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#help-41
amber waspBOT
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mild shale
hall
mild shale
o
outer hull
mild shale
so
in the 2nd one
the 3e^x one
the correction
he said that 3x-7/x-20=0 is equivalente to 3x^2-20x-7
how
outer hull
multiply both side by x
mild shale
oooh
yeah thanks make sense now
(i asked chat gpt and coulndt figure it out :p)
uh
how can i close this help chat
close
outer hull
(i asked chat gpt and coulndt figure it out :p)
!nogpt
amber waspBOT
(i asked chat gpt and coulndt figure it out :p)
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
outer hull
.close
misty cairn
what should i do
keen pawn
Let $A$ be be a nonempty, bounded above subset of $\R$. Let $c\in \R$. Define $c+A={c+a:a\in A}$. Prove $\sup(c+A)=c+sup(A)$
\
Proof:Let $s$ be the supermum of $A$, that is $a \leq s; \forall a \in A$. From this it follows that $c+a \leq c+s, \forall A$. Thus $c+s$ is an upper bound of $c+A$. We now prove it's the least upper bound. Let $s'$ be the least upper bound of the set $c+A$, then $c+a\leq s' \leq s+c$, then $a \leq s'-c \leq s$. This would make $s'-c$ the supermum of $A$, but that's $s$. Thus $s=s'-c$. Therefore $s'=s+c$ as desired
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
vernal surge
c+a <= s' <= s+a where does this come from, why s+a?
vernal surge
but then the next one makes no sense either
keen pawn
Let $A$ be be a nonempty, bounded above subset of $\R$. Let $c\in \R$. Define $c+A={c+a:a\in A}$. Prove $\sup(c+A)=c+sup(A)$
\
Proof:Let $s$ be the supermum of $A$, that is $a \leq s; \forall a \in A$. From this it follows that $c+a \leq c+s, \forall A$. Thus $c+s$ is an upper bound of $c+A$. We now prove it's the least upper bound. Let $s'$ be the least upper bound of the set $c+A$, then $c+a\leq s' \leq s+c; \forall a \in A$, then $a \leq s'-c \leq s$. This would make $s'-c$ the supermum of $A$, but that's $s$. Thus $s=s'-c$. Therefore $s'=s+c$ as desired
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
keen pawn
Is this better?
vernal surge
also how does it follow that s'-c would be the supremum of A?
keen pawn
s is the supermum of A, but I've shown that s'-c is greater that or equal to all elements of A too
so s=s'-c as s'-c\leq s
vernal surge
yeah you've shown that s'-c is an upper bound of A that is less than or equal to s. I only find the sentence a bit weird. It should be that s'-c is equal to s precisely because s is already the supremum
vernal surge
you can just say that s'-c is an upper bound of A, and as s is already the least upper bound, it follows s'-c >= s
keen pawn
That's what I;ve said when I say
This would make $s'-c$ the supermum of $A$, but that's $s$
No?
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
vernal surge
it makes s'-c an upper bound, yes, but not yet the supremum
vernal surge
I think the order is just a bit off here, it's a bit hard to explain
keen pawn
mhm
vernal surge
the way you formulated it here is that it follows that s'-c is the supremum of A, but oh surprise surprise s is already the supremum of A
but why was s'-c the supremum in the first place? That is not really that clear yet
keen pawn
s'-c wasn't the supermum, just an upper bound
but the way I formulaed it , s'-c turns out to be equal to s
vernal surge
it's not even necessary to show that s'-c is the supremum of A actually, you just need to show that s'-c = s
I would really just replace that sentence by an explanation why s'-c >= s, using the fact that s is the least upper bound of A, and the sentence after that follows very naturally
keen pawn
so the setence structure is bad, but the logic is good?
indigo cloud
Let $s'$ be the least upper bound of the set $c+A$, then $c+a\leq s' \leq s+c$,
what is a
vernal surge
I mean it's just a minor detail, otherwise your idea is correct
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
keen pawn
As defined in the question
indigo cloud
the letter a is defined nowhere in the question
stuff inside set notation doesnt count
what quantifier belongs to a in your sentence
keen pawn
what quantifier belongs to a in your sentence
for all a
Let $A$ be be a nonempty, bounded above subset of $\R$. Let $c\in \R$. Define $c+A={c+a:a\in A}$. Prove $\sup(c+A)=c+sup(A)$
\
Proof:Let $s$ be the supermum of $A$, let a be an arbitrary element of A. That is $a \leq s; \forall a \in A$. From this it follows that $c+a \leq c+s, \forall a \in a A$. Thus $c+s$ is an upper bound of $c+A$. We now prove it's the least upper bound. Let $s'$ be the least upper bound of the set $c+A$, then $c+a\leq s' \leq s+c; \forall a \in A$, then $a \leq s'-c \leq s$. This would make $s'-c$ the supermum of $A$, but that's $s$. Thus $s=s'-c$. Therefore $s'=s+c$ as desired
indigo cloud
what you can do is to introduce a at the beginning of the proof
"let a be an arbitrary element of A"
then you dont have to carry the quantifier around all the time
vernal surge
"This makes s'-c an upper bound of A, and as s is the least upper bound, it follows s'-c >= s."
