Available help channel!
#help-10
obtuse pebbleBOT
Available help channel!
grave falcon
some one can help to find limit? 😅
obtuse pebbleBOT
some one can help to find limit? 😅
@grave falcon Has your question been resolved?
obtuse pebbleBOT
@grave falcon Has your question been resolved?
obtuse pebbleBOT
@grave falcon Has your question been resolved?
timid silo
some one can help to find limit? 😅
that pic is like 100 pixels
can u write out whats in it
wise lava
can you give me a hand with part c?
obtuse pebbleBOT
can you give me a hand with part c?
wise lava
here's my work
maybe it's something related to inequalities but I cannot solve anything it seems
15 minutes and no response
so if you'll excuse me...
<@&286206848099549185>
obtuse pebbleBOT
@wise lava Has your question been resolved?
hallow hatch
can i get a hint as to how to prove or disprove that "Every row of Pascal's Triangle, except for the top row, has an even number of odd numbers"
obtuse pebbleBOT
can i get a hint as to how to prove or disprove that "Every row of Pascal's Tria...
solid heron
how do i find the number of solution for $9^x - 5^x - 4^x = 0$
obtuse pebbleBOT
how do i find the number of solution for $9^x - 5^x - 4^x = 0$
warm shaleBOT
『Marius』
tranquil arch
$f(x) = 1-(\frac{5}{9})^x-(\frac{4}{9})^x$ is an increasing function, so $f(x)$ just have a root $x=1$
warm shaleBOT
秋水
timid silo
$\sqrt{}$
tranquil arch
it's the same, you can test x=2 is a root
solid heron
still by dividing with (9^x)?
tranquil arch
yes
obtuse pebbleBOT
grizzled oriole
86
obtuse pebbleBOT
Available help channel!
neon crypt
How can I solve this? I always get one of the undefined types.
obtuse pebbleBOT
How can I solve this? I always get one of the undefined types.
timid silo
logarithms and power properties
$\ln\left(\lim_{x \to \infty} \frac{2x - 2}{2x + 2}\right)^{x+2} = \ln(L)$
warm shaleBOT
kyou
neon crypt
so x+2 goes to the front of the phrase?
timid silo
We can move the natural logarithm inside of the limit and obtain
$$\lim_{x \to \infty} (x+2)\ln(\frac{x - 1}{x + 1})$$
warm shaleBOT
kyou
timid silo
**kyou**
or u can just do this
ultimately the answer will be the same
ln(1) = 0 but so e^0 is the answer
timid silo
the point is u obtain an answer of e^something
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
amber pebble
If you have a 0.65% chance of 1 thing happening every time you do something, how can you figure out how many times you would need to perform that task for that 1 thing to happen? As in like 1/1000 or 1/60 or whatever the actual answer is. I guess I’m asking how to calculate odds from a percentage. I can give more information as needed, but I’m not sure what else is needed yet.
obtuse pebbleBOT
If you have a 0.65% chance of 1 thing happening every time you do something, how...
rigid lintel
you cannot ever guarantee for that to happen
but you can calculate the probability of it not happening in n attempts
thats what you mean right?
civic zealot
or expected value? How many attempts you'd need on average?
amber pebble
Maybe.
So for a little more context it’s video game related. There are certain items that that drop, and each item has a primary and secondary effect. The initial formula for figuring out your chances of getting the desired primary + secondary effect is Primary x Secondary (1) / 100 which gives me an 11.75% chance every time I perform that task of getting the item. But from there the item can also have 6 possible downsides, 3 possible ratings for the primary effect and 3 possible ratings for the secondary effect. So it then becomes 11.75 * 3/6 (number of acceptable downsides) * 1/3 (number of acceptable primary ratings) * 1/3 (number of acceptable secondary ratings) which gives me a 0.65% chance of getting the exact item I want every single time I perform the task to get it. So I was curious if there was a way to calculate how many times I would potentially need to perform that task to get what I want. Or is that impossible?
civic zealot
expected value is probably the best you could do.
1/(0.0065) is around 154.
so you'd 'expect' 154 attempts to get the item you want, but it could be less, could be more.
amber pebble
expected value is probably the best you could do.
1/(0.0065) is around 154.
