the last sum =1 because it is just a rewritting of (||u||^2 + ||U||^2 )/2
#help-17
frozen bobcat
humble osprey
Alright I got that, but how did he get the second inequality
frozen bobcat
and the middle inequality is because you can just take the maximum of u1 and U1, and u2 and U2 so |u1| |U1| < u1^2 or U1^2 (whichever is bigger) and similar for |u2| |U2|
then add positive things to it.
oh wait. no sorry, it's not that
(u1 - U1)^2 >= 0 implies u1^2 + U1^2 >= 2u1 * U1
and throw in absolute values as needed
thank you!
random temple
vocal sleetBOT
fair compass
313
random temple
the answer is 721 but idk why
fair compass
wut
lapis marten
have you heard of factorials?
random temple
yes
patent pine
I don't know what to do next
vocal sleetBOT
I don't know what to do next
formal charm
I don't know what to do next
What’s the question?
patent pine
the upper equation
formal charm
You can solve the equation at the bottom for one variable
patent pine
i need to get the answer knowing that x+y=1
frozen bobcat
post the original question
frozen bobcat
that's just a polynomial. I have no idea what you're trying to do with it.
what is the original question.
formal charm
You can solve the equation at the bottom for one variable
Then try this and see if something cancels
formal charm
@patent pine was there a question you tried to solve with these equations?
patent pine
yeah
formal charm
Then can you post the question
patent pine
at first it was a geometry task lol
formal charm
Because I don’t think what you are trying to do works out
formal charm
at first it was a geometry task lol
something about circlels lmao
frozen bobcat
post the original question
yeah... the original question would be nice....
formal charm
Sorry, but what does the S mean in SABCDE=¿
patent pine
Area
formal charm
ah ok
patent pine
And i used the theorwm about half perimeter
vocal sleetBOT
@patent pine Has your question been resolved?
vocal sleetBOT
@patent pine Has your question been resolved?
marble kettle
hi i need help with this question, i tried counting it by multiiplying 45/50 with 44/49. but that wont get an answer?
vocal sleetBOT
hi i need help with this question, i tried counting it by multiiplying 45/50 wit...
marble kettle
why is my way wrong?
heavy yoke
in this case there are so many students that we can assume that selecting 1 student out of 50 won't significantly change the probability for the next one
marble kettle
in this case there are so many students that we can assume that selecting 1 stud...
so do i just multiply 9/10 with 9/10 ?
twin meteorBOT
Result:
0.80816326530612
is there a way to know when i need to multiply or when do i use the set thing(like the one where P( A U B) = P(A) + P(B) - P(A n B). cuz sometimes i dont know if i need the multiply the probability or use the set method thing( i dont really know how to describe)
heavy yoke
multiplying is for AND (as in, both events happen) whereas adding is for OR (as in, probability that either thing happens)
marble kettle
P( A U B) = P(A) + P(B) - P(A n B) but what about this?
heavy yoke
the U is the union of two sets = OR, the upside down U is the intersection of two sets = AND
neon plover
same as earlier
need to use substitution method
just kinda stuck dk where to start cant get it to cancel out
vocal sleetBOT
same as earlier
need to use substitution method
just kinda stuck dk where to sta...
@neon plover Has your question been resolved?
neon plover
<@&286206848099549185>
vocal sleetBOT
@neon plover Has your question been resolved?
vocal sleetBOT
@neon plover Has your question been resolved?
neon plover
did everyone give up on my question
neon plover
<@&286206848099549185>
okay so i just gave the answer but i still wanna know how to solve it
any ideas what substitution symbollab used
vocal sleetBOT
ancient isle
nvm i did it
I was wrote the steps 😭
neon plover
where
ancient isle
here
neon plover
am i blind
ancient isle
But I saw your message that you say you did it
neon plover
ohh like rn??
ancient isle
am i blind
Damn
ancient isle
ohh like rn??
Yeah
neon plover
damn
vocal sleetBOT
Available help channel!
burnt sage
prove the following statement
a > b > 0 & n >= 2
vocal sleetBOT
prove the following statement
a > b > 0 & n >= 2
half imp
Do you have as a theorem $\sqrt[n]a+\sqrt[n]b > \sqrt[n]{a+b}$
twin meteorBOT
thewizardofOU
burnt sage
this theorem is understandable, but I don't know the proof
actually as a hint, I think we have to use Mean value theorem to prove this inequality
vocal sleetBOT
@burnt sage Has your question been resolved?
vocal sleetBOT
@burnt sage Has your question been resolved?
keen gulch
I need help with this functional equation f(x+1)-f(x)=2x+1
vocal sleetBOT
I need help with this functional equation f(x+1)-f(x)=2x+1
hard atlas
well there is one very obvious solution
steep widget
I need help with this functional equation f(x+1)-f(x)=2x+1
Z->Z?
vocal sleetBOT
@keen gulch Has your question been resolved?
keen gulch
does f go from whole numbers to whole numbers
No it's function from R to R
Real numbers
steep widget
any other restrictions?
keen gulch
any other restrictions?
