math-help

[left knoll]

do that on calc

[blissful zinc]

ok

[supple island]

we can just multiply log2(2) cuz it's =1

[left knoll]

bruv

thats the thing about maths sometimes

u have to think outside box

theres no way i wouldve gotten that

yea but i got it now

[sterile birch]

hey guys

really need help with thus

I did some of the u-sub
After integrating got -2cot(t/2)
upper limit as 4pi/3 lower limit as 2pi/3
but when plugging into calculators and trying to run it through
im getting weird decimal answers
would anyone be able to help
would be appreciated

[glad geode]

---

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed as shown in Fig.14.13. What fraction of water over flows?

[fallow jetty]

you're probably getting weird decimal answers because the answer does not come out to a rational number

your integration is correct

[sterile birch]

and the lower and upper limits change to 6pi over 3 and 2pi over 3 right?

[fallow jetty]

depends on what your sub is, i didn't do the integration by hand because im sleepy

[sterile birch]

because to get the answer, the solution showed the upper and lower limits were actually pi/6 and pi/3

the u sub = 1/2

1/2 * x

or x/2

multiplying it one way or the other gets different results, how is that so? isnt 1/2 * x & x/2 the same thing

[fallow jetty]

according to wolfram, upper bound should be pi/6 and lower bound is pi/3

they are the same thing, if you got different results then it's an error in your calculations

unfortunately i cancelled my wolfram subscription so i can't show more steps past that

[sterile birch]

well with x/2 you sub and it gets pi/3/2 which then equals 2pi/3

[fallow jetty]

pi/3/2 = pi/6

[sterile birch]

but if you do 1/2 * x you get 1/2 * pi/3 which yiels pi / 6

[fallow jetty]

pi/3/2 = pi/3 * 1/2 = pi/3*2 = pi/6

[sterile birch]

is that so?

i thought you multiplied the reciprocal which is 2 / 1?

[fallow jetty]

you're talking about

[fallow jetty]

right?

[sterile birch]

yea

[fallow jetty]

in which case the reciprocal of 2 is 1/2

because that's not division of two fractions, that's division of a fraction and a whole number

[sterile birch]

look at what wolfram gives

not pi / 6

[fallow jetty]

well yeah because you put in

[fallow jetty]

in which case it's a whole number divided by a fraction

[sterile birch]

omfg

[fallow jetty]

so then the reciprocal of 3/2 is 2/3

[sterile birch]

dude

youre a genius

[fallow jetty]

lmfao

[sterile birch]

YOURE A GENIUS

I COULDNT UNDERSTAND FOR SO LONG

[fallow jetty]

gg

[sterile birch]

GG'S

THANK YOU

[fallow jetty]

ye

lmfao

[sterile birch]

YOURE A BLESSING FROM HEAVEN

AHAHAHA

[fallow jetty]

i feel u

making simple math mistakes in hard math

i feel u man

[sterile birch]

bro thats how it ALWAYS : ((((

fucking thank you dawg

[fallow jetty]

course

[sterile birch]

so

t/2 is just

anything on top, divided by whole number 2

[fallow jetty]

yeah basically

[sterile birch]

not really a fraction in itself

or

yea

[fallow jetty]

well it is a fraction

you just defined what a fraction is in this case

[sterile birch]

yea

[fallow jetty]

you could say that 2 is a fraction, 2/1

then the reciprocal is 1/2

tomato tomahto

[sterile birch]

so if it was

pi/3/1/2

then i would multi

but 2/1

by 2/1

[fallow jetty]

yeah

[sterile birch]

how do you determine when what is a fraction and what is a whole number

coz when wolfram gives 2pi/3

it kinda confuses me

like

the bottom is a fraction

but in case of t/2

[fallow jetty]

the fraction bar on the bottom one is a bit smaller than the bigger one

[sterile birch]

the top is the fraction

[fallow jetty]

that's how you can tell that there's a fraction in the denominator

[sterile birch]

if its smaller?

then its a fraction

?

[fallow jetty]

in a sense, both pi/(3/2) and 3/2 are fractions

just you can tell that it's pi/(3/2) and not (pi/3)/2 because the shorter fraction bar is below the larger fraction bar

[sterile birch]

ah ok

OK

so like

one is the main fraction kinda

the other is the lesser

[fallow jetty]

yeah that's one way of thinking about it

[sterile birch]

depending on what youre plugging in and stuff

ok bro

thank you for your help

i appreciate it

[fallow jetty]

ye

[subtle sluice]

Hi can anyone help me convert these polar equations to cartesian?

[sharp ferry]

i am not sure if i am correct but i think r cos theeta =x and rsintheeta =y so for the 3rd part at least you can solve it by using sin(2x)=2sinxcosx then you will get 9=8xy when you take it to there other side

[sharp ferry]

for the second one you can use hmm r^2 (cos2x)=r^2 * sqrt(1-sin2x) then r* sqrt (r^2-r^2^sin(2x))

sqrt(x^2 +y^2) * sqrt(x^2+y^2-2xy)

(x-y)(sqrt(x^2+y^2))
so final answer becomes (i thinkk not sure...)
(x-y)(sqrt(x^2+y^2))=4

i think there would be a better way to do this

[supple island]

remember that cos(2x)=cos^2(x)-sin^2(x)

it will become much easier

[sharp ferry]

OH YES

i unnecessarily complicated things 🥲

[supple island]

happens

[cinder yacht]

the goal was to write : 3 = log2(something)
well, we know that 3 = log2(2^3), AKA log2(8)

that's enough, log2(2) didn't come there without any reason, the only goal with it was to write 3 as log2(something)

[left knoll]

can anyone solve this

[left knoll]

ill do one

cause its the same for the rest

dy/dx =6x

at x=-2

sub in x

so -12 is the slope for this graph

im gonna assume for this u know how to diff

[left knoll]

Can someone explain how to do this ?

I have a test tomorrow

[cyan night]

i could help

do you mind taking a closer picture

[left knoll]

Find the derivative of
e^x- e^-x/e^x+e^-x

pls suggest approach

[formal patrol]

have you tried multiplying by conjugate?

[left knoll]

no pls tell if u can do

[formal patrol]

Dm

[ember kernel]

I think I'd just use the formula for the derivative of a fraction

[left knoll]

ye but first we needed to do little simplication first also. thanks for helping doe appreciate it

[subtle sluice]

Isnt it x^2-y^2=4?

[subtle sluice]

I got the same answer as this one

[subtle sluice]

Does anyone know the answer to no. 1?

[ember kernel]

Not really, you can just dive in without simplifying anything

Actually I even think that it'd be quicker applying the raw formula rather than trying to simplify the expression, unless you're confident enough with hyperbolic trigonometric functions

[left knoll]

Hi, I'm a French student so I'm not sure if I'm giving you the answer you need: since r = sqrt(x^2+y^2), and y = r sin(theta), we have 6/(3-y/r)) = sqrt(x^2+y^2). Then we use r = x^2+y^2 again to have 6 = 3 sqrt(x^2+y^2) -y.

[left knoll]

I don't really get why x is given as an angle since its a distance but anyway: we have cos(63) = r/(x+r). So r(1-cos(63)) = x cos(63). Thus, r = (x cos(63))/(1-cos(63)). WolframAlpha gives me r= 16.6 so we choose 17.

