Find 55% of 15804
#help-33
copper comet
delicate sphinx
u cant do it?
copper comet
i tried it on the calculator and it only had 1 dp
so im guessing there is a metod for big numbers aswell?
copper comet
💀
delicate sphinx
:))
copper comet
i see
delicate sphinx
u dont know the rules of if a number is divisble by 2,3,4,5,6,7,8,9...?
delicate sphinx
do it
really useful
yea so devide 15804 by 4 and devide 20 by 4
gonna be
11/5 times 3951
delicate sphinx
ye
copper comet
11/5 times 3951
so its basically just lots of simplfying
copper comet
my teacher does it on the board normally super fast and doesnt even explain how he does them
delicate sphinx
not sure if anyone can do 11/5 times 3951 "fast"
copper comet
not sure if anyone can do 11/5 times 3951 "fast"
cant u do 11x 3951 and divide by 5?
copper comet
3/8 to a decimal
delicate sphinx
.375
delicate sphinx
2 ways really
devide is normally
how u would like
45/5
or
u can remember that
1000/8 = 125 so 1/8 equals .125
.125 times 3 is .375
do u know how to devide 2 numbers?
copper comet
wdym
copper comet
yea thats the same as 8/10 which is .8
delicate sphinx
but u cant really get 3/8 to a x/10
copper comet
but im not sure if using that process will get me full marks
copper comet
cant explain it on discord
the things you wrote above is gonna help me
copper comet
how u can dvide
in brain or with paper
delicate sphinx
paper
delicate sphinx
ight
copper comet
is ur main language english?
no its my second
Tho ive been in an english country for about 10 years
delicate sphinx
ok so
if a problem is
express 2 as a precentage of 4
the answer is 50%
express is just
write
or
state
idk
its just a word
not much to it
copper comet
So basically just write the answer
delicate sphinx
basically
copper comet
i see
that word puts me off
It makes me think it tells me to write it as an equation
delicate sphinx
if u wanna find what precentage x is of y u gotta devide x by y and multiply it by 100%
copper comet
if u wanna find what precentage x is of y u gotta devide x by y and multiply it ...
100%?
delicate sphinx
100
delicate sphinx
and then put a % symbol
thats how i was taught
100% is just multiply by 100 and put a % symbol
like
2 of 4 is 2/4 times 100% is 50%
copper comet
you too
delicate sphinx
make sure to close the channel
delicate sphinx
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hot kestrel
question -
if x^4 - 3x^3 + 2x^2 + ax + b = 0 has a multiple root at x=1, find the values of a and b
marsh citrusBOT
question -
if x^4 - 3x^3 + 2x^2 + ax + b = 0 has a multiple root at x=1, find t...
dark scaffold
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marsh citrusBOT
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
dark scaffold
what progress did you make?
hot kestrel
subbed x=1 in coz (x-1) is a factor
so i have a+b = 0
dont know what to do from here
dark scaffold
fair, (x-1)^2 is also a factor though
so you should be able to get more info from that
hot kestrel
i dont know how im gonna portray that tho
like
how do i construct the equation so that
delicate sphinx
what does has a multiple root at x=1 even mean?
hot kestrel
(x-1)^2 is there
hot kestrel
what does has a multiple root at x=1 even mean?
like
(x-1)^n is a factor
i want to find n and then i solve for a and b
hot kestrel
ight ill try
stoic slate
You cannot divide by 0
dark scaffold
are you talking to me
stoic slate
But anyways, why dont u derivate
hot kestrel
But anyways, why dont u derivate
the topic is abt derivatives but i am gettign somewhere with the suggestion she put up
stoic slate
And get p(1) and p’(1)
hot kestrel
ok ill try
OH
I GET IT
so now i have my derivative
its just a now
and i can just sub 1 anyway right
stoic slate
And u get a systen of 2 equations
dark scaffold
(x^4 - 3x^3 + 2x^2 + ax + b)/(x-1) also needs to have a root at 1
this also works btw
hot kestrel
yeah i was gettign somewhere
but the lesson was abt derivatives
i think i shouldve mentioned that
sorry
stoic slate
It works i agree but this is too straight to solve
hot kestrel
yeah
well anyway i have a=1 and b=-1
which is correct by the answers
thanks
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sour plank
how do i solve this?
marsh citrusBOT
how do i solve this?
exotic salmon
Use completing the square method.
sour plank
after that what do I do?
exotic salmon
Then the value inside the square term will lead to minimum y value.
Did you do completing the square ?
sour plank
should equal to -(2(x+5/4)^2-33/8)
i was thinking abt setting -2x^2-5x+1>0 then find x range
past frigate
Are you allowed to use differentiation?
exotic salmon
should equal to -(2(x+5/4)^2-33/8)
Yeah now this term is minimum when x= -5/4.
sour plank
Are you allowed to use differentiation?
yep
exotic salmon
Are you allowed to use differentiation?
