I'll write it to u
#help-17
livid arch
jolly lantern
Okay
livid arch
jolly lantern
Yea that thing
livid arch
Yeb
Apply the numbers in the equation and tell me what u got
Don't solve
Just put the number in the right place
U can take a pic of ur notebook 📓 if it's easier for u
livid arch
Or 10
No
It's 5
So
C²= 5
U have two c there and u want only one
How u r going to get rid of one c?
jolly lantern
Oh ok
Um
Is that a question with an actual answer
Or like re-tor-ic-al
Rhetorical
livid arch
Idk what Rhetorical means 
livid arch
Yes
twin meteorBOT
The following error occured while calculating:
Error: Syntax error in part "√5" (char 1)
swift bane
,calc sqrt(5)
twin meteorBOT
Result:
2.2360679774998
Oooh
jolly lantern
The answer was 2.2
livid arch
Yes
livid arch
Wait what do u mean
U have to round ur answer to the nearest tenth
Nothing will change in this case
But if it was
2.6794
The answer will be 2.7
Just keep that in mind
jolly lantern
Okay thank you
livid arch
Anytime
vocal sleetBOT
twin meteorBOT
sstac
Hello! I am trying to solve exercise 1 from here. (2.6 is $\dot x(t)=\pm \sqrt{\dfrac{2(E_0 - V(x(t)))}{m}$
```Compilation error:```! Missing } inserted.
<inserted text>
}
l.49 ...(t)=\pm \sqrt{\dfrac{2(E_0 - V(x(t)))}{m}$
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.```
vocal sleetBOT
delicate mantle
Hello! I am trying to solve exercise 1 from here. (2.6 is $\dot x(t)=\pm \sqrt{\dfrac{2(E_0 - V(x(t)))}{m}}$
twin meteorBOT
sstac
delicate mantle
I am wondering what would mathematically be the most appropriate method
vocal sleetBOT
Available help channel!
delicate mantle
Hello! I am trying to solve exercise 1 from here. (2.6 is $\dot x(t)=\pm \sqrt{\dfrac{2(E_0 - V(x(t)))}{m}}$. I am wondering what is the most mathematically correct method to solve this.
vocal sleetBOT
Hello! I am trying to solve exercise 1 from here. (2.6 is $\dot x(t)=\pm \sqrt{\...
twin meteorBOT
sstac
regal bane
If you just want the name of a method, check out "separation of variables ODE"
If you have any questions about the method, I'm game. But if you've never seen it before, I'll give you a sec to research
delicate mantle
Frankly that is exactly the reason why I am asking
I know separation of variables is the simplest way to get to the solution, but what I am concerned about is that I once spoke with a mathematician which (I am sure reasonably) claimed that separation of variables is not completely mathematically correct, despite it leads to correct results.
heavy yoke
separation of variables as it's usually done involves an abuse of notation, but you can avoid that without too much more trouble if you want to
delicate mantle
I want to avoid Leibniz notation if possible
heavy yoke
you can also think of the abuse of notation as essentially shorthand for the underlying math, which is really just the chain rule
delicate mantle
I know its not a real fraction but it looks too much like one to me and i don't want it in that case
delicate mantle
you can also think of the abuse of notation as essentially shorthand for the und...
In which sense
heavy yoke
usual notation:
[ \odv yx = \frac{f(x)}{g(y)} \implies g(y) \odif y = f(x) \odif x \implies \int f(x) \odif x = \int g(y) \odif y]
the chain rule:
[ g(y) \odv yx = f(x) \implies \int g(y(x)) \odv yx \odif x = \int f(x) \odif x ]
where the left integral can be rewtitten as $\int g(y) \odif y$ by substitution, if desired
twin meteorBOT
cloud
delicate mantle
What did you substitute in the left integral
delicate mantle
Ok that is kinda obvious but how did he get rid of the $\dfrac{dy}{dx}$
twin meteorBOT
sstac
heavy yoke
when you do a substitution in an integral you divide by the derivative (this is undoing the chain rule)
hybrid flicker
Ok that is kinda obvious but how did he get rid of the $\dfrac{dy}{dx}$
if u = y(x)
du = dy/dx dx
you know, usual substitution rules
delicate mantle
Ok, will check it out and text back in few minutes
vocal sleetBOT
@delicate mantle Has your question been resolved?
wicked linden
vocal sleetBOT
wicked linden
I don't understand this
silk osprey
what’s confusing
wicked linden
Everything, I don't even know where to start
silk osprey
cost sin2t
wicked linden
Is there anything I should first know?
gritty sage
Well, you have cos(theta) sin(2 theta) on the left side.
