hazy obsidian
Determine all $P \in \mathbb{R}[x]$ such that [ P(x)^2 + P(y)^2 + P(x+y)^2 = 2P(x^2+xy+y^2) ]
compact pewterBOT
Determine all $P \in \mathbb{R}[x]$ such that \[ P(x)^2 + P(y)^2 + P(x+y)^2 = 2P...
boreal girderBOT
Copter
hazy obsidian
i only got P is monic ;-;
compact pewterBOT
@hazy obsidian Has your question been resolved?
rotund sphinx
Determine all $P \in \mathbb{R}[x]$ such that \[ P(x)^2 + P(y)^2 + P(x+y)^2 = 2P...
I'm assuming you accounted for constant solutions separately. \
Note you can say that
$$x^{2n}+y^{2n}+\left(x+y\right)^{2n}=2\left(x^2+xy+y^2\right)^n$$
for all $x$, $y \in \mathbb{R}$ (why?)
boreal girderBOT
Civil Service Pigeon
compact pewterBOT
hazy obsidian
i think i got it
i think you also get P(x^2) +c = P(x)^2 and i think you can expand right
rotund sphinx
i think you also get P(x^2) +c = P(x)^2 and i think you can expand right
yeah you could also use that
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zealous radish
Between two rational numbers there's at least one irrational number
compact pewterBOT
Between two rational numbers there's at least one irrational number
zealous radish
And between two irrationals theres at least one rational
But it makes no sense to say they alternate
In fact "the next real number" is a nonsense phrase
I don't like it
Help
dense mason
And between two irrationals theres at least one rational
Between 2 irrational there at least 1 rational
still burrow
In fact "the next real number" is a nonsense phrase
its because there exist an infinite number of real numbers(both rational and irrational) between any 2 given distinct numbers
zealous radish
its because there exist an infinite number of real numbers(both rational and irr...
.close
compact pewterBOT
tranquil prawn
<:blobcry:971797574916907028> <:blobcry:971797574916907028>
i hope measure theory helps you some day
zealous radish
i hope measure theory helps you some day
violet magnet
Well the real set is dense
Density is one of its properties, yes.
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fleet flare
By "few terms" what does it mean?
compact pewterBOT
By "*few terms*" what does it mean?
fallow fractal
By "*few terms*" what does it mean?
the least amount of terms possible
sonic wyvern
no, the sum is then rewritten as another distinct sum of square roots.
fallow fractal
sonic wyvern
this new sum is the one whose term count is minimized.
sonic wyvern
correct.
sonic wyvern
what do you mean?
fleet flare
why does it rewrite the question as sqrt{a}+...? is it not the same as "the square roots of the integers from 1 to 10 are added together" not the same thing
sonic wyvern
no.
you can think of the first sum as the sq. roots of each integer from 1 to 10.
then someone tells you that they found another way to write the sum (as in, the final result) such that they are equal.
so instead of summing the square roots of 1 to 10, perhaps this person could achieve the sum in, say, 5 terms. or 7 terms. whichever it is, choose the new sum with the least number of terms.
then find out what integers were used in the square roots of this new sum.
sonic wyvern
this is all the question is asking you to do.
sonic wyvern
close but not quite.
I mean you have the correct idea, sure. nothing you wrote there is wrong according to the question.
but you're missing the fewest-terms condition.
fleet flare
yea i forgot to add that in b4 taking picture
realised after i had sent it
i assume,
we can simplify the original statement, to get 1+2+3+sqrt{2}+sqrt{3}+...+sqrt{10}
so, 6+...
and 6 can be written as sqrt{36}
so that gets rid of at least 3 terms
sonic wyvern
2 terms, not 3 (because you're reintroducing a sqrt(36) that was never there).
but that's one of the simplifications, yes.
sonic wyvern
there is only one more radical to simplify.
sonic wyvern
keep going.
sonic wyvern
right. keep going.
fleet flare
$(\sqrt{3})^2 (\sqrt{2}) \implies$ something
boreal girderBOT
･ﾟ✧ 𝓀ℬ ✧ﾟ･
fleet flare
lowk dont remember my radical rules
do they just multiply?
so, sqrt{3*2} ==> sqrt{6}?
sonic wyvern
yes, but you forgot the square on the 3.
