what about factorising
#help-0
fierce kindle
hushed locust
all of algebra is a very broad subject. here are some websites that might help you:
https://www.khanacademy.org/
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zealous silo
For the measured quantity, choose the set of numbers that is most appropriate to describe it. There is one correct answer.
Elevation in feet of Death Valley, CA
Real number
Rational number
Integer
Natural number
Which is the correct anwser?
zealous silo
For the measured quantity, state the set of number that is most appropriate to describe it.
Shoe size
Which set of numbers is most appropriate to describe shoe size?
A.rational numbers
B.integers
C.natural numbers
Choose to which group of sets the following number belongs. Be sure to account for all sets
7/8
Choose the correct anwser below
A. Real numbers, rational numbers
B. Real numbers, irrational numbers
C.real numbers, rational numbers, natural numbers
Rational numbers , natural numbers, integers
E. irrational numbers, natural numbers
Find the midpoint of the segment with the given endpoints.
(-4,-9) and (-10,8)
The midpoint is ______
(Type an ordered pair)
Why is it simplified? Isn’t it fine with (-14/2 , -1/2) usually with other problems I leave the 2
visual sonnet
dont just give the answers
then there's no learning
@zealous silo do you know the midpoint formula?
zealous silo
Yes
visual sonnet
and that is?
zealous silo
(X1+x2/2,y1+y2/2)
visual sonnet
yeah, and then plug the coordinates in
zealous silo
Yes but I was trying to confirm since sometimes in my problems I have to simplify
And I get them wrong either way
I think it’s the way the ai grades it not sure
But thank you
.close
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heady plover
I totally forgot everything and am struggling to solve this question 😵 please help!
ocean whale
I totally forgot everything and am struggling to solve this question 😵 please h...
Do you know law of sines?
ocean whale
Yes
heady plover
Can u do 5A for me as an example to see
ocean whale
Well, you know it's going to be a ratio
a/sin(A)
Where a is a side length and A is the angle opposite
So in 5A, what would a be?
heady plover
8 and 100
ocean whale
8 is the length and 100 is the angle, plug that into the ratio, a/sin(A)
heady plover
Yep
ocean whale
Do the same with the other given side and angle
Then set them equal
And solve for the unknown angle
ocean whale
Did you get a final answer or are you just showing the equation?
heady plover
Showing
ocean whale
Yes that's the equation
ocean whale
Well, you're trying to find theta, so you need to isolate for that first
heady plover
How do I do that 😵😵😵
ocean whale
If you had 5/4 = 3/x how would you solve for x?
heady plover
X=5/12
ocean whale
Explain what you did
ocean whale
Good, btw you get 12/5 not 5/12
That's the same logic you should apply to 8/sin(100) = 5/(sin(theta))
The sin(theta) is basically like the x in that example I presented
ocean whale
What did you get?
ocean whale
First, the divided by 8 is outside of the parentheses so it's actually 5 x sin(100) / 8
And second, you have not completely found theta, you found sin(theta)
Do you know inverse functions?
heady plover
First, the divided by 8 is outside of the parentheses so it's actually 5 x sin(1...
That’s still wrong though
Answer says 38
heady plover
YES
ocean whale
You should apply that to find the value of theta
ocean whale
Same process, set up your law of sines
heady plover
But for the lower case a
ocean whale
Yes
indigo anchor
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indigo anchor
Hey this is confusing me Im getting 7/5 but thats wrong
the answer is 7/19 how are they getting this?
because your finding Pr(V|P)
which = Pr(VnP)/Pr(P)
so 7/5
?
gray isle
did you draw a venn?
indigo anchor
i did
gray isle
can you show what you drew
gray isle
is incorrect
gray isle
it says V only, P only
not total
gray isle
what you've drawn indicates 5 play violin only, 5 play piano only
indigo anchor
12 | 7 | 12
gray isle
yes
indigo anchor
woulnt that make the answer 7/12 though?
gray isle
no
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tawdry pendant
Log x = sin x
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vast bane
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vast bane
how are these two equal
gray isle
(b-a)^2 = (a-b)^2,
factor that out
nimble bane
Is the solution notwrong? This is the integral I came up with instead
exotic belfry
what you call y = 0 is y=-5.
brazen wadi
just use archimedes law?
nimble bane
no
this is way I learned how to do it
Even in this video
<@&286206848099549185>
heavy reef
just use archimedes law?
