math-help

[solemn vessel]

@gusty jasper

I havent done this in forever but

sub in 2 for x in f and g

subtract f(2)-g(2)

then multiply h(2) by that value

[gusty jasper]

thank you!

[solemn vessel]

Was that correct

[gusty jasper]

yes

[green bolt]

pls help

[ember kernel]

Apply chain rule

dz/dt = dz/dx * dx/dt + dz/dy * dy/dt
(All derivatives expressed at t = 0 for .../dt and (x(t), y(t)) = (x(0), y(0)) for dz/dx or dz/dy)

Substitute the values the question gave you into the expression, and you get :
27 = 45 * 1/5 + 3 * dy/dt

(And dy/dt|t=0 is the same as y'(0))

[green bolt]

ahh right, now I get it. I was very confused because symbols for the derivatives was changed and how they were said 😆. Thank you so much!

[ember kernel]

Np !

Usually, f'(x) is the same as df/dx, with the specificity that f has to be a function of ONE variable : x
df/dx has to be used when f has 2 or more variables

[left knoll]

can someone help me with this ? thanks in advance!

i have to write it in general form btw

[modest compass]

Idk if you've done it yet but you can use m=change in y/change in x and then the general formula for a line (y - ycoordinate = m(x - xcoordinate)). Your other point would be (4,0) since the line passes the x-axis at 4 at which point y is 0

[versed orchid]

can sb help me pls

[main mauve]

anyone here good with discrete random variables?

[dreamy oasis]

@versed orchid Do you know what the answer is, I solved it, if the answer is correct, I will post it.

[strong hornet]

triangle ABC if sinA:sinB:sinC=6:5:4 how to find cosA:cosB:CosC

[cyan night]

peeps

[fervent spear]

can anyone hepl me

[strong hornet]

convergent

[fervent spear]

Yes i know

Why convergent

Limit u = e

So i think it is convergent

[quaint imp]

how is it cheesy

?

what if I didnt learn that in middle school

@languid zenith

[languid zenith]

You put the same shape around common terms and a different one over another

[quaint imp]

yeah I get ur explanation

y do u think its cheesy

that I asked a question

[languid zenith]

I don't know. Or maybe some people might think that it sounds stupid to do. IDK. It worked for me

[quaint imp]

bruh I'm not talking bout explanation

wdy even mean by cheesy

@languid zenith

[languid zenith]

Maybe the wording is weird.

[quaint imp]

of what

@languid zenith

[languid zenith]

Nevermind..

[modest compass]

Anyone know what variance and standard deviation actually mean, i understand how to find them but what actually are they?

[gilded crown]

Yo, is anyone taking math proof here?

[slate dune]

Yo horizontal asymptote is lim x-> infinity right?

[cyan night]

yes

or - infinity

[solid anvil]

someone explain this

[left knoll]

2nd step == multiply both sides by a
3rd step ==
lhs -- useing identity
rhs --- take b common

a+b=b
b+b=b

in the last step we chand "a" to "b"

coz a=b (we take this as let)

[ember kernel]

To simplify the (a-b) on both sides, what they do is divide both sides by (a-b).
What they overlook is that a=b, so they're actually dividing both sides by 0, which you can't

That's why they get to 2=1

[last echo]

It's wrong

Cuz u can't divide anything but zero

[willow basin]

lol i know this is kinda simple but...

can someone just tell me how <BOC = 29

pulling all-nighters and brain just isn't functioning so...

[left knoll]

I don t think that the second answer is correct but here is my explanation : we got ABDC a parallelogram so opposite angle is eaual therefore <BDC = 32 . And lets take P asthe middle of BD SO in the triangle PDC <C= 180-90-32 <C=58. Now <ACD=90+58=148 .

[willow basin]

...

That kind of makes sense.

But why does my teacher think it's 29.

I just don't get it.

[potent pewter]

Do you guys know why the 3 repeats in 45/54?

[coarse cypress]

is math related to science?

[gentle sky]

I need help :C

[ember kernel]

if h(t) = e^(ax), then h'(t) = a e^(ax)

That's a big hint

[ember kernel]

It is related, but if you want to ask about mechanical stuff, ask it in #science-help

[echo temple]

could anyone help me with this please? ty

[sweet idol]

hi guys i'am new here can anyone explain how this works and what should i do so i can study with you guys 🤓

[short rover]

is NML~PQR same as MNL~QPR

[ember kernel]

Here, it's mostly about sending questions or things you don't understand to get them explained to you. It's not that much about "studying together" 😁

[sweet idol]

ohh ok thanks

[cyan night]

yes, because both are N to P, M to Q and L to R

[short rover]

sometimes it makes me confused

But this one worked

[cyan night]

okkk

[ember kernel]

You're welcome !

[sharp night]

What is the notation of translating a point A through V

the result of it is A' and |AV| = |VA'|

If this does not make sense, i hope the second sentence will help

[left knoll]

Ex 7

[left knoll]

Can someone explain that how do we multiply sqrt(2) in the above equation (in blue) to result in the equation at the bottom (in red)?

[ember kernel]

⬆️ Does it help ? ☺️

[short rover]

if only a median and two sides of a triangle are proportional to the same of other triangle, can we prove the two triangles similar?

[ruby seal]

does anyone have good notes or anything on intergration?? ;;

[left knoll]

can anyone explain this?

[left knoll]

What specifically

I have everything up to Calc 3

[left knoll]

Get them in terms of sin and cosine (csc is 1/sin and cot is cos/sin)

You know that 1/sin = 1

Nvm

I can’t work it out right now

But yes, get them into sin and cos

[ruby seal]

im actually doing o level;;

additional math to be specific

[ember kernel]

1D or multivariable ?

[ruby seal]

im not sure what those are as i take IGCSE;;

[weary arrow]

1D integration = 1 integral S thingy, multivariable: several integral S things

If you don't know it's probably 1D

[frail saddle]

guys

how can i find the maximum and the minimum value of this :(

[fervent spear]

ok vietnamese

i solve by vietnamese nhé @frail saddle

[frail saddle]

yea sure can you dm me :'(

[fervent spear]

okk bros , wait 5 mins

Min = 7/8

[frail saddle]

no no but like how

how did you come up with 3.1/2√x-1

why does it equal 0

[fervent spear]

no

đạo hàm nó ra đi

:))

chứ sao equal 0 được

[frail saddle]

aight i'll go watch the organic chem tutor

[fervent spear]

you can speak tiếng việt k ?

[frail saddle]

yea i can but not good

also not comfortable

can we dm :'(

[fervent spear]

ok i can :))

[frail saddle]

don't wanna flood chat with diff language

[fervent spear]

oki i know , sry bro

[urban berry]

Hello, can you help me please with Probability theory🙏
Of the surveyed businessmen, 80% prefer to keep money in a bank (event A), 60% invest in securities (event B), 50% simultaneously hold money in a bank and invest in securities. Find the probability that a randomly selected businessman keeps money in a bank or in the form of securities.

[inland sigil]

P(A union B) = P(A) + P(B) - P(A intersection B)
This is a formula based on probability Venn diagrams

Here 50% is P(A intersection B)

And the result we need is P(A union B)

[urban berry]

Thanks☺️

[winter crow]

can anyone help?

only C pls

[left knoll]

Ist es nicht eif die Ableitung von 1 = 0 also (0|0)

Ableitung = Steigung

[winter crow]

also die Steigung ist 1/1

hä

[ember kernel]

Place radar at (0,0) and the plane trajectory on the line (x,2)

[ember kernel]

So you know for what x the two are separated by 5 miles

And since x = v * t (you know v), you can calculate for what t radar and plane are separated by 5 miles

Then, take f again, but replace x by that vt expression (you know v) and evaluate its derivative at t = the time you calculated for the plane and the radar to be separated by 5mi

In formulas :

[ember kernel]

(Only considering the positive value for x since we say the plane has already passed the radar, so it's getting away from it (assuming it moves towards the positive x)

now :

[ember kernel]

f(x) ---> f(t)

[ember kernel]

Differentiate according to t, and evaluate at t = 360 sqrt(21) / 47

Since f(t) [m] and differentiating according to t gives it [1/s], you'll get an answer in [m/s], which is what you're looking for (a rate of change of distance)

Quick tip : when dealing with physics maths, always make sure the units make sense. Analyse what units the answer needs to have, based on what you're asked

I can't stress it enough ; it WILL guide you and help you make less mistakes, because when you don't know how to apply a certain operation (multiply by a/b or b/a ?) or when you just don't know what to do to get to the solution, going through steps that make you closer to the correct units will be the best thing to do in most cases

(Disclaimer : I'm exhausted, so I may have miscalculated some values, check twice before writing)

As soon as it is a physics-related problem, I advise you to at least evaluate the units of your answer

A teacher will never ask you to find a velocity expressed in [m] or [m/s²]

[left knoll]

Decimals suck

[woven oar]

Anyone knows anything about line integrals of vector fields?

and Stoke's theorem?