sonic wyvern
well, how would you rewrite 3 as a square root?
fleet flare
sqrt(3^2)
sonic wyvern
proceed.
fleet flare
**･ﾟ✧ 𝓀ℬ ✧ﾟ･**
ah, so instead of this ^ ^, we do sqrt{3^2}sqrt{2} ==> sqrt{9*2} = sqrt{18}
so is there anything else we can simplify?
bc i honestly do not know
sonic wyvern
do you think there's anything else?
boreal girderBOT
･ﾟ✧ 𝓀ℬ ✧ﾟ･
sonic wyvern
that's a very fancy way of writing 10 = 2x5.
sonic wyvern
do you think so?
fleet flare
absolutely not
sonic wyvern
exactly.
fleet flare
i never learnt this / had a reason to know it so like...
sonic wyvern
in fact, you should have realized 10 is a no-go because 10 is squarefree (no repeated prime factors).
fleet flare
in fact, you should have realized 10 is a no-go because 10 is squarefree (no rep...
so in that case, would sqrt6 be reducible?
sonic wyvern
try it.
fleet flare
ah wait
only way it can be reduced is if it can be written in the form: sqrt{{a^2}*b}
i believe yea
sonic wyvern
in other words, a radicand is only reducible if it has at least one prime factor that has a multiplicity equal to or greater than the degree of the radical.
(which is a fancy way of saying that a number under a root of any degree can only be reduced if it has at least one prime factor that appears in its prime factorization at least as many times as the degree of the root.)
so a cube root would require that the radicand has 3 copies of a prime factor, for instance.
fleet flare
mhm, well what i got atm gives the ans
sonic wyvern
so proceed.
fleet flare
sonic wyvern
and you are done.
compact pewterBOT
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wind crown
Oi I'm taking this place
compact pewterBOT
Oi I'm taking this place
wind crown
So I'm having trouble reading Olympiad Books like Secrets in Inequalities by Pham Kim Hung where each lesson is like 2 pages of theory and the rest is just bloody problems.
This is especially difficult in this particular book where I am learning advanced AM-GM inequalities.
orchid vine
that theory is mainly for revision rather than concept clarity
wind crown
Unlike hard things like the Laplace Transform and the s-plane or whatever that is easy to visualise and stuff, this on the otherhand looks like it's from fucking never land.
wind crown
that theory is mainly for revision rather than concept clarity
Oh coulja reccomend me a book that does give me concept clarity on what the book I mentioned is trying to give for people who already have it?
solemn matrix
I think it depends on the curriculum
wind crown
My curicculum is whatever the fuck makes me understand this stuff.
The field is wide, you can gimme some reccomendations.
solemn matrix
Like in my country (prob where Phan Kim Hung) comes from, advanced math in secondary school learns inequalities like AM-GM first and didn't even learn graphs to solve inequalities
wind crown
Like in my country (prob where Phan Kim Hung) comes from, advanced math in secon...
Y'all probably memorised like 10-20 different forms and applied them like using integration tables in 'em grad school engineering lectures.
solemn matrix
Y'all probably memorised like 10-20 different forms and applied them like using ...
God damn i don't even understand a shit about inequalities apart from basic stuffs
wind crown
What I'm looking for is a full explaination as to what kind of bollocks logic people had to circus around in order to solve this shit.
solemn matrix
-# ngl where tf are a, b, c?
wind crown
-# ngl where tf are a, b, c?
Ay that's just a printing error.
Even that problem was not as bad, how the fuck do I do this one???
The book's available online for free you can view it yourself lad.
solemn matrix
Ngl i suck at those questions 😭😭😭
wind crown
Ngl i suck at those questions 😭😭😭
Damn, do you know someone that does?
wind crown
that theory is mainly for revision rather than concept clarity
Mate are ye there?
I need ya help!
violet magnet
AM-GM?
violet magnet
Then you can do it.
wind crown
Then you can do it.
Bollocks!
violet magnet
What?
wind crown
What?
Lad I don't know the first thing on how to approach 'em problems I just send before ye.
And not to mention it's the first bloody chapter in the book I'm following.
orchid vine
Mate are ye there?
ye
orchid vine
Lad I don't know the first thing on how to approach 'em problems I just send bef...
gimme a min
violet magnet
You can eliminate the denominators of each term on the left side.
orchid vine
ill brb
wind crown
You can eliminate the denominators of each term on the left side.