cant use that bc archimedes is used for calculate the buoyant force on an entire object
not the side of a plate like the given prob
nimble bane
can u solve this @heavy reef
heavy reef
yea
hold up lemme grab my pen and paper
im not really familiar with the bot and shit
nimble bane
Is the solution notwrong? This is the integral I came up with instead
this nitegral
heavy reef
nimble bane
yes
this is how my professor
did it
@heavy reef
I was assuming it was literally a 1-1
nimble bane
thats how my profesor did his problem
How I did it was a 1-1 of how he did it
just with diff numbers
nimble bane
for him y was the depth from the bottom of the plate
nimble bane
trhis is the video
heavy reef
https://www.youtube.com/watch?v=PFftQIbLxUs&list=PLj7p5OoL6vGx46ItdqVx0OZhDZfidT...
this video?
nimble bane
yes
Its a seperate problem but the problem is basically the same with diff number no?
heavy reef
yea
nimble bane
https://www.youtube.com/watch?v=PFftQIbLxUs&list=PLj7p5OoL6vGx46ItdqVx0OZhDZfidT...
Here its the same concept
but he also did 4-y
since he set y to be at the bottom
so both videos are wrong?
heavy reef
bro
your problem is trapezoid shape
the given video is a triangle
different shape differnt formula ig
nimble bane
F=Pa
where pressure = density of water * distance
heavy reef
https://www.youtube.com/watch?v=PFftQIbLxUs&list=PLj7p5OoL6vGx46ItdqVx0OZhDZfidT...
in this video, he put the y=0 at the bottom of the tri
heavy reef
bro but the point is
The trapezoidal shape's width is increasing as you go deeper
so the pressure should increase
unlike the video, where the width of the tria is decreasing
so (5-y) not wrong, but its not physically correct
thats why the pressure must increase with the width and you should use (3+y) instead of (5-y)
nimble bane
where is your y placement at then
where is y=0
ontop of the water?
all the viudeos do it how i do it
heavy reef
still at the bottom
but
its not about the y placement
its about physic
The pressure at a given depth should increase as you go deeper into the fluid.
In the original problem, y measured the depth from the surface downward, which is why the pressure is given by P x G x (3+y)
when you use (5-y) you implies that the pressure decrease as you go deeper, which its physically incorrect
alpine sable
whats is 1+1
heavy reef
1 professor and 1 student ig
If you still not understand, ask another helper bro
i need to sleep
like its 2am here
xd
peaceout
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@nimble bane Has your question been resolved?
sour mica
@nimble bane in your integral, the plate y has opposite area. What I mean to say is, if you put in the values at limits, the y=0 represents the bottom of the plate, which should have width 7m, but according to your formula, has only 4m width
so you need to change the formula to 7-1.5y so the depth of location matches the width at that location
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blissful rapids
why
blissful rapids
Well to start off, what's `0.5!`?
idk thats why I used wolfram alpha
and it gave me different results for the gamma function and factorial
cedar kelp
gamma{s}={s-1}!
this is the relation
blissful rapids
should I use the gamma function for this one
blissful rapids
should I use the gamma function for this one
sepcifically the binomial coeffecient
I wrote it as gamma(1/2) / (factorial(n) * gamma(1/2 - n)) in my program
and the series converged to 6.11 instead of pi (I multiplied the result by 4)
woven hornet
The factorial function is only defined for integers, if you want to extend it to real numbers then you need to define how that works as there's multiple ways to do that
blissful rapids
The factorial function is only defined for integers, if you want to extend it to...
do you know which one this algorithm uses
woven hornet
Maybe, but what is "this algorithm"?
blissful rapids
Maybe, but what is "this algorithm"?
the screenshot I sent
im trying to implement that series
nimble bane
founde ittan
calm fractal
should I use the gamma function for this one
No, you don't need the Gamma function for this. The usual definition of $\binom{x}{n}$ when $n$ is an integer, is $\frac{1}{n!}(x)(x-1)(x-2)\cdots (x-n+1)$
ocean sealBOT
ENStucky
calm fractal
gamma{s}={s-1}!
And also this answer by 77^2 explains the WolframAlpha response: Gamma(1/2) is not (1/2)! but instead (-1/2)!
woven hornet
I don't think that matches the terms in the series shown, but again we're just guessing without knowing what "this algorithm" is
blissful rapids
I don't think that matches the terms in the series shown, but again we're just g...
