Me and you are standing on the sidewalk. You start walking north at 5 mph, and I stay in the same spot. Question 1. How fast are you moving away from me?
#help-0
vapid shuttle
daring ferry
5
vapid shuttle
ok
if I start, moving away aswell, if I start walking south, will we be moving apart faster or slower?
daring ferry
faster
vapid shuttle
okay
So me and you are on the sidewalk. You start walking north at 5mph, and I walk south at 1mph. This will make us move away faster than before (which was 5mph). So how fast are we going apart now?
hint: the only difference is that I started moving away, this adds to the speed we are moving apart
daring ferry
7? im not sure this is my understanding
vapid shuttle
could you tell me why you think 7?
daring ferry
i dont know too but i think its 4 or 3
daring ferry
4
vapid shuttle
atleast that's faster this time! but 7 is not correct, and the reason is because you just randomly chose 7,
the answer here is not random
try to look back at the question 1 more time
daring ferry
Okay
daring ferry
we move 10 mph away from eachother
this is my last answer
if this iswrong
please explain it to me
vapid shuttle
well, it is wrong because you randomly guessed again
the reasoning is
if you go 5mph away
and I go 1mph away
the speed we are traveling apart
daring ferry
6
vapid shuttle
adds
yes!
so in total we are going apart 6mph
because instead of it only being the speed you go away, I add to the speed by going away aswell
Two passenger trains left the station at the same time and traveled in opposite directions. One traveled at the rate of 50 km/h and the other at 45 km/h. After few many hours are the trains 315 km apart?
so for this,
one train is traveling 50km/h away
and the other is traveling 45km/h away in the opposite direction
so the total speed they are traveling apart from eachother is?
daring ferry
95 km
daring ferry
thank you
vapid shuttle
how long until they are 315 km apart?
daring ferry
the trains travel apart 95 km , every hour
yes
daring ferry
how long until they are 315 km apart?
are we gonna divide?
vapid shuttle
yeah, what do you think we should divide
daring ferry
315 and 95
daring ferry
what which by what ?
ocean sealBOT
AustinU
vapid shuttle
no
if they go apart at 95 km every hour
then in 2 hours they are apart 190km
in 3 hours they are apart 285 km
and so on
so the answer will clearly be above 3
95/315 is not above 3
daring ferry
yes
vapid shuttle
315/95 is the proper next step
it answers: how many times do we have to go 95 km to get to 315 km
daring ferry
3
vapid shuttle
not exactly 3
but around that
the answer is exactly 315/95....
good luck with the rest of this, goodnight!
vapid shuttle
if you can't recognize that 315/95 is just a number about the size of 3, I'm not sure how I can help
the trains move apart 95 km every hour
how many hours will it take for them to move apart 315 km?
that is answered by 315/95
so the answer is
315/95 hours
that is how long it will take
however many times 95 goes into 315
if it asked, how long will it take for them to go 95 km apart
you would see that it is 1 hour
because they go 95 km apart every hour
if it was 190 km
then it would be 2 hours
because 190/95 = 2
so for 315 km
the answer is 315/95 hours
daring ferry
thanks austin
vapid shuttle
np
daring ferry
i understand now
vapid shuttle
great!
daring ferry
this gave me a little headache ☠️ but yes tbh ur great at teaching
can i not close this
for future purposes
vapid shuttle
well thank you! You can take screenshots and leave it open for now, but sadly it will close eventually on its own
but feel free to take pictures or something to save it if you need
daring ferry
thanks
lone heartBOT
@daring ferry Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
I'm trying to understand the integration of these $$\int^{\frac{2\pi}{\omega}}{0} e^{2i\omega t}\omega L dt = \frac{e^{4i\pi}-1}{2i}L$$ $$\int^{\frac{2\pi}{\omega}}{0} e^{2i\omega t} (\omega C)^{-1} dt = ?$$
ocean sealBOT
Hin
alpine sable
I don't understand how the first integration has ended with that result.
whole shell
also is that for fourier transform just curious
alpine sable
hmm ah no. it's electric engineering
whole shell
well since we are integrating everything with respect to t, you are integrating be^(ax) normally
theres nothing special going on
alpine sable
ah so
I thought like the omega in the interval 2pi/omega affects anything in the integrating process
whole shell
no
you just sub it in
its just a normal number to sub in
since we are integrating with respect to t
anything that isnt t
means nothing
alpine sable
its well b^-1?