I’ll take whatever I can get, honestly. I guess since it is all rng it’s impossible to pinpoint, and I’ve had items with better chances take more attempts and items with worst chances take less attempts.
topaz surge
hey, I have this problem that I solved, but i'm not sure if what I got is correct, could anyone please check? :)
Let $f: \mathbb{R} \to \mathbb{R}$ be a differentiable function, $f(1) = 0$ and $\lim_{x \to +\infty} f(x) = +\infty$, determine the value of
[\int_{0}^{+\infty} \frac{f'(1+2x)}{1+\left[f(1+2x)\right]^2} dx]
To solve this, I first did $\lim_{n \to +\infty} \int_{0}^{n} \frac{f'(1+2x)}{1+\left[f(1+2x)\right]^2} dx$, then using the substitution
[u = f(1 + 2x), du = 2f'(u)dx]
I got
\begin{align*}
&= \lim_{n \to +\infty} \frac{1}{2} \int_{0}^{f(1+2n)} \frac{1}{1+u^2} dx\
&= \frac{1}{2} \lim_{n \to +\infty}\left[\arctan{f(1+2n)} - \arctan{0}\right]\
&= \frac{\pi}{4}
\end{align*}
obtuse pebbleBOT
hey, I have this problem that I solved, but i'm not sure if what I got is correc...
warm shaleBOT
Spiwocoal
daring rock
In the second to last line, shouldn't arctan 0 be arctan 1 ?
And the 1/2 in front of your integral disappeared
topaz surge
oh, yeah, you're right
I actually did consider the 1/2, but forgot to type it in
and it is arctan 0, I just mistyped again coz it's f(1), and that's 0
daring rock
Oh, you're right, the lower bound on the integral is actually 0 then, you mean
topaz surge
yes
daring rock
Yeah, I agree pi/4 is correct
topaz surge
awesome, thanks :)
daring rock
For your substitution, though I don't think you should write du = 2f'(u) dx
topaz surge
why not?
topaz surge
mistype again... I actually did two extra steps when I did it on paper, where I first used u = 2x + 1 and then I did m = f(u)
but yeah, you're right
daring rock
Oh okay, that makes sense
lofty bloom
obtuse pebbleBOT
obtuse pebbleBOT
@lofty bloom Has your question been resolved?
lofty bloom
Yeah i just don’t understand how to prove it
i’ve been working on it for over an hour now
like how to prove angles bad and such are right angle
s
tawny fog
Ok ok
No problem
Wait I am telling you the approach
And tag me ok otherwise I can't see your message only tag me
lofty bloom
And tag me ok otherwise I can't see your message only tag me
okay thanks
tawny fog
You have to proof all the triangle congruent
lofty bloom
ah
tawny fog
In the ||gm
lofty bloom
huh
tawny fog
Then all sides will be equal so it will be a square
lofty bloom
that means it’s a rhombus
tawny fog
Oh wait
lofty bloom
a square means it has all right angles and all congruent sides
lofty bloom
yeah that’s what i’m struggling with
btw i can’t use numbers like 180-90/2 for proofs
like it had to be some sort of rule yk
tawny fog
Do you know the angle formed at the intersection of the diagonals of a rhombus is a right angle
lofty bloom
yeah
royal flint
yeah that’s what i’m struggling with
Hi, easier approach is:
Diagonals of rhombus bisect each other. If half of two diagonals are equal, then diagonals are equal. Since both diagonals are equal and all sides are equal, it is a square
tawny fog
Hi, easier approach is:
Diagonals of rhombus bisect each other. If half of two d...
Yeah exactly
royal flint
Because the property of rhombus is that all sides of it are equal
lofty bloom
the problem is i’m struggling to find a reason to put for that in my homework like
lofty bloom
Hi, easier approach is:
Diagonals of rhombus bisect each other. If half of two d...
i get how that works but does it work cus substitution or congruent angles added to congruent angles or
royal flint
i get how that works but does it work cus substitution or congruent angles added...
No need for angles, I just used the properties of rhombus and the given condition to prove that it is a square
lofty bloom
okay thanks
i’ll try figure it out cus this website looks for exact reasons with like specific property names
royal flint
Ok
lofty bloom
Ok
thanks for the help i finally found the reason it asked for
i needed to prove they AE=1/2AC and BE=1/2BD and then i needed to say BD=AC cus segments that are twice the length of congruent segments are congruent
royal flint
thanks for the help i finally found the reason it asked for
Glad to hear that!
tawny fog
i needed to prove they AE=1/2AC and BE=1/2BD and then i needed to say BD=AC cus ...
Remember ∆AEB is iscloses
You will do it
lofty bloom
Remember ∆AEB is iscloses
hey man i already did it thanks tho
lofty bloom
Glad to hear that!
thank you 🙏
lofty bloom
.close
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
untold flax
what are the 2 coordinates this function passes through
timid silo
c and 5?
timid silo
then i guess the y is 0 and x is 1 or a
untold flax
ye
we're given it passes through (1,0) and (3,0)
as at the x intercept y is 0
ok so now, we plug in (1,0) and (3,0) into the function, and you would get 2 equations with 2 unknowns, a and c
timid silo
we're given it passes through (1,0) and (3,0)
everytime i see a question with (1,0) (0,3) i cant help bbut use the slop equation. y2-y1/x2-x1
untold flax
lol
timid silo
ok so now, we plug in (1,0) and (3,0) into the function, and you would get 2 equ...
