nah
#help-10
faint marsh
so 4
glossy basalt
still nope
faint marsh
im going to kms
glossy basalt
- what is x when x+1=-4
that means solve x+1=-4
glossy basalt
im going to kms
nah, you'll be fine
faint marsh
- what is x when x+1=-4
that means solve x+1=-4
-5
glossy basalt
correct
so when we have |x+1|=4, we split cases
Case 1: x+1=4, then x=3
Case 2: x+1=-4, then x=-5
so the final answer for Q(c) will be x = 3 or -5
glossy basalt
now, a and b will be easier
faint marsh
should I we start with b or a
faint marsh
I didnāt learn cubic root
glossy basalt
I didnāt learn cubic root
oh i see
let's start with some basics
we know that 2Ā³=8 right?
warm shaleBOT
Biscuity
faint marsh
we know that 2Ā³=8 right?
yes
glossy basalt
**Biscuity**
do you understand the relation now?
glossy basalt
$$2^3=8$$ $$\sqrt[3]{2^3}=\sqrt[3]8$$ $$2=\sqrt[3]8$$
warm shaleBOT
Biscuity
glossy basalt
**Biscuity**
there we go @faint marsh
so, with numbers/variables that are of power 3, we can cancel it with a cubic root
and similarly, for numbers/variables that are with cubic root, we can take both sides to the power 3 to cancel it
$$\sqrt[3]x=-2$$
$$\left(\sqrt[3]x\right)^3=(-2)^3$$
$$x=(-2)(-2)(-2)$$
warm shaleBOT
Biscuity
glossy basalt
so would that be our answer ?
if you finished calculating (-2)(-2)(-2) then it'll be the answer
quiet bay
obtuse pebbleBOT
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
feral field
Can someone verify if my answers are correct š (not confident that they are)
glacial verge
Can someone verify if my answers are correct š (not confident that they are)
h and j is incorrect
feral field
can i ask what the answer would be and why
glacial verge
$5^+$ means that it's a little higher than 5
warm shaleBOT
Sepdron
glacial verge
and j, it's not a limit, just f(5)
so what value is the function at 5?
feral field
$5^+$ means that it's a little higher than 5
so for h, would it be 5?
glacial verge
yup
feral field
what does the open circle mean? i thought there was a difference between emepty circle vs filled in ones
since the straight line has a emepty circle at (5,5)
glacial verge
there is,
the empty circle means that that point is not there
and the closed one means that it's there
kinda like the ( and [ in ranges
feral field
oooh, i see. I don't get j. can you please explain it once more
glacial verge
look at the filled circle at x=5
what does that mean?
feral field
its -10?
glacial verge
Can someone verify if my answers are correct š (not confident that they are)
also I just spotted for f
you're right that it doesn't exist there
but if it's not a limit you should use the word undefined instead
feral field
thank you
glacial verge
also another nitpick, you generally don't use = if the limit is DNE
glacial verge
np!
obtuse pebbleBOT
@feral field Has your question been resolved?
obtuse pebbleBOT
restive gorge
around y=x axis
heady turtle
yes rotate the region around that line
restive gorge
Let me see
I think all that changes is the radius
I think radius is (y-x)Ā² = 2rĀ²
,, \pi \int_a^b r^2(x) : \dd x = \pi \int_a^b \left ( \sqrt{\frac{(y-x)^2}{2}} \right )^2 : \dd x
warm shaleBOT
bacc
deft magnet
the radius would be sqrt(x)-x I'm thinking
restive gorge
I assumed the triangle is isoscles might be wrong about that
deft magnet
given that you're rotating around the x-axis
so it would be the integral from 0 to 1 of pi (sqrt(x)-x)^2 wrt x
restive gorge
Maybe you could do a matrix multiplication and rotate the coordinate system so that it becomes a rotation around x-axis again
deft magnet
Maybe you could do a matrix multiplication and rotate the coordinate system so t...
wait why
oh
if it's around y = x
yeah it's diff
restive gorge
just an idea
applying linear algebra
not gonna lie i am genius
bruh
it's literally the same
,, \pi \int_a^b r^2(x) : \dd x = \pi \int_a^b \left ( \sqrt{\frac{(y-x)^2}{2}} \right )^2 : \dd x = \pi \int_a^b \left ( \frac{y-x}{\sqrt{2}} \right )^2 : \dd x
warm shaleBOT
bacc
tiny kelp
here's how i derived
Go sleep
timid silo
Bacc
obtuse pebbleBOT
restive gorge
I honestly don't know where that sqrt(2) factor comes from
heady turtle
Then why did you say i dont have eyes.
restive gorge
because I thought you meant the denominator
heady turtle
fINE whatever.Put away your arrogance
obtuse pebbleBOT
Available help channel!
restive gorge
fINE whatever.Put away your arrogance
.INE
jolly radish
i am in need for someone to check if my answers are correct
obtuse pebbleBOT
i am in need for someone to check if my answers are correct
jolly radish
obtuse pebbleBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
@jolly radish Has your question been resolved?
jolly radish
<@&286206848099549185>
tiny kelp
<@&286206848099549185>
What is the question
jolly radish
sorry, is the 2 image not uploaded yet ? my discord is buggy
but if it has, i am asking if my answers are correct
obtuse pebbleBOT
@jolly radish Has your question been resolved?
peak heath
Hello,
I just have a simple question please. When can I apply the directly or inversely proportional formula?