alpine sable
well since we are integrating everything with respect to t, you are integrating ...
isn't the both of integrating in the form abe^(acx) ? or something like that because of the omega being exponential
$\omega L e^{2i\omega t}$
ocean sealBOT
Hin
lone heartBOT
Available help channel!
fresh perch
need a lil help with this integral
lone heartBOT
need a lil help with this integral
ocean sealBOT
Suro
fresh perch
which is equal to $\int \frac{1}{4((\frac{x-3}{2})^2 + 1)}$
ocean sealBOT
Suro
fresh perch
which is equal to $\int \frac{1}{4} \times \frac{1}{(\frac{x-3}{2})^2 + 1}$
ocean sealBOT
Suro
ocean sealBOT
Suro
limber crow
lone heartBOT
limber crow
How do I convert this to Cartesian?
vale wigeon
lone heartBOT
@limber crow Has your question been resolved?
limber crow
<@&286206848099549185>
alpine sable
<@&286206848099549185>
Mine wasn’t ether
lone heartBOT
@limber crow Has your question been resolved?
carmine crow
could someone help me with question 8c and 8d? please
craggy token
lone heartBOT
craggy token
I let f(x) = ax^2 + bx + c. From f(2) + f(3) = f(5), I got:
4a + 2b + c + 9a + 3b + c = 25a + 5b + c
13a + 2c = 25a + c
c = 12a
Then, from f(2)f(3) = f(6), i substituted c = 12a to get
(4a + 2b + 12a)(9a + 3b + 12a) = 36a + 6b +12a
(16a + 2b)(21a + 3b) = 48a + 6b
2(8a + b)3(7a + b) = 6(8a + b)
7a + b = 1 ... (1)
From f(1) = 1, i got a + b + c = 13a + b = 1 ... (2)
so, subtracting (1) from (2), i got 6a = 0 <=> a = 0, which means c = 0
however, f is a second-degree polynomial, which means a can't be 0
in which part did i do it wrongly?
gray isle
q = 1 isn't the only solution to
pq = p
craggy token
what's the other solution?
gray isle
have a think about it
rearranging the equation to general form
and factorisation would be helpful
fickle oyster
lone heartBOT
fickle oyster
is what im doing correct?
i forgot to add lim_h->0
|0| = 0
which exists
then the function is differentiable at 0?
fickle oyster
then the function is differentiable at 0?
how?
pseudo ice
You should have |h|/h
fickle oyster
~~You should have |h|/h~~
but the function is x|x|
pseudo ice
Actually no no I’m blind
fickle oyster
not just |x|
pseudo ice
Never mind me 
fickle oyster
Actually no no I’m blind
lol its okay
pseudo ice
Yea you’re fine then!
lone heartBOT
lone heartBOT
Available help channel!
shut musk
lone heartBOT
shut musk
can someone explain why the integration of ln(1-x) turns into a negative?
vale wigeon
do you mean to ask why it is subtracted and not added
shut musk
No i mean why is the integration of ln(1-x) = -1/1-x and not +1/1-x
whole shell
chain rule
last ether
the primitive of ln(1+x) is not 1/(1+x) as far as I'm concerned
whole shell
also, since when is the integral of ln(1+x) 1/(1+x), isnt it (1+x)(ln(x+1) -1)
last ether
,w Integrate ln(1+x)
alpine sable
I can understand why $\int\left(\frac{1}{1+x}+\frac{1}{1-x}\right)\mathrm{d}x = \ln\frac{1+x}{1-x} + C$ but why the other way around?
last ether
Yeah the model solution's just wrong
whole shell
the primitive of ln(1+x) is not 1/(1+x) as far as I'm concerned
also who the ffuck says primitive
last ether
Someone whose keyboard is being a bitch
Antiderivative
There happy
I had to dodge autocorrect
whole shell
what is integral correcting as
last ether
,w simplify integrate ln((1+x)/(1-x))
ocean sealBOT
last ether
Yeah the answer key is just wrong
alpine sable
Yeah the answer key is just wrong
I think so, too.
lone heartBOT
@shut musk Has your question been resolved?
amber niche
find the parametric equation of the intersection of these two cylinders :
x^2 + y^2 = 25
y^2 + z^2 = 20
amber niche
if it was something like z + y = 20, then I would simply do
x = 5cos(t)
y = 5sin(t)
z = 20 - 5sin(t)
but since they are squared I do not know what to do
and if I take the root for z, I end up with a +-, which I don't want
whole shell
hmm
lone heartBOT
@amber niche Has your question been resolved?
