math-help

[ember kernel]

hehe

[worn mist]

what if the bots like limited

to commands/day

[ember kernel]

Maybe it's due to a modification of its rights, and it can't write in the how-to channel anymore

[worn mist]

YES I FORGOT ABOUT THAT

[ember kernel]

Haha

Yaaay

[worn mist]

amazing

oh okay it also works with 3

cuz it changed when I changed the message

[ember kernel]

Apparently, and it also auto-corrects if you change the source message

[worn mist]

there we gooo

https://tenor.com/view/noice-nice-click-gif-8843762

[ember kernel]

Again, thanks a lot for the bot and everything, it'll be much easier to provide clean answers 😁

[worn mist]

No worries :))

[covert anchor]

What on earth is this

[left knoll]

Optimization

[covert anchor]

what

how what do id o

[left knoll]

Well

You need to create an equation for the volume

Then take the derivative of that volume equation

Then set it equal to zero and solve

You’ll get the maximum volume that way

At least that’s what I remember from first year calc

[covert anchor]

how do i eve do part i

[left knoll]

So

Volume is base * width * height

Length** not base lol

A way

Anyway

Length is equal to 30 cm

However

Since you have two squares of length x cut out

The actual length is 30-2x

The width is 42cm but without the two squares it’s 42-2x

Then the height is just x

So multiply them all together

(30-2x)(42-2x)(x)

Simplify

And that’s your answer for part one

[covert anchor]

oh ik

ok

cool

[left knoll]

Yeye

[covert anchor]

then how bout b

ii

cuz im really lost

[steel plover]

what's the reason for the writing the one above ^^ as x^2/a^2 + y^2/b^2 = 1?

[polar quiver]

If you've done calc which I assume you have done since you are doing optimisation - when we find the first derivative's we often find two values (and most commonly, these values are a maxima or a minima). You must find if they are a maxima and minima by finding the second derivative, or f''(x) - and then plug the values you found in the first derivative. If the value is negative, then it's maxima, if positive, it's minima, and if it's zero, it's a horizontal point of inflection. Then, you put the mnima as and and maxima as b, a<x<b as the question requires.

[polar quiver]

Theres also another method of finding the maxima and minima, which is simply by testing the points directly next to each stationary point - and if it is neg->pos, then it's a minima, and if it's pos->neg then it's maxima (/-\ is a maxima, -/ is a minima :))

[graceful peak]

please help

[left knoll]

could someone help me, please

[ember kernel]

⬆️ Here's the answer for the second question. Unfortunately, I can't remember precisely enough how to prove bjection without going through Linear Algebra

(About the second equality of the second line : I just separated the numerator and denominator of the bigger fraction to express the two smaller fractions as big ones)

(About the first equality of the third line : the two (x-2) merely cancel each other out )

[opal flint]

There is this corollary of the intermediate value theorem that if a function is strictly monotonous on an interval, it establishes a bijection from it to its image

[ember kernel]

Oh riiiight

[ember kernel]

⬆️ We get the product of 3 consecutive positive integers. Thus, we know for sure that one of them is a multiple of 2, and that another one is a multiple of 3. Since these two are multiplied, we know that their product will be a multiple of 6. Multiplying with the last integer just gives a bigger multiple of 6
(ie : 234 = 6*4 is a multiple of 6)

@graceful peak Don't forget the conditions of existence of f and g :

[left knoll]

ohh thanks!!

[left knoll]

t is a positive whole number.
the expression 2t^2 + 5t + 2 can never have a value that is a prime number.
explain why.

help pls

[rustic shuttle]

you can separate (2t+1)*(t+2)
If it can be divided by two numbers, it isnt prime

[rustic shuttle]

.

[left knoll]

oh tysm

[left knoll]

which letter comes after S

pls tell me

im stuck with that question

[pearl crow]

Here in Brazil after S comes T

[light snow]

Yoooooo the Mathbot is the revolution

[ancient epoch]

mathbot rules

[bold dagger]

Can anyone provide me some pdf or something like that on the life history/biography of Euclid?

[left knoll]

can someone solve this

[burnt shoal]

I need help with the yellow part.

[glad sierra]

https://www.youtube.com/watch?v=7mYDHbrLEQo

a very useful video
and a useful channel (this video wasn't easy to find in general)
but if you're learning stats or anything that touches it
these concepts are going to be super helpful in the future
channel name: jb statistics

[steel plover]

can someone explain how taking the natural log of 1/2 gives -ln 2?

that's the question

[glad sierra]

because ln of 1/2 = ln 1 - ln 2
ln1 is 0, so they wrote - ln2 directly

[steel plover]

ohh thank you I missed that

[ember kernel]

The green arrow is just to show that you integrate from x² to 2x

[proper sail]

I am stuck on this question at the place mentioned in the lowest picture.My main confusion is where did the negative sign came from which is multiplied with t times dt.please help!!

[ember kernel]

It's because -dx/x(x+1) = dt
Thus dx/x(x+1)(what you have before the change of variable) = -dt

@proper sail

[peak gale]

Maybe you can try : u²= x²-a²

[craggy plume]

How do you simplify it from the second step to the third step?

[ember kernel]

⬆️ [Steps above] Just add the initial denominator (3+x)² back to the fraction and there you go

[craggy plume]

Thank you so much!

[ember kernel]

No worries 😁

[mental snow]

Hi... we can try to substitute x = 3 tan^2 theta and proceed and then put it back

[left knoll]

Hope you get it ☺️.

I dunno what it's called but I call it LCM method 😅

[tawdry dagger]

PLEASEEEEE .. if u can plz post the answers with a photo 😄

[dusky heart]

is it??

[left knoll]

@tawdry dagger

[tawdry dagger]

@left knoll THANKS DUDe, can i send some more plz ? if ur busy then its ok

A photo of the anwers would be nice 🙂

[left knoll]

i feel like my answer’s wrong, could someone help me?

[hollow portal]

What is the answer

[proper sail]

Please help in this question!!

[heady tree]

y= f(x-6) no? translation of six units right?

[heady tree]

you're right (unless u want working)

[mental snow]

integral sinx from 0 to 2pi is 0 and for |sin x | it ll be
2 times integral from 0 to pi sinx as mod sin x will repeat itself from pi now
so thats 2 x (- cosx) limit 0 to pi that is
2 x ( 1 - [-1]) -> 2 x 2 = 4

[peak gale]

there is, define a positive value alpha for Uo, and try to construct recursively the others terms, a pattern will appear.

[left knoll]

ohh thanks, i got confused lol

[peak gale]

your terms depend on Uo (or Uk according to you first term), and you will a have powers and sums

[heady tree]

haha all good but yeah -x reflects across the x axis not the y

[proper sail]

@mental snow thanks man

[mental snow]

😄

[left knoll]

For duals change sign of "or" to "and"& "t" to "c" thats it.

