math-help

[weary arrow]

Hi does anyone know of any good resources to understand commutators? Preferably with some practice exercises if possible

[ember kernel]

Leave a space between the command and the formula

[cyan night]

Can anyone do ittt

[ember kernel]

Don't think so, you have to go through sigma

[cyan night]

it was in a math competition and i couldnt do it 😦

i lost gold 😭

and now i can still not solve it

[ember kernel]

Ooh that might hurt :(

[cyan night]

i tried to brute force it but ran out of time

it follows the general formula of n^2 - 1 starting n = 2

to n = 49

[wicked perch]

Help plsss (this is ARTITHMETIC SERIES)

[cyan night]

oh

[cyan night]

can you do 1 by yourself ye?

[wicked perch]

yeaa it looks easy

just the others they are so hard

[cyan night]

Ok, fyi, the formula for arithmetic series is ((the last term+the first term)* the no. terms)/2

[wicked perch]

okayyy

[cyan night]

the no. terms can be determined by (the last term - the first term)*the difference between each term + 1

(you multiply first then +1)

now you might be able to figure it out :)?

[wicked perch]

so multiply the first term then add 1?

[cyan night]

the difference between the first and last term * the differerence between any 2 terms, then + 1

for example, for a, the first term is -6, the number of terms is 20, and the total is -690

[cyan night]

using this, you can figure out the last term right?

the formula basically means the total

total of the series

which is S

Ok, good luck, I gotta go

[wicked perch]

okioki thank you so much

[cyan night]

have you solved it yet?

[wicked perch]

Not yet

[harsh patio]

Holy crap thanks for the super detailed answer! I got to the same answer but I don’t think I fully understood what I did. 👍🏻

[hollow escarp]

lol, no worries

[hollow escarp]

this is not a , this is 1

[wicked perch]

omggg!!

whats range?

[wicked perch]

ohhhh

[hollow escarp]

they asked us to consider numbers between 2 to 43, so he numbers from 2 to 43 is the range

[wicked perch]

ohh okay

[hollow escarp]

2 d isnt clear, Is it to find the sum of the series upto the 1000th term or till the series reaches 1000?

[wicked perch]

it just says evaluate the series to the given term

wait can you check if my answer is right

[hollow escarp]

626250

i think

let me write it down and check

[hollow escarp]

it is to find the sum I think

[wicked perch]

thats what i got too

[wicked perch]

yea i think so

[cyan night]

substitute in the formula and solve

[hollow escarp]

@wicked perch Its written 1000th . If they mean to find the sum till the 1000th term of the series, this is how you do it

Get it cleared by asking some of your friends or your teacher

[wicked perch]

yes okayokay

thank you so much for the help

i really didn't know how to start this really helped so much

thankyou!!!

[hollow escarp]

You can always start by writing down what is given to you and then writing down what to find. See if there are any formulas which connects the both and start from there

[cyan night]

yes it's like applying physics formula for motion

[wicked perch]

yeaa i knew what the formulas were i was just having trouble with the steps and stuff

[wicked perch]

ohhh

ty!

[hollow escarp]

good luck Alex

[narrow bronze]

How do i simplify this ?

[echo temple]

Anyone know what's the answer to this? Been thinking for a bit but i don't have any good explanations/answers T_T

[dim path]

can anyone explain why this cancels out?

[weary arrow]

Both 46 and 4 is divisible by 2, there fore you can divide both numbers by two

Just like how 2/4 = 1/2

[sour glen]

helloo help me with this geometric sequence problem pls 🥲

[green bolt]

does anyone know why it became -sin?

[ember kernel]

You can mathematically get it using the sin(a+b) formula I guess

But the most intuitive way of seeing it is that, if you add 3pi to your angle, you make an entire turn and a half around the trigonometric circle. Therefore, 3pi+2x^5 and 2x^5 are completely opposite on the circle. That means that, when the sine of one increase, the sine of the other HAS to decrease. => opposite reactions => justifies the - sign

Do you know what I mean ?

Ok let me illustrate it

[green bolt]

I will wait, thank you

[ember kernel]

dm

[green bolt]

ok

[ancient bobcat]

can someone help me with c?

[ember kernel]

I'd say +inf, because if you follow basic paths like (x,y,z) = (s,0,0) or (0,s,0) you always get lim s->0 f(s) = +inf

Oh no nevermind

It's both + and - inf because the path (-s,0,0) leads to f(s) = -1/3s, which tends to -inf when positive s tends to 0

[winged coyote]

Can anyone help me out with 4

[winged coyote]

pls

[acoustic sentinel]

-ysin(xy) / 1+xsin(xy)

[winged coyote]

do u have any work with it

appreciate u

[acoustic sentinel]

at the end i wrote sin(xy) times x instead of xsin

[winged coyote]

Ok thanks that makes sense

[wary snow]

Can someone help me with this question?

[grim sluice]

can anyone help me to transform this into piecewise function?

[grim sluice]

PR=13, QR=12, PQ=5 so sinP= 12/13, cosP=5/13, tan P=12/5

[coarse cypress]

somebody pls elp!

[cyan night]

use pythagorean to determine pq and qr then just soh cah toa and find the ratios

[dark stirrup]

Heyyy

Help with question 9

It's a stats question .... Anyone?

[wary snow]

okaay ty

[left knoll]

Hi, can anyone help me understand how the expansion of sigma was done here?

[hollow escarp]

first, we'll give r=1 and write the equation. Then will give r=2 , rewrite the equation with r values 2, this is repeated until you give values from 1 to 10 and then sum all 10 terms

-1 powered to an odd number is -1 and powered to an even number is +1, That's why all the odd terms are negative and even terms positive

[dark stirrup]

Hi ... I need a study partner for statistics 🙋🏻‍♀️

[hardy falcon]

I got A but the books answer is D, who’s right?

It’s a 30-60-90 triangle when you draw a line down point A to the x-axis

[cyan night]

Ok so slope = rise over run

rise/run = sqrt 3

which means if we drop a perpendicular from A to the x axis, the perpendicular is larger leg

so it should be 60 degrees

since oab is opposite to that perpendicular

@hardy falcon

plz correct me if im wrong

[ember kernel]

Let's name the distance between each circle d (because it is = the diameter of all circles, but it doesn't matter that much actually) and the vertical distance between each center h

Using the formula of the area of a triangle (B * H / 2), we get that dh/2 = 3.14 for the green triangle

The key to solving this exercise is realising that the red triangle has exactly the same height H (= h) and a base B twice as long as the green triangle base (= 2d)

Therefore, its area, according to the formula = (2d)h/2 = 2(dh/2) = 2*3.14 (accordingly to what we found earlier)

Therefore the area of the red triangle is 6.28

[ember kernel]

The graph is not drawn to scale. You can clearly see it because the slope sqrt(3) ~= 1.7 is higher than 1, however on the graph it seems to be less than 1 (because under the 45° line)

@cyan night is right. Although my way of solving it would've been :
Since f(x) = sqrt(3) x and A arbitrarily lies on the graph of f(x), let's just conveniently say that A = (1,sqrt(3))
(now we have formed a right triangle with the points (0,0), (1,0) and A)

Now, let's find our angle a

Since tan(a) = sqrt(3)/1 = sqrt(3), that means a = arctan(sqrt(3)) = pi/3

Quick tip : from now on, don't try to solve graphically. You're above that level, and you'll start seeing more and more poorly drawn graphs, with a scale that doesn't match the actual info given in the question

[hardy falcon]

Do you think the answer is A or D?