wait so i just replace the x and y with (1,0) and (3,0)
untold flax
yep
timid silo
okay but it will look like this a+5+c
untold flax
= 0
timid silo
ah, thanks a lot, I do not want to be annoying but do you know how to slove this one?
untold flax
ah, thanks a lot, I do not want to be annoying but do you know how to slove this...
oh yeah sure
ok so
first thing you should do is work out the fomrula for the line T
timid silo
Formula of the line T? All it says that it's perpendicular
timid silo
you have 2 points that it goes through
Uh sure. So I can't use the lines and make it -5/2?
untold flax
?
untold flax
everytime i see a question with (1,0) (0,3) i cant help bbut use the slop equati...
use your beloved formula
untold flax
no , the gradient of a perpendicular line is the negative reciprocal
so -0.6 is -3/5, therefore the gradient of the perpendicular line would be 5/3
timid silo
Ye I was thinking the same thing but IDK what to do with 5/3
Oh I forgot. @untold flax
timid silo
C? But the question asked for the line passing through the two points (5;5) and (-5;-1)
untold flax
I'm talking about this one
K is 5/3x + c
so we need to find c
using the point that we already know it pasts through
timid silo
using the point that we already know it pasts through
Wait so I do use the shift slove method or
timid silo
you just plug in
So sorry, this question gives me a headache lol
I use (3,2) as X and y and then what? Y2-Y1 again with 5/3?
untold flax
no
y = 5/3 x + c
is the line K
y is 2
x is 3
so 2 = 5 + c
c is -3
so the line K is y = 5/3x -3
then you check what point is in this line
obtuse pebbleBOT
untold flax
np
obtuse pebbleBOT
Available help channel!
honest fjord
Hello
honest fjord
I have a question regarding differential equations
why is it that (d/dt)(mv) = m(dv/dt) + v(dm/dt) ?
wouldn't it be supposed to be (d/dt)(mv)= dmv/dt?
obtuse pebbleBOT
@honest fjord Has your question been resolved?
obtuse pebbleBOT
@honest fjord Has your question been resolved?
nocturne minnow
.close
elfin umbra
Hey, I was messing around in desmos and i don't understand what is happening. Can someone explain to me what each part of the equation does?
obtuse pebbleBOT
Hey, I was messing around in desmos and i don't understand what is happening. Ca...
elfin umbra
,,\sqrt{x^{-1.2}+y^{-7}}+.1x+2y+\frac{y^{2}}{x^{2}}+\sin\left(3x\right)=1
warm shaleBOT
Mellody
elfin umbra
i can send a picture if you want
timid silo
you aren't doing linear transformations, so you can't exactly say what each term does easily
elfin umbra
you aren't doing linear transformations, so you can't exactly say what each term...
oh ok
timid silo
cool graph tho
timid silo
sin(3x) is what makes it 'periodic' ig
elfin umbra
i also really like
,,\sqrt{x^{-1.2}+y^{-7}}+2y+\frac{y^{2}}{x^{2}}+\sin\left(3x\right)=4
warm shaleBOT
Mellody
timid silo
the squareroot makes it not exist around 0
elfin umbra
**Mellody**
,,\sqrt{x^{-1.2}+y^{-7}}+2y+\frac{y^{2}}{x^{2}}+\sin\left(3x\right)=1
warm shaleBOT
Mellody
elfin umbra
makes it where its almost a parabola without the turning point
timid silo
**Mellody**
try graphing y^{2}+2yx^{2}+.1x^{3}=x^2 on top
the squareroot and sine terms are small compared to everything else
elfin umbra
the squareroot and sine terms are small compared to everything else
can you explain further please?
timid silo
sine is bounded between -1 and 1
the thing inside the squareroot is very small if x is big
so we are left with 2y+y^2/x^2=1
elfin umbra
thats what i started with
and started modifying stuff
like
the square root
just to see what i could fin
welp @timid silo thanks for the help
.close
limber gazelle
So i have the following dilemma:
It’s nothing complex, you just want a force that pushes against the direction an object is moving, that scales with the square of its speed.****
How do i calculate sqrt magnitude?
linvel is linear velocity in Vector3 format {x,y,z}
dot is dot product
sqrt is squared root?
Here's an example of code i got so far, but it's wrong:
let drag = -0.1; // coefficient?
let drag_force = drag
* velocity.linvel.normalize() //normalized
* ((velocity.linvel.dot(velocity.linvel)).simd_sqrt()); // sqared magnitude?
@limber gazelle Has your question been resolved?
limber gazelle
<@&286206848099549185> poketh
obtuse pebbleBOT
@limber gazelle Has your question been resolved?
tardy epoch
So i have the following dilemma:
It’s nothing complex, you just want a force th...
Can you write out the math
$\sqrt{v\cdot v}$ should give you the magnitude of v
limber gazelle
a force that pushes against the direction an object is moving, that scales with the square of its speed;
So F = a * v
warm shaleBOT
riemann
tardy epoch
The rest is your programming language
tardy epoch
Most languages have a magnitude of a vector
Magnitude of v is the speed
Where v is velocity vector of course
tardy epoch
a force that pushes against the direction an object is moving, that scales with ...
