#help-42
calm coralBOT
amber basin
I would multiply both sides by 2 and also 3
and then it's a simpler equation without denominators
sterile island
yeah how do I do that?
amber basin
$2(\frac{x}{2} + \frac{x}{3}) = 1(2)$
potent lotusBOT
kihei
amber basin
that comes to?
sterile island
what is 2(x/3)?
amber basin
$a(\frac{b}{c}) = \frac{ab}{c}$
potent lotusBOT
kihei
calm coralBOT
calm coralBOT
Available help channel!
remote mural
I need help with (5^(-3)*5^(7))/(5^(8)) if anyone can help me
wise spire
x^a * x^b = x^(a+b)
leaden thunder
velvet osprey
if you squint the denominator is 9^n
foggy elm
oh i see
fathom shuttle
Each term in the sequence is less than 8^n/9^n
foggy elm
so if you make the denominator 9^n that would converge right
remote mural
yes
fathom shuttle
If you show its less than the convergent sequence, it converges
foggy elm
is there like a general rule to finding what to make the b_n
or do you just have to guess
brittle reef
whats one times six divided by seven?
calm coralBOT
whats one times six divided by seven?
amber wedge
6/7
brittle reef
thanks
amber wedge
,calc 6/7
potent lotusBOT
Result:
0.85714285714286
thanks
amber wedge
Np
calm coralBOT
@brittle reef Has your question been resolved?
sweet jolt
Can anyone see any things you could conclude from this shape?
true owl
Hello
marsh agate
All other things being constant, this is just a linear equation
calm coralBOT
@true owl Has your question been resolved?
undone charm
`
v = [1;0;0];
x = [0;1;0];
y = [0;0;1];
step = .1;
for k = 0:step:2 % 0 to 2 seconds, with step size.
x_vel = .1 + (k/5);
y_vel = .2 + (k/5);
d = x/norm(x)*(x_vel*step) + y/norm(y)*(y_vel*step);
d = d/norm(d)*tan(norm(d));
x = x - (dot(x,v) *v) / (norm(v)^2);
y = y - (dot(y,v) *v) / (norm(v)^2);
v = (v+d)/norm(v+d);
end
`
Hello, given the initial values of a unit vector "v", and initial values of vectors "x" and "y" ( x and y can have any magnitude but most be perpendicular to each other and perpendicular to vector "v") and continuous values of x_vel and y_vel for a certain time, I am able to run this code with whatever step size I want and I save the x,y,z values of the "v" vector over time. The code I am running solves an for the "v" vector through a certain step size, I am trying to find the equivalent program, but in an integral fashion. Right now I can't truly integrate the values from 0 to 2 seconds because I can't use infinitely small step sizes. The "v" values overtime are continuous.
The only thing I can do right now is interpolate between the "v" vector values I get to get an estimate area under the curve that is close but not exact.
glass heart
so you want to symbolically integrate?
with a program?
or what exactly is your question
approximating integrals is super standard
calm coralBOT
@undone charm Has your question been resolved?
undone charm
so you want to symbolically integrate?
I am wanting to get an integral without a program. I would like to somehow put my starting values into an integral and it can give me the true area under the x,y,z curves. Right now I can only get as many values as how many steps I do with my program.
So I have a unit vector "v" with 2 perpendicular vectors "x" and "y" such that x and y are also perpendicular and the magnitudes of "x" and "y" represent the angular velocity of "v" at any time, and the direction of "x" and "y" represent the direction of that angular velocity respectfully. The magnitudes of "x" and "y" are scalar and they are KNOWN. In the code I reference them at any time with a sample function. Basically given the starting vector positions and the velocity magnitude components of "x" and "y", I want to integrate the vector "v" positions overtime so I have an x,y,z components graph each over time. Currently I have code that can get the integral estimate with a certain step size. I am trying to get an actual integral formula so I don't have to interpolate and use step sizes to get all my values of "v".
The code first gets "d", the vector to add to "v" such that the sum will be the new vector "v" after the step size of "k" seconds. Then the x and y components are projected onto the new plane where "v" is. That way I am able to transfer the "v" vector again, knowing x and y are still on the same plane.
