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#help-39
midnight haven
How do I find answer to this??
pearl pondBOT
How do I find answer to this??
vital estuary
Divide by 2 on both sides and the rest should fall into place
solar gyro
Could someone plz help me w this?
pearl pondBOT
Could someone plz help me w this?
solar gyro
How would I calculate #8?
I’m also confused on #14
Aren’t I just supposed to have 7 mil/60(pi) of smth?
<@&286206848099549185>
regal herald
Aren’t I just supposed to have 7 mil/60(pi) of smth?
7mil/60pi?
regal herald
ah okay, so just 14
regal herald
the number of revolutions would be the distance divided by C
so yeah your process is alright, but mind your units
solar gyro
Why can’t I use cm?
regal herald
you can
solar gyro
So what’s wrong w what i have
regal herald
but is 70,000km 7 million cm?
solar gyro
Aren’t there 100,000 cm in 1 km?
regal herald
yeah
solar gyro
So wouldn’t I just multiply 70,000 by 100,000?
regal herald
yeah
solar gyro
I’m pretty sure that’s what I’ve been doing
But I still am not getting the right answerr
regal herald
,calc (7000000000)/(60pi)
jolly parrotBOT
Result:
3.7136153388109e+7
i assume theyve just rounded to the nearest million, you could round to 3sf and it would be fine
solar gyro
Got it
Thanks sm
Oh and also
I have another problem I’m stuck on if u don’t mind
The pool contractor question
solar gyro
I don’t think so
regal herald
you need the perimeter, my bad
solar gyro
So I don’t need to convert or anything?
regal herald
you can change the ft to inches first
solar gyro
Kk
One sec
I’m not getting the right answer tho @regal herald
The answer’s supposed to be 1399
regal herald
what are you getting?
solar gyro
But mine comes out to be 1152
regal herald
what calculations did you do
solar gyro
First 30 * 12 and 18 * 12
Then I multiplied what I got separately by 2
Then added all of them up
regal herald
Then I multiplied what I got separately by 2
wdym?
regal herald
you mean 2(30*12), 18 isnt a side of the pool
solar gyro
Oh wait
regal herald
you need the 30 sides + the circular walls
regal herald
its alright - the pools shape is a rectangle with 2 semicircles
the perimeter of that pool is the 30 sides of the rectangle + the curved edges at the ends
regal herald
im going to talk about it in ft since writing *12 every time will be a bit confusing
solar gyro
Kk
regal herald
i assume the 720 is 2(30*12)?
regal herald
okay, now you need the length of the curved edges
regal herald
why?
solar gyro
Is that not the length?
regal herald
nope, thats the diameter of the semicircles
each semicircle on the sides of the rectangle is half a circle of diameter 18ft
solar gyro
Right
regal herald
so you can get their combined perimeter by finding the circumference of such a circle with diameter 18ft
solar gyro
so you can get their combined perimeter by finding the circumference of such a c...
Is the circumference 216pi for both?
I converted to inches btw
regal herald
,calc 18*12
jolly parrotBOT
Result:
216
yeah
solar gyro
Yh
regal herald
thats for both of them combined
regal herald
Now that I have 720
so you can just add that onto this
solar gyro
How’s it for both of them combined?
regal herald
they are both half a circle of diameter 18, so put together they are just a circle of diameter 18
if there was only 1 semicircle and not 2, then we would just use half the diameter of a circle with diameter 18
regal herald
they are both half a circle of diameter 18, so put together they are just a circ...
but since there are 2 we dont need to and can just do this
regal herald
np
solar gyro
I have one last question if you’re still free
It’s #24, I have no idea how to approach it
@regal herald
pearl pondBOT
@solar gyro Has your question been resolved?
subtle inlet
pearl pondBOT
merry carbon
Do you know how to solve separable differential equations?
subtle inlet
yes but this one is weird
merry carbon
How so?
subtle inlet
because at the end if my calculations are correct I end up with P(0) = C
and then im not sure what to do for c)
merry carbon
Could you show what you've done then please? 
topaz terrace
omg its you
subtle inlet
do i just move the e^a with the other e
merry carbon
...well, for one, if you're exponentiating all of that, then you shouldn't be adding the separate logs together, as e^(a + b) is not e^a + e^b
it is however the case that e^(a + b) = e^a * e^b, maybe you meant that?
merry carbon
That isn't the case either no
subtle inlet
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pearl pondBOT
topaz terrace
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Available help channel!
rain saffron
When doing math for science, do you always need to convert to standard units before squaring and taking roots? For example if i have 4cm and i square that then i would have 16cm if i am not thinking about units
rain saffron
but in reality i would get an even smaller number
mighty citrus
If you're applying formulas, they probably require a certain unit
sour viper
I need help
pearl pondBOT
I need help
toxic lichen
what's the question
sour viper
14
toxic lichen
i can see the question is numbered 14 just fine
ok, so which part do you need help with
toxic lichen
i think the answer isn't expressed in linear centimeters.