What's a? Acceleration? How is that "scales with the square of its speed"
You need a square somewhere
limber gazelle
correct
so the vector is vec3 {x,y,z} which is represented with velocity.linvel
I guess i need to square that?
tardy epoch
Can you just show the whole original problem. Sounds like you've interpreted something wrong
limber gazelle
the original problem is producing a quadratic drag
for each tick
producing a force that is squared over the speed of a vector
tardy epoch
Screenshot or picture is best
limber gazelle
ok so
I need a force that pushes against the direction an object is moving, that scales with the square of its speed.
I tried doing this
and the answer is
not sure if this is corerct
tardy epoch
That's your code. I asked for the original problem.
Like the question your professor gave you
Probably from a textbook
limber gazelle
it's
I need a force that pushes against the direction an object is moving, that scales with the square of its speed.
Then your force equation is wrong.
Or you left out some details
tardy epoch
That's your code. I asked for the original problem.
Which is why I've asked for the original question and not YOUR interpretation
It's like the 5th time I've asked. It shouldn't be this hard
sinful bane
is it possible for two elements in Zn to have the same inverse?
obtuse pebbleBOT
is it possible for two elements in Zn to have the same inverse?
sinful bane
ur in my channel
barren portal
timid silo
My bad
sinful bane
ur all in my channel
sinful bane
yes go to the bit above this where it says math help (available)
obtuse pebbleBOT
@sinful bane Has your question been resolved?
misty kiln
i have a series from n=1 to infinity of 1/n^2-6n+10
obtuse pebbleBOT
i have a series from n=1 to infinity of 1/n^2-6n+10
misty kiln
is this telescoping? if it is how do I factor it
fierce lagoon
Try partial fraction decomposition to see if it's telescoping
final thunder
Can’t ig
high lily
comparison test?
misty kiln
whats the comparison test again
and how would I change this series algebraically to get it into the right form?
final thunder
Can use this
misty kiln
@final thunder any idea about this series?
final thunder
Yeah change the power of everything to n then group them all together
misty kiln
wdym by that
like i know I have to change the powers but the actual algebra behind it confuses me
sorry im asking such dumb questions
final thunder
Change $2^{2n+1}$ to $ab^n$ for some integers a b
warm shaleBOT
Pure
misty kiln
if i have everything to the n power dont I have to lower the counter to n = 0 for the series?
and doing that would again change the powers
final thunder
You’re not trying to reindex
You want to write this in the form ar^n which is the form of geometric sequence
misty kiln
so the numerator is good
i just have to figure out how to change the denominator to just ^n
final thunder
Use some exponent laws
misty kiln
@final thunder so I do 2^2n * 2^1
final thunder
Ye
misty kiln
but how do I split the 2^2n into 2^2 and 2^n
final thunder
2^(2n) = (2^2)^n
final thunder
Yes
final thunder
Yeah note that this will converge as |r|<1
misty kiln
ty
final thunder
misty kiln
.close
thin wyvern
can someone help me with 5 problems in vc it is "Graphing linear equations"
thin wyvern
anyone?
thin wyvern
i would like to go over it in vc because i dont even remember how to do it
What is the slope of the line represented by the equation 3x-4y=7
nocturne minnow
What is the slope of the line represented by the equation 3x-4y=7
Get it into slope intercept form, y = mx + b
obtuse pebbleBOT
@thin wyvern Has your question been resolved?
ionic cedar
Did I do this Fourier Transform correctly?
obtuse pebbleBOT
Did I do this Fourier Transform correctly?
obtuse pebbleBOT
@ionic cedar Has your question been resolved?
ionic cedar
<@&286206848099549185>
obtuse pebbleBOT
@ionic cedar Has your question been resolved?
ornate smelt
What is the best way for anyone to gain high level problem solving skills?
- Competitive Programming
2.Math (jee advanced or international olympiad level)
3.theoretical physics
4.Ted ed puzzles and logical reasoning questions
4.competition physics
5.Chess
obtuse pebbleBOT
What is the best way for anyone to gain high level problem solving skills?
1. C...
obtuse pebbleBOT
@ornate smelt Has your question been resolved?
leaden shoal
any tips for evaluating?
obtuse pebbleBOT
any tips for evaluating?
obtuse pebbleBOT
royal basin
.reopen
obtuse pebbleBOT
✅
royal basin
just gonna pop in here and say that $\sqrt[5]{-96}$ is NOT equal to $\sqrt[5]{3} + \sqrt[5]{-99}$.
uneven marsh
Can I get a hint on proving the first bit? (I found a counterexample for the second bit with some python code)
obtuse pebbleBOT
Can I get a hint on proving the first bit? (I found a counterexample for the sec...
