so 3 bisectors is all that's required
#help-36
civic ether
from a random site for "test prep"
honestly what are these questions anyway lol
idk how they're math tbh
civic ether
it's cause everything's behind a paywall
so much for a "non profit organization"
lol
tranquil pine
I'd think it's better to use a textbook or something. those are usually packed with Q's
oh 
civic ether
also the questions in their "practice books" are tbh much easier than the real ones
they gave me a pdf and asked me to find the median
i had no clue how to do that so i just whipped out an integral lmfao
but you're not supposed to know precalc or calc
tranquil pine
💀
civic ether
so yeah idk their resources (surprisingly) isn't well representative
tranquil pine
fair enough
just sucks because those internet websites can be pulling stuff from their asses
civic ether
just sucks because those internet websites can be pulling stuff from their asses
the dude who makes the questions probably just stuck to mastering math before precalc
😭
well whatever goes ig
tranquil pine
the dude who makes the questions probably just stuck to mastering math before pr...
😭
yeah good luck anywyas xd
civic ether
yeah yeah thanks
also i can live with the 90 degree explanation ig
and supplement with mine
wait @tranquil pine lmfao
you bisected twice and got 33.75
i think the answer's 3 or something lmao
tranquil pine
i think the answer's 3 or something lmao
no I bisected thrice
90 by 2
45 by 2
22.5 by 2
so it matches
tranquil pine
no worries 
final saddleBOT
Available help channel!
tranquil pine
final saddleBOT
tranquil pine
Firstly, $25 + $200 = $250??
secondly,
why even bother doing all of the gymnastics they did
why dont you just go like
(50)(4.5) = 225
okay wait
so to be compensated is $225
hard mist
If I have a parabolic cylinder with the equation z=4-x^2 , how do I determine the intersection with the x axis?
final saddleBOT
If I have a parabolic cylinder with the equation z=4-x^2 , how do I determine th...
hard mist
sketch for reference:
barren hound
If I have a parabolic cylinder with the equation z=4-x^2 , how do I determine th...
x intercept means all other variables are 0
final saddleBOT
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glad basalt
I refuse to believe I did something wrong
final saddleBOT
I refuse to believe I did something wrong
glad basalt
(1-x)(x) = 1/4
-x^2 + x -1/4 = 0
now multiply by 4
-4x^2 + 4x - 1 = 0
this is not factorable right??
does this mean I went wrong somewhere else
I did log4( (1-x)(x) )= -1
then 4^... = 4^-1
so (1-x)(x) = 1/4
Did I actuall do smth wrong?
left echo
nope
left echo
does this mean I went wrong somewhere else
Not necessarily
Well isn't that -(2x - 1)^2
glad basalt
you mean -4x^2 + 4x - 1 ?
left echo
yes
glad basalt
how the hell am I supposed to figure that out
left echo
you can factorize it like normal
left echo
yeah
glad basalt
how do I know which factor by grouping terms to pick
left echo
wdym
glad basalt
which terms to group together
left echo
Group the constant with one of the 2x and the square with the other 2x
glad basalt
whats ur reasoning
left echo
well that's how you factor
The constant goes with one split term, and the square goes with the other
left echo
factor a - out of one of those terms
(-2x + 1)(2x - 1) = -(2x - 1)(2x - 1) = -(2x - 1)^2
glad basalt
I see
(-2x + 1) (2x - 1)
but this is usuable right
just use both?
-2x + 1 = 0
x = 1/2
2x - 1 = 0
x = 1/2
same
another question
nevermind
.close
final saddleBOT
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Available help channel!
radiant reef
how to find change in y (dy)? in eulers method
final saddleBOT
how to find change in y (dy)? in eulers method
radiant reef
,rotate
soft zealotBOT
severe hawk
can you not solve it by integration?
severe hawk
i would solve the differential equation by integrating, then getting C, and thus i'd have the full function.
With the function, i'd have y(1)
severe hawk
y = (x^2)/2 + 2x
you're missing the integration constant
radiant reef
c=3
severe hawk
so with that you got the function, and thus can compute the exact value at 1
radiant reef
but what's dy
severe hawk
you'd have that:
dy = (x+2)dx
so you can integrate on both sides and get what you obtained
severe hawk
okay so.
You know that dy/dx = x+2
That means the derivative of the function y, with respect to x, is x+2
If the derivative is x+2, that means the original function is y(x) = x^2/2+2x+c
Since y(0) =3, c=3, thus y(x) = x^2/2+2x+3
Can you now get the value of y(1)?
final saddleBOT
@radiant reef Has your question been resolved?
severe hawk
assuming you're allowed to get the exact solution.