Thus s = s' - c and so on
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
indigo cloud
why are you still carrying the quantifier around
keen pawn
Let $A$ be be a nonempty, bounded above subset of $\R$. Let $c\in \R$. Define $c+A={c+a:a\in A}$. Prove $\sup(c+A)=c+sup(A)$
\
Proof:Let $s$ be the supermum of $A$, let a be an arbitrary element of A. That is $a \leq s;$. From this it follows that $c+a \leq c+s$. Thus $c+s$ is an upper bound of $c+A$. We now prove it's the least upper bound. Let $s'$ be the least upper bound of the set $c+A$, then $c+a\leq s' \leq s+c; \forall a \in A$, then $a \leq s'-c \leq s$. This would make $s'-c$ the supermum of $A$, but that's $s$. Thus $s=s'-c$. Therefore $s'=s+c$ as desired
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
indigo cloud
still a quantifier in sight
and why are you not changing the things rbit pointed out
you only showed s'-c is some upper bound
not the sup
keen pawn
I'm not sure I fully understand what they want me to do
indigo cloud
you havent shown s'-c is the sup
you have only shown it is an upper bound
so you only know s <= s'-c
from the other inequality you have s'-c <= s
so then equality
keen pawn
What I'm saying instead is I've now shown that s'-c is an upper bound of A, but it's less than s, which is an upper bound of A too, and the least upper bound, so s'-c=s is necessary
indigo cloud
but you havent written all of that
keen pawn
Let $A$ be be a nonempty, bounded above subset of $\R$. Let $c\in \R$. Define $c+A={c+a:a\in A}$. Prove $\sup(c+A)=c+sup(A)$
\
Proof:Let $s$ be the supermum of $A$, let a be an arbitrary element of A. That is $a \leq s;$. From this it follows that $c+a \leq c+s$. Thus $c+s$ is an upper bound of $c+A$. We now prove it's the least upper bound. Let $s'$ be the least upper bound of the set $c+A$, then $c+a\leq s' \leq s+c$, then $a \leq s'-c \leq s$. So $s'-c$ is an upper bound of $A$ too. However, it's less than or equal to $s$, which is the least upper bound of $A$. Therefore $s=s'-c$ is a must. Thus $s'=s+c$ as desired.
Is this better
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
indigo cloud
yes
amber waspBOT
amber waspBOT
Available help channel!
keen pawn
Assume $s \in \R$ is an upper bound for $A \subseteq \R$. Then prove $s= \sup(A)$ iff for every $\varepsilon>0$, there exists $a \in \A$ satisfying $s-\varepsilon<a$
keen pawn
Assume ( s \in \mathbb{R} ) is an upper bound for ( A \subseteq \mathbb{R} ). Then prove ( s = \sup(A) ) if and only if for every ( \varepsilon > 0 ), there exists ( a \in A ) satisfying ( s - \varepsilon < a ).
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
keen pawn
I'll first prove if $s-\varepsilon < a, \forall \varepsilon>0$ then $s= \sup(A)$
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
keen pawn
An element $b$ is said to be the supremum of a set if
(i) $b\geq a, \forall a \in A$
\
(ii) If $c \geq a,\forall a \in A \implies c \geq b$
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
indigo cloud
what would happen if there is no a with a > s-eps for some eps
keen pawn
Then The set isn;t bound from above
indigo cloud
no
keen pawn
hmm
primal holly
i think contradiction would work here
indigo cloud
yes but wai hasnt spotted the contradiction yet
keen pawn
Contrpositive may work here, if $s$ isn't the supremum, then $s- \varepsilon \geq a$ for some $\varepsilon >0$. Which is true. If $s$ isn't the supremum, there exists a number in $A$, say $a$, such that $a >s$
grizzled pagodaBOT
ƒ(Why am. I here)=I don't Know
amber waspBOT
amber waspBOT
Available help channel!
iron heath
How do I get a generating function from a singular function? We were never taught this at all.
iron heath
The book also has nothing on it.
Am I supposed to write this recursively?
The question is asking to find a closed form function of [x^n]e^2x
This is where I am thus far. I am not really sure where to go from here. I know the answer is 2^n/n!, but I have no idea how to get there from this.
<@&286206848099549185>
I know the 1/n! comes from the Taylor series of e^x. Is the 2 because of the power?
iron heath
Oh I didn't know it worked like that.
One sec
What is the closed form for just the e^x?
Is it (1^n/n!)?
thick shale
yeah
iron heath
Oh ok.
Is there some type of proof for this?
I'm supposed to do the whole 9 yards on these.
Unless I'm not. It doesn't actually say I have to now that I look at the problem.
How would this one work with the denominator then?
Does the new denominator go on top and cancel it out?
Something like this?
At this point it would just be alpha^n?