@uneven marsh Has your question been resolved?
uneven marsh
.close
scenic sable
how did my teacher find the 4 coordinates
obtuse pebbleBOT
how did my teacher find the 4 coordinates
zenith raft
all four names? what's that lol
tall tusk
for the x, it's just square root can be - and +
for y
it's effectively just subtracting 8 pi
which doesnt change anything
scenic sable
ok I see what it means I think
what?
zenith raft
8pi?
zenith raft
is multiply there supposed to be add?
gloomy valve
seems like the following process:
- start with the positive root & the smallest positive angle representing that complex number (+, +)
- subtract 2pi from the angle to get the same angle basically but negative (+, -)
- take the negative root and add pi to the smallest positive angle from before to get the "inverted"/reflected complex number (-, +)
- subtract from that angle 2pi to get the negative pair (-, -)
very hard to explain though
zenith raft
hmm the points are basically just found by using $(r,\theta) = (r,\theta+2\pi)$ and $(r,\theta) = (-r,\theta+\pi)$
warm shaleBOT
layla💜
gloomy valve
^sums it up lol
zenith raft
I'm not sure if there are any more rules on what the range the angles should be in or something but you can find points with any combination of signs with that
once you have one point
tall tusk
we lost the op
zenith raft
@scenic sablecome backkkk
obtuse pebbleBOT
@scenic sable Has your question been resolved?
stable rain
considering C2, of f, the upper semicircle closure of C1, Re^it, 0<=t<=pi, R-> inf
obtuse pebbleBOT
considering C2, of f, the upper semicircle closure of C1, Re^it, 0<=t<=pi, R-> i...
stable rain
does that work as an explanation or way of saying that we take the upper half semi circle for jordans lemma
my teach said this instead
wild swallow
LOL why is my head there 😭
stable rain
with diagram showing S as the C2 i drawn
stable rain
LOL why is my head there 😭
idk
wild swallow
what are you even asking
wild swallow
what do you want to know
stable rain
considering C2, of f, the upper semicircle closure of C1, Re^it, 0<=t<=pi, R-> i...
like does this work
when im sayin/describing the C2
upper half semi circle
wild swallow
nani is upper semicircle closure of C1
wild swallow
no like
wild swallow
what are you even trying to say
wild swallow
what about it
wild swallow
its scuffed
wild swallow
the closure of a set is the smallest closed set containing it
wild swallow
???
stable rain
so how wld i describe C2
wild swallow
thats a whole integral
wild swallow
that is how youd write it
warm shaleBOT
stable rain
wait
but then
S doesnt describe a semicircle?
oh wait it does ok
um
do i mention R->inf
anywhere
west escarp
.open
.reopen
In figure diagonal AC of parallelogram ABCD bisects show that
(i) if bisects
(ii)ABCD is a rhombus
spring trail
tall tusk
draw one bro
unique spear
yeah you have to draw it out
reef grotto
In figure diagonal AC of parallelogram ABCD bisects show that
(i) if bisects
...
huh
if what bisects what
west escarp
angle a biscts the the entire paralleogram
lemme resenf
In figure diagonal AC of parallelogram ABCD bisects angle a show that
(i) if bisects
(ii)ABCD is a rhombus
do u have to use congruence ?
<@&286206848099549185>
vestal marsh
Yeah the congruence rules
west escarp
Yeah the congruence rules
thanks
obtuse pebbleBOT
Available help channel!
outer rune
How do you get 3?
obtuse pebbleBOT
How do you get 3?
unique nebula
Seems like a memorisation problem
Breakpoints 1 sigma, 2 sigma, 3 sigma
Anyway plot a normal distribution on desmos
outer rune
yes i have a bad memory
i only remember how to get the sd for standard normal distributions
oh i think i got it now
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
drifting roost
Hello, am i dumb or how does this become
obtuse pebbleBOT
Hello, am i dumb or how does this become
reef grotto
yeah should be
rigid pine
They wrote the numerator as x^2 = (x^2 + -1) + 1 and simplified from there using x^2 - 1 = (x - 1)(x + 1).
reef grotto
They wrote the numerator as x^2 = (x^2 + -1) + 1 and simplified from there using...
no but the integral of (x+1) is not (x+1)^2
reef grotto
who wrote this
drifting roost
who wrote this
A book
rigid pine
Oh I see. Maybe a typo.