amber niche
@crisp iron
lone heartBOT
@amber niche Has your question been resolved?
amber niche
okay, so after looking carefully, it seems that there is no choice but to split it into the positive root and the negative root
i'm not sure but it looks that way...
lone heartBOT
@amber niche Has your question been resolved?
solar glade
if f(x+2) = x^4-4x^3+3x^2+x-6. find f(1), then find 2f(3)+4. im confused on how to do it
quasi vector
notice f(1) = f(-1+2)
quasi vector
you have an expression for f(x+2)
quasi vector
yes
quasi vector
sure
solar glade
if the middle term of (2b^2n-4+6b^3-n)^6 has no variable. what is the value of n
actually like 2 more questions i need help on after this lol
quasi vector
if the middle term of (2b^2n-4+6b^3-n)^6 has no variable. what is the value of n
what does the "middle term" mean
solar glade
uh
idk either
thats what the question gives
wait
how about
this other question
what is the cofeeiient of the x^2 term in the expansion of (ax+2/a)^5?
@quasi vector
/close
.close
gusty iron
hey ima kinda lost
lone heartBOT
hey ima kinda lost
tacit arch
differentiate is the verb form of derivative
tacit arch
so i to find the derivative of f(0) in the equation 2^3x
is it $f(x)=2^{3x}$ or $f(x) = 2^3 x$ ?
ocean sealBOT
riemann
gusty iron
first
gusty iron
do i use
ocean sealBOT
riemann
vapid shuttle
no, that is for taking the derivative of a product
ocean sealBOT
AustinU
vapid shuttle
first use some of the rules to simplify it
vapid shuttle
use the reverse of the product rule
vapid shuttle
and 2^3 is?
and then once it is simplified you will use these derivative facts: derivative of $C * f(x)=C * f'(x)$ and derivative of $a^{x}=ln(a) * a^x$
ocean sealBOT
AustinU
vapid shuttle
where C is a constant
worn fox
(2^3) (2^x)
Are you saying this is 2^(3x)?
gusty iron
im lost
gusty iron
Are you saying this is 2^(3x)?
confused by ur question
worn fox
(2^3) (2^x)
What did you write this for
gusty iron
reverse product rule
ocean sealBOT
AustinU
vapid shuttle
yes
gusty iron
so (a^3)^x
vapid shuttle
and a being?
gusty iron
so from here
vapid shuttle
and then the 2^3 is?
gusty iron
8 and then its 8^0 ya?
gusty iron
yeah
vapid shuttle
**AustinU**
use the second tip in this text here to take the derivative of 8^x
vapid shuttle
not quite
ocean sealBOT
AustinU
gusty iron
so thats ln(8) * 8^0
ln(8) * 1
ln(8)
i think we went wrong somehwere
if that is the final answer
vapid shuttle
can you send the original question
gusty iron
Let f(x) = 2^3x. Find fprime(0)
vapid shuttle
seems to me like ln(8) works out
gusty iron
on the practice sheet thats not an answer tho they give u 5 possibilities
vapid shuttle
what are the possibilities?
gusty iron
3, 3ln(2), 1, ln(2), 0
vapid shuttle
does that help you see the correct answer?
ocean sealBOT
AustinU
gusty iron
oh
ohhhhhhhh we did it right
i didnt know ln(8) could be 3ln(2) my bad
thank you austin
vapid shuttle
no problem
gusty iron
.close
dim matrix
Is this correct?
lone heartBOT
Is this correct?
dim matrix
Can x be 1?
tacit arch
Can x be 1?
what happens when you plug 1 into f(x) ?
dim matrix
1?
hard inlet
Try plugging it into the original function. You should notice a problem
tacit arch
what happens when you plug x=1 here
dim matrix
0
ocean sealBOT
Result:
Infinity
,wolf 1/sqrt(1-1)
ocean sealBOT
dim matrix
yeah
then x can't be 1
I was solving this and the answer given is x=0 and 1
I got 0
But not sure how can I get x =1
tacit arch
I was solving this and the answer given is x=0 and 1
solving what
gray isle
what's the original question asking for
gray isle
locations where the derivative is undefined but the original function is, are critical locations
dim matrix
locations where the derivative is undefined but the original function is, are cr...