This one is throwing me.
flat patio
12 test areas are cultivated with a new wheat variety. These areas produced the following yields per hectare:
35.6 33.7 37.8 31.2 37.2 34.1 35.8 36.6 37.1 34.9 35.6 34.0
We know from experience that the yield per hectare as a realization of independent, 𝑁(𝜇,3.24)
-distributed random variables can be viewed. Specify a concrete estimation interval at the level of 0.95 for the expected value 𝜇.
thi sis the question right
how do i solve these type of examples
it is basically asking for an intervall i guess
i have this formula right
olive yacht
well since you're given the population standard deviation, it should be sigma instead of s, but otherwise that's correct
flat patio
well since you're given the population standard deviation, it should be sigma in...
well i calculated the z*s/sqrt n
it was this number
since i used 1.96 for z
now i summed up all of these and divide by 12
this is what i got
flat patio
well since you're given the population standard deviation, it should be sigma in...
book says this is the solution no clue why
and it quotes this weird formula
sage sable
book says this is the solution no clue why
I may be mistaken but I think your result is incorrect because you are using the variance 3.24 in your calculation instead of the standard deviation.
flat patio
I may be mistaken but I think your result is incorrect because you are using the...
oh yeah that might be the case
flat patio
I may be mistaken but I think your result is incorrect because you are using the...
3.24 which is given here is the variance??
iron pond
who knows how to do higher mathematics
flat patio
oh damn
flat patio
who knows how to do higher mathematics
people with the postgraduate role a super good, they corrected many mistakes of mine
sage sable
3.24 which is given here is the variance??
yes thats why there is expponent
flat patio
yes thats why there is expponent
NIiiice 👍
both formulas are the same
i get the same result as in the book now
frank zealot
is a² + ab + b² always positive? a and b are real numbers
amber waspBOT
is a² + ab + b² always positive? a and b are real numbers
thick shale
yes
winter badge
nah
daring silo
Yes
thick shale
(a+b)^2 >= 0
winter badge
but does a and b have to be real?
thick shale
so, a^2 + 2ab + b^2 >= 0
winter badge
that is true
oh you gave us that a and b are real
my bad
i thought you asked if they are real
thick shale
(a+b)^2 >= 0
vague thorn
didn't they ask just +ab
frank zealot
i said +ab not +2ab
daring silo
and a^2 and b^2 are always positive
mellow hornet
$a^2 + ab + b^2 = (a+b)^2 - ab$, but if $ab > 0$, then $a$ and $b$ are both positive or both negative, in which the original statement is clearly positive
grizzled pagodaBOT
Ari
mellow hornet
If $ab < 0$, $(a+b)^2 - ab > 0$ already
grizzled pagodaBOT
Ari
vague thorn
ah
frank zealot
.close
vague thorn
right
amber waspBOT
thick shale
$$(a+b/2)^2 + 3b^2/4$$
grizzled pagodaBOT
Pro_Hecker
thick shale
nvm
amber waspBOT
Available help channel!
exotic trout
amber waspBOT
exotic trout
so far I proved that 0<u_n<1 for all n∈N
i tried finding whether {u_n} is increasing or decreasing
but i didnt reach anything
oh wait
i managed to prove that the sequence is increasing
i need someone to check if it is correct
nvm it is wrong
<@&286206848099549185>
amber waspBOT
@exotic trout Has your question been resolved?
amber waspBOT
@exotic trout Has your question been resolved?
viscid cobalt
amber waspBOT
pallid canopy
show answer to parts a and b
viscid cobalt
show answer to parts a and b
pallid canopy
i guess they really want you to find $\frac{d}{dN} \lp \frac{N(300 -N)}{1200}\rp$ and set it equal to 0 and then solve for $N$
grizzled pagodaBOT
riemann
pallid canopy
rate of growth here is slightly vague
amber waspBOT
@viscid cobalt Has your question been resolved?
viscid cobalt
i guess they really want you to find $\frac{d}{dN} \lp \frac{N(300 -N)}{1200}\rp...
If I do that 300 = N
i dont get it
pallid canopy
nah
viscid cobalt
oh wait the deravative of that equation
my b
so I get 1575e^-0.25t = 0
idk how to solve that tho
wait no
viscid cobalt
If I do that 300 = N
this was the deravative
how is this wrong
I multiply both sides by 1200
so then 300N-N^2 = 0
300n = n^2
n = 300
what am i missing 🙉
viscid cobalt
shit is this a differential equation
i completely forgot how to do that
u integrate both sides?
viscid cobalt
do you know what this notation means
yh idk
amber waspBOT
amber waspBOT
Available help channel!
sharp dock
Yo
sharp dock
I'm not sure how to do g or i
Idk how to start
Other than letting theta equal the numbers in the brackets
Can someone help me with g?
