math-help

[edgy sun]

yea i got the question

how to do this one

[random flame]

Ah ok nice

[sullen verge]

first the point (0;2) is part of the curve so you know that
y0=2
then you solve using you second information which is the point y(2)=5
so
2e^k2=5
e^k2=5/2
k=ln(5/2)/2

[edgy sun]

got it, thanks

[gritty epoch]

Sin(pi-Q)=sinQ
So you can find all the 3 sides of the right angled triangle

[random flame]

Eh why is it needed to find all 3 sides first?

[gritty epoch]

You need cos and tan right

[random flame]

Yea

[gritty epoch]

So cos is adjacent/hypotenuse

I meant. You can just look at sin and tell the other side is 12. But im guessin this is for an exam where u need to show the steps

[random flame]

But the unknown angle isn't in the triangle tho

[gritty epoch]

The angle in the triangle is pi-Q

[random flame]

Yeah

Not sure how that's gonna lead to the ans

[gritty epoch]

Sin(pi-Q)=sinQ

And sinQ is given

[random flame]

How do they equal exactly-?

[gritty epoch]

Angle CAB is pi-Q

[random flame]

Yeah ik but how is sin(pi-Q) = sinQ

It doesn't rly make sense to me

[cyan night]

picture it on the unit circle

so picture an acute angle

pi-x is just its reflection on the y axis

which means its y value, or "sine" stays the same

[gritty epoch]

Yea and similiarly cosQ=-cos(pi-Q)

And for tan as well

[random flame]

Ah I see

Do y’all mean smtg similar to this or am I getting smtg wrong?

[gritty epoch]

Why have you extended it below the x axis

Thats not pi-Q

[random flame]

Oh wait what

Then how is it supposed to look like?

[gritty epoch]

CAB is pi-Q

[random flame]

Uhh yeah

[gritty epoch]

yes so why is there a triangle below the x axis

its not needed actually

[random flame]

I thought need to look at it using the unit circle thing?

[gritty epoch]

yea youll the logic is the same

[atomic dagger]

how can I find the limit of this sequence? I already know it exists

I also know the limit is (x+1)/(x+2)

I need to know the in between 😭

[sonic zodiac]

Hi guys I have a fairly easy question(probably im missing something obvious) - how do you prove that the function f(x) = e^x + e*x is injective

[hollow mauve]

Hello

Pls solve this!

[atomic dagger]

I actually found the answer for this ^^' if anyone is curious they can always ask me

[ember kernel]

Both e^x and x*e are strictly increasing, continuous functions (which is enough to prove injectivity if I recall correctly), so their sum also is strictly increasing and continuous

[sonic zodiac]

Ah I did forget about the use of monotonicity in injectivity! Thank you sir!

[unreal plaza]

math peeps there is a website to help u solve math problems incase u didnt understand the whole thing

https://www.wolframalpha.com/

[cinder yacht]

that doesn't mean anything

because what is "x"?

we have X(n+1) = f(Xn) where f(x) = (x+1)/(x+2)
quick study of variations of f :
f(x) = (x+2-1)/(x+2) = 1 - 1/(x+2)
so f'(x) = 1/(x+2)^2>0
so f is increasing
knowing that f is increasing, we wanna see if (Xn) is increasing or decreaisng :
X1 = f(X0) = f(1) = 2/3 < 1
so X1 <= X0
so you can easily prove by induction (récurrence) that X(n+1)<=X(n), using the fact that if X(n+1)<=X(n) then f(X(n+1))<=f(X(n)) because f is increasing, meaning X(n+2)<=X(n+1)
now that we know (Xn) is decreasing, let's find a real number always smaller than (Xn). an easy one is 0 (because if x>=0 can see that f(x)>=0).
U prove with an easy induction that X(n) >= 0 for all integers n
(Xn) is decreasing and >=0. So it converges to a limit we'll denote L. to find L :
we know that for every n, X(n+1) = (Xn+1)/(Xn+2)
so for n->infinity : L = (L+1)/(L+2)
so you solve this equation and u find that L= [sqrt(5)-1]/2 >0 or L = [-sqrt(5)-1]/2<0
but since for every n, Xn>=0, that means that L>=0
so only the positive solution is possible : L=[sqrt(5)-1]/2

lol I just realized u alrdy found the answer

but i like to write down the steps of the reasoning clearly and one by one, so fk it no regrets for having typed this lol

[cinder yacht]

yep that's enough

to be fair u don't even need "continuous" for injectivity

but continuous helps in other things (especially finding images of intervals by F. Like finding f([a, b]) is easy when f is continuous and monotonous)

[hushed jacinth]

help 😭

[left hearth]

hello ) could you please help me with the task …

[supple island]

prove it using an absurd,
assuming x=!y you can divide by (x-y)³ since you're sure you are not dividing by 0, so now you have (x-y)²=-1 but that's an absurd because the square of something can never be negative

therefore x must be =y

assuming x,y are real numbers

[teal karma]

Anyone in calc 2 can send me the identities used for integration by parts and Substitution and the half angle identities, please if u have it in a book or notes or anything greatly appreciate it it’s for chapter 7.1-7.3 if in the us

[supple island]

can't you just... search them on google?

[teal karma]

Yes yes but there’s a lot that come up I need the ones that are used for the topics I’m just trying to memorise them before the test, teachers usually give them out my teacher didn’t so If someone’s teacher did give them I can just study the ones Imma use

Im going through the textbook to find what I can but not everything in the textbook is needed

[elfin crest]

I don't know if it is helpful but I ended up wit something like this: (x-y)^5 + (x-y)^3 = 0 --> (x-y)^3 * [(x-y)^2 +1] = 0 . (x-y)^3 = 0 because x=y, and anything multiplied by 0 is equal to 0.

[bright talon]

Hello people ! How is everyone? Hope y'all are doing well... I need help with the topic of trigonometric and derivatives. I'm studying arquitecture.

[sharp night]

in each triangle, you can assume that the 3rd angle is 180degrees - the other two angles

so beta = 180° - 1 - 2, delta = 180° - 3 - 4, alpha = 180° - 5 - 6

oh wait.. i just noticed my solution is incorrect..

[cinder yacht]

if those triangle sides thar seem aligned, are indeed aligned, then :
call a, b, c the angles without name
from that dot in the center, there are :
-the angle a (red area with 1 and 2 in it) , and another angle a in front of it (white area) [because of my hypothesis that those triangle sides are aligned]
-the angle b, and a similar angle b in front of it
-the angle c, and a similar angle c in front of it
=> and since all those, together, makeup 360°,then :
360° = 2a+2b+2c
so a+b+c = 180°
now <1+<2+<3+<4+<5+<6 = (180-a) + (180-b) + (180-c) = 540 - (a+b+c) = 540 - 180 = 360

[left knoll]

Can someone please explain where did the sec²x highlighted in the circle come from?

[lofty arch]

Chain rule, tan^3(x) = (tan(x))^3

[slow hare]

is there any good math book you guys can recommend for a high school student like me? plz

[atomic dagger]

yes that is what I ended up doing ! for some reason my teacher wrote that the limit was (x+1)/(x+2) and I was confused where x came from, which is why I asked for help. but I'm just going to leave it as the positive root we calculated

thank you very much!

thank you too I understand!