Dude why ?
sand fable
differentiation on this problem is waste of time xd
sour plank
differentiation on this problem is waste of time xd
how so?
sour plank
Yeah now this term is minimum when x= -5/4.
aight thx
past frigate
Yeah now this term is minimum when x= -5/4.
Doesn't it need to be maximum so that y becomes minimum?
sour plank
Yeah now this term is minimum when x= -5/4.
now i have the min for x but what abt y?
exotic salmon
now i have the min for x but what abt y?
Just put x = -5/4 in your simpified equation and you'll get y
sour plank
Doesn't it need to be maximum so that y becomes minimum?
Aahh so i gotta find max of -2x^2-5x+1 that's >0?
sour plank
Just put x = -5/4 in your simpified equation and you'll get y
aight gimme a sec
exotic salmon
Doesn't it need to be maximum so that y becomes minimum?
Yeah we are anyways finding y. So it doesnt matter if x is at minimum or maximum.
sour plank
Yeah we are anyways finding y. So it doesnt matter if x is at minimum or maximum...
just make sure the whole thing in square root is at max right?
if im subbing -5/4 it should be 10-sqrt(33/8)
doesnt seems right tho
exotic salmon
Yeah that is the answer.
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eternal scaffold
given the points (0,2)(1,5) and (-1,1) find the equation of the cubic and graph the equation
marsh citrusBOT
given the points (0,2)(1,5) and (-1,1) find the equation of the cubic and graph ...
eternal scaffold
is this even possible?
I tried to use system of equations but it comes up as contradictory
since i got ax^3 +bx^2 +cx +2 =y, then substitutes to get b=1, but then i got a+c=2 and a+c=1 which is contradictory
vernal forge
how did you get b=1?
eternal scaffold
i made a+b+c=3 and b-a-c=-1 equal
uh
by rearranging a=3-b-c
and then equating a
vernal forge
i made a+b+c=3 and b-a-c=-1 equal
they are are not equal?
vernal forge
uhh
vernal forge
given the points (0,2)(1,5) and (-1,1) find the equation of the cubic and graph ...
!original
marsh citrusBOT
given the points (0,2)(1,5) and (-1,1) find the equation of the cubic and graph ...
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.
vernal forge
for three points, you can get at most one quadratic but infinitely many cubics
vernal forge
in general for n points you can interpolate using an n-1 degree polynomial
eternal scaffold
tru
vernal forge
but it won't be a cubic
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oblique oar
Hi i am really struggling with this. from my understanding, z+i/z-3i will be an element of real numbers only if the Imaginary part of z+i/z-3i is 0
marsh citrusBOT
Hi i am really struggling with this. from my understanding, z+i/z-3i will be an ...
past frigate
Assume z=x+iy
You can multiply top and bottom with the conjugate of the denominator and then proceed
oblique oar
thank you let me try this
oblique oar
You can multiply top and bottom with the conjugate of the denominator and then p...
Thank you i got the right answer. out of curiosity, this is how the answer scheme does it. can u explain what it does? thank you
okay nvm. i get what it does
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oblique oar
why do they say exclude Z = 2 at the end? Z = 2 anyways does not lie on the circle, so why would it matter?
indigo jungle
what are like terms in algebra
worn plank
wdym it does not lie on the circle
z = 2 + 0i
(2-3/4)^2 + 0 = (8/4 - 3 /4)^2 = (5/4)^2 = 25/16
worn plank
it could be shown explicity at step 2.
a/b + c/d = (ad+bc)/bd is only valid when you are not dividing by 0 (when neither b and d are 0, in this case b = d)
==> iz - 2i != 0
then you don't have to check for that later
marsh citrusBOT
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oblique oar
a/b + c/d = (ad+bc)/bd is only valid when you are not dividing by 0 (when neithe...
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lilac siren
huh
urban shard
lilac siren
kk
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humble raft
What must be added to 4x^2 - 4x to make it a perfect square? I don’t understand this question exactly but I was told to use completing the square, using completing the square I get x^2-1-(1/2)^2
marsh citrusBOT
What must be added to 4x^2 - 4x to make it a perfect square? I don’t understand ...
humble raft
Does that make (-1/2)^2 the perfect square?
still temple
4
humble raft
Huh?
humble raft
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vital oracle
What must be added to 4x^2 - 4x to make it a perfect square? I don’t understand ...
is that supposed to be 4x^2 - 4 or 4x^2 - 4x?
dawn nova
Hey pls i'm new in this server can someone help me to solve a limit
dawn nova
vital oracle
thats right
now theres a few ways you can do this
do you remember any ways of doing this in school?
humble raft
Completing the square?
vital oracle
@dawn nova get your own channel instead of speaking in someone else's
vital oracle
Completing the square?
do you know what completing the square means?
dawn nova
Oh sorry
humble raft
do you know what completing the square means?