<@&286206848099549185>
grim forge
14 sin(3x)+8=5
We try to isolate sin(3x) to equal to a constant
14 sin(3x)=5-8
sin(3x)=-3/14
Then based on the range of x given
They probably stated a range of x somewhere
sharp dock
Yea ik that I have to simplify it
However idk what my teacher did here
And I can show u the part I'm mostly confused about
grim forge
Yea go ahead
sharp dock
These parts
I understand it only up to theta = sin inverse (-3/14)
= 0.216
Idk anything else
grim forge
Uh did they give a range of answers for x
Like did they say x has to be within a certain range
In the question
sharp dock
Lemme check
grim forge
Can I see the range if so
sharp dock
grim forge
Ah ok
So uh I'll just draw a diagram
Uh it's not necessary to draw this diagram
But I find it helpful in solving these kind of questions
sharp dock
Alr
grim forge
So here we have our four quadrants
sharp dock
yea
grim forge
So since
0<x<2pi
0<3x<6pi
Right
grim forge
2pi multiplied by 3
grim forge
Because 3x is x multiplied by 3
sharp dock
Oh okok
grim forge
The way I'm doing it it doesn't really matter
sharp dock
Oh okok
sharp dock
Yep
sharp dock
Yes but wdym 3 S.f?
sharp dock
Oh okok
sharp dock
Isn't this our range tho?
grim forge
Yes true
But we're solving for 3x
Not x
So our range
Is extended by 3
If 3x=6pi then x=2pi so if 3x is less than 6pi,then x is less than 2pi
You catch my drift
grim forge
We have our first two solutions for 3x
pi+0.216 and 2pi-0.216
Alright so we have these first two solutions
We need to add one revolution to them
To get our next two solutions
So
3pi+0.216 and 5pi-0.216
sharp dock
Alr
grim forge
So
3pi+0.216 and 5pi-0.216
Then for our next two solutions just do that shit again for these two solutions
You get the gist
Finally divide all solutions by 3
And you get all solutions for x
Yipee
grim forge
So the angles must lie in quads 3 and 4
I find this diagram useful because I don't really have to think about periods
You kinda just visually see what you need to add
Oh I see yall drew it too
grim forge
Sure ig
sharp dock
Ok give me like 5 minutes?
grim forge
Bet
sharp dock
Alr I'll lyk when I'm done
Yo
@grim forge
It's a bit of a mess but this is what I got
So far
No idea if the pi/3 is right or not
grizzled pagodaBOT
denzio321
grim forge
4pi+pi/2
sharp dock
Theta = 2x + pi/2
grim forge
Mhm
grim forge
Uh nah
sharp dock
Then how lol
grim forge
2 cross out?
sharp dock
Yea?
grim forge
Its mutlplied by 2 + pi/2
grim forge
Uh no
sharp dock
Idk where those numbers are coming from
grim forge
It's 2x + 0.5pi
sharp dock
Can u write it on paper? 😭
sharp dock
Pi/2
grim forge
Because that's the end points of the ranges
By subbing the end points of the range of x, we find the new endpoints of the range of theta
sharp dock
What end point?
Im so confused and fucked for this part of the test tmrw
I don't need to do this question but I need to know how
grim forge
Like you know a number line
Sometimes you draw lines representing an inequality on it
The two ends of the inequality line are the end points
sharp dock
Ahh okok
grim forge
4pi
Anyway
It's 2(2pi)+pi/2=4pi+pi/2=9pi/2
Alright now
Just continue as with the process we had before
grim forge
Mhm
sharp dock
So we multiply 4pi/1 top and bottom by 2
To get 8pi/2 + pi/2
Then that equals 9pi/2
grim forge
Yea
sharp dock
Right?
grim forge
Yea
sharp dock
Ok good
sharp dock
Get your solutions
Solutions? Huh?
grim forge
Yea
sharp dock
Wasn't 9pi/2 the solution?
sharp dock
...
sharp dock
Oh nah
grim forge
Come on man
sharp dock
So now how do I get what my teacher gets?
sharp dock
Come on man
Man I missed 4 days of school last week cuz of snow days
And my teacher was posting lessons without teaching them
grim forge
Uh so basically 9/2pi is 4.5pi
sharp dock
Yea?
grim forge
We can afford two rotations
sharp dock
Oh ok
sharp dock
I just wanna understand my teachers steps
grim forge
We also have the last 0.5pi but no solutions are in that window so we're good
How many solutions did your teacher get btw
sharp dock
This is it
grim forge
Just that one
grim forge
I figured
sharp dock
Idk what the period is tho
grim forge
Uh welp so
sharp dock
That's the thing I struggle on
grim forge
We have our first two solutions pi-pi/3 and pi+pi/3
sharp dock
Yea
grim forge
Idk what the period is tho
Your teacher likes to find the first two solutions as x before adding the rotations
sharp dock
Do u understand the way he did it tho? And can u tell me how?