Question: If fuel cost decreases by 40% when capacity increases by 100%, what is the fuel cost increase when capacity increase by 60% (note: it is not in the question that the relationship is perfectly inversely proportional)
Iāve been on this for a couple of hours. My technique now is to use āxā to equal percentage increase. So itās 60%/100% x 40% = fuel increase, which is 24%.
Iāve tried using the inverse equation (AB= A1B1) but it didnāt work and I presume this is because the relationship must be perfectly inverse. But what about for the direct equation (A/B = A1/B1)? Will it apply to all of these questions but I just need to either add or subtract (depending on whether the relationship is inverse or not)
Thank you.
obtuse pebbleBOT
Hello,
I just have a simple question please. When can I apply the directly or i...
@peak heath Has your question been resolved?
peak heath
<@&286206848099549185> thank you
obtuse pebbleBOT
@peak heath Has your question been resolved?
glossy basalt
i think this is about partly proportional relationship between capacity and fuel cost
usually such questions will be stated like
fuel cost partly varies with a constant and and partly varies inversely proportional to the capacity
But then, you'll probably need another condition to draw a conclusion
obtuse pebbleBOT
@peak heath Has your question been resolved?
fossil crag
all vectors orthogonal to every vector of W, so
if W is a subspace of some vector space V:
$W^\perp = {u\in V \mid \forall w\in W, u\cdot w = 0}$
warm shaleBOT
rafilou2003
fossil crag
this is the mathematical definition of the orthogonal of W
no matter the subspace, no matter the vector space
provided you have its inner product
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
barren flax
obtuse pebbleBOT
timid silo
because it's giving you the derivative of f and g evaluated at some point
do you know the formulae for the product and quotient rules?
@steady basin
wrong ping
@barren flax
timid silo
f'(5) but yeah
for (a)
so you just plug and chug
the same applies for (b) and (c)
timid silo
quotient rule for b and c
yeah
barren flax
.close
obtuse pebbleBOT
barren flax
.reopen
obtuse pebbleBOT
ā
void holly
which question are you having a problem on?
barren flax
the normal functions
(a)
it says find h'(4)
i found h(4) = 46
but how do i get h'(4)
fathom light
but how do i get h'(4)
By differentiating h(x) to get h'(x) then h'(4)
barren flax
and how on earth would i differentiate 46
void holly
for any function h, and h=f+g then h'=f'+g'
fathom light
and how on earth would i differentiate 46
You differentiate first then put values
a(x) = b(x)
a'(x) = b'(x)
barren flax
$h'(4) = 3f'(4) + 8g'(4)$
warm shaleBOT
Devil Wears Prada
fathom light
Yep
void holly
yes diffrentiate h(x) then insert x=4 in h'(x) after differntiating
void holly
**Devil Wears Prada**
correct
fathom light
When multiplication and division will come the you need to remember the differentiation formula
d/dx of uv or u/v
barren flax
$h'(4) = -6$
warm shaleBOT
Devil Wears Prada
fathom light
do i have to do b c and d
Those h(x) are different
barren flax
oh i see thx
fathom light
For each you need to find h'(x) then h'(4)
void holly
hmm ok remember these rules:\
$h=f \pm g\
h'=f'\pm g'\
h=f\cdot g\
h'=f'g+g'f\
h=\frac{f}{g}\
h'=\frac{f'g-g'f}{g^2}$
where f,g,h are functions
warm shaleBOT
convergence
obtuse pebbleBOT
@barren flax Has your question been resolved?
sinful falcon
Can someone explain 57 to me why does tanh get removed?
obtuse pebbleBOT
Can someone explain 57 to me why does tanh get removed?
restive gorge
Can someone explain 57 to me why does tanh get removed?
tanh(x) -> 1 for large x
ember lantern
Seems like a trigonometric approximation for when tanh goes big
ember lantern
tanh(x) -> 1 for large x
Yes
restive gorge
So if d the depth becomes very big you are essentially multiplying by 1
sinful falcon
I donāt understand how you came to that conclusion still
restive gorge
It fell on my head
sinful falcon
How does 2pi(d) over Lead to one?
restive gorge
,w plot tanh(x)
warm shaleBOT
restive gorge
The limit of tanh(x) is 1 as x approaches inf
So it's here also applicable
tan(2pid) -> 1 for very large values of d
sinful falcon
Ah
restive gorge
the light
sinful falcon
How do we know L is not greater than it though?