[ember kernel]

It is. The answer is y = f(x-6), because you shift the graph horizontally 6 values to the right

If it really were y = f(-x), the graph would symmetrical around the y-axis, which isn't the cass

[left knoll]

tysm, i get it now x)

[craggy plume]

mmm I get everything else but how did -5sqrtx went straight into -10x doe

[left knoll]

Like 1/2 + 1/4= 3/4

[craggy plume]

ohh thankss

[dusky heart]

thank you so much , i was able to transform my series into this, i just can't proceed further :(...

[peak gale]

Are you sure for your calculation?
I think you can prove it by observing a pattern after calculating the first terms of the sequence, and then prove it by recurrence by using the relationship between Un and U(n+1)

[tawdry dagger]

😮 thanks man

[left knoll]

All good man 😃

[proper sail]

So this is my question and my solution can anyone please point out where is my mistake as the real answer is 1/3 in Answer key ???

[rustic shuttle]

In the last image, the first part is 1/2, not -1/2, and the last part is - 1/3 -1/3 not +

[proper sail]

How ?

YOU are kind of right it will give answer as 1/3 but how?

[rustic shuttle]

integrating (-x^2)/2 from -1 to 0 would be (0^2/2) - (-(-1)^2/2), that would be +1/2

And (x^3/3) is right but there is a MINUS before, so everything becomes negative, so -(1/3 -(-1/3)) would be - 2/3

[proper sail]

Oooh thanks I got my mistake

[craggy sinew]

Hey anyone here good with stats

Trynna figure this out

[rustic shuttle]

Is it 89,44%?

[rustic shuttle]

.

[craggy sinew]

It was

@rustic shuttle

But now I’m stuck on the next one

Wasn’t sure if I use the same principle

[rustic shuttle]

What's the next one

[craggy sinew]

I did z = 30-32 / standard dev / sqrt(n)

then P(z)

[rustic shuttle]

i would also multiply the probabilities of those 5, cuz he said none of the 5 plants, so it's P(z)^5

[craggy sinew]

so I'd just take 30-32 / standard dev, get the Probability of that z score, and put it to the 5th power?

[rustic shuttle]

idk if just standard dev or divided by sqrt(n), i would do just standart dev

[craggy sinew]

aight thanks, my exam boutta start so pray for me LMAO

[steel plover]

in the final ans, shouldn't it be log(base 10)of 2 instead of log base 2? I feel like the answer given is wrong but I'm not sure

[weary arrow]

The formatting must be wrong, as it says log_2 of nothing. It is probably meant to be pHdil=pHorig + log(2)

This makes sense as the final equation they've just changed -logH+ into pH on both sides of @steel plover

[steel plover]

I see I thought so. thanks for clarifying

[narrow bronze]

Guys what is fabiocci series ?

[heady tree]

Fibonacci? add previous two numbers together to get next one in sequence

so its like 0,1,1,2,3,5,8,13,21...

[left knoll]

Hii can someone show me how to do this question please? Thanks :)

[tawdry dagger]

a photo of the anwerwould be helpful "D

[main locust]

Can someone please help me with this question? I don’t understand why the answer is 1/72 instead of 1/216

[heady tree]

i mean i can give it a shot cuz noone seems to be on today lmao but ima preface this by saying i had to look up what a geometric progression was so if anyone with more iq than me says otherwise go with that then 👀

the way i went about it was by finding the ratio by equating the three possible angles to pi

there was an unknown x value that was either x/x^2 depending on where the π/4 was placed in the order

so yeah i think the underlined x=_____ are the three ratios you can substitute in for the x values depending on the respective location of the π/4 in the equation above them

i tried it out for √13/2 - 1/2 and i got like π minus something * 10^-6 or something (and i think that might be cuz my calculator cant hold that many digits or something but yeah)

again not entirely sure if what I did is even in the right ballpark so

👀

[mental snow]

because there are 3 ways in which that can happen

5 5 1
5 1 5
1 5 5

so we have to multiply by 3

3 x 1/216 = 1/72

[heady tree]

conditional probability

[main locust]

Oh i see thank you 🙏

[proper sail]

Please help with this question!!!

[mental snow]

we can take lcm for x^2 and make a quadratic
the quadratic would look like

3x^2 - x - 1 = 0
and then we apply quadratic formula

[mental snow]

dVol/dt = 4 pi r^2 (dr/dt)

dVol/dt = 4 pi 6^2 (2)
dVol/dt = 288 pi inch^2/sec

[heady tree]

sorry its a bit dark lol

[left knoll]

Use Snapchat filter lol

Just kidding

[proper sail]

@mental snow thanks man

[ember kernel]

Use respectively u = 5x-7 and u = 3x+1,
You'll get :

[tawdry dagger]

thanks man 🙂 why is it so dark tho lol no offense

[tawdry dagger]

thanks 😄

[heady tree]

i was tryna get rid of the glare lmao

[tawdry dagger]

LOL its ok 🙂

[main locust]

Hello can someone please help with question 11?

I saw a similar question (2 in this picture) so i though i would do the same thing. however doing (5 0) + (5 1) + (5 2)

but i get 16 rather than 2944. what am i doing wrong?

[heady tree]

are you accounting for the fact that you can have either 0, 1 or 2 As?

[main locust]

@heady tree I am accounting for 2 As. I was just using the second pic as kind of a reference to see how i can attempt the question 11

[mental snow]

Hi
for Q 11

I tried like this
all passwords - (passwords which have all letters A + passwords which have 4 letters A + passwords which have 3 letters A)
5^5 - (1 + 20 + 160)

3125 - 181 = 2944

[main locust]

Oh i see thank you. Thank you. Do you perhaps know why the second pic was able to get the answer using combinations but question 11 can't?

[mental snow]

Yayyy, Oh ok, for the second picture when we place the 1's in their places, in all other places we just have 0 to put so no arrangement among them, they all are the same but in the question above we have to account for the arrangements of other letters as well i guess

[main locust]

Ah makes sense. Thank you

[mental snow]

😄

[tidal raven]

hiiiii can someone help me with this statistics assignment? i'm so confused what test should i do... should it be ANOVA or regression? here's the question: "Which of the following variables can be an independent variable to explain the variation of gross_per_earner (gross annual income per earner)? Explain why or why not. Or both?

1. Marital Status
2. Labor market status
3. Work status
4. Industry
5. National origin
6. Family size
7. Number of families
8. Number of earners
9. Geographic area
10. Educational attainment"

thank you so much in advance!!!

[graceful peak]

please help with this question

[untold pasture]

5 * (lvl ^ 2) + (50 * lvl) + 100 - xp

[weary arrow]

Level? What are you trying to ask here, I'm notbsure I understand 😅

[untold pasture]

just a math question

[weary arrow]

Can you post the whole question?

[untold pasture]

the question's paragraph is in turkish

¯_(ツ)_/¯

[weary arrow]

Ah rip

Maybe you can translate the whole thing, or maybe someone Turkish can help you😅

[untold pasture]

yeah, thanks

[tawdry dagger]

A photo would be nice 😄

[urban grail]

integrate it once, and put +c as well
then put the given condition of f(0)=3, so find c
that will give you f(x)

[tawdry dagger]

can u post a pic plz 🙂 if u cant then its ok 😄

[polar quiver]

gimme a minute ill do it for ya

@tawdry dagger there u go mate

[tawdry dagger]

THANKSS MANNN

[glad sierra]

is the easiest way to test this through trial and error? or any other method exists?