Substituting 1 is making the function undefined, so that's why it is considered?
lone heartBOT
@dim matrix Has your question been resolved?
lone heartBOT
@dim matrix Has your question been resolved?
merry spire
@dim matrix do u still need help
dim matrix
<@806959978770071592> do u still need help
yeah, I'm not clear if I need to consider 1 or not as a critical point.
The solution is stating that though 1 and 0 are critical points, we can't consider 1.
merry spire
yeah we actually just did this unit and it tripped me up too, what is the difference between 0 and 1 in this case
like how did you get 0 vs 1
key word is point, not number
there's a spider on my computer one minute lmao
dim matrix
Is this correct?
this
merry spire
yes your critical numbers are 0 and 1
the 0 makes your derivative = 0 and the 1 makes your derivative = undefined
dim matrix
yeah
dim matrix
The solution is stating that 1 can't be considered.
merry spire
what did you do next
dim matrix
I need to understand why I can't consider 1 here, for which reason.
merry spire
the question wants you to do the 2nd derivative test
so get the 2nd derivative 🙂
I rushed but I got 1/2(1-x)^3/2
so just please tell me you got the same thing lmao
merry spire
just do it you will see why
dim matrix
with 1 ?
dim matrix
okay
merry spire
lmk when you have it done
dim matrix
lmk when you have it done
maybe wrong
dim matrix
Can't figure
merry spire
I rushed and this is on old scrap paper that I have already used as scrap paper
you're right lmao
rewrite it so it's -1/ everything though
just to make this extra clear
that it is in a denominator
dim matrix
check with wolfram
dim matrix
okay
merry spire
dim matrix
So here, now if I use x=1, it will be 0
dim matrix
2nd derivative
dim matrix
But we need to substitute critical points into the 2nd derivative.
merry spire
yes we do
I'm trying to show you why the 1 doesn't work
plug the 1 in, you get -1/(0)
which equals what
merry spire
idk abt infinity this was where I was going
dim matrix
yeah, same thing.
merry spire
that implies that there is no second derivative at that point right?
dim matrix
yeah, or at least we can't get the answer with the second derivative.
merry spire
wasn't that what you were asking?
dim matrix
the point is, how without going through the second derivative they abandon 1
merry spire
abandon?
dim matrix
I mean they didn't consider
merry spire
who is they
dim matrix
the explanation
merry spire
could you send a screenshot of the explanation
dim matrix
yeah sure
merry spire
I think all you need to see is that because the 2nd derivative doesn't exist it cannot be applied at that point
doesn't exist at x=1 (and the original function and 1st derivative too lol)
dim matrix
this
merry spire
OH
ok sorry, they abandoned it when they saw that 1 is outside of the domain of f'(x)
that's their way of saying how they know the 2nd derivative at that point doesn't exist
dim matrix
what does 'outside of the domain' mean?
alpine sable
helloooooooooooo
merry spire
um
an x value "outside of the domain" is an x value in an area where the function doesn't exist
I'll send a picture
alpine sable
what is 2+2??
merry spire
dim matrix
what is 2+2??
merry spire
so any x value that is less than 0 is "outside of the domain" of the function
because as you can see from the graph there is no line when x is less than 0
dim matrix
It's actually hard to figure 2+2
alpine sable
GUYS WHAT IS 2+2??
merry spire
sirius u good now
dim matrix
because as you can see from the graph there is no line when x is less than 0
I'm trying to understand.
Is it bcz they mentioned in the problem?
merry spire
these are both ways of showing how the test does not apply at that point because there is no 2nd derivative at that point
watch a video on the domain of functions if you really want to understand the explanation, but as long as you can tell that there is no second derivative there I think you are good
dim matrix
watch a video on the domain of functions if you really want to understand the ex...
Okay, I will. Thank you so much @merry spire 🙂
merry spire
I feel like I didn't actually do anything lmao good luck!!
dim matrix
I feel like I didn't actually do anything lmao good luck!!
No, it helped me a lot. I need to go through an explanation on domains.
Thanks again!