No
keen gulch
well there is one very obvious solution
Yeah sure but I want general solution
hard atlas
you can set f(x) arbitrary on the interval [0,1)
and then extend it
so thats about as good as you can go for a "general" solution
keen gulch
you can set f(x) arbitrary on the interval [0,1)
How
@steep widget @hard atlas if you have any ideas type it I'll read it later
Thanks
hard atlas
well you can just quite literally make up whatever you want on the interval [0,1)
hard atlas
and then you know that f(x+1)=f(x)+2x+1 so you can then calculate for example f(1.5) as f(0.5)+2*0.5+1
steep widget
you can get the formula by guessing it and proving it with induction
if you know f(c) then you know f(c+n) and n is a whole number
btw if theres any other conditions, no matter how stupid or irrelevant they might seem they can help solve the problem(my experience with fes)
hard atlas
depending on context they are likely just supposed to guess the obvious solution. I dont know what condition you could even come up with to restrict it to that one
vocal sleetBOT
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short kraken
vocal sleetBOT
short kraken
i subtracted r3 from r1
and got - 3 -5 -62
i dont understand why that doesnt work if i got a 0 which is my goal
1 1 -2 -30
-1 -2 -3 -32
0 3 -5 -62
<@&286206848099549185>
vocal sleetBOT
@short kraken Has your question been resolved?
gaunt sparrow
1 - 1 = 0, -2 -1 = 3, 3 - (-2) = 5, 32 - (-30) = 62
Since they explicitly ask for R3 -> -R1 + R3.
short kraken
where did you get -2 -1
short kraken
Since they explicitly ask for R3 -> -R1 + R3.
but thats a weird way to do it no?
if my goal is to get a 0 why doesnt my method work
gaunt sparrow
It does work they just tell you explicitly what operation to perform.
short kraken
i see
gaunt sparrow
You essentially did what they did and then multiplied by -1.
That would be the equivalent in elementary row operations.
short kraken
i see
vocal sleetBOT
@short kraken Has your question been resolved?
vagrant wagon
if this (2nd img) is true, then wouldnt the derivative of F(g(x))-F(a) just be f(x)
vocal sleetBOT
if this (2nd img) is true, then wouldnt the derivative of F(g(x))-F(a) just be f...
vagrant wagon
so why does the first image say that the integral equals f'(x)
lime gorge
No
vagrant wagon
im really confused on the questions that ask for f'(x) or f''(x)
when theres a integral
lime gorge
They took the derivative of f(x)
Differentiated the integral using the fundamental theorem of calculus
vagrant wagon
so the top limit - bottom limit thing (FTC) is just solving for the value of f(x)?
and you take the derivitive of both sides to get f'(x)?
lime gorge
and you take the derivitive of both sides to get f'(x)?
Differentiate f(x) to get f’(x) yes
vagrant wagon
i think i understand
vagrant wagon
but wouldnt that mean that f(x) = x^3-6x^2 (equation from 1st image)
im so confused
vagrant wagon
does doing f(b)-f(a) which replaces t with x include the derivative somewhere as well
because i thought that the integral where the top limit has an x and the bottom limit is a constant just equaled the integrated function with t replaced with x
so what does just this part equal?
.close
solemn gulch
why does it have no vertical asymptote
vocal sleetBOT
why does it have no vertical asymptote
solemn gulch
ah my bad it does
potent stirrup
What do you know about vertical asymptote?
potent stirrup
What do you know about vertical asymptote?
yes, it does, but
thin vale
it does
thin vale
not exactly
solemn gulch
also when the Limxtosome number equals infinity
thin vale
does (x-1)/(x-1) have a vertical asymptote when x=1?
no idea what limxtosome number is
vast shale
I think it's limit
solemn gulch
no it doesnt it ha s a removable discontinuity
potent stirrup
Limit x to some lol
thin vale
no it doesnt it ha s a removable discontinuity
but the denom is =0
thin vale
well vetrical asymptotes happen
so for that reason you need some more qualifications here
solemn gulch
but the denom is =0
but they cancel with the num
solemn gulch
no idea what limxtosome number is
i meant when the lim(x to a)(f(x)) equals infinity, a being the suspected asymptote
okay thanks for the help guys
.close
royal elm
Each test fiber was produced 5 times under similar conditions and its strength was tested on 5 identical devices. Assuming that each fiber has the same strength, the number of breaks of a given fiber should be binomially distributed with five trials and an unknown probability p of fiber break. If all fibers are of the same strength, p should be the same for all of them, if they are of different strength, p should vary from fiber to fiber. The following table summarizes the outcome of the experiment:
a) Assuming the same strength of all the test fibers, estimate the break probability p.