Sorry Iām like super not light right now
restive gorge
L is not a variable right
it's a constant
so eventually mathematically if d still gets bigger than L the it approaches 1
sinful falcon
I see
sinful falcon
Ugh I actually hate these problems but I get it
restive gorge
but that's also why it's an approximation, not to be considered at all times
but say you have reasonable values then it works out well
tiny kelp
Note that as the argument of the hyperbolic tangent function increases, the hyperbolic tangent function itself approaches 1. If the depth is considerably deep, then the argument of our hyperbolic tangent function is very large (as the depth increases the value of the argument of the hyperbolic tangent function also increases). As we can see from the graph, this means that as d gets larger and larger,Ā tanhā”(2ĻdL)Ā gets closer and closer to 1. And so when this is the case we can writev=/gl/2pi x 1 = answer
Basically tanh(2pid/L) = 1
sinful falcon
So for my answer could I just say the approximation $v = \sqrt[\frac{gL}{2pi}]$ exists because as the depth becomes very large it approaches one, would that be appropriate
Ok.
warm shaleBOT
Light
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sinful falcon
man
sinful falcon
I donāt think he even knows who kira is
tiny kelp
restive gorge
I donāt think he even knows who kira is
agree
sinful falcon
Nvm
restive gorge
Kira is from death note
and you are in my death note
tiny kelp
and you are in my death note
Go to sleep
obtuse pebbleBOT
sinful falcon
So for my answer could I just say the approximation $v = \sqrt[\frac{gL}{2pi}]$ ...
Also why didnāt this work
tiny kelp
Also why didnāt this work
You would have done characters error
Some might be missing
tiny kelp
<@&268886789983436800>
restive gorge
You been annoyingly reply spamming this to me
tiny kelp
<@&268886789983436800>
tiny kelp
You been annoyingly reply spamming this to me
You have no right to say that
restive gorge
now you stop huh?
sour sun
I'm having trouble understanding what's wrong here. are you just annoyed that someone made a "your mom" joke?
restive gorge
i don't know this guy, he's been reply pinging me lately with this "go to sleep"
sour sun
okay. @tiny kelp can you stop pinging them with the message "go to sleep"?
tiny kelp
okay. <@1287104057349247148> can you stop pinging them with the message "go to s...
Ok say him to not say any further words to parents
sour sun
and if that's too much of an issue then just block eachother
restive gorge
i am not the one to say bad stuff usually so this was an exception, but i apologize
i figured you wouldn't stop
tiny kelp
i figured you wouldn't stop
I will stop and sorry
obtuse pebbleBOT
Available help channel!
warm stratus
was just wondering if there is any way to prove the statement is false instead of just giving a counter example ? Thank you
obtuse pebbleBOT
was just wondering if there is any way to prove the statement is false instead o...
warm stratus
shadow dagger
was just wondering if there is any way to prove the statement is false instead o...
well what do u really mean by 'prove' it's false?
warm stratus
well what do u really mean by 'prove' it's false?
by contradiction ig
shadow dagger
well what do u really mean by 'prove' it's false?
basically it's like the statement is false because counter-examples exist
shadow dagger
and like that's basically the main way u'd go about doing this
warm stratus
basically it's like the statement is false because counter-examples exist
ik but is there a way to prove its false by contradiction or is it not possible ?
shadow dagger
there might be like some weird proof that u can do using contradiction but like that'd be a lot of effort and it wouldn't really provide much insight either
shadow dagger
for questions like these, where the answer is false bcus a counterexample exists, it's much more useful to consider 'why does this counter-example exist' rather than like 'can i prove this directly'
shadow dagger
for questions like these, where the answer is false bcus a counterexample exists...
i.e. in this case, it's the fact that we can 'create' a polynomial of degree 2 with polynomials of degree 3
(i.e. x^3 and x^3 + x^2)
that means it's unlikely to be true and how we can find our counterexample
warm stratus
i.e. in this case, it's the fact that we can 'create' a polynomial of degree 2 w...
correction have a polynomial with coefficient of x^2 not equal to zero
shadow dagger
this also means like 'the standard basis' that we often think about with vector spaces is not like 'the standard way' the vector space works if that made sense
shadow dagger
correction have a polynomial with coefficient of x^2 not equal to zero
yh
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fair wharf
are these correct
obtuse pebbleBOT
are these correct
tardy epoch
5 is correct
fair wharf
ok isn't there a mechanical way to just do it without graphing
tardy epoch
i mean if you can visualize it in your head sure go for it
fair wharf
9
fair wharf
nevermind
obtuse pebbleBOT
@fair wharf Has your question been resolved?
fair wharf
ok its 9
fair wharf
is this 21
obtuse pebbleBOT
is this 21
tardy epoch
is this 21
!show
obtuse pebbleBOT
is this 21
Show your work, and if possible, explain where you are stuck.
brazen viper
For the record, it is not 21.
brazen viper
$\int_0^2 5 , \dd{x} + \int_2^4 3x - 1 , \dd{x}$
warm shaleBOT
OmnipotentEntity
brazen viper
If this is what you meant, this is the correct first step
fair wharf
solving the first integral gives 10 and the second gives 6 giving 16
fair wharf
ok you are right
fair wharf
the second becomes 5 to 11
brazen viper
Show your work
fair wharf
3(4) -1 replaces upper limit
3(2) -1 replaces lower limit
brazen viper
You never found the antiderivative
fair wharf
the anti derivative is 3x^2)/2 -(1x)
fair wharf
138
which is not right..