[left knoll]

wha-

[rustic pine]

Hi guys I need some help writing a proof for this , i know the answer is right i just don't know how to go about explaining it with logic 😥, I've been breaking my head for last couple hours. I just started classes couple weeks ago so I'm kind of lost still .

[peak gale]

@rustic pine maybe show that your set belongs to [0;1[ (easy) and then show that any value of [0;1[ belongs to your set by finding a contradiction if it exists x such that x doesn't belong to your set

[frozen kestrel]

I need to master linear algebra anyroadmap's ?

[final plume]

hello does anyone know how to solve this

[winter crow]

can someone help with C

only

[winter crow]

Can someone tell me how to i get the slope of a tangent at a specific point in a polynomial function

[solemn vessel]

@winter crow

Take the derivative of the function

Sub in the point into that derivative

[vapid osprey]

determine the coordinates (x,y), with respect to the canonical basis of the plane vectors, of the vector, with the same norm as the vector (2.8) and which is orthogonal to the vector (2.8)

[ember kernel]

The vectors are orthogonal

So (2,8)•(x,y) = 2x + 8y = 0

And they have the same norm

So x² + y² = 2² + 8² = 68

[ember kernel]

Two equations, two unknowns, just solve the system to get the solution

[short rover]

Is there any way to know if you've to do construction in a question or not...
I can't figure out which questions require what type of construction

[ember kernel]

What do you mean by "construction" ?

Like steps to get to the answer ?

[short rover]

yep like draw AB perpendicular to BC

[ember kernel]

I don't know what you mean. Like, just draw it ? That question seems pretty straight-forward and what you're required to do looks clear

[short rover]

I mean it's not implicit in question

have you never come across a question which doesn't ask to draw anything but we do it anyway

[cyan night]

i have encountered this problem

angle xoy, point m inside the angle. construct a,b such that m is the midpoint of ab

if this is what u meant

[cyan night]

is it

is u meant this

[short rover]

no no

if there's "construct" in question it is explicit

[cyan night]

the question is to construct

what conditions a,b have to meet

aight i dont get u then

[ember kernel]

If your question is "do we sometimes have to draw intermediate constructions in geometry to get to the solution ?", the answer is "obviously, yes"
If you were always asked one-step-answers questions, you wouldn't grow your thinking skills. All you'd do is brainlessly draw what the question explicitly tells you to draw

[rich mauve]

ca n someone help me??

here'

[buoyant stag]

Does anyone know about GCSE maths who can help please?

[peak gale]

What are you supposed to do?

[left knoll]

hi, I am doing gcse maths, i can try to help

[buoyant stag]

what year are you in?

[left knoll]

11

[buoyant stag]

same

[left knoll]

ok, did u want any particular help, cos i can try haha

[buoyant stag]

yes pls do you know compound growth/decay

[left knoll]

yeah i think so

[short rover]

like 22/7×(49)^2×360
how does one do this quickly without error and calculate

[shy cloak]

would anyone be able to helpl me out with this question? since the z-score table only goes up to 2 decimals (1.06), i was wondering what i should do with the 3. do i do a weighted sum kind of thing or should i pretend like it's 1.065 :")

thank you in advance

[ember kernel]

You write it down and take the time to calculate it ????

[winter crow]

Can someone help me with C

[olive trail]

Hi could anyone help me with this problem? Thank you so much!

[short rover]

how do you do the last part you said

[distant walrus]

BEDMAS or PEMDAS

[short rover]

someone up? help me with this logic

if the cloth is hexagonal, what are the designs drawn on?

table?

[wraith sun]

the other desing are the segment

[ember kernel]

You misread the question. The table cover is round, so the designs are also drawn on it

[short rover]

yes the table is round but the CLOTH IS HEXAGONAL

Designs drawn on whole table? or just that portion which isn' covered by cloth

[left knoll]

How do you solve this?

Ping me

[peak gale]

Consider the 6th Power of that equation, then write any term in terms of power of 2

[left knoll]

What

[cyan night]

write all the terms under the power of 2, the essence is to make all of them with same base (ex 8= 2^3)

[left knoll]

I still dont get it

[peak gale]

Try it

[left knoll]

Can you do this?

[left knoll]

I cant because i dont understand

[peak gale]

You need to understand, not to copy what someone else can do....
Your equation is only a multiplication right?

No addition

[weary arrow]

considering there's only one equation for 2 variables we don't have enough information to solve this question

If U is 10 x is 5.

it's math help, not tinder 😛

[vital bronze]

lol

[vapid wolf]

apply logarithm

[left knoll]

Pls someone solve this...i dknt knkw how

[vital bronze]

-_-

[vapid wolf]

CamScanner 10-17-2021 19.47.10

I'll ask money next time

jk

[vivid veldt]

hmmm anyone here that could explain to me how to predict the chance for a T/student distribution? It is given that P(T_8>3,25) but i don’t really have a single clue how to begin

[ember kernel]

"Round table cover"

And even if it was drawn on the table, it wouldn't change the total area of the designs, so you could still solve the problem and get the proper answer

[short rover]

so there's no mention of table?

[ember kernel]

Read your question again ^^
No mention of a table, only the table cover

[short rover]

well thanks

it makes its understanding easy

[stable dew]

so you're trying to find the probability that T > 3.25, where T is a Student t-distribution with 8 degrees of freedom?

[vivid veldt]

Indeed

well i assume the answer would be between 0,005 and 0,006 if using a t-table as i wrote down during class but i don’t remember exactly how to get there

Do you just count up 1 degree of freedom and count 1 down respectively for lower and upper boundaries? But how do you then exactly decide what values to pick (from a t table) as boundaries?

Because when looking at T_9 i get a boundary of exactly 3,25 (which is my lower boundary?) then i get the 0,005; but i don’t know how my professor came up with the 0,006 part as there is no probability value like that linked to a value of T_7 in my table

(Perhaps he used a more exact version of a t table?)

[modest compass]

Anyone know how i could solve (x-2)^(-½) = 0?

[stable dew]

did you try graphing the left-hand side?

[stable dew]

i don't think you'll want to do this. if you change the degrees of freedom, you're looking at a different probability distribution

so you should only look at the 8 degrees of freedom case

[vivid veldt]

Well it is rather an estimate that i need to predict, i probably should’ve said that earlier haha

(My professor does use some weird tactics, but i’d be more than open to hearing another method)

So feel free to explain haha

[stable dew]

i think the first thing to remember is that the t-distribution is symmetric -- so P(X > a) = P(X < -a)

so if I want to find P(X > something), but the table only tells me about P(X < something), that's okay

so P(X > 3.25) = P(X < -3.25). make sense so far?

[vivid veldt]

Yes!

[stable dew]

so like you said, some tables are more precise than others; here's one

you'll just want to look at the n=8 row, ignore all the others. because you're working with a t(8) distribution

[vivid veldt]

So you would just need to pick a value that is an overestimate and an underestimate and then read the values at the top? (Of course in the form 1-…)

[stable dew]

yeah exactly. so P(X < 2.896) = 0.99, and P(X < 3.355) = 0.995. so P(X < 3.25) must be between those two

[vivid veldt]

Which would mean the value 3,25 would have a probability between 0,005 and 0,010?