[ember kernel]

I answered

[cyan night]

do you read me

surtic

we both answered

[hardy falcon]

I never got a clear answer

Option A or option D

[steep swan]

yall answered in degrees they want the answer in radians

[hardy falcon]

Thank you 😭😭😭

[steep swan]

it's D

but also u need to learn degrees to radians conversion

[hardy falcon]

The book also taught me that

[steep swan]

then u should know that 60º is pi/3

[hardy falcon]

Lemme check (degrees to radians is fairly new to me, I learned it this morning)

[steep swan]

pi radian = 180º

[hardy falcon]

Yea I got pi/3 😄

[steep swan]

so to convert degrees into radians you have to divide by 180 and to convert from radians to degrees you have to multiply by 180

[hardy falcon]

Degree • pi radian/180

^^^

[steep swan]

yep

[ember kernel]

@steep swan @hardy falcon Well I answered in radians, knowing that the possible answers were also expressed in radians ?

[steep swan]

ah apologies i didnt see the radians answer among the wall of text x

[ember kernel]

np ^^

[hardy falcon]

I dum 🥲

[dim path]

where did they pull 3 from?

[ember kernel]

Substract 6 to both sides, then substract sqrt(s) from both sides

[ember kernel]

There you go

[left knoll]

Hi, thank you so much for explaining this. But, I'm still a bit confused about how we are giving negative power to the expression. Can you please help me understand that?

[hollow escarp]

we are not giving negative power

the number is -1

-1 powered to 2 is -1 * -1 which is +1

-1 powered to an even number would similarly give a positive 1

Because two negatives , when multiplied , would give positive

(-1)^3 = -1 * -1 * -1 = -1

similarly when powered with an odd number answer will be -1 and when powered with an even number , it will be +1

did you get it?

[left knoll]

i am not exactly getting how sigma is working here & what is the significance of (-1)^r here

[hollow escarp]

that's given in the equation right?

we just go by the given equation

[left knoll]

Alright, thank you so much!

[coarse cypress]

ayayay okii thankyou soo much

[fossil basin]

2nd step?

After (a+lambdab).c=0

[ember kernel]

a•a = 1 for all a in {i,j,k}
a•b = 0 for all a,b in {i,j,k} such that a != b (is not equal)

Develop with a basic distribution

[left knoll]

i just reflected the graph over x by -f(x) but some dude raised a question about it being over the origin so it has to be both over x-axis and y-axis

not too sure on what the question means by over the origin ngl

[fierce bone]

the value of X is

help me please

[cyan night]

try relating it to 1/1x2 + 1/2x3 +...+ 1/4041x4042 = 2-1/1x2 + 3-2/2x3 +... + 4042-4041/4041x4042 = 1 - 1/2+1/2-1/3+1/3-1/4...-1/4041+1/4041-1/4042 = 1-1/4042

idk how to latex sorry

[lofty arch]

you can take a factor of 2x out

[lofty arch]

that inside sum is a well known result, which you can derive by hand by taking partial fractions

[lofty arch]

I would highly encourage you to actually go through and derive that, it's a really good exercise in pattern recognition

But from there, you can just substitute in n = 4041, and solve for x!

[cyan night]

Yeah

[ember kernel]

There's a whole channel dedicated to that if you want

[cyan night]

yeah the channel that latex dms me whenever i run the ,help command

[ember kernel]

=help

[cyan night]

oh this is mathbot not latex

@candid moth

aight thanks

[ember kernel]

Ho no I was referring to #how-to-use-math-bot

(Btw MathBot is latex-based)

[cyan night]

Ok, thanks

[tough elk]

can someone pls help me on B

[ember kernel]

f'(a) is the slope of the tangent line of f at point x=a

Since you are given two points that belong to the line tangent to f at x=40, all you need to do is calculate the slope of that straight line to find f'(40)

@tough elk

[tough elk]

oh thats it

thanks I was overthinking than

[left knoll]

pls help ;-;

do i just reflect in the xaxis or yaxis and leave it there or is there something im missing

[hardy falcon]

Quick questions guys, can a square root be in the denominator?

[left knoll]

yes but it better not be -1 in that square root

[green bolt]

are the first and last choices correct?

[shut skiff]

i think the last one is the correct answer

[upper parrot]

My calc Ab and BC teachers told me a function is continuous if you draw the line on the graph without picking up the pen so I'm gonna agree with @shut skiff and say the last one is correct. Also, endpoints have to be defined

[gentle sky]

im a little lost can someone help me?

[agile trench]

i think thats right

[gentle sky]

thank you!

[agile trench]

🙂

[agile trench]

i think it is (4,6)

[agile trench]

f is not continuous in x=2, x=4 and x=6

and the only answer that has not those numbers are (4,6)

actually, (2,4) is right too

[lofty oasis]

anyone know how to differentiate "f(xf(x^2))"

[vale cloud]

How to solve B

[ember kernel]

Chain rule

I have no access to paper and it'll be a mess if I write the development here, but I'll try to do that later

[candid moth]

Do more with Wolfram|Alpha pro

Query made by

@ember kernel

[ember kernel]

@lofty oasis ⬆️

[lofty oasis]

AH knew it, i got confused with the x^2, thank you!

[vale cloud]

can anyone help me please

[empty inlet]

does anyone know how to tell if this particular function is continuous (#3)

[languid zenith]

Okay. I am taking Stats but I want to be able to understand Bayes Rule.

[lofty arch]

We know for certain that f(x) is continuous everywhere except for x = 0 (since x^2 + 1 and -x are both continuous everywhere), because of this we just need to test the point x = 0 on both x^2 + 1 and -x , which shows that the function is not continuous at x = 0

This way of doing it is essentially a lazy man's way of taking values from both the left and the right, since we know that x^2 + 1 and -x are both well defined at x = 0

[lofty arch]

3b1b has a great video on Bayes rule

https://www.youtube.com/watch?v=HZGCoVF3YvM

[left knoll]

Pls help me

Find x

[empty inlet]

thank you!

[cyan night]

i have problems finding the difference between contradiction and contraposition proofs

i watch videos and i keep feel like they are similar

habibi

[left knoll]

I thought it was like calculation stuff

[cyan night]

do you know about this?

its conceptual

[left knoll]

I don't know, sorry to disappoint you

[cyan night]

ok, illl wait for quentin

maybe he can help hes very good

[left knoll]

What is this from?

