But at any point 2nπ (n is integer) cosx is 1 so itll be 0/infinity

(Sorry if I made a mistake in that message, im tired)

[gentle aurora]

that is still 0

[modest pumice]

Ok

Thanks

[granite torrent]

^ 0/infinity is not an indeterminate form

[modest pumice]

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[marble flume]

is this the right direction or am i lost 😭

[midnight niche]

Where do you need help in trig identities

[marble flume]

i wanna know if i’m doing it right or not

it’s confusing 😭

[midnight niche]

So you should be at 1/cos over 1/sin^2

[marble flume]

oh so i messed up

can you point out where i went wrong?

[midnight niche]

Slightly

[marble flume]

(or how do fix it)

[midnight niche]

Thsi is my soloution

Also are you in functions

[marble flume]

yeah grade 11

[midnight niche]

Yeah same do you understand

@marble flume

I know it’s a little messy but I can explain if you want me too

[marble flume]

how come the l.s became multiplication?

oh wait

reciprocal

nvm i get it!!!!

[midnight niche]

Yes there we go

Good job

[marble flume]

thank youu 😭😭🙏🏼

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[craggy tapir]

Given 4 points A(1, 2, -3), B$\left(\frac32,\frac32,\frac{-1}2\right)$, C(1, 1, 4), D(5, 3, 0). Let $(S_1)$ be the sphere with center A and radius of 3, $(S_2)$ be the sphere with center B and radius of $\frac32$. How many planes are there that touch both spheres and parallel with the line passing through C and D?

[craggy tapir]

this is the equation of 3 objects given

now im not sure what to do next from here

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[craggy tapir]

i just went for a lunch, not done yet

[craggy tapir]

original question #help-28 message

still stumped

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[brittle oxide]

im homeschooled and stuck someone pls help

[flint crane]

minus 4 on both sides

[brittle oxide]

so just 3x = -13?

[flint crane]

-17-4 =/= -13

[brittle oxide]

hmm

i think i get it now

thx i get it now

[flint crane]

yw

[brittle oxide]

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[civic bay]

<@&268886789983436800>

[thick hedge]

<@&268886789983436800>

[restive veldt]

<@&268886789983436800>

[quaint prawn]

<@&268886789983436800>

[nocturne shoal]

Dead

[nimble crane]

Dami!

[civic bay]

our hero

[thick hedge]

thank you

[hushed stone]

?

What happened?

[thick hedge]

someone was sharing NSFW content

[viral jasper]

https://tenor.com/view/bulanci-you-missed-it-sleepteam-pillow-fight-say-goodbye-gif-25656079

[hushed stone]

Dam

[hushed stone]

Not sure if that good or bad

[viral jasper]

we're here for math

[thick hedge]

you shoud be happy you missed it

[hushed stone]

Very well

[thick hedge]

I need to scrub out my eyeballs now

[hushed stone]

Also can u help

[thick hedge]

#❓how-to-get-help

[hushed stone]

Its in help forme

Someone else's question

I can't understand how

[thick hedge]

this channel is going to be locked soon

got to #help-42

[hushed stone]

Rip

[hushed stone]

Y

[thick hedge]

just ask there

[hushed stone]

This one

[thick hedge]

which one?

[hushed stone]

https://discord.com/channels/268882317391429632/1251039048449921034

[viral jasper]

.close

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[scenic dagger]

um i need help

[thick hedge]

do you know about interior alternate angles

[astral sinew]

hint: the two lines are parallel

@thick hedge

[thick hedge]

yes?

[thick hedge]

the lines are parallel

[short niche]

they are indeed parallel

[odd cobalt]

is there anyone who is good with percents that can vc rq?

[scenic dagger]

no

[full forum]

@scenic dagger Has your question been resolved?

[scenic dagger]

nuh uh

[runic shuttle]

can someone helpme

with a math question

[scenic dagger]

send it thru trheyll prob answer

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[latent rapids]

For these types of problems, if all numbers under the radicals are integers, are we allowed to assume that a and b, from sqrt(a)+sqrt(b) (the expression it will simplify into) are also integers?