[left knoll]

can i ask to those with depth knoweldge in mathematics, what truly is an integral

i ask this as i feel i have stumbled upon something new found (although unlikley)

[supple island]

just say it

"what truly is an integral" is pretty vague depending on what you're actually thinking about

[left knoll]

no no i dont want anyone to steal it as stupid as it sounds

[left knoll]

what is happening when you integrate geometrically

[supple island]

you mean Riemann's integration?

[left knoll]

i dont know what that is

ik i sound out of my league here

but i need to know if there is more to integration than just area under curve

[supple island]

this guy

[left knoll]

oh ok ok ik this

[supple island]

ofc

[left knoll]

didnt know it was called that

ok when we integrate we have infinite of these?

correct?

now what is happening for area above curve

[supple island]

we take deltax->0

[left knoll]

ok ok ok

if we want to find area above curve

lets say x^2

then what is happening

so integration above the curve

[supple island]

wdym "integration above"

doesn't really make sense

[supple island]

i mean

there's really no limit

unless you want to stop at a certain point

like y=5

[left knoll]

sure

lets stop there

its definite

ok

whats happeining

geometrically

@supple island

[supple island]

you integrate 5-x^2 between -sqrt(5) and sqrt(5)

[left knoll]

but whats happening

[supple island]

you are doing the integral of 5 and the integral of x^2, you know that the area "above" x² is the difference between them

[left knoll]

yea but what is that

[supple island]

you can also imagine it as the integral of -x²+5, so a parabola pointing downward raised by 5

then imagine it using riemann

the little coloumns guy

[left knoll]

ok ok and that would work for above graph??

@supple island

[supple island]

i mean i didn't do anything strange, it's quite literally the same thing

you can just imagine the same thng in 2 different ways

[left knoll]

oh ok ok ty

@supple island

[winter dove]

can anyone help me?

[cinder yacht]

that Riemann thing is too advanced I think

an integral of f(x)dx between x=a and x=b
is basically the "algebraic" (meaning it can be negative if f(x) is below the x-axis) surface area between the x axis and the f curve, from x=a to x=b

[supple island]

Isn't that how they introduce you to integrals?

[cinder yacht]

hmm I don't remember how I was introduced to it in high school

in uni that's how they introduced it to me

[cinder yacht]

it can also be seen as the sum of little areas f(x) * dx (dx being very small) from x=a to x=b

and it's close to the notion of "primitives"/"antiderivatives" (which is the opposite of a "derivative")

that's how I'd sum up the intuition behind integrals (it requires actual lessons, not a discord chat, to master it)

[crisp lodge]

thanks

[thick rock]

how to prove this?

[uncut yoke]

you can square it and continue with it

[sullen verge]

i would work on this intuitively:
on the trigonometric circle, on this specified interval
0<cos<1
alternatively
1>sin>0
if you try to find to maximum and minimum of
cos+sin on the interval [0;pi/2]
you will find
if cos is at its maximum (=1)
sin is at its minimum (=0) (and vice versa
so the minimum of sin+cos=1
therefore
1<=sin+cos

now for sqrt(2) its the same way of thinking but instead of finding the minimum you try to find the maximum of the sum.
that is reached on the intersection of the line y=x with the trigonometric circle so, at the point (sqrt(2)/2 ; sqrt(2)/2)
so, sin +cos = sqrt(2)/2 + sqrt(2)/2 = sqrt(2)

so,
1<= sin + cos <= sqrt(2)

[frigid basalt]

evening, quick question: i need to check if ax^2+ax+2 has any solutions for x which are real. how can prove this?

[pulsar osprey]

How Can i solve

4 sin²(x) + cos(2x) + cos(x)

[cinder yacht]

that isn't an equation, I guess u mean ax^2+ax+2=0

[frigid basalt]

mb

[cinder yacht]

then if a=0 : 2=0 has no solution
if a!=0, then it's a quadratic equation. it has a real solution if and only if a^2-4 * a * 2 >= 0 (it comes from the "b^2-4 * a * c>=0 of ax^2+bx+c"), meaning a(a-8)>=0, meaning a<0 or a>=8

[frigid basalt]

thanks m8!

[left knoll]

1+3 ??? pls help meee

[sullen jacinth]

Can anyone help me with statistics?
Q: for C(n,r) state the restriction on n and r explain why these restrictions are necessary

[ember kernel]

1+3 = 0 in the base 2 modulus set

[ember kernel]

Just apply mindlessly that formula ⬆️ and simplify whatever you can afterwards

Example : using the identity m²-p² = (m+p)(m-p) or other similar formulas

[pulsar turret]

Please help me with this question

The answer I got is incorrect but I don’t understand how

The correct answer is this

[supple island]

@crisp lodge

[unkempt brook]

At street level, the parabola has a span of 123 m, the foundations of the arch are 165 m apart. The road is 12m above the foundations. Calculate how high the arch is and how long the 3rd suspension cable is.

i dont know what i should do i am done with this ,_,

[unkempt brook]

do they mean those cables?

[edgy sun]

how to integrate this

[bold moon]

you can use u substitution, with u = e^x

[cinder yacht]

and when ur more experienced u'll notice it's e^x * Arctan'(e^x) so a primitive of it is Arctan(e^x)

[ancient prawn]

(calculus) when solving revolving volume problems using disks, why is it y and not dy, arent you filling up the shape with disks with a changing radius? why is the height "dx" changing, or is that not what the variables mean

nvm i got it

[fervent tide]

does anyone have an idea of what to do here? I can't seem to understand how Euler's formula will help with this. The problem is in the context of the Discrete Cosine Transform

[delicate cave]

let the terms be of the form, e ^ (ix) = cos (x) + i sin (x)
x varies linearly, so you have a GP on the left

use formula for sum of GP on left, then equate real and imaginary parts

[floral jungle]

Does someone need help with your math problems? I am using Gauthmath, it has LIVE tutors who will give answers and step-by-step explanations 24/7 for FREE. Here's my invitation code: KCGGJY.
https://s.mathme.xyz/lp/invite?code=KCGGJY

[cyan night]

stop

[cyan night]

60o

for it to be a kite then angle BCI = BNI <=> BNI = 30o

IBC is a right triangle so BIC = 90o-30o = 60o

[low oriole]

ohh i see so BCI and BNI are 30 degrees

[low oriole]

but why is it that we need to subtract 30 degrees from 90??
I'm quite confused.

[cyan night]

sum of 3 angles in a triangle

is 180o

and there is already a right angle (90o)

[low oriole]

ahh okay sooooo where is the other right angle?

[cyan night]

that is the angle IBC

the intersection of two diagonals in a kite forms a right angle

[ember kernel]

Factorise the denominators beforehand

That way, you might realise it's possible to simplify some terms

[crisp lodge]

okay got it thankss

[low oriole]

oh i see but where do i put the 60 degrees?

[low oriole]

alright! i get it nowww thank youu!

[low oriole]

ah btw can triangle sum theorem be used??