As we’re looking for everything greater than 3,25

[stable dew]

right, 0.99 < P(X < 3.25) < 0.995

[vivid veldt]

Okidoki! Thank you!

[stable dew]

actually wait, what i typed is wrong haha

fixed it

[vivid veldt]

Hahaha i do get what you mean luckily :))

[stable dew]

yep

hope that helped!

[vivid veldt]

Thank you very much! :))

[stable dew]

np

[harsh barn]

I can´t do it, I´ve been almost 1 hour to complete it and nothing

The result is: " 1/e " according to the book

Help me pls :c

[left knoll]

ok

so

[peak gale]

Try a change of variable like: u=1-x, then study it

[left knoll]

if you plug in 0 directly in its not possible

since there is an asymptote at x=1

so what you do next is you will

[harsh barn]

I catch u, in my country that method it´s called "Chain Rule"

I will try it

[olive trail]

Hi could anyone please help out with the second part of this question?

[peak gale]

Try to express t in terms of s, then inject the relationship into the velocity

[harsh barn]

I did it!

[left knoll]

whats the answer? the guy's teacher keeps saying his answer is wrong

[buoyant stag]

i beleive it is $147

[buoyant stag]

I may be incorrect but that is my attempt

[left knoll]

same but his teacher insists that its not

[buoyant stag]

oh that is weird

maybe the tax needs to be found prior to the $16 reduction

[buoyant stag]

maybe ask the teacher to explain?

[left knoll]

ye prob

[buoyant stag]

ohh wait

[buoyant stag]

Okay I think i got it

[left knoll]

how

[buoyant stag]

$126

[left knoll]

howd you get to that?

[buoyant stag]

one sec let me check

[buoyant stag]

that is my process

so i took 12 percent of the full price instead of what you did which was taking the 12 percent tax from the reduced price

[velvet coyote]

Can someone help me with this? ;-;

Idk whats elimination or substitution

[left knoll]

https://www.mathplanet.com/education/algebra-1/systems-of-linear-equations-and-inequalities/the-elimination-method-for-solving-linear-systems maybe this could help

[velvet coyote]

thank you!!

[left knoll]

you're welcome

[ember kernel]

Substitution is :

• in eq. 1, isolate x. You get x = ... (... depends on y)
• in eq. 2, replace all instances of x by ..., and solve for y.
• Once you get the solution value for y, go back to x = ... and substitute in the expression of "..." the value lf y you found in eq. 2 to get the solution value of x

[clever isle]

i dont get it 😦

[stable dew]

do you get what the first equation means?

[clever isle]

yepp, that 4 raised to t/3 is 25

[stable dew]

yeah exactly

try playing with that equation a little bit: 4^(t/3) = 25. can you change it so that it's more relevant to the log_2 equation?

for example, what's another way to write 4?

[clever isle]

2 raised to 2

or 2 x 2

[stable dew]

yeah

so you've got (2^2)^(t/3) = 25

do the same thing with the right-hand side, and see if you can get to an expression that tells you "log_2(5) = something"

[fallen minnow]

log_4(25) = log_2(5) = t/3

[teal karma]

Is the answer to finding the 101th derivative of cos just (cosx)^101= cosx

[earnest oak]

am not really great with logic ;~;

[ember kernel]

The question tells us there is a 7 among the three integers

• So Kevin's perspective :
  7 + x + y = perfect square (1, 4, 9, 16,...)

Assuming Jim has the z = 7 (but only Michael and Dwight see it, but read it as 1)

• Jim's perspective : x + y + z is a perfect square
  -Michael and Dwight's perspective :
  1 + x + y is a perfect square

Since the perfect squares HAVE to be 9, 16 or 25 (because the integers range from 1 to 10 and aren't duplicates),
That means 7 + x + y = 16 OR 25 (9 is not possible in this scenario)
and 1 + x + y = 9 OR 16 (25 is not possible in this scenario)

[earnest oak]

Ohh, cuz I was thinking that it had to be both perfect squares whether z = 7 or z = 1

[ember kernel]

Yup that's it

[earnest oak]

Bcuz Kevin did say that it was a perfect square knowing that there was a number 7, but at the same time, the other 3 also guessed their number based on the fact that the sum was a perfect square.

so is it possible that both sets of numbers sum up to be a perfect square?

my groupmates and I tried all possible combinations and they both don't come out as perfect squares

[ember kernel]

I'll give it a try after my class

[earnest oak]

Tysmm

My groupmates and I have been stuck on this certain problem the past few days

[vivid void]

Hi, can someone explain what a line with a nonzero slope is?

[cyan night]

that means it is not a horizontal line i guess?

[limpid dagger]

Very simple explanation: A line with a nonzero slope is a line that isn't flat, or has a slope of some kind, but it cannot be equal to zero.
Line with a slope of 0: ___
Line with a nonzero slope: /
If the line is on a coordinate plane, then if the line is parallel to the X axis and the Y coordinate doesn't change, then that line's slope is 0.
If the line is on a coordinate plane and the Y value is not the same for the entire line or it intersects with the X axis eventually, then your line has a nonzero slope.
Pretty simple explanation, I hope this helps :)

[cyan night]

^

[vivid void]

@cyan night @limpid dagger thank u both!! this helps a lot

[cyan night]

yes i hope you understand it

[vivid void]

yess i do now :D

[limpid dagger]

That's awesome :) I hope you have a good day

[vivid void]

thanks, you too :>

[willow basin]

For recurring decimals

imagine 0.037

some people put a dot on the second zero and the seven

other people put a dot on the 0, the 3 and the 7.

In both cases, the number is 0.037037037

But I was marked incorrect b/c I was supposed to put a dot on just the second zero and the seven.

I don't understand the difference though.

I wanna tell my teacher that maybe there's a mistake

but i don't wanna embarrass myself in case i'm actually wrong

anyone know if i'm right or not?

[lofty arch]

Math is kinda pedantic like that. If I saw three dots I'd wonder if it was a mistake and I couldn't say for certain whether that'd be 0.037037... or 0.037373737...

[mystic gate]

guý

guys

can help me with this problem

When Uncle Minh was the same age as baby Mi, Mrs. Hanh was the same age as Uncle Minh and baby Mi now plus
again. Which of the following statements is true?
A. Now, Mrs. Hanh's age is twice that of Uncle Minh's age
B. Now Mrs. Hanh's age is three times that of Uncle Minh's age
C. Now, Mrs. Hanh's age is one and a half times that of Uncle Minh's age
D. All other answers are wrong

[kind mural]

Can someone show me a worked out step by step solutions to these questions?

[blissful zinc]

https://cdn.discordapp.com/attachments/898372860911947821/899809278939004968/Screen_Shot_2021-10-18_at_8.00.46_PM.png Can someone help me with proofing

[cyan night]

leverage this following logarithmic property : log_(a^n) of (b) = 1/n * log_a of (b)

[hardy hare]

yoooo im kinda confusedLMAO how do u get the length of x

[cyan night]

is that just a arbitrary quadrilateral?

or is it a parallelogram?

[frozen meadow]

Its not parellelogram

Adjacent sides are same

[cyan night]

wait

yeah

this uses trig?

[frozen meadow]

Its not rhombus.... wait what is that shit?

[cyan night]

just a quadrilateral

[frozen meadow]

Nah cant use trig. Its not right triangle

[cyan night]

it doesnt have to be right triangle smh

[frozen meadow]

There are two isosceles triangles in it

[cyan night]

but nah i dont think use trig

yh

[frozen meadow]

I think we need to use properties of isosceles

[cyan night]

theres not much

[cyan night]

can u give us the problem in words

[sharp ferry]

Try using Pythagoras theorem

[frozen meadow]

If its a rhombus the answer would be 50....