Since you're asked for the error, i expect you would be asked for both
tranquil pine
I tried to mess around with this a bit but that shape seems so irregular to derive anything out of it
final saddleBOT
I tried to mess around with this a bit but that shape seems so irregular to deri...
tranquil pine
any ideas?
tranquil pine
what?
fallow wren
i can t read ...it was too small for me 😭
fallow wren
annghost i bet that you didn t use duolinguo
tranquil pine
yeah this is the Turkish foreigner exam
tired walrus
annghost i bet that you didn t use duolinguo
you'd be right, but also you're being weird to me right now.
fallow wren
😭
tired walrus
I tried to mess around with this a bit but that shape seems so irregular to deri...
it's a circle minus two segments
or a rectangle plus two segments
your pick
tranquil pine
hmmm 
tired walrus
angle EOB is fairly easy to find
soft zealotBOT
everg
pliant saffron
is there an official way to visualize division? i always thought for example 30/3 means how many equal parts of 30 can you fit into 3 sections, so 10. or for example 30/1 means how many equal parts of 30 can you fit into 1 section, so 30. but when i think of 30/0.1, my brain breaks. how many equal parts of 30 can you fit into 1/10th of the section?
final saddleBOT
is there an official way to visualize division? i always thought for example 30/...
stone wagon
pretty much all visualisations of basic operations break down when you consider a case of non-whole numbers lol
stone wagon
is there an official way to visualize division? i always thought for example 30/...
but also your last sentence is correct
actually no
pliant saffron
something is happening though, since if you use the reasoning: "How many 0.1's is in 30?" you get the answer, 300
stone wagon
yes
this is correct
it's about counting the number of times something (denominator) is in something (numerator)
you can also consider the case of just 1/x
stone wagon
something is happening though, since if you use the reasoning: "How many 0.1's i...
if x is an integer, you get a number smaller than 1, because to fit x different sequences in 1, you need the segments (of length 1/x) to be smaller than 1
if x is a number less than 1 (but greater than 0 ofc), then the number of times you can fit that number in 1 is clearly greater than one (just one segment won't suffice)
final saddleBOT
@pliant saffron Has your question been resolved?
pliant saffron
if x is an integer, you get a number smaller than 1, because to fit x different ...
thank you!
obtuse zinc
am i allowed to do this? mathematic induction problem
final saddleBOT
am i allowed to do this? mathematic induction problem
worldly vale
you would need to show that 4^n/3 + 5/3 is always an integer
stone wagon
or go that way ig
worldly vale
that would amount to doing induction again lmao
stone wagon
lol
stone wagon
i mean you can prove that (4^n + 5) divides 3 but i think there is a simpler way
worldly vale
yeah i think proving 4^n + 5 is always a multiple of 3 is your best bet
stone wagon
i mean you can prove that (4^n + 5) divides 3 but i think there is a simpler way
i don't see the simpler way tho 💔
worldly vale
yeah i think proving 4^n + 5 is always a multiple of 3 is your best bet
the induction for this isn't so bad at all, easier than the initial question
obtuse zinc
i look at the answer
they broke down 15n as 4 * 15n - 3*15n
an than 14 as 18 -4
bruh
.close
fallow wren
hey
fallow wren
can I ask a question ?
tranquil pine
!da2a
final saddleBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
hybrid heath
hybrid heath
can I ask a question ?
you just did
fallow wren
wait 1 sec
fallow wren
I don t understand the classical proof $\frac{\sin x}{x}\to 1$ as $X\to 0$
don t bully me pls 😭
stone wagon
z?
soft zealotBOT
everg
worldly vale
geometric squeeze?
fallow wren
yes
red line is sin x
blue line is x (in radiant)
green line is tangent x
i understand why red line is shorter than blue one (segment are always shorter than curve line)
but why is blue line shorter than gren line ?
fallow wren
geometric squeeze?
did you study this proof ?
worldly vale
you're supposed to consider 2 triangles, and the sector cut out by theta
fallow wren
oh
worldly vale
draw a chord from the red line intersection with the circle to the tangent point of the green line
worldly vale
yeah now that line with the two radii gives you one triangle
fallow wren
oh i see that has red line s hight
worldly vale
yeah
then you also have the sector and the big triangle with the two radii and all the green lines
worldly vale
mhmm so just find the areas of them all and then you have the initial inequality
fallow wren
ok ..but i think we don t know the area of the sector
worldly vale
you know theta and you know the area of the unit circle
fallow wren
i know that $\pi$ is the length of half circumference of radius one
soft zealotBOT
everg
fallow wren
but i dont know that $\pi *1^2$ is the area of the unit circle
soft zealotBOT
everg
fallow wren
mhh...