[sharp ferry]

yeah i overcomplicated things yeah it should be x^2 -y^2 =4 my bad

[subtle sluice]

Thank you

Can anyone verify if this solution is correct?

[sharp ferry]

ye could be simplified a bit further but seems correct to me

[subtle sluice]

I tried another method

[left knoll]

It is correct, just simplify by sqrt(x^2+y^2) to get 6 = 3 sqrt(x^2+y^2) - y.

[subtle sluice]

You mean divide the LHS with sqrt(x^2+y^2) from 6?

I see

Thank you

[left knoll]

Yes you can divide both sides by sqrt(x^2+y^2), the left one gives you 1 and the right one gives you 6/(3 sqrt(x^2+y^2) - y). You're welcome

[subtle sluice]

Yeah

[left knoll]

ye u r right

[ember kernel]

Btw, that expression is tanh(x)

Which is = sinh(x)/cosh(x)

So if you know about those yeah that simplifies it

But you're 17- so I don't think you've learnt about those yet

[left knoll]

ofc we learnt it and idts trigonometry is going to be used in that derivation

[ember kernel]

No

I'm not talking about sin and cos

I'm talking about sinh and cosh. This is not trigonometry, and that's why I'm not sure you've been taught those yet

[left knoll]

oh ok

i learnt smth new ig😄

[ember kernel]

Forget about them then, and use the raw formula 😉

Hyperbolic trigonometric functions are quite advanced concepts

[left knoll]

i use them but

i sometimes lack approach

i am getting demotivated bc of tha in maths

[left knoll]

in questions we get simply using formula won;t help

you sometimes need tricks

in which i lack

[ember kernel]

Learning how to approach problems is one of the easiest things in maths yet, since the approaches are generally redudant (especially in highschool). It's all about deeply understanding the concepts, and then training over some exercices to get used to the approach

[ember kernel]

For the question you sent, using the formula was enough to solve the problem

[left knoll]

mhm i get it

[ember kernel]

And along a solid understanding of the chain rule, it feels intuitive

[left knoll]

you are so good in maths...how much you practice it?

[ember kernel]

Not much, although I study it 5 days a week

[left knoll]

but like someone is like me which sometimes lack in subject...how much should i do maths? cause now i hv maths exam tmrw and i am panicking bc my prev one didn't went well😮‍💨

[ember kernel]

One thing I wish I'd been told in highschool is that mathematics are very logical. In hs, you're having formulas, concepts and theorems thrown at you with little to no explanation about how they were found or what makes them valid. It's mostly stuff you need to know by heart (even demonstrations steps, which are meant to prove something, mostly come out of nowhere). But in college, you learn how all the concepts are actually linked. You realise how logical and natural maths actually is. It's really like studying a language by being taught its grammar and semantics, not only unrelated vocabulary words

[left knoll]

oh thats helpful bc i really want to pursue maths in college but i am scared cause i am strugglin a lot in hs

[ember kernel]

I'll be painfully honest with you. If your exam is tomorrow and you don't feel ready yet, then it's highly possible you'll have a bad time sitting in front of your copy 24h from now. But don't give up yet. You still have an entire day to get ready, to train as much as possible, and give it your best shot to correct the big mistakes you're still make. It's now the last sprint, and now is not the time to stop. Go at full speed for the day, and tomorrow you'll be free. Maybe you will fail this exam, and failure is part of life. But at least, you will know that you gave it your best shot, and that topping that would've been next to impossible in less than 24h

I can help, too

[left knoll]

actually i have completed my syllabus, done with important questions, attempted 3 mock papers but i have a fear of failure

and its not that i'll fail

its of getting low marks than expected

[left knoll]

thankyou sm but ig i am done with doing maths now. its 9pm here i hv exam at 9am tmrw

[ember kernel]

Then you have even less reasons to worry, since most of the outcome is already determined

Although I know it's difficult not worry the day before an exam

But just think about it. You now have little responsibility over the outcome of your exam, it's all up to how your past "you" studied, and how your exam "you" will react to the questions. The best thing you could actually do now is read the key parts of the course again, but that would only slightly increase your chance at getting better marks tomorrow. So worrying about something you have little responsibility for is unnecessary

[left knoll]

mhm you are right

i am revising formulas and difficult topics

[ember kernel]

At least, that's my way of thinking while in exam session, where I usually go into coma for 2 months. During this period, I eat, breath and sleep exam preparation, so the days before exams I just remind myself it's better to get a good night sleep to make sure those study hours don't go to waste due to lack of sleep, rather than worry about the next day.

Anyway, good luck

[left knoll]

thankyou sm again for helping me hun. best of luck to you too🍰

[gritty cloud]

Help🥺

I need (iii) soultion

The other 2 i did solve them

[gritty cloud]

Anyone please

[nocturne island]

is it asking you to write that expression in code?

[gritty cloud]

Yes

[nocturne island]

i dont know visual basic, but it should be something like (sin(x)^2-cos(x)^2)^0.5

[atomic dagger]

hi! I was given the alpha angle inside the grey triangle. I don't understand why we can claim that the angle between the y axis and the vector mg is also alpha ?

[sharp night]

I hope it makes sense

you know that the vector mg is perpendicular to the bottom line

better picture*

so you know angles ACB and DCE are the same

and both CBA and EDC are right angles, so the triangles are similar

so angles BCA and DEC both have to be alpha

[atomic dagger]

how come they're the same ?

[sharp night]

they are vertical angles

[atomic dagger]

oh i see

since x axis is parallel to bottom line

[sharp night]

when 2 lines intersect, the 2 opposing angles are similar

[atomic dagger]

well top line

[atomic dagger]

thank you for your thorough explanation, i understand it now!

[sharp night]

no problem!

[atomic dagger]

.close

[left knoll]

sinx-sin2x=0. How do i find all the angles for this?

sin(x) - sin(2x) = sin(x)(1-2cos(x)) because sin(a+b) = sin(a)cos(b) + sin(b)cos(a). So we are now searching x so that sin(x) = 0 or 2cos(x) = 1.

[left knoll]

thank you so much i now understand

You're welcome!

would it be -2cos(x)=1?

ive got cos(x)=-1/-2, what would be the next step

No, you are searching for x so that sin(x) = 0 (1) or 2cos(x) = 1 only (2), so that we can have sin(x)(1-2cos(x)) = 0 (your first equation). So for the equation (1), x = n pi with n a natural number or n = - n pi. For the equation (2), cos(x) = 0.5 so its x = n pi/3 or x = - n pi/3 since cos(x)= cos(-x).