[cyan night]

yes thats what i did

[low oriole]

alr thank you again 😭😭😭

[cyan night]

no problem

[cinder yacht]

that formula is wrong

also "solve" is a verb that's too often wrongly used

anyway

basically u use the formula :
(g(h(x)) ' = h'(x) * g'(h(x))
here h(x) = 1+x and g(y) = y^2/3 [which gives us f(x) = g(h(x))]
so h'(x) = 1 and g'(y) = 2/3 * y^(-1/3) meaning g'(h(x)) = 2/3 * (1+x)^(-1/3)
so f'(x) = h'(x) * g'(h(x)) = 1 * 2/3 * (1+x)^(-1/3)

a mathematically uglier, but simpler, way of seeing it is :
df/dx = df/d(1+x) * d(1+x)/dx
= [ 2/3 * (1+x)^(-1/3)] * [ 1 ]

[warm olive]

You are standing on a hill looking at a castle that is 175 feet away from you. The angle of elevation to
the roof of the castle is 8° and the angle of depression to the bottom of the castle is 14°.
Find the height of the castle.

^trig hw

[half crater]

anyone know how to solve for x? im not sure what proportion i set up

[gritty epoch]

Its just pythagoras theorem

There are 2 right angled triangles
Using them you can get an equation for x

[half crater]

ohhh ok thanks

[teal karma]

I’m watching a video about integration by parts and the Instructor is saying that before we use integration by parts we should check to see if the integral is in the table first, does anyone know what the table is referring to, I looked up table of integration and I’m not too sure about it

[cyan night]

yeah you can use proportions which i believe is quicker

triangle ABC and HAB are similar a-a case (both have a 90 degree angle, and they share the angle ABC)

=> BH/AB = AB/BC or 36/60 = 60/x you just need to solve for x

[blissful zinc]

How will i be able to find Y

nvm they are supp

[half crater]

sorry for late reply, thank you so much!!

[cyan night]

no problem

[cyan night]

😅

[ember kernel]

It's the 4th time you've asked this and got no reply. I'm suggesting you ask your teacher about it because it looks like nobody here's able to help you

[atomic dagger]

Does anyone know how can I find if a function allows continuous extension to a certain point?
For example a function f defined on R\ {0}, and we want to know g(0) the continuous extension of f.

My idea was to derivate the function to find if it admitted a continuous extension, but I don't think that would make sense since 0 isn't part of the domain...

[cinder yacht]

if lim 0+ f = lim 0- f

then you can extend it to g with g(0) = that limit

it's best to imagine this in curves instead of just formulas

like if u have 2 ropes, one on the left of the vertical line x=0 and one on the right of x=0

the only way u can only join them by adding a point at x=0 is if they're already almost joining (lim 0- f = lim 0+ f), and in that case u do so by adding the missing dot (at the right height : g(0) = lim 0 f)

[atomic dagger]

ohh thank you i understand the concept now, but then how do I find the expression of g ?

[cinder yacht]

g(x) =
f(x) if x!= 0
lim 0 f if x = 0

there's no unique expression for all x in R

u distinguish the 2 cases in ur definition of g

(and it still gives a continuous function, even if it has 2 different expressions depending on whether x = 0 or not)

[atomic dagger]

I only need to know g(x) in the point where the function is "missing" though right? For example if it's 0, I need the expression of g(0)

[cinder yacht]

yes

I alrdy answered that

[cinder yacht]

here

it's g(0) = lim x->0 f(x)

you have to compute the limit

[atomic dagger]

okay thank you i understand now!

[cinder yacht]

if lim x->0+ f(x) = lim x->0- f(x) = 666
then g(0) = 666

[atomic dagger]

right, so in cases where the function has two different expressions on the right of 0 and on the left of 0, I calculate both limits, is that what you mean?

[cinder yacht]

well u basically do when u need to

for example for f(x) = |x| / x for x € R\0
u see that lim 0+ f(x) = 1 and lim 0- f(x) = -1
so u can't extend it to a continuous function

even though f has "the same expression" on both sides

same for f(x) = [sqrt(1+x^2) - 1] / x^2 for example

(im surprised that I found this example lol)

[atomic dagger]

i see ^^thank you very much that was confusing me!

[dusky cloak]

So um basically yeah

[cloud sky]

helpp

[dry cypress]

Here in number 7
The domain of the function is (-infinity,-1]and[1,infinity)
And range is also the same as domain
Is this correct?

[supple island]

it seems to me that the function is also defined between -1 and 1

[cinder yacht]

tell me why 0 isn't included for u

the domain is R, the range is (-inf, 2]

[dry cypress]

Okay I didn't saw x<1 I thought x>1 so the domain is R
But why the range is (-inf,2]?

[supple island]

look up the definition of range

[cinder yacht]

that would not have made sense, because then f(x) would have had 2 different definitions for x>1 (and x<-1)

[dry cypress]

Okay I got it
I was doing the math on my head I should write it down o did so many silly mistakes and messed up the whole thing

Thanks!

[pallid fable]

anyone know how to solve this ?

[gritty epoch]

assume p(x)=ax^2+bx+c and using the conditions given you can find a b and c

[pallid fable]

ai imma try that

so ive subbed it in and i tried using the quotient rule now im kinda confused on what else to do

[sterile birch]

Hey guys I really need some help with this problem if youre able to help me out

I get all of the work until the bottom of the page

it says each slice only has to travel up and out of the tanks spout... How is that so?

Wouldnt each slice have to travel from the bottom - up... So some y value?

Any help appreciated

OOOO

I GET IT

NVMMMM

ITS Y + 1 LOL

[maiden sigil]

I dont really understand this concept of geometry

[distant walrus]

i believe a heptagon has a sum of 900 degrees of interior angles?

x = 900 - (sum of the angles)

[maiden sigil]

ohhh ok thank you

so in this case x=121

[frosty tide]

Can anyone teach me limits?for class 11 th level??

[left knoll]

Hi, can anyone help me to solve this?

[warped bolt]

sub cos pix = t

[warped bolt]

use youtube there are plenty of good teachers

[warped bolt]

take e ^x = t

[dreamy ember]

can someone help me with this question

im not sure how to start

nvm, I think i solved it by plugging in P(-1) and proving that P(-1) = 0

[regal flicker]

hi, does anyone know what happened to the 7x and the 63x?

im kinda confused

[silk rivet]

anyone wanna help me here?

[silk rivet]

factored out, try using long division

[regal flicker]

thx

[atomic dagger]

Hi! I’m trying to find for which values of alpha and beta will the function be derivable in x =2.

I already know I’m supposed to calculate the derivative of the function whether on the right or left side or x, but my calculations never give me alpha or beta so I’m confused. 😭

Like this. But alpha is outside of the square root so alpha cancels itself… I also can’t simply replace the expression with the values given to me because they will all work

[dry cypress]

(x+2)⅓
In this function stationary point (1,1.44)
How to find the interval of increasing and concave down?

[supple island]

do the second derivative and study the sign

[dry cypress]

Increasing (0,infinity)
And concave down(-infinity,0)?

[supple island]

do the derivatives and to the limit, if f(x)=bx f'(x)=b

[supple island]

the intervals should change at the stationary point

[dry cypress]

I'm confused if the interval of increasing is (-2,infinity) or (0,infinity)

[supple island]

yes

it's correct

the stationary point is in x=-2 thou

[dry cypress]

Which one?

[supple island]

this

ok

wait

it's -2

[dry cypress]

Or increasing (1,infinity)
And concave down(-infinty,-2)

[supple island]

how is it 1

[dry cypress]

F'x=1

[supple island]

you have a problem only in x=-2 for the derivative

[dry cypress]

F"x=-2

[supple island]

in which point?