.close
frozen charm
need help with c i
elder wyvern
Yh Yh Ik Unrelated but, Can Anyone Decode this Binary? 00010111 11010001 11000110 00100110 00100011 00100010 00001111 01001011, Pls Just idk into what maybe Pls Ya Can try everything and then see what makes the Most Sense or smthn pls, Pls Help me out here 
lone heartBOT
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tacit arch
close one of your channels
lone heartBOT
.question
Please read #❓how-to-get-help
elder wyvern
!help
lone heartBOT
Please read #❓how-to-get-help
elder wyvern
Yh thx
lone heartBOT
@frozen charm Has your question been resolved?
tacit arch
close one of your channels
@frozen charm
frozen charm
yes
tacit arch
close one of your channels
do this or i'll do it for you
frozen charm
y tho theyre two different questions
tacit arch
doesn't matter. read the bot message
pseudo ice
[and ideally don't blank replies either 
]
pseudo ice
<@788085606483361802>
For your other question, I said this:
#help-2 message
As to how you could have done it
frozen charm
oh sorry i didnt see your msg but was able to do it thanks tho
pseudo ice
oh sorry i didnt see your msg but was able to do it thanks tho
As long as you got it in the end 
frozen charm
@pseudo ice any tips for c i ?
lone heartBOT
@frozen charm Has your question been resolved?
frozen charm
Never
lone heartBOT
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frozen charm
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waxen dove
So, I kinda need a lil help, at least some guidance I guess, I'm trying to generate equations for motion in what is basically a linkage mechanism of N links, in any configuration (but I'm trying to do it in a continuous configuration first), however I'm kind of lost
This of course using differential equations and such
Any help or guidance would be appreciated
waxen dove
maybe share what the aim is to find?
Some extra context, I made this software that simulates a 4 bar linkage mechanism, however I just derivate the positions, velocity and acceleration vectors using trigonometry, I'm trying to simulate this, and any other mechanism of greater number of linkages (in any configuration)
I was reading a paper regarding pendulums that kind of help me but... a series of n segment pendulums is not that similar to what I'm looking for
woeful pulsar
hmm, okay so the assumptions are typically that that the input is not overdetermined and everything is rigid
waxen dove
Is a mechanism, so it moves, but each linkage is rigid, yes
woeful pulsar
also, velocity and acceleration can probably be first ignored
so focusing rigidness + position is probably the way to go
waxen dove
yeah, my initial attempt with a n linkage mechanism was using unity physics system but... it simply freaked out and it didn't really work, so I'm trying to code myself the physics simulation
woeful pulsar
hmm I don't think a full physics simulation is required
waxen dove
I mean, I won't code any kind of collision, is not necessary for what I'm looking for
woeful pulsar
though there must be an assumption that the positions pretty much define finitely many configurations
waxen dove
I only really care about position, velocity and acceleration, and technically I can derive velocity and acceleration out of the position
waxen dove
though there must be an assumption that the positions pretty much define finitel...
yeah this kind of a problem... if you don't mind let me give draw you a diagram of what I'm looking for
woeful pulsar
yeah drawing would help
formalise all the parameters you have and what you want to calculate
because to do it in generality would be hard but doing small examples is not too hard
waxen dove
This is a simple 4 bar mechanism linkage, all I'm given at the start is the positions A and B (and by extension the vector AB), the lengths, r1, r2, r3, and the masses of r1,r2,r3
Being that is a mechanism the rotational movement on r1 with respect to A will move r2 and subsequently will move r3
Assuming only those parameters I'm trying to find
- a general movement equation for the joint points
- the same as 1, but given a rotational force in r1
This is the simplest setup, my goal is to extend it up to r_n and in different configurations
waxen dove
because to do it in generality would be hard but doing small examples is not too...
forgor to ping
woeful pulsar
This is a simple 4 bar mechanism linkage, all I'm given at the start is the posi...
you can calculate the endpoint E between r1 and r2, then you have the distance EB, then you can use trigonometry to find the configuration of r2, r3
of course the next question is because r2, r3 don't have a uniquely determined solution (there's two configurations), so one would probably need to estimate the velocity of each of the nodes to figure out which configuration is more appropriate
waxen dove
of course the next question is because r2, r3 don't have a uniquely determined s...