Not really I just know the process
dawn nova
<@1213479253954400280> get your own channel instead of speaking in someone else'...
I'm new i don't know how
Really sorry
vital oracle
I'm new i don't know how
here's a hint:
the channel that says "how-to-get-help" will tell you how to get help
dawn nova
Thanks
vital oracle
Not really I just know the process
thats a good distinction youre making there
lets start with what a square should look like
(a - b)^2 = a^2 - 2ab + b^2, right
humble raft
Yes
vital oracle
now lets try to match up what we're seeing with the square formula
a^2 - 2ab + b^2
4x^2 - 4x + ????
humble raft
We’re missing the b^2?
vital oracle
yea, its not there
if we want a square, we'll need to add one in
your question wants to figure out what must be added to complete this square
humble raft
I see
vital oracle
now lets try to identify what we're looking at
first, the a^2 matches up with the 4x^2
what do you think a would be?
humble raft
4
vital oracle
4^2 is 16
so a cant be 4
remember, a^2 must be 4x^2
as a hint, 4x^2 is 2^2 x^2 or (2x)^2
can you tell that 4x^2 is the same thing as 2^2 x^2?
vital oracle
so what should a be?
@humble raft wait let me ask something else first
can you tell that 2²x² is the same as (2x)²?
vital oracle
alr making sure
humble raft
so what should a be?
2
vital oracle
a² = 4
so not it
shouldnt this a have an x in it?
because a² = 4x²
its not just a² = 4 or anything
humble raft
So 2x
vital oracle
thats correct
a² - 2ab + b²
4x² - 4x + ???
a = 2x
now knowing a is 2x, we can fill that in
a² - 2ab + b² should then be (2x)² - 2(2x)b + b²
we made sure the a² matches, so thats 4x² from before
the middle term -2(2x)b is now -4bx
humble raft
Okayy
vital oracle
we know this matches up with -4x
so what should b be?
(you need that -4bx is the same as -4x)
humble raft
1
vital oracle
thats correct
now since weve seen the a and b, we can now see what the square should look like
a² - 2ab + b²
4x² - 4x + 1²
4x² - 4x + 1
so compared to the original 4x² - 4x, what completes the square is a 1
humble raft
Oh so that’s pretty much it?
vital oracle
hold on there
Im not done yet
dont get too excited
you can prove that it should be a square beacuse
a² - 2ab + b² = (a - b)²
so (2x)² - 2(2x)(1) + (1)² = ((2x) - (1))²
so 4x² - 4x + 1 = (2x - 1)², a perfect square
so starting from 4x² - 4x, adding 1 will complete the square to be (2x - 1)²
vital oracle
I can just compare
you could do that but theres a faster way now that you know whats happening
to figure this out, lets modify the formula slightly to be more convenient
a² - 2ab + b² = (a - b)²
(ax)² - 2(ax)b + b² = (ax - b)²
a² x² - 2ab x + b² = (ax - b)²
then an additional change
I divide both sides by a²
x² - 2 b/a x + b²/a² = (ax - b)²/a²
x² - 2 b/a x + (b/a)² = ((ax - b)/a)²
x² - 2 b/a x + (b/a)² = (x - b/a)²
now heres the important thing to notice
if you have x² - 6x + 4 for example,
you can match -6 with -2 b/a
then get b/a = 3
so (b/a)² = 9
paying close attention, this is why you take the middle term, divide by 2, then square
it follows the same steps youd do to complete the square by matching
x² - 6x + 4
do 6 / 2 = 3, 3² = 9
x² - 6x + 9 - 5
(x - 3)² - 5
humble raft
so (b/a)² = 9
So here 9 is what’s going to make it the perfect square ?
vital oracle
yea
and if the 4 is already there, you still need a 9 anyways
so 4 = 9 - 5
and then use the 9 part of it
humble raft
But when I used this same approach or tried to use it for 4x^2-4x I was left with x^2 - x + (-1/2)^2
vital oracle
thats the problem here
look closer at what I did
I divided by a²
now I forgot to say but then that means your answer is now a² times smaller than it should be
so youll need to multiply it back in afterwards
if you multiply that by 4, you get back 4x² - 4x + 1
let me rewrite what I said:
humble raft
so youll need to multiply it back in afterwards
Oh
So you always have to multiply back after doing that?