[dry cypress]

If I do 1st derivative the ans is like 1/something and f"x=-2/something

[supple island]

yeah i mean it's pretty different

[dry cypress]

Yes

This is the graph

[supple island]

it is not

this is (x+2)^1/6

cancel the sqrt

[atomic dagger]

I tried to, but alpha cancels itself 🥲 and when I do the same thing with the first expression I obtain f'(x) = Beta

[supple island]

Yep

That's correct

Now you gotta do b=f'(2)

[atomic dagger]

I get Beta = [ sqrt(h^2 + 4h + 9) - 3 ] / h ... How can I go from here?

oh wait

[atomic dagger]

okay nevermind I get 2/3 + alpha = Beta ... I know that at the end I'm supposed to find that alpha = -5/3 and beta = 2/3 but I'm not sure how to solve this equation now ?

[supple island]

Alpha Is not under the root

You get b=2/3

[atomic dagger]

ohhh omg thank you so much it's been hours i'm stuck on this

[supple island]

this isn't correct

as dx=dt/t

what you actually get is integral of 1/(t^2+1) dt which is arctan(t)

e^x=t

so dx=dt/t

e^x=t

e^xdx=dt

tdx=dt

dx=dt/t

happens

yup

[valid comet]

how would i prove that the cosine rule (where a is 90 degrees) is just the pythagoras theorem

[olive trail]

Could anyone please explain why this isn’t correct?

[thick haven]

integral of u^5=u^6/6

so the second term of your answer should be -(secx)^6/6

[floral jungle]

Can someone help 🥲

[leaden flicker]

If the number of ducks and rabbits in a house is 17 and the sum of the number of legs is 44, how many ducks are there in this house? A) 10 B)11 C) 12 D) 13 E) 14 @rancid mist

Here's the question

[rancid mist]

oh is this complete question?

pretty much u will end up with only one eqn

[leaden flicker]

Yeah it's kinda basic but i just can't do it

Can u explain

Oh thanks

[rancid mist]

ah sorry lmao

i was high just make two eqns x + y = 17 and 2x + 4y = 44 and solve it u will get it

[leaden flicker]

Btw there is can't be mutual option

[leaden flicker]

İ already found the answer thx anyways

[rancid mist]

ya ya i was solving smth else misunderstood it lol too basic

cool

[leaden flicker]

No problem

Good night

[crisp lodge]

Solve the following system of equations by substitution method:

3.3x + 2y = 11

2x + 3y = 4

[slow hare]

are there any maths textbooks or books that any of you guys can recommend for me I am in year 9 /9th grade

[ember kernel]

1. Isolate y in the first equation (rewrite the equation to get y = ... something that depends on x)
2. Replace the occurence of y in the second equation by the expression (y=...) you found in step 1. That way, only x will remain in the second equation. Isolate x to get its value (it should be a constant number)
3. Now that you've found x, go back to the expression you had for y (y=...) and replace the occurence of x (contained in the "...") by the value you got in step 2

And just like that it's done

It'll always be those steps when solving systems by substitutions.
Also, note that :

• I isolated y first, but I could also have chosen to isolate x first. The solution would have been the same
• I started off with the "first" equation, but the order of the equations in a system doesn't matter, so I could also have isolated y in the second equation for step 1, then substitute the expression y=... in the first equation. Again, I would've ended with the same solution

[crisp lodge]

okayy

[terse niche]

can someone verify my answer?

[delicate fractal]

You chose u correctly, but the integral would be e^u

[olive trail]

Hi could anyone please explain why this is the wrong way to integrate this?

[delicate fractal]

because you cannot distribute the division like that

[terse niche]

you right, thanks

[olive trail]

@delicate fractal Oh oops thank you so much

[modest frigate]

hi, i need some help with this question

[delicate cave]

the pattern is that the numbers basically concatenate (so third row evaluates to 166,500,333 and fourth is 166,650,003,333)
to prove this, you'll have to express all three numbers in the nth row in terms of n
for this you'll need a basic idea of GPs & some summations
then add these three numbers and from here it should be easy to prove the pattern

[vague dagger]

guys do u know any 5 digit perfect number

[olive trail]

Could anyone help me to understand this solution for number 13? We were supposed to find the volume using the shell method, but in the solution they draw the rectangle perpendicular to the axis of rotation and for the shell method isn't the rectangle always supposed to be drawn parallel?

[primal pagoda]

Can someone help me on this

[sullen verge]

post it in the science help channel i think it's more appropriate

[sullen verge]

#science-help

[primal pagoda]

Thanks!

[low oriole]

pls help

[floral jungle]

Does someone know how to solve this 🥲

[supple island]

a is just the derivative of V

i don''t quite undertand what b is saying thou

[floral jungle]

Howw?

Can u explain a bit more

[supple island]

i mean

dV/dh is quite literally the derivative of V

[floral jungle]

Oh

Chain rule?

[supple island]

yep

[floral jungle]

Wait ,,, are this question same like above?

[hallow arch]

they are similar types

[floral jungle]

How is it same?

[hallow arch]

the previous qn part b involves rates and so does this one

and differentiation is like rates if im not wrong

[cyan night]

is b) just dv/dt = dv/dh*dh/dt?

sorry im new to calculus

[hallow arch]

thats what i think also

but the context is so weird HAHAH

[cyan night]

yeah its relatively simple compared to other related rate problems

[cyan night]

use the volume formula

then differentiate both sides wrt time

[floral jungle]

Why is it weird??

[floral jungle]

Volume formula?

[cyan night]

but im just ưodering about the height

wondering

[floral jungle]

Hxw?

[hallow arch]

i dont get why the volume is decreasing LOL

[cyan night]

for a cylinder

v = pi*r^2 *h

[floral jungle]

Ohhh

[hallow arch]

have you figured out the previous question you sent?

[cyan night]

but did they giv no other info for the height?

oh wait @floral jungle i misread

it said sphere

[floral jungle]

Wait

[cyan night]

i misread with the next q

u just need to use V formula for sphere

4pi/3*r^3 i think

[floral jungle]

Im not good at math and i tried ask my friendn she showed me this

Is this coorreect?

[floral jungle]

Ohhh yeah same i wasn’t checking the q

[cyan night]

thats correct

remember chain rule cuz they are all a function of time

[floral jungle]

Where’s the part tht showed chain rule in the answer? 😅

I mean ik but i kinda confused with her solution

[cyan night]

the step that they differentiated both sides wrt time

line 4

[floral jungle]

Ohh yeahhhh now i see

Thnkuu

[cyan night]

thatss the thing anout related rates

[floral jungle]

Ohhhh

[cyan night]

therre are things that relate to each other through time as well

like here u used the formula for the volume of the sphere to relate radius and volume

and thus their rate of changes

later on their will be problems that relate variables using other stuff like puthagorean theorem or similar triangles

[floral jungle]

Wait i can ask is the answe worth to get 6 marks? Or are there any missing steps ?

[cyan night]

idk cuz i dont really mark but the solution and methods are correct

idk about the formatting errors or such

[floral jungle]

So Whenever the q ask me to get rate, i hv to use chain rule?

[floral jungle]

Ohhh really ok then

[cyan night]

in this unit things are usually a function of time

[obsidian sage]

the shell method is used to find volume of 'the area under curve and y-axis rotated about the x-axis'

thus the rectangles are horizontal in that case

[floral jungle]

Can someone help without the question c) ?