[lofty arch]

As in testing the limit?

as you take n to infinity, you can approximate the fraction by just taking the highest powers of n

so we can say that as n -> infinity, (2n-1)/(n^2) approaches 2n/n^2 = 2/n, and for large n this tends to zero

[glad sierra]

well im not sure tbh
it just concludes that it tends to zero
how do i test that it tends to zero?

do i integrate wrt n?

[lofty arch]

This is all that's needed!

for limits at infinity of a polynomial, you just ignore all terms other than the highest power of x

Think about it this way,

if you want to take the limit as x-> infinity of x^3 + x^2, then for large x, x^3>>>>>>>>x^2

[lofty arch]

And for a fraction made up of polynomials, we just do this to both the numerator and the denominator

If that's making any sense?

[glad sierra]

are we just looking at the terms 'n' here?
for example
doesn't matter if its 5n-1/ n2 or anything
just isolate the n?
and then it becomes n/n2 =1/n ?

if it was 5n^2 - 1 / n^3, then it becomes n^2/n^3 = 1/n ?

[lofty arch]

You still keep the coefficients, sorry

so it'd approach 5n^2/n^3 = 5/n

[glad sierra]

Ah, sounds fair then
so in the question i posted, it's 2n/n^2 = 2/n ?

[lofty arch]

Yeah, just fixed that up now

Which is still zero as n tends to infinity

[glad sierra]

alright no worries
really appreciate the explanation !

[lofty arch]

if we had something like n->infinity 5 +(6n^3)/(2n^3 + 3n)

that'd just be 5 + (6n^3)/(2n^3) = 5 + 3 = 8

All good!

[glad sierra]

ohhh
so we take the highest powers in the num and den
not ALL the n terms
so we chuck 3n here

gotcha
thanks man
you've been of great help to me ❤️

[tawdry dagger]

a photo of the answer would be helful 😄

[heady tree]

whats the question asking though

find x?

or like prove stuff or what

👀

[ember kernel]

For all, remember the identity ⬇️

[ember kernel]

But remember that, since x is in a log, then it must be positive

You finally get the answer 0 < x < 9

@tawdry dagger

But beware, you may need to switch the inequality signs in some cases

[tawdry dagger]

X 😄

[tawdry dagger]

:I thankss mann u really helped me a lot

[glad sierra]

anyone know a fast way to interpolate?

apart from the traditional formula?

[ember kernel]

What's the "traditional" formula ?

[cerulean walrus]

hi..can anyone help me with this plz? :(

[rustic shuttle]

2 days before, so 28th

[cerulean walrus]

i've thought about that..but how can i prove it🥲

[glad sierra]

y2-y1/x2-x1 * x-x1 + y1 = y

[rustic shuttle]

Size(days)=(initial size)* 2^(number of days), since it doubles every day
if size(30th)= initial size* 2^30= Full lake,
initial size* 2^30/4= Full lake/4
initial size* 2^28= full lake/4
so, 28th day

[rustic shuttle]

Something like that but with a better notation lol

[cerulean walrus]

yow..thank uu!

[ember kernel]

I may be wrong, byt I honestly don't think there's any other formula/way to interpolate 2 points with a first degree polynomial

[rustic shuttle]

Agree, two points make a line, so there would be only one formula for it

[rustic shuttle]

What you can also do is get the angle and the point where it intersects with y,
so it would be y=(angle)*x+(point of intersection with y), but it's kind of the same thing

[glad sierra]

i mean, if thats the same concept then haha no worries

thanks both ! appreciate you replying 😄

[ruby tinsel]

Could someone plz help me with this🥲 !!!!

[left knoll]

hi

anyone

[rustic shuttle]

integrate ae^(-bx) from 0 to infinity, equals to 1 (cuz prob density function)
it wil be -(a/b)* [e^(-bx)](from 0 to inf) = 1
0-(-a/b)=1
a/b=1
a=b

[ruby tinsel]

got it thank you!!!

[opal pivot]

can someone help me with this question

For what values of the numbers a and b does the function f(x)=axebx2 have the maximum value f(2)=5.

f(x)=axe^bx^2

[ember kernel]

@opal pivot Is it that function ? ⬇️

[opal pivot]

yes

i don't know how to solve this kind of question

[ember kernel]

I'm on it

[opal pivot]

thank you

[ember kernel]

If you can't read, notify me and I'll send you a better shot

[opal pivot]

thank you

[shell hamlet]

hey can anyone here help me with probability and statistics?

[tawdry dagger]

Algebra of Logic 🙂 a photo of the answers would be helpful 😄

[left knoll]

may some explain why shear force at section c is -1.5kN instead of 1.5kN?
Thanks ;-;

[wild rover]

If they pick 75 apples, and have six bags, how many different ways can the apples be assignedto the bags?

Assume that they pick 19 Pink Ladies. Both Alice and Bob really like the Pink Ladies, sothey want each of the six bags to have at least two apples, how many different ways can thePink Ladies be assigned to the bags?

Bob picks 32 Cortland apples and has them in seven bags. He bets Alice, without looking atthe bags that two of the bags have exactly the same number of apples. Will he always winhis bet? Why or why not?

[left knoll]

Not sure about 2nd question

[brave prairie]

i can help with probability..which grade tho???

[shell hamlet]

it's probability for CS

@brave prairie

[brave prairie]

ohh okay m not sure but can u send me 1 or 2 questions

i'll let u know if i'll be able to solve

[brave prairie]

ohhhh

oop

damn this is difficult..m in grade 10, icse

[shell hamlet]

oohhhh ooppp

[brave prairie]

sorry :((

[shell hamlet]

that's ok bud

i appreciate it

[brave prairie]

: )

okaye

[tawdry dagger]

ARIGATO! THANK U ! whAAT ARE U!? u know almost everything !

[fervent tide]

I'm unfamiliar with the concept, but I assume the Bernoulli in the name means that a maximum of one job can enter the queue in a frame

P_A = 0.2
P_S = 0.3

P_decrease: We have to have a service without having an arrival in a single frame for this to happen
Therefore we must find the product of these two happening, which is: P_S * ( 1 - P_A)

P_increase: We must have an arrival without having a service for this to happen
Therefore: P_A * (1 - P_S)

P_nochange: There are two ways to achieve this; either by having both an arrival and a service, or by having neither. Therefore we need the sum of these two probabilities.
ie.: P_A * P_S + (1 - P_A) * (1 - P_B)

[shell hamlet]

great! thanks!

[fervent tide]

👌

[tired shuttle]

does someone know how to calculate the weighed harmonic average when only an amout of cars and their speed is given?

[heady tree]

can probability density functions be for discrete random variables, or are they only for continuous random variables?

[lofty arch]

PDF’s are only for continuous random variables

You use a probability mass function for discrete RV’s

For a PDF you integrate for the CDF, while for a PMF you take the sum for the CDF

[heady tree]

yep got it, thanks

[fast nacelle]

Can someone tell how the answer is 0??