ok, let's see what you got then.
sour viper
14
toxic lichen
your pi looks mutilated
sour viper
?
old geyser
It looks like 几
toxic lichen
the way you write pi
sour viper
So is the formula right
toxic lichen
it does not look like a pi to me at all
sour viper
it does not look like a pi to me at all
Sorry
toxic lichen
anyway, did you just calculate the surface area of a cylinder of the same dimensions?
sour viper
Yes
toxic lichen
notice that the question asks,
How much sheathing is needed to make the shell?
sour viper
I’m. It sure what I did id right
toxic lichen
there's two things you glossed over.
one is that the shell of the drum does NOT include the top and bottom,
and the other is that the drum is made from 5 layers of sheathing.
sour viper
14 137 cm squared
So what do,I do to get that
<@&286206848099549185>
What is the formula
toxic lichen
... okay so like first off my internet cut out for a bit
and second
think about it for at least a moment
you know how to find the lateral surface area of a cylinder
toxic lichen
pi, not pie.
sour viper
Ya
toxic lichen
okay, let's first make one thing sure
one is that the shell of the drum does NOT include the top and bottom,
and the other is that the drum is made from 5 layers of sheathing.
do you understand these two points
yes or no
toxic lichen
ok
well tell me now
if we cover the lateral surface of the drum
in 5 layers
how do we find out how much area we need for that
given we know the lateral surface area itself, ie the area of one layer...
sour viper
Pi d h
toxic lichen
we cover the lateral surface in FIVE LAYERS. do you know what this means
sour viper
Yes
sour viper
formula?
toxic lichen
if we know the area needed to cover 1 layer
how do we find the area needed for 5 layers
toxic lichen
yes!!!!!
toxic lichen
the shell of the drum does NOT include the top and bottom,
with no offense intended, are you reading what i am saying?
i'm repeating myself many times here.
toxic lichen
ugheurghuehteithjeh
"Which of 2πr^2 and 2πrh computes the top/bottom area and which computes the lateral surface area? I've only seen these referred to symbolically and don't understand the origin of either one, so I don't know which is which."
is this what you're asking?
toxic lichen
the top/bottom of a cylinder is two circles
sour viper
Yes
toxic lichen
the lateral surface is a rectangle of length 2πr and height h rolled around the cylinder
sour viper
So 2pir
toxic lichen
you are very hard to communicate with.
sour viper
Sorry
toxic lichen
you should tell which formula is which now. i've explained it in the clearest language possible.
and i've explained that you need to multiply it by 5 afterwards since we're doing the sheathing in 5 layers.
i don't know what else to do. all i can do is repeat myself and hope that it gets through at least once.
toxic lichen
you first say you're going to "show me", but then go ahead and ping all helpers on the server.
sounds kind of rude.
sour viper
Sorry
toxic lichen
,calc 2pi * 15 * 30 * 5
jolly parrotBOT
Result:
14137.166941154
i can see your 14365.5 which is presumably your answer
toxic lichen
i don't know, but based on the size of your error it's probably some rounding bullshit or arithmetic fuckup.
sour viper
,calc 2pi * 15 * 30 * 5
I got it wrong
toxic lichen
,calc 2pi * 15 * 30
jolly parrotBOT
Result:
2827.4333882308
where did 2873.1 come from?
sour viper
.close
faint eagle
Largest four digit number which when divided by 15 leaves a remainder of 12 and if the same number is divided by 8 it leaves the remainder 5. How can I approach this problem? I don’t need a solution, just the basic direction which I could go. I tried the division algorithm but I got nowhere
toxic lichen
do the words "Chinese remainder theorem" ring any bells to you
faint eagle
Hmmm I haven’t heard of it
faint eagle
Sometimes in the module I get from my school it has some topics that aren’t taught to us but I think this isn’t one of them. Rn I’ll just try with every number given in the options for the question if there is no alternative
faint eagle
Hmm
toxic lichen
okay so
you're looking for one particular solution of the system of congruences
x = 12 (mod 15)
x = 5 (mod 8)
faint eagle
That’s exactly what chat gpt said so I got confused and came here
toxic lichen
chatgpt...
what i suggest is: if we look at all solutions of this system, we'll find that they are in fact evenly spaced apart on the number line. namely that two adjacent solutions will differ by 120 (and more generally any two solutions will differ by a multiple of 120)
120 is 15*8
faint eagle
Mod is used for making things positive and in programming it’s used as % to get the remainder that’s all I know
toxic lichen
those are two different objects referred to by similar though not identical names
i am talking about the % kind of mod
not the |x| kind
faint eagle
what i suggest is: if we look at **all** solutions of this system, we'll find th...