4x5 + 6x2)/2
answer is 26
but how do i do it with antiderivative
brazen viper
3/2 * x^2 - x evaluated at 4 and 2:
3/2 (4)^2 - 4 - (3/2 (2)^2 - 2)
3/2 * 16 - 4 - 3/2 * 4 + 2
3 * 8 - 4 - 3 * 2 + 2
24 - 4 - 6 + 2
16
brazen viper
yes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
bitter portal
how did we get the range here
obtuse pebbleBOT
how did we get the range here
tropic sand
well that means y^2 has a max value of 4
bitter portal
is there a systematic way to do this
tropic sand
now multiplying both sides by -1
tropic sand
i think i get it
great
bitter portal
then adding 4
tropic sand
then adding 4
yes
bitter portal
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
safe stirrup
Hello friends, quick question.
obtuse pebbleBOT
Hello friends, quick question.
safe stirrup
What is the small thing that allows us to go from there to there?
I have a hard time going from 2^(n-1) to 2^n
(and the minus 1)
I know this geometric serie is important and popular. But I feel I should understand how.
timid silo
geometric sum
tropic sand
im assuming geometric series formula
safe stirrup
Yes it is this formula.
timid silo
obviously
tropic sand
now just plug in r = 2 a = 1 and so on
safe stirrup
My issue is not this. I feel like I should be able to see that conversion without the formula.
timid silo
alright
safe stirrup
From that line to th enext one.
safe stirrup
Which is why I'm asking. Looking for what is what I,m missing.
My maths are very rusty hehe. š
tropic sand
well its not one thing your missing
safe stirrup
(Did summations about 10 years ago...)
unreal musk
(it is also a common sum in itself too, for one thing)
tropic sand
the more you solve problems the more you build an intuition
safe stirrup
Yes I plan to practice more.
tropic sand
like how initially we had to write all the steps while solving algebra, but now you skip most steps while solving cuz it kinda automatically happens
safe stirrup
Very helpful. Thank you. š
tropic sand
just solve more and more, itll slowly develop
safe stirrup
Nah seriously. How would you go from the line to the next one? What was the trick?
tropic sand
there was no trick
timid silo
just geometric sum
safe stirrup
So I needed to know that whenever I have this, I should know it's the geometric sum??
tropic sand
if you were actually solving this, you probably would have to apply the geometric sum, but im assuming the book didnt since you can see its a series and so they can save some space
timid silo
So I needed to know that whenever I have this, I should know it's the geometric ...
yes
safe stirrup
The issue is I'll probably need to solve some stuffs and come up to a generic formula similar to the geometric formula.
tropic sand
So I needed to know that whenever I have this, I should know it's the geometric ...
its a matter of looking at the pattern, yes. a geometric series in general is of the form a + ar + ar^2...
safe stirrup
I have no clue yet if it could be similar or more complex.
timid silo
its the same as $1 + 2 + ... + 2^{n-2} + 2^{n-1}$
warm shaleBOT
icannotdoanymorecauchy
safe stirrup
Yes I see it is a geometric formula.
But what if I don't see it yet? Or it's not a geometric formula.
timid silo
well then
u have to write it as a series
Defining $S_n = 1+2+...+2^{n-2}+2^{n-1}$.
\begin{align*}
2(S_n) = 2 + 2^{1} + ... + 2^{n-1} + 2^n\
\therefore 2(S_n) - S_n &= (2 + 2^{1} + ... + 2^{n-1} + 2^n) - (1+2+...+2^{n-2}+2^{n-1})\
&= 1 + \underbrace{(2-2) + ... + (2^{n-1} - 2^{n-1})}_{=0} + 2^n\
&= 1 + 2^n\
S_n &= 1 + 2^n\
&= 2^n + 1
\end{align*}
u can do that
but why
safe stirrup
Because I want to practice.
Oh wait, we have 2^n-1 in my notes. Looks like it's an issue.
le tme check if that was a mistake on the teacher part.
Oh that sounds more fancy than expected. I understand better why I should be able to notice the geometric pattern.
warm shaleBOT
icannotdoanymorecauchy
safe stirrup
Just to confirm, should it be
(2^n) - 1
or
(2^n) + 1
?
safe stirrup
But it's fine I kinda see the gist of how "fancy" this was. In other words, I need to be able to spot the generic pattern of a geometric sum.