Wait actually no

[cyan night]

it clearly isnt a rhombus smh

rhombus needs all 4 sides to be equa

[cyan night]

theres no right angle

[frozen meadow]

We just have to make one

[cyan night]

what

[frozen meadow]

Altitude of both triangles

[cyan night]

the altitudes arent collinear

[frozen meadow]

F yea

Does that quadrilateral have name. Adjacents are equal and opposites are diiferent

[cyan night]

no

it doesnt

[hardy hare]

well its much more confusingin words LMAO i just simplified it to that problem

[hardy hare]

how exactly

[cyan night]

no just give words pls

[hardy hare]

ok

[cyan night]

yeee

[hardy hare]

WAIT NVM

i did Not read the question right

[cyan night]

i knew it

[hardy hare]

whatever thank u lol

[hardy hare]

LMAOFSAKJ

[cyan night]

yesss

i dont think that x is solvable

unless it is

🙂

[frozen meadow]

Oh the question was wrong. Was it meant to be a parellelogram

[sharp ferry]

nah i meant if you drop another diagonal then u get 4 right triangles maybe that could have helped

but it would have been nice if we had any one angle :)

[left knoll]

sorry is anyone here familar with desmos?

[cyan night]

you cant assure that the diagonal is perpendicular to the sides

[sharp ferry]

thats a property of a kite

[cyan night]

ohhhh i didnt realize that xD sorry

i forgot the kite thing

is it solvable?

[sharp ferry]

idek dude if i get just one angle then its pretty easy

otherwise i dont see i mean there might be a trick idk

[left knoll]

could use any help thanks

[sharp ferry]

you know how to find the derivative right?

[left knoll]

yep

confused on =-4 part

[sharp ferry]

basically when you differentiate you get an expression in terms of x right?

dy/dx=-1/2sqrt(x)+ something something

[left knoll]

yep

[sharp ferry]

then you just have to equate the polynomial to -4

then u will get some value of x after solving

lets say u get x=4 after solving

i havent solved just saying

then to find the point basically you can substitute x=4 into the first expression which is y=sqrt(x)+3x^3/2+2

then u can solve for y and voila

[left knoll]

oh ok thanks I'll try to solve it now

[turbid haven]

Anyone in here know taylor expansion for complex analysis?

I'm struggling with how to do the taylor expansion for this one

z_0 is 2i

radius of convergence should be sqrt(2). I want to use the geometric series 1/(1-w), where w=z-2i*some factor but idk how to write the function in that form.

[drowsy widget]

Hi, is 10 the only result for √[(-10)^2]? Can someone explain why it can't be -10?

[ember kernel]

Because a square root can't be negative

sqrt(...) >= 0
No matter what "..." is

"But Quentin, then why do we say that the square roots of 25 are 5 and -5 ?"

Because the square roots of 25 are ± sqrt(25). The - sign doesn't come from the sqrt() itself

(Otherwise we wouldn't write ± sqrt, we would just write + sqrt and imply the - is given throught the sqrt)

[drowsy widget]

so we cannot do the exponent calculation of 2*(1/2) as sqrt is value over (1/2), so we also cannot, for example, do the calculation of ((-23)^(2))^3/8 without first taking the square of -23 right?

[ember kernel]

Exactly, because of PEMDAS rule

Bracket (P for parenthesis) first, only THEN exponent (E)

[drowsy widget]

ah truuuuuue

thank you

[ember kernel]

Np

[willow basin]

thanks

[rustic sapphire]

hey, can anyone help me out with this?

how is the highlighted term evaluated as '0'.... please explain

[weary arrow]

Cos(0) = 1, 1-1 =0

[rustic sapphire]

dude denominator also will be zero, so it will be in an indeterminate form

[weary arrow]

I think it's like top one will become zero "faster" than bottom one, idk been a while

[lean quiver]

What have you learned so far ? l'hopital's rule or just the limit operation

[rustic sapphire]

well we have to solve this question with just limit operation

i know it can be solved using l'hospital's rule

[lean quiver]

ok the hint is applying x->0 (sinx/x) ,

[lean quiver]

https://drive.google.com/file/d/1caRzfT7cgSfNZ4mgM5PgP3kkwIVkRs7U/view?usp=sharing

[pure garden]

does anyone know how to do question 13 a and b

[weary arrow]

A) h'(t) = 0
B) h(t) = 0

[weary arrow]

I haven't checked the math 100% but you seem to have forgotten a +1

Don't think that's the issue though, idk your math seems right to me

OK assuming that the equation you wrote in the top right is correct, this is what I got. Is that the answer?

[boreal meadow]

The answer for the question is y=(x^2 +4x -12)/x^2 -4

[weary arrow]

Then I think your first equation is wrong

[boreal meadow]

What should it be

[weary arrow]

Sorry I don't remember asymptotic functions enough to help you there

[boreal meadow]

Ok thanks anyways

I actually just figured it out the y-intercept shouldn’t even be included in the equation

[fallow vine]

can anyone help me out with this one

[rustic sapphire]

@lean quiver thankyou

[eternal hazel]

you got the first zero right

2/3

have you learned synthetic division?

you can divide the function by x-2/3 and then apply quadratic formula to get the imaginaries

[fallow vine]

oh thanks! that helped alot

[worldly copper]

Hey! Can someone help me with this?

A square ABCD is given. Points P and Q are taken on the sides AB and BC such that the BP is equal to the BQ.BH is the height of the triangle BPC. Find the angle DHQ

[cyan night]

height of triangle bpc not bpq right

[worldly copper]

Yes

[cyan night]

pretty tricky in that case

[worldly copper]

yeah, idk where to start from

[cyan night]

it could be plainly adding angles

since we have an isoceles right angle

but idrk

dhq is 90o

[cyan night]

are u vietnamese?

[worldly copper]

no

[cyan night]

we have the same problem in vietnam

[worldly copper]

oh haha tough bish is this problem

[cyan night]

i can give u a hint

try using similar triangles

[worldly copper]

thank you pal

ill try

[cyan night]

so ill give u the ending point: at the end u would wnat to prove that angle qhb = dhc since qhb+qhc = 90

its not too tough

[worldly copper]

oh ok

i will try my best

[cyan night]

yep

good luck

[worldly copper]

thanks again!!! have a nice day

[cyan night]

u2

use similar triangles

[left knoll]

g(x) =
∫ x
1
√1 + t dt for x > 1.

Determine whether g has an inverse function. Note: if an
inverse function exists, there is no need to find it

[lean quiver]

find the g'(x) and for any x>1 g'(x)>0 (*)

(*) ==> strictly increasing function ==> one to one function ==> the inverse function exists

[left knoll]

Can someone please help at this 3 questions

[pearl tusk]

sorry i don't know such advanced math

please help !! @ember kernel

@here

please solve all 3 parts pleaseee

[left knoll]

i) c
ii) d

[pearl tusk]

iii. ??

[cyan night]

what have you thought of?

[pearl tusk]

huh?

anyways i got my answer

[cyan night]

what have you thought of for iii?

i am implying that you should have progress before asking people to solve everything for you unless you dont know how to start you should just ask how to start not for the answers alone

[pearl tusk]

i was stuck at v = 1/70

then i realised i had to find u not v

[wild ruin]

Heyy, could someone please explain why ( A ∧ ¬ B ) => (A ∨ B ) is 1 even though A ∧ ¬ B is 0 ?

[weary arrow]

The last term in the second line of 2 should be ln(-3), which is not valid. The integral doesn't converge

Nr 3 I think is just 1/x? Idk if it's supposed to be more complicated than that..

[ember kernel]

@pearl tusk no time to read the discussion, it is answered yet ?

[pearl tusk]

i got the answer quentin

[terse niche]

Hello, can someone explain where 1,3 and 5 came from?

[pearl tusk]

i am i high school so i don't know much math eheh

[terse niche]

it's okay 🥲

[ember kernel]

Hi ! Looks like B got wrongly defined. I'd recommend you ask your teacher about it, to confirm it is indeed a mistake

(got wrongly defined in the first line)

[terse niche]

Unfortunately I don't have teacher for this material. so B = { 1, 3, 5 } then, right ?