vital oracle
you were treating x^2 - x + (-1/2)^2 the same thing as 4x^2 - 4x + 1
theyre not the same because you divided by 4
for that, you can see a reason to multiply it by 4
the equations are still equal but it only gets you a close answer, not the final answer
youre getting that final answer from multiplying by 4
humble raft
I thought you always had to have your leading coefficient as one hence why I divided
humble raft
Okay
vital oracle
(ax)² - 2(ax)b + b² = (ax - b)²
= a² x² - 2ab x + b² = (ax - b)²
= a² (x² - 2 b/a x + b²/a²) = a² (ax - b)²/a²
= a² (x² - 2 b/a x + (b/a)²) = a² ((ax - b)/a)²
= a² (x² - 2 b/a x + (b/a)²) = a² (x - b/a)²
so if you want the same expression as before, you get that a² x² - 2ab x + b² is the same as a² (x² - 2 b/a x + (b/a)²)
this is similar to going: 4x² - 4x + 1 is the same as 4 (x² - x + 1/4)
the result you get at the end is similar
instead of 4x² - 4x + 1 being (2x - 1)², you have 4 (x² - x + 1/4) being 4 (x - 1/2)²
the proof shows how you can transform either side to look like the new 4() versions
inside of those 4()s, you have one as your leading coefficient and you can do the /2 ^2
do you see that?
humble raft
Yea I do
vital oracle
very good
now theres two catches you may not have noticed
first off, usually you dont want to change what you have, only change how it looks
so adding 1 to 4x² - 4x will change it because then it will be 1 higher than it originally was
you fix this by doing + 1 - 1 instead of just + 1
4x² - 4x
4x² - 4x + 1 - 1
(2x - 1)² - 1
so 4x² - 4x is equal in value to (2x - 1)² - 1
you can see its equal to being slightly less than a square
vital oracle
yea
thats good that youre noticing that
now for the second catch
lets say youre solving
4x² - 4x + 1 = 0
now here, youre solving for x,
so you dont really need to preserve the expression as much
you still can only do algebra rules so that you still know that 4x² - 4x + 1 is equal in value to 0
but that doesnt stop you from say
dividing both sides by 4
x² - x + 1/4 = 0/4 = 0
x² - x + 1/4 = 0
so the reason you can divide by 4 is because youre in an equation where you only care about finding a correct value for x, not a correct value for 4x² - 4x + 1
(the equation tells you that 4x² - 4x + 1 is equal in value to 0 anyways, and 0/4 is still 0)
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still temple
Segment MN is the midline of triangle ABC. Line MD intersects the continuation of side AC at point D, and side BC at point E (see figure).
1.What fraction of the area of triangle ABC is the area of quadrilateral AMNC?
2. Prove that Triangle MNE ~ triangle DCE.
marsh citrusBOT
Segment MN is the midline of triangle ABC. Line MD intersects the continuation o...
still temple
I know that AC = 2 * MN
sick trellis
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simple quiver
marsh citrusBOT
simple quiver
Need help got similar solution for x and y but there not exact
I did it by hand and calculator and got the same things
For the first one I got 3.66666877 and for the second one I got 3.66666667
<@&286206848099549185>
<@&286206848099549185>
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stark trail
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light swift
marsh citrusBOT
light swift
heep plz
I did this
I assume solution means when y = 0 ?
and doesnt y = 0 only if x = 0 so all are false?
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light swift
@sharp wing
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pale blade
Math question I need help with : What is the expected length of the shortest segment formed when n points are dropped randomly uniformly in the interval [0,1]? The answer is supposed to be 1/(n+1)^2. There is supposed to be some slick way being able to find this using only expectation but can't make progress?
Any hint would be highly appreciated
he average length of any segment would be 1/(n+1) but the smallest segment would take on a value less than that always, so it's average values has to be smaller as well.
Also, I was hoping if the argument of Yuval Filmus in this stackexchange post could be extended https://math.stackexchange.com/questions/13959/if-a-1-meter-rope-is-cut-at-two-uniformly-randomly-chosen-points-what-is-the-av
marsh citrusBOT
Math question I need help with : What is the expected length of the shortest seg...
pale blade
<@&286206848099549185>
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cunning scaffold
molten moss
love the negative expectation value for the length of the segment thanks chatgpt
cunning scaffold
(i dont understand shit here)
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molten moss
I'M GETTING SOMEWHERE DON'T GIVE UP SKELETON
Am I just reinventing the beta distribution
molten moss
I'm starting to feel like every rigorous proof of this uses complicated stuff like the beta-distribution somewhere along the way
@pale blade I find it hard to imagine that you're going to find a slicker proof than something like this: https://math.stackexchange.com/a/724384/79482 (for finding the minimum rather than the maximum replace the boundary coordinates in this proof by $(0,\dots,0), (0,\dots,0,1/2,1/2),\dots, (1/n,\dots,1/n)$; to be rigorous, in this answer, the proof that the center of mass of this piece equals the average of the coordinates still uses complicated calculations about the gamma/beta functions, see https://www.geometrictools.com/Documentation/CentersOfSimplex.pdf
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Lartomato
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molten moss
I would be positively surprised if there was a way to skip that, but it just feels like this question is so intrinsically related to calculating the mean of order statistics, which just require tough calculations like this? Man...