Thank you! š
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
I have an exam in a week or so. I need to learn the following:
- Number theory: modulo, divisibility, GCD, LCD, and prime stuff e.g. Euler's totient
- Functions
- Real Number Systems
- Operations
- Geometry and tortuous trigonometry
- Probability (i got one weird elevator problem, i didnt even know where to start)
obtuse pebbleBOT
I have an exam in a week or so. I need to learn the following:
1) Number theory:...
timid silo
what should i do
which topics should i study first
what free online books are recommended
shadow dagger
I have an exam in a week or so. I need to learn the following:
1) Number theory:...
what is that one weird elevator problem?
shadow dagger
I have an exam in a week or so. I need to learn the following:
1) Number theory:...
also r u high school or uni?
timid silo
high school
timid silo
what is that one weird elevator problem?
bunches of people clicking elevator and floor thing
i dont really remember
i took it last month
shadow dagger
ah k
shadow dagger
I have an exam in a week or so. I need to learn the following:
1) Number theory:...
if u already know all the content then u should probably just do questions
shadow dagger
huh
shadow dagger
I have an exam in a week or so. I need to learn the following:
1) Number theory:...
also wdym by real number systems and operations?
timid silo
inequalities and stuff and those if rational + irrational must be rational things for real number systems
ill find question in english for operations
they like to ask what id the inverse or identity for the operation
my country's curriculum is ass
shadow dagger
which topics should i study first
if it's multiple exams, then i'd just do it in the order of the exams
otherwise i don't think it really matters too much
shadow dagger
what free online books are recommended
ngl i never used books
shadow dagger
I have an exam in a week or so. I need to learn the following:
1) Number theory:...
i initially thought u were uni cus of the first 4 topics, so if it is kinda like early university, maybe
or
could help?
it's hard to give more targetted advice cus idk what exactly ur questions are like
shadow dagger
my country's curriculum is ass
also what country r u?
timid silo
thailand
shadow dagger
ah k
timid silo
https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/
are the solutions provided
shadow dagger
unfortunately whilst oxford and cambridge provide all their questions, bcus u go over answers in supervisions, there r no answers
shadow dagger
are the solutions provided
but i have done both the cambridge things i sent and i still have the answers with me somewhere
so i can send them to u if u want them
shadow dagger
nw
shadow dagger
they provide all their lecture notes online
you don't have access to all the recordings tho
timid silo
reading's fine
Operations are just relations anyway
i think all good
thank u
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
slate agate
im gonna keep it a whole buck
obtuse pebbleBOT
im gonna keep it a whole buck
slate agate
i fucking suck ass at differential equations
y'' = wx
is there even anything i can do with these
im not sure where i should even look to read about this honestly its been so long
i want some expression for y, and I want some expression for x
w is shorthand for a set of constants
i dont necessarily need a ton of help with the problem itself off the bat but just an idea of what i shoudl even be looking into concept wise would be great
pseudo swift
w is shorthand for a set of constants
wdym a set of constants
slate agate
hold on im way too behind on this to be asking for help. im gonna work on this a bit longer and come back later
.close
obtuse pebbleBOT
pseudo swift
aight
obtuse pebbleBOT
Available help channel!
chrome widget
hello someone with a good heart who can explain this exercise to me please
hidden compass
Add the fractions on the left hand side
(unless you know the cover-up method, but I guess you don't)
chrome widget
I don't know the method but I already did the sum on the left that you told me.
hidden compass
And what did you get?
marsh geyser
I don't know the method but I already did the sum on the left that you told me.
Factor x in the numerator then
chrome widget
Now do what i said
OK, I'll see if I can get the result
I'm stuck, I don't know what to do, I did what you told me but I get confused about the A and B letters.
HELP
hidden compass
I'm stuck, I don't know what to do, I did what you told me but I get confused ab...
Show where you got at
hidden compass
Ax + Bx = (A + B)x, do you agree?
chrome widget
yes and after?
obtuse pebbleBOT
@chrome widget Has your question been resolved?
worn ermine
obtuse pebbleBOT
worn ermine
I used the quadratic formula and got t = 1.52 for my second solution
T is time in seconds
So 1.52 seconds
Now how do I figure out how long the ball is in the air before being caught
And when it will reach 12 feet
I tried to plug t = 1.52 in but I got h = -0.0464
h is the ending height so I donāt think the ball was underground
Im going to go eat dinner please help
obtuse pebbleBOT
@worn ermine Has your question been resolved?
obtuse pebbleBOT
worn ermine
.reopen
obtuse pebbleBOT
ā
quick dove
molten spear
And when it will reach 12 feet
y is height, just sub in and solve for t
worn ermine
y is height, just sub in and solve for t
There is no y in this equation
worn ermine
y is height, just sub in and solve for t
We need to solve for t using the quadratic formula
molten spear
h(t) = y by definition
worn ermine
h(t) = y by definition
Ok then say h
molten spear
We need to solve for t using the quadratic formula
yeah and when you sub in y you'll see that you need it
molten spear
Ok then say h
I meant the vertical co-ordinate
worn ermine
yeah and when you sub in y you'll see that you need it
What is y though
I need to find y using t
molten spear
y = h(t)
molten spear
12 feet is the one you were looking for
worn ermine
12 feet is the one you were looking for
How do I figure that out
molten spear
the question asked for when it is 12 feet, so you just sub in 12 feet as h(t) then solve for t.
for the ending height, I'm frankly not sure what you mean by that. I don't see a domain restriction. If you mean a maximum, b/2a
worn ermine
the question asked for when it is 12 feet, so you just sub in 12 feet as h(t) th...