[polar heron]

yes.

[terse niche]

Okay thanks both of you

[left knoll]

Thanks

[left knoll]

Can someone help me understand how both got cancelled in the sum? As in how sin(8pi/9) = sin(pi/9)?

[left knoll]

If you think about the unit circle, the sin(8pi/9) (y-axis) = sin(pi/9). Therefore you can cancel these two out when dividing

8pi/9 and pi/9 are both above the x axis, therefore their y-values are the same.

[left knoll]

Someone could help me?

It says
"Show that..."

[left knoll]

@oblique current

[oblique current]

Let me try

[cyan night]

limit definition of derivative right

[oblique current]

I sloved it but I don't think it is right

[oblique current]

Did u try to watch any youtube videos can help u to understand this equation ?

[left knoll]

Idk how to search it
Btw, sorry for my English :(

[frozen meadow]

Use google lens to scan it.

I use it for my hw when i dont know how to do it

[oblique current]

Dosent help all the time

[frozen meadow]

That question looks like. Common one. Maybe there might be

[oblique current]

Just typ the name of the equation which Ig is definition of the derivative explantion in your language on youtube. This will help u alot

Wish u luck

[left knoll]

Thank you so much!

I'll let you know if I solved it.

[hollow mauve]

9th and 10th question pls

[ember kernel]

Examples of [x] :
[3.14] = 3
[15] = [15]
[-3.14] = -4

Therefore, when x tends to 0-, that means [x] = -1 (because x is very close to 0 and negative)

Also, since x is negative, |x| = -x

Now you know how to simplify [x] and |x| in your expression, you just need to solve it 😉

[hollow mauve]

Okayyy thanks Quentin!

[ember kernel]

9. When you sub in x = 0, you get an undefined value 0/0 -> Try using l'Hospital's rule

[hollow mauve]

Yeah the ans comes out to be (A) -sin1, thankss

[hollow mauve]

its a 4degrer eq, you suggest using LH rule?

I'll try once tho!

[ember kernel]

Yup

[hollow mauve]

In these (11/12) should I try the same way you suggested in 10th^^^

[hollow mauve]

Thanks man!

[ember kernel]

Np !

[hollow mauve]

@ember kernel if you still there pls help 😀

I always face problem solving these series type questions, pls help

[lofty arch]

For very small values of x, 15/x >>>>>>>> 14/x

so you can kinda just ignore everything inside the brackets apart from the 15/x

no wait that's a lie

[ember kernel]

For small values of x, 15/x is not >>>> 14/x, they keep the ratio 15/14, which is not that great (even when dealing with large numbers)

[lofty arch]

yeah

[ember kernel]

I'll give it a try when I'm done with my work

[lofty arch]

I'm too tired to be answering thins ahahaha

[left knoll]

I don’t have a paper in front of me but for 15/x as x approaches 0 from the right side, that limit should approach infinity

Because 15/0.000000000000001 is a large ass number

Therefore it’s unbounded

I could be wrong though I literally just woke up lol

[cyan night]

thats approaching from 0+

if you approach from 0- then its - infinity

the limit diverges, yeah no limit

[ember kernel]

@cyan night they're asking for lim at 0+, wo no mention of 0- needed

[cyan night]

Oh

[lean quiver]

the limit is 120. consider integer part + decimal part and construct inequality equation for using the squeeze theorem

[wanton shadow]

need some help idk how to solve it

urgently needed

[peak gale]

Merge x and (x)^3/5, then put outside the exponent

[hollow mauve]

Can you send a proper solution for it ? I dont know the working of the squeeze theorem..ik what it means tho :)

[sand agate]

can anyone help me to construct the formula of this ball

i dont know why the L = 12 but z is 7

[hollow mauve]

Those are just some points at which the data has been gathered

[sand agate]

so i think i only use the ellipse equation is enough, right

[hollow mauve]

Yes.. ellipse eq is to be used thats it

Thats what I figured, in a cab rn sorry, will try once I get back home

[sand agate]

thank youu

[lean quiver]

Have you studied/known the squeeze theorem ?

[cyan night]

this is how i did it

[lean quiver]

like this example

if comfortable with this example, then the solution

https://drive.google.com/file/d/1dZOBcIxnILfln2YDZx2cUgZRjFTnJYsV/view?usp=sharing

[wanton shadow]

hmmmm

[wanton shadow]

thanks ima see if that will do it

i came to the same result after trying again

[sharp ferry]

would this help?

[sharp ferry]

i dont understand how no limit tho because the solution that i came up with does not care whether its 0+ or 0-

[ember kernel]

Wrong channel my dude

[floral marlin]

Hello, can someone help me with this problem: i have a triangle and have to calculate the b side and i have this: a=25 c=30 and γ=2α help pls

[vital bronze]

but that's math

[ember kernel]

Oh I misread lol

sry

[hollow mauve]

@sharp ferry @lean quiver thanks guy, I understand it now! Cheers 🙏🏻

Learnt eng but eh never understood grammar, anyone feels the same?😂

[dusky rose]

felt the same. But I worked hard over it while I was in school. Now its never a cause of concern for me. I recommend this to you as well. After all, grammar is important.

[dusky rose]

use sine rule for sides a and c. You get cos(alpha)=3/5. now use cosine rule. there is your answer 😋

[floral marlin]

Thank you so much! Will try it

[ember kernel]

x^3 = -1, therefore, x^6 = (x^3)^2 = 1

that means x^12 = x^(2*6) = (2^6)^2 = 1

Quickly enough you realise 2^6n = 1 for n = 1, 2, 3, 4, ...

That means x^2021 = x^(2021%6) = x^5

(since 2021 = 6 * 336 + 5, because x^2016 = x^(336*6) = 1 )

Therefore, you are able to simplify |x^2021 - x^2| = |x^5 - x^2| = |x^2 (x^3 - 1)|= |-2 x^2| = 2*|x^2| = 2x^2 because x^3 = -1

Solved :D

Quicker way : x^3 = -1 ===> x = (-1)^(1/3) = -1

So |x^2021 - x^2| = |(-1)^2021 - (-1)^2| = |-1 - 1| = |-2| = 2

[ember kernel]

But I prefer the first method because, although it doesn't provide a precise answer (there's still an x^2 in it), it doesn't require you to interpret the value of x. Throughout the whole answer, you just work with what you've been given (x^3 = -1) and nothing more

[left knoll]

@oblique current I did this .
What do you think?

[hardy falcon]

Can someone PLEASE confirm this (x = domain & theta = range)

[vapid osprey]

Find all points on the line r of the equation (x, y) = (1 + 2t, 5-t) whose distance to the line s containing the points (4,0) and (1, -4) is equal to 5 .

I'm having difficulties in interpreting, I've already found the s line, how do I develop the rest with the parametric equation and this s line?

[left knoll]

What do you mean by x = domain and theta = range? Domain and range are limits that define where a function is continuous. In this case the arcsine function is going to be defined for all x values between -1 and 1 (included) which is the domain. Inversely, arcsin(x) = θ is continuous for all y-values such that -π/2 <= θ <= π/2 which would be the range.

[left knoll]

To get x, simply take the cube root of -1, so x = -1. This is because any negative number raised to an odd power is going to be negative, likewise any negative number raised to an even power will be positive. That being said, if you raise -1 to ANY odd power (1, 3, 5, 7, 9…) it will stay at -1. However when raised to ANY even number, it will change to a +1. Therefore since x^2021 is raised to an odd power, you know (-1)^2021 = -1. Moreover since x^2 is raised to an even number, you know (-1)^2 = 1. You are then left with |-1 - 1| = |-2|. Take the absolute value and you’re left with 2 as your answer.

[left knoll]

That’s a good problem solving strategy in like linear algebra or multi variable calculus, but mans is in algebra 1 it’ll only confuse him haha

Hey can someone write me a detailed proof as to why 1^infinity is indeterminant and why 1^infinity ≠ 1?