I am trying to get an integral equation equivalent of the code I have right now. It would integrate the vector "v" components overtime. Right now I can only get an estimate with a step size. This is for a control theory project and I am getting these values to integrate position of a vehicle moving from one orientation to another.
Sorry to bombard with information, this might help explain what I am doing
calm coralBOT
@undone charm Has your question been resolved?
calm coralBOT
@undone charm Has your question been resolved?
split wind
Do you know the geometric interpretation of the slope of a line?
Or how to calculate the slope from two points?
remote mural
Do you know the geometric interpretation of the slope of a line?
no not really
calm coralBOT
@undone charm Has your question been resolved?
split wind
no not really
Geometrically the slope of a line tells you how much you go up or down on the y-axis, as you go 1 to the right on the x-axis.
Example: a line with the slope 3 would go up 3 in the y-axis every time you go 1 to the right on the x-axis. Likewise you would go 6 up the y-axis if you went 2 to the right on the x-axis and etc. This gives us the following relation:
If a line has slope we call "a" then the change in y called "Δy" is equal to "a" times the change in x called "Δx". Also written as Δy = a ∙ Δx. Dividing by "Δx" on both sides, we get the the slope "a" can be calculated as a = Δy/Δx.
Now, how do we find Δy/Δx from two points? Remember that "Δy" is the change in y. From two points this would be the difference between the y-values of the points. (Example: if you had the points (5, 4) and (3, 1), then Δy = 4 - 1). Likewise with "Δx" it is the difference between the x-values of the points (Example: if you have the same points (5, 2) and (3, 4) then Δx = 5 - 3).
When you have these two values calculated, you can substitute them into the equation we had earlier (a = Δy/Δx).
General formula if you are still stuck: ||For two points (x₁, y₁) and (x₂, y₂) the slope "a" of the line between these points is calculated by a = Δy/Δx = (y₁ - y₂)/(x₁ - x₂)||
remote mural
Geometrically the slope of a line tells you how much you go up or down on the y-...
OMG TYSM FOR THE HELP YOU SAVED ME!!!!
split wind
OMG TYSM FOR THE HELP YOU SAVED ME!!!!
Of course 😄 I hope it helped you get a better understanding of slopes for lines 💪
remote mural
Of course 😄 I hope it helped you get a better understanding of slopes for lines...
AGAIN TYSM SO HELPFUL
.done
calm coralBOT
@undone charm Has your question been resolved?
remote mural
are these correct?
calm coralBOT
are these correct?
lusty rampart
are these correct?
well in q2, the angles in the middle are vertically opposite
so i guess it would be aas
remote mural
alright, ty.
lusty rampart
np
lusty rampart
saa and aas?
they would be the same
two angles and a side
but it would be aas/saa
calm coralBOT
@remote mural Has your question been resolved?
native pine
Hello how do you solve this equation?
calm coralBOT
Hello how do you solve this equation?
native pine
the 3 = 1,03x specifically
remote mural
Logarithms
calm coralBOT
calm coralBOT
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valid trail
for example
a = 45%, b = 75%
if a is worth 60% of the total and b is worth 40% of the total how do i calculate the total? (what should be a percantage)
calm coralBOT
*for example*
a = 45%, b = 75%
if a is worth 60% of the total and b is worth 40%...
@valid trail Has your question been resolved?
valid trail
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runic scroll
Help on question 10)
And in general how do "direct" triangles work and how do I name them
calm coralBOT
@runic scroll Has your question been resolved?
calm coralBOT
@runic scroll Has your question been resolved?
calm coralBOT
@runic scroll Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
tawdry crescent
$\frac{18- \frac{18}{\pi+4} (\pi + 2) }{2}$
calm coralBOT
$\frac{18- \frac{18}{\pi+4} (\pi + 2) }{2}$
potent lotusBOT
minor2ndchar
tawdry crescent
how to simply this
dusk rock
Can somebody help with a practice problem I have
calm coralBOT
Can somebody help with a practice problem I have
dusk rock
So far I have shown that 1|a+3b and 1|5ab. Which implies that 1|a and 1|b. But im not sure how to proceed
warm wren
So far I have shown that 1|a+3b and 1|5ab. Which implies that 1|a and 1|b. But i...