Yeah but I need to find t using the quadratic formula
molten spear
ok $12 = -16t^2 +21 t + 5$
warm shaleBOT
eththorn
molten spear
rearrange and solve for t, that's all you have to do for that part of the question
worn ermine
rearrange and solve for t, that's all you have to do for that part of the questi...
So do I bring 12 to the other side then solve using quadratic. Formula
molten spear
yes
worn ermine
Ok
obtuse pebbleBOT
@worn ermine Has your question been resolved?
void quartz
So 1.52 seconds
wrong
you solved for t the equation h=0
and not h=11
the ball is caught when its height is 11
obtuse pebbleBOT
@worn ermine Has your question been resolved?
outer python
Is there a way to prove the following statement using proof by induction?
Statement: For all natural numbers n greater than or equal to 2, there exists a prime p such that
n is less than or equal to p which is less than or equal to n!
obtuse pebbleBOT
Is there a way to prove the following statement using proof by induction?
Statem...
@outer python Has your question been resolved?
obtuse pebbleBOT
@outer python Has your question been resolved?
gray kiln
I don't understand your question, like maybe more context might help
The expression at the bottom is Taylor series around f(a) up to the second order. That is general form
tardy epoch
You should watch a video on the derivation again. All the variables have important meanings that you're missing
merry elm
Hi, i just dont get this question at all LOL pls help
obtuse pebbleBOT
Hi, i just dont get this question at all LOL pls help
orchid wind
ok
so
if you subtract 20 centimers from each jumps
would the shape of the graph change
orchid wind
if everyhting data point
is moved to the left
in the same maginutde
would anything about the shape change
orchid wind
not b/c of outlier
but if you move everything to the same direction
in the same units
here let me draw
merry elm
okok
merry elm
yeah
ohh i see
so the shape of the graph would remain left skewed with the same shape
cuz its just transformed left
orchid wind
i would say a little more skewed right but
orchid wind
or symmetric
idk
ok for the mean and median
if we switch everything to the left
what do you think we do
merry elm
so would it be subtracted by 20
orchid wind
oh oops
your orignal mean is 577.3
so your new mean is 557.3
sorry tped out wrong answer
merry elm
ok cool
merry elm
yeah for standard deviation and iqr
orchid wind
lets look like this
imagine q1 is red the dot
and q3 is green dot
How does the IQR (Q3-Q1) change between this, if at all
merry elm
well it should change yeah? and then would you also subtract 20 from the values within the iqr?
orchid wind
do you see that
merry elm
so the iqr would stay the same?
orchid wind
yes
orchid wind
one more thing
merry elm
savior
orchid wind
overall leason
merry elm
mhm
orchid wind
Shifting ā add or subtract a constant to all values (Ex: add 5 points to all test scores)
ā¢ Measures of center: mean and median
o add or subtract the constant to the statistic
ā¢ Measures of spread: standard deviation, IQR, range
o these statistics DO NOT change
Rescaling ā multiply or divide all values by a constant (Ex: multiply by 2.54 to convert inches to cm)
ā¢ Measures of center: mean and median
o multiply or divide the statistic by the constant
ā¢ Measures of spread: standard deviation, IQR, range
o multiply or divide the statistic by the constant
(copied from somewhere)
but
merry elm
ok thanks man
orchid wind
np
round pewter
obtuse pebbleBOT
round pewter
Hi
So basically, I'm mainly confused on 3 and 7
So on 3
It's positive when it's less than 0 and more than 2
So would I say like 0 < x > 2
wary badger
So would I say like 0 < x > 2
you donāt use this notation
alternatively
you can say
round pewter
No like the infinite thing
wary badger
x<0 and x>2
round pewter
only when x is between the 2
Could you explain
round pewter
Yes
round pewter
weād say itās negative for -1.5<x<1.5
When I gotta say it's positive I just flip the arrows yeah?
wary badger
hmm but the arrow on the left indicates that it will be negative
round pewter
Yeah but we haven't learned the arrow yet so we can ignore that
wary badger
When I gotta say it's positive I just flip the arrows yeah?
what
wary badger
Like -1.5 > x > 1.5
yea thatās fine i guess
wary badger
youāre welcome
round pewter
.close
obtuse pebbleBOT
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Available help channel!
dreamy birch
obtuse pebbleBOT
dreamy birch
could some one help
I was thinking about using L'hopital rule, but we arent at that unit yet, so that method is not usable
@haughty stream
tardy epoch
maybe multiply by the conjugate
dreamy birch
what would be the conjugate? the square of (1+x)-(1+x)^7-2?
tardy epoch
- sign on the square root term and everything else remains the same
dreamy birch
sorry i dont follow
wary badger
no
warm shaleBOT
riemann
haughty stream
<@932893747929288755>
Oh hi!
