#help-10
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was this correct approach?
I'm not great at this, but why did you immediately assume that 1+a^3*b is positive
couldn't both a^2 b^3 c and 1+a^3 b be negative
Oh wait
division
Well technically if it was negative signs would be reversed
no cos it won't be >0 then
?? what
Let me explain
if a^2 b^3 c and 1+a^3 b are both negative, then them multiplied would be positive
You divided it, but it could still be either positive or negative
also I don't get why you just removed a^2 and c
This is where I get help?
@stuck herald Has your question been resolved?
so i didn't need to go further like that what i did
i could have deduced there itself u meant to say??
It's possible that
1+a^3 b < 0, a^2 b^3 c <0
It gives a different set of possible answers
well 1 + a^3 b < 0 cannot be true because rules but like it's there
why
it can be negative no?
Yes
but a<1 and b<1 therefor it cannot be <-1
so like ur solution was correct
although why did you cancel ur c
where
a^2 b^3 c > 0
c just disappeared
you can cancel the a^2 since we know that
but b^3 c > 0 can yield negative for b and c
since we know b^2 is positve
we can remove the b^2 in b^3 and get that bc>0
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thanks
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Consider a polynomial P(x) = 8(2x^3 - 9x²+12x-5)+ a. Consider a function g(a) which is defined as number of real roots of equation P^a(x) = 0 in the interval (0,1) where p^a (x) = P(P(P.........P(x)))) (for example, P³ (x) = P(P(P(x)))). a times
Then find the value summation a 1 to 4 g(a)
got a picture...?
G1 is 0
ok so
... fuck how the hell are you even supposed to do this without being a human calculator
like
for g(4)
they expect you to... what, consider a fucking 81st degree polynomial?
Use brain 🧠 isuppose
are you sure g(1) = 0 btw?
i don't know what you meant by G1.
but i assume you meant g(1) but typed it very badly.
sorry, did you just "Hello?" me for 30 seconds of absence?
It always works
Ok let it be
idk take these screenshots and count them yourself
i dont really want to let it be when people are rude to me
!volunteers
Helpers are just people volunteering their time to help you. Be polite and patient.
it's disgusting how impatient you just behaved there
@merry topaz Has your question been resolved?
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Ok so I am trying to find the ambient temperature of an oven(Ta)
I found the expression
But I could not figure out how to find Ta, given I have many unknown variables
The conditions given were:
initial temperature of liquid = 25c
After 1 minute of oven temperature increased by 25C
After 2 minutes in oven temperature of liquid is 73C
.close
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Okay what about it
yo
dang, am in 6 th grade we only learned plus and minus💀
How old are you
sorry i can't say, am not allowed
guys what does x mean?
Is it below 13?
i can't say
????
bro
i said i can't say
stop forcing me
what does x mean?
can u help me with my homework?
please
okay
what is a 90 dagree angle?
??
dang
90 degree angle
ok, is that u?
ur pfp?
is that u?
bye
pls stop saying am young
i said, stop saying what my age is
its not cool
i dont wanna say my age in discord
!redir
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for legal reasons we need to know if you're over or under 13.
ah, rip them.
@vocal marsh do you still have a question to ask?
@vocal marsh Has your question been resolved?
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Would f(0) here be equal to 2 here?
And f(x) would be 1?
✅
❌
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does anyone know what this equation is about? I don't get how the partial of 2 terms on the left become 4 terms on the right
yea but i dont get why
∂/∂t of f_x * x_s = f_xt * x_s + f_x * x_st
$\pdv{}{t}\left( f_x x_s\right) = \left(\pdv{}{t}f_x\right)x_s + f_x\left(\pdv{}{t}x_s\right)$
aPlatypus
I'm pretty sure you had calc 1 at some point
it's the same thing here
except with the partials
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Determine all functions f (x, y) that solve the equation
for example with a variable change u = ax + y, v = x, for any suitable value of the number a
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4
@austere hound
<@&286206848099549185>
Is my work correct
Hi. Can anyone help me in choosing one of these four topics for my mathematics projects: 1)Mensuration: Applications and
illustrations from daily life situations, etc.
2)Applications of Arithmetic
Progression in daily life situations, etc.