Is the break probability here 69 + 25 + 17 + 1 + 1 / 157 + 69 + 35 + 17 + 1 + 1
Or is it (69 + (35 * 2) + (17 * 3) + (4 * 1) + (5 * 1)) / 157 + 69 + 35 + 17 + 1 + 1
vocal sleetBOT
Each test fiber was produced 5 times under similar conditions and its strength w...
vocal sleetBOT
@royal elm Has your question been resolved?
vocal sleetBOT
@royal elm Has your question been resolved?
orchid pier
can anybody help me out with this one?
vocal sleetBOT
can anybody help me out with this one?
orchid pier
im bad at limits 😦
tidal dock
multiply top and bottom by conjugate
orchid pier
i meant the same approach
multiplying both with conjugate
i think so yeah? @tidal dock
vocal sleetBOT
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orchid pier
.close
fallen sandal
vocal sleetBOT
tribal moss
because w = -2 does not satisfy the original equation
fallen sandal
because w = -2 does not satisfy the original equation
Fr
I tested 2
On accident
😭
But it still doesn't work right
With -2
plain badge
!help
vocal sleetBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
plain badge
prove the identity
tribal moss
prove the identity
I give you a hint:
$\sec\left( x \right)-\tan\left( x \right)=\frac{1}{cosx}-\frac{sinx}{cosx}=\frac{1-sinx}{cosx}=\\=\frac{sin\frac{\pi}{2}-sinx}{cos\frac{\pi]}2{+cosx}}$
twin meteorBOT
Joanna Angel
vocal sleetBOT
@plain badge Has your question been resolved?
feral helm
Need help on these two questions
vocal sleetBOT
Need help on these two questions
vocal sleetBOT
@feral helm Has your question been resolved?
feral helm
<@&286206848099549185>
vocal sleetBOT
@feral helm Has your question been resolved?
vocal sleetBOT
@feral helm Has your question been resolved?
crimson grove
Can someone help me understand why I'm wrong here?
vocal sleetBOT
Can someone help me understand why I'm wrong here?
velvet torrent
are you perhaps missing a comma in your answer?
crimson grove
are you perhaps missing a comma in your answer?
even then its still wrong 😦
crimson grove
<-3y, -3x>
still wrong
crimson grove
<@415124030408884245> works?
Worked! But why?
velvet torrent
lmaooo. ofc it worked.
idk, i just hit and trial
since x is given, y is given. their values are given
crimson grove
lmaooo. ofc it worked.
Oh, also. Do you understand why I'm getting b wrong?
velvet torrent
Oh, also. Do you understand why I'm getting b wrong?
wut have you done exactly? could you explain?
crimson grove
wut have you done exactly? could you explain?
for part b?
velvet torrent
ye
crimson grove
ye
The limits of integration a and b are 0 and 1, respectively, since we want to go from t=0 at point P to t=1 at point Q. To find r′(t), we differentiate r(t)with respect to t:
r′(t)=−4i^+5j^
Substituting r(t) into F gives:
F(r(t))=−5ti^+(4−4t)j^
So wouldn't line integral become (−5ti^+(4−4t)j^)⋅(−4i^+5j^)dt?
from 0 to 1?
velvet torrent
So wouldn't line integral become (−5ti^+(4−4t)j^)⋅(−4i^+5j^)dt?
and wuts the dot product of this?
crimson grove
and wuts the dot product of this?
Oh, I should actually calculate it..
velvet torrent
So wouldn't line integral become (−5ti^+(4−4t)j^)⋅(−4i^+5j^)dt?
this
and the answer you submitted
are not the same
vocal sleetBOT
@crimson grove Has your question been resolved?
bleak remnant
vocal sleetBOT
bleak remnant
i currently have this (40x^(4/3) +8x^(-2/3) )/ 9x^(1/9)
can i manipulate that to turn into the one i sent or did i mess up my derivation
the function is
spiral inlet
i currently have this (40x^(4/3) +8x^(-2/3) )/ 9x^(1/9)
this isn't quite equivalent to your first picture, the 1/9 in the denominator becoming 4/3 doesn't add up
I'm not really sure what you're trying to do. what is the entire problem?
bleak remnant
its graphing stuff but im struggling with the derivative
bleak remnant
the function is
i cant get the derivative of this
spiral inlet
can you show your work?
spiral inlet
oh yeah that's good now
spiral inlet
i currently have this (40x^(4/3) +8x^(-2/3) )/ 9x^(1/9)
up here you had a 1/9 exponent in the denominator
spiral inlet
but yeah what you have now is correct
spiral inlet
I'm guessing they wanted to get rid of the negative exponent
what do you think you could do to get rid of the negative exponent by the 8? 🤔
bleak remnant
i can separate the two?