I’m having a hard time piecing together the reasoning for it. Even if you take the limit to infinity of 1^n, it should still = 1. I mean think about it, common sense tells you that if one raised to any positive finite integer even if it’s like 1^999999999999999999, it still equals one. Yet, 1^infinity is indeterminate. I don’t understand it

[hardy falcon]

I wish I could tell ya

[hollow mauve]

Yes you're correct, do you want me to send you a list of all the domains and ranges; Standard Ones..

[hardy falcon]

That would definitely help a lot. Please do!

[timber cosmos]

So |x^2021 - x^2| = |(-1)^2021 - (-1)^2| = |-1 - 1| = |-2| = 2
@ember kernel Thx a lot, I was getting -2 but answer is given -1 , it's wrong I guess . I got to say this is a friendly and helpful community ( I am new to this server )

[oblique current]

Can plz someone help us with this

[dusky rose]

The guy who had asked this Q has solved it

[dusky rose]

[sharp ferry]

See (exact 1)^infinity is indeed 1 and its not an indeterminant form consider lim x-->inf (1)^x this limit is precisely equal to 1 and IS NOT and indeterminant form, butt (1+)^inf and (1-)^ inf is indeed indeterminant for example consider the limit x-->inf (1+1/x)^x as x approaches infinity 1/x approaches 0 but is not EXACTLY 0 so (1+1/x) is basically slightly bigger than 1 and the limit is indeed not 1. This limit is precisely equal to e!

[sharp ferry]

(EXACT 1)^inf form

[sharp ferry]

(1+)^inf form

[sharp ferry]

(1-)^inf form

[oblique current]

So is it right what he answered ?

[dusky rose]

yeah...its correct

[median scaffold]

lads can i ask for some help

im not sure what this question is trying to say. im pretty sure x/x=1 is not a false statement

is this a case of the question being worded poorly or am i missing something

[sharp ferry]

0/0 ≠ 1

[median scaffold]

o crap

i forgot about that

[oblique current]

One in the chat said it is correct ✨

[oblique current]

Thankk u🫂

[left knoll]

Thanks!!

Does Sin(45 + theta/2) = sin 45????

[woven orchid]

A wikipedia page has 4,9*10^9 words, 1 page of word dokument has 700 words
how many word page is needed to get same amout of words

how do i do this?

anyone?

[dusky rose]

no

[dusky rose]

I didn't get the question completely, but it seems that you just need to divide them

[left knoll]

Thank you!

[ember kernel]

Totally, depends on the value of theta. It's like asking if 3 + x² = 7
^^

[ember kernel]

@woven orchid Exactly. I like using fake units in this kind of cases (where we don't know how to multiply/divide certain given values), just to be sure my answer makes sense "physically" speaking.

Eg. the question gives you values expressed in [words] and [words/page]
You want a number of pages, so [pages] = [words] / [words/page]

I also use that trick to not get lost when converting time (eg. 370 [s] / 360 [s/min] = ... [min] )

[thorny stump]

How would you work out 9b?

[dusky rose]

express y in terms of arcsin(or sin inverse) of 1/x and the differentiate

[tame dome]

please help

[weary arrow]

Nr 2 is just the expression in 1 to the power of 5: x^5 = (p+q)^5

[cyan night]

substitute the value of y into z under x

z = 9(4x-9/x+4) -4/(4x-9/x+4)

[tame dome]

yep but after that I kinda struggled with simplifying dw I already submitted it. thanks tho 🙂

[cyan night]

dw u'll get used to it

[tame dome]

I would love to see that day

[cyan night]

👍

practice makes perfect bro keep working

[tame dome]

yesss

[cyan night]

yiz

[timber cosmos]

https://cdn.discordapp.com/attachments/838057776584327198/901092009404661810/bandicam_2021-10-22_18-24-29-760.jpg

what is being done in step 3 ?

[weary arrow]

just algebra, try finding what (p+q)^3 is

and try adding p^5 and q^5 , see what you get

[left knoll]

can anybody help me ?
i'm doing pythagoras theorem and i need to find the square root of 260
(hypothetically the / is the square root symbol)
i know the answer is 2 / 65 ( 13 x 5 x 2 x 2 )
but i need a number

it is confusing

[uneven wolf]

do you guys know matrix?

[cinder ibex]

I would like to help but i didnt understand what u didnt understood

[left knoll]

fair enough

[left knoll]

i dont like using calculator unless i know how to work it out

[cinder ibex]

Is this what u needed?

[left knoll]

it's difficult to see

i'm sorry

[cinder ibex]

Well if u have 260 in a square root u will didive 260 by the prime numbers, for instance u start diving by 2, then when it dsnt work anymore u divide by 3, then by 5... and so 260 = 2 x 2 x 5 x 13. Since u have two times 2 u can take it out of the square root and so it gives u 2 square root of 5 x 13

Oh im sorry the multiplication symbol makes it weird

[left knoll]

thank you

[cinder ibex]

Np, hope it helped : )

[quaint imp]

guys....

[left knoll]

what is ur answer coming?

[quaint imp]

wdym

what I think?

[left knoll]

its your question.

[quaint imp]

ya

so...

I think its A

[left knoll]

its correct
if it wasnt a fluke

[quaint imp]

fluke?

wdym

@left knoll

[left knoll]

nothing..

[quaint imp]

So i'm correct?

@left knoll

[left knoll]

A

[quaint imp]

thanks

I thought so

[left knoll]

All other are false

[quaint imp]

k

[quaint imp]

guys....

[ember kernel]

Take an arbitrary number, and remove 3 units from it. Eg., for x = 5, then y = 2 will become y = -1 (moved three units down)

[quaint imp]

so its....A

[ember kernel]

How do you go from 5 to 2 ?

[quaint imp]

-3

[ember kernel]

Yup

[quaint imp]

so its A

[ember kernel]

Ok let's imagine it's A.
At x = 5, I said that we needed to expect y = 2. Does answer A fit the solution ?

[quaint imp]

no

wait

lemme think

ITS c

@ember kernel

C

[ember kernel]

Yup

[pallid mason]

Can someone explain to me how to find the phase shift of a sine and cosine graph?

[left knoll]

Can someone please help me understand the blue line segment?

[quasi owl]

You mean [x] part?

[left knoll]

Yeah

[quasi owl]

I am not sure if I can explain well but I'll try

If you take a no. Between 0 and 1.....like say 0.5...it's integer part is 0

Between 1 and 2 ...say 1.4...1 and 0.4...the integer part is 1

It means that if you take any no. Between 1 and 2 then you get the integer part as 1 so the graph is a straight line between 1 and 2

Similarly other numbers

[left knoll]

Shouldn't the graph be like the one I drew in green?

For y = [X]

[quasi owl]

No

[left knoll]

Why not?

[quasi owl]

What you drew is y=x

[left knoll]

And [X] is?

[quasi owl]

It is integral part of x

Other functiom

[left knoll]

Mind explaining that?

I am kinda confused

[quasi owl]

Did you see the abv explanation

[quasi owl]

...

[left knoll]

Yeahh I did understand that

So that's what it basically is?

[quasi owl]

Ya.....on taking all the numbers between 1 and 2, we definitely have the integral part as 1

Now if you try plotting for every no. Between 1 and 2

It would be 1....a constant

Did you get it?

[left knoll]

Ohhh!! Yeah! Fr, thanks a lot. I think the integral part was misunderstood by me

Thank you!

[quasi owl]

Ok😁

[upbeat cedar]

a/b is a real number. what is the value of b?

anybody can help me?

[magic inlet]

Ms margie is 3 times as old as a grade 9 student is now. In 5 years, she will only be twice as old as you are then how old is ms margie? help me please this is very confusing and because apparently an actual grade 9 students age has nothing to do with the equation please help we're meant to turn it into an equation and show working out

[cyan night]

as "you" are?

how old are you?