I found it on a list of algorithms on wikipedia but there is no page dedicated to it
blissful rapids
No, you don't need the Gamma function for this. The usual definition of $\binom{...
wait ill try this one
thank you
it worked
.close
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woven hornet
I'm curious where this came from as it's just the Leibniz formula with and extra bit: https://en.wikipedia.org/wiki/Leibniz_formula_for_π
blissful rapids
I'm curious where this came from as it's just the Leibniz formula with and extra...
https://en.m.wikipedia.org/wiki/List_of_formulae_involving_π#Efficient_infinite_series search for "euler number" in this article and the algorithm just below that one is the one we were talking about
blissful rapids
I'm curious where this came from as it's just the Leibniz formula with and extra...
how did multiplying that binomial coeffecient to the leibniz formula (which outputs pi/4) still give the same output (pi / 4)
.reopen
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blissful rapids
how did multiplying that binomial coeffecient to the leibniz formula (which outp...
reopened because of this
woven hornet
I included a very inefficient infinite series that yields pi/4 discovered by me, that involves the binomial coefficient of 0.5 and n (for easier locating of the series)
https://en.wikipedia.org/w/index.php?title=List_of_formulae_involving_π&diff=prev&oldid=1027894405
So no further information there
blissful rapids
💀
mf discovered a whole series
and put it on wikipedia
and refused to elaborate
.close
lusty token
what would be a simple way to construct an infinite amount of sets A_1, A_2 ..., each A_i consists of an infinite number of elements and A_i shares no common elements with A_j if i and j are not equal such that the union of all A_i is equal to the natural numbers (N does not contain 0 in this case)
lusty token
i was thinking of using primes, but it seems quite convoluted
stiff hound
What an interesting question
lusty token
i quite agree
$A_i = {p_i * n | n \in \mathbb N \land \forall j(j \in \mathbb N \land j < i \to p_i * n \not\in A_j)}$
this is quite disgusting im not gonna lie
ocean sealBOT
someone1010
cerulean grove
lone heartBOT
cerulean grove
tribal axle
i dont have the capabilities to solve this question but my geometric interpretation is that:
$\g_{t,\epsilon}(s) \geq f(s)$ g is always either above f or touching f.
$\g_{t,\epsilon}(t) = f(s)$ t is the specific point in which g and f touch.
$\g''_{t,\epsilon}(s) \leq \epsilon$ g's second derivative (the curvature of g) is always less than or equal to epsilon, we can always chose epsilon to be arbitrarily small so basically g's curvature barely/(doesnt at all) change
ocean sealBOT
woomy
cerulean grove
Fair enough!!
tribal axle
im not sure if the last one is correct
cause since epsilon is a constant
i guess it would say something about the amount of curvature rather than its change
what do you think? @cerulean grove
so a picture you can have in mind is:
g doesnt curve yet is always above or equal to f, intuitevly that means f must either equal to g or curve inwards
cerulean grove
Yea, so it's concave
cerulean grove
i guess it would say something about the amount of curvature rather than its cha...
What's the difference between amount of the curvature and its change? I don't quite understand the last one ig
cerulean grove
2x, x>0,f'>0
tribal axle
see how the derivative depends on x
i.e. the slope on each point is different
since it depends specifically on which point we talk about
j(x) = 5x?
the derivative is simply 5
this means the slope is always 5
no matter the value of x
in other words. Since h'(x) depends on x, its slope changes. Meanwhile since j'(x) is a constant, the slope is always the same
cerulean grove
Yea
tribal axle
Yea, so it's concave
oh
sorry i havnt really learnt any of this at school yet, convex means positive curvature and concave negative?
cause like this is the picture that i draw when looking at the problem
cerulean grove
You're right, it's just my typo
tribal axle
okay np
If the teacher is looking for something rigurous then i guess you could show that g(s) must be linear since it doesnt have curvature and thus f(s) must be concave since it touches g only at t
tribal axle
basically
but
epsilon cant be 0
so we cant take epsilon to equal 0
you must take the limit as epsilon approaches 0+ as your value for epsilon
cerulean grove
When will Epsilon approach 0 then
tribal axle
it doesnt really matter as espilon is arbitrary and we can chose it to be anything we want
so just chose it to be veeeeeeryyyy small
so small
that it must be linear
let me explain it better
Epsilon cannot be 0 as the problem states, so we cant directly prove g is linear. Our proof breaks as it was all based on the assumption g is linear. If g werent linear we could construct a function f thats convex and satisifes all the properties:(g is purple, f is blue)
But what we can do is: every time we chose a value for epsilon thats not 0 and then find a function f that satisfies all properties but is still convex, lets just chose a smaller epsilon so f doesnt work anymore. Do this repeativly and no matter the convex f, we can always find an epsilon where f doesnt satisfy g >= f Lets chose epsilon do be arbitrarily small and f must be concave
Do you follow?