[rapid rain]

here you can indeed assume that the value you're looking for is a + bsqrt(10) or smthg else where a and b are integers

otherwise no real ways of finding the simplification

you can also look for something like asqrt(2) + bsqrt(5)

[latent rapids]

We were taught to do split it into sqrt(a) + sqrt(b) because like you pointed out we wouldn't know if it was sqrt(10) or sqrt(2)*sqrt(5), would a and b still have to be integers in this case?

[rapid rain]

yeah you can keep a and b integers

and so compute (sqrt(a) + sqrt(b))^4

[latent rapids]

Ight ty, do you have an explanation why?

[rapid rain]

no xd

it's just "the solution should be simple"

[latent rapids]

Lol ok

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[ancient willow]

help

[ancient willow]

i never learned this ):

[wheat cradle]

Alright you know the three forms of a quadratic equation right

[ancient willow]

whats that

[fringe bronze]

Hello

[wheat cradle]

Have you learned about standard vertex and zero form?

[ancient willow]

hi

no

[fringe bronze]

So this is the question?

[ancient willow]

yes

[fringe bronze]

oki

[wheat cradle]

Ok so you didn’t learn about vertex max/min or x intercepts? In that case jus search it up on YouTube first

[ancient willow]

ok

[fossil wren]

well i'm pretty sure you could just look at the x axis

the parabola intersects it at x = and x = 5

x = one

that key is broken

[ancient willow]

y = (x – 3)^2 – 4

that was asnwer

[fringe bronze]

So if I'm not wrong (I haven't done parabola's in a hot minute) the vertex origin is 0,0 no?

[ancient willow]

idk anything watching yt rn

[fringe bronze]

oki

As it turns out I suck at parabola's

Sorry

[ancient willow]

whatever man

this sucks

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[wheat cradle]

If you’re still seeing this jus saying looking for important points on the parabola

Such as vertex

X int or y int

Or any other obvious points and then plug them into either one of the equation based off of what information was given

For example if you’re given the vertex then plug that into vertex form f(x) = a(x-d)^2 + c

Or if you’re given the x intercepts then plug them into zero form f(x) = a(x-r)(x-s)

Then solve for whatever variables are left

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[marsh cove]

could someone help me with this proof I dont see their point of their definiton of phi like how its used and I also dont get why they say φ(vj ) = 1

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[sacred yarrow]

What problem are you facing rn?

[torn jolt]

why will the normal reaction not pass from the centre of the cube

@sacred yarrow

[sacred yarrow]

For question.21, it does

[torn jolt]

but the third option is the answer

try solving 28

[full forum]

@torn jolt Has your question been resolved?

[sacred yarrow]

What have you tried about this one?

[torn jolt]

nothing

[sacred yarrow]

Alr

How about now? Do you have any idea?

@torn jolt

[torn jolt]

no

[sacred yarrow]

What have you learnt about torque?

It’s a tough chapter ik

[torn jolt]

torque is responsible for rotating a body in presence of a force that acts at a distance

this is all what i can think about rn

[sacred yarrow]

yes

ok, do you know the definition of "distance" in the chapter of torque?

It’s a crucial part that you have to acknowledge before this question

[torn jolt]

perpendicular distance from the point about which the torque needs to be calc

[sacred yarrow]

incorrect, try again

There’s an incorrect info in your statement

A word, precisely

[torn jolt]

perpendicular distance of force from the axis about which the torque needs to be calculated

[sacred yarrow]

Correct

[sacred yarrow]

Find all of the distance on this graph

[torn jolt]

about which axis??

[sacred yarrow]

There are three forces on the graph, to begin with, do you know the r of F?

r stands for distance

[torn jolt]

why is the normal rxn not on the center

[sacred yarrow]

The rxn can be at any place inside the box

Since the box remains stationary

Even you draw the rxn at the middle, the result remains the same

[torn jolt]

idk....tbh i don't know how to solve these Qs on shift in normal rxn

[sacred yarrow]

Hint: consider the box is about to flip

[torn jolt]

ooohk

....still not getting

can u explain?