3)E-commerce -Impact on World
economy -Discusswith-illustrationss, etc.
But g(3x)=x
k
I just ignore the the x on the RHS
Np
So my work aren’t correct
Homework
So I integrated on both sides I got v=g(u)
Then I changed u to 2x+y
And plugged in f(x,x)
So we got g(3x)=x
What happens next
What
I don’t understand
Plug what
I already plugged in f(x,x) which gave me 3x
But
How did you got 4a+b
What is a and what is b
5?
Wait where did c come from?
So you can’t help me?
Np
Thanks anyway
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What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
what did you do to get ur incorrect answer
Added parallel lines then time by 2
4 and 6
10
Yes
whats A=?
Area
20cm2
Divide by 5 on both sides?
4
yeah
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Why is the square root of 2 equal to the fourth root of four?
2^2 = 4
,tex .exp rules
riemann
$2^{\frac{1}{2}}=2^{\frac{2}{4}}$
Good
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Is this derivative correct?
,rccw
@indigo cipher Has your question been resolved?
@indigo cipher Has your question been resolved?
@indigo cipher Has your question been resolved?
Looks good
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my math teacher gave this problem as a practice and i think x = 1 but that is only using the short leg and hypotenuse. When i try to double check with base leg i get stuck
30-60-90 triangles have this neat property that the hypotenuse is twice the length of the short leg
And the long leg is short_leg*sqrt(3)
when i set the long leg equal to 3.5√3 it dosent work.
there is no 0
is the problem written wrong?
no the math looks good to me
That might be the solution though
that for no value of x is that triangle a 30 60 90 triangle
Because the rules of geometry are pretty strict and sqrt(3)/2 * 1 + sqrt(75) != sqrt(3)*3.5
yeah
Your graphical solution work well as a proof too, showing there are no roots to the equation is proof
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Is anyone able to help me with this linear algebra problem. Question 22 please : )
!status
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2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
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6. None of the above
1
@tiny spire Has your question been resolved?
@tiny spire Has your question been resolved?
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I do need some help with something
pray tell
@mellow pelican Has your question been resolved?
what have u tried
I understand how to do the first part but I am confused on how to do the second part
plug in the point (0,1) into ur value of dy/dx
then use point slope form to make a linear equation
wait both values
what dy/dx did u get
ok now plug in ur values of x and y into that to find the slope at that point
Ok so then: y-1=(-1-e)
what happened to the x part
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hint from google
well it means 10^4
9999 is divisible by 101
i don't get it though
oh okay
@fierce ocean
remember the rule for divisibility by 3, especially why it's like that
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hello i need help with relative rate
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"determine the new equation after the following transformations."
8x^2 +y^2 =2
a horizontal expansion by a factor of 2, then a vertical compression by a factor of 1/3
here is what I'm doing
1/2(8x^2) + y^2 =2
then 4x^2 + 1/3(y^2) =2
and in the end I get 4x^2 + y^3 =6
but the answer is 2x^2 +9y^2 =2
where did I go wrong?
wont 8(x/2) result in the same thing?
How did you get the 4 in the denominator’s place?
Oh my goodness, I can be such a dunce sometimes
Maybe it’s a good idea to fully write out what I’m doing lol
Now I’m wondering just how in the world there is a 9 beside the y
Yeah, I now see how it could be y^2/9
That’s what makes this confusing lol
@sterile vale Has your question been resolved?
@sterile vale Has your question been resolved?
@sterile vale Has your question been resolved?
@sterile vale Has your question been resolved?
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can 3x^2+11x−20 be simplified further?
you mean can it be factored?
yes
yes it can be
b
nothing ads to give 11 and multiplies to give 60
or is it -60
wait...
It is -60
yes
$3x^2+15x-4x−20
$3x^2+15x-4x−20$
B-eard
cool, i know where to go from here
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Hey there! I'm doing some intercepts on the plane and I was wondering why in some cases you have to sqrt all the equation, meanwhile in others you don't. Here is the example:
The operations on the whiteboard is what I think i should do, but apparently nop.
Thanks in advance!
My question is, why on the first screenshot you can sqrt all and have the result, meanwhile in the other operation, you cannot sqrt all
sqrt(a^2 + b^2) is not a + b
$(-2)^2+y^2$ is not $(-2+y)^2$
Good
mmm
still don't understand
I mean, why i cannot just sqrt all the equation for eliminating those ^2?