[left knoll]

yes but how to i get the second angle for cos(x)=0.5 as im looking in the range of 0-2pi

It's known to be pi/3 or -pi/3 but I can search for a proof if you want.

what i was asking for was for 5pi/3 but i got it thank you :)

Oh okay, sorry. You're welcome

[cinder yacht]

ENS? :o

which one

[cinder yacht]

and it's "x = +-pi/3 + 2 * n * pi" not n pi/3

[left knoll]

Oh yes, thanks, my bad! I went to fast...
I'm taking the entrance examination in two months. I would like to enter ENS ULM but it will not happen if I make such mistakes 😆

[restive wedge]

The second picture is my question and I have found the solution on gauthmath but can anyone explain what the person did to find the coordinates of C? I'm still confused

[drowsy oriole]

that's the only thing i could think @restive wedge

[torpid lake]

can anyone help mee

• differential equation orde two has 3 option

-id D<0, enterprise what will happen with the graph

[cinder yacht]

everyone makes such mistakes, don't worry abt it and good luck :p im at l'X

[left knoll]

Thanks and congrats for l'X!

[left knoll]

I need a tutor for math

[ember kernel]

Like, private regular tutor or just occasional one for moments when you have questions ?

[teal karma]

Help please

[candid moth]

Support the bot on Patreon!

Every little bit helps

[left knoll]

I'm writing f' = df/dx, R the set of real numbers and Z the set of integers.

For two differentiable functions f and g, (g(f))' = f' * g'(f).

The tangent function is defined for all x in R not equal to pi/2 + k * pi, k in Z. It is differentiable on this interval. Its derivative is 1/(cos^2) = 1+tan^2.
The sinh function is defined for every x in R. It is differentiable on this interval. Its derivative is cosh.

For (a), we have f = sinh and g : x -> tan(3x).

f is defined and differentiable on R.
g is defined and differentiable for all x in R so that 3x is not equal to pi/2 + k * pi, k in Z. In other words, x is not equal to pi/6 + (k/6) pi, k in Z. Its derivative is x -> 3/(cos^2(3x)).
In that case, the derivative of x -> sinh(tan(3x)) is x -> 3/(cos^2(3x)) * cosh(tan(3x)).

[left knoll]

For (b), we have f = exp and g = cosh + tanh.

tanh is defined for all x in R. It is differentiable on this interval. Its derivative is 1/(cosh^2)= 1-tanh^2.
cosh is defined for all x in R. It is differentiable on this interval. Its derivative is sinh.

Since everything is fine with exp, for all x in R, the derivative of x -> exp(cosh(x) + tanh(x)) is x -> exp(cosh(x)+tanh(x)) * (sinh(x) + 1/(cosh^2(x))).

[teal karma]

Thank you so much

[left knoll]

Welp

[cinder yacht]

they tend to justify much less that something is differentiable before computing the derivative, prépa is a quite particular thing lol

[mossy sigil]

hey can someone help me with maths?

[blazing urchin]

@mossy sigil I hope this helps :)

[blazing urchin]

@left knoll thank you ☺

[atomic dagger]

how do I find the inferior and superior limit to a sequence? Is there a specific method or is every case different

[left knoll]

There are a lot of methods depending of the sequence you are studying. The sequence you will have to study will depend on your level in asymptotic analysis. Sometimes you will have to use Taylor expansion, equivalents, the Stirling formula, Cauchy theorems, Cesaro theorems, etc. If you are studying sequences of functions and series (which are sequences too), there are much more methods but the easiest problems will rely on comparing the sequence to a known one (of which you know the limit).

[left knoll]

On the basic exercises, you can easily deduce the limit with equivalents (first term of the Taylor expansion) or using a Taylor expansion. You can also study the function associated with the recurrence relation (if you have one). But it is sometimes long.

[atomic dagger]

i see thank you so much! yes it's still confusing to me right now but I guess the more I practice the more I'll know what to use and when. Thank you!

[golden merlin]

A, B are vectors. If |A + B|= |A- B| , then vector A,B are

1. AxB
2. A.B
3. A=B

Can anyone help me understand this ??

[left knoll]

At least one of the vectors is equal to 0. Thus A.B = ABcos(A,B) = 0. AxB = ABsin(A,B) = 0. But A=B isn't always true. 1. and 2. seem correct.

[cinder yacht]

what?

first of all I don't understand the question, I don't think you copied it right @golden merlin

"vector A,B are AxB", "vector A,B are A.B" and "vector A,b are A=B" aren't valid sentences

[left knoll]

Yes, he meant equal to 0 for 1. and 2.

[cinder yacht]

and I think that by |A+B| = |A-B| they meant the norms? and in that case, |u| = |v| doesn't mean u=+-v

[golden merlin]

Do you understand now? Btw, the question is actually written in other language.

[cinder yacht]

for me i would say it implies
|A+B|² = |A-B|²
so |A|² + |B|² + 2 A.B = |A|² + |B|² - 2 A.B
so 4 A.B = 0
so A.B = 0

[cinder yacht]

okay now the question makes sense

[left knoll]

Thanks, sorry I was totally wrong, I didn't think about the norms

[cinder yacht]

I think the question was just not very clear :p

[ember kernel]

Hi ! Here's the deal :

(The dude had sent a friend request. These are dm's)

I get this kind of messages at least once a week (not counting actual math questions) and I'm getting sick of those
Please, don't do that.
Thanks for your attention

[delicate fossil]

guys how do i do this
im thinking of l'hopital rule but it hasnt been mentioned in this chapter yet

[cyan night]

can u explain further on that

im also curious

i cant seem to factor x^8+2x^2+x+2

what is first principles

f(x+h)-f(x)/h lim h-> 0?

this thing u meant?

yea

but i thought this is computing the limit

not a derivative

ok can you show me

i understand that

can you show me for that problem up there

ok

yea

yea l hopitals

it seems like it is indeterminate form infinity/infinity?

indeterminate form allows us to leverage L hopitals

the thing inside the brackets goes to infinity and the natural log doesnt really dominate

wait @left knoll quick question

im doing this

and it seems like none are correct

okay

it doesnt decay 0.5 grams after 29 years

it decays by a factor of 0.5

this is so wrong

this question

is so wrong

or is it me that is bad at english

okay

im here

im rereading

but

the strontinium 90 doesnt lose 0.5grams each year like option D) said

it loses exponentially not linearly

i think d) is saying that the sample loses 0.5 grams each year for 29 years

that is exponential

[cyan night]

this is linear

i dont have the answers

yes

but i think the question is referring to a lienar decay

or a linear reductino

but d) is saying linear

ok ill pick d because others are wrong

what happened

@still cloud 's messages got deleted

[delicate fossil]

ok tks guys i'll use l'hopital anw

[cyan night]

ok

[delicate fossil]

oh what he just disappeared

[cyan night]

yes

also @still cloud B) actually seems reasonable

0.5 of the sample is left after 29 years

[delicate fossil]

yeah id choose B too

[cyan night]

ok

[hollow mauve]

Pls help guys !

[smoky egret]

i'd choose c

no. b

[red spruce]

B IS right

ig

[smoky egret]

ye

[red spruce]

real good question tho

like i can find the rate , and all other types but this took time for me

[smoky egret]

same yeah

i chose c first but didnt read the number of

if number of was not written, i would've chosen c

[cyan night]

these questions have too many words

[smoky egret]

yes

i like these questions though, they're usually easy.

[cyan night]

yea its sat math

pretty easy

[smoky egret]

ye i know

im taking it this march

[cyan night]

good luck!

[smoky egret]

thank you :)

[cyan night]

sat english is very hard

for me at least

[smoky egret]

oh ye same

especially reading

[cyan night]

i always feel like ima score like 100/800

[smoky egret]

i know:(

when are you taking it?