vagrant gull
(i dont understand shit here)
!nogpt
marsh citrusBOT
(i dont understand shit here)
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).
fleet mauve
Are both of these indefinite integral result equivalent? What's the connection between the tangent inverse and the secant inverse
marsh citrusBOT
Are both of these indefinite integral result equivalent? What's the connection b...
sand fable
Are both of these indefinite integral result equivalent? What's the connection b...
draw out a right triangle or smth
will become quite clear why for positive x we have those two expressions as equal
fleet mauve
Like this?
fleet mauve
I can't find the connection..
sand fable
take that bottom left angle to be ur reference angle or wtv
consider tan() of that angle and consider sec() of that angle
fleet mauve
U mean the tan(t) and the sec(t), then what?
sand fable
can u tell me what tan(t) = ?
and sec(t) = ?
fleet mauve
tan(t) = √(4x²-1)
sec(t) = 2x ?
sand fable
ye
therefore
t = arctan(sqrt(4x^2 - 1))
t = arcsec(2x)
which means these two expressions are equal
sand fable
Are both of these indefinite integral result equivalent? What's the connection b...
one thing i do want to point out:
i say "positive" values at the start bcz
absolute value bars are necessary on the arcsec(|2x|) to make the statement true
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hazy swan
I understand it would be better to factor here first but can someone explain to me why dividing by 8 first here isnt legal?
marsh citrusBOT
I understand it would be better to factor here first but can someone explain to ...
hazy swan
am I forgetting something
final skiff
What are you trying to achieve
haughty portal
I understand it would be better to factor here first but can someone explain to ...
it is legal
nothing's stopping you from doing so
hazy swan
it is legal
But when I do that I end up with x-2+1/4
haughty portal
it's the distributive property
hazy swan
and then when I solve for x I get something different then if I were to factor it
haughty portal
ok so what is 2(x+1)?
hazy swan
2x+2
haughty portal
so what's (1/2)(x+1)
hazy swan
x would be -1 if your asking me to solve for x
haughty portal
ok and what is it if you separate x and 1
hazy swan
x/2 +1/2
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odd sparrow
marsh citrusBOT
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slim spire
that's all right
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odd sparrow
cheers
neon willow
Evaluate for a = 4 and b = -3.
I’m having trouble getting the same answer written on the answer sheet (720). Can anyone help me? Thanks
marsh citrusBOT
Evaluate for a = 4 and b = -3.
I’m having trouble getting the same answer writt...
upper timber
First simplify and then substitute
neon willow
First simplify and then substitute
5a^2b^2?
upper timber
Looks right to me
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feral ibex
How do I solve c? ie find the upper bound of the times taken by the 10 fastest typists?
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How do I solve c? ie find the upper bound of the times taken by the 10 fastest t...
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feral ibex
<@&286206848099549185> ?
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twin dome
Assume that the function (f) is defined on the entire real axis and that (f), (f'), and (f'') are continuous everywhere. Further assume that (f(0) = f'(0) = 0) and that (f''(x) \geq 0) for all (x). Show that the series (\sum_{k=1}^{\infty} f(1 / k)) is convergent.
marsh citrusBOT
Assume that the function \(f\) is defined on the entire real axis and that \(f\)...
elfin berryBOT
dgh
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waxen nest
What
waxen nest
What Is difference between radical equation and radical expression
crystal wraith
More or less your question is equation vs expression isn't it? Radical is just one of the cases.
waxen nest
But What Is difference between radical equation and radical expression
crystal wraith
Answer my question.
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remote fable
Hi! So I'm trying to use the Fundamental Theorem of Calculus here and I keep doing something wrong but I can't figure out what it is.
marsh citrusBOT
Hi! So I'm trying to use the Fundamental Theorem of Calculus here and I keep doi...
frail orbit
the antiderivative of 4-x^2 is not -2x
you need to find the antiderivative to the integral
not the derivative
remote fable
you need to find the antiderivative to the integral
ohhh okay. so 4x-(1/3)x^3?
frail orbit
yes. then you need to compute 4(2)-(1/3)(2)^3-(4(-2)-(1/3)(-2)^3)
remote fable
ah oki doki! Thanks so much :D
frail orbit
np
remote fable
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amber tulip
Can someone explain completing the square and the concept behind it
marsh citrusBOT
Can someone explain completing the square and the concept behind it
amber tulip
I don’t understand the quadratic function in the form of complete the square
I know it’s like (x+p)^2+q
sand kindle
say we have a quadratic like x^2 + 4 x + 5, and we want to write it in the form (x + h)^2 + k
can you figure out what h has to be?
willow bison
Can someone explain completing the square and the concept behind it
you use completing the square in order to get into so-called "vertex form"
amber tulip
can you figure out what h has to be?