yes but what is the proof ? I am scared that for that proof we need the limit sin x /x -->1
is easy area (unit circle)=pi' s proof ?
worldly vale
the proof for the area of a circle?
fallow wren
yes ...because pi is defined as a lenght not an area
so we need a proof to use that one in a proof
i think
worldly vale
the area of a circle is $\pi r^2$ where r is the radius
soft zealotBOT
ΣΑCu
worldly vale
if you want a proof of that go look it up
fallow wren
are you sure that all the rpoof doesn t use thta sin(x)/x-->1 ?
if not this argument is a little bit circular
fallow wren
for exaple i know thta sin x/x -->1 is used to derive derivative of sin x
so we cannot use integral
you don t know that proof ?
worldly vale
yes i am aware you can't use lhopital to prove this limit
fallow wren
or you cannot measure the unit circle with an integral i think
worldly vale
you dont even need to know that the area is pi, just that area is proportional to r^2 and the circumference is proportional to 2r with the same constant of proportionality
something proved centuries ago
fallow wren
i don t say that it is hard math ...but i don t know thta proofs
if they are so simple to you ...can you give me a sketch ?
worldly vale
look them up
worldly falcon
final saddleBOT
sturdy otter
Let’s think to a more simple example. x^2 = 25.
You could write this as x = 5 or x = -5, but if you did -x = 5 or -x = -5, they would just simplify to the former two anyway.
For actual polynomials, quadratic equations on a graph only pass the x-axis twice, where the +/- x would suggest it should cross four times.
final saddleBOT
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crisp epoch
final saddleBOT
crisp epoch
can someone please expalin the notation for c - f
i dont get what multiplying does in those cases
or is it just notation that for example in c it would be f(g(0))
final saddleBOT
Please stick to your channel.
worldly vale
yeah its all just composition
not sure why they switched notation in the middle of it
tranquil pine
We know that heat is a form of energy, and its units of measurement are the joule (J) and the calorie (cal) (1 cal = 4.186 J). How many joules does a person who consumes 3000 kcal each day receive in their diet?
I am doubtful whether I kcal is equal to 1 000 cal here
final saddleBOT
We know that heat is a form of energy, and its units of measurement are the joul...
novel rover
final saddleBOT
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Available help channel!
ebon sonnet
if 100 grains of rice have a volume of 2.5 mL and the area of Pennsylvania is 119,280 Km^2, how deep in miles would Pennsylvania be covered in rice if a mole (6.022*10^23) grains of rice were poured onto Pennsylvania?
final saddleBOT
if 100 grains of rice have a volume of 2.5 mL and the area of Pennsylvania is 11...
ebon sonnet
little python
PA?
ebon sonnet
my work needs to be shown in the "chemistry conversion" method i.e. 1000ml= (1L/1000mL)
yes PA short for pennsylvania
i'm mostly stuck at turning the km^2 label into a volume
i have this but i’m not sure if the last step is correct
final saddleBOT
@ebon sonnet Has your question been resolved?
slow blaze
final saddleBOT
slow blaze
what am i doing wrong here
graph for reference
so from my understanding there are two integrals, one starting from 0 to arctan(9/8) where cos is subtracted from sin, then arctan(9/8) to pi where sin is subtracted from cos
is this the wrong approach or did i make a math error somewhere?
final saddleBOT
@slow blaze Has your question been resolved?
slow blaze
<@&286206848099549185>
slow blaze
i plugged it into mathway and the answer is wrong, so it must be something with how i set up the integral
this is correct, i just dont know how to get here
final saddleBOT
@slow blaze Has your question been resolved?
final saddleBOT
@slow blaze Has your question been resolved?
worthy shale
this should be a plus
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Available help channel!
fathom stag
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fathom stag
I'm a bit confused with both of these questions
you have to use the compound angle identities in reverse to simplify it
so for question C
could I take out the negative
abstract walrus
yes you can
fathom stag
right but then the answer says sin(B-A)
but my answer would then be
-sin(B+A)
is that the same thing?
abstract walrus
ye
fathom stag
right but then the answer says sin(B-A)
would that be the same as this?
abstract walrus
yes
fathom stag
oh ok
abstract walrus
ye
fathom stag
so for the second one
could I say
-[cosAcosB-sinAsinB]
then that gives
cos(A+B)
fathom stag
cos(-x) is cos x
so when faced with questions like this, I should just take the negative out and rewrite it?
abstract walrus
its not general
youll learn some more identities soon
you have to manipulate the question
to form the identities you know
fathom stag
youll learn some more identities soon
the double angle ones?