Sure but Imma be needing something more general.
Like as in the topic of AM-GM Inequalities as a whole.
'Cause covering every typa 'em inequalities gonna take forever.
orchid vine
so what you can do is look at some solved examples of AM-GM or smth
to get a hang of how qs are done
perhaps
wind crown
so what you can do is look at some solved examples of AM-GM or smth
So are you telling me there are only a limited amount of ways AM-GM inequalities exist?
orchid vine
no like what i meant is, just to get a hang of the concept
also for this q
lemme attempt
wind crown
Even then what are the basis of the thought process of going into these proofs?
Like is there some kind of graphical explaination where there is some kind of clear relatinship between two points so that I could figure out what that relationship is?
orchid vine
you build that by solving qs lol
orchid vine
you build that by solving qs lol
intuition
orchid vine
Like is there some kind of graphical explaination where there is some kind of cl...
oh
am-gm inequality?
wind crown
am-gm inequality?
I know how the inequality itself works graphically.
orchid vine
i dont have its graphical proof
wind crown
I am talking about the problems I am presenting here.
orchid vine
this 1 right
wind crown
Like how am I supposed to visualise or see it in a different light that would allow me to solve it besides some shallow trick like cancelling out stuff or something.
wind crown
this 1 right
Yeah sure.
Other than the xyz relationshiop, I don't see any other relationship in the question that makes sense to me.
wind crown
Sure I can piece together some kind of relationship where the denominators cancel out but that's where I get stuck lad.
orchid vine
this 1 right
from what i can see
x,y,z are symmetric
and substituting x = 1, y = 1, z = 1 balances the equation so we wanna prove that any deviation from 1 makes the sum greater
wind crown
and substituting x = 1, y = 1, z = 1 balances the equation so we wanna prove tha...
so plug in some values that make sense based on any other relation given in the question?
Okay that seems pretty good.
orchid vine
so plug in some values that make sense based on any other relation given in the ...
no no
i just mentioned
thats what we have to prove
wind crown
.close
compact pewterBOT
orchid vine
ye
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unborn chasm
A motorcycle rider weighs 60kg is coasting down a 24 degree slope the weight of motorcycle is 30kg at the top of slope the speed of bike is 3.2 if the kinetic friction force is 100N what will be speed of the bike 72m downhill
compact pewterBOT
A motorcycle rider weighs 60kg is coasting down a 24 degree slope the weight of ...
violet magnet
What have you done?
unborn chasm
What have you done?
I understood the q
still burrow
!status
compact pewterBOT
pulsar wagon
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
Having a prob with making components
violet magnet
You tried anything yet?
unborn chasm
Lemem send pic
unborn chasm
You tried anything yet?
Ye i made the fig as in q
violet magnet
Nice.
unborn chasm
violet magnet
You can just use work energy formula.
violet magnet
I don't think you need to, since they gave you friction force 100N already.
unborn chasm
I don't think you need to, since they gave you friction force 100N already.
Oh lemme see
unborn chasm
I don't think you need to, since they gave you friction force 100N already.
Nope i wont be able to find the work done
unborn chasm
The force of gravity that makes it go downhill i have to find that
unborn chasm
Recall the formula?
W = change in Ke
violet magnet
Great, what is it then?
unborn chasm
The force is kinetic frictional force which is acting opposite to the motion
violet magnet
$\frac{1}{2}mv^2_f - \frac{1}{2}mv^2_i$
boreal girderBOT
Mercury (ヤフォダ)
violet magnet
Familiar?
violet magnet
What is the mass here?
unborn chasm
What is the mass here?
90kg
violet magnet
Initial speed?
unborn chasm
3.2
violet magnet
Distance and slope angle?
unborn chasm
72m 24 degree
violet magnet
Great, now let's calculate gravitational force.
unborn chasm
Great, now let's calculate gravitational force.
Sure
violet magnet
Well what is the formula for it then?
violet magnet
Mgsin(theta).
unborn chasm
Mgsin(theta).