(x+2)^2+3
amber tulip
you use completing the square in order to get into so-called "vertex form"
What’s that
willow bison
What’s that
vertex form is a quadratic in the form of
a(x-h)^2 + k
where (h, k) are the coordinates of the vertex (peak)
sand kindle
(x+2)^2+3
can you show how you got that?
and using that as an example, here's why it's called "vertex form":
amber tulip
can you show how you got that?
you half the middle term and square it
that's what my teacher said
sand kindle
right
sand kindle
because (x + a)^2 = x^2 + 2 a x + a^2
amber tulip
and square
sand kindle
so if our goal is x^2 + 4 x + 5, we want 2 a = 4
so (x + 2)^2 = x^2 + 4 x + 4, and our goal is x^2 + 4 x + 5
we're off by 1, so we get (x + 2)^2 + 1
amber tulip
k
but how is the min/max TP is when the term is 0
and how to answer these questions
<@&286206848099549185>
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dense wadi
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dense wadi
Help me get the 2nd answer plz
bold ice
,rotate
elfin berryBOT
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dense wadi
what u mean rotate
brisk abyss
Would the equation just be the equation of the function? Because doesn't the asymptote come from the function itself?
marsh citrusBOT
Would the equation just be the equation of the function? Because doesn't the asy...
final skiff
Would the equation just be the equation of the function? Because doesn't the asy...
equation of asymptote will be a line; the line that the function approaches but never reaches
brisk abyss
Oh so it's just like, y = 3?
final skiff
ye
final skiff
np
hard goblet
Hello I have a mathematics question and I have calculated it but I am not sure if my answer is right I would really appreciate it if someone helps me a little bit. its basic math but i do not know why the numbers dont add up.
With Bitcoin reaching it all time high I thought I invest 10 euro in it and see how it goes.
its called crypto trading so you trade it with something else.
I traded it with USDT wich is a coin that has the same price as the dollar.
I bought the USDT from someone on a website but I had not properrly checked the prices.
Now I would like to calculate'his profit percentage on our trade.
given:
euro to dollar: 1,09
dollar to euro: 0,92
I bought for 10 euro
He sells USDT for 1,029 euro
calculation:
I calculated it by doing this:
profit = 1,029 - 0,92 = 0,109
in percentage:
0,109/ 0,92 * 100 = 11,85%
proof:
10 * 11,85/100 = 1,185
10 - 1,185 = 8,815
but i have more money in my wallet
marsh citrusBOT
Hello I have a mathematics question and I have calculated it but I am not sure i...
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still temple
Yo
still temple
I just finished a practice for advanced functions polynomial unit
and I got these wrong
Can someone help me confirm what I did wrong and if the answer is actually wrong because they tend to have mistakes
<@&286206848099549185>
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hushed oracle
im not crazy right this question doesn't make sense at all
marsh citrusBOT
im not crazy right this question doesn't make sense at all
cobalt sentinel
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strong pecan
Does anyone know how to know whether there will be 1 or 2 LI solutions to the diff eq when doing series solution, and the singular point creates 2 r's that via frobenius r2-r1= positive integer
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Does anyone know how to know whether there will be 1 or 2 LI solutions to the di...
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chilly hound
I need some help with this problem. It has to do with simplifying and stating the restrictions.
marsh citrusBOT
I need some help with this problem. It has to do with simplifying and stating th...
chilly hound
I've managed to simplify the problem down to -(1/2x)
wary kite
division is multiplying by the reciprocal
chilly hound
The restriction would just be x=3 right?
sharp canyon
division is multiplying by the reciprocal
i would personally try to get rid of the complex fractions
wary kite
I've managed to simplify the problem down to -(1/2x)
yes
wary kite
i would personally try to get rid of the complex fractions
it does
the top fractions have x-3
x-3 cancels
it’s -(1/2x)
you did all there was to do
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finite tusk
how to do this difference of 2 squares ? i dont know what to do with the 2
burnt abyss
Do you know the difference of 2 squares formula
finite tusk
yes
finite tusk
done
burnt abyss
Show me
finite tusk
finite tusk
oh yeah now 2 is seperate so (x-y)(x+y) -2 (x-y)
hard gull
finite tusk
oh wait no, so (x-y)(x+y) -2 (x+y)
hard gull
nvm u got the correct thing even with wrong signs
burnt abyss
oh wait no, so (x-y)(x+y) -2 (x+y)
Is -2 (x+y) = 2x-2y?
finite tusk
ok I got it this time
finite tusk
x - y
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burnt abyss
You're welcome
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atomic ruin
Can someone please explain how is empty set ∈ M? im kinda new to set theory, thanks
marsh citrusBOT
Can someone please explain how is empty set ∈ M? im kinda new to set theory, tha...