[cyan night]

in a few years

im just in 8th grade

im just doing a test that the teacher require for me to get into his class

english class

[hollow mauve]

Guys? Pls try!

[cyan night]

sat english class

[cyan night]

which questin

[hollow mauve]

All of them

Try 10th and 8th first

they are easier

[cyan night]

okay

[smoky egret]

sorry, i dont know to prove stuff.

[smoky egret]

oo damn

nice

[hollow mauve]

There are finding sums also

[smoky egret]

good luck :)

[smoky egret]

okay. i'll try

[cyan night]

@hollow mauve may i ask which level math is this

[hollow mauve]

some questions from this paper are class 10th some are till standard 12th

11 12 is high school

[left knoll]

HI can someone please explain the concept of this integral part?

[cinder yacht]

[x] is the closest integer not bigger than x
[x] is the largest integer not bigger than x

[left knoll]

Well.. [4.999999] would be 5?

[delicate cave]

"not bigger than"

[cinder yacht]

5 isn't "not bigger than 4.999999"
so 5 can't be [4.99999]

[left knoll]

Okay alright

Thank you so much! @delicate cave @cinder yacht

[left knoll]

can anyone help ?

[neat osprey]

what do u want to do with it?

[blazing urchin]

@left knoll pls correct me if I am wrong but shouldn't c be the correct option?

[left knoll]

it is no need for explantion was just making sure

oh thx lol

[blazing urchin]

🤗

[left knoll]

ive some extra questions ill send them in few mins is that fine ? @blazing urchin

[blazing urchin]

Yeah sure@left knoll

[left knoll]

@blazing urchin

[left knoll]

nvm

[restive wedge]

So I'm given and equation which is y=6sin(3x+π/4) we have to substitute y=0 and work out the x axis intercept. Can anyone help me how this is done. I can't understand anything on the internet

[left knoll]

Substituing y=0 will give you the values of x so that f : x -> 6sin(x+π/4) intercepts the x axis (f equals 0).

Let x in R.
If y = 0, then 6sin(3x+π/4) = 0.
Thus, sin(3x + π/4) = 0.
Thus, 3x + π/4 = π + kπ, k in Z.

3x = 3π/4 + kpi, k in Z.

x = 3π/12 + kπ/3, k in Z.

x = π/4 + kπ/3, k in Z.

[restive wedge]

Yeah but please explain why equation became 3x+π/4=π

[left knoll]

Because it’s where the sinus function is equal to 0.

[granite shard]

you cansolve it if you observe that the function is 2*pi / 3 periodic so you gotta only work on [0,2pi/3] interval and then reproduce the shape, the curve of sin is known you ve got only to see when it s null and when it s maximum and then link the points to get a good approximation pf the curve , because the max and when it s null are the ones that give you a good approximation of how the curve looks like

[atomic dagger]

we want to integrate v(t) = ... , can someone explain to me how we obtain the result in the blue rectangle?

I obtain -vlambda * e^(-lambdat)

[cinder yacht]

exp(0) isn't 0
and primitive of exp(-lambda * t) isn't -lambda * exp(- lambda * t)

that's the derivative not a primitive

a primitive is - (1/lambda) * exp(- lambda * t)

[atomic dagger]

oh you're right i tried to derivate for some reason 😅 thank you!

[left knoll]

srry i got banned lmao

[cyan night]

wot

why

[maiden ember]

anyone here understand boolean algebra?

I am capable of doing it, but I just get lost at the start when given a large function. Im looking for someone to give me tips on how to start the simplification

[native dawn]

help

[maiden ember]

9+3 = 12 * 2 = 24 --> 48/24 = 2

No thats wrong sorry, 9+3 = 12 --> 48/2(12) --> 48/2 = 24*12 = 288

[native dawn]

kk

thx u

[maiden ember]

Anyone able to help with a boolean algebra problem?

part B my answer is acd' + b'cd'

[floral marlin]

Hello, can someone help me with this:
I have to write the equation of a tangent on the graph of y=x^(-2), which goes through the point T(0,12).

[gritty epoch]

is the answer ABC' + D ?

[cyan night]

first you can take its derivative with respect to x to determine the equation for the slope of the tangent line of the graph

wait

[warm badge]

What is the answer of this puzzle?

[floral marlin]

Yes, but if i take the derivative its y'=-2x^(-3) and if i put in the 0 of the point its 0... Doesnt match the answer... Idk really haha

[cyan night]

undefined

also

-2x^-3 = -2/x^3

x = 0 makes it undefined

[ember kernel]

It isn't -2x^(-3) that needs to be defined at (0,12), it is the tangent line of x^(-2)

They're not the same

A tangent is a linear function, which can be expressed as t(x) = ax + b and therefore it is defined everywhere

[cyan night]

oh

[ember kernel]

You just need to find the values of a and b such that :

1. t(x) = ax + b and f(x) = x^(-2) are tangent at some point.
2. t(x) goes through (0,12), which is just like saying that t(0) = 12

You've then got two equations, which is just enough to find the values of both a and b

[warm badge]

What about me guys

[ember kernel]

Hey hey hey be patient, your question has only been posted for 20 minutes

[warm badge]

I know 😭😭

[ember kernel]

Besides, I really don't understand how the puzzle works

[cyan night]

yea

me 2

[warm badge]

I guess it is like sudoku

[floral marlin]

So its b=12? And how do i get the first equation? Bcs if i do the derivative and put in the x of the point i get a=0, which isnt right
But thank u for help

[ember kernel]

Yeah b = 12

Now you want a such that f(x) and t(x) are tangent at some point x' (unknown for now)
That gives a = f'(x') = -2x'^(-3)

But now, you need to figure out where the intersection takes place (because two tangent functions have to intersect as well), which is at x'. To do that, use the formula of intersection
f(x') = t(x')

From there, you should be able to find x', and then a

[floral marlin]

But i have the point where the tangent is intersecting with f(x), its in (0,12)

So if i do f(0)=0, t(0)=12

[ember kernel]

No

The tangent goes through (0,12)

And the tangent intersects with f(x) at some point x'

But f(x) never goes through (0,12) (for it is undefined at x=0) so it's impossible for t(x) to intersects with f(x) at x=0

Just think of it that way

[maiden ember]

yes, but how did you get that? I used Demorgans to make it a SOP from a POS. Can I not do that?

[lucid hollow]

Can someone explain me why is the result 0? doesn't make any sense

[floral marlin]

Ohhh i get that now

[gritty epoch]

you dont need to
you can just expand normally and use the rules of boolean algebra

[ember kernel]

"f and t intersect at x' " means :
f(x') = t(x')
f'(x') = t'(x')

[gritty epoch]

theres no hard and fast rule that if you convert to SOP or vice versa, the simplification is easier
it all depends on the expression

[ember kernel]

How could that "not make sense" ? What step have you trouble with ? Be specific pls

[lucid hollow]

The result being 0

[ember kernel]

Yeah

Well -0.5 -0.5 + 1 = 0

Facts

[maiden ember]

thank you for the help i’ll try and solve it again

[lucid hollow]

🤦‍♂️

[ember kernel]

No no no

No facepalms here

Be specific with your question pls

[lucid hollow]

facepalm for me

i feel dumb now

[ember kernel]

Oh ok

[lucid hollow]

🤣

[ember kernel]

Yeah that happens don't worry

[lucid hollow]

Thanks for your help 😄

[ember kernel]

No worries

[gritty epoch]

yea try it again
if you want a step by step solution so that its more clear to you, lemmino

[floral marlin]

So i get a collection of quations, with a and x to solve...?