Is that because LCM (15,8)=120?
vestal tapir
the positive thing is not called mod
toxic lichen
Is that because LCM (15,8)=120?
sure
faint eagle
the positive thing is not called mod
Yeah ik it’s modulus but sometimes people refer it as mod
toxic lichen
the positive thing is not called mod
modulus. in some languages it's identical to the word for modulo
i'd rather say the reason it works in the first place is because 15 and 8 are coprime, so their lcm is their product.
vestal tapir
i know, like in russian, but it doesn't happen in English
faint eagle
Ohh
toxic lichen
anyway, the key insight here is that the number -3 satisfies both congruences.
and so we now just need to find the biggest four digit number of the form -3+120n
faint eagle
Yeah but what are congruences
toxic lichen
$a \equiv b \pmod{m}$ is the statement that $a$ and $b$ have the same remainder when divided by $m$
jolly parrotBOT
Ann
toxic lichen
read as "a is congruent to b modulo m"
faint eagle
I see
There’s just 4 options so it’ll take lesser energy to get the answer like that. I just wanted to know if I was slowly dying cause of staying up or was it something I didn’t learn yet
It’s definitely something I haven’t learnt yet
I’ll ask my math teacher for a proper basic explanation tomorrow since it’s like 2:30 am rn
Thanks for the info tho now I know what to ask
.close
pearl pondBOT
pearl pondBOT
Available help channel!
visual arrow
pearl pondBOT
pearl pondBOT
@visual arrow Has your question been resolved?
karmic fern
,rotate -90
jolly parrotBOT
karmic fern
honestly I don't know what this is LOL
oh wait
you computed the standard deviation of the sample proportion, yeah?
and the expected value of the sample proportion is 45%?
so use that information to find P(0.35 < sample proportion < 0.5)
visual arrow
@karmic fern how do i do that though
pearl pondBOT
@visual arrow Has your question been resolved?
pearl pondBOT
@visual arrow Has your question been resolved?
forest dew
<@&286206848099549185>
ionic kestrel
Using what you've computed already you can convert the problem of calculating P(0.35 < sample proportion < 0.5) into a problem of calculating a probability with the standard normal distribution, at which point you need to either consult a table or use software to get a number out at the end
karmic fern
the sample proportion is N(0.45, 0.45(1-0.45)/229)
pearl pondBOT
@visual arrow Has your question been resolved?
jolly olive
Identify the quadrant in which θ lies if sin>θ and tan<=θ
pearl pondBOT
Identify the quadrant in which θ lies if sin>θ and tan<=θ
amber orbit
toxic lichen
Identify the quadrant in which θ lies if sin>θ and tan<=θ
are you sure you wrote those down correctly?
pearl pondBOT
@jolly olive Has your question been resolved?
jolly olive
are you sure you wrote those down correctly?
yeah i did mb, i ended up figuring it out anyways
pearl pondBOT
jolly olive
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pearl pondBOT
Available help channel!
midnight haven
how can i show that $c_1+c_2=kc_2-kc_1$ and $c_1e^{4k}=c_2$ only has the solution $c_1=c_2=0$ for all $k$?
jolly parrotBOT
collie
midnight haven
(where $k\neq0$ is real)
jolly parrotBOT
collie
midnight haven
i've tried using logarithms, hyperbolic funcs, and all sorts of algebra but I keep getting stuck
midnight haven
but i need to show this for all values of $k\neq0$
jolly parrotBOT
collie
glacial sequoia
$$c_2[e^{-4k}(k + 1) - (k - 1)] = 0$$
$$c_1[(k + 1) - e^{4k}(k - 1)] = 0$$
jolly parrotBOT
NEONPerseus
glacial sequoia
Did you end up with something like this?
glacial sequoia
**NEONPerseus**
Yeah this works I suppose
If you assume c1, c2 not to be 0
Then the other terms must be 0
And if you equate them and solve you see that the solution is independent of k
Is that satisfactory 
Multiple edits, forgive me
midnight haven
if the solution only contains k, does that mean there are no solutions for c1,c2?
glacial sequoia
And if you equate them and solve you see that the solution is independent of k
Well you get 0 = 0 which means it's true for all k
midnight haven
so you mean as in $e^{-4k}(k + 1) - (k - 1)=(k + 1) - e^{4k}(k - 1)$ gives $0=0$? (im currently working this out myself)
jolly parrotBOT
collie
glacial sequoia
Well technically but that's not what I did
I let each individual term be 0
And then I mutliplied the two
Which lead to 0 = 0
And I'm sorry I need to leave right now, I'll let someone else help you
midnight haven
algs thanks for the help
pearl pondBOT
@midnight haven Has your question been resolved?
modern monolith
Is the perimeter of this trapezium 46.87cm?
pearl pondBOT
Is the perimeter of this trapezium 46.87cm?
modern monolith
I got 46.87 but it says its 48?
inland ivy
how did you get 9.43?
modern monolith
I cut it up and did Pythagoras theorem to get the sides bc they don’t give it
Is that wrong?