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ruby cape
Can someone please explain how is empty set ∈ M? im kinda new to set theory, tha...
hopefully it should make sense that X is an element of M
if we dont use all of the elements of X to form the algebra, then whatever the unused elements are extraneous, making it a weird definition
but by ii, if X is in M, then so must its complement, the empty set
the motivation for the sigma-algebra is that we want it to be closed under complements and countable unions
so these properties must hold
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still temple
why is this inequality true? shouldnt 1/n^pln(n) be less than 1/nln(n) because n^pln(n) > nln(n)?
marsh citrusBOT
why is this inequality true? shouldnt 1/n^pln(n) be less than 1/nln(n) because n...
sharp vessel
n^pln(n) < nln(n) because 0 <= p < 1
For example
sqrt(2)ln(2) < 2ln(2)
n^1/2 < n for n > 1
still temple
ohh i see i missed the inequality part
still temple
tysm!
sharp vessel
np
still temple
.close
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long ivy
A question about Gauss Sum proof:
marsh citrusBOT
A question about Gauss Sum proof:
long ivy
I did part (a)
But how is part (b) true? Of course it's obvious that x^2-y^2 can be written as (x-y)(x+y) = ab
The only issue seems to be the bounds of the summation
x+y can actually be greater than p-1
so why is p-1 the upper bound for the b summation
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long ivy
.close
nobody helps :(
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astral trout
Can anyone explain why the eigenvalues and eigenvectors of a projection onto a line or a plane always is 1 or 0?
And if I am told to find the transformation matrix F(x) = A(x) for the orthogonal projection of a plane, does that mean my matrix A always has said eigenvalues and eigenvectors?
marsh citrusBOT
Can anyone explain why the eigenvalues and eigenvectors of a projection onto a l...
whole sleet
If the vector is already on the projection space, then nothing happens to that vector. In other words, it's an eigenvector with eigenvalue 1
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paper musk
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whole sleet
How did you get that denominator?
whole sleet
If, on the other hand, you had two of those cube roots...
Oh wait you're taking x to infinity anyway so this isn't the right strategy
charred pelican
If you have lim tending towards infinity
paper musk
charred pelican
you should take out the largest power outside from both the numerator and denominator
charred pelican
numerator: x (3 -2/x)
Denominator: x (1+6x/x^3 - 3/x^3)^1/3
cancel out the x,
since x tends towards infinity, constant/oo is 0
so you have,
numerator: 3
denominator: 1
paper musk
okok i see how do i do it through the cube root though
charred pelican
Can I cube the top and bottom?
you can rationalise but thats just a lot of effort
charred pelican
okok i see how do i do it through the cube root though
you can still take x common
take x^3 common inside the root
and then take the x^3 outside the root
which will be x since the power of root is 3
$(x^3)^(1/3)$
man
yeah nvm lmao
just understand the steps
basically if you take the highest power common, the remaining ones will become zero
paper musk
ok wait sorry im a bit confused im factoring it out of them like
ill show my work
one sec
charred pelican
ill show my work
yep
charred pelican
yep
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static kernel
PLEASE HELP how did this get simplified??
marsh citrusBOT
PLEASE HELP how did this get simplified??
static kernel
I tried literally every way and I could not get it to simplify in these terms
pearl pulsar
express in partial fractions
step 1:
divide f(x) by the denominator
(x³ + 4x² + x - 1) ÷ (x³ + x²)
= 1 + (3x² + x - 1)/(x²)(x + 1)
express this in partial fractions:
(Ax + B)/x² + C/(x + 1) + 1
where (Ax + B)(x + 1) + Cx² = 3x² + x - 1
static kernel
express this in partial fractions:
(Ax + B)/x² + C/(x + 1) + 1
where (Ax + B)(...
Im a bit confused at how to find a, b, and c at this last part
so, C = 3, ax+b = 1x + (-1)
pearl pulsar
think about it this way
static kernel
but then you dont have the (x+1), how would you get the values of a b and c?
pearl pulsar
cross multiplication
resulting in (Ax + B)(x + 1) + Cx² = 3x² - x + 1
we can solve using simultaneous equations or by substitution methods
- simultaneous
comparing x² coefficients:
A(1) + C(1) = 3
comparing x coefficients:
B(1) + A(1) = -1
comparing constants:
B = 1
- substitution method:
let x = -1
as f(-1) in (x + 1) = 0, (Ax + B)(0) = 0
therefore
0 + C(-1)² = 3(-1)² + 1 + 1
C = 5
let x = 0,
since f(0) = C(0)² = 0,
(0A + B)(0 + 1) + 0 = 1
B = 1
still temple
Can you solve for what Sigma goes to? Like say I have n=, the equation, and what Sigma=, and not what it goes to, can I solve for what it goes to?