So, replace cos(theta) with their exponential form.
wicked linden
Ohh now I understand
gritty sage
Replace sin(2 theta) with the sine exponential formula, but replace theta with (2 theta).
vocal sleetBOT
@wicked linden Has your question been resolved?
delicate mantle
you know, usual substitution rules
Those substitution rules is also what requires "multiplying" the whole expression by dx, which again isnt completely correct
As far as I can see all the methods you suggested use some kind of using substitution method, or at least it's still not clear to me how do i solve that equation for variable t without doing some substitutions, multiplying by derivative etc. which is not purely mathematically rigorous (i assume)
.reopen
Sorry, substitution is ok i guess but multiplying by a derivative isn't?
delicate mantle
I mean it's not like i have something against multipliying by a derivative thats what all the physics books do but I was just curious how would that look like as i said if we did it completely rigorous?
vocal sleetBOT
I mean it's not like i have something against multipliying by a derivative thats...
delicate mantle
Sorry if i am not using channels properly btw
delicate mantle
Scroll up a bit you'll see, i sent the initial question like an hour ago and then got a time out
hard atlas
ok. for the future, link to that. no one scrolls up
tidal dock
delicate mantle
Ok will do in the future, thanks for the tip
delicate mantle
is this about separable odes?
But yeah i assume thats mostly it
regal bane
tl;dr:
The way we typically carry out separation does not use mathematically valid objects, but you can carry it out using proper derivatives and the chain rule.
We just do it this way to avoid using the same trick every time and writing more than we would need to
delicate mantle
tl;dr:
The way we typically carry out separation does not use mathematically val...
This means something like it's not completely valid but it works and gives correct results?
regal bane
The word "valid" is carrying a lot of weight there lol
delicate mantle
I know
delicate mantle
I gave the word the wrong context in this case here
regal bane
But that lazy way of writing it is the common way to do it
To the point where if I did it correctly, people would look at me like I'm weird
delicate mantle
But in any case what I am interested in is how would the long and completely rigorous way look like
regal bane
https://math.stackexchange.com/questions/1252405/is-it-mathematically-valid-to-s...
This
First answer proves the method
heavy yoke
it would be essentially carring arround a bunch of notation but the same problem solving steps otherwise
delicate mantle
Ok, I didn't open the link tbh, i just read your tl;dr 😄
heavy yoke
i like to think of it as like writing dittoes on a repetitive table rather than writing out each entry in full. it's good to know what the dittoes correspond to, but for most purposes it's easier and simpler to write them than write out every entry
delicate mantle
I am even more confused now kinda, i am not even sure if its possible to do substitution method in solving composite function integrals without multiplying by a derivative?
vocal sleetBOT
@delicate mantle Has your question been resolved?
delicate mantle
Does anyone know how would i justify substitution rule for solving integrals then?
signal quarry
In doing this problem, I believe I have found that the MLE for $\lambda$ is the "total sample average", which is $\frac{\sum_{k=1}^{n_1} x_k + \sum_{k=1}^{n_2}}{n_1+n_2}$.
vocal sleetBOT
In doing this problem, I believe I have found that the MLE for $\lambda$ is the ...
signal quarry
I'm not quite sure why that didn't compile correctly, but hopefully it's clear.
Anyway, I found that the MLE is unbiased.
And I believe the standard error of this estimator is $\sqrt{\lambda/(n_1+n_2)}$. I next need to conduct the hypothesis test, although I wanted to check if my calculation for the SE is correct.
signal quarry
If it is then I think I use these values to approximate the distribution as a normal distribution, with a critical value if the total sample average is too low (with probability tail less than $\alpha/2$) or too large. For now I'll focus on the "too low" part. So we want $P(\overline X < c) = \alpha/2$ which is
twin meteorBOT
addem
signal quarry
$P\left(\frac{\overline X-\lambda}{SE} < \frac{c-\lambda}{SE}\right)$ where this is now a standard normal and I use the CDF to find what $\frac{c-\lambda}{SE}$ is. Am I doing this correctly?
twin meteorBOT
addem
vocal sleetBOT
@signal quarry Has your question been resolved?
vocal sleetBOT
@signal quarry Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
woeful adder
hi, can someone help me with this? I'm not sure what exactly I'm doing wrong here.
vocal sleetBOT
hi, can someone help me with this? I'm not sure what exactly I'm doing wrong her...
regal bane
If you are intended to use this method, then you are correct.
Are you intended to use a different method? Some methods are approximations and may have a different answer
woeful adder
Can u explain what the different method is? This is the one method I know
shell mirage
I need some help with the bounds:
steady ice
I'm not really sure which region its talking about
whether its the upper or the lower one
hm
shell mirage
I'm not really sure which region its talking about
I believe they mean like the 3d shape made from the two 3d shapes
steady ice
I mean like. there's the region A where the upper bound is the sphere and the lower bound is the cone. Adn then the region B where the upper bound is the cone and the lower bound is the lower part of the sphere. So im not sure which of those region E is, as they both fit the conditions
anyway
shell mirage
oh i see what you mean
steady ice
have you heard of rotating an area around a line to get a volume?
shell mirage
yes
steady ice
The cone, and the sphere are both symmetric around the same line, so that would be a method to compute the integral relatively simply
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
Can't figure out what the x-intercepts are
vocal sleetBOT
Can't figure out what the x-intercepts are
tranquil trellis
from eyeballing it looks like +/- 1
brazen gulch
Can't figure out what the x-intercepts are
look at the y asymptote
nvm i misread
it might eb DNE
atleast one should be 0,0 because of y but 
rancid kestrel
Hi guys!