Like this
modern monolith
Is the perimeter of this trapezium 46.87cm?
Because the overall base is 20, if i cut up the trapezium to make a triangle, im halving the half
Or is each side 20?
inland ivy
Because the overall base is 20, if i cut up the trapezium to make a triangle, im...
why are you halving the half?
the center part isn't half, it's 8 cm
you're halving (20-8)cm, which is the leftover part
modern monolith
Oh okay, so whenever u do Pythagoras theorem you minus base 1 from base 2 ?
This?
inland ivy
yes
that's correct
but I don't know why you've written 10 where it should be 6
,rccw
jolly parrotBOT
pearl pondBOT
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Available help channel!
ebon python
After finding the derivative using the definition of derivative, I checked my answer using the chain rule and got a different result. What did I overlook?
ebon python
<@1088497091157954563>
I’m terrible at geometry, so I can’t help.
ebon python
I found the issue. Thank you!
old marsh
No problem
ebon python
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pearl pondBOT
pearl pondBOT
Available help channel!
wind holly
Hi
wind holly
A- yes
B-yes
C-no
D-no
Would that be correct?
Please tag or mention me if u can help
pearl pondBOT
@wind holly Has your question been resolved?
midnight haven
pearl pondBOT
@wind holly Has your question been resolved?
midnight haven
pearl pondBOT
midnight haven
I'm not sure what to do
I've considered taking natural log after some rearranging
I've tried factoring
this is non calc btw
midnight haven
this looks like implicit differentiation
ah ok nvm then that's the next thing to cover
thanks
.close
pearl pondBOT
near echo
for future reference, calc usually means calculus and not calculator (in the context of these questions) @midnight haven
midnight haven
for future reference, calc usually means calculus and not calculator (in the con...
Ah my apologies then
pearl pondBOT
Available help channel!
sharp yoke
wth i want to ask but i cant upload picture
pearl pondBOT
wth i want to ask but i cant upload picture
sharp yoke
bro what
i cant upload the picture for some reason
let me type the question then
Let ABC an acute angled triangle, AD be the bisector of angle BAC with D on BC and BE be the altitude from B on AC. If angle CED > π/n, where n is a natural number then find the least value of n
<@&286206848099549185>
midnight haven
<@&286206848099549185>
autumn fossil
Let group be defined by following axioms:
- is the binary operation or whatever its called
a*b is element of the group for any a and b (closure)
a*a^(-1)=e (inverse)
a*e=a (identity)
(a*b)*c=a*(b*c) (associativity)
I am trying to prove:
a*e=e*a
Can I prove it as follows?
a*a*e*a=a*e*a*a
a*(a*e)*a=(a*e)*a*a
a*a*a=a*a*a
e=e which is true for any a
autumn fossil
the a*e was replaced with a because thats one of the axioms
and to get to e=e from a*a*a=a*a*a I just added few inverse a's
tropic saddle
pretty sure you either need a^-1*a=e or ea=a additionally
cause structures with just left/right inverses exist
autumn fossil
oh, at what step did my proof go wrong?
tropic saddle
not yet sure about that
autumn fossil
was it the assumption that if I can simplify it to e=e it will be correct?
tropic saddle
ah, multiplying by a from the left is not necessarily invertible
you cant do the steps backwards
ae=ea does imply e=e but not the other way
autumn fossil
oh
wheat onyx
Can Someone help me
tropic saddle
Can Someone help me
read #❓how-to-get-help
pearl pondBOT
Can Someone help me
Please read #❓how-to-get-help
tropic saddle
you need one additional axiom
I dont think the stuff you currently have does define a group
maybe you need both axioms additionally
autumn fossil
in video I watched it they said that it can be proved just from these axioms
the only different axiom was a*e=e*a=e (it was assumed at start and then they proved that left inverse = right inverse). But then they said that it can be also proved just by assuming a*e=e
snow suggested using (a^(-1))^(-1), I tried that but I still wasnt able to prove it
tropic saddle
ah indeed they are enough. there is a proof on wikipedia. but you need all axioms
autumn fossil
can you send link please?
tropic saddle
wikipedia group
if you wanna cheat
otherwise indeed use the hint from snow
e=a^-1 * (a^-1)^-1
autumn fossil
ohh
tropic saddle
and then work with that a bit
autumn fossil
Damn I am idiot, its actually one of the first thing I proved. I was trying too much to get it to the form a*a^(-1)=a^(-1)*a, and I didnt realize I just need to prove a^(-1)*a=e
thx denascite
.close
pearl pondBOT
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Available help channel!