[sacred yarrow]

I see

Should I guide you from the easiest question?

Since it’s kinda hard to demonstrate

[torn jolt]

sure

[sacred yarrow]

Do you know the force of the question mark?

[torn jolt]

hold on

[sacred yarrow]

Solitary

[torn jolt]

no

[sacred yarrow]

You don’t know the answer?

[torn jolt]

no

[sacred yarrow]

okay, what’s the magnitude of the force?

[torn jolt]

its ok...i will figure it out

thnks for your help

[sacred yarrow]

no….I’m supervising you

I won’t let you leave unless you figure it out ==

[torn jolt]

.ok

3F?

@sacred yarrow

[sacred yarrow]

Correct

Do you know why?

[torn jolt]

cuz net torque is 0?

[sacred yarrow]

yeah

[torn jolt]

got it

[sacred yarrow]

Do you know what will happen if I shit the force a bit left?

[torn jolt]

it will rotate?

[sacred yarrow]

yes, in which direction ?

[torn jolt]

which F will u shift?

[sacred yarrow]

No matter which force you shift, the result remains the same lol

[torn jolt]

it will rotate anti clockwise

[sacred yarrow]

Correct

What if I add a force on the right side?

[torn jolt]

it rotates cw?

[sacred yarrow]

What if I shift both forces a bit left?

Like I shift them r/2

[torn jolt]

acw

[sacred yarrow]

yeah, that’s all

[sacred yarrow]

Now tell me why the normal reaction would change its position?

I don’t want answer, I’d like you to tell me why

[torn jolt]

to balance the F and prevent the box from toppling

?

[sacred yarrow]

ye

Remember that, the normal reaction is the force that is trying to balance a system

Do you know what will happen if the magnitude of F grows greater?

There are two consequences

[torn jolt]

box topples

[sacred yarrow]

And slip

[torn jolt]

yes

[sacred yarrow]

Why?

explain

[torn jolt]

but since the surface is rough it won't slip

[sacred yarrow]

I will, as long as the magnitude of F is great enough. But F in the question isn’t great enough to let it move

[torn jolt]

yes

[sacred yarrow]

Explain

Just try, even if you don’t know , just make up one

[torn jolt]

as the F increases it will eventually outgrow the frictional force

and will make the box slip and topple

[sacred yarrow]

Why the box will topple

You didn’t explain that part

That’s only the reason of why the box would slip

[torn jolt]

because of the net torque created by the F

[sacred yarrow]

yes, more explanation on this

Hint: The position of the normal force

[torn jolt]

away from the center of the mass towards the right?

[sacred yarrow]

Pretty close

The normal force would shift to the edge

Trying to balance the vertical force created by gravity

And trying to balance the torque given by mg and F

Eventually, the box will flip because the normal force cannot go any left further from the box

[sacred yarrow]

If you increase F, x will grow greater

Once x>a/2, the box will flip

[torn jolt]

then we can balance the torque to find the shift in the normal reaction?

[sacred yarrow]

yes

I’ve given you everything in our previous chat

1. How to calculate the distance
2. How to determine acw cw
3. How normal force works
4. Why it would flip

Dawg, it’s been 1.5 hours

Hope you don’t mind my vivid guide, without these guide, you would not have the ability to combat similar questions next time.

[torn jolt]

thanks for your help, i was struggling to solve such kind of questions. Also i am very sleep deprived right now and i will surely go again through the chats again tmrw for better understanding. 🙏😸

[sacred yarrow]

Same, but I still need to study XD

It’s 1:42 am here

Have a good one!

[torn jolt]

oh ok

[torn jolt]

all the best

good night

[sacred yarrow]

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[abstract root]

hloo any one know how to improve math aptitude.

[sacred yarrow]

The function has no roots

[thick hedge]

practice

[abstract root]

how you learnt.

[thick hedge]

practice

and by helping others

[abstract root]

bro i need to crack aptitude do u know any resource.

[thick hedge]

khan academy

[abstract root]

tq

[spice rose]

just keep doing it, that's how you generally get better at things

[abstract root]

btw what you guys do?