Ye this part i dont udnerstand i m having problem making components in diagrams
I can normally make them idk i am a bit confused here
violet magnet
You dont understand why multiply with sintheta?
unborn chasm
You dont understand why multiply with sintheta?
I do because thats the component acting grpahically along the slope
I have to show this grpahically as well so
I need to make a fig showing the components
Can u help me with that
violet magnet
Let just solve it first and draw later.
unborn chasm
Let just solve it first and draw later.
Alr
violet magnet
Then can you find gravitational force?
violet magnet
Great.
Now frictional force is 100N for uphill.
The one you just solved is downhill.
violet magnet
m = 90, g = 9.8, and sin 24?
unborn chasm
Ye
violet magnet
You multiply them together and get 20?
unborn chasm
358
violet magnet
Are you sure?
unborn chasm
Then sub the frictional force
violet magnet
Correct.
unborn chasm
Then multiply by 72 for work
violet magnet
What's next?
violet magnet
Well you want to find the net work.
unborn chasm
What's next?
Now making components graphically
On a simple cordinate plane its so easy here i am jst confused
violet magnet
I think you would need to draw the perpendicular component starting from the object and point vertically to the slope.
That's what I think of.
boreal girderBOT
sleek meadow
A motorcycle rider weighs 60kg is coasting down a 24 degree slope the weight of ...
-# forgive my english but 72m downhill means the length of the hypo of the incline right?
unborn chasm
-# forgive my english but 72m downhill means the length of the hypo of the incli...
Yes
The distance that biker covers from top to the end
sleek meadow
Thats wrong
unborn chasm
Thats wrong
Ye ig
So i jst realized there's a component of weight balancing the normal force as well
sleek meadow
you would need to resolve the vectors of the gravity by keeping the gravity as the hypotenuse
sleek meadow
So i jst realized there's a component of weight balancing the normal force as we...
Yeah but thats isnt reqd for ur Qsn
I read some of the earlier convo here
Applying conservation of energy is the right way to proecced
unborn chasm
So i have a problem eith drawing components graphically
Could you like maybe guide me here
On normal plane its easier here i am jst confused
sleek meadow
Keep the vector whoose components you are resolving as the hypotenuse
unborn chasm
Keep the vector whoose components you are resolving as the hypotenuse
Always?
sleek meadow
Yes
unborn chasm
Alr
sleek meadow
Always
sleek meadow
Here you made it seem like mg and mgsin are components of mgcos
sleek meadow
Yes
boreal girderBOT
unborn chasm
Now that is jst projected to slope?
solemn matrix
looks wrong to me?
unborn chasm
you made mg inclined?
Oops
sleek meadow
looks wrong to me?
-# how r u not helpful yet
solemn matrix
-# how r u not helpful yet
-# mods won't allow me to
boreal girderBOT
solemn matrix
but here your mg is one of your legs
sleek meadow
I thought of mg as hyp
doesnt look like so in the diagram tho
solemn matrix
you gotta determine it through the right angle
sleek meadow
also i dont even understand why we are resolving mg in the first place @unborn chasm ??
unborn chasm
also i dont even understand why we are resolving mg in the first place <@1377218...
Because net work done
Gotta find the component of g force qcting along slope
sleek meadow
Because net work done
oh you could do this way ig
unborn chasm
oh you could do this way ig
So whats the right way to make it
open plaza
do you know how to represent forces
sleek meadow
sleek meadow
Does this make sense?
Yeah nice
unborn chasm
Ye bro i tried tk make this
open plaza
do you know how to represent forces
you got the correct magnitudes
unborn chasm
Yup
unborn chasm
finally it has some KE say KEf
Yup
sleek meadow
there is energy loss due to moving down the incline by gravity and friction
so we can rewrite it as?
unborn chasm
Btw is it allowed that i choose other side as x comp?
sleek meadow
Btw is it allowed that i choose other side as x comp?
other side as in?
unborn chasm
so we can rewrite it as?
Loss in pe =gain in ke +fh?
sleek meadow
Loss in pe =gain in ke +fh?
yeah
unborn chasm
other side as in?