timber zinc
wait i think i dont really understand this one
for example GCD(27, 16) = 1, how can ther be a r or s such that the sum of 27r +16s = 1?
timber zinc
it would make sense if it was lcm instead of gcd
oh wait the integers can be negative ?
oh yea
(r, s) = (3, -5) would work
.close
pearl pondBOT
frail hatch
what quantities do i multiply
<@&286206848099549185> i thought it was p12 pii+1 but it is not just that
pearl pondBOT
@frail hatch Has your question been resolved?
frail hatch
anyone?
alpine tangle
how do we know this is divergent
pearl pondBOT
how do we know this is divergent
alpine tangle
i tried ratio test and that was inconclusive
timid spindle
If a sum is convergent then the summand must tend to zero
So if the summand does not tend to zero then your sum does not converge
drowsy ingot
how do we know this is divergent
the absolute value of each term should be decreasing, not increasing
thats one of the rules for alternating series
alpine tangle
the absolute value of each term should be decreasing, not increasing
yea that's why i didn't apply alt series test because 3^sqrt(n) is increasing as n->inf
so if that rule fails and ratio/root test are inconclusive
does that mean it's divergent
pearl pondBOT
@alpine tangle Has your question been resolved?
cursive wraith
does that mean it's divergent
as people before said, since the general term of the series doesn't tend to zero, the series cannot be convergent
and when a series is not convergent, it is...
alpine tangle
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pearl pondBOT
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Available help channel!
covert sierra
why is there abs value next to the ln?
pearl pondBOT
why is there abs value next to the ln?
covert sierra
copper kestrel
because ln is not defined for negative values
pearl pondBOT
merry carbon
[and in particular, the original function is itself defined for negative values]
pearl pondBOT
Available help channel!
midnight haven
Something looks fishy here
pearl pondBOT
Something looks fishy here
midnight haven
The bars represent the percentage of each type of vehicle that had travelled over 200,000 km before breakdown
pearl pondBOT
@midnight haven Has your question been resolved?
midnight haven
looks fine
Should it not be like the percentage of vehicles of each type as a percentage of all the vehicles that last over 200,000km
Cause this is supposed to be a misleading graph
But then we’d have to consider the fact that there might be different number of cars of each type on the road in general
I got it thanks
.close
midnight haven
This is a released question from the 2017 Colombian High School Mathematics Olympiad. I was practicing but I don't know how I could start solving this problem
vital estuary
write each in polar form
pearl pondBOT
@midnight haven Has your question been resolved?
midnight haven
Sorry, I'm trying to do a little more. It's gonna take me few minutes
vital estuary
take your time
midnight haven
Maybe I could do something with the vertices and treating them like points in the complex plane and its conjugates, so that's why I chose the vertices in that way. I hope I didn't misunderstand the problem, and also hope there are 6^12 different ways to combine the vertices. I am not sure what should I do now if the above is correct
Assuming I wrote the problem correctly, there's something telling me that maybe I could take another complex number to represent the multiplication of z1z2z3... to rewrote it like |z1z2z3...| times [cosine(sum of "fixed" arguments) + i sine(sum of...)]? . I still don't know how to make the connection between some chosen vertices v1, v2, v3... and zj
zj = {v1, v2, v3, v4, v5, v6}
midnight haven
Yep, I'm stuck, I'm highlighting the message with the image just in case
midnight haven
This is a released question from the 2017 Colombian High School Mathematics Olym...
.
midnight haven
<@&286206848099549185> may I move this to help-forum? I feel this problem has some abstract thinking? So I don't have to ping you helpers a lot since now I feel that, maybe, I would probably need more help than usual with this problem
karmic fern
I think it's just a matter of making the magnitudes + angles match up
for example, you could probably use some combinatoric argument to make sure that the magnitudes match up
the first two vertices are the only ones that can increase the magnitude
the rest of them decrease it
as for the angles, I think this is basically making the rotations add up mod 6 or something
midnight haven
I don't get it with "mod"? This could be technically solved with the equivalent of 11° or 12° US high-school grade math topics. But I think I maybe get your idea? somehow add some constraints? (sum of angles add up in the negative x-axis (real) and then using some symmetry to match the angles below th
I think I can continue on my own now
.close
subtle monolith
Mathway says that the simplified form is y¹⁶/2x⁴
How did that happen?
subtle monolith
Original in the left
maiden hatch
You are doing it correctly, there is one more step though!