[lean quiver]

hint) u - w= (u-w)*(u+w) / (u+w) = u^2-w^2 / (u+w) ; Let u=2x-3 , w= sqrt(...)

[ember kernel]

Not sure, but what I'd try is apply the limit to each term separately (because lim (a+b) = lim a + lim b), then get the indeterminate form inf - inf

[torn torrent]

How do we solve this question using derivatives?

[ember kernel]

Find a function f that, given an input in volume (cm³), returns the height of the water

The easiest way to do that is to find the function g that given a height h, returns a volume V (much easier) and calculate its inverse, to isolate h

[torn torrent]

could you solve it?

[ember kernel]

I'm sorry, I'm quite busy right now so I can't

But getting g is easy ; you just need to calculate the volume of a circular cone of height h and of circular base radius b = B * h/H (because the proportions are conserved when h varies ; it stays a right circular cone) with B=4cm and H = 8cm

Just use the formula of the volume of a cone to get V(h) = g(h) using h and b= h/2

Then isolate h to inverse g and get h(V) = h(V(t)) (because the volume varies with time)

Then, using chain rule, calculate :
dh/dt = dh/dV * dV/dt
(dV/dt = -3 according to the question)
Therefore, you just need to calculate dh/dV using your function h(V) and multiply it by -3 to get the answer dh/dt

Oops, ended up solving it

[ember kernel]

Got it ?

[left knoll]

how would i simplify (81x^8)^-3/4

[weary arrow]

As a starter, 81 is 3^4

[left knoll]

yeah,

[ember kernel]

Yup

But you could also use (a^b)^c = a^(bc)

[left knoll]

i dont understand what happens to x^8

[ember kernel]

Well (x^8)^(-3/4) = x^(-3*8/4) = x^(-6)

[left knoll]

hm, alright, thanks

[ember kernel]

You didn't understand ?

[left knoll]

i get it

[ember kernel]

Okok

[cinder hatch]

can someone help me with this? thank you!

[dusky rose]

25= u cos(theta) X time. you'll get the time in which water reaches the building. now use this --- s = ut + 1/2g*t^2.

u= 20, g=10, s=displacement= 11

[cinder hatch]

Hello, why would it be s in the second equation? thank you!

[dusky rose]

yeah, there is a mistake. In the 2nd eq. , its u cos(theta) instead of u. It is the vertical motion of water. s is the vertical displacement of water till the time water hits the building.

[half stream]

hello, i am trying to solve this but i don't really know where to start. I tried computing the first 50 values and they converge to 1.750 but idk how to prove it analytically
Does anyone know where to start or have any advice?

[cinder hatch]

sorry but I didn't quite get where the second equation came from, can I ask what concept was applied to it?

[dusky rose]

its the eq. of 2 dimensional motion, applied to vertical motion instead of horizontal. when the water hits the 3rd story, its displaced by "s" distance in upward direction

feel free to ask if you didn't get it

[cinder hatch]

I'm still looking into it. Thank you for your time!

[weary arrow]

<@&717391911132069929>

[left knoll]

??

[weary arrow]

Looks like it got deleted, it was a scam link

[left knoll]

oh okkai, thanks for reporting

[slate wolf]

Heyy could y'all please suggest any good youtube channels to study and understand college level calculus?

[merry carbon]

https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

[merry carbon]

pretty nice for intuition

[valid vine]

How do you learn to enjoy maths?

[ember kernel]

Maths is like a language, full of terms, definitions and relations between the concepts. Idk about other people, but what I like about maths is that, when you really get into it and try to deeply understand what you learn, you become "fluent" at it ; solving becomes intuitive and you're able to make links between many maths concepts, and apply them to everyday problems. It's really satisfying

And there are a lot of YT videos to help you discover more about what you don't know yet or to help you understand what you don't

Mastering maths requires the same kind of rigor needed to master a language's grammar and vocabulary, but at the end of the day it's very accessible when you approach it the way it works best for you

Hope this helps ☺️

[meager girder]

https://www.youtube.com/watch?v=iiBWzAXmPls&list=PLLyqGZba3Xv0dk0CsCK-ua95z4i_eFzF8&index=3

i understand whats going on till 5:42

but after that i don't understand what formula he is using to get his answer..........edit; nvm i went over it again and got the explaination

[dusky rose]

As you improve your grip at maths and develop problem solving skills, you will start seeing maths as joyous ,rather than a burden. I was not good at it too. When I was in 5th grade, I had scored 1/25 and 0/25 in maths **proficiency **tests. But at present, I have secured a seat in the best engineering college in my country.
All that I did was that I never stopped focusing and working hard on what I was studying at that moment. Yes, the journey is a long one ,but definitely gives you extraordinary skills

[dusky rose]

just focus on what you are currently studying. Try to figure out why do we conduct the basic mathematical operations like division and multiplication. In many word problems, all you have to do is division, but still that problem stumps many. WHY?? That is the reason why you need to get every concept at the grassroot level. If you didn't get what I was trying to convey, let me know Coz this is very important

[valid vine]

I see, thank you!

[valid vine]

I'm not sure if I quite understood, what do you mean by the grassroot part

[dusky rose]

by grassroot level, I mean you should know why we perform each and every operation. Only then you can tackle their difficult applications. EX- division is repeated subtraction. we see its application in word problem for kids. Questions like - if you have X amount of money, and an object costs Y, then how many objects can you buy. This is just a childish question but can serve as a nice example. One shouldn't just remember that in such Q's we have to divide. Instead, they should see that if you repeatedly take out Y Y Y Y from X, then you get the amount of objects you can buy. Its a bit difficult to explain, but not as difficult to learn. Just be consistent and work on maths everyday. A consistent person can do wonders!

[urban berry]

Hello everyone)I need some help, do you know different sites or a source with information about "Probability theory in forensics"?

[fiery haven]

sqrt(56-r)=r

when solving this how come the solutions aren't both -8 and 7? when you substitute -8 and u get sqrt(64)=-8, isnt -8 squared 64?

[ember kernel]

sqrt is a positive operator by definition

In other words : when you say, "8 and -8 are the square roots of 64", that means the square roots of 64 are +sqrt(64) = 8 and -sqrt(64) = -8

Notice how, in the latter, we manually added a - sign before the sqrt ; therefore, it doesn't come from sqrt operator itself

@fiery haven

[turbid hill]

Can someone help me with this?

here's the function and the graph

Logically i would say that x cant be 90, bc cos(90)=0, but the graph says otherwise. Help, im so confused

[spark surge]

help pls

[dusky rose]

I guess x is in radians. So if you wanna put 90 in the cos function, then take x=1.57 (pi/2).

[ember kernel]

Well there is no value at x = pi/2 ≈ 1.57

There's just a vertical asymptote

[plush dragon]

if you have a matrix equation can u take the determinants of both sides? like if AX=B will |AX|=|B|?

[dusky rose]

yes, but only if both A, B and X are square matrices

also, they all must have same no. of rows

[plush dragon]

ah ok thanks!

[turbid hill]

but its still there??? TT

[ember kernel]

What you mean by "it's still there" ?
Zoom as much as you want into your graph
You will never ever find any definite value for f(pi/2)

[ember kernel]

Keep in mind that 1.57 is not equal to pi/2, it's only an approximation

Just like pi ≈ 3.14

[dusky rose]

even 984.8 is a large value. If you put exactly pi/2, it will tend to infinity

[cyan night]

π = 3
e = 3
π = e

3 ≠ 3

[molten flower]

A bacteria culture grows with a constant relative growth rate. After 2 hours there are 400 bacteria and after 8 hours the count is 50,000.
(a) Find the initial population.
P(0) =
Correct: Your answer is correct.
bacteria

(b) Find an expression for the population after t hours.
P(t) =
Incorrect: Your answer is incorrect.