I have to go shower now. If you still have some questions or dont understand something then ill respond as soon as im back :)
cerulean grove
So you mean no matter how convex a function (f) might start out as, by choosing a smaller (\epsilon), you can always find a scenario where (f) fails to remain convex and must become concave to satisfy the conditions?
tribal axle
Exactly!!
cerulean grove
Wow
tribal axle
Good job!
cerulean grove
So when choosing a sufficiently small (\epsilon), g will be linear, f will be concave
tribal axle
epsilon needs to be 0 for g to be linear but epsilon cannot be 0 as stated in the problem. A better way to think of it is that for every f thats convex we can find an epsilon that causes a contradiction
tribal axle
see how here it says epsilon is stricly greater than 0
cerulean grove
So actually g will never be linear?
tribal axle
practically no
you could take the limit as epsilon approaches 0 and g will approach being linear
pulsar iris
Got a no for the answer since the denominator of the first by plugging 3 turned into 0. But still not sure if the answer is correct since my understanding is still unclear. Please help!
gray isle
you are concerned with the limit as x→3^-
not the value of (cbrt(2x+2)-A)/(x-3)
i.e. you want
$$\lim_{x\to 3^-} \frac{\cbrt{2x+2}- A}{x-3}$$
to exist
ocean sealBOT
ℝαμOmeganato5
gray isle
and for that, the numerator would also need to approach 0 as x→3^-
lone heartBOT
@pulsar iris Has your question been resolved?
gray isle
after finding A, consider the factorisation for the difference of two cubes to rationalise the nuemrator
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@pulsar iris Has your question been resolved?
dusky crypt
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dusky crypt
i have been trying to solve this problem, but i am not getting the right result on the RHS
here are my steps. Pls see if you can find the error
hopefully my handwriting is legible
btw my gamma symbol is a little weird and looks like a distorted v
<@&286206848099549185>
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@dusky crypt Has your question been resolved?
dusky crypt
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echo void
whats x13-16x=
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@hearty dove Has your question been resolved?
ivory flame
- The book Michelle was reading went from page 1 to page N. The total number of digits used for the page numbers is 300.
How many pages are there in Michelle's book?
cinder tundra
What have you tried?
meager sphinx
Ooo I've seen a variant of this problem before
still herald
First ask yourself - how many two digit numbers are there, how many one digit, and how many three digit numbers between 0 and 100 (let)
Just forst the first one, a hint:
There are 9 pages between pages 1 and 9 and each page will add 1 digit to the sum.
fallen verge
how about we wait for OP to respond
cinder tundra
!noans
lone heartBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
cinder tundra
!nosols
lone heartBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
still herald
dramatize me
lone heartBOT
@ivory flame Has your question been resolved?
meager oriole
hey I needed help with b onwards
lone heartBOT
hey I needed help with b onwards
hybrid dust
OooooOOO, this is interesting!
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@meager oriole Has your question been resolved?
meager oriole
<@&286206848099549185> hey was wondering if anyone had ideas
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@meager oriole Has your question been resolved?
remote solar
lone heartBOT
finite linden
you’re starting this early, anyway is this an angles thing for geometry?
mind sending me a more clear photo so I can try to help you?
finite linden
yeah i’m tryna figure it out rn
finite linden
thank you for helping nobody wants to they dont know how
i’m doing it rn
chill
I messed up the diagram
remote solar
ik
remote solar
Angle FOE is half of DOE, DOC is twice of DOE
i dont get it
remote solar
Then BOC should be four times of DOE
can u write it on paper dont get it
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@remote solar Has your question been resolved?
fresh sapphire
NEed help with boolean algebra question.
looking at 38 - 42 in binary with signed 8 bit 2s comp
I get
38 = 0010 0110
-42 (2s comp) = 1101 0110
so when i add them together i get 1111 1100 ... is this correct/is there overflow?
fresh sapphire
if i take the 2s comp of 4 (to get -4) it's equal to my answer, but im still not confident LOL not sure why it feels wrong.
remote solar
Then BOC should be four times of DOE
u mean BOF
arctic lintel
looks correct
to check ur answer in 2 bits, u can take the first bit and make it negative i.e (-128) and add the positives of the other bits i.e (64+32+16+8+4) which totals to -4 which is the expected result
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rancid tartan
naive valley
rate of change of what?