spiral inlet
you could, but then you'll have two different denominators
bleak remnant
ohh
spiral inlet
looks like they just multiplied the numerator and denominator by x^(2/3)
spiral inlet
looks like they just multiplied the numerator and denominator by x^(2/3)
just this
spiral inlet
it's just making an equivalent fraction
you can multiply by $\frac{x^\frac{2}{3}}{x^\frac{2}{3}}$ because it's equal to 1
twin meteorBOT
tatpoj
spiral inlet
you're essentially just multiplying by 1
bleak remnant
.close
stuck girder
How do you prove that
vocal sleetBOT
How do you prove that
stuck girder
For integers 1 to 3 for a b, show that 100a^2 + 10ab + b^2 is composite
and NO they don’t allow brute forcing
You have to show it
How do you show it
I’m stuck completely
At the start
Bruh who put that
raven owl
For integers 1 to 3 for a b, show that 100a^2 + 10ab + b^2 is composite
Trippin
Nvm im trippin but that does not seem to be true
For a=1 and b=3 this is prime
vocal sleetBOT
Available help channel!
patent storm
vocal sleetBOT
patent storm
What should k be so that there are no result
maiden iron
I believe k is just a constant
patent storm
K should be replaced with a number but I have no idea which
velvet torrent
K should be replaced with a number but I have no idea which
10
cuz y is already 9
if k is 10, then the x term from 2nd eq. dissaprears
and youre left with 9=0
patent storm
Thanks 🙏
velvet torrent
which cannot be
warped dragon
in future try and avoid just giving solutions
patent storm
.close
fading forum
vocal sleetBOT
fading forum
how can I convert it a recurrence relation
should I divide stairs into parts or add 1 step at a time
think it is
$a_n = a_{n-3}+2$
twin meteorBOT
Ñøïr
vocal sleetBOT
@fading forum Has your question been resolved?
twin meteorBOT
Ñøïr
vocal sleetBOT
@fading forum Has your question been resolved?
fading forum
hint: consider the first step you take
n0 = 3?
oh, not base case
mm depends on the size of step you take it either down to a_(n-3) or a_(n-1)
tall patio
yes
so to climb n stairs
you have as many ways as n-1 stairs + n-3 stairs
so there yoi have your recurrence
fading forum
should I make a combination with repeating elements then?
fading forum
i dont get it
whats a_n then?
like for n=4 I can use 1-3, 3-1, 1-1-1-1 steps
thats why I asked combination
vocal sleetBOT
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vocal sleetBOT
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vocal sleetBOT
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crimson pasture
im still trying to do the problem and I just notice that 13/5 is probably incorrect
twin meteorBOT
🐵
crimson pasture
Ok..... Don't call yourself dumb your just not at that math level yet
Are you trying to simplify it?
Its cut off what does the instructions say
7a?
@vast shale
lol
Oof
Have you posted this question in the help forum?
ionic dagger
vocal sleetBOT
@fading forum Has your question been resolved?
rare nest
bro just assume arctan(-12/5) = theta
you'll get sec(2theta)
its 1/(cos^2(theta) -sin^2(theta))
so -12/5 is in 4th quadrant where 12 is perpendicular and 5 is base (no need to worry about signs here b/c we're going to square them eventually)
we can write tan(theta) = -12/5 = P/B
by calculations hypotenuse is 13
cos(theta) = B/H = 5/13
sin(theta) = P/H = 12/13
1/(cos^2(theta) -sin^2(theta)) = 169/(25-144) = -169/119
fading forum
how can I convert it a recurrence relation
should I divide stairs into parts or add 1 step at a time
reposting question it gone too high up
bronze osprey
how can I convert it a recurrence relation
should I divide stairs into parts or ...
if you are at n stairs, then you have 2 ways to make it to n + 3 stairs
1 + 1 + 1 or 3
this suggests you should break the problem into when n = 0, 1, 2 mod 3
also note that for n = 5, you can have 1, 3, 1 or 3, 1, 1 or 1, 1, 3 or 1, 1, 1, 1, 1
twin meteorBOT
Ñøïr
fading forum
but it has an +1 when n mod 3 is 2
fading forum
n= 8 has 13 ways
bronze osprey
ahhhhhh
if that's true, then 1 * 3 + 1 = 4
4 * 3 + 1 = 13
do you see the pattern here?
fading forum
I do, but it depends on mod 3 so dunno how can I interpret it in recurrence relation formuyla
bronze osprey
nah, it shouldn't depend on mod 3
bronze osprey
also note that for n = 5, you can have 1, 3, 1 or 3, 1, 1 or 1, 1, 3 or 1, 1, 1,...
so there are 6 ways to have 1, 1, 3, 3 in any order for example
and then 6 ways to have 1, 1, 1, 1, 1, 3 in any order
I'm not sure
bronze osprey
oh right, and then all can be 1
yeah, the same logic should apply for n = 4 to n = 7
so here it's just 1, 3; 3, 1; or 1, 1, 1, 1
so for n = 7, we can have 1, 3, 3 in any order = 3 ways
1, 1, 1, 1, 3 in any order = 5 ways
all 1s = 1 way
yep it depends on mod 3
fading forum
I dont really remember the formula for combination with repititve elements
or whether should I use combination or permutation in this case
bronze osprey
or whether should I use combination or permutation in this case
nah that's not it
ok so 4 has [1, 3] or 2 elements
that's equal to ceil(4/3) = 1.3333 rounded up = 2
bronze osprey
i dont get it
yes
the 3 ways, 5 ways, 1 way for n = 4
or the 6 ways, 6 ways, 1 way for n = 5
it depends on the number of elements n
fading forum
wdym ways
fading forum
ok but 5 ways for 4?