Exams on my head... I left helping since a while š
haughty stream
I think riemann might be enough
dreamy birch
Oh hi!
Exams on my head... I left helping since a while š
good luck
riemanns sum?
haughty stream
riemanns sum?
lol talking about @tardy epoch
tardy epoch
+2 instead of -2
dreamy birch
ok i see
slender glade
I was thinking about using L'hopital rule, but we arent at that unit yet, so tha...
Don't hesitate to use L-hopital rule on exam to just confirm the correct limit, and then try to reach that limit by rearranging wildly
slender glade
Even if you might not be allowed to use it to solve the question, you can use it to confirm if you've done right
tardy epoch
you're probably not meant to expand b^2
dreamy birch
?
tardy epoch
nevermind you need to in order to cancel the 1 from 1+x
dreamy birch
im really confused
tardy epoch
im really confused
About?
tardy epoch
you want (a^2 - b^2) with a = sqrt(x+1) and b = [(1+x)^7 - 2)]
Did you follow this
dreamy birch
i dont think the conjugate is the right way
its too complicated to expand
it gives like 9 different tihngs
dreamy birch
thats integration no?
surreal forge
i assume u have never heard of āgeneralized binomial theoremā before?
dreamy birch
no we are only supposed to solve with the things we learnt so far
surreal forge
ok
surreal forge
it complicates the equation so much
proceed from here
dreamy birch
it would take way too long on the test
ive tried it
theres no way thats the method
surreal forge
ur numerator should be smth like ((1 + x)^7 - 2)^2 - x - 1
obtuse pebbleBOT
surreal forge
we have a 15 min test time slot
should be fairly clear u can replace (1 + x)^7 with 1 + 7x
then problem is pretty much easy to finish
surreal forge
we have a 15 min test time slot
idk what u mean by this but this approach I describe above combined with conjugate manipulation should not take longer than a few min maybe 5
obtuse pebbleBOT
Available help channel!
cold brook
obtuse pebbleBOT
cold brook
Can someone help me identify where I might be going wrong. I am getting the final answer as e^-3x/5 while the right answer is e^-3x/10. The question is to solve the differential equation 2y"+3y'+y=e^-3x using method of variation parameters. We need to find the particular solution
obtuse pebbleBOT
@cold brook Has your question been resolved?
obtuse pebbleBOT
@cold brook Has your question been resolved?
cold brook
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
autumn onyx
Hello, I need help on how to solve this since I have been stuck here for three days with no progress.
obtuse pebbleBOT
Hello, I need help on how to solve this since I have been stuck here for three d...
autumn onyx
Need help calculating the initial angular position.
Although the 4th step doesn't also make sense since I used 189 instead of 172 and it actually worked.
<@&286206848099549185>
void holly
!15mins
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
autumn onyx
Sorry
I know the formula but I just don't know how to properly apply it at this situation.
autumn onyx
Is this correct?
What I basically did was
set my calculator to radians
then tried solving it
But it won't accept my answer
I did indeed used the formula btw
Or did I do something wrong?
latent walrus
,w arctan(77/172)
warm shaleBOT
latent walrus
1.15?
autumn onyx
Hmmm I will try wait.
autumn onyx
,w arctan(77/172)
Mine is basically the opposite and I landed at 1.149878038
latent walrus
,w 2pi-arctan(77/172)
warm shaleBOT
latent walrus
maybe try that
autumn onyx
Thank you. It worked.
Hmm I haven't found this one online.
Even though I have already answered step 4
I kind of have a problem justifying my own answer since I just happened to stumble upon it on an image in chegg
turbine blade is 58.5 m. calculate one pixels length in meters. record in lab data to 3 decimal places.
autumn onyx
Hello, I need help on how to solve this since I have been stuck here for three d...
172 pixels x 77 pixels
What would be the correct formula or solution in this case?
void holly
Will I get banned for tagging helpers too quickly?
no,but if you do repeatedly maybe
autumn onyx
no,but if you do repeatedly maybe
Alright. I will wait.
obtuse pebbleBOT
@autumn onyx Has your question been resolved?
modern cosmos
actually it has been resolved already
You can close this channel then
autumn onyx
You can close this channel then
How btw
uneven notch
@autumn onyx type .close
autumn onyx
.close
obtuse pebbleBOT
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Available help channel!
vocal edge
hi sorry, so i think i couldn't type as i went over time (sorry about that) but i still can't figure out this coding deciphiring question. the p8 p5 etc is the prime numbers like the 8th prime number is 19, but idk how that helps...
obtuse pebbleBOT
hi sorry, so i think i couldn't type as i went over time (sorry about that) but ...
fossil crag
perhaps if these were transformed into letters...