Instead of
16^1/4 =4 (r^4)^1/4
r=2
Can I just square root r^4 = 16 and get a 2
flat whale
That's not called square root, but fourth root
rancid kestrel
Oh sorry
Yes okay fourth root
I didn’t know how to mention the 4
lol
So it’s ok to do?
Bc that other method doesn’t make sense for me
1/4 business ew
flat whale
,tex .exp rules
twin meteorBOT
riemann
acoustic tulip
but whenever you take an eventh root, the variable can be both positive or negative, in this specific case r= +- 2.
vocal sleetBOT
@rancid kestrel Has your question been resolved?
vagrant kraken
I'm stuck on proving the reverse direction. Specifically, proving that W1 intersect W2 = {0}.
vocal sleetBOT
I'm stuck on proving the reverse direction. Specifically, proving that W1 inters...
vagrant kraken
this is what i have so far
sly sierra
looks fine so far
vagrant kraken
maybe I could say:
x=x+0 where w1=x and w2=0.
x=0+x where w1=0 and w2=x.
So by the assumption of uniqueness, x=0.
sly sierra
you could now observe that your last line implies:
x = x + 0
and
x = 0 + x
which are two expressions
yea
vocal sleetBOT
vocal sleetBOT
Available help channel!
bitter briar
Got 240° for jml just want to know if it's right
vocal sleetBOT
Got 240° for jml just want to know if it's right
acoustic tulip
no, it's not
bitter briar
Is it 296° ?
acoustic tulip
uhm, no
paper depot
maybe tell us how you're getting these numbers
bitter briar
128° ????
paper depot
i mean, OP could've explained it himself rather than you speaking on his behalf
paper depot
128° ????
show how you are getting it
do not throw a million numbers at the wall until something sticks
that is not how you solve problems
bitter briar
.close
vocal sleetBOT
bitter briar
.reopen
vocal sleetBOT
✅
bitter briar
The whole circle is 360 so JL should be 128 so 360-128 gives us arcJML
paper depot
hold on
when you say JL
do you mean arc JKL
given that you're distinguishing it from arc JML
like do you mean the arc that goes clockwise from J to L
bitter briar
Yes J to L goes clockwise
paper depot
then why's that 2*128
bitter briar
Sorry Its just 128
bitter briar
Because if a inscribed angle is JKL then arcJL will be 2 times the angle of JKL
paper depot
yeah but the inscribed angle is looking at arc JML actually is it not
JKL is "behind" it
acoustic tulip
do you mean the arc?
bitter briar
Yea
acoustic tulip
ok, after that?
acoustic tulip
yes, using arc = inscribed angle * 2, right?
bitter briar
Yes
acoustic tulip
yeah, you're correct
acoustic tulip
.close
bitter briar
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
vocal sleetBOT
near pawn
first, reorient the problem so that the x-axis runs along the slop and the y-axis is parallel to N
since the box is not moving, the net force is 0
so the net-force must be 0 in the x-direction and in the y-direction
now see what the force equations would look like
so since the forces are 0 in the x-direction, that means the x-component of gravity (the component pulling along the slope) would cancel the x-component of the Tension force in string
exactly
since the x-component of the normal is 0 by definition
y-component of the weight* yes
for now just look at the x-forces
what is the x-component of the weight
and what is the x-component of the string's tension
near pawn
wait lemme draw it out
trig is a pain in the ass smtimes dw about it
so for now we'll forget about the y components
the upwards arrow is the string force
we're trying to find the magnitudes of the two red lines
(they should be equal, i kinda screwed up the drawing 💀 )
so we have this relation, that W_x = T_x
but we dont know what W_x and T_X are
so we need to express each of them in terms of things we already know
i added the magnitudes of the two forces
what about in terms of the angle
we know that alpha is 20 degrees because the ramp was at a 20 degree incline
so we know the angle, we know the hypotenuse, adn we want to find the opposite side
(hint: a tringometric ratio can be used here)
yessss
exaclty!
bingo
ohhh fair enough
no problem!
vocal sleetBOT
vocal sleetBOT
Available help channel!
haughty barn
hi
uncut holly
???
fervent wasp
Tough one
river kettle
tranquil charm
I know
Like I wanted to know if they were asking about the BODMAS stuff so
That's why I said lol after
vocal sleetBOT
@haughty barn Has your question been resolved?
snow hedge
This is my problem, I'm not able to understand the 2 3 4 rows. Can anyone give some good example please...
vocal sleetBOT
This is my problem, I'm not able to understand the 2 3 4 rows. Can anyone give s...
snow hedge
This is my problem, I'm not able to understand the 2 3 4 rows. Can anyone give s...
This is the image
I can't understand the 1st 3 rows
tranquil charm
looks like a NOT P OR gate
snow hedge
Can you give some real life statements...
paper depot
ok sure
imagine that i make this promise to you:
"If it rains tomorrow, I will give you a million dollars."
paper depot
This is the image
when tomorrow comes, there are 4 possible scenarios as to what might happen regarding the weather and my payment, corresponding in order to the rows of this table:
- It is sunny and I don't give you the money.
- It is sunny and I do give you the money.
- It rains and I don't give you the money.
- It rains and I do give you the money.