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soft pagoda
i did this and got 2 solutions
one is x-8 which is the right answer
but i also got x+5
i did factoring
just wondering what i did wrong if anything
fresh wedge
but i also got x+5
It will be a quadratic equation so you should get 2 answers
fresh wedge
Yep
soft pagoda
But I guess my job is to check
And I would’ve found out that d+5 is just incompatible
X+5*
So I guess I just missed that last step
Okay thanks
.close
soft pagoda
Yep
Ok sorry this is very priimitive algebra but
I’m getting back into it after a very long time
fresh wedge
Ok sorry this is very priimitive algebra but
No worries at all
soft pagoda
No this part haha 😂
I’m allowed to divide by 3 and leave the other side alone right
Does that count as just simplification and it’s ok?
Or do I need to do both sides for balance
soft pagoda
I’m so bad at the basics of algebra
Oh ok cuz I thought
9x-45+3 was meant to be simplified
Cuz it makes it look very divisible Lol
But I guess I can’t Ok
soft pagoda
Oh I mean like
So this is what it looks like
And I guess I was just wondering if I can divide the right side by 3 and then finish the rest
Is that not allowed though
fresh wedge
I think it's wrong, can you write the whole equation?is it something like
(√9x-45) +3 =x
soft pagoda
Oh sorry you can’t see the whole thing
I did the process like before where I squared the x on the left to remove the root
fresh wedge
Yahhh see there is a formula of
(a+b)² = a² +2ab + b²
fresh wedge
Yahhh see there is a formula of
(a+b)² = a² +2ab + b²
Once you do
x² = ((√9x-45)+3)²
On right side you need to use this formula
You can't simply do
9x-45+3
fresh wedge
But wait @soft pagoda
soft pagoda
?
fresh wedge
Instead of that try a different approach
x=√9x-45 +3
Can you get the 3 to left side ?
soft pagoda
Yes just by subtracting
fresh wedge
Exactly, then do a square on both side
soft pagoda
Hmmm what do you mean
fresh wedge
Get 3 to left side then do
()²
As you were doing for above questions
a = b + 3
a-3 = b
(a-3)² = b²
soft pagoda
Oh so like
fresh wedge
Like this ^^
soft pagoda
Oh okay yeah
fresh wedge
Now to solve the left side use the formula of (a+b)² that I gave above
(a+b)² = a² +2ab + b²
(a-b)² = a² -2ab + b²
fresh wedge
Excellent
soft pagoda
Okay
And I’m just wondering
Is it not possible tocdo factor pairs on this one
I’m so bad at factoring I feel like there’s so many methods idk how I’ll remember them all
soft pagoda
okay
Ok so I was confused cause I though
I thoigbti could just
Square the root, move alll to one side, subtract the 45-3, and then just facotrbpair
Is that not possible at all
That’s kinda what I did on the old question
fresh wedge
No , you need to have a simplified form first like
ax²+bx+c then only you can find factors
soft pagoda
Okay
Yeah my original strategy I tried to do was the one I marked in red arrows
so the two solutions i have now is (x-9)(x-6)=0
x = 9 and x = 6
fresh wedge
This was wrong
(√9x-45 + 3)² is not equal to 9x-45 +3
soft pagoda
oh sorry i thought i could only square the square root
i thought i could just avoid doing the 3
fresh wedge
Correct
soft pagoda
okay 1 sec
fresh wedge
Sure
soft pagoda
okay so
just to verify what i did wrong
for the (root9x-45) + 3
if i square rooted that
it would become x^2=9x-45+9
right?
x^2=9x-36 then
x^2-9x+36
or does that method not work
ohh no thats not factorable
ah
fresh wedge
for the (root9x-45) + 3
You mean
x = (root9x-45)+3
If you squared it
Then it would have become quite complex that's why I asked you to move 3 to left side , still FYI it would have become like this
x² =(9x-45)+ 2(root9x-45)3 +9
soft pagoda
Then it would have become quite complex that's why I asked you to move 3 to left...
hmm im confused
so say i squared it
x^2=9x-45+9
fresh wedge
Okk
soft pagoda
would it not look like this?