Cuz his way seems shorter idk why
grim forge
Yes but
I think it's prone to careless mistakes
Basically if you solve everything as just theta first
All you have to do is add 2pi for one period
Which I think you'll remember better
Alright so
sharp dock
Ok
grim forge
We have our first two solutions pi-pi/3 and pi+pi/3
Now we add our second revolution
To get solutions 3pi-pi/3 and 3pi+pi/3
And we're done I figure
sharp dock
Oh
grim forge
**denzio321**
So remember that theta is equal to this
So for all the solutions solve for x
This is a pretty no think plug in and do process
sharp dock
So what do I plug in exactly?
grim forge
There were four solutions right?
sharp dock
3 I think
grim forge
Well ill check with desmos
sharp dock
Alr
sharp dock
Ok
grim forge
,w -3cos(2x+pi/2)+6=15/2 for 0<=x<=2pi
grizzled pagodaBOT
grizzled pagodaBOT
sharp dock
Oh ok
Yea ima review this a bit more later tonight
Thanks for ur help
I gtg now
.close
amber waspBOT
amber waspBOT
Available help channel!
sour plume
need help with a question that uses piecewise functions number 22
amber waspBOT
amber waspBOT
Available help channel!
viscid mesa
Hello for b
amber waspBOT
Hello for b
viscid mesa
I understand the case where |G| = p, then |Z(G)| has to be equal to p because G is abelian. I am not sure how to disprove the cases where say |G| = p^n n>1 and |Z(G)| = p^n-1
oh woops
.close
amber waspBOT
viscid mesa
.reopen
amber waspBOT
✅
viscid mesa
never mind yeah I am still unsure of the case above
amber waspBOT
@viscid mesa Has your question been resolved?
viscid mesa
.close
amber waspBOT
amber waspBOT
Available help channel!
quiet osprey
How to find an inverse of a function
amber waspBOT
How to find an inverse of a function
quick ridge
!xy
amber waspBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
quiet osprey
It's a theoretical doubt
quick ridge
solve for x
robust willow
Generally, you'll want to flip the x and y and then solve for y
quick ridge
Generally, you'll want to flip the x and y and then solve for y
*y
robust willow
Or if you're fine with abstraction, just solve for x
amber waspBOT
quiet osprey
.close
amber waspBOT
Available help channel!
young adder
whats up, im struggling with a right now and quite simply don't know how to solve this, if anyone could tell me how to solve or what kind of problem this is so i could find an online resource for it would be much appreciated ty
spark elk
whats up, im struggling with a right now and quite simply don't know how to solv...
You might find something like Parallel axis theorem useful
young adder
thanks, just watched a video on it but i'm still confused how to apply it here. i got the rods inertia as 1/3ml^2, but for the inertia of the cylinder my teacher got 1/4mr^2 + 1/2ml^2 using something called the perpendicular bisector?
fluid pumice
thanks, just watched a video on it but i'm still confused how to apply it here. ...
Yeah there’s a derivation for that too
I can send it to u if u want
young adder
please do and ty
i know where to use the parallel axis theorem now but i still dont understand where the inertia of the cylinder came from?
young adder
ty
fluid pumice
No problem
broken hinge
Hello, I am trying to find the derivative of this function, but I got stuck and don't know what to do..
grizzled pagodaBOT
split sail
Seems like you applied the product rule here which is wrong
broken hinge
may I ask why it's wrong to apply it there?
split sail
Also if you plan on differentiating one term at a time it's better to write d(..)/dx for the rest of the terms rather than writing them as the same
broken hinge
The only lecture I missed were about chain and product rule, so it's not my strongest
broken hinge
Also if you plan on differentiating one term at a time it's better to write d(.....
ohh okok I think Ik what you mean
split sail
may I ask why it's wrong to apply it there?
We could use the product rule if we had $ln(5x^3) \cdot \frac{2}{\sqrt x}$
grizzled pagodaBOT
broken hinge
omg
split sail
But instead of the product what we have here is a difference
broken hinge
Idk why I keep making such small mistakes
I don't know why I thought it was being multiplied, and I have a final tomorrow and I'm just stressing over the small mistakes I'm making
Can you give me like 5-10 minutes to try and solve it again?
split sail
Ping me
split sail
again you didnt write d(...)/dx for -2 x^ -1/2
broken hinge
omg
bro
its x sqrt(x)
I'm telling you I keep making these small mistakes that mess up everything
split sail
you made one again lol
split sail
its 1/(x sqrt(x))
split sail
you got it
broken hinge
okok thank you, do you think chatgpt is a good way to generate practice problems
hollow wolf
okok thank you, do you think chatgpt is a good way to generate practice problems
not in my experience, it's prone to hallucinate things that are wrong and it can be hard to check for that if you're learning
that said, my experience is mostly me asking it about advanced math (e.g. complex analysis) to try it out
it probably does better with simpler things and might be worth a try, but basically never take what it says at face value
the Internet and books are full of exercises too
broken hinge
it probably does better with simpler things and might be worth a try, but basica...
oh okok yeah I understand, I've used it to learn and it's given me really off answers
broken hinge
the Internet and books are full of exercises too
Do you know any by chance?
hollow wolf
Do you know any by chance?
the usual ones for calculus are Stewart and Spivak, first one has more exercises focused on calculations like this
there's also Paul's notes, the exercises there are a bit simple but I like them as a quick reference https://tutorial.math.lamar.edu
amber waspBOT
amber waspBOT
Available help channel!