[gritty epoch]

think the answer is 6
cuz
(3+2)x2 is 10
(1+9)x2 is 20

so similiarly (0+8)x2 is 16

[maiden ember]

i sent pm if that is ok

[gritty epoch]

yea no worries

[hollow mauve]

try please

Please help with these, anyone?

[cinder yacht]

if you know the formula of a tangent of y=f(x) at point A, which is y = f'(A) * (x-A) + f(A)
the equation of the tangent of y=x^(-2) at some x-coordinate "A" is, knowing that dy/dx = -2x^(-3) :
y = -2A^(-3) * (x-A) + A^(-2)

we're looking for what x-coordinate A allows for x=0 and y=12 in that equation

meaning 12 = -2A^(-3) (0-A) + A^(-2)

so 12 = 2A^(-2) + A^(-2)
so A^(-2) = 4
so A^2 = 1/4
so A=1/2 or A=-1/2 (both work)
we can now replace in the initial tangent equation (for A=1/2) :
y = -2 (1/2)^(-3) * (x - 1/2) + 1/2^(-2)

so y = 16(x-1/2) + 4
so y = 16x-4

im a bit late but yeh I wanted to write the solution this way (which is basically the same idea as written in other answers)

[lucid hollow]

Can someone explain me this one?

Im confused

2x180/3 is 120

[left knoll]

@lucid hollow what r u confused about?

[lucid hollow]

why is it 2pi/3

[left knoll]

whats pi-pi/3

pi is 180

the answer for cos is negative

so it has to be in the 2nd or third quad

so for the 2nd quad u minus pi

or pi minus to avoid negatives

get it? @lucid hollow

[lucid hollow]

ohhhhhh i get it now

i was confused because 2x180/3 is 120

[left knoll]

it is

[lucid hollow]

but now i understand

[left knoll]

i meant for this

it is 120

[lucid hollow]

yeah i got it, thanks @left knoll

[left knoll]

alg

[floral marlin]

Thank you so much for your help!

[left knoll]

my son....

[buoyant stag]

Yall I need help please

It’s 11pm and due tomorrow and I can’t work out this maths question

[weary arrow]

I'm not 100% sure I understand what the question is asking, but I think you're supposed to find the mean for the boys, and then write the mean for the girls as a percentage of that: 35/X*100%. So if the mean for the boys was 100£ then the percentage would be 35%

[left knoll]

yea same i think thats how ur meant to do it although i do not know what the final column in the table is for

[buoyant stag]

yeah its pretty unclear

[fringe stratus]

Hey guys ! I got this question and I actually don't know how to do it. Any help is appreciated !

translation of the subject even if the words are pretty similar to english: Let (Xn)n∈N be a Markov chain on the state space S = {1, 2} with transition matrix
Calculate the probability shown, "et" means "and"

[cinder yacht]

since this is a Markov chain, u don't care abt old values of Xn
so that probability is equal to
P(X7=1 and X5=2 | X4=1)
and that's
P(X5=2|X4=1) * P(X7=1 | X5=2 and X4=1)
= P(1,2) * P(X7=1 | X5=2)
= P(1,2) * P^2 (2,1)

P(1,2) is 0.6

cuz line 1 corresponds to x=1, and column 2 corresponds to x=2

then for P^2(2,1)
u gotta compute the matrix P * P
and take the element in 2nd line 1st column

it'll be 0.48 if my mental math is correct

i have an exam in Markov chains (and martingales) today actually lol

[radiant venture]

https://discord.gg/4g8gkVmK

Use this server for Chegg solutions

[fringe stratus]

Thank you man, sorry that I made you do this as I found the answer like 30mins ago haha. Good thing is that I found the exact same thing !
Good luck for exam ! In which uni are you enrolled in in France ?

[fringe stratus]

For that you can simply square p2,1, it works too and it’s easier 🙂

[cinder yacht]

no it doesn't work like that

xD

squaring 0.8 doesn't give the right result

P^2(i,j) needs to be seen as "the (i,j) element of the matrix P^2"

the reason squaring p(2,1) doesnt work is that, it basically would mean :
p(2,1) * p(2,1)
AKAprobability of going from 2 to 1, then again from 2 to 1

while actually P^2(2,1) means "probability of going from 2 to 1 in two steps"
so that can be 2->1->1, or 2->2->1
so it's P(2,1)P(1,1) + P(2,2)P(2,1)
which is basically the definition of the element of coordinates (2,1) of the matrix P^2

[cinder yacht]

i'm in Ecole Polytechnique, you?

[fringe stratus]

oh shi yeah you're right lmao

[fringe stratus]

lets goooo, congrats !I gratuated from an economic analysis bachelor last year and I just started a second bachelor, this time in CS/Maths, quite struggling with all this maths ngl xD

[cinder yacht]

ohh, yeah its normal math is the hardest subject that exists imo lol, good luck

[strong lodge]

Hey guys, i have a question for Linear algebra.

Given the set (s)

How do i find the span of S?

[peak aurora]

Can anyone help me with the 32 number math? I'm not getting the concept, any video or link will help too

[cinder yacht]

the unit digit of a product is the product of unit digits
so when doing those products, only care abt the unit digit
for example in 17^3 aka 17 * 17 * 17, only look at unit digits
so from first multiplication only care abt 7*7 which is 49. but we don't care abt the 4 here, so let's think 7 * 7 = 9
so now the 17 * 17 * 17 is 9 * 7
so 63 so 3
so think of (17)^3 as just 3

for (24)^(5+2x)
thats like 4^(5+2x) = 4^5 * 4^2x
so 4^5 = 4 * 4 * 4^3 = 16 * 4^3 = 6 * 4 * 4^2 = 24 * 16 = 4 * 6 = 24 = 4
and 4^2x = (4^2)^x = (16)^x = 6^x
and notice how whenever u multiply 6 by 6,u keep the same digit unit : 6 (cuz 6 * 6 = 36)
so actually 6^x = 6
finally : 24^(5+2x) = 4 * 6 = 24 = 4

and for 36^6, well that's 6^6 for us, and we saw that 6^(anything) = 6, so 36^6 = 6^6 = 6

now that we got the unit digit of every one of those 3 big factors : the final result is digit unit of 3 * 4 * 6
so 12*6 so 72
so the unit digit is 2 if i didnt get it wrong

[peak aurora]

omg thank you so much! the answer is 2 yes

[cinder yacht]

what major is this? im curious

an MBA?