The reason why you are allowed to cancel the squared in the first photo, is that the expression is one. In the third picture, you're trying to cancel out two expressions, which is not allowed.
okey so, in the first image it's correct because it just sqrt((x-2)^2) meanwhile what i tried to do it's incorrect because its sqrt((-2)^2+y^2)
and why it's not allowed?
$$(x-2)^2 = (x-2)(x-2) = y \cdot y$$ meanwhile $$(-2)^2 + y^2 \ne (-2+y)(-2+y)$$
Good
okay so, you in this cases you can just sqrt when you have those special identities?
$$\sqrt{x}=x^{\frac{1}{2}}$$ so $$\textcircled{1} (x-2)^2 => \sqrt{(x-2)^2} => x-2$$ but $$\textcircled{2} \sqrt{(-2)^2 + y^2}$$ you cannot do the same as $\textcircled{1}$.
Good
Welcome.
.close
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Do you know the SOH CAH TOA?
that isn't how the command is used
in fact, if you type anything beginning with a . in an available channel, it PREVENTS the channel from opening on your message
also yeah @junior jay do you know basic trigonometry

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but how to find tan 27
I think
anng host
You have a given of adjacent and an angle
you can use tan value and find it
You're trying to find the Opposite
yep
tan = opposite/adjacent
yes
Use TOA
from the SOH CAH TOA
yea
I got another
I still study in like high school
that's good
yep
130 degress
130 degree
because when we add both angles a and b we need to get 180
soo 180-50
is 130
wait bro one sec
yess its 130
we had the same question
see
if we add both angles A and B
we are supposed to get 180 degree
because both form straight line
therefore
the missing is 130
angle A=50
A+B=180
50+B=180
B=180-50
B=130
soo angle B is 130 degree
co interior angles
gott it
alright let me get another question cause I need to practice to learn
wait I think you might be wrong
yeah I used the same one
alr thanks Im gonna go now
ill ask if I need help
oke
goodbye
bye
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.reopen
✅
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what's the deriv of 2x^3+x?
yes you did
thanks so much lol
also don't forget parentheses, also don't quite your sixes like b's.
what are those again
those = who?
parenthases
oh oh okay
hi
did i do it wrong somewhere?\
!redir
like the brackets
formally no but you'll need them in the corrected version
oh u mean like () instead of writing multiply
ok my bad it used to be a factoid but now it's not
anyway uh
k
if you have a question of your own then take your own channel, otherwise go to #discussion or #chill
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huh strange
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For number one. If a^2 - b^2 equals (a+b)(a-b) why is exercise number one doing something else? Could somebody explain please?
,rccw
Having kind of a hard time reading but are you referrring to the task
,, \Big( \sqrt{x} + \frac{1}{\sqrt{x}}\Big)^2 - \Big(\sqrt{x} - \frac{1}{\sqrt{x}}\Big)^2
Joachim
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39a
@fathom schooner Has your question been resolved?
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<@&286206848099549185> tell me if this is correct or not.
I'm using the quadratic formula to solve
yes it's correct
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can someone plz explain this from the 2nd last step
so we factored the quadratic
and for the last step you can either treat (m-4)(m-6) as a quadratic
or consider two cases: case 1 which m-4 is positive and m-6 is negative, and case two of m-4 being negative and m-6 positive
@tacit scarab didnt get it
ok let's remember that a quadratic open upwards with positve coefficient
thus it's negative between the roots
i dont get it
can u explain it in a simpler way (english isnt my first lang srry )
im not getting things from this part
a general quadratic can be written as ax^2+bx+c=0
yes
and when a is positive, it open upwards
what does open upwards mean
ok
as you can see if the graph curves upwards, it is negative between the roots
negative between the roots ?
@tacit scarab is it ok if i revise my theory (as i dont remeber it) and then come back to u
ok
let a<b and they are the roots, then the quadratic is negative for a<x<b
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what's the procedure to do this exercise
@vivid yew Has your question been resolved?
help
Yeah thanks
fine
Okay, this question is not very well posed. But the lines in each family all pass through a single point.