[obsidian sage]

almost same line equation as b) except the gradient is -1/4 instead

[floral jungle]

Ohh can i ask why?

The gradient is negative

[left knoll]

first, calculate the gradient of the tangent in x=1. u know that the gradient of a straight line (in this case, the tangent) by the gradient of the normal to the straight line itself is -1. knowing the gradient of the tangent to the curve and the product with the gradient of its normal, you can find the gradient of the normal

english is not my first language, so if you still have any doubt please tell me

[floral jungle]

Put number x into the y=mxtc?

And find c again?

[obsidian sage]

a better formula would be y-b=m(x-a)

with this you dont have to solve for c

so in c) the equation would be y-10 = -1/4.(x-1)

[floral jungle]

This?

[obsidian sage]

yes

[floral jungle]

Okay tysm and wht should i find next? Is it x

[obsidian sage]

thats the equation itself

[floral jungle]

Ohhhh

[obsidian sage]

yeah thats what i meant by not having to find c :))

[floral jungle]

Is tht the final answer?

[obsidian sage]

well you can simplify it but yes thats the answer

by bringing the -10 to the other side

[floral jungle]

Oh well tysm !!

[obsidian sage]

np

[random flame]

Hey can someone help me with Q2h and Q2i? Ping if you do help and thanks in advance!!

[left knoll]

Can someone help me with this problem?

Pls ping me in case u know the solution.

[supple island]

to be short i'm gonna say log as logarithm in base sqrt(2)ok so log(ab)=log(a)+log(b), so you have (log(sqrt(2))+log(x))^1/{x}= (1+log(x))^1/{x} we know write y=x-1 so lim for y->0+ of (1+log(y+1))^1/{y+1}=lim y->0+ (1+y)^1/{y+1}, and lim y->0+ {y+1}=lim y->0+ y, so our expression is lim y->0+ (1+y)^1/y, we rewrite t=1/y and we have lim t->+infinity (1+1/t)^t

which is =e

i should have written that on paper lol

would have been easier

[left knoll]

Thx a lot man

Appreciate it.

[jolly plume]

can someone help me with some trigonometry?

thank you so much 🙏

[hollow blade]

it's been a while since I've done trig, so I will instead redirect you here: https://brilliant.org/wiki/trigonometric-graphs-amplitude-and-periodicity/
hopefully this clears a bit up for ya

[wide geyser]

Is it possible for those two lines( tangent at the first point and normal at the second point) to intersect? I genuinely cannot see that

[left knoll]

Yea it can happen

Do you need help or just someone’s validation for your statement?

[wide geyser]

yes pls help me

[cyan night]

but (2,1) isnt a point on the curve

wait

[wide geyser]

i already know that both points do not lie on the curve

[cyan night]

sry misread

the equation for the tangent line of the curve is y' = 4x - 5

[wide geyser]

the correct point is (2,4) and (1,3) right?

[cyan night]

(2,4) and (1,3) yeah

[wide geyser]

so i have to differentiate the equation, okay

[cyan night]

thats for the slope of the tg line

so at x = 2 the slope of the tangent is 4*2-5 = 3

hence the slope of the normal is -1/3

and then you can create the equation for the tangent and normal and set them equal

alright

[wide geyser]

okay i understand that, but what about another point? Does it intersect with the tangent?

[cyan night]

i dont think its saying that the point intersects the tangent

but the normal to it

intersects the tangent

my answer is ||Q (8/5, 14/5)||

im not too sure tell me what u get

[wide geyser]

mine is Q (3/2, 5/2)

[cyan night]

hmm

can u explain how u got iot

[wide geyser]

i used the other point and created another equation though

[cyan night]

was the equation for the tangent y = 3x-2?

[wide geyser]

it is

[cyan night]

what baout the normal?

about

[wide geyser]

and another one is y= -x +4

[cyan night]

-x?

i think the slope of the normal is -1/3 not -1

wait

actually one sec

sorry no

[wide geyser]

its still so confusing

[cyan night]

ok so

the tangent at x = 1 is 4*1 - 5 =-1

so the normal's slope should be 1

y = x + 2

i think

so the point is Q(3,7)?

[wide geyser]

oh that's kinda make sense

[cyan night]

here sorry

i am also new to calculus

red is the curve, purple and light blue are tangents, black is normal

[minor dragon]

i need help with the pythagremthrom join chill room

[polar crystal]

hi hi!i currently need help in understanding simple graph theory / basic graph theory. Im having a hard time grasping the topic if there is anyone who took general math. send help :<<

[wide geyser]

isnt it y = x + 2? You put x + 4

[cyan night]

bruh idk whats wrong with me

let me check

[wide geyser]

that's fine, your explanation actually helped

[cyan night]

yeah they do intersect at the same point xd

[wide geyser]

alright thank you so much 😊

[left knoll]

sorry i couldnt help u i had work to do but glad someone helped u out!!😊

thanks so much @cyan night

[cyan night]

gg

[left knoll]

can someone help me out pls

[cyan night]

i think you can just compute the first and second order derivatives and plug in?

are you having difficulties with computing the derivative

[left knoll]

You can substitute the y in the equation with the expression they gave you (the one with the log) and then compute the first and second order derivatives. When you arrive at the point when 0=0 then you have showed that ln(lnx) is a solution

Remember that ln(lnx) is a compound function so you have to derive ln(lnx) first and then multiply it by the first order derivative of lnx

[cyan night]

chainrule

[left knoll]

exactly, didn't know how to say it in english ❤️

[left knoll]

what language is ok?

just asking cause i might be able to speak it

[left knoll]

nah just need a quick method i could do that but takes years ngl

although @left knoll ur explanation is very good

[cyan night]

i think thats the only approach?

[left knoll]

really?

[cyan night]

i havent studied many calculus approaches

[left knoll]

oh ok

k ig if there is no shorter method ill do it the normal way then lmao

but ty everyone

[left knoll]

i'm italian, idk if you are too tho

[left knoll]

i think that's the only approach to solve it

[left knoll]

nevermind....

[left knoll]

yep yep ok tyy

[warped bolt]

c ?

[cinder yacht]

yeh ur right

[blazing urchin]

Can anyone tell if this is correct?

[cinder yacht]

wrong cuz u kept it "5"instead of turning it to" - 5"on right side

and u didn't put the conclusion : what's the set of solutions of the inéquation ?

[blazing urchin]

@cinder yacht okayy ... I understood ... thanks a lot :)

I will do the corrections

[left knoll]

can any1 do this its based on bayes theorem

[minor dragon]

y=limn→∞(∑m=1n1m−log(n))

need help with that

[wide geyser]

can anyone check my answer please

and do I need to prove the extremum? The triangle is on the positive side

[supple island]

x(49-x²)=49x-x³

you did 49-x³

also the area is (x+c)(49-x^2), because we don't kown the coordinate for A

[delicate fractal]

You can expand the serie using the gauss formula, then you have lim n(n-1)/2-logn, and you can say that log n < n for all n greater than 1. Then, as n goes to inf, that holds, and you can get that the sequence in your limit is greater than n(n-1)/2, so because that diverges, yours diverges too.

[wide geyser]

oh I just noticed it

[wide geyser]

how do I get the c ?