I find mistakes all the time in my current book and it's a second edition.
drifting roost
I find mistakes all the time in my current book and it's a second edition.
so it should be -x^2/2 - x - ln(x-1) + c instead right?
rigid pine
-(x + 1)^2/2 should be in place of -(x + 1)^2.
drifting roost
-(x + 1)^2/2 should be in place of -(x + 1)^2.
why would you consider (x+1) as a term though?
rigid pine
It's more similar to the way they've wrote it.
reef grotto
why would you consider (x+1) as a term though?
really doesn't matter
drifting roost
why not consider it as integral of x + integral of 1 + integral of 1/(x-1)
reef grotto
why not consider it as integral of x + integral of 1 + integral of 1/(x-1)
cuz it also works
no idea
rigid pine
If I saw (x + 1) in this context I'd integrate using the reverse chain rule. x^2/2 + x is perfectly acceptable too though.
reef grotto
I guess the extra part is part of the c constant?
no
you can't just be like
yo x is a constant now
drifting roost
i see what you mean
I'm confused though :V what's the final answer then? cuz i assume there probably is a way to get rid of the lingering 1/2 in front of the -(x+1)^2
so far from what i know it should be -(x+1)^2/2 - ln(x-1) + c
which should be -(x+1)^2 - 2ln(x-1) + c
tardy gull
why not consider it as integral of x + integral of 1 + integral of 1/(x-1)
If you don't want to have an additional constant, you can use the method you gave here
drifting roost
which should be -(x+1)^2 - 2ln(x-1) + c
This looks right to you? @tardy gull
I could still work it and probs say -x^2 -2x - 2ln(x-1) because the -1 is also part of c ig
raw heath
drifting roost
.close
smoky dove
Does the leading term of any line equation in general form have to begin with x?
smoky dove
Alright thanks
Yeah people were telling me the x has to be positive and the leading term
tawny fog
Means general quadric equation?
ruby stone
help me
fast moon
spice citrus
ruby stone
Use Pythagoras
square root PQ^2-PL^2 ?
spice citrus
Not quite
There is one new point you need
What's the difference between PL and QM?
ruby stone
radius?
spice citrus
What is the length of PL?
ruby stone
5cm right?
spice citrus
Yes, and length of QM?
ruby stone
3cm
ruby stone
yeah
spice citrus
In this case you need to use the right triangle ODA
ruby stone
so the new picture will be like this?
spice citrus
Yes
obtuse pebbleBOT
@ruby stone Has your question been resolved?
spice citrus
PL - QM
ruby stone
oh 2 cm
ruby stone
the answer will be 7.74?
spice citrus
7.75, you need to round up
ruby stone
ah sorry my bad
spice citrus
It's fine
ruby stone
thanks man I really appreciate your help
obtuse pebbleBOT
Available help channel!
surreal spruce
obtuse pebbleBOT
thick oracle
So we solved case 1
surreal spruce
yep
thick oracle
This is case 2
The right side is negative in this case
And the left side is positive
So
It doesnt matter what number i plug in for x
The equality will always be true
Right?
A positive number is always bigger than a negative number
surreal spruce
ye
surreal spruce
sqrt(3)x-sqrt(3) < 0 ?
thick oracle
Yes
surreal spruce
we gonna factore it ?
warm shaleBOT
Master Oogway
surreal spruce
ye
surreal spruce
you said we need to solve it
surreal spruce
x < 1 ?
thick oracle
Yes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
.reopen
silk birch
obtuse pebbleBOT
silk birch
Can someone help me with this question?
I kind of just want the solution and the way to solve it
ive spent wayy to much time on this already
silk birch
My guess was 39/100 but im quite confident that is going to be wrong.
tranquil quiver
whyd you guess that
cant you use demorgans law
(A u B)' = A' n B'
i guess thatll give you your guess
idk the tricky part is going from P(A u B) to P((A u B)')
idk if you can just do 1 -
tranquil quiver
i guess so
silk birch
Ill check it
tranquil quiver
100-(46+25-10)
silk birch
Yep, it was correct, thanks man!
obtuse pebbleBOT
@silk birch Has your question been resolved?
torn cape
how to prove this?
obtuse pebbleBOT
how to prove this?
alpine raven
$\log_a (x) = \frac{\ln(x)}{\ln(a)}$
and $\lim\limits_{x \rightarrow 0} \ln(x) = -\infty$
warm shaleBOT
Ｈｅｒｅｌｓ
alpine raven
with $\ln(a) > 0$
warm shaleBOT
Ｈｅｒｅｌｓ
normal dagger
obtuse pebbleBOT
untold flax
uh what's your question
normal dagger
sorry
sync issue
so why do you subtract 2n and n on the top if you want to get r=n+1 to the max value of 2n
untold flax
because you want to count the n+1 term
normal dagger
I mean the top number of summation
you can't use the formula if you have 2n on top
untold flax
what do you mean
spice citrus
You can still use the formula, if you just plug in 2n into the sum of squares formula
Instead of just n
untold flax
they just made it so it starts from r=1 so you can apply the sum of squares formula
you want all the terms up to 2n
subtract the terms up to n
so you're left with n+1 to 2n
high lily
$\sum_{r=1}^{2n} a_r = \underbrace{a_1 + a_2 +\dots + a_n}{\sum{r=1}^{n}a_r} + \underbrace{a_{n+1} + \dots + a_{2n}}{\sum{r=n+1}^{2n}a_r}$
warm shaleBOT
ℝamonov
untold flax
damn pro
high lily
uh what's your question
sync issue
we saw the image, we just didn't know what you wanted
frank shell
im working on numerical sequences on a math exercises book and in the solution to a question they put:
if
p^2 (a+b+c) + p (3a+2b+c) + 2a = 1
• with a,b,c real numbers
• and p in IN* (natural integers without 0)
then
a+b+c = 0
3a+2b+c = 0
2a = 1
how did they get to this?
