Given the points A(- 2, -6, 3) and B(3, -4, 12), determine AB
#help-23
tight kelp
safe radishBOT
Given the points A(- 2, -6, 3) and B(3, -4, 12), determine AB
lean otter
if AB is meant to denote a vector, then you should be subtracting http://mathonline.wikidot.com/determining-a-vector-given-two-points
tight kelp
ok thanks
lean otter
but why do you do it backwards
draw a diagram and use "head to tail" addition
tight kelp
ok
lean otter
tight kelp
im confused
why for this one i added
. If 𝑎 = (1, 3, -3), 𝑏⃗ = (- 3, 6, 12), and 𝑐 = (0, 8, 1), determine |𝑎 +1/3𝑏⃗ − 𝑐 |
i added each x y and z
why didnt i subtract here?
tight kelp
so when would i know when to add or subtract can you give me an example?
If 𝑣 = (2, -14, 5), which of the following vectors are parallel to 𝑣 ? (4, 28, 10), (-1, 7, -2.5), (3.2, -22.4, 8)
how do you do thid
this
<@&286206848099549185>
slate hedge
If 𝑣 = (2, -14, 5), which of the following vectors are parallel to 𝑣 ? (4, 28,...
same direction or ?
safe radishBOT
@tight kelp Has your question been resolved?
slate hedge
yeah the two were working
tight kelp
can you show me how
hasty wagon
shall i pick up from here?
safe radishBOT
@tight kelp Has your question been resolved?
hollow siren
How do I simplify this?
safe radishBOT
How do I simplify this?
hollow siren
Second part is 4 not 4x
tranquil sentinel
y' is dy/dx, so you should try to isolate it to on one side. It's not correct to set that equal to d/dx
You're just taking the derivative of both sides of the original equation, so saying that's equal to d/dx isn't correct
hollow siren
y' is dy/dx, so you should try to isolate it to on one side. It's not correct to...
What should I do first to isolate
tranquil sentinel
y' is dy/dx, so you should try to isolate it to on one side. It's not correct to...
Btw even d/dx by itself doesn't mean much, you should specify what you're taking the derivative of (whether that's y, so dy/dx, or f(x), so df/dx or d/dx [f(x)]).
d/dx is just the notation you use to specify you're taking a derivative of something (which you put next to it) with respect to x
tranquil sentinel
What should I do first to isolate
I would start by separating the first set of parentheses multiplied together in (...)*4x-(...)*dy/dx
lean otter
Help me please Solve the inequation :
tranquil sentinel
Help me please Solve the inequation :
#❓how-to-get-help
You should open a new channel, this is occupied
You need to go in the MATH HELP (AVAILABLE) section and open a new channel from there
hollow siren
I would start by separating the first set of parentheses multiplied together in ...
So subtract 9y^2 dydx and then divide over the other part with dydx?
tranquil sentinel
So subtract 9y^2 dydx and then divide over the other part with dydx?
I'm not sure what you want to do, can you send a pic of your work? I don't think you even need to subtract by 9y²dy/dx
hollow siren
I'm not sure what you want to do, can you send a pic of your work? I don't think...
I don’t have any work besides taking the derivative lol. I’m not sure how I should start to isolate dydx
tranquil sentinel
I would start by separating the first set of parentheses multiplied together in ...
I suggested to do that, have you tried?
If there's something not clear in what I wrote you should ask about it
hollow siren
That’s why I asked if I should subtract the 9y^2 and then divide that over to separate those. Because if I just separated them by dividing over it would be divide by zero
I mean 0 over that
tranquil sentinel
No.
You have (...)(4x - dy/dx)
Where (...) is 4(4x - y)³
You can apply the distributive property of the multiplication to get:
(...) * 4x - (...) * dy/dx
tranquil sentinel
Ok, don't worry.
Once you've done that you can bring everything which is not multiplied by dy/dx on the right side
hollow siren
Ok cool
hollow siren
Ok, don't worry.
Once you've done that you can bring everything which is not mul...
Can you spot anything wrong?
Besides that -8 on the last row
tranquil sentinel
I actually just noticed you made a mistake in the first step. What's the derivative of 8y? You put 0 but it's not correct
hollow siren
That’s an 84, but I got it. My brain is getting fried and I’m making dumb mistakes.