I would locate that point in each case and then draw five lines through it.
i know that , i mean what's the correct sentence and procedures to used.
i will do an exam next week linked to this, so i want to see someone do an example.
if it's too long for you, give up, some else will try
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I want to understand the geometrical proof of d(sin(θ))/dθ = cos(θ).
I was watching Grant's video on derivatives and he used a unit circle to prove that d(sin(θ))/dθ = cos(θ). The image attached below shows how he did it.
My question is, how is the smaller triangle similar to the bigger one, so that the angle between d(sin(θ)) and dθ is equal to θ?
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how can I solve for the x's?
basically x^2(9-x)=44, x=?
its guess and check time
x = -2 is an obvious solution
you can use that to factorize the cubic into a linear and quadratic
damn ur right
how do u do this?
i can do quadratics
okie thanks!
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Im confused by this question. I have no idea how to start, the only thing i know about is the formula for the volyme but other than that i dont understand the question very well.
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Can some one help me solve this problem?
yes
what's your progress?
I know that height is changing at -1.4 in/sec and I know that the formula is V =1/3pi(r^2)h
Bc I am differentiating with respect to h, I could treat everything else as a constant
I feel like I already messed up somewhere
I have a feeling I might need similar triangles
Can I compare my radius to my hypotenuse
I just realized there are 2 variables here R and H
I ignored r before and treated it as a constant but bc it is a cone, the further away you get from the base the smaller the radius becomes
So I think my next step is to differentiate the volume formula with respects to time
So am I on the right path
?
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If the number 1,1010101… that has 1 as a whole and a random decimal place which we will call k, that for each whole positive k is: 0 if k is even and 1 if its uneven, is it irrational or rational?
@severe forum Has your question been resolved?
what do you think
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Is this enough as proof (Is it even correct?), or am I missing something?
I is an index set, C is a set, (Ai)i ∈ I is a family of sets with Ai ⊂ C for all i ∈ I.
I hope the terms are correct cause I'm just translating as best as I can from german.
Wait, it formatted the first part wrong. Here's a better picture.
@tawdry arrow Has your question been resolved?
On the second line shoudln't it be "x not in A_i"?
Ah wait I just noticed the bar
Yeah it's all correct @tawdry arrow
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how did they come from left side to the right side? lets pretend we dont know how the right side look and we want to go turn the left side to right side, how do i do it?
I suppose you could try to convert it to factorials and see if something nice comes out
I just know it as an identity
Yeah if you defined binomial coefficients with factorials straight away then you just need to directly show that the equation is true
its combination
k let me send the whole problem: so i have to proof this summation using mathemathical induction. I got kinda stuck and i looked up the answer and couldnt understand how they rewrite that red underlined thing
Yeah well how have you defined the binomial coefficient?
sorry i dont understand the question
How were you introduced to the binomial coefficient? Just using this formula?
[ \binom{n}{k} = \frac{n!}{k!(n-k)!} ]
A Lonely Bean
yes
Right, then you would first need to show that this is true
Just apply the formula and the fact that (n+1)! = (n+1) * n!
The rest is simplification
nope i tried that, it wont work
if you look at the answer i send, they write it as this, so first number + whatever in the middle + the last number
but i dont understand how they got this
to this
yes but its the opposite thing of what im asking
you showing me how to get this
to this
Just write it the reverse way then
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can anyone help me with this?
Yeah
idk how to type it in a keyboard tho
A/1-r?
is that it?
Yes
this
Yes
alr
How much did it travel in going up and coming down once
two thirds?
It went up 6m feet and came down 6 feet
ohh
How much did it travel
two thirds?
oh
12 feet
mb
So it went 12 feet the first time
yh
howd u come up with that
Ok
Let's ignore this
ok
Let's not even calculate two thirds of six
ait ait
wtf
Did you get this one?
from here
.
nope
dont we have to lay out the given?
like a sub 1 is 6
Two thirds of something is 2/3 × the thing?
Fraction bro?
i have math exams tmrw
Bro you know fractions?
no xD
What grade are you in?