(c) Find the number of cells after 3 hours. (Round your answer to the nearest integer.)
P(3) =
Incorrect: Your answer is incorrect.
bacteria

(d) Find the rate of growth after 3 hours. (Round your answer to the nearest integer.)
P'(3) = bacteria/hour

(e) When will the population reach 200,000? (Round your answer to one decimal place.)
t = hours

can someone help me with this, I can't seem to find the right exprfession

[valid vine]

Why is this 180 plus 45 instead of 180 subtract 45

[left knoll]

because tan is in the third quadrant

[valid vine]

So does the 180 come from the 0<X<180 instead of tan

[dense wadi]

You can use the rule that angles in alternate segments are equal the calculate the secondary value by doing 45°+180°=225°, thats how its obtained

because the range is 0<x<180 the value 225 is invalid @valid vine

[random flame]

Can someone help me with Q4d? I've been stuck at this question for ages- Any help is appreciated!! (Also pls ping me or I wouldn't see your msg)

[green root]

do let me know if the answer is incorrect or if you need any further explanation

@random flame

[random flame]

I don’t get the 2x+3 = 7.0059 part

[green root]

thats actually the base angle + 2pi

i think the base was 0.7227, but its not in the accepted range, but if u add a 2pi its one of the angle in the accepted range

its like the next cycle of it

[coarse cypress]

please help me math lords

[ruby tinsel]

I'm not too sure,, I get 19 mins? the girl takes the family home every time so 10 + 1 + 5 + 1 + 2 = 19 mins. I'm pretty sure there must be a trick to this question so I'm not so sure.

[coarse cypress]

i also got the same but ans key shows 17min ._.

[ruby tinsel]

So 2 and 1 goes first, then 1 stays. 2 comes back, then stays. 10 and 5 goes together. 1 takes the brollie then comes back with 2

[coarse cypress]

wheres the father?

[ruby tinsel]

with his dad

[ruby tinsel]

hopefully that makes more sense?

[coarse cypress]

ye it does thankyou so much

[flint crest]

anyone can help . i stuck at the last part

[cyan night]

this problem has roots from a teded riddle btw

the answer is indeed 17

[cloud night]

Hi can someone help me with 62b ii?

Here my previous steps for reference

[bright ingot]

hi does anyone have experience using MATLAB/simulink software ? can do process control too,,

[molten flower]

can someone help me i only have on attempt left : (

[viscid heart]

Hi does anyone here know matlab and could help me with this? Been stuck at it for ages don't know how to go about it so any hints would be helpful. Even writing the steps out in words would be appreciated 🙏

[ember kernel]

Taylor:
f(x+dx) ≈ f(x) + f'(x) * dx

Here, the values for dx are -0,01 and 0,01

[peak pollen]

can someone explain something for me?

[ember kernel]

Yeah

[ember kernel]

The ways this channel works is, send your question right away. Someone will answer 😄

[fringe stratus]

Hi!
Does any of you guys know how to **prove **the following expression:
|A U B| = |A| + |B| - |A ∩ B|
I understand it but I just don't know how to prove it 🙂

[ember kernel]

Sure

[ember kernel]

Give me some time, it's very easy to visualise actually

[fringe stratus]

Yeah it is, and it makes perfect sense when applying it to real sets but I don't know where to start to prove it for any finite set

[ember kernel]

Paint skills yeaaah

Hope this helps

But I don't recall any rigorous demo for it tho

Like, even mathematicians seemed to agree it was intuitive

[fringe stratus]

Alrightyyy, I had this in mind too but I didn't know I could simply put words on the process instead of doing as you said, a rigorous demo. Quite new to the world of maths demonstrations haha
Thanks my dude I asked two questions in this discord and the two of them were answered by you ❤️

[marble canopy]

Anyone else doing uk A levels Year 1/AS

hmu and we can make a gc or sum

[left knoll]

help

ping me pls

[ember kernel]

Np !

[ember kernel]

I don't recall ever seeing such a thing. What's this about ?

[left knoll]

whats your answer for this 2(x-5)=7(x+1)

-3.4 or 3.4

[ember kernel]

Oh ok, I had never saw this kind of notation for multiplication

[left knoll]

ye same someone asked me this but ive never seen it

[left knoll]

this

@ember kernel

[cinder ibex]

i think its - 3,4

[left knoll]

but it says the answer is 3.4 for some reason

[left knoll]

thats also what i got

[ember kernel]

Impossible

[cinder ibex]

probably a mistake in solutions

[ember kernel]

3.4 - 5 s negative, while 3.4 +1 is positive

so 3.4 could not be a solution

[cinder ibex]

u sure that is what this means?

[left knoll]

i even used photomath but it says -17/5 HUH

[ember kernel]

Are you sure the strange notation is for multiplication and = only, with no mention of a - popping up somewhere ?

[left knoll]

no thats different

dont mind the picture..

[ember kernel]

ok

[left knoll]

2(x-5)=7(x+1)

[ember kernel]

Then yeah 3.4 is not a solution

couldn't be

[cinder ibex]

probably a mistake in ur solutions

[left knoll]

so its not -3.4?

[cinder ibex]

it is

its not positive

[left knoll]

ok

[cinder ibex]

kinda curious about this notation tho

[left knoll]

me too......

someone asked this question on me but i wasnt sure how to do it

[ember kernel]

I think in your shoes I just would've replied I didn't know either

That's what I usually do

[cinder ibex]

yah ive never seen that before

might ask my teacher out of curiosity tho

[left knoll]

aight tell me what they say

[cinder ibex]

If i dnt forget to ask i will tell u : )

[tidal meteor]

If you want a straight demo, look for the "inclusion-exclusion" principle, witch is a general form of this expression for any countable union of finate set.
I had to know it from a combinatorics point of vue as part of my studies, it's quite an heavy proof :v

[fringe stratus]

Yeah I saw that earlier before I asked a question about it. The general demonstration is one of the question at the end of the exercise I was doing, the beginning was only proving it for n=2 finite sets of elements 😉
But yeah as you said, quite heavy haha, noticed there was multiple pages for the demo and saw a tear dropping 😂

[tidal meteor]

I see ☺️
Good luck ahah :D

[fringe timber]

Hey, i need help with this please ☺️ : One point P is on the graph for the function y = x2 ; 0 < x < 2 The P point is one of the corners in a rectangle, where one of the sides is on the x axis and one on x = 2. Decide the biggest possible area, that the rectangle can have.

[tidal meteor]

You could draw a graphic, then notice that the area of the rectangle can be express in terms of x ( Area = LenghHeight = x^2(2-x) )
Once you got this expression, as you're looking to maximize it, you'd want to do a studying of its variation between 0 and 2.
To do so, you could calculate it's derivatives ( -x^3+2x^2 ) to then being able to tell where it's maximum lize, thus answering the question.

I hope it helps D:

[left knoll]

@regal oxide

Is it right?

The way i said it?

[zenith sparrow]

I think it will be 3.75 for 1/2 a cup soy sauce

[left knoll]

Oh ok thanks just checking i was hvaing a dilemna

[oblique current]

U do like this
2=15
0,5=x
Then 15 • 0,5 /2 = 3,75

[left knoll]

quick and kinda dumb question, is -2 the same as -2/1....

[left knoll]

yeah

[left knoll]

Whats ▪︎ ?

[oblique current]

X ( in sweden we use • too for multiplication )

[regal oxide]

yup its 3.75

[knotty nymph]

could somebody help me with circle theroerems and circles at some point aha? im quite hopeless at maths

[verbal tangle]

https://mathsolver.microsoft.com

im just gonna throw this out here for anyone who if looking for a solver that explains the steps for free\

[left knoll]

are there any youtube lectures that solve calc problems from Thomas Calculus?

[inland sigil]

Solution manual is available for Thomas Calculus, iirc

[left knoll]

ah i didn't know that, thank u

[empty hinge]

any suggestions on how to be good at maths? Im studying at high school so maths is a very difficult and intense subject. I think that mere practicing is not enough since the subject has become extremely complicated and it takes nearly an hour for me to fully grasp a single lesson. Therefore, my grades have been dropping quite badly so im kind of tired and bored with maths right now 😔

[ember kernel]

My math Bible for beginners

Oops missclick