abstract walrus
it not necessary that just taking - out will give you them
cos a + cos b
sin a + sin b
etc
fathom stag
to form the identities you know
right
river lance
Welp I can’t figure out the slope, I’d need to know one more side of the triangle to figure the slope but can’t think of a way. From there ig I could use pythagoras to figure out the hypotenuse
final saddleBOT
Welp I can’t figure out the slope, I’d need to know one more side of the triang...
willow pilot
stone wagon
Welp I can’t figure out the slope, I’d need to know one more side of the triang...
is there a picture to assist? what's the original language?
opal plinth
What's the area of a right triangle?
opal plinth
I mean of any right triangle
river lance
both sides multiplied together and then divided by 2
opal plinth
Name the triangle vertices if that helps
opal plinth
$\frac{6 * otherside}{2} = 6$
soft zealotBOT
Nel
opal plinth
Yes
river lance
okay I got the hypotenuse but idk if I can even figure out the slope from it
opal plinth
You don't need the hypotenuse
opal plinth
Well, you're not wrong but you made a mistake
river lance
??
opal plinth
If point 2 is at (2,0) then delta x is (0 - 2), not (0 - (-2))
Unless you meant to write 0 - 6 for delta y
river lance
so then the slope is -3 and not 3?
opal plinth
If point 2 is at (2,0), then it's either $\frac{0-6}{2-0}$ or $\frac{6-0}{0-2}$
soft zealotBOT
Nel
opal plinth
Both give -3
river lance
ya
river lance
right of course
opal plinth
Two different triangles, both with a side of the form y=kx+6
So the question has two answers, but I assume they want the -3 (blue triangle)
river lance
yes yes makes sense
alrighty
ima do both
tho
since it doesn't require only 1 answer
okey ty, ima close this chat now
.close
lime breach
Hey can I get help with question 8a and 8b
final saddleBOT
Hey can I get help with question 8a and 8b
lime breach
Oh my god
dry light
It's not too bad
Factor k to expand, and then algebraically move everything to one side
lime breach
Yeah sorry, been doing maths all day my brain is fried
So I get 5x^2 - 13kx^2 +12kx +6 = 0
No wait
Nvm
.close
final saddleBOT
brave river
$7+5$
final saddleBOT
Available help channel!
cinder wadi
Hi
cinder wadi
Let V be the set {1,2,3,4}. How many different partial orders exist on V? (Determine all possible Hasse diagrams on V)
I was wondering if anyone knows what's meant with that
As no relation is given
tired walrus
how many ways could you draw a hasse diagram on 4 points and label it with the numbers 1-4
cinder wadi
4! ?
no sorry that's not correct
Not the power set right?
just 1, 2, 3 and 4?
I really have no idea ..
wait it is 4! right?
because it's all possible ways to just combine the four elements?
ripe sinew
final saddleBOT
ripe sinew
hi can anyone tell me whats going on here
ripe sinew
so i apply the power rule first
ripe sinew
first 3 rules are all being applied at various stages
but what will the equation be after i apply the power rule
4log_a?
worldly vale
you can ignore the a in the subscript its just the base of the log, your log has no base written so its probablt either base 10 or base e
but yeah it'll be 4log(stuff)
ripe sinew
so 4log(ab/c)
worldly vale
what happened to the power on b and c?
ripe sinew
oh no theyre still there i was just too lazy to type
i guess ill apply the quotient rule
nevermind
ripe sinew
what happened to the power on b and c?
im stuck on 4log(ab^3/c^3) rn
cant figure out whch rule
worldly vale
you said you were going to apply the quotient rule
worldly vale
the 4 should be applied to everything
ripe sinew
now keep going
i cant really find any rules that help me here
worldly vale
you only need the product rule and the power rule from now on
ripe sinew
power rule needs to be positive though no?
worldly vale
i dont know what you mean by that
ripe sinew
4log(ab^3) - 4log(c^3)
this log is negative
sorry i meant product rule
here its positive
worldly vale
if youre trying to use the product rule then you should be looking at just log(ab^3)
worldly vale
yeah youre nearly done
you just need to deal with log(b^3) and log(c^3)
they are logs of things to powers
1 guess which rule to use
final saddleBOT
@ripe sinew Has your question been resolved?
worldly vale
im left with 4loga + 4logb^3 - 4logc^3
oh here why did the 4 get applied to the last term
ripe sinew
why wouldnt it
worldly vale
yeah good point i was looking at the answer in your picture and it didnt match up but thats because its wrong
what you've done is right
latent tangle
final saddleBOT
latent tangle
Hello, this is my attempt so far but I'm not really sure how to approach this integral
final saddleBOT
@latent tangle Has your question been resolved?