[peak aurora]

no. I'm from Bangladesh. Here we have to sit for an admission exam to get into our desired universities. I'm an aspirant for Bachelor's is business studies for which I need to sit for an aptitude test. So currently I'm preparing for this entrance exam

[cinder yacht]

oh ok

[ocean mesa]

Can anyone help with this set of questions ? The questions are in French tho

[left knoll]

ask mr coly

[ocean mesa]

Can u also help me ^

[opal pivot]

We wish to test the hypothesis that the average weight of a population of students is 60 kg. Using
σ = 6.4, a significance level of 0.5 and a sample of 32 people, find the following.
(a) Formally state the hypothesis test.
(b) The values of ˆx that would lead us to reject the hypothesis
(c) Do the previous calculation but for a significance level of 0.01 .

Can someone help me out with this

I understand a but there is no sample mean which is why I am stuck unless I am missing something

[near fog]

what can i do to learn calculus?

im having a hard time even understanding it

[sharp night]

3blue1brown has a series called the essence of calculus

I watched it even though I already had calculus and it helped me understand it a bit more I think

so maybe it will help u as well

[near fog]

thank you i'll go through it

[waxen storm]

how to do this please

[urban willow]

the denominator is the same

so sth with 5

idk im not good

trigonometry is hella hard too

[waxen storm]

bruh

[cyan night]

i think it leverages the identity 2sinxcosx = sin (2x)

A = cos (4pi/5) * cos (6pi/5) * cos (8pi/5)

= 2sin(4pi/5)(cos4pi/5)*cos(6pi/5) * cos (8pi/5)/2sin(4pi/5)

= sin (8pi/5)*cos(8pi/5) * cos (6pi/5)/ 2sin(4pi/5)

= 2sin (8pi/5)*cos(8pi/5) * cos (6pi/5)/4sin(4pi/5)

= sin (16pi/5)*cos(6pi/5)/4sin(4pi/5)

sin (16pi/5) = sin (6pi/5) because sin x is a periodic function

= sin (6pi/5) *cos(6pi/5)/4sin(4pi/5)

= 2sin(6pi/5)*cos(6pi/5)/8sin (4pi/5)

= sin (12pi/5)/8sin(4pi/5)

= sin (2pi/5)/8sin(4pi/5)

= sin (2pi/5)/8sin (2*2pi/5)

= sin (2pi/5)/16sin(2pi/5)cos(2pi/5)

= 1/16cos(2pi/5)..?

i may have made a mistake

but i can verify for you that the answer is equal to the question

[supple island]

idk if it helps but cos(4/5pi)=cos(6/5pi)

[cyan night]

o

o yeah cos x = cos -x

f

[cinder yacht]

better : imagine the trigonometric circle

[supple island]

you could also say that since cos(x)=sin(x+pi/2), cos(8/5pi)=sin(pi/10), using sin(2x)=2sinxcosx

[cinder yacht]

less confusion

[meager sleet]

can someone explain how to do this

[supple island]

sin(pi/10)=2sin(pi/5)cos(pi/5) but sin(pi/5)=sin(4/5pi) and cos(pi/5)=-cos(4/5pi)

so in the end we have -cos³(4/5pi)sin(4/5pi)

but idk if that's "the solution"

[cyan night]

hm

[cyan night]

4 is the common factor for i)
7 is the common factor for l)

[meager sleet]

but how does one fine that

[supple island]

well both 8 and 44 can be divided by 4

you need to find the maximum common denominator

that's it

[cyan night]

yeah so there are 2 variables that means the common factor must lie in the coefficient

if you ask how i found the highest common factor of 8 and 44 is 4 then its just through inspection

[meager sleet]

oh cheers

[cyan night]

ok i probably havent articulated this well because it couldve been 4xy + 2y^2

[cyan night]

so for example you have 2 terms

first you consider the variables of each term

if they have no common variables then the common factor lies in the coefficient

the coefficient is just the constant before the number

for example 4x, x is the variable and 4 is coefficient

you would want the highest common factor so that u can factorize fully

[meager sleet]

ah ok thanks

[west torrent]

How would I go about making 'z' the subject of the formula? I know it involves some integration🥲

[ember kernel]

Like T = z/m ?

Thus z = Tm

If that's not what you're expecting, then we need more details because I have no idea what you're talking about

[simple knoll]

can sm1 explain a function to me in a single line??

i just forgot what that means and its confusing now

[ember kernel]

A function is something that takes a number input x, and returns a number output f(x)

[solemn vessel]

^ such that each x has a unique f(x)

[left knoll]

how do i do part 2

[gritty epoch]

you just substitute x=22.3 in the regression expression and whatever you get as y is the predicted average brain weight

[left knoll]

why 22.3

nvm im an idiot

@gritty epoch can you show me how to do the entire question, i keep getting it wrong

ill send my working

as in post it here

[gritty epoch]

yep gimme a bit

[left knoll]

ok ok tysm

[gritty epoch]

Lemmino if the answer is right

There is a chance i may have done some silly mistake somewhere

But the formulae for least squares method is the same as wat ive done

[left knoll]

sir thank you so much your answer is correct, i salute you for your help and impeccable penmanship!!!

thank you once again!!!!!

[gritty epoch]

Happy to help mate

[green swift]

i don't if anyone's heard of the the riddle with the sailors and the seesaw but it would really help if someone could give a few guesses because i'm really stumped but i feel like googling it is copping out

anyways the riddle is "there are 12 sailors on an island, and they're all completely identical except one of them is different in weight, could be heavier or lighter. you have a seesaw that will break after 3 uses, how do you figure out which is the outlier also you can put as many as you want on one side or the other"

if anyone has any guesses feel free to leave one because i am completely out of ideas

[left knoll]

could anyone here explain me how i should study maths best? im in high school right now, i have six hours (out of 32) maths a week yet i dont even know how i should begin to study the subject

[gritty epoch]

Divide them into 3 groups of 4
Now choose any 2 groups and place them on the seesaw.
There are 2 possible outcomes

1. If the seesaw is equal then the 3rd group contains the heavier person. Divide those 4 into 2 groups of 2 and place them on the seesaw. Seesaw will tilt to one side. Take those 2 people and place each of them on the seesaw. You will get to know the heavier person
2. If seesaw tilts to one side, take that group and repeat the above steps. (Divide the 4 into 2 groups of 2 and so on)

[gritty epoch]

Practice practice practice
Thats the best way to get good at math

[green swift]

see this is the assumption one is heavier but what if they're lighter

[left knoll]

alright, thank you ill definitely start practising more. good to hear that its not just because im stupid lmao

[green swift]

tbh i would just take an aptitude test and see where you land

then study on the things you missed

and continue building from there

[left knoll]

ah wow wait yeah thats also something i should try out

aight thank you

[gritty epoch]

Ahhh overlooked that

[fervent tide]

Wow that was quite the brainpuzzle! The hint is that you need to keep track of which sailors are cleared of being lighter, and which ones are cleared of being heavier

[pulsar turret]

Can anyone help me solve this radical equation? The answer is 4 but I keep getting a quadratic equation.

[gritty epoch]

as far as my knowledge goes
from the quadratic equation you will get 2 answers, but only one of them will fit the equation
i got 4 and 39 as the solution
but obviously 39 doesnt satisfy the equation

hence 4 is the answer

[pulsar turret]

I keep forgetting that you have to check the solutions in the end! Thank you so much

[cyan night]

extraneous

[silver pier]

Can anyone check them if they're correct

[pine kindle]

Can someone help me how to make probability distribution table?