What happens if you divide 2x^12 / 4x^16?
subtle monolith
I thought you cant because they have different exponents?
toxic lichen
$x^{4^3} \neq (x^4)^3$ just saying
maiden hatch
Ah. Imagine the following: You have ( 2 * 4 ) / 2
jolly parrotBOT
Ann
maiden hatch
Yes it's x^(4*3) not x^4^3.
subtle monolith
Ah. Imagine the following: You have ( 2 * 4 ) / 2
The 2's would cancel out, and youd be left with 4 alone?
mossy canopy
(x^4)^3=x^(4×3)=x^12
x^(4^3)=x^32
maiden hatch
Mathway says that the simplified form is y¹⁶/2x⁴
How did that happen?
Your notation is wrong, but you still have the correct outcome. If that makes sense.
subtle monolith
The twos would cancel out, and youd be left with 4
Because Factor factor something
maiden hatch
Better understanding ?
I mean that doesn't highlight the above, Why he can divide by 4x^16
mossy current
Im not sure i just joined :3
maiden hatch
@subtle monolith Still confused why you can divide by 4x^16?
subtle monolith
Not anymore. Thanks
Now left with x¹²y¹⁶/2x¹⁶
If it's top exponent minus bottom exponent, id end up with an exponent of -4
maiden hatch
Yes, which is the answer.
subtle monolith
Well its positive 4. Not negative four. 12 - 16 is negative 4. Im kinda wondering how they end up with positive 4 but I got negative 4
maiden hatch
x^(-4) = 1/x^4
subtle monolith
Thanks. I also realized why its the right answer thanks to cancelling
Cancelling save lives
maiden hatch
Remember that you cannot simply cancel if you have (ab + b)/b 🙂
At least you cannot say that it equals 'a'
subtle monolith
Just a quick question, why is x^n*x^n =|= (x^n)²
pearl pondBOT
Just a quick question, why is x^n*x^n =|= (x^n)²
subtle monolith
According to mathway it simplifies to x^2n
midnight haven
Just a quick question, why is x^n*x^n =|= (x^n)²
Is this (x^n)*(x^n), x^(n(x^n)), or something else?
subtle monolith
Its problem no.4 currently I have 2x^n/(x^n)^2
subtle monolith
remember exponent laws
Ooh. What exact law was that?
meager flax
You'd be correct. Just a different way of expressing the same thing.
And you can google exponent laws to see them all. I dunno if they have specific names.
midnight haven
Its problem no.4 currently I have 2x^n/(x^n)^2
That is correct, you can now simplify it further
boreal crescent
A series Un with n≥0 is defined by Un = U[n/2]+U[n/3]+U[n/6] the bracket is the floor function show that for all integer n we have Un ≥n+1
boreal crescent
I don't know how to make strong induction on this
toxic lichen
U_0 through U_5 can be computed directly, i believe
kindred delta
I don't know how to make strong induction on this
try replacing [x] by x-{x}
toxic lichen
try replacing [x] by x-{x}
how is that going to help?
boreal crescent
Euh yes sorry with U_0 = 1 I forget to mention
toxic lichen
$U_0 = 1$ fails to satisfy $U_n = U_{\floor{n/2}} + U_{\floor{n/3}} + U_{\floor{n/6}}$
jolly parrotBOT
Ann
boreal crescent
? Why
boreal crescent
Euh yes with positive integer for all n in N*
toxic lichen
ok so the recurrence holds for n ≥ 1
i think computing the first few U_n manually is still a good idea
if only to get an idea of it
boreal crescent
Yes I already did that
toxic lichen
as far as strong induction goes, though, you need to prove $$\forall n \in \bN : n \geq 1 \implies \floor{n/2} + 1 + \floor{n/3} + 1 + \floor{n/6} + 1 \geq n+1$$
jolly parrotBOT
Ann
boreal crescent
Yes
toxic lichen
which reduces to $\floor{n/2} + \floor{n/3} + \floor{n/6} \geq n - 2$
jolly parrotBOT
Ann
boreal crescent
as far as strong induction goes, though, you need to prove $$\forall n \in \bN :...
Euh wait a sec sorry how Can you Say that we want to prove
How the +1 goes out of the floor function
toxic lichen
it does not "go out of the floor function"
i was imprecise about this but it would come from application of the inductive hypothesis
you would argue $$U_n = U_{\floor{n/2}} + U_{\floor{n/3}} + U_{\floor{n/6}} \overset{IH}{\geq} \floor{n/2} + 1 + \floor{n/3} + 1 + \floor{n/6} + 1 \overset?\geq n + 1$$
jolly parrotBOT
Ann
toxic lichen
where the IH is by the inductive hypothesis and the ? is your new goal
boreal crescent
I don't understand how the IH works here
toxic lichen
the inductive hypothesis is that the inequality U_k ≥ k+1 already holds for k strictly less than n
boreal crescent
Yes
toxic lichen
i am using it here, three times
toxic lichen
once for k = floor(n/2), once for k = floor(n/3) and once for k = floor(n/6)
boreal crescent
Yes
Yes true it's me dont know why I Said that
Ok I will try to conclude, I will come back
Ok so just do it for n mod 6 and see if it works for all ?