fresh relic
I would change the order of integration
so do $\iint_D xe^{y^2}\mathop{dx}\mathop{dy}$
soft zealotBOT
Edward II
fresh relic
in fact it's impossible to do the y first because e^y^2 has no closed form antiderivative
latent tangle
Hi
This is what I tried with your advice
I obtained this answer a while ago but it seemed way too large
oak arrow
final saddleBOT
oak arrow
i got that this is undefined
actually i have no idea where to even start. all i know is that i need to take the derivative with respect to x of that function
oh it's 0 lol
it tells me right?
worldly vale
no you need to use the limit definition
oak arrow
wait so how would i do that? I first start by taking the partial derivtaive with respect to x right
worldly vale
the limit definition of partial derivatives
oak arrow
so don't i need to calculate the derivative first?
worldly vale
no
oak arrow
yeah then i really don't know how to do this problem
i don't really understand the limit definition
worldly vale
plug x=0 y=0 into this and evaluate the limit
sonic thistle
Can someone help me with these kind of problems?
final saddleBOT
Can someone help me with these kind of problems?
sonic thistle
I understand that they are different ratios but I dont understand how to find the initial cos?
Cause I need cause to do the rest
I did sqrt(1-sin(-12/13)^2)
To get the 25/13 not sure if thats correct though
scarlet sequoia
all you can use for finding cos is that sin^2 + cos^2 = 1, so cos^2 = 1 - sin^2
then, use the quadrant to find if cos is positive or negative
scarlet sequoia
I did sqrt(1-sin(-12/13)^2)
how did you compute sqrt(1-sin(-12/13)^2)? it's the correct answer but the 25/13 isn't
soft zealotBOT
scarlet sequoia
oops sorry
sonic thistle
Do I need to squre sin
scarlet sequoia
I know what we did wrong now
sonic thistle
I dont know how to do that on a ti-84
scarlet sequoia
it's sqrt(1-sin(t)^2)
but SIN(t) = -12/13, not t
so just
,w sqrt(1 - (-12/13)^2)
soft zealotBOT
scarlet sequoia
yyes
rain barn
-2sqrt(n+2) + 2sqrt(n+1) + (1/sqrt(n+1))
n = n
n+2 > n+1
sqrt(n+2) > sqrt(n+1)
2sqrt(n+2) > 2sqrt (n+1)
-2sqrt(n+2) < 2sqrt(n+1)
So :
2sqrt(n+1) - (-2sqrt(n+2)) > 0
So
-2sqrt(n+2) + 2sqrt(n+1) + (1/sqrt(n+1)) > 0
final saddleBOT
-2sqrt(n+2) + 2sqrt(n+1) + (1/sqrt(n+1))
n = n
n+2 > n+1
sqrt(n+2) > sqrt(n+1)
...
rain barn
Can i do that?
fallow wren
what?
opal plinth
No
opal plinth
$2\sqrt{n+2} > 2\sqrt{n+1} \implies -2\sqrt{n+2} < -2\sqrt{n+1}$
fallow wren
2 is right
soft zealotBOT
Nel
opal plinth
Yeah ok, I thought the previous line implied this one
rain barn
Oh well
opal plinth
It only has to do with the fact that sqrt(n+1) is positive
rain barn
It only has to do with the fact that sqrt(n+1) is positive
So?
opal plinth
So it's correct, not sure if the reasoning is well put together
rain barn
So do you think that Would unifying denominators and calculations be better?
Like
[( 2sqrt(n+1) - 2sqrt(n+2))*(2sqrt(n+1) + 2sqrt(n+2))]/[2sqrt(n+1) + 2sqrt(n+2)]
.....
Sqrt(n+2) - sqrt(n+1)/ .... > 0
final saddleBOT
@rain barn Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
fossil shuttle
what formula would I use for this?
final saddleBOT
what formula would I use for this?
final tangle
no
final tangle
to find the midpoint
as the name suggests, the midpoint formula will give you what you want
no
final tangle
poor representation of the slope
final tangle
please google midpoint formula, and apply that
then also google slope formula (irrelevant to your question)
fossil shuttle
tranquil pine
I do not have enough practice with 'x approaches a' method.
Could someone help find out what my problem is? Work is included in the photo.
final saddleBOT
I do not have enough practice with 'x approaches a' method.
Could someone help f...
bold oasis
You need to know difference of cubes
tranquil pine
here is a different method being used
tranquil pine
You need to know difference of cubes
Ahh I learned this just now by talking to a tutor!