bronze osprey
like how did you get 13 ways for example for n = 8? did you write all the ways out
fading forum
n=8*
fading forum
I meant you would reach n=4 certainly in less than 5 steps
fading forum
like how did you get 13 ways for example for n = 8? did you write all the ways o...
for 3,3,1,1 combiinations there are 6; for 3,1,1,1,1,1 combinations there are 6 and for all one combination there is only 1 possibility, adds up to 13
fading forum
I thought
just imagine you add 3 more steps to n step stair
now you have your previous combinations in your hand
you assume a_n satisfies for inductive step and try to prove a_(n+3)
think of a_n as a one big intact step
you can climb n+3 in n,3
3,n
1,1,1,n
bronze osprey
yeah right ok
fading forum
so on
hence a_(n+3) = 6*a_n/2
I am just not sure how I will implement the case n mod 3 = 2 here
also tbh I am not sure how to actually calculate the 2 in denom
it just worked so I kept it
vocal sleetBOT
@fading forum Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vale ermine
How do i rotate my parabola by 45° , i know something like multiplying ( x + iy)(cos theta + i sin theta) theta be pi/4 then the new X coordinate is the real part and Y cordinate is the imaginary part i did this
vocal sleetBOT
How do i rotate my parabola by 45° , i know something like multiplying ( x + iy)...
vale ermine
but it rotated clockwise and the vertex changed ??
do i need to multiply by the conjugate for anti clockwise
vocal sleetBOT
@vale ermine Has your question been resolved?
vocal sleetBOT
@vale ermine Has your question been resolved?
hushed nebula
You might have to parameterize the parabola and multiply this positional vector you get from the parametrization with a rotation matrix
The rotation matrix has the form $\begin{bmatrix}
\cos(\theta) & -\sin(\theta)\
\sin(\theta) & \cos(\theta)
\end{bmatrix} $
twin meteorBOT
edwardborn
hushed nebula
Parametrization of a parabola may be $\begin{bmatrix}
t\
t^2
\end{bmatrix}$
twin meteorBOT
edwardborn
hushed nebula
This basically gives you that
$x(t) = t\cos(\theta) - t^2 \sin(\theta)$ and
$y(t) = t\sin(\theta) + t^2 \cos(\theta)$
twin meteorBOT
edwardborn
hushed nebula
Not sure if it's cheating to parameterize the curve but it is possible to turn it back into a function as long as you limit the range of t, although the expression for it might not end up that pretty
vocal sleetBOT
@vale ermine Has your question been resolved?
sharp furnace
Can someone explain to em what the difference between "total area" and "net area" is
vocal sleetBOT
Can someone explain to em what the difference between "total area" and "net area...
sharp furnace
one seci m sending pics
my other pic of my work is still sending
it says -5 is right for the net area.. but like.. why
heres the previous question which i got right but it just says area nothing about net or total
velvet torrent
so, like when integrating, area above the x-axis is considered +ve area and below it is -ve area.
so, when you sum all of it as is, you get net area.
but, if you sum the absolute values of all the areas, (meaning, the "true" area), you get total area
sharp furnace
but theres only one area theres only one fucnction
velvet torrent
yess. only one function
but, when integrating for net area, you take the entire interval
sharp furnace
heres the previous question which i got right but it just says area nothing abou...
yeah like i did for htis question
velvet torrent
while, when integrating for total area, you break down the interval to where the value of function is negative. you multiply this area with -1, so you get a +ve area. then you sum it all up
sharp furnace
so it would be positive 5?
vocal sleetBOT
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@sharp furnace Has your question been resolved?
sharp furnace
.close
pseudo whale
Hello i have to do a variation board of the derivative function :
f(x)= 3-5/x
which is f'(x)= 5/x²
I know how an inverse function works but the ² disturbs me, does it changes something or the board is still like this :
frosty mural
What is 3^-2
frosty moss
i identify as a 8l w16 quad turbo buggati engine
frosty mural
i think that will be helpful
frosty moss
actally nah
frosty mural
3^-2 is 9/1 correct?
frosty moss
i identify as a quad core playstation 5 cpu with gold pins
frosty mural
@pseudo whale
pseudo whale
What is 3^-2
Wait my wifi sucks 2 sec
frosty mural
if u can understand this, im assuming that u know how 2 rewrite 5/x
That is a small hint
pseudo whale
SO yes it is
pseudo whale
if u can understand this, im assuming that u know how 2 rewrite 5/x
5/x * -2 ?
pseudo whale
Ok so 5*x^-2 here right
frosty mural
yes
actually it is -5*-1*x^-2
-5*-1
u k why right?
and it is same as 5x^-2
which is 5/x^2
pseudo whale
Yeah yeah sure mb
@frosty mural I got it so just to be sure, is this the correct board here ?