Like n=6k , n=6k+1,....n=6k+5
And if all are above it's true for all value of n
Sorry to bother but on the second part of the problem I have to find C superior to 0 in which Un≤C(n+1) but when I do your technique I found something like the previous inequality but inverse it's not ≥ but ≤
@toxic lichen
Dont think the technique works bcs [n/2] ≠n/2 or am I wrong
toxic lichen
Ok so just do it for n mod 6 and see if it works for all ?
i never involved n mod 6
was busy with irl shit sorry
boreal crescent
Np
pearl pondBOT
@boreal crescent Has your question been resolved?
pearl pondBOT
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Available help channel!
wicked flicker
can someone explain how this is true?
pearl pondBOT
can someone explain how this is true?
wicked flicker
or why anything has to do with this?
timid spindle
Did you try using the hint?
wicked flicker
I mean I dont understand how law of cosines have anything to do with this?
timid spindle
Well try applying it to that diagram
wicked flicker
I get y-x = sqrt(x^2 + y^2 - 2xycos(theta))
so if I solve for cos(theta)
I get (x-y)^2-x^2-y^2/-2xy
but this is not wut that says?
pearl pondBOT
@wicked flicker Has your question been resolved?
cedar salmon
I need help with solving rational equations
pearl pondBOT
I need help with solving rational equations
long herald
what's here you don't understand
cedar salmon
I’m not sure how to start it
I know I have to multiply the denominators with the numerators but does that mean I combine both denominators?
And multiply them to the numerator?
long herald
you essentially need to put numbers on 1 side and variables on the other side
and simplify
here you have +2 that can go first
and then do some changes so x goes above
cedar salmon
Huh?
pearl pondBOT
@cedar salmon Has your question been resolved?
undone glen
Can anyone help me in doing integration by parts here?
pearl pondBOT
Can anyone help me in doing integration by parts here?
pearl pondBOT
@undone glen Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
gusty prism
pearl pondBOT
autumn topaz
yes
gusty prism
thnx
pearl pondBOT
Available help channel!
zinc grove
pearl pondBOT
zinc grove
How did they get bIe to be 1/2 [...]? im a bit confused how to do this question. from my understanding, we can rref with an augmented matrix where B is on the left and v is on the right?
autumn topaz
looks like it is probably the inverse of the basis matrix
crystal folio
help
grand portal
Trying to create a tournament bracket. I understand the math for equal number of teams. Can't figure out how a 21 person team bracket works having 5 matches in round 1. Thanks
pearl pondBOT
Trying to create a tournament bracket. I understand the math for equal number of...
@grand portal Has your question been resolved?
grand portal
Looks to me anything past 16 teams an extra round is created. For example an 18 person tournament round 1 is 2 matches and round 2 is 8 matches.
pearl pondBOT
@grand portal Has your question been resolved?
random thorn
pearl pondBOT
midnight haven
x^2, y^2 are always nonnegative
midnight haven
i did some expansion like 4x²+9y²=72
you can deduce bounds for x and y from this expression
pearl pondBOT
@random thorn Has your question been resolved?
pearl pondBOT
random thorn
.reopen
pearl pondBOT
✅
midnight haven
eg, if $x=10$, then we have that $0\leq 9y^2=72-4x^2=-328$ which is impossible
jolly parrotBOT
Toby
random thorn
hmm
let me try
a few mins
but how can we know that both x and y are integers
we ought to find the integer xy
midnight haven
everything I said holds for x,y real
random thorn
there is a really great range for y²
4/9*(18-x²)
it doesnt have to be a perfect square
so just trial and error?
i found (+-3,+-2)
but how can we prove that there are no more solutions
okay i just thought about it for a bit
am gm inequality
yeah
(x²/9+y²/4)/2>=√x²y²/36
1>=|xy/6|
|xy|/6<=1
-6<=xy<=6
13 values
okay
.close
sand coyote
I need to use a definition of a limit to prove that it is the same answer
I have to show that this is valid by using this equation
pulsar lark
What is the C(q)?
sand coyote
Its just a saying for derivative
pulsar lark
Is the C(q) given or so you need to find the anti derivative of C'(q)?
sand coyote
everything is given Its just that i have to prove that C'(q)= 1/2square route of q using the definition of a limit
pulsar lark
What is the C(q) given?
sand coyote
its not given
pulsar lark
You plugged in C'(q) in the formula instead
sand coyote
oh i have to plug C(q)
How do i find the anti derivative
Like i know how to find the derivative
But
sand coyote
ohhh nvm
I just realised I did something wrong
Thanks anyways I found the C(q) it was hidden on the bottom of the page
C(q) = square route of q +2000
So like this right sorry my q looks like a 9
sand coyote
Can you send the original question?