For cubic, it would be
A^2+AB+B^2, yes?
bold oasis
Multiplied by A+B
tranquil pine
oh right
its (a-b) * a^2+AB+b^2 for a^3-b^3?
bold oasis
Yeah
tranquil pine
thank you!!!!
bold oasis
Ight
tranquil pine
Just a question, how did you learn this? I never did any of that in precalculus, even in the honours I've never seen that.
.close
final saddleBOT
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Available help channel!
wild delta
The perimeter of an isosceles triangle is 48 inches. The length of the base is 1 inch less than half the length of one of the two equal sides.
final saddleBOT
The perimeter of an isosceles triangle is 48 inches. The length of the base is 1...
wild delta
Can you write it out?
tranquil pine
write an equation relating the special side to the others
final saddleBOT
@wild delta Has your question been resolved?
wild delta
No
The perimeter of an isosceles triangle is 48 inches. The length of the base is 1 inch less than half the length of one of the two equal sides.
Help me plz am so confused
I need to write a system of equations
final saddleBOT
@wild delta Has your question been resolved?
final saddleBOT
@wild delta Has your question been resolved?
onyx onyx
How does number 18 make sense?
final saddleBOT
How does number 18 make sense?
onyx onyx
The directions are to factor completely.
plush scarab
What are you confused about?
onyx onyx
I think the solutions are x=1/16, -1/16
plush scarab
I think the solutions are x=1/16, -1/16
That's not right
onyx onyx
Idk the process of factoring
plush scarab
Are you confused by how they got (1/4)x?
plush scarab
Left or right
plush scarab
And what difference of 2 squares mean
I think this will explain that well
plush scarab
Left and right
You don't have to worry about the right side too much, it's just a different way of displaying it
The left side is used much more commonly
To get the square on the left side, you have to find what number squared would equal 1/16
and what number squared would equal 1
plush scarab
Yep that's correct
plush scarab
1/4? I am bad at mental math
An easy way is just ignore the 1 at the top and just find the square root of 16
So then following the formula I sent (difference of squares)
You would plug that in
a would be your (1/4)x and b would be your 1
onyx onyx
So we want to get rid of the square in 1/16x^2
So square root whats in the grouping symbols?
plush scarab
Yeah we're trying to factor as much as possible
plush scarab
Yeah, that's the left side of the formula
So then you'd plug it into the right side of the formula
onyx onyx
What?
plush scarab
(a+b)(a-b)
plush scarab
a would be your (1/4)x and b would be your 1
plug this into it
onyx onyx
So 1/4-1?
plush scarab
Not quite
plush scarab
(1/4)x but yes
That's correct and you would plug that in now
Do you know how you would plug that in?
plush scarab
What's the other side of the equation?
onyx onyx
So -1(1/4x+1)(1/4x-1)= (a+b)(a-b)?
plush scarab
So -1(1/4x+1)(1/4x-1)= (a+b)(a-b)?
Yeah that's it
You don't need to keep the (a+b)(a-b) though
onyx onyx
Yeah I'm slow thinker and needed to type faster
So left side=(1/4x+1)(1/4x-1)
And then solve for x?
plush scarab
Yes
onyx onyx
So do I distribute -1 into the left side?
plush scarab
Also just something when you're typing it online, put brackets around the 1/4
Otherwise it looks like 1 over 4x
onyx onyx
Good idea
plush scarab
So do I distribute -1 into the left side?
Sorry I'm a little confused what you mean by left side
onyx onyx
Distribute -1 into the ([1/4x]+1)
plush scarab
Are you sure you're supposed to solve for x?
plush scarab
Yeah you could do that
plush scarab
The one with -1/16?
onyx onyx
Yes
plush scarab
I think you should be able to
onyx onyx
Thanks
onyx onyx
no?
plush scarab
Because sqrt(4ac) wouldn't work
plush scarab
Okay wait sorry yeah you can
onyx onyx
Man I was avoiding learning how to actually understanding factoring
By just using QE to reverse engineer answers
I think I'm good now
Thnaks man
.close
deep stump
how would you find the amount of time in seconds that the ball is in the air? its vertical free fall motion
final saddleBOT
how would you find the amount of time in seconds that the ball is in the air? it...
tranquil pine
this will correspond to when the height is zero
deep stump
i tried finding the zeros of t and finding the distance from the 2 zeros but it didnt give me the right ans
tranquil pine
show what u did
deep stump
tranquil pine
okay but like
deep stump
i found the zeros using quadratic formula then put in the absolute value of the zeros and added them to find t
deep stump
yeah but i think it has to do with the zeros being wrong
tranquil pine
the second time should be what you want
deep stump
like i should probably plug in the height of 83 in some way to compensate for the intial height the ball is thrown at
tranquil pine
hm
tranquil pine
like i should probably plug in the height of 83 in some way to compensate for th...