Yeah, that's kind of the thing, I do have the trigonometric formulas for this case, the four bar linkage, and I have solved the problem of multiple configurations, however this doesn't take into account the mass of the bodies to determine their motion, nor what happens with an applied force to each linkage
idk if I'm being clear on that, sorry
woeful pulsar
I think you are looking at a different problem than just finding the configuration, we need to refine that
mass generally isn't too much of an issue, unless you are doing something which involves checking the strain at each joint
waxen dove
Like I said, this is linkage mechanism, is expected to move, it freely moves
well "freely" there is some level of constraint of course
woeful pulsar
perhaps an example of how these applied forces can occur can help
waxen dove
let me show you a vid of the app I made, give me a sec
waxen dove
perhaps an example of how these applied forces can occur can help
https://www.youtube.com/watch?v=9GzszKnLJTg
This is an old video of what I'm trying to illustrate, each link is rigid, but is connected with a rotating joint, I'm taking in consideration the mass because I want to determine its movement if I simply let it rest, as well if I apply a force to the input linkage
And here is my original simulator if you're interested, is the interactive version of what the video shows (and more)
https://vakogp.itch.io/simuladorbarras
woeful pulsar
so you only care about forces on the input linkage, not other parts
waxen dove
yeah
woeful pulsar
yeah it's quite close to a physics simulation, so we need a better model than "just rigid bars"
waxen dove
wdym?
woeful pulsar
we can't ignore the forces on each joint since we need to consider forces
waxen dove
yeah, it would need to propagate
Right now what I was doing was basically generating solid shapes based on n vertex, then generating a centroid from it and then having each point (including the centroid) have a list or an array of the acceleration and velocity
woeful pulsar
okay we can model each linkage as a mass at the center and write down the equations for torques and force to find their linear and angular velocity, and we need to model the 2d contact forces at each joint
plus the length conditions
but i'm not sure how to solve that entire system
maybe throw numerical methods at it
waxen dove
yeah.... this shit sucks
my initial idea was basically kind of a propagation method, basically give the input priority, each frame I'd update the input first, and then based on the calculations of the first link update each subsequent link, you know?
and then at the end, check if the output (last link) breaks, if so then simply return to the previous state
Anyway, this is good enough for me, thank you tho!
.close
lone heartBOT
<#490557019623915520>
halcyon monolith
I have several doubts regarding this problem.
red dot line: Why was y^y made 0? I mean, that would have been true if y wasn't a function of x. But it's given that x = y = z
yellow line: I don't know how they found out the f12
I mean, did they multiply it?
tacit arch
red dot line: Why was y^y made 0? I mean, that would have been true if y wasn't...
interesting question
they're definitely assuming x, y, z are all independent of each other
they're asking you to prove x=y=z so i can understand why you think it contradicts y is not a function of x
but y can be anything to start
worn fox
i think they're going for z being a function of independent variables x and y
halcyon monolith
i think they're going for z being a function of independent variables x and y
they were perhaps trying to. is this a good question btw, or is it just that I can't under this
worn fox
well given that there is ambiguity in how to interpret the question, its probably not a great question
halcyon monolith
also, we are asked to prove partial diff of (z) with respect to y and then x is equal to something.
if z = x = y, it just would be freaking zero, wouldn't it be?
halcyon monolith
take x, partially differentiate wrt x
and then you get 1
now partially differentiate again with rt x
0?
worn fox
why are you partially differentiating x wrt x
halcyon monolith
you calculate the partial diff and *then* you sub in x=y=z
ok that makes sense.
worn fox
infact, thats what they do in the solution you posted
halcyon monolith
we have to assume that z is a function of x and also y until we apply x = y = z
worn fox
yeah its implied here that z = f(x,y)
halcyon monolith
but we are assuming z is a function of x and y only because we are asked to partially differentiate it with respect to x and y
yes.... you are right
a bad question nonetheless
worn fox
yeah its implied here that z = f(x,y)
agreed, but with nothing else to go on, this is what you should assume
its the "standard" ig
vestal imp
are u dumb?
i was using that channel. i decided to stop learning because u were interfering with it
serene junco
<@&268886789983436800> ?
sly mantle
.close
radiant pecan
What are youre guys thoughts on this? I think the proof is flawless, however, the way the question is framed it seems like it shouldnt be. Any help would be appreciated
woeful pulsar
there is a problem with the proof
in fact the claim is wrong
(draw a venn diagram to check)
@radiant pecan
radiant pecan
wtf]
im clearly an idiot
ill ahve another look at it that way
thank you
.close
vestal imp
Hi peeps! Just wondering if I've got the right idea for this question. Thanks XD
lone heartBOT
vestal imp
Hi peeps! Just wondering if I've got the right idea for this question. Thanks XD
Kind of stuck on this question, not sure if I used a correct method
gilded vessel
what about proviingusing contrapositive
gleaming granite
your approach was good, but n^3 + 11 does not equal n?