soft pagoda
oh
fresh wedge
It doesn't work like that
soft pagoda
i thought when u square it just got rid of the root mb
fresh wedge
(Root9x-45)+3 is like a+b
So square then will be
a²+2ab+b²
What you are doing is
a²+b² which is wrong
soft pagoda
ok well heres a different one
what i did here is
square both sides
i end up with m+6root m + 9 = m + 10
fresh wedge
Yesss
fresh wedge
Square again
fresh wedge
Yep
soft pagoda
for some reason the answer on the calculator says thats no solution
lemme see if i can solve putting it through
crap i dont get how to solve this
ughhh i feel like im going to fail this class..
soft pagoda
yes but how do i solve
soft pagoda
fresh wedge
That's the answer
soft pagoda
But for some reason the calculator says there’s no solution
so i want to put it through and check
but idk how to do the solving there
root of 1/36 is
1/6 ?
oh
nvm
it didnt ask me to solve
alr mb
god theres so amny
different ways
x^4
i want to try do this one a bit on my own but can you hint me for the first step
fresh wedge
That's alright assume x² =y
And change this to a quadratic equation
fresh wedge
Yes
soft pagoda
hmmm what do you mean
fresh wedge
x⁴ is what ? (x²)² right?
soft pagoda
oh yeah that makes snese
fresh wedge
So if you assume x² = y what will x⁴ become?
fresh wedge
BINGO
soft pagoda
i mjsut putting the y in the place of the
oh
but why do we do that where can we put yh ere
fresh wedge
X⁴-50x²+49 = 0
You need to find factors for this first.
You know how to solve ax²+bx+c things, do you know how to solve ax⁴+bx²+c ??
soft pagoda
ahh probably not no
fresh wedge
That's why I am helping you convert x⁴ to x²
See you have
x⁴-50x²+49=0
If you assume x²=y, your equation will become
y²-50y+49=0
Can you find factors for above ^^
fresh wedge
It is 😅
soft pagoda
like what process was used to turn the x^4 into a y^2 and then the 50x^2 into a y
like what did you do i guess is what im wondering
fresh wedge
Nothing, we just assumed
fresh wedge
I can solve without converting, but maybe that would be difficult for you to understand
Yesss
soft pagoda
so we can substitute and bring it down
to make it easier to solve
okay
i guess thats fair
ok let me try to solve
soft pagoda
god im still so lost i barely remember factoring methods other than the freaking factor pair method 😭
but that wont work with the 50 and the 49
so what should i do to factor out
wait im wrong
i can do factor paIR
-49 and - 1
so
(y-49) (y-1)
so far
soft pagoda
yes
fresh wedge
±7
±1
soft pagoda
oh yes
soft pagoda
okay thanks
fresh wedge
Np
soft pagoda
i guess i can do it with your help i just dont know how ill manage to
memorize all of these different methods for a test
crap
my algebra foundation sucks
fresh wedge
Once you start practicing it will be easy
Don't worry about it
The more you practice
The better you will get
soft pagoda
so for this one, should i first simply
i guess i need to make the 10m^1/2 not that
wouldnt -10m^1/2 just be
root - 10m
because thats what the 1/2 means right
if its a power t
that means root i tihink
fresh wedge
You can again assume something here to make your task easy @soft pagoda
Like we did in last case
fresh wedge
Hmmm you think first
You need to make above as x²+x kind of term
How will you do that?
soft pagoda
so if last time we did
x^2 = 1y
ok im very confused so im just going to go ahead and pretend
fresh wedge
Here m½ is there
fresh wedge
Yeahhhh
soft pagoda
so try to get rid of the m^1/2
fresh wedge
Yesss I was saying
m½= x
But that is same as m = x²
soft pagoda
oh ok
ok let me try
(x-6)(x-4)
x = 6
x = 4
which turns into
m^1/2 = 6
m^1/2 = 4
fresh wedge
Yes so what would be m??
fresh wedge
Noooo
soft pagoda
oh wait
fresh wedge
M½ is root m
soft pagoda
so dont we have to root both sides
soft pagoda
oh
fresh wedge
If it was m² = 36 then m would have been ±6
fresh wedge
Yup
soft pagoda
is there a way to simplify down the 164 and 6400
what if i divide
considering other side is 0
fresh wedge
No then you will get something under y² too
soft pagoda
okay
fresh wedge
That would make it more complex
soft pagoda
okay so lemme factor
soft pagoda
y=-100
y=-64
therefore
x^2 = -64
x^2 = -100
and then we root -64 and then -100
soft pagoda
+- 8 and +- 10
?