obtuse pebbleBOT
im working on numerical sequences on a math exercises book and in the solution t...
tardy hatch
<@&286206848099549185>
marble jasper
Result of Quiz came out today I just wanna understand why the answer of this question is false(it’s T/F)
obtuse pebbleBOT
Result of Quiz came out today I just wanna understand why the answer of this qu...
uneven palm
they didn’t state f(x) is continuous
so you don’t know that it goes through there
have you learned IVT?
marble jasper
So that’s why it’s false
uneven palm
yep
marble jasper
have you learned IVT?
Ye I just assumed it’s cont
uneven palm
nahh you can never assume that in calculus
unless they tell you it’s continuous or they give the function and you can check if it is
frank shell
you can never assume a function in continuous when it comes to calculus
marble jasper
Alright my bad thanks for clearing my doubt
uneven palm
frank shell
the only condition is for them to tell you that direvtly or maybe they give a function to check it by urself
case closed i guess but fun exercise
.close
marble jasper
.close
sleek marsh
Given a continuous function f defined on closed interval [a,b], if f is constant on (a,b) is f also constant on [a,b]?
obtuse pebbleBOT
Given a continuous function f defined on closed interval [a,b], if f is constant...
alpine raven
f is continuous on [a,b] right ? so f(a) and f(b) are constants
sleek marsh
yeah
alpine raven
and it is continuous on (a,b) too
sleek marsh
yep
alpine raven
so huh, you have your answer
sleek marsh
I understand it intuativley, but im wondering how to prove
alpine raven
just draw a graph, youll see
alpine raven
I understand it intuativley, but im wondering how to prove
ah
sleek marsh
any ideas?
alpine raven
I think you need to prove that f is continuous at the point a and b
alpine raven
constant in (a,b)
constant function i think
alpine raven
what does (a,b) mean ?
interval
sleek marsh
could i do: since f is cont on [a,b] for every epsilon>0 there exits a delta such that for all x with |x-b|<delta we have |f(x)-f(b)|<epsilon -> |c-f(b)|<epsilon
so f(b) =c?
timid silo
[a,b]=(a,b)? nah ?
sleek marsh
then similarly for a
sleek marsh
mate get your own channel lol
alpine raven
it's ]a,b[
American education use (,)
timid silo
mate get your own channel lol
I'm trying to help
alpine raven
I use ],[ for open since im not american
alpine raven
so f(b) =c?
why
sleek marsh
since we can make epsilon arbitrarily small
alpine raven
you said |c-f(b)| < ε
it doesnt mean c = f(b)
you can say f get closer to f(b)
and since f is constant
therefore c = f(b)
rigid pine
I think you need to use a definition for left and right sided limits since f(x) might not be defined on the left of x = a or on the right of x = b.
alpine raven
limit
alpine raven
I think you need to use a definition for left and right sided limits since f(x) ...
indeed
sleek marsh
ah yep
But for an arbitrary epsilon>0 doesnt that imply the difference goes to zero?
tranquil quiver
its continuous over [a, b] right
alpine raven
it is
tranquil quiver
so limit x approaches b must exist
alpine raven
yep
tranquil quiver
its easy to find the left sides limit
then you can conclude the right side limited HAS to be the same
and use the same for a
then using the definition of continuity f(a) and f(b) are equal to the limits
idk if im doing smth wrong there
@sleek marsh hows this sound
i havent learnt anything about using epsilon and delta to prove stuff but this is just going off definition of continuity idk
sleek marsh
Yeah thats pretty much what im thinking
rigid pine
If $f(x)$ is continuous at $x = a$ then $\lim_{x \to a+} f(x) = f(a)$
warm shaleBOT
stabulo
rigid pine
You know the limit part is equal to the constant so f(a) is also equal to the constant.
sleek marsh
let $\epsilon>0$. Then since f is continous there exists $\delta>0$ such that $x\in(b-\delta,b)$ implies $|f(x)-f(b)|=|c-f(b)|<\epsilon$. since $\epsilon$ arbitrary f(b)=c.
tranquil quiver
oh is epsilon delta basically proving the limit
rigid pine
It's involved in the formal definition of the limit.
warm shaleBOT
F♯A♯ℵ0
rigid pine
**stabulo**
The epsilon-delta definition will explain precisely what this statement means but I don't think you need to worry about that since it's assumed in the hypothesis of the problem.