gilded vessel
if n is odd then n^3 + 11 is even
vestal imp
what about proviingusing contrapositive
I will try that, ty bro
gilded vessel
its much simpler imo
lone heartBOT
Available help channel!
high palm
lone heartBOT
woeful pulsar
well you can solve a linear system
or you can use part a to find two more points it passes through
lone heartBOT
@high palm Has your question been resolved?
viral solstice
put the values then solve the linear equation
high palm
put the values then solve the linear equation
like the coordinaties?
high palm
is a = -26 and b = 20
ocean sealBOT
alpine sable
,w (2^3) -26(2^2) + 20
ocean sealBOT
ocean sealBOT
ocean sealBOT
lone heartBOT
Available help channel!
clear vault
Help pls
clear vault
I'm stuck in here
exotic river
Problem is find H(x)?
clear vault
h(-2)
exotic river
Trying to understand that notiation by H circle F circle g, do yuu mean H(f(g)) or H(x) x F(x) x G(x)
clear vault
h(f(g))
exotic river
H(x) = x^4 ?
H(sqrt(x+4)) = (x+4)^2
f(g) = (x+4)^(1/2)
h(x) = x^4
H(-2) = 16?
clear vault
Ohh I see
exotic river
solved?
clear vault
Yea, thx btw 🙂
exotic river
allg
craggy token
It is known that the function $$f(x)=\frac{x^2+ax+b}{x^2+2x+3}$$ for real number $x$ has a minimum value of $-5$ and maximum value of $4$. If $a$ and $b$ are integers, find all the possible values of $|a+b|$.
ocean sealBOT
$nichoals$
craggy token
How do I go through this problem?
vale wigeon
there are different ways of going about this
you could rewrite the equation y=f(x) as a quadratic in x parameterized by y, then require that its discriminant be positive precisely for y between -5 and 4
craggy token
i see
i'll try first
discriminant be positive precisely for y between -5 and 4
what do you mean by this?
i got D = -8y^2 + (12 + 4b - 4a)y + (a^2 - 4b)
lone heartBOT
@craggy token Has your question been resolved?
lone heartBOT
@craggy token Has your question been resolved?
gray oxide
lone heartBOT
gray oxide
Omg
severe ruin
💀
gray oxide
That's true hahaha
rocky grove
DEB
gray oxide
What's SEB?
severe ruin
angle
severe ruin
DBE= 180-(y+x) thats why DEB = x ,
gray oxide
A = Y
B = 180-Y-X
X = 180- (180-Y-X) - Y
rocky grove
You describe the angle by starting at D, going to E and ending at B
So that you avoid mistaking it with other angles
Like E can be the angle inside and can be the angle outside
gray oxide
isn't DBE and DEB the same thing?
severe ruin
nah
rocky grove
Nope
severe ruin
dbe is b angle
gray oxide
SO THE MIDDLE letter is the angle?
severe ruin
yes
gray oxide
and the ends of the formula is the sides?
rocky grove
Yeah
severe ruin
ye
gray oxide
ah ok i understand now makes much more sense
rocky grove
But the left and right letters are needed or else your angle description will stay incomplete
rocky grove
ah ok i understand now makes much more sense
gray oxide
But then
severe ruin
so you wont mistaken it with other e angle
gray oxide
DEB and BED would be the same no?
gray oxide
but the middle is them same and the sdies
gray oxide
oh ok
sorry
I didn't read it
alright so how do I solve this what am I supposed to be thinking?
how do I get X?
or ACB
severe ruin
lemme try on paper
gray oxide
ok
if what I've written is true
does that mean that x = 180-y
meaning that C would be the correct answer
x= 90-Y/2
rocky grove
Hmm
severe ruin
DEC = 180-x in my opinion
severe ruin
so
rocky grove
And similarly ADE = 180 - y
severe ruin
yea
gray oxide
So then x = 180-y
severe ruin
i dont think thats true
rocky grove
Let's call angle B as B
gray oxide
sure
rocky grove
So 180 = B + x + y
gray oxide
yep
rocky grove
So that means B = 180 - (x+y)
gray oxide
oohh yeyeye
severe ruin
its D
severe ruin
u sure ?