I’m only in Geometry so this is all still out of my league, I’m just curious. I think I’ve gotten a grasp on and understanding of Sigma, how to do the summation stuff at least, but I’m just genuinely curious about the question.
marsh citrusBOT
Can you solve for what Sigma goes to? Like say I have n=, the equation, and what...
whole sleet
We need more context than this
still temple
We need more context than this
Uh let me draw it out on a sticky note.
still temple
Sigma
Ligma
Male
So I’m thinking it’d be like this. We know what the summation would be equal to (9), but we don’t know what the limit (Y) is.
Subtract 1
N = 8
sinful geyser
your n would be on the top no?
still temple
N
still temple
Subtract 1
Oh so to solve for the limit you just do basic algebra to find the limit?
It's possible
I feel like that’s off though, no? Cause for this one Y would be 3.
1+1=2
2+1=3
3+1=4
2+3+4=9
whole sleet
Oh I see you're taking a sum. This one is doing:
(1 + 1) + (2 + 1) + (3 + 1) + ...
Up until you've got y terms
You could use sum formulas to turn this into a quadratic in y
still temple
So I could use… another Sigma to find the limit of the first one?
Assuming the top number on the Sigma is the limit, I dunno the official name.
whole sleet
Σ n + 1 = 9
Σn + Σ1 = 9
[y(y + 1)/2] + [y] = 9
still temple
Ah I see. And I’m assuming the equation for Σ1 is just y?
primal umbra
how will i simplify this?
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still temple
for this differential volume in some arbitrary coordinate system (u,v,w)
still temple
why is the differential surface equal to this?
as far as i know like
,, \dd\sigma = \norm{\vj r_u \cross \vj r_v}\dd u \dd v
elfin berryBOT
still temple
where r is the parameterisation of the surface and the subscripts denote the first partial derivatives
the negative is what i dont understand tbh 
oh nvm i see
.close
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ebon depot
(a) Derive F's mapping matrix A, such that F(x) = Ax. Show that A4 = I4 and that AT = A−1 = A3.
(b) Show that if λ 4 = 1, then λ is an eigenvalue of A with associated eigenvector (1, λ, λ2, λ4)T.(c) Brilliant and diagonalize: Find a diagonal matrix D and an invertible P such that A = P DP −1
marsh citrusBOT
(a) Derive F's mapping matrix A, such that F(x) = Ax. Show that A4 = I4 and that...
ebon depot
0 1 0 0
0 0 1 0
0 0 0 1
1 0 0 0
Is this correct about matrix A?
Considering that:
F(e1) = e4
F(e4) = e3
F(e3) = e2
F(e2) = e1
lilac siren
si
ebon depot
lilac siren
🐛
ebon depot
For the next part it says that i should show that A^4 = I_4
A^4 isn't that just A?
$A^4 = A$
elfin berryBOT
Merineth
ebon depot
Since it's just 1s and 0s
lilac siren
what's I_4 in your notation?
ebon depot
It should be the unit matrix
lilac siren
It should be the unit matrix
well look at e1 for instance
e1 gets mapped four times: e1 -> e4 -> e3 -> e2 -> e1
which is true for any of the unit vectors
which means all of them get mapped onto themselves
meaning A^4 = I_4
ebon depot
Hmm i'm not sure i understand what mapped means.
I thought it just meant that F(e1) gets transformed into e4 because of the e1 -> e4 -> e3 -> e2 -> e1 notation
lilac siren
Hmm i'm not sure i understand what mapped means.
I thought it just meant that F...
yes that would be A*e1
ebon depot
the same way a function can transform an x value into something else
lilac siren
= e4
A*A*e1 = e3
A*A*A*e1 = e2
A*A*A*A*e1 = e1
which is
A^4*e1 = e1
same is true for the others
ebon depot
hold on let me digest hahah
What do you mean by A*A*e1 = e3
Are you multiplying matrix A by itself?
lilac siren
hold on let me digest hahah
because the function is four-cyclic
if you map e1
it becomes e4
ebon depot
Right
ebon depot
Aye
lilac siren
therefore, if you map e1 four times, it lands on e1 again
ebon depot
ooh i see
lilac siren
:3
ebon depot
That makes sense!
ebon depot
$A^T = A^{-1} = A^3$
elfin berryBOT
Merineth
ebon depot
How do you know it's orthogonal?
lilac siren
all of the image vectors are orthogonal to each other
since they're just unit vectors again
ebon depot
Ah right
lilac siren
so from that follows A^T = A^-1
which is true for any orthogonal matrix
but you can also show it by hand if you want
and then for A^-1 = A³:
well let's multiply both sides by A:
A*A^-1 = A*A³
I_4 = A^4
which is true, as we've shown before A^4 = I_4
wish thee good luck with the other tasks 🦇