ohhh
wait
its negative ur right
so that means
OH
it was a long time ago
that means u have to use like
a fake number right
cuz its not actually possible
fresh wedge
There is something called i but I think you have not studied them yet
soft pagoda
i = imaginary right
soft pagoda
so 10i and 8i
soft pagoda
weird
it only give me .5 of 1
so i did something wrong?
oh okay so ti says
it can be
10i, -10i, and 8i and -8i
so its kinda the same but it needs the i
because of the negativw
fresh wedge
You think I will be back a bit later, I need to get up I am still in bed
fresh wedge
Ping other helpers if need
soft pagoda
ok i go tthat one
lone heartBOT
@soft pagoda Has your question been resolved?
charred flint
yes that at some large x you get ce^x > any polynomial
sour verge
$f(n) \in O(g(n))$ specifically means that $f(n)$ is eventually bounded \emph{above} by $g(n)$ (give or take some coefficient).
ocean sealBOT
Azyrashacorki
sour verge
Polynomials are O(exponentials), but exponentials are not O(polynomials).
lone heartBOT
@final oak Has your question been resolved?
tacit jewel
lone heartBOT
tacit jewel
what this smybol mean
in probability
or maybe what is the name
from stack overflow: "The two arguments of DKL
(Kullback-Liebler divergence) are often denoted with the double vertical bars between them instead of a comma, doesn't mean anything special."
tacit arch
from stack overflow: "The two arguments of DKL
(Kullback-Liebler divergence) ar...
Yes the answer is essentially right. The notation isn't anywhere in probability theory, just information theory
tacit jewel
Yes the answer is essentially right. The notation isn't anywhere in probability ...
kk, thanks
.close
lone heartBOT
lone heartBOT
Available help channel!
barren goblet
hey! ive got a question. its about derivatives
so derivates are basically the rate of change right?
so if i consider an equation like y = x^2 and plot some points it would be something like this (0,0), (1,1), (2,4), (3,9), (4,16) and so on
and if differentiate the same eq i get y' = 2x and if i plot the points i get (0,0), (1,2), (2,4), (3,6), (4,8) and so on
why dont the y values match for corresponding x values?
also rate of change is tangent to the slope, right? so basically does a point have a rate of change? say i take multiple points then do i average them out to find the rate of change
hushed locust
the derivative only gives the slope of the tangent line, not the position
hidden pier
why dont the y values match for corresponding x values?
the corresponding x values of what? y=2x?
barren goblet
the derivative only gives the slope of the tangent line, not the position
what do i with the slope of just one point
mortal trellis
the point (4,8) tells you for example that at the point (4,16) of the original graph, the tangent has a slope of 8
hushed locust
what do i with the slope of just one point
you can construct a tangent line using the value of the function and the value of the derivative at a point using the point-slope formula for a line
barren goblet
you can construct a tangent line using the value of the function and the value o...
but i also need to take multiple points into consideration right?
hidden pier
does a point have a rate of change?
cloud can help with the rest, but in response to this question: it's like the speed of your car; at a certain instant it's going 60mph.
so just like you can calculate the "rate of change" of your car you can calculate the rate of change for a y-value at a certain x-value
barren goblet
> does a point have a rate of change?
cloud can help with the rest, but in resp...
ooh
hushed locust
but i also need to take multiple points into consideration right?
well remember that the tangent line is essentially the limit of the secant line (constructed from any two points), as those points approach each other. so while the tangent line is "based on" the behavior of the function in a neighborhood, you only need the value of the function and its derivative at 1 point exactly
barren goblet
well remember that the tangent line is essentially the limit of the secant line ...
lol i dont understand anything
hushed locust
so let's consider the bottom formula. we can see that we need two points on a graph to find the slope of a secant line, plut one point to use point slope form from there
barren goblet
ok
hushed locust
but if we take a close look at the bottom formula, this is a familiar quantity, because it shows up in the definition of the derivative
specifically, we say that [ f'(x) = \lim_{h\to0}\frac{f(x+h) - f(x)}{h} ] in other words, $h$ is the separation between the two points, and the derivative is the limit as $h \to 0$ (in other words, what the slope approaches when the two points get really close together!)