severe ruin
1min
gray oxide
ok
severe ruin
so look
gray oxide
I'm looking
severe ruin
b=180-x-y
CED =180-x
ADE=180-y
now put random numbers that would work for example x=50
y=40
in that case DBE=90 and if you check answers 180-80=100 100/2=50
gray oxide
sure I follow so far
severe ruin
so i think its D idk
gray oxide
can I give my theory and can you correct it if it's wrong?
severe ruin
sure
gray oxide
is this correct?
is Dec = y
and is ADE = x
?
severe ruin
waity
gray oxide
consists of x+ y
severe ruin
i still believe my theory was correct 💀 idk how to solve but answer is D
just putting numbers
gray oxide
here's the thing I thought it was correct because ADEC create a rectangle so there fore it would end up 360deg and if x+y = 180 then it would be correct because
A = y
D=x
E=y
C=x
which equals 360
but DBE fucks that up
severe ruin
it would be correct if it was Parallelogram its trapezium
severe ruin
in Parallelogram diagonal angles are equal but not in trapezium
lament forge
it does sum to 360 in total, but that's not enough information to determine the angles
x, y, 90, 90, also sums to 360
severe ruin
yea
lament forge
but also yeah x+y is not 180
severe ruin
i think its D
gray oxide
so how do we get X = 180-Y or x = 90-y/2?
gray oxide
but also yeah x+y is not 180
Why not?
severe ruin
just did basics and put numbers
gray oxide
lament forge
so what's DBE
gray oxide
but also yeah x+y is not 180
So this drawing is wrong?
severe ruin
180-x-y
lament forge
So this drawing is wrong?
yep
gray oxide
Ok then I'm back to square one fuuuuck
severe ruin
bro you sure answer is 100% C cuz i thinks its D
gray oxide
this is a national test
that has the correct answers next to it
the chances of it being wrong is very low
but never 0 I guess
severe ruin
oh
lament forge
ok wait hang on
there isn't enough information
what exactly does the question say?
severe ruin
.
lament forge
it says more than that
gray oxide
I forgot to say
severe ruin
define x with y
severe ruin
I forgot to say
?
gray oxide
ABC Is a triangle
DE is paraell with AC
DE=BD
That is the info
lmao sorry about this I made a huge mmistake
severe ruin
💀
lament forge
oh
so DBE is isosceles
severe ruin
yea
gray oxide
What's isosceles ?
severe ruin
2 side equal triangle
severe ruin
same
severe ruin
i FOUND
gray oxide
so B = X?
gray oxide
Wait does that mean that B = x?
severe ruin
DBE triangle
gray oxide
I think I understand
lament forge
DEC is not x
but DEB is
gray oxide
yea sorry DEB lol
severe ruin
@lament forge can you confirm that ?
severe ruin
180-x-y=x
2x=180-y
x=90-(y/2)
to be sure
gray oxide
ye so finally lmao we got it LET'S GO BOISSSSSSSSSSSSSS
lament forge
yep that looks right
gray oxide
you guys are sick thank you so much for helping me out this took too long because I did not give enough info so sorry about that again thx guys good luck on helping the rest of the channels that are open
severe ruin
<3
gray oxide
.close
craggy nebula
How is the integral symbol used? (∫)
lone heartBOT
How is the integral symbol used? (∫)
quasi vector
do you mean how to write it in latex?
craggy nebula
No, I've never learned what it does.
craggy nebula
Hm?
quasi vector
if you really want to learn integration, I would suggest watching 3Blue1Brown's series on the essence of calculus
it will give you a sense of calculus beyond what school curriculum's will
craggy nebula
All right. Thanks.
whole shell
How is the integral symbol used? (∫)
have you learnt of the summation symbol
$\Sigma$
ocean sealBOT
doctor99268
craggy nebula
I know a little about it.
whole shell
the integration symbol
is basically
its brother
@craggy nebula do you know what discrete vs continous are
craggy nebula
Like capital pi is? (∏)
whole shell
Like capital pi is? (∏)
i get what you are thinking, but in a different way
craggy nebula
I've stumbled across it when developing games, but never really understood what they mean, so no.
craggy nebula
Yeah.
whole shell
this would be continuos
craggy nebula
Oh, so interpolation?
whole shell
you use interpolation for discrete values
because you dont have information
on whats between
while continous
you have the information for everything
craggy nebula
Linear interpolation?
whole shell
linear interpolation is one form of interpolation