[random flame]

Hi can someone help me with Q3bi? The answer in part a is what I got. Ping me if you do and thanks in advance!! ^^

[supple island]

you don't, it's a parameter, the farther we put A the greater the area is

[supple island]

you have L, H and you know how many sides the polygon has, you also know that it is composed by n triangles

[random flame]

Ah yeah

Hm

Oh wait I have to use the cosine rule?

Or sine rule, either one I don't rmb which

[supple island]

none

you got L and h

isn't the area of a triangle Lh/2?

[random flame]

Yeah

[supple island]

hm

so you have n triagles

of which you know the area

and the polygon is just the sum of n triangles

[random flame]

Hmm

Yeah

[wide geyser]

oh.. so I just have to plug in the x value?

[supple island]

you do (x+c)(49-x²), find the derivative and then the whole thing again

[random flame]

I still don't get how it's gonna get the ans

[supple island]

you have the area of a triangle, you have n triangles, what's the area of n triangles?

[random flame]

(LH*30)/2 ?

[supple island]

yep

[random flame]

Then

Uhh

Cosine and sine rules are not needed right?

[supple island]

this is the answer

[random flame]

Wait what

[supple island]

you don't have to do anything else

[random flame]

But it's asking for the value of the unknown angle tho

And the equation

[supple island]

oh i thought you were doing the iii lmao

[random flame]

OH HAHAHA

It's okay fam

[supple island]

ok so

[wide geyser]

I see, thank you so much 😭

[supple island]

@random flame we start from the tip of the triangle, we know we have n sides, so we have n triangles, and we know that the sum of the angle of the n tips =360

[random flame]

Yeah

[supple island]

so 360=nx

so you find the angle x

we also know that the sum of the angles on a triangle is 180

so 180-x=2theta

and now you have theta too

[random flame]

Hmm

[supple island]

to link L and H we just use the properties of a right triangle

[random flame]

So x is 12?

[supple island]

if n is 30 yes

[random flame]

After I did that I wrote 180-168-12 and it gave me 0

Sed

168 is cuz of the angle that's already given

Maybe my part a is wrong-

I did this-

[supple island]

n is 30

just checked

[random flame]

Ah okay

Uhh

I then wrote this

[supple island]

well of course

your equation is 180-12=2theta

so you have theta=168/2

[random flame]

Then how abt the 168 that’s already given here?

[supple island]

it's not theta

[random flame]

Uhh yeah

Um

[supple island]

it's 2theta

[random flame]

Wait a minute

Wait an actual-

OH MY GOSH

ARE YOU SRS- ;-;

All this while I could've done 168/2

[supple island]

yup

[random flame]

To get theta

Thanks man

[supple island]

np

[random flame]

Now I know that I need glasses 😂

[left knoll]

help

with b

https://en.wikipedia.org/wiki/Combination this the lession

this the main formula

[mellow sky]

Pythagorean theorem is to ez

[ember kernel]

Well Pythagorean theorem is middle school stuff

[frigid violet]

Kaitlyn wrote several positive numbers smaller than 7 on a piece of paper. Riya then crossed out all of Kaitlyn’s numbers and replaced each of them with their difference from 7. The sum of Kaitlyn’s numbers were 22, and The sum of Riya’s numbers were 34. How many numbered did Kaitlyn write down

Someone pls help TvT

[cinder yacht]

the formula is (22+34)/7 = 8

the explanation of the formula isn't immediately obvious tho

[floral jungle]

Can someone help

Can someone help

[solemn vessel]

you want help solving the integral?

[floral jungle]

Integration

Yes i want help

[solemn vessel]

well before i spoil the answer what have you tried

[floral jungle]

Only this cus my mind is blur

[solemn vessel]

Hm okay well i’m not sure what you did to get that

Do you know u substitution?

[floral jungle]

Wht is tht

I forgot ;-;

[solemn vessel]

Let u =

[floral jungle]

Ohhh yes

[solemn vessel]

then du = __dx

[floral jungle]

I remember

[solemn vessel]

right so that’s what you need to use here

you can also split this integral into two integrals

[floral jungle]

Ohhh but where

[floral jungle]

How

[solemn vessel]

using the linearity property of integration

i would write it out on paper but i don’t have paper

but you also don’t have to do that

anyways for the u sub

do you want me to just tell you?

or do you want to try to figure it out

[floral jungle]

Just tell me the whole solution pls 🥺

[solemn vessel]

lol okay

[floral jungle]

😅ty

[solemn vessel]

x - (1/x^2+1)

i mean sure but if you’re going to be in calculus you absolutely need to know how to do a simple u substitution such as this one

it is essential

[floral jungle]

Sorry i cant focus in class 😢

[solemn vessel]

Well you can learn it now too!

I’m not trying to be harsh

[floral jungle]

I try my best to understand now

[solemn vessel]

it’s just the truth

[floral jungle]

Is this the first step?

[solemn vessel]

that’s the answer

[floral jungle]

Ohhh

Like yhis

[solemn vessel]

yes

if you need to show work.... you need to figure that out

[floral jungle]

How 😢

[solemn vessel]

and also dont forget the arbitrary constant

since your integral is indefinite

Well I asked you "do you want to try to understand or do you just want the answer" and you said just the answer lol

[floral jungle]

Yeah the answer

[floral jungle]

Ohhh

[analog stirrup]

Anyone good @ cal 2?

will someone be down to help me?

[solemn vessel]

Send it @analog stirrup

[random flame]

Hey can someone help me with this question? I was thinking of Pythagoras theorem but wasn’t sure how to slot it in this? Ping if you do and thanks in advance!!

[analog stirrup]

anyone available to help with cal 2?

[ember kernel]

Yeah, post the question here

[ember kernel]

Pythagorean theorem is indeed not needed here

• Denote x the horizontal distance between O and A. (In other words, x is the distance between the center of the circle and the left side of the rectangle) Through Pythagorean th., you can get
  x = r cos[(360°-310°)/2] where r is the radius of the circle
  (I leave the details of the calculations that lead to this result for you to understand by yourself)

And w = x + r

[random flame]

I see

Thanks ya I'll try the question now

[dreamy oasis]

One of the lines in the figure is tangent to the g function at point A, the other is tangent to the function f at point C, and the tangents intersect at point B. How many degrees is the angle m(CBA)?

[cyan night]

im also curious to see the solution for the problem above i managed to find the equation for the tangents but idk how it helps i think we can use law of cosines

[supple island]

you can find the rect AC, then you find the rect BD perpendicular to AC, now you have CBD and ABD as 2 right triangles, you know A,B,C,D, now you just find the angles DBA and DBC with the properties of right trinagles and sum them @dreamy oasis @cyan night

idk if this is viable cuz the numbers could be a bit annoying

since you do sin^-1 and stuff

[cyan night]

well if you can do that then finding BC and BA arent too hard either

then do law of cosines to find angle B

CBA

i think finding the equations of the tangents still useful

[dreamy oasis]

If you have found the correct equations, can you write? Also, how do we apply the cosines theorem here?