@snow hedge among these four scenarios, in which one(s) would you accuse me of breaking my promise?
gentle nimbus
true never implies a false statement
snow hedge
any others?
and 2 ig
paper depot
why do you think i broke my promise in scenario 2?
maybe i just decided to give you the million anyway out of the goodness of my heart.
snow hedge
why do you think i broke my promise in scenario 2?
Because its not rainy but still you're giving me the money
paper depot
Because its not rainy but still you're giving me the money
ok, so what?
i didnt say "I will give you the money if and only if it rains tomorrow."
the implication only goes one way
steep crater
Thanks ann for the money
gentle nimbus
snow hedge
i didnt say "I will give you the money **if and only if** it rains tomorrow."
Ahh i see
paper depot
on a sunny day, i am under no obligation whatsoever!
and i am not under obligation not to give you money
snow hedge
Okay...
paper depot
scenario 3 is in fact the only one in which i would have broken my promise.
gentle nimbus
might've been a bit too convoluted
gentle nimbus
would've been nice if you considered that implication means when p is true, q must be true, it wouldnt make sense for q to be false when p is true 😔
snow hedge
Oh okayy
gentle nimbus
and that means that q could be true evem when p is false
but that it must be true when p is true
gentle nimbus
happy mathing 
vocal sleetBOT
vocal sleetBOT
Available help channel!
unique rampart
vocal sleetBOT
forest umbra
what is the definition of x^y ?
forest umbra
if $y = \pi$, what does it mean to multiply "$\pi$ times" ?
twin meteorBOT
ηαθαη
unique rampart
huh
knotty cloud
y times
unique rampart
multiply y times
forest umbra
Your definition is right for integers
For example 2^3 is 2 multiplied by itself 3 times
But when you deal with real numbers the definition doesnt mean anything
For example $2^{\pi}$ would mean "$2$ multiplied by itself $\pi$ times" according to your definition.
twin meteorBOT
ηαθαη
forest umbra
But "$\pi$ times" has non meaning
twin meteorBOT
ηαθαη
unique rampart
ok
forest umbra
So you should have a proper definition for $x^y$ when dealing with real numbers, do you know it ?
twin meteorBOT
ηαθαη
unique rampart
no
forest umbra
For all real numbers $x > 0$ and $y$, $x^y$ can be defined as $\exp(y \ln(x))$.
twin meteorBOT
ηαθαη
unique rampart
what is exp
proud terrace
exponential
forest umbra
$\exp$ is the exponential function
twin meteorBOT
ηαθαη
unique rampart
ok
forest umbra
If you know the basics about is you can solve your exercise quickly using the definition I gave you
unique rampart
still cant solve it
forest umbra
Can you send what you got ?
forest umbra
Did you replace the first line with the definition I gave you ?
forest umbra
Do you know the definition of $\log_b(x)$ ? For example what is $\log_2(3)$ ?
twin meteorBOT
ηαθαη
forest umbra
Well that's right, but we usually define it as $\frac{\ln(x)}{\ln(b)}$. You can check that such a value is indeed the solution of the equation you gave me
twin meteorBOT
ηαθαη
unique rampart
i can do that but what good does it do
forest umbra
I just show you : $b^{\frac{\ln(x)}{\ln(b)}} = \exp(\ln(b) \frac{\ln(x)}{\ln(b)}) = \exp(\ln(x)) = x$
twin meteorBOT
ηαθαη
forest umbra
i can do that but what good does it do
The good to understand what you're doing
forest umbra
**ηαθαη**
first equality comes from the definition of $x^y$, last one comes from the fact that $\ln$ is the reciprocal of $\exp$.
twin meteorBOT
ηαθαη
forest umbra
So the second step is to use the defintion $\log_b(x) = \frac{\ln(x)}{\ln(b)}$ and then try to simplify a bit the expression
twin meteorBOT
ηαθαη
unique rampart
what to do of the root
forest umbra
Can you show me the expression you now have
unique rampart
forest umbra
Well that's right but you didn't use my first advice which was to use the defintion of $x^y$
twin meteorBOT
ηαθαη
forest umbra
For example, what is $3^{\sqrt{\frac{\ln(2)}{\ln(3)}}}$ ? What is this number ?
twin meteorBOT
ηαθαη
unique rampart
exp( the power x ln3)
forest umbra
RIght. So you can rewrite your whole expression knowing this
You're just replacing numebrs with their defintion, that's the most basic thing to do
unique rampart
exp( underrroot ( ln3 x ln2)
unique rampart
same thing
forest umbra
👏
unique rampart
wow
so basically u took the natural log and then simplified
and converted the base of the log power to e
i mean the log in the power
first u changed the base to e then took natural log
forest umbra
and converted the base of the log power to e
I don't really like this way to see things. I simply used the definition of $x^y$, which happens to match the base $e$. Just remember that $\exp$ and $\ln$ are the most friendly functions in that kind of exercise
twin meteorBOT
ηαθαη
forest umbra
But technically speaking, yes.
tight shard
Hello guys, what to do with the squared logarithm at the end?
vocal sleetBOT
Hello guys, what to do with the squared logarithm at the end?
vast shale
sorry, I messaged in the wrong channel.