[ember kernel]

Is n a real value or an integer ?

If n is real : the given answer isn't valid
If n is an integer :

[ember kernel]

And it it thus substracted by the second cos(nc)

[fast nacelle]

Oh now I understand

It was so easy but idk why didn't get

Thank you so much buddy

[ember kernel]

No worries 😁

[bleak pendant]

Ples help

[ember kernel]

Replace S by (A+B+C)/2 in all the sines, apply Simpson once (to the first two sines), simplify, apply Simpson a second time (including the remaining sine), then simplify again

@bleak pendant

For the last sine, use the identity -sin(x) = sin(-x)

[proper sail]

Please help as I don't know what to do after this in my calculation !!!

[ember kernel]

Using the formula of the differentiation of a product :

[ember kernel]

4th line : you get 81uv^{80}*v' via :

• Power rule ( for the 81 v^{80} )
• Chain rule ( for the v' )

On an unrelated note, are your notes from someone else ? Because I always see that the correct answers are circled, even though you haven't solved the problems yet.

(That's just out of curiousity, no judgement or anything 😅 )

[mental snow]

distance = 8m
displacement = 4m

[tawdry dagger]

DAMn that was fast @mental snow

[mental snow]

haha yes the timings were nice u just posted and i just opened discord

[tawdry dagger]

😄

i got some more too 🙂

[mental snow]

displacement depends on final and initial positions only
whereas distance is the actual distance that was traveled during the journey

[tawdry dagger]

ooooooh yeahhh

[mental snow]

ohh sure

[mental snow]

a. t = 12 seconds
b. Tmin = 5 sec Min Posn = -4m
c. we'll plot the given equation -> it ll be like a quadratic graph with roots at t = 12 and t = -2 (negative value of t is not possible so we wont draw for that )
d. 21 and 12
e. -9 m
f. 41 m

please check the answers

[tawdry dagger]

Thanks man ❤️

[mental snow]

for e and f part we plot this graph and see the distance and displacement

okie dokie gotta go see u 😄

[mental snow]

😄 yayy

[tawdry dagger]

😄

[mental snow]

a. 2m/s
b. 2m/s

[tawdry dagger]

ur fast af @mental snow

[left knoll]

Differentiate wrt to t

[tawdry dagger]

😮

[tawdry dagger]

thanks

[left knoll]

V= dx/dt and a=dv/dt

If you want pic of solution I'll send it

[tawdry dagger]

PLZ DO 😄 @left knoll

[ivory pumice]

[40×0.301]+ 1

[log n] + 1 []- integral part

[left knoll]

Take log and add 1

[proper sail]

@ember kernel I try to solve the questions on my own first then I ask you.About the circled answers I mostly also circle the correct answer as in msqs you can back solve from the options but this doesn't work everywhere so I need to ask you.

[brave ledge]

does anyone know how to solve this equation?

mine C but im using calc for calculate the log

[brave ledge]

the question find X

[proper sail]

So I was trying to apply this formula but I don't know why it's not giving me y^2 in any answer. Please help!!

[spring ore]

https://www.youtube.com/watch?v=Zy6VBqdrDD8

[proper sail]

Thanks

[late thunder]

Thenksss

[proper sail]

Ok please help as I don't know what to do after this and I don't know why my calculation is going towards an answer without ln.!!!

[left knoll]

Is A the correct option?

[left knoll]

We have to use logarithmic differentiation

Not product rule

[bright needle]

Agreed

[bright needle]

Option B is correct

[proper sail]

A is correct

[left knoll]

Lemme send solution

[bright needle]

Sorry yes didn't see the options properly

A it is

[proper sail]

Ya they seem close so it's easy to get confused

[bright needle]

Yah

Where are you from

[left knoll]

@proper sail

[left knoll]

Mathematics with chemistry lmao

[proper sail]

Ya I was also looking at benzene molecules

[left knoll]

Dunno much about reactions 😅

[bright needle]

I messed up in the formula

[bright needle]

I tried this but my and didn't match the options

[ivory pumice]

You can't get log(-ve number)

Check calc

[ivory pumice]

You did wrong in 3rd line

√(3-2√2)= +-1/√(3+2√2)

like x²=y²

x= +- y , I think you will get the correct answer

[lilac ruin]

can you guys help me with this?

Find the minimum value of the function f(x)= (tanx)' -8tanx +8

I tried but I can't solve

[heady tree]

Fairly sure it doesnt have a min

👀

Holup calc in radians :/

Bot moment

[rustic shuttle]

i think the first tan is a derivative, so it would have a min

[ivory pumice]

Use chain rule , it would be c

d(sec²x)/dx = 2secx.(secx.tanx)

[proper sail]

@ivory pumice OK thanks

[bright needle]

Yeah but it won't matter as -ve inside a root is imaginary. So I would be taking the positive term only

[proper sail]

Ok so I am stuck on this question so I found this formula of instantaneous rate of change on internet but I don't know how to apply it and if you have a better and more easy way to do this question please suggest that too!!!

[glossy summit]

Q3 ii help please

[ember kernel]

The link between the two formulas (the one in the question and the one in the picture) is x = a + h

Thus it's f'(a)

[ember kernel]

It doesn't have a global min, but f does have local minima

[proper sail]

@ember kernel can you show working somewhere I didn't understand how you got the answer?

[gentle axle]

Am i doing something wrong here? Trying to work out y intercept and it just seems wrong

the question is Find the equation of the line passing through the p oints (1, 7) and (−1, 1), and determine the x- and y-intercepts of the line

and im currently trying to find the y intercept

[ember kernel]

You used (-1,7), instead of (-1,1) or (1,7)

@gentle axle

[ember kernel]

In the formula in the picture, replace h by x - a, since x = a + h.
And there you have the formula used in your question

[gentle axle]

omg im an idiot thank you

[ember kernel]

@proper sail Both ways of writing the definition of derivative are valid (with h & a, or with x & a)

[proper sail]

Ok

Thanks

[weary arrow]

Is it possible to get more context?

To me it looks like an S, and e or o, something I can't decipher, and a y

[uneven pulsar]

ok

1 sec

@weary arrow

[weary arrow]

Hmm

Hard to say, but I don't think it's that important

[uneven pulsar]

ok thx

[uneven pulsar]

is shrink vertically as sketched horizontally?

[left knoll]

Guys

Imma test something

So don't say me dumb

Huh

[left knoll]

Wat

[terse swan]

hey can someone explain how this happens? i'm confused how 2^k + 2^k = 2^(k+1)

[terse swan]

pls helppp 🙏

[fervent tide]

2^k + 2^k = 2 * (2^k) = 2 ^(k+1)
This only works because the base is 2

[ivory pumice]

It's say, like we are assuming sinx = g(x)

[terse swan]

thank you

[thick pine]

nice

[cyan night]

what should i study in math if im going for HL math IB?

im in 8th grade

[proper sail]

Please help in this question I did it but I don't know where my solution is taking me!!