10
They teach fractions in like 3rd grade or sum
yh ik
Like did you ever learn 1/7 or 2/3, 4/9 stuff like that?
yep
i j forgot abt how to divid or multiply them
also integers
and idk how to divide
Ok show me you syllabus for tmr
What's coming in the exam
i need it rn lol
lemme send u the pointers
MATH
- Generating Patterns
- Arithmetic Sequence
- Arithmetic Series
- Arithmetic Mean
- Geometric Sequence
- Geometric Series
- Infinite Geometric Series
here
You know arithmetic sequences?
wdym
Sum of arithmetic sequences
n?
S=n/2(2a + (n-1)d)?
wtf is that
ahh
its geometric sequence?
Can you give me an example of any arithmetic sequence
all ik is we have to lay out the thingies
1,4,7,10,13,16.... Is an arithmetic sequence
can i explain to u how i answered it?
Basically you add something to get the next term
yeah
You start with a number
Add something to it
Get the next number
You keep adding you keep getting numbers
this
yh and u gotta find the 47th term
u gotta start with 4 i think
cuz its the first one
I said stop looking at the questions
dam ok
yhyh
So like in series 2,6,10,14,18... The first term is 2 and common difference is 4
You get this right?
@fierce matrix ?
yhyh
You got that or no?
Be honest
So basically "a" and "d" can be any numbers
Like negative too
So 9,6,3,0,-3,-6 and so on
Here d is -3
Cuz you keep adding -3
@fierce matrix bruv you wanna do this or no?
Bruh you have test tmr you gotta focus up
i am focusingg
im j watching a vid abt infinite geometric sequence
cuz the vid i sent u was the one my sir sent
aka the guy who made the vid
Hm
Ok
First do arithmetic series and related stuff tho
Thenn geometric
That'd be easier
If you have video
Then do it from video
That's easier
Not sure if you still need help but the first question is simply adding by 3, repeat this process 47 times by multiplying to get your answer.
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hi, i've been asked to mathematically prove that there this functions graph is symmetrical to a point
and find that point
i've read about some thing like this
if:
then:
where omega is the point of symmetry
but i'm skeptical
btw these are the same thats how i read about that
Why are you skeptical
idk i just like something with proof
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<@&286206848099549185>
@vast sun Has your question been resolved?
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Could anyone double check my proof here?
@fathom flicker Has your question been resolved?
from where are you pulling the primes
$9000=2^3 3^2 5^3$
SWR
the first paragraph is clear, you are using that argument already to show that a,b,c,d need to be of that form with the exponents being less than 3,2,3
(well yes I know but its not clear in the proof)
I have no idea how to read || * *| * *
same
I gave the example for that reason
That means | 1 power
And every star after it
Gets it
even with the example its not clear
||*
Means a being the first star
Gets 2 powers
And placing the stars in order like that garuntees the non decreasing
What isn’t clear in the first paragraph?
Oh well yeah I can just state the prime factorization of 9000
I should do that
I forgot when I was writing it up
and when you then argue that a,b,c,d have to be of that form then you basically already give the argument for why the exponents have to be nondecreasing
are there really 35 nondecreasing sequences with 0-3? that seems super high. I am not convinced by your stars and bar argument somehow
I suppose there are quite a bit more total
ehh probably works out
Yeah because like for example if d=2^3 there can also have c=b=a=2^3
And so like it kind of cascades since they can still be equal to the preceding variable
2^3 2^3 2^3 2^3 , 2^3, 2^3 2^3 2^2, 2^3 2^3 2^2 2^2, 2^3 2^2 2^2 2^2
like that is just 16 i think real easily
so 35 is fari
fair*
how about you just write the exponents instead of this mess
but yeah I think it works out
but your argument needs to be rewritten. not clear currently whats happening
which part of it unclear besides the prime factorization
how to read the stars bars thing
SWR appearance
how r u
long time no see kinda
been busy
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Does this make sense (if it does, is it complete?), or did I misunderstand certain rules of sets?
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forgot to close 💀
.reopen
✅
@tawdry arrow that user was banned for giving random, not necessarily true advice.
Oh.
I would expand your reasoning between these two steps
Specifically, have you shown in the past that $(A\times B)\setminus(C\times D)=(A\setminus C)\times (B\setminus D)$?
SWR
No, I haven't. For some reason I thought they would just be equal without showing it.
Let me try.
(hint: they will not be equal)
So, the entire thing is just bullshit.