Like sin side as cos
sleek meadow
Like sin side as cos
nope that would mess it up
unborn chasm
How do you know which side is perp and base here
Is that bc of slop angle or is there sm other way to tell?
sleek meadow
I made the right angle triangle and then theta asw in it
you should be able to identify that
sleek meadow
aight then am js gonna go
unborn chasm
Sure
sleek meadow
Tho i still am not sure if this method is valid lmk if your ans matches
unborn chasm
Sure lemme try
unborn chasm
Tho i still am not sure if this method is valid lmk if your ans matches
Well then i need tk make components of distance
To find hieght
Answrr still same
.close
compact pewterBOT
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light raft
What do they mean by scaling factor, I don't understand this example
compact pewterBOT
What do they mean by scaling factor, I don't understand this example
still burrow
-# ok u can take this
strange spear
What do they mean by scaling factor, I don't understand this example
oh. the number you multiply by to get from kW to MW
light raft
oh. the number you multiply by to get from kW to MW
and that scaling factor is 1x10^3?
strange spear
and that scaling factor is 1x10^3?
yep
light raft
so if i want to convert something that is kW to MW, i multiply by 1x10^3?
strange spear
so if i want to convert something that is kW to MW, i multiply by 1x10^3?
err i made a mistake, it should be the other way around
from MW to kW
strange spear
multiply by 10^3 to convert from MW to kW right?
yes
compact pewterBOT
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wind crown
ay imma rent this place
compact pewterBOT
ay imma rent this place
wind crown
Guys how in the actual fuck do I solve this?
Whatever logic the author used sounds like a load of shit to me.
wind crown
Yes, AM-GM is helpful.
Yeah how?
violet magnet
Well look at the first line.
wind crown
Well look at the first line.
Sure the lad squared it, so what?
paper rune
Guys how in the actual fuck do I solve this?
.pin
compact pewterBOT
Guys how in the actual fuck do I solve this?
wind crown
.close
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light raft
where did they get the numbers for the bathtub for question c? there was no additonal info given
compact pewterBOT
where did they get the numbers for the bathtub for question c? there was no addi...
light raft
im just confused where they get 0.375 from and if i missed something
strange spear
where did they get the numbers for the bathtub for question c? there was no addi...
It should be mentioned somewhere else
strange spear
nope
Oh well that is an ass pull indeed
Ask the teacher
Cuz the bathroom size, if mentioned nowhere else, should not be guessed
solemn matrix
do we have to look up the ARCHITECTURE of every single bathtub to conclude this?
strange spear
do we have to look up the ARCHITECTURE of every single bathtub to conclude this?
Yes
Bathtubs can be of any size tbh
God knows what bathtub are they talking about
strange spear
where did they get the numbers for the bathtub for question c? there was no addi...
Wait, but
compact pewterBOT
rigid perch
it seems you are expected to remember from the top of your head the approximate dimensions of your bathtub (given the wide range of acceptable volumes)
strange spear
This was a stupid question I hope there aren't any more like this in the book
Ye kinda, but there is that section saying "if you got the calculations correct using any volume from 0.2 to 0.8 you get the mark"
Still rather stupid tho
light raft
Ye kinda, but there is that section saying "if you got the calculations correct ...
so the question expected me to guess or make up values?
strange spear
so the question expected me to guess or make up values?
Kinda
light raft
smh
strange spear
This shouldnt be a thing imo
strange spear
You should not be pulling values out of your ass while doing math
solemn matrix
so that's why this exists 😭
strange spear
so that's why this exists 😭
So you can use any reasonable value and it would still give you points
cerulean bramble
where did they get the numbers for the bathtub for question c? there was no addi...
It's a bathtub
You're being tested on your measurement/estimation skills; it suffices if you can roughly gauge its measurements [saying that a bathtub is 15m long for instance is blatantly wrong, so would be marked as such]
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Available help channel!
vale moat
compact pewterBOT
vale moat
not sure how to do part b
we know
sinxtanx = sinxtan(3x - pi/9)
sinx = 0, so x = pi
3x - pi/9 = x
2x = pi/9
x = pi/18
but there is also other solutions idk how to find them
compact pewterBOT
@vale moat Has your question been resolved?
vale moat
@latent lodge
strange ermine
3x - pi/9 = x
2x = pi/9
x = pi/18
Another possible solution is: 3x - π/9 = π + x
vale moat
Another possible solution is: 3x - π/9 = π + x
yeah i know there is another solution
but idk why
strange ermine
Because that's how you get equal values of tangent
In other words, how would you solve tan(x) = tan(π/5)?