[pulsar turret]

Diameter of a Cone As sand is poured from a chute, it forms a right circular cone whose height is one-fourth the diameter of the base. What is the diameter of the base when the cone has a volume of 144 cubic feet? Round to the nearest foot.

The answer is 13 ft but I keep getting 23 ft

[opal pivot]

The theoretical probabilities of female and male births are 50% in each case, and consequently, they follow a Bernoulli probability distribution. We wish to test if these probabilities hold using a random sample of 100 births. Answer the following: (a) State the appropriate hypothesis test if we wish to test the theoretical statement. (b) Calculate the proportions of female births above which (and below which) we can reject the null hypothesis of a probability of a female birth being equal to 0.5.

[edgy sun]

what method of integration would you use for this

[random flame]

Heyo can someone help me with Q16? The numbers written in black pen are the answers. Ping if you do and thanks in advance!!

[gritty epoch]

You can take x^2=t and write the integral in terms of t
That way the 2x part will get canceled

And then integrate by parts

[edgy sun]

i get left with sin^-1(t)

how do i integrate that part

[gritty epoch]

By parts

Take u=sin^-1(t) and v=1

[edgy sun]

what would dv be

[gritty epoch]

I didnt understand your question

This is the integral by parts formula

Integral of v is x and differtial of u in 1/sqrt(1-x^2)

[edgy sun]

oh i was using this one

[gritty epoch]

If you use this then you will have to take v=x i believe

If you use the one i sent you can take v=1

[edgy sun]

which method for this one?

[gritty epoch]

You can write tan^2 as sec^2 (x) -1

Xsec^2(x) can be integrated by parts

[edgy sun]

would it be Xsec^2(x)-X

when u rewrite the tan^2

[gritty epoch]

Yes

[gritty epoch]

To find actual area you need to multiply 24 with 40000^2
For find the length you can just divide 8.6 by 40000

[random flame]

Wait so the ratio is actually 1cm : 40 000cm ?

I thought it was cm^2 instead whoop

Thanks man

[gritty epoch]

The units dont matter for a ratio

The scale just means 1 unit on the map is equal to 40000 unit in real life

[random flame]

Oh

Ohh okay

[gritty epoch]

That unit can be cm, m or km

[random flame]

I see okay thanks man

[green barn]

how do i go about this?

[ember kernel]

Trace y lny and picture what it'd look like in 3D, if it were an object and symmetrical around the y-axis

[cinder yacht]

id just like to say that the "horizontal" axis should be y
and the "vertical axis" should be z
and you draw z = y ln(y)

[olive trail]

Could anyone help me out with finding the area between these two curves?

[gritty epoch]

You want to find the area of shaded region of option c right?

[olive trail]

@gritty epoch Yeah the are enclosed by the given curves at the top

[gritty epoch]

So you need to find the x coordinate of the point where they intersect

[olive trail]

@gritty epoch This is my work but I’m getting the wrong answer

[gritty epoch]

Your method is right

I got the area as 0.126
Or 0.063 if you consider only one side

[olive trail]

@gritty epoch I’m sorry how did you get that? When I add everything together I’m not even getting a positive number lol

and do you think you could leave it in a whole number form

[gritty epoch]

Oh wait. Instead of taking limits like you did. Take it from 0 to pi/15

And double the answer

[olive trail]

@gritty epoch I tried that as well

[gritty epoch]

Cuz the area on the left side of the y axis will be counted as negative area so youll just end up getting 0 if you take limits from -pi/15 to pi/15

[olive trail]

Oh

[gritty epoch]

Thats what i did
Idk if wat i got is right but thats wat i got when i did it

[olive trail]

This is what I get for some reason

[gritty epoch]

Well u definitely shouldnt get a negative answer

Maybe you went wrong in the integration

Can double check using a scientific calc

[left knoll]

my lord look at the size of those integral signs

[olive trail]

@left knoll LMAO

🥲

[left knoll]

hahahaha bro but seriously those are like some big ass integrals. like damn they lookin fine 😉

@olive trail

[olive trail]

@left knoll honestly never even realized how abnormally large I drew them lol

[left knoll]

they sexy tho

[olive trail]

I will never draw an integral the same now

[left knoll]

lmao

think of me when you draw them @olive trail

[olive trail]

@left knoll fs fs

[left knoll]

HAHAHAHAHAHA I OWN YOUR INTEGRALS NOW

WHEN EVER U SHALL INTEGRATE, YOUR THOUGHTS I SHALL PENETRATE -OOGWAY

[crimson obsidian]

If i have to graph the quadratic y=-2(x-5)^2+10
i have the point (5,10) which is the vertex but how do i graph that? I dont have any other points

[left knoll]

u dont need any other points

u have the y intercept

which is 10
so u know the graph will pass through that

also u know the graph will be concave down since it is negative

in addition to this we know that a parabola is y=x^2

make that negative

shift it right by 5

dialate vertically by 2

and then move it up 10

follow the colours

they will lead you

[olive trail]

Would anyone know how to solve the equation in the box? I’m trying to find the intersection of the two curves.

[left knoll]

is that pi?

what is that

[olive trail]

yes

pix

[left knoll]

k give me a sec

haha get it

sec

sorry

[olive trail]

😦

[left knoll]

do you want me to write out the steps

?

[olive trail]

yes please

tysm

[left knoll]

give me like 5 mins

[olive trail]

ok

[left knoll]

wait and do u want complex solutions

or no

ill assume not

[olive trail]

no

[left knoll]

ok ill just tell u an easy way

instead of doing it algebraically

cause i didnt realise until now

cause im an idiot

tf

wtf is that

graph both of the,

m

them*

and then the intercepts are you solutions

only the x values though

cause ur finding x

@olive trail

get it?

the algebra is too finiky

[olive trail]

yeah thanks bro

[left knoll]

all good bro

gl with ur maths

anymore questions, you know what to do!

just think of me when solving ur integrals

[olive trail]

lol ofc

[grim sluice]

hi! how do I integrate tan^4(x/3)dx ?

[gritty epoch]

Write it as tan^2(x/3) x tan^2(x/3)
Convert one of them to sec^2 and expand

[grim sluice]

thanks!

[cyan night]

show us the algebra like a sigma

[atomic dagger]

question, how come we can say sin(1/n) is superior to 0 if sin(x) is comprised between -1 and 1 ?

[cinder yacht]

huh

do u mean :
how come we can say "for every integer n>=1, sin(1/n) >0" when we know "for every x€R, -1<=sin(x)<=1

"

?

the 2nd claim is so unrelated to the first though

anyway, the proof is : since n>=1, 0<1/n<1
and since 1<=pi/3, 0<1/n<pi/3
so if u look at it in the trigonmetric circle : 0<sin(1/n)<sin(pi/3)
so 0<sin(1/n)<sqrt(3)/2
(I proved a bit more than what u asked for : I proved its also smaller than sqrt(3)/2)

[ember kernel]

1/n is in the first quadrant if n is positive and big enough. So yeah sin(1/n) is positive then

[dry cypress]

To find the concave up and down only (-infinity,0)and (0,infinity) this interval is okay or do I need to mention about at x=-2,2 intervals of f"

[left knoll]

im confused what you are asking

[dry cypress]

😅

(-infinity,0)concaveup and (0,infinity)concave down is this the right interval for this function?