does it make sense
pulsar lark
Seems good
sand coyote
I think its a multiplication by the conjugate right?
pulsar lark
Yeah
pearl pondBOT
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Available help channel!
slender glen
how do you know it's negative on LHS without even looking at the graph first?
slender glen
if anything from at x=0, it wouldnt be - or +, it would be neutral. or since its going from -infinity to 2. that means it increased going to 2. meaning +
thats how i see it anyway, would be cool if someone could help me understand this
pearl pondBOT
@slender glen Has your question been resolved?
pearl pondBOT
@slender glen Has your question been resolved?
slender glen
<@&286206848099549185>
long herald
sup
slender glen
help with this problem im having please
slender glen
how were they able to determine the "sign of f'(x)" bottom of that photo
for x=0 and x=3, without looking at a graph?
long herald
is the example refering to the function above?
long herald
you just plugin the value
it's basically a cubic root for x 0 it's gonna be a positive over a negative number
for x 3 it's gonna be positive over positive
slender glen
"positive over a negative number" " positive over positive" are you referring to the fraction?
long herald
yes after putting in x
basically it's a simple calculation you don't have to compute the cubic rute
root*
it's certain it's a negative fraction
long herald
it's a cubic root
if you plugin x=0
you have 3 times cubic root of negative 2
what number is multiplied 3 times to get negative 2?
a negative number for sure cause a positive can't give a Negative
and this negative number will stay negative after being multiplied by 3
2 divided by negative gives us a negative y value
for x=3 is just cubic root of 1
so it's a positive fraction
they should have just taken x=1 rather x=0
with -1 cubic root of -1 is just -1
@slender glen
slender glen
with -1 cubic root of -1 is just -1
^ this i mean
think u meant to type positive 1
or were u just trying to give me an example
long herald
no that's the example i took if they used x=1 instead of the given x=0
slender glen
of what cubicroot of negative number equals
long herald
cubic root of negative numbers exists for any negative number and the solution is always negative
slender glen
gotchu
long herald
the reason square roots don't have real solutions is because there's no way a number multiplied with itself gives negative
slender glen
ty
anyway, if there were two x's in that problem
then what would u do
would u still pllug in 0 and 3?
long herald
yes always
slender glen
like lets say its x/(x-1)
long herald
you can't just guess
slender glen
then what
long herald
just plugin the values
slender glen
at 0 you get 0
at 3 you get 3/2
so does that mean at 0, it doesnt exist
the critical value/min/max
but at 3, it does, and its 3/2?
long herald
in your case problem acknowledges the unallowed value and it says we study what happens left and right of this point
in your example now it's a complete different problem so you would have a new different table
of left and rights
long herald
it is cause you have 2 unallowed values not just 1
slender glen
oh makes sense?
so lets not use 0 and 3
my bad
lets use
their respected
values
1 and 0
at y'(X) = 0 , x=0 and x=1
long herald
also I can't think of a function that's it's derivative would be x/x-1 it's a stretch but even if we take it for granted
we are looking at a graph that would require a bit more than just two values on the table
slender glen
ok then give me an example then
were there is 2 x's
a fraction
the point of this is to find out "sign of f'(x)" (bottom of the photo) for a different example, with an extra variable
long herald
for your example
if we integrate
this would be the primitive
we can clearly see
a straight line at 0
since the graph is going up and then down after 0
and at x 1
goes down and then up but more rapidly
long herald
king frank
basically derivative f'x shows us the rate of change of a function right?
long herald
and if f'x is equal to 0 at a certain point, the original graph behaves as a straight line or a constant
and if the limit of f'x is infinity (in the case of a number over 0)
it means the rate of change is infinite or the graph appears to go straight vertically
in both cases we can determine how the graph behaves without drawing it
is it going up and down
meaning is it reaching a max or a min
and when the rate is infinite are we heading towards+inf or -inf
in the case you create where f'x is x/x-1
for x being 0 we have f'x 0
for x being 1 we have limit of f'x is infinity
and it's clear that on the fx graph i integrated
it shows both points 0 and 1
first one the rate of change at 0 is 0 and second at 1 the rate of change is infinite
the graph cut the line btw the line heading downwards goes to negative infinity
@slender glen aight I'm heading to sleep read what i said and tomorrow i can answer more questions
pearl pondBOT
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pulsar lark
Linear transformation - Draw a figure to show how the two basis vectors, e_x [1, 0] and e_y [0 1 ] are mapped by the given matrix A.
A = [1 0
0 1 ]
For this I multiplied each of the the vectors by A, like Ae_x and Ae_y and plotted the result vectors. Is that what I am supposed to do?
pearl pondBOT
Linear transformation - Draw a figure to show how the two basis vectors, **e_x**...
@pulsar lark Has your question been resolved?
pulsar lark
.close
gusty prism