[cyan night]

i just read wikipedia of

proofs

[left knoll]

mhm wait

[cyan night]

Ok

[left knoll]

Ig its from mathematical logic

[cyan night]

can you elaborate?

[left knoll]

Yes it is from mathematical logic- chapter

https://calcworkshop.com/proofs/indirect-proof/#:~:text=Proof By Contradiction,-Now it is&text=Like contraposition%2C we will assume,false%2C then it must true.&text=Then show that this assumption,original statement to be true.

[cyan night]

Ok

[left knoll]

Check this out it has examples even

Shut up

np

[cyan night]

why

[urban berry]

Can you help me please🙏

A batch of 30 products contains 10% of the defect. Find the probability that among the 7 products taken by chance: a) only 2 defective; b) no defective.

[left knoll]

I mean don't say Thankyou haha

[echo temple]

anyone know how?

[marble basin]

It's because you're getting head at the xth flip so you'd get (x-1) tails before that
Both head and tail have a probability of 1/2

So you'd multiply (1/2) x-1 times

And then the probability of getting a head

[echo temple]

i see

thanks a lot man

[ember kernel]

Heeeyyy

Despite your confusion, contraposition and contradiction are indeed different

Contraposition means that proving that P => Q (if P then Q) is equivalent to proving that ~Q => ~P (if Not Q then Not P)

Quick example :

If you're carrying a banana in your hand (P), that means you're carrying a fruit (Q)
On the contrary, if you're NOT carrying any fruit in your hand (~Q), that means you CANNOT be carrying a banana (~P)

[oblique star]

a quick dumb question from someone not so well equipped in maths: when calculating percentages why does x*0.90=90% of x and x÷1.10=/= 90% of x

:))

[ember kernel]

But don't get mislead ; carrying a fruit (Q) does not necessarily mean you're carrying a banana (P)

Showing P => Q is equivalent to showing that ~Q => ~P, but it has NOTHING to see with Q => P (the dependency relation of P and Q is one-sided)

---

Proving by contradiction means that, instead of starting a proof with P to show a theorem holds, you'll start with ~P (Not P) to show that, with such initial conditions (hypothesis), you can't get to a conclusion without having to contradict your hypothesis (~P) or run into a critical error. Therefore, your initial condition HAS TO BE P for the theorem (or whatever you're trying to prove) to hold

Quick example :

Let's prove that all integers have to be "either even or odd" (P)

Method 1) You could take all the integers one at a time, and verify that they are indeed even OR odd (P)

Technically, it would work, but would require an infinite amount of time and energy to get to the end of the proof (I'm sure you know there are many ... many existing integers)

Method 2) Or you could use contradiction. Take any integer that is both even and odd (~P) and let's call it c (we just imagine c exists, but we have no idea about its value). Now, our goal is to try to prove that c exists and to get its value.

Since c is even, we could write c = 2n (where n is an integer).
But since c is also odd, we could write c = 2m+1 (where m is another integer).

Therefore, using c = 2n and c = 2m+1, we can get to 2n = 2m <=> 2(n-m). n and m being integers, that means (n-m) is also an integer, and thus 2(n-m) is an even integer. But 1 is odd. That would mean that, if c was both odd and even at the same time (no matter its precise value), we'd get to an impossible situation where an even number (2n-2m) would be equal to an odd number (1). Thefore, c CANNOT be "odd and even" (Starting with any integer c that respects ~P always leads to an error, that means all integers must respect P)

[obsidian laurel]

TakeRep <User:User> [Num:Whole number]

Invalid arguments provided: Too many users with the name: (Amoxicillin_, potatomato, -Dr Chlorine, -red, -🔰Lofi Boy®, - Ave Maria, - Deadfall) Please re-run the command with a narrower search, mention or ID.

[ember kernel]

---

Conclusion
Contraposition : you use the depedency of two theorems (P and Q) to switch your proof from P => Q to ~Q => ~P
Contradiction : to show that P => Q is true, you show that ~P => ... inevitably leads to some error (or contradiction with ~P)

[obsidian laurel]

TakeRep <User:User> [Num:Whole number]

Invalid arguments provided: User "-\nConclusion\nContraposition" not found

[ember kernel]

Hope it helps @cyan night

[hot vortex]

anyone have any good sources for learning eigen vectors / values with the use of matrices ??

[ember kernel]

Because 1/1.1 = 10/11 != 0.9 = 9/10

[ember kernel]

For visualisation of the concept : 3brown1blue's yt video will do

For the technical stuff and a deeper approach : G. STRANG's lectures in MIT (1806 Linear Algebra) are perfect to me

[hot vortex]

cheers 🤙🏻

[oblique star]

haha makes sense when u say it like that ty

[languid zenith]

I will watch it. Thanks

[ember kernel]

5th line is wrong. It should be :
y(x-1) = 3x-2

-3x shifts from the left side to the right side, but the -2 stays on the right side : it shouldn't have been turned into +2

Nope, this is wrongly drawn. You could ease the task by sketching the y = x graph so that it acts as a mirror

[gentle sky]

I forgot what f''(x) means

[onyx hare]

J bro

[cyan night]

yesss tysm for the effort! i tried correlating the examples ive seen of contraposition and contradiction and it does really make sense. briefly, does it mean that contraposition shows that when the result doesnt apply (~Q) then you cannot obtain P, and contradiction shows that when the hypothesis doesnt apply (~P) then you cannot obtain Q?

[olive trail]

Hey could anybody help me with 16 and 17 please? Much appreciated!

[left knoll]

Find the area of ​​the surfaces of the shapes made up of rectangular parallelepipeds.

Pls help

[cyan night]

divide it into many rectangles

especially the top

divide the top into 3 rectangles

find area of each then add

[cyan night]

can you prove this using contradiction?

i want to use contradiction

[lofty arch]

You can use contradiction, but it's not the simplest way to do it

For questions like these, you're basically going to want to find where equality is

And then test either side

[cyan night]

it isnt a =< actually

i just used algebra to do it

[onyx hare]

anyone know how ? i need help for the probablity test 😦

[cyan night]

damn

[ember kernel]

Yeah it pretty much sums it up. For contraposition : you show that the absence of consequence is due to the absence of cause

[ember kernel]

17. cos(x) = sqrt[1 - sin²(x)] = sqrt[1 - (8/17)²]

From there :
sin(2x) = 2 sin(x) cos(x)
cos(2x) = cos²(x) - sin²(x)
tan(2x) = sin(2x)/cos(2x)

[ember kernel]

16. looks good to me, but maybe your teacher was expecting 1-sin²(x) instead of (1-sinx)(1+sinx), even though they are the same

Or you could also replace cos(x) by sin(90°-x)

[dark sorrel]

For the First equation : px(x) gives you the odds that the first heads appears on the xth flip. Now Pr(X=1,3,5,...) = Pr(X=1) + Pr(X=3) + Pr(X=5) + .... = (1/2) + (1/2)^3 + (1/2)^5 + .... So you are summing up all (1/2)^k for every odd number k. A different way to do this is to sum up all (1/2)^(2x-1) for every natural number x, because 2x-1 will always be an odd number. That is how you get to that first infinite summation of Px(2x-1)