bleak nexus
(2x - 3) / 5 = (4 - 3x) / 7
what
obtuse pebbleBOT
(2x - 3) / 5 = (4 - 3x) / 7
**what**
teal turret
Cross multiply
Multiply numerator of first by denominator of second, and denominator of first by numerator of second, and set them equal to each other
obtuse pebbleBOT
@bleak nexus Has your question been resolved?
thin cave
Teach me 14c (I)
bold bane
Teach me 14c (I)
There is a point W between S and T whose distance from S and T is 2d and d respectively. Find that point. The line at which point W will always maintain that ratio will be perpendicular from the line made by S and T. Find the inverse slope of that line and use the point W to make an equation.
obtuse pebbleBOT
@thin cave Has your question been resolved?
thin cave
There is a point W between S and T whose distance from S and T is **2d** and **d...
So is the ratio will be SW : TW = 2:1 ??
bold bane
Yes.
lavish tapir
obtuse pebbleBOT
lavish tapir
Help me pleaseeee
cold thistle
Do you remember your types of angle pairs?
obtuse pebbleBOT
@lavish tapir Has your question been resolved?
nova nimbus
A pair of vertically opposite angles are always equal to each other.
so e = 73
d = 90 is right angle as other part is right angle
complete line angle is 180.
so "f + 73 = 180"
f = 180 - 73 = 107
d = 90 , e = 73 f = 107
neat oxide
Out of 15 books 5 are with defects. What's the probability that out of randomly taken 6 books 4 of them are with defects?
obtuse pebbleBOT
Out of 15 books 5 are with defects. What's the probability that out of randomly ...
obtuse pebbleBOT
@neat oxide Has your question been resolved?
onyx dust
obtuse pebbleBOT
onyx dust
can someone pls explain where i went wrong here?
obtuse pebbleBOT
@onyx dust Has your question been resolved?
obtuse pebbleBOT
@onyx dust Has your question been resolved?
onyx dust
.close
obtuse pebbleBOT
twin sapphire
whats #?
cinder lava
are steps that I did.
twin sapphire
euclidean division ?
cinder lava
Not 4,23 but 4.0
cinder lava
It removes the remainder yes.
twin sapphire
ok so it doesnt matter
cinder lava
Yes.
cinder lava
Yea I hope it does not matter that much at the end.
Can you check if I did a mistake here?
obtuse pebbleBOT
@cinder lava Has your question been resolved?
cinder lava
Must be a very hard question...
timid silo
Is 0 a natural number
obtuse pebbleBOT
Is 0 a natural number
sage geode
Define a natural number
timid silo
Why does it depend on the definition
reef grotto
Why does it depend on the definition
because there's no convention
ig to avoid confusion you could use the notations
$$\mathbb{N}_0$$
warm shaleBOT
Asagao 朝顔
reef grotto
that this is the natural numbers with the number 0
tawny fog
Is 0 a natural number
What is number
See Natural number are the set of
{1,2,3,4,5,6,7,8,9,10..............}
It doesn't have any zero in it
high lily
there is no consensus on whether 0 is included if you just say natural number
obtuse pebbleBOT
Available help channel!
dense yoke
had a quick question about the chain rule. As long as there is something along with X you use chain rule right. So doesnt matter as long as something is multiplyed, plus or minus the X ?
obtuse pebbleBOT
had a quick question about the chain rule. As long as there is something along w...
versed cave
Can you give an example?
versed cave
yeah you can (you have to) use the chain rule for both
dense yoke
like somethin next to (x in parantese) and a function on the outside
final thunder
Basically when you have a composite function
versed cave
if you have a function and inside there's x only, you don't have to use it, if there is more inside, you have to
reef grotto
hmm like sqrt(2x) or sqrt(x+3)
in the case with the sqrt(x+3) you still need to use the chain rule, it's just that the derivative of x+3 is 1
versed cave
Nice thing: you can actually use the chainrule for stuff like sin(x) too
It becomes d/dx [sin(x)] = d/dx[sin(x)] · d/dx[x] = cos(x) · 1 = cos(x)
dense yoke
if you have a function and inside there's x only, you don't have to use it, if t...
so something as in anything as long as its someting. so x+something, x-something, x*something
versed cave
x/something too I guess
Or something like
sqrt(sqrt(x)) or log(sqrt(x))
As long as you have composite functions (aka functions inside other functions)
another classic example is this:
(2x + 4)²
the first function is x²
And the function "inside" of that is 2x + 4
dense yoke
another classic example is this:
(2x + 4)²
the first function is x²
And the func...
oh thanks everyone for clearing it up 🙂
made it alot clearer
with the examples 🙂
versed cave
dense yoke
.close
arctic granite
obtuse pebbleBOT
arctic granite
I tried to make something out of the constant but not sure.
knotty crow
u can check it plugging some a's into, for example a = - 1 and a = 2