vocal sleetBOT
@tight shard Has your question been resolved?
vocal sleetBOT
@tight shard Has your question been resolved?
vocal sleetBOT
@tight shard Has your question been resolved?
gloomy portal
Show me your task
vocal sleetBOT
@tight shard Has your question been resolved?
grizzled sapphire
I was wondering if anyone had any tips/advice on how to study for the AP Calc BC exam
vocal sleetBOT
I was wondering if anyone had any tips/advice on how to study for the AP Calc BC...
gilded holly
Im not in AP
I study IGCSE
Theyre the same regardless
Read the book, answer the important part of each chapter
Like skip excersises and do unit/chapter questions
Go on savemyexams and get a subs (or don't)
answer all exam questions
on paper
do past papers and record mistakes make it realistic
You're good
hvae a good schedule and make sure you finish one month b4 the exam
analog urchin
how do u know if it will be positive or negative here
vocal sleetBOT
how do u know if it will be positive or negative here
analog urchin
when f''(x) = 3
vocal sleetBOT
@analog urchin Has your question been resolved?
flat whale
what math error are you getting
flat whale
,w 1 / (-1)^(8/5)
twin meteorBOT
heavy yoke
,calc 1/(-1)^(8/5)
twin meteorBOT
Result:
0.30901699437495 + 0.95105651629515i
,calc -8/5 + 2
twin meteorBOT
Result:
0.4
i just need to know if its positive or negative so i can tell if its cu or cd
flat whale
,w plot (x-4)^(2/5)
twin meteorBOT
flat whale
i just need to know if its positive or negative so i can tell if its cu or cd
can you show the entire problem
heavy yoke
,calc 1/((-1)^8)^(1/5)
twin meteorBOT
Result:
1
raw granite
vocal sleetBOT
raw granite
can someone help me understand how to find area and preimeter of rhombi and kites
hidden turret
pdfs are notoriously known for being unsafe so im pretty sure you are only supposed to send png or jpg
steady ice
~~ lel i just downloaded it without knowign that~~
wait hold up
nvm ur correct
You got your area correct
hidden turret
im not laughing at you im just laughing at the fact bro left without knowing he was right and is probably still converting the pdf
steady ice
its ok 🙂
raw granite
oh ok
raw granite
I thought it was wrong 😭
steady ice
oh you downloaded it too lel
steady ice
I mean, you did all the steps I would do.
There'es nothing wrong and you did it the way I did it, so I don't think there's much to do?
vocal sleetBOT
vocal sleetBOT
Available help channel!
nimble wedge
vocal sleetBOT
nimble wedge
There's gotta be a trick behind this question right?
We can't just go on list all 2 digit numbers where their digits sum to 9
Like 18
27
36
paper depot
i mean there are not that many but also yes there is somewhat of a trick
nimble wedge
i mean there are not that many but also yes there is somewhat of a trick
What is the trick
Other than manual labour
paper depot
if you know the first digit then the second digit is locked in
so really you just need to look at what options you have for the first digit
fallow igloo
if you know the first digit then the second digit is locked in
so like an equation on 2 variables?
x+y=9
10x+y=(number)
?
paper depot
yes
fallow igloo
you gotta find a pattern like i did?
or you can see how many 10s are there in between
nimble wedge
but what if they were talking bout 3 digit no
paper depot
but what if they were talking bout 3 digit no
that would be many times harder
nimble wedge
Ok I get it
Thanks
Thanks Ann and trollstar
What about this one guys
@paper depot @fallow igloo
paper depot
do you have any ideas yourself so far
if not: ||what can you say about your number minus 1?||
nimble wedge
if not: ||what can you say about your number minus 1?||
what
2-1 = 1
3-1 = 2
4 -1 = 3
5-1 = 4
6-1 = 5
nimble wedge
i don't get it
paper depot
call your number N
nimble wedge
x - 1
paper depot
we are told N must leave remainder 1 when divided by 2 or by 3 or by 4 or by 5 or by 6
i am asking you to make a conclusion about the number N-1
nimble wedge
So n cant be 1
but it is also not equal to 2
if its 3
we'll get decimal divided smaller numbers like by 2
WhaT is IT
im lost
vocal sleetBOT
@nimble wedge Has your question been resolved?
paper depot
@nimble wedge ok let's try to think about it this way
suppose i have a mystery number and i tell you that it leaves remainder 4 when divided by 9
if i now subtract 1 from my number, what will be its remainder when divided by 9?
flat bloom
I quadruple checked this and can't figure out what part I've entered incorrectly. Why is this not outputting the correct answer?
vocal sleetBOT
I quadruple checked this and can't figure out what part I've entered incorrectly...
deep hound
I quadruple checked this and can't figure out what part I've entered incorrectly...
you got the bounds wrong
flat bloom
The output should not have any variables
Why would the bounds for theta be 0 to pi and not 0 to 2pi?
deep hound
It's different to what you did because when you integrate Theta over 0 to 2pi you're basically cancelling out the integral
So your upper bound for Z basically goes negative when theta goes above Pi
flat bloom
Ohhhhhhhhh and that gets cut out since it's above z=0
Idk how I didn't realize that tysm man
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
waxen hawk
SOS
waxen hawk
SOS
SOS
I CANNOT GET MY CALCULATION RIGHT
Plug x=-13/4
Fk
I’m so depressed, can someone check my process
gritty sage
It's unclear where you'd plug x in. The input fields are for coefficients, not for the value of x.
waxen hawk
It's unclear where you'd plug x in. The input fields are for coefficients, not f...