[onyx hare]

thank you my friend

[small canyon]

how do u solve this?

kind of confused on what to do next after reading the question

[cloud ocean]

help

please

[cyan night]

if that's an actual test, we're not able to help

rule 5

[ember kernel]

Answer lol

Nah seriously, transpose both sides, you'll get a 3x3 linear system Ax = b, where A is the big 3x3 matrix in the question, x = (p, q, r) and b = (3, 0, 1)

To solve the system, try and see if the determinant of A is different from 0. If it is, pre-multiply both sides by the inverse of A, so you'll get something like x = A^(-1) b, since A^(-1) A = I, which is the identity matrix

Once you have solved the system for p,q and r, just use the values you got for them to compute the little 2p + q - r at the end

Note : x and p are 3x1 vectors (thus vertical)
Note 2 : The reason A and x switch places when transposed is because transposition works such that (AB)t = Bt At

[left knoll]

help lol

[weary arrow]

X+20/y+20 = 5/7
X-5/y-5 = 5/6
Use these two equations fo solve it

Lmk if you need me to explain the equations

[left knoll]

oooooo okayy okay, thanksss

mwah!

[rustic pine]

Hi, so we had to answer true or false and give an explanation

is there anything wrong with what i've written

any answers are appreciated

[olive trail]

@ember kernel Thank you!

Could anyone please explain the first couple lines of this example? I have never seen this trig identity before.

[inland sigil]

Looks good

[green root]

I believe it's the harmonic form of trig functions, here in the first few lines, it seems to be deriving it, the first line is expanding sin by using compound angle formula, the second line is making comparisons

R is same as your A

[small canyon]

ah got it, did this and solved it, did think of going for this approach thx alot

[viral locust]

Does someone know how to simplify this even further?

[rustic pine]

Thanks :))

[left knoll]

Hi can someone help me out? I need to find all the coordinates between (0, pi) where the tangent t to the graph of the function parallel is with L

This is what I had but it’s not correct what did I do wrong/ forgot

[left knoll]

Can someone help me with some math stuff?

Hmu in dms if you can

From the EU

[ember kernel]

uhm ... I ... I can't understand what it means

[left knoll]

Danish

[ember kernel]

Yeah but ... well ... I still can't work and help you if you don't give me proper material to work with, like a translated screenshot

[unreal sandal]

Guys, pls help

That rounded equations will kill me

[obtuse summit]

Explanations look good but the only thing I would adjust is your reasoning for the first part. “An empty set does not contain anything”. I would change “anything” to “any element” here since the empty set does indeed contain the empty set (but as a set).

[rustic pine]

Thanks I'll keep it it mind :))

[random flame]

Hi can someone help me with Q8b? I just need help with finding the value of A. The A value I found doesn’t match the book’s answer. Any help is very much appreciated!! [PS: pls do ping me thks :)]

[coarse cypress]

im sorry i suck at math ._.

[ember kernel]

A few tips for a solid start :

• The sizes of the whitesquares don't matter, since we're only interested in the intersection areas.
• For each overlapping white/cyan area, trace a line that goes from the center of the cyan square to its corner, to split each area in two. That way, you'll transform 3 undefined shapes into 6 triangles. You know the formula for the area of a triangle

[coarse cypress]

thankyou thankyou but what should i take as bases of triangle hights will be the same as theyre from centre

bases will vary right?

[ember kernel]

Yup, but you know that the angle a the corner of a square is 90°

[twilit pulsar]

how to factor:
z^4 + 64

[ember kernel]

(I also found another, very easy way, of solving this exercise, but it's not really "good" as it exploits the amount of info contained in the question)

So not very rigorous

[coarse cypress]

whats the point of spliting all triangles into 2,ig two of them are already right angled

[coarse cypress]

aight show me

[ember kernel]

On the drawing yes, but they could be rotated in all kinds of way

[coarse cypress]

wait if we rotate white squares

it will be 1/4

[ember kernel]

Yup

That's what I found out

[coarse cypress]

is this allowed?

[ember kernel]

But it relies on the fact that the question gives you no precise rotations info for the triangle, so you just """guess""" the cyan area must be the same no matter how the white squares are placed

But """guessing""" isn't the math way of solving it

[coarse cypress]

ye agreed

[ember kernel]

I'll show you the proper way

Give me some time

[coarse cypress]

aight i grant you 2hrs do what you can comrade!

thankyou tho

[ember kernel]

Ummh

Have you learnt about cosine rule ?
a² = b² + c² - 2bc cos(alpha)

@coarse cypress

[onyx hare]

can someone help mee ? :((

[echo temple]

this too if anyone could help

[limpid harness]

can anyone help me with this question?

[fierce jewel]

Can anyone help me with bisecton method i just want to know what im doing is right or not. I dont need answers .

Please ping me if anyone is ready to me help me . Again im saying i want to make sure im doing in the right way only . We can discuss n close within 5 minutes i guess
so please. . .

[gritty shale]

Can someone help me with question g?

[left knoll]

it should be B

[gentle kraken]

Can anybody tell me the approach?

[cyan night]

try setting the speeds under x

let p's speed be x

p = 2r

q = 1.5r

[gentle kraken]

Yea I hab tried but my answer doesn't match with my options😭

[cyan night]

p = 4/3q

hm

[left knoll]

A = 4.3 , b = 1/2

tell me if it is correct

[fierce jewel]

Thankyou soo much no one came forward to help ! You guys are amazing ! Keep going god will bless you as always.

[left knoll]

can you ask again , i just joined

[craggy plume]

can someone explain how do i look at this?? 40 1/2 was given in the question

[left knoll]

it's just a notation

read as "Forty and a half"

[craggy plume]

oh

thanks

[left knoll]

I suggest you read the stuff i send about this topic. Its called pulley constraints. Give it a try after reading

[fierce jewel]

Not today .

[green bolt]

hello can someone explain why d/dx was squared to find d2/dx2?

[limpid harness]

thank you!!

[weary arrow]

It's just finding the derivative twice, using regular chain rule :)

[green bolt]

Thanks!

I just realized now that i have to use quotient rule 😂

[green bolt]

I need help again. Is du/dy = (excos(r))/y correct for this problem? Because after inputting the respective values of x, y, z, the answers I'm getting are not in the choices even after rounding them off. Am I missing out on something?

[broken stirrup]

Which of the following point can lie on the line which passes through (12/7,6/7)

and the product of whose intercepts are 6?

[short rover]

which chapter is the easiest?
expect the dotted ones, I've done that already

[ember kernel]

10, 12 or 13 I'd say

[weary arrow]

Not sure, as there is only 4 significant figures. Are you sure your calculations are correct? If you are, I suggest asking your teacher about it

[green bolt]

Hello, I still can't figure this out, please help me. I don't really need answers from the choices (if there are). I just wanna make sure I'm on the right track. Thank you!