simple drum
Let x,y be constant positive numbers
Let's define two sequences like this:
$a_1=x, : b_1=y \ a_{n+1}=\frac{a_n+b_n}{2}, : b_{n+1}=\sqrt{a_nb_n} , , n \in \mathbb N$ \
Prove that the two sequences converge, and that they have the same limit
grizzled pagodaBOT
prograce
simple drum
I'm not able to find a way to do this
I tried to prove that they're montone and bounded but I did not succeed
reef mesa
**prograce**
use the am gm inequality
amber waspBOT
@simple drum Has your question been resolved?
simple drum
Using am gm inequality we get:
$a_{n+1}= \frac{a_n+b_n}{2} \geq \sqrt{a_nb_n}=b_{n-1}$ and $a_n=\frac{a_{n-1}+b_{n-1}}{2} \geq \sqrt{a_{n-1}b_{n-1}}=b_n$ \ therefore $a_{n+1} \geq b_{n+1}$ and $a_n \geq b_n$ \
How do I get $a_{n+1} \geq b_{n+1} \geq a_n \geq b_n$ ?
grizzled pagodaBOT
prograce
simple drum
<@&286206848099549185> please
simple drum
Yes I thibk
reef mesa
Yes I thibk
oki lmk if you try it and it works
amber waspBOT
@simple drum Has your question been resolved?
amber waspBOT
@simple drum Has your question been resolved?
amber waspBOT
@simple drum Has your question been resolved?
pseudo saddle
hey. So I have a trainning homework from robotics class. Work is accumulating and also just signed a student job contract in the lab, so time is very short and I want to impress the professor. ( I am a very hands on guy and very bad at doing maths) Can someone help me with it ?
amber waspBOT
hey. So I have a trainning homework from robotics class. Work is accumulating an...
@pseudo saddle Has your question been resolved?
short pendant
short pendant
help
distant quartz
Translation..?
short pendant
rezultalul calculului 1, (6) + 06^-1 este:
the result of calculation 1, (6) + 06^-1 is:
help me out
is 3,(3) correct?
tepid verge
https://media.discordapp.net/attachments/1298555366442926122/1316440856739319830...
what is this number system?
short pendant
what is this number system?
HEOL PEM
hel pme
REAL NUMBERS
IS THE ANSWER 54?
OR WRONG
tepid verge
https://media.discordapp.net/attachments/1298555366442926122/1316440856739319830...
what is the difference between 3,3 and 3,(3)?
short pendant
what is the difference between 3,3 and 3,(3)?
I ALREAD
graceful cradle
what is the difference between 3,3 and 3,(3)?
1.66666666666666666666666
i mean
3,(3) is 3,333333333333333333333333333333333333333333333333 (infinite)
correct me if I'm wrong
amber waspBOT
@short pendant Has your question been resolved?
floral fiber
*A quadratic function can always be written in the form ƒ(x) = a(x − p)2 + q, where p and q represent the coordinates of the vertex." Be as detailed as possible and explain if this statement is true or false.
ionic terrace
*A quadratic function can always be written in the form ƒ(x) = a(x − p)2 + q, wh...
well, a quadratic equation has the form bx^2+cx+d. I suspect if you expand the f(x) you have there, and write bx^2+cx+d= whatever you get after expanding. Find a, p and q in terms of b, c, and d, and then check if p and q verify the formulas for he coordinates of the vertex...
floral fiber
well, a quadratic equation has the form bx^2+cx+d. I suspect if you expand the f...
slow down, what?
im kinda slow
ionic terrace
you were probably taught a quadratic equation / function is of the form ax^2+bx+c?
floral fiber
yes.
ionic terrace
I changed the letters a little bit, since you already have "a" in your exercise.
floral fiber
yes
ionic terrace
we check if he general equation bx^2+cx+d can be written in the form you mentioned
aka we do bx^2+cx+d=a(x-p)^2+q
$bx^2+cx+d=a(x-p)^2+q$
grizzled pagodaBOT
Wild123
floral fiber
and set corresponding coefficients to be equal
how do i do that
ionic terrace
example: x^2 has coefficient b on left side. whatever it has on right side, after expanding, should be equal to it.
here, after you expand, you should get b=a.
you have to do the same for coefficient of x
and then the free term
(x-p)^2=?
ionic terrace
so a(x-p)^2+q=?
floral fiber
a(x^2-2xp+p^2)+q?
floral fiber
ax^2-2axp+ap^2+q
ionic terrace
so we set $bx^2+cx+d=ax^2-2axp+ap^2+q$
grizzled pagodaBOT
Wild123
floral fiber
is it true
ionic terrace
so c=?
floral fiber
c = -2ap
ionic terrace
and d=?
floral fiber
ap^2+q
ionic terrace
I'll rewrite them:
b=a
c=-2ap
d=ap^2+q
we can switch the "a" for "b" in 2nd and 3rd due to first equality
floral fiber
whats first equality
ionic terrace
b=a xd
floral fiber
yes
ionic terrace
soo, we can find p now (from 2nd eq): p=c/-2b
floral fiber
ye
grizzled pagodaBOT
Wild123
ionic terrace
and...we finally get q: q=d-c^2/4b
what we proved this way, is that yes, every quadratic function can be written like this.