you don't need to
deep stump
bc the question is about a person throwing a ball from an elevated height to ground
tranquil pine
can you post the full question then
deep stump
right..?
okay
i might be thinking about the full quadratic when y is above 0 but i should be thinking about a quadratic thats cut off
does that make sense?
light kestrel
i might be thinking about the full quadratic when y is above 0 but i should be t...
if the initial height is not ground-level, you'll just get one time (root) that is negative, which you can discard given the context
light kestrel
time in air can be found by setting your kinematic equation to zero and solving for t and maximum height can be found by using that Vf = Vi + at knowing that velocity will be temporarily zero at maximum height. solve for t here, plug in to your kinematic equation, solve
for part c, use answer to part b and the aforementioned equation
light kestrel
i agree with your approach and answer, i also get approx. 6.54s spent in the air
wait
deep stump
ohh
did you set the equation to 83?
or wut did u do
bc thats the answer
just wanna understand it
light kestrel
so, you're using the kinematic equation Yf = Yi + Vi*t + (1/2)at^2 which represents y as a function of time
you picked Yi to be 86ft above ground, with down to be the negative direction, so a y value of 0 represents ground level
you want to set Yf to zero to solve for time spent in air
deep stump
so set it equal to 0 and solve for t?
light kestrel
yep
valid pulsar
final saddleBOT
valid pulsar
How to do it guys?
final saddleBOT
@valid pulsar Has your question been resolved?
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valid pulsar
.close
indigo plover
final saddleBOT
indigo plover
is there some type of formula for this
I remember doing something like this but for interest
gentle barn
What is the initial population for mice?
formal trail
is there some type of formula for this
if you find the formula for this then you can substitute any other starting population and growth rate and it should work
final saddleBOT
@indigo plover Has your question been resolved?
final saddleBOT
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Available help channel!
split yacht
.help
final saddleBOT
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daring pendant
final saddleBOT
daring pendant
Can someone verify 4? Was wrong before just tried it again. Lmk
final saddleBOT
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spare bone
Do you know why algorithms based on barrett reduction is sometimes off by 1?
I made an algorithm that is kind of mix of https://en.m.wikipedia.org/wiki/Barrett_reduction and fixed point math. I read above wiki but didn't really get why. I really suck at math but I'm curious, I hope someone can teach me with easier words.
My algorithm: Assuming we have unsigned integer 128bit, and the goal is to compute a/b, note that b should be a constant bigger than 1, else first step causes overflow or divide-by-zero.
First we calculate c = (1<<64)/b (essentially, 1/b but since it's an integer, the entire 64bit is used for number after the decimal point.
Then, do a * c >> 64 (assuming a * c gives full 128bit - at max - product)
I can also post the small code in a online playground reproducing the issue.
final saddleBOT
Do you know why algorithms based on barrett reduction is sometimes off by 1?
I m...
spare bone
here is the playground, if anyone is interested :)
thanks! https://go.dev/play/p/eiguRhGKNxm
you can press run to see how many wrong results get delivered.
final saddleBOT
@spare bone Has your question been resolved?
spare bone
<@&286206848099549185> sorry to ping, glad if you can help.
What's rape? Is that related to my problem?
tranquil pine
brah
final saddleBOT
@spare bone Has your question been resolved?
vital crag
Do you know why algorithms based on barrett reduction is sometimes off by 1?
I m...
#old-network for CS server
heavy laurel
final saddleBOT
heavy laurel
Could I ask for some help on this mock problem?
Specifically, I am trying to answer/do this: I can explain what it means for a function of two variables to have a limit at a point or show that the limit of a function of two variables does not exist.
Seems pretty simple, we take the path along the x axis(when y=0), and plug 0 in for y. doing so, we get x/x^2 = 1/x
When we take the path along the y axis (when x=0), and plug 0 in, we get y/y^2=1/y
tranquil pine
y = 0 and x = 0 mean the whole thing is 0
robust sedge
A nice family of paths you can use is y = kx too.
heavy laurel
y = 0 and x = 0 mean the whole thing is 0
I thought we were meant to plug in 0 for either variable depending on the path we are taking, and derive the simplified functions..
ahh wait, either way, x is being multiplied by y and vice versa
so numerator will always be 0.
tranquil pine
yes thats my point
heavy laurel
yes thats my point
So we have (0/x^2) and (0/y^2).
both equal 0, then what?