[brazen spire]

guys need help how can I solve thiss

A circle with diameter 10 centimeters has an arc that is made from a central angle with degree measure 75. Find the arclength in centimeters. The following steps and conclusion form part of the solution: Step 1: Write the formula for arclength, s = rt. Step2: Substitute r = 10 and t = 75 into the formula, s = (10)(75). Step 3: Simply to s = 750. Therefore, the arclength is 750 centimeters. Is the suggested solution correct? Explain.

[ember kernel]

The formula s = rt is only valid for t (theta) expressed in radians

@brazen spire

So you need to first convert 75° into radians

Hint : ||75° = 5/12 * 180° and 180° = pi [rad]||

[gentle kraken]

Pls help..... Solve this out

[cyan night]

there is no point D

if u meant acl then they are equal because angles abc + acl = 90o

and abc + bal = 90o

so bal = acl

[north island]

yep we were confused over same thing guesss quetion is printed wrong then

HELP

7. The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°, find all the three angles.

[languid karma]

Q.If two parallel lines are intersected by a transversal, prove that the bisectors of the two pairs of interior angles enclose a rectangle.

[left knoll]

Second one is - 1/cosa?

Btw they re different questions?

[sand python]

I don't know, the answers are only in my teacher, but there is an option about -1/cosa.

[sand python]

yes

[left knoll]

Okayy imma send ya my solution

[sand python]

thank you so much

[left knoll]

If you don't understand it, I can write clearly

Actually I have to write it is really seems bad

[sand python]

no it is okey i can understand

[left knoll]

Okayy

And for first question, can you tell me options if there are options

[sand python]

63/169 99/169 109/169 119/169 129/169

[left knoll]

Jeez

I found soo different answer

[sand python]

me too :"

[left knoll]

Wait I guess I found it

[olive trail]

Hey guys could anyone explain this to me please? Thank you so much in advance!

[surreal hound]

Can anyone here give me a hand with a simple discrete math graph problem?

It says: given a graph G with 10 edges and n vertices, how many sub-graphs of n vertices and 8 edges can be formed from G?

[dusk jackal]

Hi, i'm honestly confused with this question, i think option 4 is incorrect cause generalised eigenvectors are linearly independent so it might be possible to get 2 linearly independent solutions.

The other options are quite confusing and I couldn't find anything helpful from my lecture notes

It would be nice to get an explanation on whether the other options are correct or incorrect ;;

I'm not sure if option 1 is right or not since the equation for generalized eigenvector is (rI-A)^k*u=v

[left knoll]

Shall i have to learn Calculus before Coordinate geometry?

[ember kernel]

I'd say coordinate geometry first

[frozen meadow]

cos^x-sin^x= cos2x. thats the first answer

[left knoll]

Oh..okay thanks@ember kernel

[left knoll]

Anyone knows where's my wrong?

This is the ans

[devout heath]

hello can someone help me on this please

[sonic mango]

If I have a continuous non derivable function f(x) and I apply a continuous derivable function g(x) is g(f(x)) derivable?

[ember kernel]

No. See for yourself :

[sonic mango]

Thanks!

I was trying to understand why the derivative of a Brownian process Wt does not exist but the derivative of the cube (Wt)^3 does exist

I suppose I will have to ask my uni profesor

[ember kernel]

Verification :

[sonic mango]

https://quant.stackexchange.com/questions/17526/how-to-differentiate-a-brownian-motion

[sonic mango]

Apparently it has something to do with Itos properties

[left knoll]

😦

[vivid knot]

hi, anyone can help me with a combinatoric problem? i dont get the ideo for this one :

How many three-digit numbers are divisible by three by all of their constituent digits?
is a member of S {2, 3, 5, 6, 7, 9} i
thankyou

[inland oracle]

I have to find a set of parametric equations.
I don´t know how to do this exercise):

Translation:
The line passes through the point (-1,3, -3) and is parallel to v = 5i - j

[devout heath]

thanks bro

[left knoll]

The sides of the right rectangular pyramid are inclined to the base at an angle of 60 degrees. If the distance from the center of the wall of the foot to the side is 4v3 cm, find the area and volume of the lateral surface.

Anyone?

[steel sapphire]

the parametric equation of the line would be : (-1,3,-3) and x(5,-1), where x is a scalar multiple

[ancient epoch]

help :(

[ember kernel]

Have you learnt the reduction formula ? That's what Wolfram Alpha starts with for its demonstration

[ancient epoch]

yes

[ember kernel]

Then, you need to go through it

[tough sonnet]

How to do this

Last one

My answer was wrong

[quaint imp]

how do I simplify (−12r to the power of 6) to the power of 2

[quaint imp]

hello

[cosmic sequoia]

Can u share the pic it's gonna be easy to understand

[quaint imp]

kk

here

@cosmic sequoia

[cosmic sequoia]

216 r^6

[cosmic sequoia]

@quaint imp

[quaint imp]

how

[cosmic sequoia]

Cube of six is 216 and I multiple the power of r (2 ) from 3 =r^6

[quaint imp]

ohhhhh

ok

THANK U SO MUCH

[quaint imp]

wait..wdym cube of six is 216...what does that mean @cosmic sequoia

[cosmic sequoia]

If u multiple 6 three times u will get 216

[quaint imp]

y by 3

[cosmic sequoia]

6×6×6 = 216

[cosmic sequoia]

If someone power is 3 we multiple is 3 Times

[quaint imp]

OHHHH

[cosmic sequoia]

Like power of r^2 is 3, than
r^2 × r^2 × r^2 = r^6

[quaint imp]

so for this example what wud the answer be

or what wud we multiply -12 by

how many times

[cosmic sequoia]

Here we will multiple both the things twice

[cosmic sequoia]

2

[quaint imp]

what things

[cosmic sequoia]

-12 and t^6

-12 × -12 = 144
t^6 × t^6 = t^12

Final answer = 144 t^12

[quaint imp]

hmm I'll try to understand

thank u...for now!

[cosmic sequoia]

Ask anything if u have in your mind ?

[quaint imp]

will do!

[cosmic sequoia]

Don't worry,cyaa

[quaint imp]

cyaaa

so foe this the answer wud be...

this.

@cosmic sequoia

[cosmic sequoia]

Yup

I m here

[quaint imp]

Yay

thank u

[cosmic sequoia]

Multiple 3 Times

[quaint imp]

yah

thx

man

[cosmic sequoia]

U r getting better genius best of luck 👍

[quaint imp]

Einstein on the way!

let me solve this

@cosmic sequoia

its this right?

46656

@cosmic sequoia

[cosmic sequoia]

@quaint imp

[quaint imp]

yyess?

[cosmic sequoia]

Multiple 3 Times and than put the value

First solve the function

[quaint imp]

its asking for the answer

[cosmic sequoia]

-5832

@quaint imp

[quaint imp]

how

its not

[cosmic sequoia]

Put t= -3 in -8 t^6

[cosmic sequoia]

Is the answer wrong ?