To convert it into the vertex form, I always differentiate it to get the x coordinate of the vertex. Subsequently, I put the x coordinate into f(x) and find the y coordinate of the vertex. By knowing the vertex and the leading coefficients, it should be able to convert it to the vertex form
That’s what I do all the time
Chai, do you find the whole process laborious
Or there’s any other way that would be more convenient in terms of calculation
gritty sage
Well, they don't just want it in vertex form. They want you to complete the square.
To do that, you put the x^2 coefficient in the box before the parentheses.
Then, you divide the x coefficient by 2a.
That's the middle box.
Then, you have (c - \frac{b^2}{4a}) in the third box.
twin meteorBOT
Chai T. Rex
paper depot
Well, they don't just want it in vertex form. They want you to complete the squa...
is there a difference
waxen hawk
What is your leisure activity
What do smart people do in their leisure time
Is it the key to be smart
gritty sage
Smart at what?
waxen hawk
Calculation
waxen hawk
is there a difference
Ann, which way is more convenient
Conversion by differentiating or completing the square
hazy nebula
Is it the key to be smart
there's no one thing that makes a person smart and there's many ways to be smart
ivory pawn
It was because you didn’t subtract from the 20
paper depot
differentiation is for if you want to minimize thinking and be a calculator in a meat suit
hazy nebula
imo anyone can be good at math if they're willing to put the effort into practicing and learning
waxen hawk
differentiation is for if you want to minimize thinking and be a calculator in a...
Really
But you did not tell me which way is more convenient. I would be a meat suit if necessary. I have no soul
waxen hawk
imo anyone can be good at math if they're willing to put the effort into practic...
Is it music
hazy nebula
id recommend completing the square
waxen hawk
id recommend completing the square
Why
hazy nebula
Is it music
no? everyone has a different music taste. id suggest to take a break after this question if possible because you seem really stressed out over this
hazy nebula
Why
it's good practice to do it via CTS because the way you solve this problem with CTS can apply to all problems
waxen hawk
CTS
hazy nebula
knowing how to complete the square is also helpful down the road in other math classes
ivory pawn
Yes
ivory pawn
Honestly the picture didn’t show enough of your work to see where you went wrong
vocal sleetBOT
@waxen hawk Has your question been resolved?
digital glen
Can someone check this question real quick?
vocal sleetBOT
Can someone check this question real quick?
chrome panther
I am getting k >/= 0 and don't know what the answer is
show your work
digital glen
I got the centre and radius for both circles and then sketched it roughly
It looks to me like for the circles to touch, the second circle should have a radius of at least 1?
So I set the radius of the second circle to be >/= 1 and solved
Not sure if it's right
chrome panther
It looks to me like for the circles to touch, the second circle should have a ra...
to "touch" they have exactly one point in common, so it will be just k=0
digital glen
to "touch" they have exactly one point in common, so it will be just k=0
They would still touch if the second circle is larger, right?
Just at more than one point?
chrome panther
They would still touch if the second circle is larger, right?
touch generally means at a single point, if its larger then you say they intersect
digital glen
Oh ok
digital glen
touch generally means at a single point, if its larger then you say they interse...
But the question is asking for values of k
Not a singular value
For exam purposes I'd have to write k >/= 1 no?
chrome panther
Not a singular value
there is another case you didnt account for
when they touch internally
chrome panther
like this
digital glen
Oh
But the centre and radius for the first circle is fixed
(4, 1) and r = 2
And we know the second circle's centre is (1, 1)
digital glen
It's never inside though
The intersection point should be at (2, 1) and the second centre is at (1, 1)
chrome panther
the dotted circle can be bigger
digital glen
Yeah but the other circle has a fixed radius and centre
chrome panther
so this is what happens when you increase the dotted circles radius just a little
now keep increasing it
this is the exact graph
hasty pike
Can I ask what is a three figure bearing
vocal sleetBOT
Can I ask what is a three figure bearing
heavy yoke
the three figure bearing is the clockwise angle from north to the direction of travel, to the nearest degree
it's customary to append a zero to the front of angles less than 100 degrees so they have 3 digits each time (hence the name 'three-figure')
examples: North is 000°, East is 090°, South is 180°, West is 270°
vocal sleetBOT
vocal sleetBOT
Available help channel!
quasi quest
please help me solve this question...
vocal sleetBOT
please help me solve this question...
patent sable
please help me solve this question...
do u know how you can tell if a quadratic equation's solutions are real or complex
bitter pilot
consider the discriminant
patent sable
:/
quasi quest
discrimnant should be positive
patent sable
discrimnant should be positive
are you sure
bitter pilot
discrimnant should be positive
rather for which case?