[sacred yarrow]

Study

[abstract root]

phd in math??

[sacred yarrow]

Doing Math for 8 hours a day

[abstract root]

nice bro i love to do the same

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[twilit apex]

How do i know if a co-ordinate lies on a curve of a cubic graph?

[hallow walrus]

!original

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[hallow walrus]

the coordinate should satisfy the equation of the cubic

[sacred yarrow]

Just plug them in and see if they meet with the solution

[unborn gulch]

yup

[sacred yarrow]

For example, when you plug in 1/3, you’ll get 1/27 as a result. Therefore, A isn’t the correct answer. You’ll do the rest

[twilit apex]

What do you mean by "plug in", sorry?

[unborn gulch]

substitue the value

[hallow walrus]

as in, replace y with the y-coordinate given in the point

and replace x with the x-coordinate

[unborn gulch]

and check LHS = RHS or not

[hallow walrus]

in the equation of the curve

and see if it satisfies the equation

[twilit apex]

ohh i see, thanks for the help

[sacred yarrow]

!done

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[twilit apex]

.close

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[desert aurora]

How can I solve expanding this: -2 (ax + by - c) ?

[sacred yarrow]

Do you know distribution law?

[hot herald]

distribute/multiply the -2 to each term inside the parentheses

[desert aurora]

Im not sure

Its about how do i make it?

[sacred yarrow]

Do you know how to expand it?

[sacred yarrow]

ye, let’s just test it out

[desert aurora]

I know something more like : 3x(2x⁴-2x)

Those types i can

But i dont know if they are variables

Is it something like -2ax + -2by - c?

[sacred yarrow]

Close, you forgot to distribute-2 to -c

[desert aurora]

To the expand to -2 (ax+by-c) its -2ax+-2by-2c?

[sacred yarrow]

You have to change the sign of -c

[civic bay]

multiplying two negatives gives a positive

[desert aurora]

A yes yes

[sacred yarrow]

It’s no longer negative after being distributed with -2

[desert aurora]

True

[civic bay]

(-2)(-c) is that last term

[desert aurora]

Oki doki

Thanks 🙂

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[torn jolt]

This highlighted part is something I don’t understand

I think the domain is the x

But isn’t cos also x

[coarse chasm]

x is an input to the function

[torn jolt]

So saying cosx like how do I understand it

Oh ok

[coarse chasm]

the domain is the values that we can set x to

[torn jolt]

Why isn’t cosx understood as x x then

[coarse chasm]

What do you mean?

x isn't the function, x is the input

cos is the name of the function

[torn jolt]

I thought cos was the x coordinates on a unit circle

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[coarse chasm]

!xy

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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[coarse chasm]

#help-28 message

[keen agate]

Are you trying to say g(sqrt(3x-3))?

For g(x) = -x^2 + 5?

If so,
-(Sqrt(3x-3))^2 + 5

[keen agate]

For functions where you have g(x) = ... and you are asked to plug something in for x. You replace every x in the old function, g(x), with the new function

Yes

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[torn jolt]

what is 2+2

[torn jolt]

2+2?

[coarse chasm]

Let's not troll in help channels.

[quaint prawn]

<@&268886789983436800>

[reef sparrow]

.close

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[torpid perch]

find all $a \in \mathbb{R}$ such that $\\\sum_{n = 1}^{\infty} \frac{(1+a)^n}{n}(x-2)^n\\$ has radius of convergence equal to 2

[glossy valve]

938c2cc0dcc05f2b68c4287040cfcf71

[torpid perch]

I tried one of the convergence tests called root test but idk if its correct

basically I am getting $\left|x-2\right| < \frac{1}{|1+a|}$

[glossy valve]

938c2cc0dcc05f2b68c4287040cfcf71

[coarse chasm]

Right, so what do we need to be true for it to converge

[torpid perch]

|1+a| < 1

[coarse chasm]

Well, we want |(1+a)(x-2)|<1 to be true for exactly x in (2-2,2+2)=(0,4) right

[torpid perch]

we want

|(1+a)(x-2)| < 1

but unsure about the (2-2, 2+2) part

[coarse chasm]

The series is centered at 2 and they want a radius of 2

[torpid perch]

okay

you mean because of the (x-2)^n

okay

I mean they also are telling us we need radius of convergence of 2

[full forum]

@torpid perch Has your question been resolved?