[quaint imp]

hmm

wudnt u do -2x(-3)

then power of 2

[cosmic sequoia]

Check it again it should be -5832

[quaint imp]

hmm ok

[cosmic sequoia]

Tell me something

What's the power of -2 in question

It's 3, I multiplied it 3 times I get -8 , same goes for t^2

And than put the value of t as -3 u will get the answer

[quaint imp]

OHHH

OK

THANKS

@cosmic sequoia

[cosmic sequoia]

Yup

Try it ask questions as much as u can, spend time with problems u will get better @quaint imp

[quaint imp]

got it

[fiery haven]

Someone help with problem #4 please 😭

[tough sonnet]

i is the root of -1 ryt

[quaint crag]

عرب؟

[fervent spear]

Pls hepl 🥺🥺

[short rover]

someone draw a diagram please:
that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

[ember kernel]

Admire this skillfully-finger-drawn sketch I did while in the bus

However, I'm not entirely sure it is correct. Please sketch it correctly, with proper scales, etc. and check if both angles actually add up to 180°.

[ember kernel]

Edit

[short rover]

I've a question:
shouldn't the question say "...angle subtended by the line 'segments' joining..."

since there are two lines

joining the points of contact

[ember kernel]

Yeah it should

Because I sketched my guess on Geogebra and it works (see the 180° at the bottom left)

So there must be a mistake in the question

[crystal bolt]

anyone know how it can be like that? (the red one)

[ember kernel]

First red circle : trigonometric identity
cos(2a) = cos²a - sin²a ===> cos(2*4x) = cos²(4x) - sin²(4x)

Second red circle : fundamental trigonometric identity
sin²a + cos²a = 1 ===> cos²(4x) - 1 = -sin²(4x)

Just sum that to the other -sin²(4x) in the parenthesis to get -2sin²(4x)

[quaint imp]

can anyone help me with this: A restaurant sells 33 bowls of soup every 3 days. At this rate, about how many bowls of soup can the restaurant sell in 7 days?

[solid anvil]

Ans is 77

?

[frozen meadow]

answwr has to be 77

[quaint imp]

how

explain

[frozen meadow]

11 in 1 day. so 7x11

[solid anvil]

Ok

[quaint imp]

ohhh

THANKS

[solid anvil]

Want pic

?

[quaint imp]

sure

[quaint imp]

ohhh got it

thanks

that was easier..I was overthinking

[solid anvil]

😁 👍

[past finch]

sat question

[solid anvil]

?

Huh

[quaint imp]

really?

[past finch]

Nop, too easy for SAT

[quaint imp]

lol thats what i WAS THINKING

[frozen meadow]

who said it was sat

[past finch]

Thats why you need to study a lot😼

[quaint imp]

yeah.lol

[quaint imp]

which shows equivalent ratios

[left knoll]

last option

[opaque violet]

yes d also

[left knoll]

(d)

[quaint imp]

sum1 says A,B,and D

in genera'

ok

thx

IT CAN ONLY BE ONE

IT DOESNT LET U PIK 2

[fierce jewel]

Guys i solved one question , but i dont know i did right or not . Its bisecton method , can anyone please have a look . . 🤒

[cosmic sequoia]

It's D

Correct answer

[quaint imp]

lifesaver is back

thx

everyone

[frail saddle]

hi guys
does anyone have recourses to study about ways to solve problems that involve AM- GM inequalities, Cauchy Schwarz inequality or anything about AM-GM inequalities
something like this?

[quaint imp]

question

[slender osprey]

Ramp A and Ramp C ig

[slender osprey]

if u take tangent of both the ans will be same thus the steepness is the same ...i hope i could help...my studies aren't in english so i don't know if i could explain correctly

[quaint imp]

yeah I was thinking the saame

thanks!

[slender osprey]

Ur welcome!

[quaint imp]

LAST QUESTION

[slender osprey]

Ans will be A ..cuz the base are the same ...so the 5+3-4=2

[quaint imp]

yup got it!

[past finch]

A and C

[quaint imp]

🙂 thanks!

[hidden spindle]

could anyone help me with this pde chain rule problem? I know that the answers are 2s and 2t

[ember kernel]

The best way to put this is to use the notation where each function has its variables beside

Therefore we have :

[ember kernel]

It's easier to see what is a function of what variables

Now, using chain rule :

[hidden spindle]

so thats where I got to, I dont see how its simplifies to 2s... do I plug in values for t?

thanks btw

[ember kernel]

That's the answer

You want to get dw/ds, you got dw/ds

[hidden spindle]

I'm saying I dont know how id use the trig identity to get from 2scos^2(t) + 2ssin^2(t) being equal to 2s

[ember kernel]

sin²(t) + cos²(t) = 1

Just factorise the 2s before and that's what you get

[hidden spindle]

omg

[ember kernel]

yup

[hidden spindle]

I see now

[ember kernel]

that's it

[hidden spindle]

thanks a lot!

[ember kernel]

np ^^

[boreal meadow]

In this function form

What does a, h, and k mean

I’m learning rational functions

[cyan night]

a number is rational when it is expressable under a fraction form

i think

wait

[boreal meadow]

Ok? What does the variables mean i don’t get it

[cyan night]

its just a parameter

that indicates y is expressable under a fractional form

therefore rational

i think thats what its trying to say

can u take a picture of the whole question

[boreal meadow]

It’s not a question I’m looking for but this formula goes into most questions I’ll just show u an example

How do ik what is a h and k

[cyan night]

k is the y intercept

i think they're trying to say that the numerator is 1 number and the denominator is a difference

so for example 11x+12/x = 11+12/x where k = 11 and a/x-h is 12/x

[boreal meadow]

Ok I get where k and h are

How about a?

[cyan night]

this is for limits right

[boreal meadow]

Rationals

[weary arrow]

You rewrite the expressions to have that form

First one for you, you see how you just rewrite the expression to fit the form? Then use those values to find what you need I assume

[boreal meadow]

Thanks

I figured it out

I used synthetic division

[olive trail]

Could anyone please @ me with help to these problems would be super appreciated really struggling with calc haha

[ember kernel]

1st question is just asking you for the derivative of f(x). You can use the rules you've most likely learnt to differentiate x² and x

[left knoll]

PLSSS

simplify and resolve

[harsh glacier]

i need some help on combination math

bc i can't understand anything

[left knoll]

Can someone explain how they went from that to that step? ://

@ember kernel

[lapis lodge]

f"

can someone help?