[left knoll]

@proper sail what is i here

@proper sail btw you didn't use log property properly (log A^x= xlogA)

[proper sail]

Iota

[left knoll]

@proper sail

Differentiate and get your answer :)

[midnight gazelle]

Can someone help me convert this into Latex?

[proper sail]

@left knoll OK thanks

[loud kiln]

\frac{x^m}{x^n} = x^{m-n} like this?

[midnight gazelle]

I'll try this

[ember kernel]

I've always been wondering what y_2 means ... 🤔

[midnight gazelle]

Thank you it works

[ember kernel]

Because if it means d²y/dx², then the answer is (c), but the notation seems bad to me

@proper sail @left knoll

[left knoll]

I guess y2 means y''

Not sure tho 😅

[ember kernel]

Yeah that's what I thought

[ember kernel]

i is the complex number such that i² = -1

Thus :

[ember kernel]

Note : ' is the symbol of derivation

[proper sail]

@ember kernel y is function
y1 is ist derivative
y2 is 2nd derivative

I understand that question thanks but please help me with this question!!

[ember kernel]

Replace (1+x²)^(3/2) by y, it'll be easier

[left knoll]

@proper sail

Did I solve it correctly @ember kernel

[ancient epoch]

help pls :(

[ember kernel]

I wouldn't have used that method (because I wouldn't have thought about it) but that seems okay ?

That identity du/dv = (du/dx)/(dv/dx) seems weird to me, since chain rule requires du/dv = du/dx * dx/dv instead (and I'm not sure that's the same thing), but this seemed to work out

[left knoll]

It's simple method so I prefer using it :)

[ember kernel]

Proving the equality is equivalent to proving that f(x) only has one root. Here's how you can get to that conclusion :

[ember kernel]

From there, I don't know how to rigorously prove it (some help would be welcome) but there's a way :

1. Prove that f is continuous

[ember kernel]

Since its derivative exists and is continuous on the interval ]0,inf[, so is f

2. Prove that f only has one extremum (minimum or maximum) and that it is a min :

[ancient epoch]

or i have to prove that there’s only one minimum and its equal to zero? because then that would mean the function never hits the Ox axe again

[ember kernel]

No, because there could be roots that are not minima. Think about x²-1.

Thus, before applying your method, you would have to prove that f(x) is positive on its domain before

Which is tough without going through step 2 at some point

[ancient epoch]

this is what im thinking. im not studying math in english so im a bit confused with the specific names of the terms, but im thinking maybe i could prove that for the x of the minimum, whatever value i find, the y of the value of the function for that is zero

[ember kernel]

I mean, yeah ? That doesn't seem like the most rigorous way to do it, but I'm not into long, rigorous proves myself.

[ancient epoch]

thanks!

[proper sail]

@left knoll @ember kernel OK thanks

Please help in this question!!

[left knoll]

Decreasing

@proper sail

Value of cosx is Max at 0 and min at π/2

Easy question 🙃

[proper sail]

Min value is 0 or -1 ?@left knoll

[left knoll]

I'm talking in the range of [0, π/2]

@proper sail

[proper sail]

ah OK then min is zero thanks

[pine dust]

That is trigo right

[proper sail]

Please help with this question!!

[ancient epoch]

no, minimum value is -1 for cos π

both cos and sin take values from -1 to 1

[proper sail]

@ancient epoch OK I get it

[ancient epoch]

you have to find the derivate using some formulas

[ancient epoch]

i have a question, i thought the formula that you applied only works when both numerator and denominator have to be variables and not constants

you got the same answer as me tho so now im not sure

[spring ore]

f(x) = 1 is still a function, even if it's a constant

I think in general most people would use the chain rule here, but I was being lazy :^)

[ancient epoch]

ooh yeah thanks!

[proper sail]

@spring ore Ok I don't know why I get -3/4 here can you point out my mistake?@ancient epoch

[weary arrow]

It is the bottom part of the equation, remember that (a+b)^2 is not a^2 + b^2

Or am I tripping

[proper sail]

@weary arrow ooh OK

I forgot basic algebra lol

[spring ore]

you don't actually need to simplify (x + sqrt(x))^2, you can just fill in f`(1) there

[ancient epoch]

nah you good lol

[spring ore]

it's much easier

[weary arrow]

Man I give up math bot it's too late in the evening, Jasper will help you lol

[spring ore]

it's almost midnight here 🤣

but it's a good distraction from being stuck on the same dumb bug for the past hour

[weary arrow]

Hahah okay then😅

[ember kernel]

They were talking about the [0,pi/2] interval

[ancient epoch]

oh yep i see

[proper sail]

@spring ore @weary arrow @ancient epoch OK thanks

[steel plover]

can smone explain why the n outside of the ln disappears? not quite show what cancels that out

[ember kernel]

It doesn't get cancelled out, it's just replaced by the h (which is = 1/n as said in the first line) that lies in the denominator of the fraction

There's no mathematical step involved, just a reformulation of the problem

[steel plover]

oh okay. thank you!

[opal pivot]

A wire 9 meters long is cut into two pieces. One piece is bent into a square for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be cut to minimize the total area of both figures? Give the length of wire used for each:
For the square:

For the circle:

(for both, include units)

Where should the wire be cut to maximize the total area? Again, give the length of wire used for each:
For the square:

For the circle:

(for both, include units)

can someone help me with this problem and how to solve problems like this

this is an optimization problem and I struggle with solving these kinds of questions

[ember kernel]

I'll answer it in 8h, when I wake up, if nobody has

But, using c as the side length of the squaee and r as the radius of the circle, you know that :

[ember kernel]

The total area (square + circle) =

[ember kernel]

If I'm correct, you should be able to find a min/max for that latter expression (which only uses one variable : r)

Note : don't forget that r must be in the interval ]0 , 9/(2pi) [

@opal pivot

[opal pivot]

@ember kernel I will see how you solve the problem when u are free to solve it. I am not in a rush. I am trying to get practice in with optimization problems and the main problem I have is understanding what the question is asking and how to draw the diagrams. Thanks for the help.

[left knoll]

We were talking in the range [0,π/2]

ie first quadrant

[ember kernel]

You can do it by hand :
A = {*0,*1,5,7,11,13,17,19}

[ember kernel]

What does the function n() do ?

[tawdry dagger]

lol sorry i wanted to send the other one i was in a hurry

[tawdry dagger]

its not given

[tawdry dagger]

in the question

[ember kernel]

Then it has to be something you saw in class

[tawdry dagger]

😮 i see

thenks anyways @ember kernel

i got some more can i send them ?

[ember kernel]

Yes

[ember kernel]

I already did half the job with the substitition of c in the formula of the total area. All you have to do is now to optimise the one-variable function that it became the classic way :

• Simplify the expression
• Derivative = 0
• Min or max depending on the sign of the 2nd derivative
• Verify that r is indeed in the physically correct interval ]0 , 9/(2pi)[

[ember kernel]

Draw a Vienna diagram with 3 circles, name them A, B, C, identify what A - B clearly is, then test the answers given one at a time. Only one should give you the same result

[tawdry dagger]

can u send a pic of the answer plz ?