[cyan night]

im in class right now but be sure to manipulate that the intersection between the tangents have the y-coordinate as 0. the cosines theorem is used after I manage to find AB,BC and AC and do AC^2 = AB^2 + BC^2 - 2AB*BC * cos CBA which you can find CBA thereafter

you have to manipulate that y coordinate because in g(x) there is that a right there that we dont know

also im not sure if my equations are correct we may need to both check

[dreamy oasis]

Alright, i'll try if i can't solve i'll ask again

[cyan night]

ok

[cyan night]

@dreamy oasis so did you try it

[dreamy oasis]

@cyan night heyy sory for late reply!! I tried to find the slopes of the lines using derivatives, but I came to a point. I wrote the equation of the line tangent to f(x), but I could not write the equation of the line tangent to g(x). Do you have any other ideas?

@cyan night @supple island

[cyan night]

yes ok so here is where i think their intersection having a y-coordinate as 0 comes into play

the slope of tangent line of g(x) which is g'(x) at 23/6 is 1/3 as u found

so the equation is y = 1/3x + b

you set f'(x) = g'(x) = y

their equations

the equation for f'(x) at -13/4 as u found is -1/2(x+13/4) = y-193/16 or y = -1/2x +167/16 (assuming your calculations are correct)

[dreamy oasis]

But Why do I have f'(x) and g'(x) equal to each other, don't they both have different slopes?

[cyan night]

from here we can deduce that y = -1/2x + 167/16 = 1/3x+b\

[cyan night]

sorry i used the wrong terminology it should be the equation of the tangents

not just the slope

[cyan night]

which is here

and we know that y = 0

so 0 = -1/2x + 167/16 = 1/3x + b

solve for x and thus for b

after you determined the equation for the tangent lines, are you able to proceed?

[dreamy oasis]

My english is poor that's why i am slow but i really dont understand
How do we write the equation of the line tangent to the g(x) function, or let me ask you where did the b come from?

[cyan night]

its ok

so the general form of a tangent that i often use is y = mx + b

m is g'(x) which is 1/3

y = 1/3x + b

[wet gorge]

Can I ask what class u r in to solve this problem?

[cyan night]

me?

[wet gorge]

Yea

[cyan night]

i am in middle school

[wet gorge]

And that other guy too

Standard?

[cyan night]

i think @supple island is undergrad

[cyan night]

8th grade

[wet gorge]

Ohh

I'm in 10th

The question looks difficult 😕 we haven't solved such question in my entire school life

[cyan night]

i am also just starting calculus

[wet gorge]

Oh

We don't have that subject

[cyan night]

i think its also an incorporation of other skills

[cyan night]

yeah its ok if you arent able to solve it because you arent familiar to the concept

[wet gorge]

Yea

[cyan night]

if you understand it, and you are already in 10th grade, you can solve it without much difficulty i believe

[wet gorge]

Oh thanks sweetheart

I really appreciate coming here

[cyan night]

you never stop learning

[wet gorge]

People here are so beautiful

My exams are going on and geometry is difficult for me

Becz I never practice

[cyan night]

geometry requires a lot of practice

do you do euclidean geometry or 3d?

[wet gorge]

Yea and algebra too

[cyan night]

math is a game of practice

memorization is a last resort, or it could never work

[wet gorge]

It's basic geometry like problems based on circles, Pythagoras and coordination and also similarities of triangles plus trigonometry

[cyan night]

good luck !

be persistent with practice

[wet gorge]

You know I am indian therefore syllabus is difficult

Yup practice is key to be perfect

[cyan night]

indian is very rigorous

their examinations are so tough

[wet gorge]

What's rigorous?

[cyan night]

well hard and precise questions

[wet gorge]

Yup that's pretty true

[cyan night]

i heard of the jee stuff

[wet gorge]

Yeaa

[cyan night]

a billion people country and very competitive

[wet gorge]

Gosh it's hardest exam

After cracking that exams once you give another exam named JEE advance u get into well known Indian engineering college

Named IIT

In India IIT worth Harvard

[supple island]

Correct

[versed fjord]

I need help with algebra

[supple island]

post your question, someone will probably answer

[left knoll]

5.x²-15.x-350=0

i need an explanation for this, pls

[ember kernel]

Start dividing all terms by 5, to simplify the expression

Then, apply the quadratic formula

[left knoll]

tho i need to get 2 answers, for x1 and x2

[ember kernel]

Yeah, and the quadratic formula provides two answers

d = b² - 4ac

x1, x2 = (-b +- sqrt(d) )/2a

The two solutions come fromthe +-

[left knoll]

my mind broke

[ember kernel]

like, in a good way ?

[cinder yacht]

im assuming her mind broke cuz she doesn't know what b a and c are?

and +- maybe

[ember kernel]

Plaisible

[wet gorge]

I have explained

You can solve this by factorization method

If u don't understand what I did with that -70 pointing 2 arrows down to 7 and -10....free feel to ask me

[lapis shell]

does anyone why James is not uploading any videos?

[errant scarab]

wtf is james

who*

[left knoll]

wtf

[ember kernel]

the owner of this server

who used to study for hours everyday on stream during lockdown

[errant scarab]

ohh sorry

[ember kernel]

I feel like explaining who Mickey Mouse is in a DisneyWorld park ^^

yeah np

[errant scarab]

sorry dude i know noone here

[ember kernel]

how did you find this server then ?

[supple island]

wrong chat for this

[errant scarab]

idk some friend invited me and here i am

[flint sparrow]

Hey guys, do u have any idea how to use the absolute convergence theorem for this integral?

[cinder yacht]

smth that can work is
|x|<=e^(x/4) for x large enough
|e^(-x^2) |<= e^(-x) for x>=1
|x^2 sin(x) - cos(1/x)| < e^(x/2)+1 for x large enough

[left knoll]

does anyone know how to prove this?

[fresh isle]

does the 2 mean squared?

cos^2 a?

[left knoll]

no its 2a

[supple island]

know that sin2x=2sinxcosx and cos2x=cos²x-sin²x

so you have 2sinxcos²x/(1+cos²-sin²)(1+cosx) but 1-sin²x=cos²x (since cos²x+sin²x=1) so you have 2sinxcos²x(2cos²x)(1+cosx), simplify and have sinx/(1+cosx)

[supple island]

now applying this again we know that sinx=2sinx/2cosx/2 and cosx=cos²x/2-sin²x/2

if you do that and simplify you'll find exactly tanx/2

[left knoll]

hold on could you explain how you got to 2sin²xcos²x(2cos²x)(1+cosx) again please?

[supple island]

you have sin2xcosx on the numerator

which is 2sinxcosxcosx

so 2sinxcos²x

on denominator you have (1+cos2x)(1+cosx)=(1+cos²-sin²x)(1+cosx)=(1-sin²x+cos²x)(1+cosx)=(cos²x+cos²x)(1+cosx)=(2cos²x)(1+cosx)

[left knoll]

oh right okay i understand that part now!!!

[left knoll]

huh is it really possible to simplify it if 2sinx/2cosx/2 isnt squared?

[supple island]

you wrote too many /

idk what you asked

[supple island]

after this you should have sinx/(1+cosx)

[left knoll]

so you got 2 sinx/2 cosx/2 and on the denominator you have (1+cosx)= (1 + cos²x/2 sin²x/2)
but since the nominator isnt squared you cant simplify it or can you?

[supple island]

the denominator is (1+cos²x/2-sin²x/2)=2cos²x/2

you simplify the 2 and cosx/2

leaving you with (sinx/2)/(cosx/2)

[left knoll]

OH ofcourse, my excuses its 1am the lack of sleep is taking me out. thank you for your help!!