[sterile sun]

@lapis lodge f" is the second derivative. So take the derivative of that given rational twice

[cobalt mural]

to get f’(x) use:
quotient rule - (gf’-fg’)/g^2
or
product rule - (fg’)+(gf’)
… then take the derivative of f’(x) to get f’’(x)

[cobalt mural]

they foiled it:
cos(2x) * (1+cos(2x))
they multiplied the outer number w each of the values in the parentheses so

cos(2x) times 1 and cos(2x) times cos(2x)

which will be:
cos(2x) + cos^2(2x)

[cobalt mural]

o you can use the practice another option and it should show u like answers to similar questions plus it gives a walkthrough sometimes too

[cobalt mural]

not too sure how they wanna answer #11 but that second equation they give u is limit definition so prob just input the first one into that format and simplify

[cobalt mural]

for the second one, i think they’re trying to isolate cos x in one side so
for the first box: they put x² with 1/2 or: x²/2
second box would be: 1 - x²/2

[ember kernel]

As @cobalt mural
It just as easy as a(1+a) = a+a²

[short rover]

why is TO angle bisector and OT perpendicular to PQ

[frozen meadow]

in integers these are positive integers(1,2,.....) and these are negative integers (-1,-2,-3,....) then what do we call 0. where does zero belong in integers?

[ember kernel]

It belongs to none, it's just zero

But it does belong to the natural set (integers >= 0)

[short rover]

An integer is a number having a positive or negative sign

[short rover]

you might understand it in this way

[terse adder]

Who can help to solve this problem?

[short rover]

what class is this?

[terse adder]

??

[cyan night]

it's mathematics

[short rover]

what grade are you in?

[terse adder]

11

[proud fable]

https://gyazo.com/d904f3cb32ae45f4386893411749ea13

i got 7/10, s stands for true and f stands for false, it was corrected by computer, can anyone tell me which 3 i got wrong so i can learn them 😀

2^3^2 = (2^3)^2 is wrong i belive, that one should have been f

should sqr(144) be +− 12?

[cyan night]

2^3^2 = 2^(3^2)

-2^4= -16 because no parentheses

[cyan night]

yes

(-2)^-3 = -2/8 = -1/4 i believe

or no

or yes

yes

so you got 5,6,7 incorrect

i believe

5.6.7*

[ember kernel]

• Isolate y in both expressions to get actual functions.
• Perpendicularity depends on their slopes, so differentiate them first

[proud fable]

ok thanks alot, but number 8 is correct then? sqr (144) is not +−12 but only +12?

[cyan night]

why did i get a thumbs down

[ember kernel]

7 is correct

Last one isn't

[cyan night]

oh

i am not working then

[proud fable]

yea i was thinknig 7 was correct

[proud fable]

can you explain it to me?

[ember kernel]

Because in the last one sqrt(-16) = sqrt(-1) * 4

But sqrt(-1) gives you a complex number (if you haven't learnt about these, just ignore it and remember you can't get a real number from a negative square root)

[cyan night]

yes and double check (-2)^4 = 16

[ember kernel]

In case you're wondering :
(-16)^(1/4) = sqrt(sqrt(-16))

[proud fable]

ty very clear!

so number 5 and number 10 are incorrect, whuch is the last one?

[ember kernel]

6

a^(b^c) is not (a^b)^c

Convince yourself by plugging values 2,3,4 into both expressions and using a calculator

[proud fable]

yea first one says 2^9 and 2nd says 2^6 right?

[ember kernel]

No (EDIT : WRONG ACTUALLY IT'S YES)

Pemdas rule

Parenthesis first in the order of operations

So (2³)² = 8² = 64

[short rover]

i panicked because I'm in 10th and i can't do this question

[terse adder]

Ah, I get it))

[proud fable]

and the one with parenthesis? 2^3^2=2^9=512?

[ember kernel]

Forget what I said

Both are correct I'm braindead lol

(2³)² = 2⁶

[terse adder]

I'm trying, but it doesn't work on step 2 and 3.Maybe, I'm doing something wrong.

[proud fable]

huhh so is 2^3^2=(2^3)^2

i understand the one with parenthesis but not the first one

when i do it on calculator i get the same answer but im not sure if im typing it wrong

[proud fable]

ohhh now i see

thanks

thanks alot for the help quentin, ill give the test another try

[ember kernel]

Show me what you got

[proud fable]

https://gyazo.com/00752007c00644f791475469506880f1

one of my answers is wrong

its asking for k which in swedish is angle or inclination of the straight line and also where it crosses the y axis when x =0

i feel like my answer is 100% correct on this one though?

[ember kernel]

Usually m is for the slope, and k for the y-intercept

Have you tried swapping the values ?

[terse adder]

3y=4x+2 y=4/3x+2/3 k1=4/3
y=√2x³ x>0 y=√2x^3/2 y'=3/√2√x
y=-√2x³ x<0 y'=-3/√2*√x
k=-1/k1

I don't even know what to do

[proud fable]

ahh its for sure not like that in sweden and i got half point so in that case id get 0 points🤔

perhaps computer is wrong on this one?

i suspect they wanted me to answer 2x on k instead of just 2

[ember kernel]

Can you send your question again pls ?

Don't want to scroll too much

[terse adder]

yep

[ember kernel]

Wtf my answer is nowhere

[terse adder]

By the way, there are answers here

[ember kernel]

Ok that's what I thought, no real answer

I thought I was going crazy

Oh wait

No

I am going crazy

Nah sry I really don't understand

I tried again and again while in the bus

But I just can't, it's Friday and my brain is off

[terse adder]

my brain too))

[celest cradle]

is the ans 4x^2+y=0 ?

[terse adder]

Yes

[celest cradle]

is the doubt clear or should i explain how?

[terse adder]

Can you explain please?

[celest cradle]

diffrentiate the curve and put dy/dx=-3/4(as they gave all tangents to be perpendicular to the line with slope 4/3.. then you will get the locus of points

got it?

[terse adder]

Understand about diffrentiate

[celest cradle]

whats the relation btw slopes if two lines are perpendicular?

[terse adder]

product is -1?

[celest cradle]

yup

so we need to find all points whose tangents slope is -3/4

[ember kernel]

But then sqrt(9x/2) = -3/4, which makes absolutely no sense in the real set

[celest cradle]

how did you reach up there?

[terse adder]

Can you pls show me the solutions? if it's not difficult for you, of course. Just I really confused

[celest cradle]

yup

just a sec

[terse adder]

Dude, thnx a lot))

[celest cradle]

😉

[ember kernel]

Ooh right

Didn't think about applying chain rule to y²

[oblique star]

I need to find the derivative of 1/x^2 using the definition of derivatives

How do I fit the last expression into the definition ?

Like this looks a little clumsy

[weary arrow]

OK I'm not familiar with math bot idk why the fractions didn't work

But basically just put the delta x into the fraction

[weary arrow]

@oblique star like this, and then - f(x)/delta x

[oblique star]

This correct?

Tyty

[quaint imp]

guys question

[left knoll]

c

[quaint imp]

c? how

@left knoll

[left knoll]

its c

[quaint imp]

OF?

lol

ok

[left knoll]

just use distributive law

multiply it

[quaint imp]

can u explain how we wud simplify these

[left knoll]

add/subtract like terms

all terms with x^2 are like

similarly, all terms with x are like terms

[quaint imp]

ohh

ok

[left knoll]

should be c again

[quaint imp]

ok lemme check first

🙂

yeah I think ur right

it works

is the answer for this c?