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sharp furnace
How on earth do I start this? I tried to search it up before asking for help but i just dont undestand
vocal sleetBOT
How on earth do I start this? I tried to search it up before asking for help but...
lean forge
you have to compute the area
sharp furnace
i know. and i tried to do that but how do i find the formulas
like for 6 and 4
i got the formula was 2x
so i did it all
and the intergration
lean forge
Cut the function into triangles and squares
sharp furnace
2(1/2x)^2
lean forge
And use area formula for triangles and squares
sharp furnace
no it has to do with intergration
so i dont think id use the area of this graph
i think i have to find something else
lean forge
why ?
sharp furnace
intergration
lean forge
seems to me like this function was drawn to make the computations for area simpler
since every point is an integer
sharp furnace
yeah but this is the intergral
graph
we wanna find the area so we're gonna have to antiderivative
somewhere
and use the definite intergral function
sharp furnace
yes
lean forge
not integral of f(x)
fathom ridge
Interesting function
sharp furnace
I cant just split this up and find the area with boxes and squares
it has definite intergral functirons
lean forge
brother what
sharp furnace
on the bottom
lean forge
Yes
fathom ridge
@sharp furnace u wanna calc the area?
sharp furnace
sharp furnace
the entire hw has made me use antiderivatives and area functions.
this homework will as welll.
lean forge
Lets take the first one
sharp furnace
sharp furnace
ok yeah but where does the intergration fit into this
it cant be as simple as finding the area of a triangle.
lean forge
3*4/2 is the area then
lean forge
ok yeah but where does the intergration fit into this
Because integrating is the same as finding the area ?
just dont forget to put a - sign in front of the area
when the function
is under the graph
fathom ridge
Just question :
|| What the function that u use to calc the area ||
sharp furnace
ok but some of these u cant draw triangles or
sharp furnace
Just question :
|| What the function that u use to calc the area ||
definite functios
functions
intergral
definite intergrals
lean forge
ok but some of these u cant draw triangles or
which one
sharp furnace
which one
literally the rest of them
one of them has a singulairty too
3 is a singularity
sharp furnace
the height?
lean forge
yes
sharp furnace
wahhh
lean forge
and lenght is one
sharp furnace
so (-2)(1)/2
sharp furnace
-1 + 1.5 +
lean forge
maybe you'll use it for 4th one
lean forge
wait why wont we use the red one
we integrating from 0 to 3
sharp furnace
yea
lean forge
the red one is from 3 to 4
fathom ridge
I think u can calc the block Under the graph
Make it very smooth to be like integral, but it's will little bit hard to calc it
Or call whole the block so it's will be like the sum of this function, But the result will be inaccurate
fathom ridge
You can cut everything like that
Yea that better
sharp furnace
ok so the next one is 18
fathom ridge
Hmmm yeah true
fathom ridge
ok so the next one is 18
Which one?
lean forge
ok so the next one is 18
yes
lean forge
No
sharp furnace
oh -3
lean forge
-(3+3/2) is the area
sharp furnace
its sayin thats not correct : (
lean forge
so -3-3/2 = -4.5
lean forge
its sayin thats not correct : (
all of em ?
sharp furnace
ohhh
sharp furnace
all of em ?
no i got the first 3
the last one is gonna be
18 + whatever is under
sharp furnace
ok so
lean forge
Maybe too many calculations
Just take your precedent results
You already have the 0 to 3 one
So the only one missing is 3 to 4
sharp furnace
ohhhh
my bad
tysm haha i feel stupid
i can do calculations so easily but visually i suck
i just cannot do graphs
tysm 😭
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shell jolt
A+B = 31 so A = ? | B = ? + 2 units and ½ (Not here for anyone to do my homework at my place but can anyone help me?)
pale perch
!original
vocal sleetBOT
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.
shell jolt
shell jolt
like A=x and B=x+2
yeah
pale perch
whats written there confuses my mind honestly, is that literally what was given to you
shell jolt
whats written there confuses my mind honestly, is that literally what was given ...
yeah bro
pale perch
like 32AB+2+1/2
shell jolt
yes
mild flower
you are not OP
shell jolt
(the thing is that im a kid who needs help in math im in the beginning of college i want help for maths)
pale perch
just not sure how to help with that, regardless of how i interpret it, its not like i can solve for A or B as far as i can tell
theres just one equation and one ambiguous expression
lean forge
Is there any information on A and B in the instructions eg primes ?
pale perch
i could even read it as maybe A+B=32AB+2+1/2 but even then i cant do anything with it
you sure there was absolutely nothing else
shell jolt
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zealous coral
so is this just.. graphing the piecewise g(x) on the graph next to f(x)? 
how do i plug a written equation into a graph?
vocal sleetBOT
so is this just.. graphing the piecewise g(x) on the graph next to f(x)? <:cutet...