quasi quest
are you sure
for real
quasi quest
and to prove for complex, then negative
patent sable
so the discriminant should be positive or zero for only a = 5/3
so calculate the discriminant
and see where it is 0 or positive
quasi quest
so i have to put the value of 'a' in The equation?
bitter pilot
but that doesnt show it's the only value
you have to show that it is the only one
by deriving it
quasi quest
by deriving it
?what's deriving
quasi quest
is it right
bitter pilot
is it right
I would have worked with inequalities
=
but you basically derived exactly one root for a
that means -36(a-5/3)^2 >= 0 basically but that only implies the -36(a-5/3)^2 = 0 equal case because else you get a contradiction and then thats how you showed it's the only value for which you get real roots
quasi quest
that means -36(a-5/3)^2 >= 0 basically but that only implies the -36(a-5/3)^2 = ...
why you didn't take 120a -100
bitter pilot
I know the root so i can write it in the form of y=a(x-r1)(x-r2) where a is stretch factor and r1,r2 roots
its more convenient to work now with the square
-36 times something non negative yields something negative
from that you can derive that only the equal case is true
for D > 0 no sols and else for D < 0 you always get one since the parabola is open downwards
vocal sleetBOT
@quasi quest Has your question been resolved?
quasi quest
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
vocal sleetBOT
twin meteorBOT
The following error occured while calculating:
Error: Undefined function ln
scenic ravine
,calc log(5.3)
twin meteorBOT
Result:
1.6677068205581
,w log_{10} (5.3)
twin meteorBOT
paper depot
,calc log(30)/log(5)
twin meteorBOT
Result:
2.1132827525594
yes 2.113 is correct.
quasi quest
what topics are the prerequisites for quadratic equation chapter...
outer warren
basic algebra and solving linear equations
quasi quest
basic algebra and solving linear equations
and graphs?
bronze osprey
yeah basically all aspects of linear equations
quasi quest
.close
molten gale
I am doing some practice examples because my exam is getting close but i cant figure out how to solve this kinematics question. I already know I have to set v(t)=0 but i have no idea what to do after that
vocal sleetBOT
I am doing some practice examples because my exam is getting close but i cant fi...
bronze osprey
I am doing some practice examples because my exam is getting close but i cant fi...
IB maths eh
molten gale
yess unfortunately
bronze osprey
I am doing some practice examples because my exam is getting close but i cant fi...
it's a GDC question
you could just use NSolve to get that value of t for part a
bronze osprey
i tried but i got 3.35 and it didnt make sense
yeah that's what I get too
molten gale
yeah that's what I get too
oh!
bronze osprey
why do you think it doesn't make sense?
molten gale
i dont know i tried looking up the answer and ik ai isnt good at math but thats not what they got
but im sure 3.35 is right now that u tried it too
bronze osprey
i dont know i tried looking up the answer and ik ai isnt good at math but thats ...
because AI isn't reliable
molten gale
yea i figured lol
molten gale
oh i forgot about desmos
bronze osprey
it has the advantage of you can click on the graph and it tells you the x-coordinate
to be fair that's how it works on your GDC too
molten gale
so wait how would i solve b cus im still learning this kinematics crap
bronze osprey
I am doing some practice examples because my exam is getting close but i cant fi...
right, so it's about figuring out what the question means
take rightwards to be positive, and leftwards to be negative for example
if the particle changes direction, what must happen to the sign of v(t)?
molten gale
wdym leftwards and rightwards
bronze osprey
wdym leftwards and rightwards
the particle moves on a straight line
molten gale
if the particle changes direction, what must happen to the sign of v(t)?
it goes from positive to negative?
molten gale
the particle moves on a straight line
oh right
bronze osprey
it goes from positive to negative?
yeah! it changes sign
it could also go from negative to positive
that's not what happens for this graph but it is a possibility
bronze osprey
the instant the sign changes, that must be when the function equals zero
molten gale
so i can use any point on that part of the line
like doing downwards
going*
if i wanted to
bronze osprey
nope, that's not what the maximum of v(t) means
molten gale
nope, that's not what the maximum of v(t) means
wha
bronze osprey
this is what's happening with the velocity vector
molten gale
OHHHHH
so when x is negative then the velocity changes direction?
i mean
y
oops
when y is negative?
bronze osprey
so when x is negative then the velocity changes direction?
not quite also
molten gale
LMAO
bronze osprey
when y is negative, the particle is moving leftwards
molten gale
ok
bronze osprey
when y is positive, the particle is moving to the right
molten gale
ya so when y changes signs, the particle changes direction?
bronze osprey
ya so when y changes signs, the particle changes direction?
yes!
bronze osprey
so changes signs is y = 0
molten gale
okok i understand but isnt 0 considered positive
bronze osprey
okok i understand but isnt 0 considered positive
no it's considered neither positive nor negative
molten gale
or wait neither so why is that the answer for changing direction
bronze osprey
you've confused it with "0 is an even number" or something
bronze osprey
or wait neither so why is that the answer for changing direction
if it goes from positive to negative
the direction changes from right to left
molten gale
but zero is not positive or negative so how does it change direction
bronze osprey
but zero is not positive or negative so how does it change direction
yeah, so at that instant
the particle is instantaneously at rest
molten gale
ahhh
bronze osprey
that always happens if the particle changes direction
it has to be moving neither left or right at that instant
molten gale
ok i understand it now
so the total distance is found by finding out how long the line is?