floral fiber
bro chilll
ionic terrace
we took a random quadratic eq, and made it look like the one in your exercise
floral fiber
what just fkn happened
floral fiber
and...we finally get q: q=d-c^2/4b
first of all, how does this even prove anything
ionic terrace
we started with a general quadratic eq bx^2+cx+d
we found coefficients a, p, and q, so that a(x-p)^2+q=bx^2+cx+d
floral fiber
we found coefficients a, p, and q, so that a(x-p)^2+q=bx^2+cx+d
sure yeah
ionic terrace
so any quadratic can be written like that
if you know the b, c, and d, of a quadratic
you can calculate a, p and q (with the formulas we just found)
to change its form
now need to do 2nd part of your question
ionic terrace
*A quadratic function can always be written in the form ƒ(x) = a(x − p)2 + q, wh...
"where p and q represent the coordinates of the vertex."
floral fiber
ok
ionic terrace
did you understand the first part?
ionic terrace
🙂
That's pretty good, I think; might have to read it again, to make sure.
got the formulas for p and q?
floral fiber
uh, maybe
ionic terrace
p=? in terms of b, c, and d
ionic terrace
soo, we can find p now (from 2nd eq): p=c/-2b
p=c/-2b
ionic terrace
and...we finally get q: q=d-c^2/4b
q=d-c^2/4b
floral fiber
oh ye
ionic terrace
so we have the equation bx^2+cx+d.
and we wonder if the vertex has coordinates $\frac{c}{-2b}, d-\frac{c^2}{4b}$
how do we figure this out?
grizzled pagodaBOT
Wild123
floral fiber
idk put it in cas
ionic terrace
na, we need formula. probably from class
you should have formula to get vertex coordinates from bx^2+cx+d
floral fiber
dont u need the quadartic formula
ionic terrace
dont u need the quadartic formula
for the vertex? I dont think you need to find the roots with the quadratic formula.
How do you usually find the coords of vertex from the equation?
floral fiber
what is vertex even? is that the highest point
ionic terrace
so to speak. it's either highest point or lowest. depends if parabola is upwards or downwards
floral fiber
ohhh
floral fiber
i dont remember how to find the y coordinate
sorry i was reading literature in class
ionic terrace
np
first thing we do
is adapt the formula a little
since our quadratic is bx^2+cx+d instead of ax^2+bx+c
different letters
so instead of -b/2a we have...?
floral fiber
-c/2b
ionic terrace
**Wild123**
which is just like p we had
so, it looks so far like the answer to the question is 'yes'
now we have to check 2nd coordinate if it's like the q we calculated earlier. alright?
floral fiber
yes
ionic terrace
we have the point (-c\2b, ...) which is on the graph of quadratic bx^2+cx+d
to find the 2nd coordinate...we plug in the first, in place of "x".
ionic terrace
I don't think so. probably not
floral fiber
idk
floral fiber
why
ionic terrace
and whatever we get ... is 2nd coord
because the graph of the quadratic is made of points (x, value of quadratic in x)
floral fiber
so hypothethically if m was the x cord, then putting m in the equation would give us the y cordinate in that specific graph
ionic terrace
yes 🙂
floral fiber
broooo i dont wanna repeat another year but im so screwed
ionic terrace
and if j was the y coord, we'd have to solve "equation=j" and find x
ionic terrace
broooo i dont wanna repeat another year but im so screwed
I think you'll need to practice more, to make sure you do alright.
floral fiber
my task is to film a video of me explaining this
and to confirm if its true or not
i have 1 day left due to procrastination
ionic terrace
Sounds like you still have some time left. The solution doesn't take more than 1 page, I think.
floral fiber
so technically i dont need to understand this shit, ill just say what u said and ill get top grade right?
ionic terrace
I think you might be asked about what you did, and not understanding it will make it pretty hard to explain it on video?
floral fiber
also the vid has to last 10 mins
floral fiber
I think you might be asked about what you did, and not understanding it will mak...
hmm that is true
ionic terrace
also the vid has to last 10 mins
10 min just for that exercise?
floral fiber
no i have to explain 3 things, 1 hard, 1 middle and 1 easy. this was the hard one. i havent glanced at the other two yet. but i think am supposed to combine answer here with the other tasks
ionic terrace
Oh. then this one on 5 minutes might be ok.
Still, seems like you have to record yourself solving and explaining. need to understand it.
here's a rundown of what we did:
- we chose a random quadratic bx^2+cx+d, and set it equal to the form you had there, a(x-p)^2+q
- we found a, p and q, in terms of b, c, and d. since we could do it, all quadratics can be written in that form
- we compare the formulas we got p and q, to the one for vertex. we are careful that our quadratic is NOT ax^2+bx+c, so we adapt formula.
we didn't yet finish 3) 🙂 we are checking q
floral fiber
ok but finishing q will be hard i think
putting b/-2c as x seems like a lot of work
floral fiber
also, there are the tasks. i need to choose one from each thershold. we are currently doing K. i chose g and c as the other tassks, do u think they combine well with K?