tulip flower
facts
vale moat
In other words, how would you solve tan(x) = tan(π/5)?
x = pi / 5 ?
strange ermine
Only that?
strange ermine
Yeah but without taking the periodicity of 2π into account there's another possible solution
vale moat
x = pi / 5 + pi?
strange ermine
Yup
If you want, you can use the fact that tangent has a periodicity of π, not only 2π
strange ermine
Awesome, you're welcome 🤗
jagged stump
compact pewterBOT
jagged stump
help pls
fading flicker
consider switching y to the other side
drowsy lagoon
system of equations?
fading flicker
isolate y basically and express it in terms of x and substitute into the curve
jagged stump
idk i just need answer
fading flicker
idk i just need answer
!noans
compact pewterBOT
idk i just need answer
The purpose of this server is to help you learn; please don't ask for direct answers. Ask for guidance, explanations, or feedback instead.
jagged stump
The purpose of this server is to help you learn; please don't ask for direct ans...
k
fading flicker
oh wow I thought it was nosol
jagged stump
alr so
vapid yacht
yup and then did you find the intersection points?
vapid yacht
,w solve x^2 + 3(2x + 1) = 19
boreal girderBOT
vapid yacht
yeah great
jagged stump
perpendicular bisector:
vapid yacht
now find an equation for the line joining A and B
fading flicker
x = -8
x = 2
have you gotten the y-values yet
jagged stump
now find an equation for the line joining A and B
2x - y + 1 = 0
vapid yacht
what values of y did you have for the corresponding x values?
fading flicker
2x - y + 1 = 0
oh yeah lmao
jagged stump
what values of y did you have for the corresponding x values?
-15
5
vapid yacht
nice
fading flicker
2x - y + 1 = 0
the perpendicular bisector of line segment AB would be intersecting the midpoint of A and B with slope -1/slope of the initial line
vapid yacht
now we can find the equation of the perpendicular bisector
jagged stump
now we can find the equation of the perpendicular bisector
this correct?
fading flicker
x + 2y + 13 = 0
yeah
jagged stump
perfect now find where it intersects the x-axis
(-13, 0)
vapid yacht
Either you can use the formula
$$\frac{1}{2} |\vec{AB} \times \vec{AC}|$$
boreal girderBOT
Klein Bottle
vapid yacht
Either you can use the formula
$$\frac{1}{2} |\vec{AB} \times \vec{AC}|$$
or you can use the idea that they are perpendicular
so AB form the base
jagged stump
so AB form the base
is this typas math ez for u?
vapid yacht
and the perpendicular distance from the midpoint of AB and C is the height
fading flicker
**Klein Bottle**
where did vectors come in, it's a lot simpler than that
they can make a rectangle around the points and subtract the areas of the triangles around it
vapid yacht
is this typas math ez for u?
relatively yes
vapid yacht
~~where did vectors come in, it's a lot simpler than that~~
they can make a rect...
yeah or just directly use the fact that
1/2 * base * height
where base is AB and height is the distance between the midpoint and C
jagged stump
ABC = 125
fading flicker
yeah or just directly use the fact that
1/2 * base * height
where base is AB ...
why use distance formula when u have rectangles
vapid yacht
Sure mate . I suppose that could work too
jagged stump
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real hazel
@gritty kestrel
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real hazel
which mod foiled my plans
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naive phoenix
Can someone help me understand all this stuff for my Alg 1 Final: Factoring quadratics
Solving quadratics by factoring
Completing the square
Quadratic formula
Graphing parabolas
Difference of squares
Exponential functions
Exponential equations
Exponent rules
Negative exponents
Rational exponents & radicals
Function notation
Systems of equations
Linear + quadratic systems
Graphing systems
Finding intersections/solutions
compact pewterBOT
Can someone help me understand all this stuff for my Alg 1 Final: Factoring quad...
violet magnet
Start with first part.
What have you studied?