How can we determine if limit DNE or exist based off of this if the limit approaches 0 for both y=0 and x=0..
vital crag
A nice family of paths you can use is y = kx too.
Do this and find different limits depending on k
heavy laurel
A nice family of paths you can use is y = kx too.
Doing so we get (x^2)/2x^2 =1/2
So the limit is 0 along y and x axis, but along the line y=x, the limit is 1/2.
So does this mean limit DNE?
tranquil pine
yes
heavy laurel
yes
Why? Is it because along both y and x axis the limit is 0, but on a different line, the limit is 1/2?
robust sedge
Doing so we get (x^2)/2x^2 =1/2
We get something in terms of k by my suggested approach.
heavy laurel
We get something in terms of k by my suggested approach.
Right, but how do we deduce the limit DNE because of that?
robust sedge
Well each path, for each k, gives a different output.
heavy laurel
Well each path, for each k, gives a different output.
Okay..so we cannot simply say that because the limit along the path of both x= and y = 0 both equal 0, the limit DNE?
robust sedge
The limit does not take into account what is happening at (0, 0) only what is happening in its neighbourhood.
heavy laurel
The limit does not take into account what is happening at (0, 0) only what is ha...
Okay, but for a problem that asks to find the limit as x,y approaches 0,0 of the function: (2x^(2))/4x^(2)+3y^(2))
when we take the path along the x-axis (y=0), we get 2x/4x^2 = 2/4=1/2, and the path along the y axis (x=0), we get 0/3y^2 = 0.
robust sedge
Are you changing problems?
heavy laurel
here, do we have to do your step again?
heavy laurel
Are you changing problems?
Yes, for comparative reasons.
robust sedge
My idea was tailored for that particular problem and might not work for others.
heavy laurel
Like, I'm not abandoning the other problem. I just want to understand why the steps to get an answer for the previous problem differs to this
robust sedge
It appears as it might work for that one though.
heavy laurel
My idea was tailored for that particular problem and might not work for others.
How can we tell when to tailor an idea for a specific problem and when not to? Is there some general rule?
robust sedge
Let me find something for you.
heavy laurel
ok.
final saddleBOT
@heavy laurel Has your question been resolved?
mighty scaffold
To
mighty scaffold
Yo
You know when we doing the product rule yeah
When we have something like 3xy
Why does u become 3x
And V become y
past bluff
Differentiation?
cold gorge
Why does u become 3x
It doesn't have to...
mighty scaffold
It doesn't have to...
Elaborate prince
cold gorge
You can let u = x and V = 3y
zinc slate
a level maths?
mighty scaffold
Why is one without a 3 tho
mighty scaffold
a level maths?
AP
cold gorge
Not sure what you mean. But there's only one 3.
mighty scaffold
You got 3xy
mighty scaffold
What
cold gorge
u = 3, v = x and w = y lol
past bluff
You got 3xy
3xy = 3x * y = 3y * x
mighty scaffold
But couldn’t I
Just do
Doesn’t the 3 apply to the y as well
Why only the.
X
cold gorge
Like I said it doesn't have to be X. It could be Y if you'd like.
cold gorge
No.
mighty scaffold
Why
mighty scaffold
That'd make uv = 9xy
So then it would be 9x and Y 💀
cold gorge
You could do u = sqrt(3) x and v = sqrt(3) y
mighty scaffold
This is very ambiguous maths
cold gorge
You could do u = sqrt(3) x and v = sqrt(3) y
If you're really all about justice for x and y.
But again, too unnecessary.
mighty scaffold
its like 3(2x) is not 3 * 2 and 3 * x
@cold gorge it was this simple fam
zinc slate
ok....
zinc slate
he litteraly said what i said
gaunt scroll
whats the question huh?
cold gorge
<@748029603087384657> it was this simple fam
I knew very well it was, it was you who didn't quite know that...
cold gorge
he litteraly said what i said
We get one of these every once in a while.
mighty scaffold
U were waffling cuz shut your mouth
mighty scaffold
Nah he isn’t he’s calling me dumb but he is the one that’s dumb
gaunt scroll
u saying that 3 should apply to both when differentiating 3xy right?
cold gorge
Nah he isn’t he’s calling me dumb but he is the one that’s dumb
Are you having an alright day?
mighty scaffold
u saying that 3 should apply to both when differentiating 3xy right?
YHYH
gaunt scroll
ye it will apply to both
gaunt scroll
3xy will be equal to 3xdy/dx+3y
mighty scaffold
Wait let me cook the numbers I’ll be back in 30 seconds
gaunt scroll
kk