[left knoll]

no

[quaint imp]

how

[left knoll]

distributive law

-2x is being multiplied

[quaint imp]

i did

[left knoll]

not added

[quaint imp]

so it wud be -2x times +7

[left knoll]

it would be -2x times everything

[quaint imp]

but we need like terms

[left knoll]

u need like terms for addition and subtraction

[quaint imp]

its d

[left knoll]

yea

[quaint imp]

oh ok

guys im so confused

[naive rapids]

wtf is this lang bro damn

[quaint imp]

lang?

@naive rapids

wdym lang

[left knoll]

d

[quaint imp]

how

[naive rapids]

language

[left knoll]

are you elementary student

[quaint imp]

its english....but its also math

[quaint imp]

no

[naive rapids]

r/woosh

[quaint imp]

shh

[quaint imp]

grade 11

[left knoll]

its just a simple logical math, product of negative with negative numbers is positive

[quaint imp]

lol ik but I havent done thistype of math for a long time

@left knoll '

[quaint imp]

guys: I Need help on this one Im almost done

[young sable]

a rectangle of area 672 cm2 is inscribed in a circle of radius 25 cm. determine the perimeter of the rectangle, should I do a system? i am stuck

no wait, i had already done it

The area of a right triangle is 240cm2 and the difference between the areas of the squares constructed on the sides is 644cm2.
determine the length of the hypotenuse of the triangle. was this

[quaint imp]

here

[ember kernel]

4x + 6 - 2x + 8
= 4x - 2x + 6 + 8 (A)
= (4 - 2) * x + (6 + 8) (B)
= 2 * x + 14 (C)
= 2x + 14

(A) Via the commutative property of addition (a+b = b+a)
(B) By factoring x out and grouping 6 and 8 in a single parenthesis
(C) By developing the inside of the parentheses

[left knoll]

Can anyone here explain concave up vs concave down and how we use that to find the sign of second derivatives? If so please ping me!

[languid zenith]

This is very cheesy. I learned this in Middle school. You group the like terms together(put a circle around one type of like term. A square around the other types of like terms) and you add them or subtract them. So you group all of the x^2's, then the x's, and then the constant values(the one's without an x next to them.

That is the general way to do it.

I hope my explanation was comprehensible.

[late thunder]

HEELPPP

[tiny rover]

can some one help me with this

[late thunder]

this may help: https://www.mathsisfun.com/calculus/concave-up-down-convex.html

[short rover]

A student argues that-there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability 111. Do you agree with this argument? Justify your answer.

[lofty arch]

Im just going to assume that you meant 1/11. Since we aren't given any information about the distributions of the outcomes, just a list of final outcomes, we cannot make a determination of the probability of each outcome. Suppose we had a jar which held exactly 1000 2's, and then one of each other number. Then the probability of getting a 2 would be 1000/1010, and the probability of getting {3,4,5,6,7,8,9,10,11,12} = 10/101. Clearly the possible outcomes are the same as above, but the probability of each is not 1/11.

[short rover]

Suppose we had a jar which held exactly 1000 2's, and then one of each other number. Then the probability of getting a 2 would be 1000/1010

I didn't understand this @lofty arch

[languid zenith]

I would prove it by plugging in p into the function and seeing if you get q as the output

[cyan night]

the number of outcomes is still 11 (2,3,4,5,6,7,8,9,10,11,12) but there are a lots of 2s. therefore, the probability of receiving the outcomes are not the same

the number of outcomes still remain, but the quantity of each outcome is dissimilar

[short rover]

explain to me what "a jar having 1000 2's means"

[cyan night]

so lets put it in a context that we're picking the numbers out of a jar

the jar has 11 outcomes

but there are 1000 2s and just 1 of each other number

still 11 outcomes, right?

@short rover

[short rover]

yes

[worn lava]

does anyone know how to do this q

[royal wadi]

yeah thats easy

[cyan night]

how do i get good at algebraic manipulation

advanced algebraic manipulation

[ember kernel]

Practice

What kind of "advanced algebraic manipulations" ?

[cyan night]

i dunno like being able to manipulate algebra at a high level

[ember kernel]

Practice

[cyan night]

it's pretty abstract and hard to describe

is there a website specified for it?

[ember kernel]

Go through all the steps at first, even the most basic ones

Like 3x+4x = (3+4)x

= 7x

[cyan night]

Yeah

also, is there any way i am able to know all these special laws and equations

[ember kernel]

And the more you do it, the more you'll identify patterns and shortcuts that'll make it possible for you to understand that 4x+3x = 7x at first glance

[cyan night]

yeah i want it to become intuitive

[ember kernel]

Practice

[cyan night]

do you have resources

[ember kernel]

Mmh not really

Sry

[cyan night]

Ok thanks

[ember kernel]

That's not something you can read from somewhere

Just practice your exercises and get some advanced one online

[cyan night]

i feel like the homework at school is too easy for me and i want to become specialized in math

[ember kernel]

Search for advanced exercises online

Or give yourself a messed up expression and try to simplify it

[cyan night]

yeah, also wont i need some algebra laws or equations beforehand to solve hard problems?

i find myself not knowing any at all

other than some simple rules

[ember kernel]

I'm going afk

[cyan night]

and popular stuff like the binomial theorem etc

Ok

[ember kernel]

Send me just one dm so i remember to answer you in a few minutes

[cyan night]

Ok, ill also go dinner now, cya later

[weary arrow]

How much you have left is not a sum

[weary arrow]

They don't need to add up to the same number

[ember kernel]

No. What I mean is : give yourself hard problems that you can solve now. I'm not asking you to demonstrate every existing theorem in the world from scratch. Just find something adapted to your level

[cyan night]

Ok, so how would i search google if i want to find them

[grizzled lotus]

Wait where did u get the 2 and 1

[cyan night]

have 3

[weary arrow]

It's a different example to highlight how the original picture is a bit silly.

If you have 50$ and spend 50$, you will have 0$ left. The left and right side won't add up then either.

[cyan night]

tiktok sketchy

[weary arrow]

See how they don't need to be the same at all? The video is just made to be confusing on purpose

[cyan night]

yes

[shadow garden]

Can anybody explain how the 2nd line of 4(iii) solution happened? My brain is lagging

ok nevermind I got it lol

[grizzled lotus]

Uuu thanksss

[ember kernel]

Just browse what you literally want

Say you want to train your fraction simplification skills, just type in "advanced exercises fraction simplification"

I mean, you're asking me how to google something there, how should I respond ?

[solemn vessel]

Anyone here good at linear algebra

[sly arch]

Ya

@shadow garden @shadow garden
There numerator and denominator both is multiplied by 2cos1/2

[gusty jasper]

can anyone help me with this one? 😦

[solemn vessel]

Ya

I think I can