[ember kernel]

I can't, and it's a Venn diagram* (not Vienna)

Look it up, it's easy enough you'll see

[tawdry dagger]

OOKK thenkssss

[tame comet]

Hey all can someone please tell me how to determine other variances and standard deviation using just the variance?

[heady tree]

if X is multiplied, you square it and then multiply.

addition/subtraction can be ignored, because if you shifted the whole group of data to one direction or the other (adding/subtracting) then the overall spread would be the same

[ivory pumice]

n is not a function , n(A) = number of elements of set A

[ember kernel]

You have A = {1², 2², 3², ... 10⁶}

Since 10⁶ = 10³*² = (10³)², that means that A = {1², 2², 3², ... (10³)²}

Thus, n(A) = 10³
(Because A is the set of all non-zero natural numbers up to 10³, squared)

Thank you @ivory pumice

[ivory pumice]

👍

[spring ore]

10^3

[ember kernel]

I corrected my answer. Thank you 😁

[spring ore]

👍

[tawdry dagger]

THANKS MAN

[knotty ridge]

Anyone here master of math?

[ivory pumice]

Send questions here , someone will definitely answer

[ivory pumice]

Maximum area when circumference of circle = 9 , for minimum use calculus

[proper sail]

Please help in this question and also try to use this formula of integration of parts as I am stuck when using it!!!

[ember kernel]

I'll be honest with you, your formula of integration by part seems wrong to me

[ivory pumice]

It's correct

[ivory pumice]

substitute t²=x , and then use Integration by parts

[ember kernel]

Ok mb, I haven't learn it that way (and didn't bother to double-check I admit)

[spring ore]

Sorry if it's a little messy

substitute u = sqrt(x) and then apply integration by parts where f = u and g' = cos(u)

also, a constant, obviously 🙃

[fading basalt]

👋 hi i am new i need help with maths
I am in 8th grade

[ivory pumice]

Send questions here , peeps will help you :)

[fading basalt]

Peeps you mean people

Really getho way to say it

[ember kernel]

Hey !

[ember kernel]

Is the help you need more about precise questions/exercises that you have to solve, or are they about some concepts you struggle with ?

[fading basalt]

Imma start a topic tomorrow

Profit and loss

If i have any problems i will ask then

Thanks for being generous

[ember kernel]

Don't hesitate !

[fading basalt]

Kk sure

[proper sail]

Please help in this question!!!

[tidal galleon]

it's the option c bc you are integrating respect to t so everything that has no t acts like a constant and a^x^2 has no t

[proper sail]

@tidal galleon OK thanks

[slow cipher]

The 68-95-99.7 rule of the normal distribution should also apply to the binomial distribution, right?

because if it does, I don't know what I'm doing wrong.

i tested it with:
n=100
p=0,5
μ=50
σ=5

plugged it into the calculator

and got 0,728

it should have been 0,68 right?

[unreal quail]

i am sorry i going dumb the q is -0.76 close to 1 or is it 0.85

[ivory pumice]

0.85 is closer to 1

[atomic cipher]

ayyy we're doing probability theory?

oh that was yesterday 😦

[ivory pumice]

y= 0

[proper sail]

Page help in this question!!

[tawdry dagger]

thanks

[spring ore]

What steps have you taken so far?

[left knoll]

what would the reciprocal of 7/-1 be

it cant be -7/1 right

[spring ore]

-1/7? isn't the reciprocal of x just x^-1, so 1/x?

so 1/7/-1 -> 1/1 * -1/7 = -1/7

[left knoll]

oh, okay

thanks

[spring ore]

👍

[spring ore]

See if you can solve it after these steps

Note that we can change the numerator from e^x + 1 to e^x - 1 + 2, simply because -1 + 2 = 1

[tame comet]

Hey all, wondering if anyone knew how to calculate the number of shots needed without having to subtract the probability of 49,48,47,46 etc. from 1? Takes too long...

Also ty @heady tree actual legend

[heady tree]

no prob man

@tame comet if you're just looking for the answer it should be this (correct me if im wrong)

as for working it out manually, I either cant remember or wasn't taught it by my teacher, but this one seems somewhat useful

https://youtu.be/IAx21BWpdsw

[ember kernel]

All these probs-related questions remind me of how bad I am at probabilities xD

[proper sail]

@spring ore OK I will try

[spring ore]

Yeah same.. I just couldn't ever get into it, I barely passed my stats course

[proper sail]

Please help in this question!!

[opaque coral]

i would differentiate the options , since it wont be much of a hastle.

[tidal galleon]

i would solve it using integration by parts. Take f=(x-1) and g' = e^-x so f' will be 1 and g will be -e^-x. Put that into the formula and for the integral of -e^-x you could use u substitution, take u=-x and you will get the integral of e^u du, so the final answer will be (a)

[left knoll]

Big brain 🧠

[opaque coral]

it is a MCQ , so short tricks work

[left knoll]

Yea 😅

I'm way too bad at integration :(

[tidal galleon]

if you struggle with derivatives and integrals i would recommend you to check this to pages, they are in spanish but you don't need to understand the 2 or 3 words that appear hahaha (if you want you could use google translate). Well the point is that this to pages integrate and derivate explaining step by step, they are extremely usefull

https://www.calculadora-de-integrales.com/

https://www.calculadora-de-derivadas.com/

[opaque coral]

honestly its just abt practice

[left knoll]

I'm just bad at integration

[left knoll]

Yea but I can't solve simple questions lmao

[opaque coral]

lmao

[tidal galleon]

it's kinda cliche but Rane is right, integration is just about practice, once you integrate a lot of functions you start to just know what you have to do

it helps a lot to see other people solutions bc you learn the tricks

[opaque coral]

you start to see specific patterns and start solving basic - medium level probs mentally

[proper sail]

@tidal galleon ook it's a Calculator

[tidal galleon]

Yes, but it has the peculiarity of also explaining what it does, which is particularly useful when you are learning these things

there are others online but you have to pay for the full explanation

[proper sail]

Yeah thanks I hate these paying aaps everywhere free education is best.Paying ones are good but I don't know

@tidal galleon @opaque coral OK thanks

[weary arrow]

<@&717391911132069929>

Several channels

[untold relic]

did i get the one you're referring to?

[weary arrow]

Yes!😊

[fading basalt]

Anyone here preparing for sat

[mild valve]

Probability's my weak spot so id appreciate some help:

Three letters are chosen at random from the word HEART and arranged in a row. Find the probability that both voewls are chosen

how does the working out work??

[sharp pilot]

the probability of something happening is the number of times it can happen divided by the number of possible things that can happen. What i mean is that you need to count the number of ways to choose 3 letters from HEART such that two of them are vowels, then divide that by the number of ways to choose three letters from the word HEART.

@mild valve

let me know if you need more clarification/help

[random flame]

Hi can someone help me with part a? The final ans is 20cm. I was thinking that if I drew a line AB and a line BC the shape AOCB would be a rhombus. However, it's proven not to be a rhombus. Ping if you do help and thanks in advance!!