💀what
in what way is it useful that 1 divides a and b
dusk rock
we're trying to show that the gcd(a,b) = 1, so we need to show that 1 is a divisor of a and b
warm wren
💀
That's not how it works
lmao 1 divides every number
you need to show that no other numbers divide them both
dusk rock
how do i show that though?
warm wren
contradiction
assume that some d that isn't 1 divides them both
and show that that is impossible
also remember that 1 divides anything so there is no meaning to saying that 1 divides a
dusk rock
alright 👍
shrewd ibex
.reopen
calm coralBOT
✅
shrewd ibex
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calm coralBOT
calm coralBOT
Available help channel!
vivid frost
calm coralBOT
patent salmon
winter hazel
hi
calm coralBOT
Available help channel!
coarse beacon
for the collection
calm coralBOT
for the collection
coarse beacon
A = {1,2,3....,8}
how many different injectives are there from A to A?
one right?
same with the amount of bijectives
just one?
or is it 8 since there's 8 elements
and 1 goes to 1, 2 to 2 and so forth
calm coralBOT
@coarse beacon Has your question been resolved?
coarse beacon
<@&286206848099549185>
coarse beacon
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silent adder
Hello, im just wondering how to prove the product of any 3 consecutive numbers is divisible by 3
silent adder
cause by 2 its easy but idk exactly how you would prove them by 3
and i dont really think the probability thing would be solid enough for my teacher tbh
wait i gtg ill be back
ok im back
<@&286206848099549185>
is there no proof for it like the proof for 2 consecutive numbers being divisible by 2
with 2k and 2k+1 and stuff
yeah i know
in our proof system the more solid proof would be to define the product as n(n+1) and take the 2 cases where n are even and odd
for instance
1: n = 2k
=> 2k(2k+1) = 2(k(k+1)) => 2|n(n+1), (∀)k∈ℕ*
2: n = 2k+1
=> (2k+1)(2k+1+1) = (2k+1)(k+1) * 2 => 2|n(n+1), (∀)k∈ℕ*
from both => 2|n(n+1), (∀)k∈ℝ (we work in ℝ)
thats the proof for the first statement
im wondering if there is some simmilar proof for divisible by 3
and 3 consecutive numbers
why is that
what is the concrete proof that that occurs
its definately not an axiom
i know its true but i have to prove it
yeah ok thank you
i got it
so that basically encompasses all possible numbers in terms of 3
with long division and stuff
thank you
i never knew you could do that
.close
violet glacier
Hello, I was trying to solve this problem but ended up with a wrong answer, can someone correct me when I did wrong?
potent lotusBOT
Modus
violet glacier
e.g?
violet glacier
There are 3 equations for polynomials
and sometimes I cannot switch the order
And need to fit one of the equations
silent adder
can you send the questions?
violet glacier
Not from an English speaking country so excuse me
silent adder
dw youre fine
violet glacier
(-x-6)^2 - (x+8) (x-8)
silent adder
in this case at the first one you can put it in a seperate parantheses:
=(-(x+6))^2 - (x^2 - 8^2)
since minus squared is always plus just solve for (x+6)^2 in the first one
and the 2nd one difference of squares but make it x^2 + 64 due to the minus
minor patio
I just need help finding the roots to this problem
calm coralBOT
I just need help finding the roots to this problem
merry lantern
oh sorry
heady knot
how do you generally find roots of quadratic equations=?
high igloo
how do you generally find roots of quadratic equations=?
theres 3 methods
factoring, quadratic equation, completing the square
(or graphing)
oh ur not the one that asked the question lol
minor patio
I tried factoring with the Diamond, but that does not work
heady knot
if all else fails
the quadratic formula does not
you can always relly on it, it's your only friend in life
solve the equation with the quadratic formula, the sollution are the roots
high igloo
it even gives u complex numbers
minor patio
I did quadratic formula and I got this as an answer
But i feel as if there is more to this
warped rampart
nope thats it
glad trench
how do i know when i got the correct answer?