timid silo
how to learn trigonometry
boreal cliff
3b1b.
timid silo
and
talk to hipparchus
who is that
i need to learn from scratch
jk
study about circle and angle first
and then u move on to right triangles
boreal cliff
do not disturb the circles yes
bold bane
Regrading your last question that you closed. If (x+1) and (x-1) both leave zero remainder, that means you can divide the function by (x+1)(x-1).
timid silo
yes @bold bane
i got the answer as $60 @bold bane
then what should i read
for trigs
should i watch some lectures
fur that
bold bane
Umm, you can find free books online by Google searching --> trigonometry filetype:pdf
void holly
Khan academy is a good place to learn
timid silo
for calculus and trigs?
void holly
but the best will be to read a book on it
timid silo
ok,'
boreal cliff
if you truly do want youtube stuff then 3b1b is a goood intro
void holly
for calculus and trigs?
they have claculus and trig
void holly
if you truly do want youtube stuff then 3b1b is a goood intro
3b1b is more of visual show than actual math
boreal cliff
3b1b is more of visual show than actual math
hard disagree
great for understanding concepts
not for practice or proficiency but that's not what it ever aimed to do
void holly
practice a lot
try asking in #competition-math because there they focus on it more kinda
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
obtuse pebbleBOT
timid silo
I think it's C, but I didn't calculate the value of t exactly, can someone help?
granite panther
,w sqrt((8-5)^2+(9-5)^2)
warm shaleBOT
granite panther
Yeah that is right
runic arrow
is it enough for me to prove that Q(x) is a polynomial
obtuse pebbleBOT
is it enough for me to prove that Q(x) is a polynomial
runic arrow
if l(x) and P(x) touch in point a that means the y coord is equal to a0 = b then i took the derivative of P(x) which is P'(x) = a1 so a1 should be equal to m
but is there a way to prove that m is infact equal to a1 with the bottom equation
light flume
if l(x) and P(x) touch in point a that means the y coord is equal to a0 = b then...
just use point gradient form to show that
gradient at P'(a) = a1
the point is (a, P(a))
or rather (a, a_0)
pt gradient form of tangent at that pt is
y-(a_0) = a_1(x-a) ==> y=a_1(x-a) + a_0 directly
tbh i dont really understand the intuition behind them telling u P(x) - l(x) besides just showing that l(x) contains a_1(x-a) + a_0
runic arrow
yeah i dont understand it either
void holly
*hint Q(x) is a polynomial 
runic arrow
void holly
i see you didnt get it
runic arrow
i certainly didnt
void holly
$P(x)=a_0+a_1(x-a)+\dots +a_n(x-a)^n\
l(x)=m(x-a)+b\
P(x)-l(x)=(x-a)^{2}Q(x)$
warm shaleBOT
convergence
void holly
Q(x) is a polynomial that means that the powers are non negative integers
$a_0+a_1(x-a)+\dots +a_n(x-a)^n-(m(x-a)+b)=(x-a)^{2}Q(x)\
(a_0-b)+(a_1-m)(x-a)+(x-a)^2(a_2+a_3(x-a)+\dots+a_n(x-a)^{n-2})=(x-a)^{2}Q(x)$
warm shaleBOT
convergence
void holly
so from this we can get a1=m
and we know that m is the slope of l(x)
did you understand @runic arrow ?
runic arrow
let me read
void holly
runic arrow
ok i get that but how would you see that a1=m?
void holly
hm?i dont understand what you mean by that
runic arrow
from that last equation line
void holly
ah i see
since every term of Q(x) is multiplied with (x-a)^2 that means that (a0-b) and (a1-m) are both zero
since those terms are extra
void holly
close the channel if you have no other questions 
runic arrow
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
full musk
Hey, can someone work this out with me? I don't know if I'm doing this right, since it's getting really messy.
obtuse pebbleBOT
Hey, can someone work this out with me? I don't know if I'm doing this right, si...
full musk
Pls
serene tide
How far have you come?
full musk
Okay, I think i did it wrong but basically, I got the formula and i distributed
Now i have the two integrals, and im trying int by parts for the first
requires trig sub, but then it gets messy really quick
serene tide
The method sounds right, did you complete the calculations?
full musk
I can't integrate after trig sub + int by parts
I'm either not good enough or I did it wrong
obtuse pebbleBOT
@full musk Has your question been resolved?
full musk
How did you set up the integral
hang on rq
i gave up partway through
<@&286206848099549185>?
If anyone is willing to help, please dm me or talk here. I will be gone for about an hour and a half now.
Thanks in advance.
obtuse pebbleBOT
@full musk Has your question been resolved?
obtuse pebbleBOT
@full musk Has your question been resolved?
full musk
Can someone please help with this <@&286206848099549185>? I have time now
knotty vessel
yeah
full musk
okay, thanks, i'll try it rn
knotty vessel
-int(sin^2(x)cos^(x)) dx
this is the second trig sub integral
the first one is usub
full musk
.close
obtuse pebbleBOT