or noo
bronze osprey
so the total distance is found by finding out how long the line is?
no
bronze osprey
bronze osprey
how
you're forgetting this
there's also a trick for part c, where it's asking you for the total distance
molten gale
but distance isnt displacement
bronze osprey
let me illustrate with a quick example
bronze osprey
if I go to uni, where I travel 5 km
and then I go back home, where I travel another 5 km
the total distance I travel is 5 + 5 = 10
molten gale
yep
bronze osprey
but my total displacement is zero: I end up where I started
you would need the signs for that
molten gale
yep
bronze osprey
so (+5) + (-5) = 0
molten gale
ok
bronze osprey
now when you integrate, you're always working with the signs
you take the area above the x-axis as positive
and the area below the x-axis as negative
bronze osprey
this is what's happening with the velocity vector
so we need to find a way to remove the signs, and then add both areas together
molten gale
what both areas
bronze osprey
there's one area above the x-axis and there's another area below the x-axis
bronze osprey
so we need to find a way to remove the signs, and then add both areas together
but that's what the absolute value does
bronze osprey
so u change the negative sign to positive?
yepp!!
bronze osprey
but that's what the absolute value does
the absolute value just removes the sign if it has one
so |5| = 5
but |-3| = 3
molten gale
so how do we find that number? is it just the x values?
idk how to do that on the graph stuff
bronze osprey
so how do we find that number? is it just the x values?
you're forgetting that we need to integrate
but integrate both areas separately first
remove the negative sign, then you can finally add both areas
molten gale
you're forgetting that we need to integrate
integrate the velocity to find displacement
bronze osprey
integrate the velocity to find displacement
yep!
molten gale
but any negatives in the integral i use absolute value?
bronze osprey
but any negatives in the integral i use absolute value?
yes
molten gale
and boom i have my distance
bronze osprey
so in fact you could absolute value both integrals and then add
molten gale
wdym both integrals
bronze osprey
but you only need to absolute value the negative integral, the one from t = 3.35 to 6
if you're even smarter
molten gale
im not smart lmao
bronze osprey
you know how 5 + |-3| = 8 right
molten gale
yes
bronze osprey
well, 5 - (-3) does the same thing
molten gale
yep
bronze osprey
you could just subtract the negative integral
molten gale
oh tru
bronze osprey
and it gives you the exact same
molten gale
ok im gonna try to find the integral of v(t)
im gonna fail so bad tho cus i suck at trig and e integrating
bronze osprey
ok im gonna try to find the integral of v(t)
you have your GDC though!
in fact there's no possible way you could integrate that (where it gives you the integral function)
molten gale
WAIT U CAN INTEGRATE ON UR GDC???
bronze osprey
WAIT U CAN INTEGRATE ON UR GDC???
yeah.......
molten gale
im on an old ass ti-83 plus
bronze osprey
oh
bronze osprey
go to your calculator mode and find the calculus menu
it should be under there still
molten gale
ehh whats the calculus menu
molten gale
i dont understand the commas
oh i got it
ok i finally figured out how to get the absolute value and i got 20.8
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
nimble wedge
vocal sleetBOT
nimble wedge
try adding and subtracting 4x^2 - what happens?
i dont get it
scenic ravine
i dont get it
$x^4 +2x^2+4 - 2x^2$
twin meteorBOT
What a wonderful world !
nimble wedge
tbh no
strong isle
try adding and subtracting 4x^2 - what happens?
do this
vast shale
Look up a 2 minute video on YT for this it’ll be way quicker than any of us can teach u
It’s not hard at all once u get it
nimble wedge
Look up a 2 minute video on YT for this it’ll be way quicker than any of us can ...
what should i search yt
strong isle
Did you first try adding 4x^2 to the expression?
twin meteorBOT
BrutalCandor
nimble wedge
@strong isle
strong isle
$x^4 + 4 + 4x^2$
Yep, now what do you recognise?
If you haven’t recognised anything yet, try the hint: || let a = x^2 ||
nimble wedge
If you haven’t recognised anything yet, try the hint: || let a = x^2 ||
say no more
i get it
nimble wedge
however why are we adding stuff to the expression is that even possible
i thought we must subtract something right after adding it so the results is unchanged
strong isle
however why are we adding stuff to the expression is that even possible
We can then subtract it later. It’s a trick used to factorise some polynomials
strong isle
i thought we must subtract something right after adding it so the results is unc...
As long as we subtract the result equally at the end, that’s all that matters
That’s why someone else said to both add and subtract 4x^2 to the expression
nimble wedge
(a+2)(a+2) @strong isle
strong isle
(a+2)(a+2) <@703251436485738526>
Yes, that’s if we have added the 4x^2 to the original expression. And it’s better if you write it like (a+2)^2
strong isle
(a+2)(a+2) <@703251436485738526>
Now subtract this by 4x^2
twin meteorBOT
BrutalCandor
strong isle
you had before (a+2)^2-4x^2, right? So now what do you recognise 4x^2 to be?
nimble wedge
4a?