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@torpid perch Has your question been resolved?

[leaden ermine]

are you still stuck on this

[torpid perch]

lowkey yes

you saying we can ignore the (z-a)^n part

?

aka (x-2)^n

[leaden ermine]

yeah

1/(1+a) is the correct limit

[torpid perch]

wdym

how

[leaden ermine]

this

[torpid perch]

can you do a drawing

[leaden ermine]

now what

R = 1/(1+a)

and you want to find an a such that R = 2

,,\frac{1}{1+a} = 2

[glossy valve]

𝔸dωn𝓲²s

[torpid perch]

right

1=2+2a

[leaden ermine]

yea

now what

[torpid perch]

,w solve 1=2+2a

[glossy valve]

Results provided by WolframAlpha

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

Requested by 938c2cc0dcc05f2b68c4287040cfcf71

[leaden ermine]

blud you didnt need wolfram but sure

💀

[last vapor]

did you really wolfram for that

[leaden ermine]

💀
≤))≥
 Λ

[torpid perch]

but this can’t be the only A or no?

[leaden ermine]

well looks like it is the only a

[torpid perch]

okay ty

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[torpid perch]

.reopen

[leaden ermine]

graphically there is only one solution

[full forum]

✅

[leaden ermine]

and the limit was 1/(1+a)

that basically what I wanted to add on lol

[torpid perch]

oki

thanks both

[leaden ermine]

now what

[torpid perch]

.close

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[orchid iris]

<@&286206848099549185>

[wispy flare]

hi

[orchid iris]

hello there.

[wispy flare]

i can help with this

is this literal equations?

[orchid iris]

wdym?

[wispy flare]

like will w amd m be part of the answer

[orchid iris]

im not sure

it just says sovle for z

[wispy flare]

k this is most likely that

[orchid iris]

i think its a interger

[wispy flare]

idts, becasue w and m do not have values

[orchid iris]

oh

[wispy flare]

which unit in khan academy is this in?

[orchid iris]

algerbra 1

[wispy flare]

ohhh yea

[orchid iris]

how u know its khan ?

[wispy flare]

the format

i use khan too

[orchid iris]

oh

[wispy flare]

im in alg 2

k,

[orchid iris]

nice

[wispy flare]

so let me walk u throught

[orchid iris]

okay

[wispy flare]

first, multiply the coefficent (w), with the other value (-4+z)

tell me what u get

[orchid iris]

so subsitued it?

[wispy flare]

no,

[orchid iris]

or distuibutive proptety?

[wispy flare]

yes

yes

[orchid iris]

ok

[wispy flare]

w(-4 +z)

do that firs

[orchid iris]

-4w + zw = mz +17

[orchid iris]

ok

[wispy flare]

ok,

now the purpose is to isolate z

right?

[orchid iris]

yes

[wispy flare]

so, take the constant from the right and bring it to the left

write your solution

[orchid iris]

so isolate z?

[wispy flare]

yes

but thats next

[orchid iris]

so now?

[wispy flare]

so, now, take the 17 to the left

[orchid iris]

ok

[wispy flare]

write your solution

[orchid iris]

-4w + zw -17 = mz

[wispy flare]

yes

[orchid iris]

but y

[wispy flare]

because we are isolating z

and taking all other values to one side

[orchid iris]

oh ok

[wispy flare]

now, divide both sides by the coefficent of z, and you are done

k gotta go bye!

[orchid iris]

ohok thx

[wispy flare]

right or wrong?

[orchid iris]

what?

[wispy flare]

like did u put the answer in?

[orchid iris]

im figuring it out

[wispy flare]

?

k

[orchid iris]

/z

[wispy flare]

yes

[orchid iris]

-4w+w=m

[wispy flare]

so whats ur final answer