i feel like i could reduce these trig functions forever
latent steeple
,w simplify (1+sinx)/cosx
latent steeple
tan (x) + sec(x) looks the simplest
calm coralBOT
@glad trench Has your question been resolved?
glad trench
tan (x) + sec(x) looks the simplest
oh shit my bad, i didnt see your response
glad trench
tan (x) + sec(x) looks the simplest
so just simplify until i only get a few function with no fractions right?
latent steeple
Seems to be the right yeah o
eternal orchid
calm coralBOT
eternal orchid
need help with this question
please
just all of it, mainly where to start
i just need someone to tell me where to start and i'll be good
.close
odd epoch
There is a linear correlation between y'(t) and y(t). The 2 points (0,0) and (4,3) are on the graph that describes the correlation between aforementioned. What differential equation describes the correlation
calm coralBOT
There is a linear correlation between y'(t) and y(t). The 2 points (0,0) and (4,...
@odd epoch Has your question been resolved?
Available help channel!
proper dome
calm coralBOT
proper dome
I need help having this explained
ocean cypress
Finite strings?
calm coralBOT
@proper dome Has your question been resolved?
proper dome
Finite strings?
Uhh I guess so
I couldn't attend the last lecture, so I don't know what this is 🥴
warped warren
claim
warped warren
(-44/5+(sqrt)3)
attempting to rationalize this
and i just cant seem to get an answer that the online learning tool i am using likes
.close
calm coralBOT
calm coralBOT
Available help channel!
topaz thunder
calm coralBOT
topaz thunder
Does anyone know how to solve this? I know the quadratic equation, but the answer apparently had to be two fractions..
clear sapphire
Can you show your work?
topaz thunder
Alright, one moment (I’m working with paper)
placid vortex
Does anyone know how to solve this? I know the quadratic equation, but the answe...
quadratic formula will give you 2 answers
placid vortex
Oh, then I probably did this wrong 😅
u have to move the x on both sides
u can't leave it alone an use the formula
formula only works when equaled to 0
-6x^2+x+1
now u can use the formula
topaz thunder
Okay, so the answer would be x= 4/12 or x= 6/12
placid vortex
Okay, so the answer would be x= 4/12 or x= 6/12
which one is negative?
topaz thunder
One sec..
placid vortex
also u can solve this by factoring
topaz thunder
Oh that’s a good idea
placid vortex
but i assumed there would be root but thats alright
placid vortex
factoring is always the number 1 way
topaz thunder
Like complete the square?
placid vortex
all else fails do completing the square or formula
topaz thunder
Yeah the T135 or whatever the number is
The $100 one
placid vortex
there is a quadratic solver on it
topaz thunder
Can you just go to calculate and type it in?
hidden elbow
Can you just go to calculate and type it in?
pic of ur calc
placid vortex
how does a scientific calc cost 100 dollars 💀
placid vortex
my TI-84 costed $109 BRAH
ce is better
hidden elbow
wtf
topaz thunder
FRRR my school requires it when some students just don’t have the funds for that stuff
hidden elbow
is that
topaz thunder
Wait fr?
placid vortex
yea
topaz thunder
Well it is over 5 years old so I guess it’s an older model
hidden elbow
bruh
topaz thunder
But it works fine
hidden elbow
okay it’s fine
placid vortex
yea no way its gonna have the quadtraic solver
but did u factor it and get the answer?
topaz thunder
I’ll find out, maybe I’ll ask my teacher or sum
hidden elbow
ask YouTube
topaz thunder
Oh no I just finished the equation through the quad. Formula cuz that’s what I was already doing
But yeah I got it
placid vortex
a right?
topaz thunder
Hell yeah
I’m smarter
I’m stronger
I’m better
I am better
Anyways sorry lmao
calm coralBOT
calm coralBOT
Available help channel!
split kayak
How would I go round solving this? I knoew position vector for S is (3t+9)i+(4t-6)j
calm coralBOT
How would I go round solving this? I knoew position vector for S is (3t+9)i+(4t-...