Any uncertain questions in that part?
naive phoenix
ummmmm... none i am so lost i kinda slept through the class
i get the idea but i gotta lock in
violet magnet
Okay.
naive phoenix
my biggest question is the Bottoms Up method for functions
naive phoenix
thats what my teacher called it
violet magnet
Would you mind explain it?
naive phoenix
factoring trinomials
also how to find a square root of a number because i got no idea
tall wadi
also how to find a square root of a number because i got no idea
to find sqrt of a number a, you just think what number squared gives you a
that’s really it lol
also not all numbers have whole number square roots
naive phoenix
i d k my multiplication tables so thats a struggle
tall wadi
well…you may have more to learn than just algebra 1 then
flint wing
Can someone help me understand all this stuff for my Alg 1 Final: Factoring quad...
I recommend going to khan academy for such a long list, it’s better than what anyone can teach you here through text and if you still have doubts you should open up a channel
naive phoenix
okay thanks
naive phoenix
well…you may have more to learn than just algebra 1 then
i am a history kid not a math kid
😭
tall wadi
no i get it
naive phoenix
i do have a b in the class tho
tall wadi
but still like id recommend going through what water beam said and then doing practice problems on khan academy
tall wadi
then if you have a question on those problems you can ask here
violet magnet
!done
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naive phoenix
.close
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hard quartz
help me ques 7.1 please
compact pewterBOT
help me ques 7.1 please
hard quartz
What is the approach to find M here
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tiny cove
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
i know that i have to compare with M , something bigger than the original then prov its convergent then the function is uniform convergent
rotund sphinx
I'd consider the absolute value
$$\left \lvert a_n (x) \right \rvert=\left(\frac{|x|}{x^2+4} \right)^n.$$
From this, $\left \lvert a_n(x) \right \rvert$ is maximised if and only if $\boxed{\text{what}}$ is maximised?
boreal girderBOT
Civil Service Pigeon
rotund sphinx
Hint: ||Note that n is at least 1||
hard quartz
i think x run from 0 to 1 . Bc |x|^n < x ^2n except range ( 0,1 )
rotund sphinx
i think x run from 0 to 1 . Bc |x|^n < x ^2n except range ( 0,1 )
I don't follow
My intention was for you to realise that it suffices to maximise $\frac{|x|}{x^2+4}$
boreal girderBOT
Civil Service Pigeon
rotund sphinx
since n being at least 1 means that t^n is an increasing function of t
rotund sphinx
**Civil Service Pigeon**
ig you can be lazy here and restrict x to be positive since this an even function
which means you can ignore the absolute value
I'm not sure if that's what you meant to say
hard quartz
do u mean x / x^2 +4 is the maximum ?
rotund sphinx
do u mean x / x^2 +4 is the maximum ?
Yes you can find $M$ by considering when $\frac{x}{x^2+4}$ is maximised
boreal girderBOT
Civil Service Pigeon
hard quartz
but i just found that how can we prove x/x^2+4 is convergent ?
hard quartz
so u are trying to say that x/x^2+4 is the maximum and for all x this will give us a exact number . so the sum of the function < sum ( exact nnumber ) ?
rotund sphinx
so u are trying to say that x/x^2+4 is the maximum and for all x this will give...
$\frac{x}{x^2+4} \leq M \implies \left(\frac{|x|}{x^2+4} \right)^n \leq M^n$ by monotonicity.
hard quartz
and the sum of exact number is divergent
boreal girderBOT
Civil Service Pigeon
hard quartz
im really sorry but i dont really know how to continue. i just know that x < |x| thats it and i dont know how to prove (|x|/x^2 +4 ) ^n convergent
< 1/x^n . and prove 1/x^n is convergent ?
so the function < sum of 1/x^n . and sum 1/x^n = x/x-1 -> convergent
then the function is convergent is this what u mean
i think i solved the problem.
Thanks for help me .
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@hard quartz Has your question been resolved?
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silver nest
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silver nest
can somebody explain this solution?
how can he affirm that without calculating the angle of incidence of these segments (AB and CD) betweens those parallels of the square
the center of rotation is E?
or can be any idk
silk steeple
It's saying if you rotate the square by 90 degree then AB is parallel to where CD is now.
since the line are parallel, and passing through the same sides of the square (after the rotation), they must be the same length.
silver nest
It's saying if you rotate the square by 90 degree then AB is parallel to where C...
yeah but how can he affirm that theyre gonna be parallel
silk steeple
because they meet at a right angle, and you're rotating it 90 degrees