[sharp pilot]

Let D be the midpoint of AC. Look at the right triangle AOD. @random flame

Another hint: ||Let the radius be r. Then AO=r and DO=r-8||

let me know if you need more clarification/help

[random flame]

Wait so it’s like
r^2=16^2+(r-8)^2?

Lmao me and my tuition teacher had been stuck at this question for ages

[sharp pilot]

That's right. you then use that equation you wrote to solve for r=20.

[random flame]

Thank you so much!!

[fading basalt]

Hey ello

Help me with this

[bleak pendant]

Is cos mod x

Graph

And cos x graph same thing?

[ivory pumice]

Hmmm you can do by general mathematics but that would be lengthy , shorter way would be assume that the work has 60 parts to be done , A does 6 parts per day , B - 5 parts , c - 4 parts , now after A left , 30 parts were done now let's assume b left after x days (x after a left) , parts done would be 30+5x+4x , remaining portion would be 30-9x , it took c 3 days to complete it means 30-9x = 12 , x = 2 , so total time it took would be 2+2+3 = 7 days. @fading basalt

[ivory pumice]

Yes

[bleak pendant]

Exact same?

[ivory pumice]

Yes

[fading basalt]

Please also send general method too

[fading basalt]

Plus how you get that part thing

[surreal gazelle]

Sup

where is it

[raven halo]

sup

[fading basalt]

@surreal gazelle

[surreal gazelle]

oka

[fading basalt]

Place a h before your name

[ivory pumice]

I assumed it... Took LCM of 12,10,&15

[raven halo]

im on my way to achieve that h tbh

soon

[fading basalt]

K

[fading basalt]

Hmm

How the lcm works

[ivory pumice]

lowest common multiple

[fading basalt]

Why you take lcm

[surreal gazelle]

I am confused as heck

[fading basalt]

I know that

[surreal gazelle]

all the integration

and calc2

has burned my mind

i am idiot officially

an*

[raven halo]

brb

im gonna take a paper

[fading basalt]

Kk

[raven halo]

this thing is gonna be serious

[ivory pumice]

To minimise calculation

[fading basalt]

Can you send general method pls

[ivory pumice]

Hmmm ok will send it later then

[fading basalt]

Kk

[fading basalt]

I am gonna do a test real quick brb in an hour take you time

[ivory pumice]

Just replace 60 with x and do everything same

[raven halo]

ye its 60

explain it in english is harder than i thought lmao

[raven halo]

u can ask me if theres anything that you haven't understood yet

[charred hedge]

can anyone help me to find the value of x?

[raven halo]

it's two third

2/3

[raven halo]

@charred hedge

[charred hedge]

Thank you but can u explain it?

[left knoll]

@charred hedge Replace 8 with 2^3. Then take 2^(3x) as some variable k. Solve for k. Then use log on both sides to find the value of x.

[charred hedge]

Thank u i really appreciate it

[ember kernel]

@charred hedge Even easier :
2^(3x-2) = 2^(3x)/4 = 8^x / 4

With 4 and /4 cancelling each other out, you get :

[raven halo]

wow that bot is cool

[ember kernel]

Yeah but I'm not even capable of writing code without making the same mistake twice in a row xp

[raven halo]

i think it should stay in 2^(3x)

because it's gonna be easier to calculate than 8^x

[ember kernel]

It could, I only realised it when I finished writing the code

[raven halo]

XD

[charred hedge]

@ember kernel thank u so much for ur effort

[ember kernel]

:D

[fading basalt]

In the test or the question that i sent

[raven halo]

the question

if i understand your test then u can ask about it too lol

[fading basalt]

Oh

[fading basalt]

It was a easy test

[raven halo]

nice

thats mean you did it good

[fading basalt]

Haha ye

Ok so for the question i have a different answer

[raven halo]

oh

whats the answer

[fading basalt]

Ye i used the concept of efficiency

I had 20/3 days

Which is approximately 7

[raven halo]

how did you do that

[fading basalt]

Wait let me send you the solution

[raven halo]

ight

[fading basalt]

@ivory pumice

Look at this

[raven halo]

that's a wrong calculation

[fading basalt]

Ye i just figured it out

[raven halo]

you were wrong in 2 place

ye lmao

[fading basalt]

😩

Aw man

[raven halo]

it's 7

welp

that's another method

it works

[fading basalt]

Yessir

It’s easy and fast

Xd

[raven halo]

yea you don't have to find lcm

but i prefer the lcm method

because im bad with the a/b thing XD

[fading basalt]

Ooo

[ivory pumice]

Good job

[fading basalt]

Thanks

[raven halo]

wait what do you call the a/b

[fading basalt]

Algebra

[raven halo]

dvided numbers?

oh

[ivory pumice]

Fraction

[raven halo]

thanks

[fading basalt]

L zebra*

Oh you meant fractions

[raven halo]

im need to study more about maths in english

damn

ye

i know some words

[fading basalt]

Lol

[raven halo]

not all of them so it'd be hard to fully explain an equation

[fading basalt]

Oh

[raven halo]

or any maths problem above primary lmao

[fading basalt]

Btw is it allowed to chat here?

[raven halo]

er

i think so

[fading basalt]

Oh

Kk

[raven halo]

i chat english in non english chat

XD

[fading basalt]

Ye me too

[proper sail]

Please tell me what are the middle steps between the both expressions on either side of equal to sign!!

[opaque coral]

expand

[opaque coral]

oh wow

[rustic shuttle]

damn it's hard to use this bot

lol

[mossy tendon]

can someone could explain the last processing pls

[naive cape]

the last expression needs brackets in the bot solution

[bleak tree]

Did you get it know ?

[mossy tendon]

@bleak tree ho yeah now i got it thank you

[fading basalt]

How this work

expand

Nothing happen

[tidal galleon]

is a latex bot, in #how-to-use-math-bot is explain how to use it

https://manualdelatex.com/simbolos#chapter2 here is a list of a lot on commands that you could use, you call them whit \ (except ^ for powers and _ for sub indexs) the things that you want inside a command go inside { }. The inside is for things that affect a lot of characters like fractions or sqrt, if you wanna call a symbol just use \namesymbol.
Example: If i wanna put 2 to the power of 3 times i would write 2^{ 3 * 4}

ah and you call the bot using = tex

and by last if you wanna write text between the equations you must use \text{ and put your text here }, otherwise it would compile as equations and would appear like this andputyourtexthere

[tidal galleon]

the command was =tex \text{hi, testing } \sum^{n^2}_{k=0} k^5

[thorny flicker]

yo can someone help with this

[glad sierra]

found this helpful for stat students
https://youtu.be/wsvfasNpU2s

[fading basalt]

Kk thanks

[slate wolf]

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
A. 1 : 3
B. 3 : 2
C. 3 : 4
D. None of these

could someone please help me out?

[jaunty cosmos]

Please help me out to do differentation division

10 question

[heady tree]

you have to use the quotient rule

[left knoll]

Divide them separately and then differentiate

[heady tree]

^

quotient rule

[left knoll]

It's bit lengthy process.