5+12x-x³ is the function

[left knoll]

no

its wrong

look at the graph

for the concave up part

[dry cypress]

I have to find the f"x in 2,-2 interval

[left knoll]

its going up to positive infinity

[dry cypress]

Right?

[left knoll]

what is the actual question that you are trying to answer

send photo

or copy and paste it

dont try to explain it or we will get no where

[dry cypress]

2nd one

The function is 5+12x-x³

[left knoll]

ok thank you

now i can help you @dry cypress

lets look at part a

concave up means a smiley face

right?

[dry cypress]

Yes

[left knoll]

we know both of the (arms of the graph lets call them) go up forever

correct?

[dry cypress]

Yep

[left knoll]

yea go ahead

[dry cypress]

Yes carry on

[left knoll]

ok ok

so as your graph is not just a parabola

we can see only one arm is going up forever

right?

[dry cypress]

No but it stopped at 2

At max

[left knoll]

yea yea but ur not getting my point

even if it stops at two

the arm on the left most side still goes up forever

[dry cypress]

Yeh

[left knoll]

so it will be +infinity for the concave up

get it?

and b will be the opposite

why did u delete the message

what do u not understand @dry cypress

im here to help

[dry cypress]

Okay I got your point

[left knoll]

ask me as many questions as possible

[left knoll]

are you sure

[dry cypress]

So in the left side it's concave up

And right side its concave down

[left knoll]

yes, think of it as smiley face

when graph is happy concave up

when graph is sad concave down

[dry cypress]

I asked the same thing

[left knoll]

concave means it caves in, so whatever side has the dent inwards and points up is concave up

[dry cypress]

But

[left knoll]

go ahead

[dry cypress]

Do I need to explain about -2 and 2?

I mean

[left knoll]

what do you think

[dry cypress]

If I put -2 and 2 at f" we can find 2 interval which is in -infinity,0 and0,infinity

To visualise the graph with intervals do I need to use -2,2

?

[left knoll]

why are you using -2 and 2

the only reason to do that is to find nature of stationary points

[narrow cosmos]

does anyone understand what the answer would be because I thought I could express a to be cos (theta) * b + sin(theta) * c. I don't understand where the magnitude would function into the equation

[dry cypress]

Yah

[left knoll]

concave up or down can be visually seen

[left knoll]

bro do u mind.. jk jk

[dry cypress]

I think I'm thinking way too much

[left knoll]

i think ur over complicating the question

[left knoll]

haha yea man

or woman

i dont know what u are

look do u want me to go through the whole question in dm with you

[dry cypress]

I just wanted to visualise the graph with concave up and down intervalz

[left knoll]

ok ok

[dry cypress]

No no I got it

Thanks!

[left knoll]

u sure?

[dry cypress]

Yeah

[ember kernel]

|a| is should be the coefficient of both terms

[left knoll]

and do u need help with part c @dry cypress

[narrow cosmos]

so how would i factor this into an equation?

that's my issue rn

[dry cypress]

No I know the ans but i was just overthinking about it

[left knoll]

ok ok and part c is good?

[dry cypress]

Yep

@left knoll thank you so much!

[left knoll]

ok ok gl man/woman!

[left knoll]

haha no worries !

[ember kernel]

|a| cos(t) x + |a| sin(t) * y
With x := b/|b| and y := c/|c| (unit vectors)

The presence of the |a| is plain trigonometry

[left knoll]

@ember kernel once your done helping lil chef is it ok if i ask you a phys question?

[ember kernel]

#science-help and someone will answer

[left knoll]

i tried no one answered 🥲

[narrow cosmos]

so I could express a to be equal to ||a||cos(theta)*b/||b|| + ||a||sin(theta)*c/||c|| would be a good way to express a

[ember kernel]

Double check that answer, but to me that looks correct

[narrow cosmos]

better way to express it by replacing || a | |

with what it was in question

[ember kernel]

I'm on my phone, can't type alpha

[ember kernel]

Where did you type that

[narrow cosmos]

symbolab

just for simplicity

| | a | | = alpha

[barren eagle]

hi can anyone help me with simple maths

it looks so easy but my minds gone blank

NVM GOT IT

[cinder yacht]

yeh

[cinder yacht]

im so confused by your explanation wth

[left knoll]

?

[cinder yacht]

@dry cypress
since f''(x) = -6x
a) the concave up interval is (-infinity, 0)
b) the concave down interval is (0,+infinity)
c) inflection point is x=0

[left knoll]

but look at the graph its self

[cinder yacht]

you said "it will be +infinity for the concave up"

[left knoll]

i understand the secodn derivative gives that interval but the graph literally opposes it

[cinder yacht]

this sentence means nothing to me

what is the interval there

in ur sentence

the concave up interval

[left knoll]

oh this, this was to demonstrate a point

no i wasnt defining the interval

all i was explaining was that the branch of soemthign like y=x^2 goes to infinity

thats all

not the interval

[cinder yacht]

the graph says the same thing as my answer

[left knoll]

bro what

[cinder yacht]

on the right side of x=0 it is concave down

on the left side of x=0 it is concave up

[left knoll]

yea

the left goes to infinity

[cinder yacht]

that's exactly what I wrote here

[cinder yacht]

that's not a great way of understanding "concave up"
for example log(x) goes to infinity when x-> infinity, yet log(x) is concave down

[left knoll]

i was just trying to explain what concave up meant

[cinder yacht]

then why did u say his answer was wrong there

[left knoll]

his def of concave up

ok miscommunication by me maybe

his interval is fine

[cinder yacht]

u also never mentioned the number "0" in the conversation, that's why I was so confused

even though x = 0 is very important there

[left knoll]

once again was not talking about the interval

i was trying to define the concavity

my apologies if my messages were a bit complicated to understand

@cinder yacht may i ask something from you

if you dont mind

[cinder yacht]

yeah?

[left knoll]

could you help me with a physics question?

[cinder yacht]

im about to sleep but what is it?

[left knoll]

ok ok tysm

[left knoll]

its in the science chat

just to save ur time

i just dont know where i have goen wrong

tysm again!

[dry cypress]

Thanks @burnt geyser !

[olive trail]

Hey does anyone know if the radius here is incorrect? Shouldn't it be y-1 not just y?

This is the solution that came with the textbook, but the integral is going from y=1 to y=3 so I don't understand how the radius is just one

*y

[crisp lodge]

(2x + 3y)^2– 2(2x + 3y)(3x – 2y) – 3(3x – 2y)^2

Hint: Put 2x + 3y = a and 3x – 2y = b

plz help me to get the ans

[random flame]

Are you trying to solve for x and y or simplify the equation?

I’m tryna solve part a but the question doesn’t make sense-
Ping if ya do help and thanks in advance!!

[edgy sun]

what would be the formula for 19b?

[random flame]

Try converting the months into x years? Like eg if it's 2 months then it's 0.166... years then sub in to the compound interest formula
I hope this helps in some way-

[edgy sun]

isnt it asking to find the amount of time

[random flame]

Oh crap sry

Are you allowed to use log?