[supple island]

np

[obsidian brook]

Hey there, I'm new here but can someone explain to me how this works? My lecturer gave her notes to us but I can't seem to understand them. It's about linear equations and matrices.

[errant scarab]

you need to solve the equation and find x=[1-2]t and to prove somehow thta y...is not the solution but idk math is not my subject...hope it helped a bit

[ember kernel]

Replace x1 by 1 and x2 by -2
Boom you just proved that 2 -3*(-2) = 8
Do the same with x1 = 1, x2 = 1
You get 2 - 3 = 8, which is wrong. Thus (1, 1) is no solution to the equation

The equation takes a vector as input. The first item of that vector is named x1, and the second item x2

[mellow sky]

in what year are you guys in

[nocturne bloom]

Guys

Can i ask a simple math question

So which one is the lower speed
Going 2 kms per 5 secs
Or 5kms per per 5 secs

Omg am losing my mind

No wait its not like that
Well try to compare it with this one knowing its the fastest speed

Ik it doesn’t make sense but yh

[mellow sky]

idk srry man

iam dumb af

[nocturne bloom]

1 km per 10 secs is that faster

So which one is the lower speed
Going 2 kms per 5 secs
Or 5kms per per 5 secs

[nocturne bloom]

According to this

@naive seal

@polar sun

[mellow sky]

this chat is dead lol

[cinder yacht]

holy sh*t

my brain lags reading this

2 kms per 5 secs
is a lower speed than
5kms per 5 secs

and 1km per 10 secs is slower than both of those (because it's the same as 0.5 km per 5 secs)

[nocturne bloom]

Thank u

[naive seal]

U got the same timescale, so if you cover a bigger distance in the same time, of course you're faster

If you'd flip it, 5km per 2sec would be faster than 5km per 5sec

[obsidian brook]

Thanks a lot @ember kernel @errant scarab Now my brain can rest easy...For now.

[wet gorge]

Can someone pls solve this for me it's tooo difficult 😭😭

[errant scarab]

its 1

its obvious

[obsidian brook]

thought it would be 2 but this question's way harder than what the eye can see

[ember kernel]

You're so funny and quirky haha lol

[left knoll]

it should be 2 but if watch closly, i can see the number 1 is bigger than number 1
in conclusion, 1 + 1 = 11 because the number 1 is string and the number 1 is number

[cinder yacht]

languages that allow concatenation of strings and ints must be cursed

[left knoll]

i won't say it is java||script||

[left knoll]

hi! im having a really hard time here can anyone help me understand?

[left knoll]

well your just wrong

its 83 obviously

[wet gorge]

You think out of box Musk

[wet gorge]

It's easy

[obsidian brook]

mhm...

[wet gorge]

Q A)

1. arc AB, arc AD, arc BC are minor arcs
2. arc BAD, arc DC, arc ABC are few major arcs
3. angle AOB, angle DOC , angle AOD, angle BOC are central angles
4. Angle ODC and angle OCD are inscribed angles
5. arc ADC and arc ABC are semicircle

Q B)

1. M AOB = 80°
   2.m arc AD =40°
2. m ACD = 20°
3. m BCD = 240°
4. m BDC = 260°

[wet gorge]

Did u get it?

[left knoll]

omg thank you!!! yes i tried looking up tutorials on youtube but it was really hard to understand i kept rewatching it for like 40 mins but i think i got it

thank you again!!!!!

[wet gorge]

U can ask if u have doubts 👍👍

[obsidian brook]

I still remember the good old days of learning circles.... intense math flashbacks

[frozen meadow]

Is this javascript. Or math

[final wave]

anyone know arthmatic progresstion

[ember kernel]

I guess you meant arithmetic progression ? Ask here your questions about it and someone will answer

[final wave]

ohk

[ember kernel]

The question reads that a, b, c, d and e are in arithmeric progression
That means that :
b = a+p
c = b+p
d = c+p
e = d+p
... where p is the difference between two consecutive terms of the progression (I forgot the actual name)

In other words :
b = a + p
c = (a + p) + p = a + 2p
d = (a + 2p) + p = a + 3p
e = (a + 3p) + p = a + 4p

Subsitute the b, c, d and e in the question by those expressions and you get :
a - 4 (a+p) + 6 (a+2p) - 4 (a+3p) + (a+4p)
= ... (just compute the sum)
= 0 * a + 0 * p = 0

@final wave

[wet gorge]

Correct and the difference between two consecutive terms in AP is called common difference denoted by letter d

@ember kernel

[cinder yacht]

a fun (but not allowed cuz not a proof) way to think of it is
"there are 2 unknown variable, and they want us to sum linear combinations of those 2 variables. so those variables must get canceled out.
so it's 0

another one : "there are 2 unknown variables, and they want us to find a numerical value for the sum.
so the sum doesn't depend on those 2 variables.
so the sum is the same as in the case a=0 and p=0 (the null sequence : only 0s)
so it's 0"

ofc the only real proof is the one Quentin wrote, but there are ways like this to guess the answer

[ember kernel]

Yeah that's what I thought after realising all the terms summed to 0

Like, at highschool level they would otherwise explicitly ask you to express the total sum in terms of a and p

[cinder yacht]

yeah same

[final wave]

oh thanks guys

[silver pier]

i dont understand the part in cyan green

like why can i just subtract without taking lcm

[ember kernel]

That's straight up wrong

[silver pier]

how so

[silver pier]

i got that from here

[ember kernel]

Idk why they did that

But that looks awful

never add or substracts numerator that don't have a common denominator

Maybe there's some "intuitive" step I missed, but otherwise there are mathematically speaking 2 major mistakes. I really hope it's the first one, otherwise your teacher should just get fired on the spot

[ashen wind]

oh help

27^3n−1/3x9^3n+1

it;s scientific notation

*it's

[ember kernel]

What's the question ?

[ashen wind]

wait

let me cab my scrren

screen*

[sinful lily]

help! what possible topics are good about measure of position in conducting a statistical mini research for students?

[ashen wind]

this question

[ember kernel]

Dude use brackets

The expression you sent was not the one on your screen

It should have been 27^(3n-1) / (3 * 9^(3n+1))

[ashen wind]

i am sorry!

[ember kernel]

Np, you're still learning

But yeah that's kind of important to know

The best method I see here is converting 9 and 27 in terms of powers of 3

[ashen wind]

oh

ok

lemme try

[silver pier]

its C

[ember kernel]

So you only have three bases of value 3, and you'll be able to simplify everything

[silver pier]

wait no

i think i miscalced

[ashen wind]

kk

[silver pier]

nvm

its C

me dumb

[ember kernel]

Remember that :
x^a * x^b = x^(a+b)
x^a / x^b = x^(a-b)
(x^a)^b = x^(a*b)

[ember kernel]

With these three formulas you should be alright

[ashen wind]

oh

lemme try

[ashen wind]

may u show the question in a better angle?

thx

[ember kernel]

Wow that's one flexible thumb for sure

[ashen wind]

i would like to ask why is there are +1 at the beginning of the question

[silver pier]

isnt tha t normal

[silver pier]

thats because

[ember kernel]

Mine's stiff af ^^

[silver pier]

so 3x3x3 = 3^3

or