@split kayak Has your question been resolved?
calm coralBOT
calm coralBOT
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autumn stirrup
hey
autumn stirrup
the sequence (Un) : Un+1 = f(Un)
i need to show that for every U0 in R no matter what the first term is , (Un) converges
mortal orbit
here's a hint : consider the case when U0 >= 0 and the case when U0<0. Then, can you find an upper/lower bound to the sequence (Un) ?
mortal orbit
what are you having trouble with ?
autumn stirrup
suppose there is a A such as for every n : A<Un
f(A)<f(Un)
so f(A)<Un+1
but i don't have A<f(A)<Un+1 to use induction
mortal orbit
so that's for the case when U0 is positive I imagine
but have you got any idea of what A works ? :)
A doesn't have to be strictly negative btw
mortal orbit
yep
mortal orbit
No problem
autumn stirrup
i have a harder question if you're interested
@mortal orbit
are you french ?
or spreak french
autumn stirrup
ayyy
vive la france
ce problème est hyper intéressant
j'ai tout fait sauf la dernière
on a (n+1)wn = Sigma(vk)=1/(Un+1)^B - 1/(Uo)^B
comme limite do wn = m
mortal orbit
Oui
mortal orbit
Oui
mortal orbit
Pas besoin de ça il me semble
autumn stirrup
je pense que c'est nécessaire vu qu'il faut dessencdre le beta de puissance à coefficient
vu que y'a (1-a)xm
mortal orbit
Il me semble pas que le 1-alpha vienne de là
Pour moi il faut revenir à la toute première hypothèse sur un
autumn stirrup
oui
mortal orbit
Que (un+1 - un)/un^alpha -> m
autumn stirrup
et ducoup comment on le rend coefficient ?
mortal orbit
Laisse moi essayer de lecrire
mortal orbit
Ok mais c'est quoi le dl de 1/un+1 ^ beta ?
autumn stirrup
déjà pour simplifier les chances on travaille avec Un en remplacent tout n+1 par n
donc on cherche celui de 1/Un^B
autumn stirrup
att
ah mais qsq j'ai fais j'ai considéré que Un tends vers 1
j'ai essayé de faire un retour en arrière
mortal orbit
En fait, tu repars de 1/n × 1/un^B -> m
autumn stirrup
il suffit de montrer que = 1/Un^B equivaut (mn(1-a))
autumn stirrup
un dl ?
mortal orbit
Non je crois pas
autumn stirrup
je vois pas ce qui pourrais faire descendre a d'une puissance à un coefficient à pars le dl et le binomial
autumn stirrup
quand j'ai essayé de calculer j'ai trouvé m
mortal orbit
Il me semble que ça doit être égal à m(1-alpha)
autumn stirrup
t'as fais comment
mortal orbit
T'as peut être un tricks de DL
mortal orbit
Ah ouais mais ça ça marche pour n entier xd
mortal orbit
Tu fais un equivalent du dénominateur avec l'hypothèse
autumn stirrup
(Un)^2B
mortal orbit
(Un)^B - (Un+1)^B ça parait tellement inutilisable
Et si tu forces une factorisation de ça par un^alpha
autumn stirrup
1/un - 1/un+1
mortal orbit
Ah pardon
autumn stirrup
eq a un^2 * un^a * m
mortal orbit
Et si tu forces une factorisation de ça par un^alpha
Factorise par un^(B-1) à la place
mortal orbit
Ouais c'est bizarre attends je refais
Je crois que je l'ai
C'est bizarre mais il faut se forcer à retrouver l'hypothèse, donc on multiplie et on divise par (un+1 - un)/un
remote mural
J'aurai aimé vous aider mais je n'apprends pas encore ça.
autumn stirrup
J'aurai aimé vous aider mais je n'apprends pas encore ça.
merci :D
en gros on multiplie par m * un ^(a-1)
mortal orbit
C'est bizarre mais il faut se forcer à retrouver l'hypothèse, donc on multiplie ...