[heady tree]

unfortunately

but thats the only way we've been taught at school so

im assuming its the same, that they want you to use it

[left knoll]

Maybe

@heady tree

@jaunty cosmos

[heady tree]

yo nice

[jaunty cosmos]

Thank you !but still I have one doubt..

[heady tree]

yeah?

[jaunty cosmos]

Thanks

[jaunty cosmos]

How you have cancelled those powers according to answer? In step -3

[heady tree]

because the left side of the subtraction and right side of the subtraction are in brackets

so whatever you cancel from one side you have to cancel from the other

its like kittykat said

you can rewrite it all as individual fractions

and since x^2 is the HCF that you can cancel, you cancel x^2 from each variable

does that make sense or not really

[jaunty cosmos]

OK I got it thanks

[heady tree]

nice

i wrote out an explanation thing if you'd like at any point

just in case

[jaunty cosmos]

Yeah

[jaunty cosmos]

Thank you so much l have got the right answer 😀😀

[opal pivot]

Using linear approximation we estimate that for f(x)=ln(x^2-8), the value of f(2.9) is approximately

can someone help out with this question

[polar heron]

for linear approximation, we can write the function as f(x)= f(a) + f'(a) (x-a), where a is the point around which we are expanding the function. (it is basically taylor series of a function upto first order .) for the above case we can expand around x=3, which is near to the x=2.9 where we have to evaluate the function. then simply plug in the values.

[opal pivot]

@polar heron I did the linear approximation but I want to confirm if my answer is correct

Is it -.6?

[polar heron]

yes. i also got -0.6.

[opal pivot]

@polar heron okay that was what I wanted to make sure thank you

[small python]

can someone help?

[summer wigeon]

a=35, b=25
but i might be wrong

[small python]

yeah you're right

thanks

[cyan night]

Given a,b,c,d are real numbers that satisfy: a^2+b^2+(a-b)^2 = c^2+d^2+(c-d)^2
Prove that a^4+b^4+(a-b)^4 = c^4+d^4+(c-d)^4

yo guys

can anyone give me hint

is that a trapezoid

[twilit wasp]

it is a cyclic quadrilateral thats all i know

[sharp pilot]

are you familiar with supplementary angles?

[cyan night]

im stuck

i tried expanding and now i got cubes

[sharp pilot]

ill see if i can help you after i help juice

[cyan night]

ok

[twilit wasp]

supplementary angles add up to 180 degrees

[cyan night]

is that a trapezoid

are the lines parallel

[twilit wasp]

lines are not parallel

[cyan night]

whats the circle for

[twilit wasp]

because its a cyclic quadrilateral opposite angles add up to 180 degrees

cyclic quadrilaterals are quadrilaterals in circles

[cyan night]

b is 60?

[twilit wasp]

yup

i already solved that

[cyan night]

ah

[sharp pilot]

this fact might help you with that

[twilit wasp]

whats the diagram

i dont really get it

[sharp pilot]

let me make one for you

one minute

thats right!

[cyan night]

ee

im so stuck with my algebra

[sharp pilot]

alright im trying it

[twilit wasp]

thank u !!!

[cyan night]

wait

mine is actually easy

[tawdry dagger]

PLZ PLZ A PHOTO OF THE answers 🥺

[ember kernel]

Use trigonometric identities like :

sin(270°+A) = || sin(270°-A) ||

cos(180°+A) = || -cos(A) ||

cos(-1710°) = || cos(1710°) = cos(4*360° + 270°) = cos(270°) = 0 ||

tan(90°+A) = || sin(90°+A)/cos(90°+A) : ||
|| • sin(90°+A) = sin(90°-A) = cos(A) ||
|| • cos(90°+A) = cos(90°-(90°+A)) = sin(-A) = -sin(A) ||
|| => tan(90°+A) = cos(A)/-sin(A) = -cotan(A) ||

How did I get these ?

1. Symmetries in the trigonometric circle. Example for sin(270°-A) = || sin(270°+A) || : at the "bottom" of the circle, no matter which way you go (= if you add or substract x at the same rate), the sine still goes up at the same "rate" = symmetry

2. The formulas sin(90°-x) = cos(x) and cos(90°-x) = sin(x), which you can also verify using the trigonometric (when you think about it, these two formulas also come from symmetries)

3. For tan and cotan, express them in their sin/cos or cos/sin form, then simplify the sine and cosine accordingly to 1) and 2)

[ember kernel]

tldr; try to visualise the trigonometric circle in you head, and find symmetries of sine and cosine

[jaunty cosmos]

Can somebody help me out to do differentation division l have a doubt on my answer.

[cyan night]

yo guys, i got this problem:
Given real numbers x,y,z that satisfy xy+yz+zx = 0
Prove that (x+y)^2 * (y+z)^2 * (z+x)^2 + 2x^2 * y^2 * z^2 = x^4 * (y+z)^2 + y^4 * (z+x)^2 + z^4 * (x+y)^2.
so my interpretation was that xy+yz+zx = 0 => either x = y = 0 or y = z = 0 or z = x = 0
from that, i can just easily substitute every situation into the proof and get both sides 0. am i doing anything wrong?

[ember kernel]

x = y = 1 and z = -1/2 => xy + yz + zx = 0 is verified, yet none of your variables is 0

[cyan night]

oh thats why

what should be my first step?

[ember kernel]

Thus, taking that two out of the three variables are 0 for granted means you're not proving the equality for any real x, y,z that satisfies

Use this instead :

[cyan night]

ok

u mean x+y

[ember kernel]

a and b are just parameters names

[cyan night]

okay

[ember kernel]

That means you can replace them with any value you want (including x, y and z)

[cyan night]

yeah i get it

[glad sierra]

did you finish the previous problem?

[cyan night]

i did

[glad sierra]

ah man i was attempting it lol

[cyan night]

ah

u could just give it a try xd

[glad sierra]

did you equate them and multiply both by 2 ?

[cyan night]

divide

wait let me finish this chess game

[cyan night]

so do i just expand everything there

[glad sierra]

na
ill just get back to my studying xD
share teh solution if you dont mind tho

[cyan night]

okie

[ember kernel]

Tbh I'm not home, so I haven't solved it myself

But those (a+b)² forms are just asking to be expanded

[cyan night]

ok thanks

rainar check dms

[covert anchor]

How do I expressed I partial fraction

[cyan night]

Does there exist
b-c : a-b (: means divisible cuz im lazy)
c-d : b-c
d-e : c-d
e-a : d-e
a-b : e-a

this actually wasnt the original problem

it was from a more complex one and i made it turn out like this

i think i gotta subtract stuff

and get 2 equal sides like a-c : c-a and c-a : a-c

[opal rock]

What is this?

[cyan night]

does there exist real numbers a,b,c,d,e that satisfies that

[ember kernel]

Hold on

Do all of these divisions have to be equal, or just exist ?

[cyan night]

oh i forgot

a,b,c,d,e are all different numbers

sorry

[ember kernel]

Then, yeah, if they are different, then they always exist

Because a-b = 0 is impossible, as well as b-c =0, c-d=0, ...

[cyan night]

wait

let me send u the original problem