@zealous coral Has your question been resolved?
vast shale
[
\int x^n \dd x = \f{x^{n+1}}{n+1} + C \q n\in \R\setminus\set{-1}
]
twin meteorBOT
vast shale
for the case where $n = -1$: [
\int x^{-1} \dd x = \m\ln{\abs x} + C
]
twin meteorBOT
gaunt pelican
possibly? it's where you choose a u thats in your integral and replace it with u
vocal sleetBOT
gaunt pelican
no prob;em
vocal sleetBOT
Available help channel!
gaunt pelican
honestly no idea where to even start. could someone provide some insight?
vocal sleetBOT
honestly no idea where to even start. could someone provide some insight?
@gaunt pelican Has your question been resolved?
vocal sleetBOT
@gaunt pelican Has your question been resolved?
dire drum
hello, does anyone know how to compute the state of lsfr?
vocal sleetBOT
hello, does anyone know how to compute the state of lsfr?
heavy pine
initial state + updates?
vocal sleetBOT
@dire drum Has your question been resolved?
dire drum
what do u mean by updates?
dire drum
initial state + updates?
i have already found the first 15 bits of the lfsr output
vocal sleetBOT
@dire drum Has your question been resolved?
restive lance
vocal sleetBOT
restive lance
I proved everything circled in red.
But I don't know how to prove the last part of "d"
I did the tip but i dont know how to conclude
vocal sleetBOT
@restive lance Has your question been resolved?
restive lance
<@&286206848099549185>
restive lance
I want to simplificate Jn-1/In-1 -Jn/In
I think this is correct. In case n is a even number.
I forget n
Is π/2n
<@&286206848099549185>
restive lance
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vocal sleetBOT
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Available help channel!
grave mason
can someone help me with 10?
vocal sleetBOT
can someone help me with 10?
grave mason
the one at the top
and honestly if you know how to do any of them feel free to respond bc i’m soo fucked
vocal sleetBOT
@grave mason Has your question been resolved?
vocal sleetBOT
@grave mason Has your question been resolved?
livid helm
how did they get the 1 and 0?
livid helm
twin meteorBOT
nebula40
bright yew
you are just substituting the known values of sin and cos at pi over 2, yes
bright yew
are you familiar with the "well-known" values of trignometric functions?
mainly 0, 30 deg, 45 deg, 60 deg and 90 deg
livid helm
not so much
bright yew
well you should learn about them then
livid helm
ik that it looks like this !
bright yew
sin(pi/4) = sin(45 deg) = 1/root(2) = root(2)/2 is something you should know directly
vocal sleetBOT
@livid helm Has your question been resolved?
rain shell
vocal sleetBOT
cyan crest
I'm going to assume you don't know where to start?
a good hint would be the gradient using two points
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
twin meteorBOT
_Kookie
wooden stump
quartz helm
what's the derivative of tan(x)*ln(5)?
vocal sleetBOT
what's the derivative of tan(x)*ln(5)?
quartz helm
i'm getting ln(5) but i'm like 99% sure that isn't right
gaunt sparrow
What is the derivative of tan(x)?
quartz helm
sec(x)^2
gaunt sparrow
Ok what is the derivative of 5*tan(x)?
grand stone
QR - 4 , RS - 1/4 and for lengths use distance formula
quartz helm
ohhh, 5sec(x)^2
sleek flame
can someone explain how to prove that, for all positive integers a and b, there are integers s and t such that gcd(a,b) = sa + tb with strong induction?
vocal sleetBOT
can someone explain how to prove that, for all positive integers a and b, there ...
sleek flame
I have the solutions if that helps, but I just would like to go through the steps
flat whale
Just show the solution and ask where you don't understand
late ingot
gcd(a,b) = sa + tb
everywhere i go i see dot products.
vocal sleetBOT
@sleek flame Has your question been resolved?
sleek flame
Yall sorry Im back
ok, so this is the example in the text book, from what I see I think they found 3 base cases, where n=0,n-1,n>=2... i think strong induction is like you have some n <= m and you suppose k <n and prove n? Not sure whats happening in the solution
starting from the top, Im guessing the sequence of nums produced by the euclidean algorithm is just the remainders?
and the last term in the sequence is =0 which is what you want when applying the euclidean algorithm
and all the terms before the last num is a linear combination of a and b which is true as seen in bezout's identity and extended euclidean algorithm (what we want to prove)
So the Suppose n is a natural number part basically shows cases of numbers smaller than m, not sure why 3 cases.. and for strong induction, you gotta suppose the cases of m < n and prove n right??
after case 2 im not understanding, why is rn the remainder?