ocean sealBOT
cloud
hidden pier
yea
barren goblet
and if we differentiate it we get y' = 2x
and if i take soem points like x =3 i get y = 6
hidden pier
mhm
barren goblet
what is the slope telling me
hidden pier
well y'=6 not 6
barren goblet
yeah
hidden pier
it's telling you that on the graph of y=x^2, at the point (3,9) at x=3, the rate of change is 6 units y
barren goblet
and what about x = 4
barren goblet
but 4^2 = 16
hidden pier
yeah
think of (4,16) as a position
and 8 as how fast you're going "up" or increasing
barren goblet
but 4^2 = 16
it say as i move 4 in x i move 16 in y
hushed locust
we can visualize the tangent line here:
https://www.desmos.com/calculator/u5gfivlo2j
hidden pier
y' isn't supposed to give you 16
it's supposed to give you the speed at which the graph is increasing at that point
so if (x,y)=(4,16) you're not expected to get y'=16
barren goblet
isnt x^2 telling the same thing
tangent would be just the average rate of change of x^2
hushed locust
on our car, we have two meters. the odometer measures how far the car has gone, and the speedometer measures how fast it is going. so we can think of the function as the odometer and the derivative as the speedometer, in that analogy
barren goblet
so if x = 3 i get y'=6
it means that if i move 3 in x
ill move 6 units in y
right?
hushed locust
not quite. the tangent line only works well as an approximation quite close to the point.
hushed locust
so near x = 3, if i move 0.01 in x, i would expect to move about 0.06 in y
hidden pier
yea
barren goblet
so like if i move 3 units from the origin
hidden pier
if im in a car and its speeding up, at one point it may be 60mph but that doesnt mean i'll go 60 miles in one hour since the speed is speeding up
barren goblet
i would move 6 units in y
hushed locust
yes the tangent line can be used to estimate points near the point we chose, but only close by
hushed locust
but also the slope is (change in y)/(change in x). so you should actually expect to move 6 in y for every 1 in x (near the point x = 3)
barren goblet
but also the slope is (change in y)/(change in x). so you should actually expect...
for every 1?
6 for 1?
wouldnt that be 2 for 1?
hidden pier
and what the derivative 2x tells us is that for an x value the rate of change is twice as much as the x-value
hushed locust
no. the slope is 6. that means (change in y)/(change in x) = 6. x = 3 is irrelevant to that
barren goblet
and what the derivative 2x tells us is that for an x value the rate of change is...
yess
but if i move 1 unit shouldn i move 2 units in y for that 1 unit
hushed locust
no. the slope is 6. that means (change in y)/(change in x) = 6. x = 3 is irrelev...
x = 3, y = 9 tells us where we are physically. it does not tell us anything about how fast we are going. dy/dx = 6 tells us how fast we are going
barren goblet
so if im at 3 im moving 6 units in y for every 1 unit i move at 3?
barren goblet
at that instant
oh it does mean i move 6 for every 1 on desmos
can you explain how does it make sense?
@hidden pier
hidden pier
oh it does mean i move 6 for every 1 on desmos
we've established that this is only for really close values of x
dont expect to move 6 up, 1 over, and find yourself at the value for (4,16)
like how if you're constantly speeding up in a car that goes 40 miles per hour you're not gonna expect to go 40 miles in one hour because after the hour's up your car has already sped up to a faster speed and is traveling farther
all the derivative tells you is at the point x=3, the rate of change is 6 units y for every x
idk what else to say lol
barren goblet
no no
lets just take 3 as x
what i mean to say is
in the context of x being 3
how do i move 6 up for every 1 unit
barren goblet
thats what is confusing
hushed locust
we can say that since f'(3) = 6, then f(3 + 0.01) ~ f(3) + 0.06
sick ibex
I need help with a text problem about exponential functions
"John wants to invest in shares. First he invests €1000 in a share, then he invests €50 every month thereafter. The annual return is 3% ."
- Create a suitable function!
- How much money will he have in 10 years?
sick ibex
So i dont have a problem with the first part
f(x) = 1000×1,03¹⁰
I dont really understand how i can execute the second part
Adding 50 won't do the trick
<@&286206848099549185>
lone heartBOT
@sick ibex Has your question been resolved?
lone heartBOT
@sick ibex Has your question been resolved?
sick ibex
The agony😮💨
strange heath
just use ur function
sick ibex
What do you mean?
strange heath
f(x) = 1000×1,03^x
just plug x = 10
that how much money you have
if u make function correctly
otherwise
i just ate so dont wanna think
strange heath
i think u made ur function wrong
sick ibex
f(x)=a×x right?
strange heath
i told u bruh
i just wanna sleep
so idk
<@&286206848099549185>
just help here
alright wtv
stray spruce
<@&286206848099549185>
Wheres the ques?
strange heath
so he investes 50 pound every month