floral fiber
we deduce it
how do we do that
ionic terrace
how do we do that
we put b/-2c as x in the quadratic 
ionic terrace
putting b/-2c as x seems like a lot of work
we do this
ionic terrace
are you allowed to do that at tests/in class?
ionic terrace
we'll practice without then
floral fiber
ok
ionic terrace
we'll solve the hard way 😛
ionic terrace
also, there are the tasks. i need to choose one from each thershold. we are cur...
is a) the first sentence,
b) starts with "there", and
c) starts at "the function ..."?
floral fiber
is a) the first sentence,
b) starts with "there", and
c) starts at "the functi...
here better photo from chat gpt
idk why i tried pasting it in onenote
its in norwegian so i got it translated
give me a second i need to use the restroom
ionic terrace
e) might be easier than g), as far as my experience goes
floral fiber
can u combine e with k tho`? i asked chat gpt for the best combination and it told me k, g, c
also i think G is untrue, according to chat gpt
ionic terrace
I am not 100% knowledgeable on asymptotes and rational functions. I don't have a solution in mind.
floral fiber
hmm ok
ionic terrace
e) is pretty straightforward, though.
floral fiber
which task in low thershold is good u think
ionic terrace
I don't know if you were taught that:
$a_{n+1}x^n+a_{n}x^{n-1}+...+a_1x+a_0=a_{n+1}(x-x_1)(x-x_2)...(x-x_n)$
grizzled pagodaBOT
Wild123
floral fiber
**Wild123**
no i dont know this
ionic terrace
oh...
floral fiber
or i probably learned it but i didnt pay attention maybe
math is just too hard and logical for me i think
i need to start doing it daily
ionic terrace
**Wild123**
I think this is just a)
ionic terrace
i need to start doing it daily
good idea. practice makes perfect.
ionic terrace
**Wild123**
yea this is basically "a)"
but it's not the proof; I am not sure how you're supposed to prove it, or why it's considered easy.
floral fiber
uhh idk
but i think i did good today, maybe ill do more tmrow. if i dont finish ill beg my teacher for an extension
thanks for helping with task K
ionic terrace
🙂 you're welcome
good luck with maths.
Don't give up; it might take some time to catch up.
But if you work on it, it's possible.
floral fiber
bro i want to become a dentist and i need good math for it. i dont think i can do it
chemistry and biology is fine for me
ionic terrace
those have a medium level of maths too
In chemistry, I remember we'd calculate lots of stuff
and have to remember some formulas
floral fiber
nooo
willow karma
In chemistry, I remember we'd calculate lots of stuff
true for physical chemistry but I doubt that's taught for dental courses
ionic terrace
besides chemical formulas, you'd have to calculate with mass or molecules
ionic terrace
true for physical chemistry but I doubt that's taught for dental courses
oh sorry, yes, I mean "lots" as far as my chemistry knowledge goes, middleschool + highschool.
Half of it was maths, the other was theoretical knowledge, how substances react etc.
I have no idea what they teach in dental courses; in my country though, you do have a chemistry exam to pass to enter, and it has some math in it (although I suppose it's nothing more than arithmetic)
floral fiber
I have no idea what they teach in dental courses; in my country though, you do h...
ill catch up with math, but its getting late now so imma go sleep. are u available tmrow?
ionic terrace
I don't know for sure; but I think someone else might help, if I cannot.
There's quite a few people here who'd gladly help, if they know how. 🙂
amber waspBOT
grizzled pagodaBOT
hearty inlet
i don't like the look of this
amber waspBOT
@severe vigil Has your question been resolved?
amber waspBOT
@severe vigil Has your question been resolved?
hollow wolf
.close
foggy nest
I forgot how to do this help pls
amber waspBOT
I forgot how to do this help pls
timid vector
or if u wanna be cool per 1 ml
mortal forum
Hello
foggy nest
I only know what the first one is
mortal forum
I forgot how to do this help pls
Convert all to liters
grizzled pagodaBOT
grizzled pagodaBOT
Result:
0.8
,calc 1.25/1.50
grizzled pagodaBOT
Result:
0.83333333333333
,calc 0.6/1.20
grizzled pagodaBOT
Result:
0.5
,calc 1.2/2.2
grizzled pagodaBOT
Result:
0.54545454545455
Ooooo
mortal forum
C) 600 ml bottle for $1.20
mellow hornet
you're dividing the wrong way bro
mortal forum
you're dividing the wrong way bro
No?
amber waspBOT
mellow hornet
Yes?
A) $1.25 per liter
B) $1.20 per liter
C) $2 per liter
D) $1.83 per liter
mortal forum
It’s 😌
mellow hornet
@foggy nest it ain't C buddy
foggy nest
Okay then
mellow hornet
ago did though
robust willow
Either way works if you interpret your solution correctly. The way Ago did it was calculating liters per dollar, where highest value is the most cost effective. The way Ari did it is calculating dollars per liter, where lowest value is the most cost effective
Neither solution path is "wrong", you just have to take care to interpret the solution you get correctly
mellow hornet
right
foggy nest
Thank you
amber waspBOT
Available help channel!
dusky moat