Je crois que ça aboutit à quelque chose
autumn stirrup
la multiplication c'est avant les équivalent ou aprs ?
mortal orbit
Je te conseille de ne pas te lancer dans les equivalents quand t'as affaire à une somme
autumn stirrup
je sais, mais ici je ne parle que du produit
mortal orbit
Même en parlant du produit ici j'attendrais avant les equivalents
autumn stirrup
mec c'est dûr
mortal orbit
Oof
autumn stirrup
c'est bizarre pck la question ne te demande même pas de calculer la limite
mais juste de justifier qu'elle est non nulle
mais après pour wn, qu'on doit calculer à l'aide du théorème de césaro, on est obligé de trouver la limite 💀
mortal orbit
Mais il la faut quand même pour la dernière question
autumn stirrup
mec même pas la dernière mdrrr
mortal orbit
Tu peux me montrer comment t'avais obtenu m comme limite ?
autumn stirrup
c'étais faux enfaite j'ai utilisé un dl dans le mauvais voisinage
mortal orbit
Non mais il faut un DL ça cest sur, surtout pour trouver que la limite vaut -m*B
autumn stirrup
il y'a literallement un seul dl qui fais descendre les puissances, et çelui là s'applique au voisinnage de 1
😭
mortal orbit
Ah bah OUI on force le DL, on facto par 1/un^alpha et on a du (... - un) en facteur, le truc en pointillé qui a une expression chelou
autumn stirrup
j'ai une idée en tête mais je sais pas si ça va marcher
en gros essayer des crées des puissance B-a
mortal orbit
Bah c'est à peu près ça mon idée quand tu factorises par 1/un^alpha
autumn stirrup
mUn^a eq Un+1 - Un
donc mUn^(a-b) eq (Un+1-Un)/Un^b
donc mUn^b eq (Un+1-Un)/Un
on peut remplacer ça dans la formule de vn
mortal orbit
Oui et au passage tu obtiens que comme un^b ->0, alors Un+1 ~ Un
autumn stirrup
= o(Un)
mortal orbit
?
mortal orbit
Oui
autumn stirrup
ça aide pour les équivalent
mortal orbit
Oui mais fallait le démontrer
mortal orbit
Maintenant tu l'as
mortal orbit
Lim Un = 0 xd
autumn stirrup
car la limite c'est 0
mortal orbit
Et oui
autumn stirrup
on est tellement pret
autumn stirrup
la partie de 'limite nulle ssi b=a-1 est faisable
c'est le calcul de la limite en elle même qui clc
calm coralBOT
@autumn stirrup Has your question been resolved?
calm coralBOT
calm coralBOT
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obsidian forge
calm coralBOT
obsidian forge
Can someone help me with number 10?
cloud topaz
,tex \polylongdiv{3x^3 + x^2 +7x+38}{x+2}
obsidian forge
cloud topaz
-6+1 = -5
obsidian forge
someone told me the answer was -6 but i wanna know how to actually do it, its a take home quiz
cloud topaz
You wrote -6 + 1 = 5
cloud topaz
Do the same for the other one
obsidian forge
also i appreciate the help
hushed knot
@cloud topaz what about reminder theorem
cloud topaz
<@607479321350635520> what about reminder theorem
Youre right
hushed knot
Yes
obsidian forge
what do i do about the k
remote mural
,tex \polylongdiv{3x^3 + x^2 +7x+38}{x+2}
,tex (fyi \polyhornerscheme[x=-2]{3x^3+x^2+7x+38})
hushed knot
Take f(1)=x^3+kx^2-5x+4=4 if the reminder is 4
potent lotusBOT
Toby
obsidian forge
wait so
hushed knot
${f(1)}={x^3}+{kx^2}-{5x}+{4}={4} , {f(x)}={1} $
obsidian forge
and plug in one right?
hushed knot
Yes
potent lotusBOT
hushed knot
4=1^3+4-5+4
Right 👍
I checked it
${f(1)}={x^3}+{kx^2}-{5x}+{4}={4} , {f(x)}={1}$
obsidian forge
potent lotusBOT
𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛
obsidian forge
can you help with 11 as well?
obsidian forge
Both reminders are same
OHHH THANK YOU YOURE SO SMART
hushed knot
Oh
obsidian forge
what do i do for 11?
hushed knot
,w plot x^3+kx^2+5
obsidian forge
is -3 the remainder?
hushed knot
what do i do for 11?