ohh I think r_n-2 is the bigger number right? in the sequence, so this is just a step in euclidean algorithm, like where you solve for gcd
okok but theres no way I'll actually be able to write all this myself
YALL IM SO SCARED
FOR MY EXAM
😱
sleek flame
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limber snow
vocal sleetBOT
limber snow
Can anybody help with the first part
Like I know why it works but I’m not sure how to explain it
I can’t just say that the coefficients coincide with n \choose k
vocal sleetBOT
@limber snow Has your question been resolved?
river minnow
It's true because, when expanding (x + y)^n, you need to choose either x or y from each parenthesis; So, to obtain, say, a term with y^k, you would need to choose y exactly k times out of the n parenthesis, and there are n choose k ways to do so
vocal sleetBOT
@limber snow Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
outer oracle
Can somoene help with this?
vocal sleetBOT
Can somoene help with this?
native kestrel
what grade are you in?
outer oracle
Tbh not really but i have nothing to sketch it down on but is there a way to find the integer's without sketching it?
floral ledge
ok erm
floral ledge
Its fine
to sketch it you first have to factor it
which wld come out to be (x-5)(x+2)
since its a x^2 graph the graph would be a U shape meaning it would have a lowest point
you can graph the points where x=0 on the graph
where x=5 and x=-2 those are the points where y=0
after that you need to find the minimum point x^2 graph U shape minimum -x^2 wld be maximum
you can do a+b/2 or -b/2a or completeing the square method to find the coordinates of the minimum point and just state it
outer oracle
what would be a and what would be b?
floral ledge
for part 2 (for the eqn to be smaller than 0) not sure if u have learnt discriminiant b^2-4ac but if u know the points on the curve where y=0 -2 and 5
x would be greater than -2 and smaller than 5
floral ledge
what would be a and what would be b?
a+b/2 in this case wld be -2+5/2
outer oracle
I have never learnt what discriminiant is
floral ledge
for -b/2a you use the quadratic coeficent
floral ledge
I have never learnt what discriminiant is
thats fine how shld i explain it you want y to be smaller than 0 that would be inside the graph
outer oracle
Ah ok
floral ledge
its the interger values before the letters
i gotta buck up on my eng ..
do u have the point on the graph sketched alr?
outer oracle
I have no paper or anything so i had to search up on google 'graph sketcher'
So i have a sketched one
floral ledge
you ned 3 main things 2 points where y=0 and max/min point x and y coordinates
aight sure if all 3 points are fufilled for part b
how do i explain this if u havent learnt discriminant erm
basically when x=-2 and x=5 subbing x into the calc you get y=0
you want interger values of the eqn to be <0
-2 and 5 rmb this 2 numbers if you want it to be smaller than 0 it has to go inside the graph 2 random points wld be -1 and 4 if u want it to be >0 you wld need it to be outside the graph -3 and 6 wld be a example
so ur ans for part b wld be -1 to 4
vast shale
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outer oracle
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final birch
Hello, I've learnt about geometric sequences, but but I do not know how to start this question.
vocal sleetBOT
Hello, I've learnt about geometric sequences, but but I do not know how to start...
sweet birch
I think the approach would be to split it into 3 sums
lucid bane
Then you can use known formulas for sum of geometric series (finite terms), sum of numbers from 1 to n
vocal sleetBOT
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Available help channel!
dreamy marsh
What do you guys get for how far the mass will go if it weights 200 grams? The "h" on the table isn't the "h" in the diagram, it's the height from the place the mass is dropped to the point the spring starts acting on it.
vocal sleetBOT
What do you guys get for how far the mass will go if it weights 200 grams? The "...
@dreamy marsh Has your question been resolved?
dreamy marsh
<@&286206848099549185>
vocal sleetBOT
@dreamy marsh Has your question been resolved?
round eagle
vocal sleetBOT
round eagle
is this a mistake? they neglected gravity both times
this is the full question for reference:
the working out's for part ii
nvm i figured it out
if any1 wants to know the specific weight = density* gravity ie density = 11.8/9.81 so it'd be (11.8/9.81)9.814 and it just cancels out
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vocal sleetBOT
vocal sleetBOT
Available help channel!
rain hollow
That is the bisector need to find all the sides
vocal sleetBOT
That is the bisector need to find all the sides
rain hollow
<@&286206848099549185>
iron zealot
That is the bisector need to find all the sides
all of the longuer ?
rain hollow
what?
iron zealot
what's the question ?
frank forum
That is the bisector need to find all the sides
a line tangent to a circle's radius is always going to be perpendicular, therefore you can turn this into 2 right-angled triangles
frank forum
just draw it out first
those 2 triangles
you're able to deduct more information when you look at it like that
rain hollow
i see the 2 right triangles now?
frank forum
i see the 2 right triangles now?
yeah, and you can deduce some information about those 2 right angle triangles from what you've drawn
frank forum
show me what you drew
howd you get 5x?
that looks like $\lambda x$ not $2x$, therefore it would be $(\lambda+3)x$
twin meteorBOT
Xerunox