Wait
obsidian forge
so -3=(2)^3+k(2)^2=5
hushed knot
I this if x=2 and y = -3 you have to put the value of x and check the constant k
Am I right@cloud topaz
hushed knot
11
cloud topaz
,w solve -3=2^3+k(2)^2+5
potent lotusBOT
Requested by Pure#9389
obsidian forge
i got a=43 💀
cloud topaz
Bruh
potent lotusBOT
hushed knot
,w a=4^3-4×4^2+5
potent lotusBOT
obsidian forge
17
hushed knot
Bro I am 14
obsidian forge
im in grade 12 math
hushed knot
☠️
obsidian forge
i know i saw your bio
hushed knot
i know i saw your bio
Bro how
obsidian forge
thats crazy how good you are at math compared to me
obsidian forge
for fun?
hushed knot
Yes
obsidian forge
question 12
hushed knot
why multiply by 8?
Length is 8 given
obsidian forge
so divide byt -2 and then 8?
hushed knot
You can do that
obsidian forge
with synthetic division right?
potent lotusBOT
𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛
potent lotusBOT
hushed knot
Solved
☠️
Cause it's a cubic polynomial it have many sol
But x=-2 is wrong
I failed computer
hushed knot
Let$f(x) ={x^3}+{5x^2}-{4x}-{20}$
So,
$\frac{f(x)}{x+2}
=\frac{f(x)}{-2+2}
=\frac{f(x)}{0}$
So ${x}\neq {0}$
potent lotusBOT
𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛
hushed knot
See my explanation
obsidian forge
crazy how 14 y/o is smarter than me
hushed knot
,w factor x^3+5x^2-4x-20
potent lotusBOT
obsidian forge
wait cant i
hushed knot
And you are dividing x+2 by by this
obsidian forge
one sec
hushed knot
So you will get (x+5)(x-2) ☠️
obsidian forge
i wanna try something
obsidian forge
i got the same answer
hushed knot
😂😂😂😂
obsidian forge
i did synthetic like before
hushed knot
Factor was the real thing
obsidian forge
then factor
hushed knot
You learn from your mistake
obsidian forge
yes, the best way to learn
hushed knot
(x-2)(x+2)(x+5)
obsidian forge
oops i missed a negative
potent lotusBOT
𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛
potent lotusBOT
obsidian forge
for q13 do i factor the first eq then divide?
hushed knot
As I have found
hushed knot
for q13 do i factor the first eq then divide?
Ok aait
obsidian forge
wait how did you get that
hushed knot
Quadratic formula
hushed knot
wait how did you get that
Bot
I am not writing it in my copy
It's 2am in my country
I don't have the energy but still I am doing maths ☠️
obsidian forge
It's 2am in my country
o lmao, its 2 pm over here. what country
hushed knot
o lmao, its 2 pm over here. what country
India
obsidian forge
lmao i appreciate your time and help
hushed knot
Where are you from
obsidian forge
canada
hushed knot
lmao i appreciate your time and help
,w plot x^2 + {y -3/4(x^2)^(1/3)}^2 = 1
potent lotusBOT
obsidian forge
wait so to get the width what did you do
hushed knot
🤔
hushed knot
like i know it was the bot
I just multiplyed it by the length then I got the area
Length is given which is 8
And width is x+2
Area of rectangle is x^3+5x^2-4x-20
L×B = Ar
obsidian forge
i mean this
potent lotusBOT
obsidian forge
brb im gonna make food, can you bee back in15?
hushed knot
So
(x+5)(x-2)(x+2)=(x+2)8
=(x+5)(x-2)=8
obsidian forge
ok
hushed knot
,w x^2-3x-4=0
potent lotusBOT
hushed knot
Ok
hushed knot
What are you making?
hushed knot
Like 1/cos
Ik
obsidian forge
Rice
hushed knot
Rice
Ou
Ok take your time
Today is full moon here I would like to watch it
@obsidian forge tell me whenever you are done
calm coralBOT
@obsidian forge Has your question been resolved?
obsidian forge
<@495239139009232896> tell me whenever you are done
k im back
obsidian forge
factors of the first eq are (x+1)(x-4)
hushed knot
f(-1),f(4)
obsidian forge
so do one with -1 and one with 4?
hushed knot
,w 4^3-6×4^2-c×4+d=0
obsidian forge
kk one sec lemme do it
hushed knot
Ok
potent lotusBOT
obsidian forge
you right
hushed knot
Yes
obsidian forge
hushed knot
and then subract right?
Actually
-c+d=7
c-d =-7
Add the both equation
obsidian forge
yeah one sec
hushed knot
Ok
obsidian forge
yes r=1
hushed knot
-34 = -8p-2q
obsidian forge
for p1 or p(-2)?
hushed knot
-34=-2(4p-q)
=4p-q=17
hushed knot
for p1 or p(-2)?
They are looking right
p+q=2
4p-q=17
Add them
Question completed
obsidian forge
ok lemme try
hushed knot
Yes
obsidian forge
-32=9p-q
hushed knot
How?
hushed knot
Ok
obsidian forge
obsidian forge
oops
obsidian forge
so -32=-7p-q
hushed knot
With the simplified version
4p-q=17
obsidian forge
wait back a second
obsidian forge
It would be
-34=-2(4p-q)
4p-q=17
how
hushed knot
4p+p+q-q=17+2
5p=19
p=19/5
It would be
-34=-2(4p-q)
Dividing -2 in both sides
4p-q=-34/-2
4p-q=17
hushed knot
34÷2?
hushed knot
Yupp
hushed knot
I DIDNT REDUCE
It would be easier if you reduce
It
Cause you can cancel q directly
obsidian forge
do i add or subtract
hushed knot
Adding will be better
obsidian forge
but
obsidian forge
divide -34=-8p-2q by -2
hushed knot
,w -34/-2=(-8p-2q)/-2
potent lotusBOT
hushed knot
19/5 is p
obsidian forge
i subtracted
obsidian forge
yay
hushed knot
P=5
It's 3 am here bro 🥶
Yaameto qudasai let me sleep
,w plot x^2 + {y -3/4(x^2)^(1/3)}^2 = 1
potent lotusBOT
hushed knot
yeah lmao i wont keep you hostage
💀
hushed knot
i appreciate the help
🫂🫂🫂
hushed knot
yeah lmao i wont keep you hostage
I m boy don't be gay ☠️
obsidian forge
me too lmao
desert ocean
calm coralBOT
remote mural
draw a dashed line that runs in the middle there to create a triangle and rectangle
calm coralBOT
@desert ocean Has your question been resolved?
remote mural
calm coralBOT
remote mural
Why did they made the base of 2 units why not make it of 1 unit
Q is to reprsent sqrt five on number line
mellow crater
Q is to reprsent sqrt five on number line
because 5 = 2^2 + 1^2
mellow crater
aka Pythagorean Theorem
remote mural
Because a and b can be 1 or 2 right
mellow crater
if base was 1 then hyp would be sqrt(2)
remote mural
But c is 5 yea
remote mural
if base was 1 then hyp would be sqrt(2)
Wat
It would just be
Addition is commutative
Ion think it should matter
mellow crater
you want to constract segment which length is sqrt(5)
this is why
base 1 and another leg 1 gives segment which length is sqrt(2)
not sqrt(5)
remote mural
Because
remote mural
a ^2 + b^2 = c^2 whether a is 1 or 2 it would be still be same
Yea just flipped
So in pic
They made the base 2 and im asking why not 1
sweet pier
(Proving identity with sum formula) My brain seems to just, shut down when it comes to rearranging fractions like this. What’s the next step lmao
coral osprey
Simplify tan(pi/4)
sweet pier
Simplify tan(pi/4)
oh my god I literally forgot pi isnt a variable
jesus christ
oh actually I don't know where to from there either
coral osprey
Well what is tan(pi/4)
coral osprey
oh actually I don't know where to from there either
It's in the unit circle
sweet pier
oh nah I know how to get to the value of tan(pi/4), but I'm not sure what to do with the equation when I have that value