Thank you!
tranquil sentinel
That’s an 84, but I got it. My brain is getting fried and I’m making dumb mistak...
Oh, ok, sorry. I'm going to check the rest
tranquil sentinel
Besides that -8 on the last row
Besides that, everything is correct 👍
safe radishBOT
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inner carbon
x^2+mx-2=0, the ecuation has 2 solutions in the interval (-1,2) find m∈R
inner carbon
i calculated delta d=m^2+8>0 which is always greater than 0
cosmic grove
if it has two solutions, then delta > 0 indeed
inner carbon
how do i find the solutions
cosmic grove
m^2 + 8 is always positive so it works for every real numbers m
inner carbon
oh i just use the quadratic formula now, right?
cosmic grove
if you want to find the two solutions, do it
cosmic grove
what do you want to do ?
inner carbon
to find the m for the both solutions to be in the interval (-1,2)
cosmic grove
then find every m that respects -1 < x1 < 2
devout bramble
\
devout bramble
safe radishBOT
@devout bramble Has your question been resolved?
devout bramble
<@&286206848099549185>
slate hedge
Would have said the same
tulip arrow
I too think it’s A
slate hedge
well 3 of us think it's A so
devout bramble
k
obtuse plover
foggy salmon
try to
send a specific Q
i..
dont think thrs a special name
no its not the coefficient
foggy salmon
dont think thrs a special name
idk
nova creek
Why do you think it has a special name
nova creek
I don't think there's a special name either
nova creek
Constant maybe? But that's not special, thats just a number in general
nova creek
A coefficient is a number multiplying a variable
nova creek
If it was 5y, 5 would be the coefficient of y
nova creek
It's still a coefficient, actually
According to Wikipedia anyway
It's a "constant coefficient"
Cuz it doesn't have a variable attached
nova creek
Thank wikipedia 
nova creek
If x was 3 and y was 5, you'd have 15 = 5 which is nonsense
nova creek
There are no solutions, there's no variables left
No
3 times 2 is not 9
Yes
Yes
I don't know you
tulip arrow
5 is a term
nova creek
I don't friend people I don't know
tulip arrow
💀
nova creek
Id rather think of you as a random guy I helped on discord one time and leave it at that
Please don't make this weird
tulip arrow
Just ask the questions to anyone, you cant force them
foggy salmon
..
dim berry
hi
tulip arrow
Too far
foggy salmon
hi
dim berry
help
foggy salmon
tulip arrow
👍
nova creek
Dude was spamming help channels with it
safe radishBOT
safe radishBOT
Available help channel!
astral matrix
I dont understand how they got the answer
safe radishBOT
I dont understand how they got the answer
@astral matrix Has your question been resolved?
flat frigateBOT
foggy salmon
$1=x(y+9)$
flat frigateBOT
foggy salmon
$1=xy+9x$
flat frigateBOT
foggy salmon
$xy = 1-9x$
flat frigateBOT
foggy salmon
$y=\frac{1-9x}{x}$
flat frigateBOT
lean otter
Not sure what the other answer is
nova creek
What have you tried
I'm not asking you
This isn't your channel
Just pick any two points on the line
Yea
Yes
Can I see exactly what you put in
Oh
The y axis isn't going up by units of 1
Also note the x axis units
Wrong way around but yes
Doesn't matter, as long as you're consistent about the signs
Left/down is negative, right/up is positive
safe radishBOT
worthy hemlock
Left/down is negative, right/up is positive
Did that user just delete all their messages?
safe radishBOT
Available help channel!
lean otter
what does is mean by the divergence of the gradient of a function
also, what is meant by the laplacian operator
i understand that it is all of the derivatives of a function
dx, dy and dz
but what does it mean conceptuall
safe radishBOT
@lean otter Has your question been resolved?
lean otter
<@&286206848099549185>
safe radishBOT
@lean otter Has your question been resolved?
lean otter
<@&286206848099549185>
unique vortex
What is the y-intercept of y = 2|x − 1|?
safe radishBOT
What is the y-intercept of y = 2|x − 1|?
elfin yew
think of the parent graph |x|
unique vortex
and I would like to know how to do it in a quick way without substitusion
if possible
unique vortex
because this is in multiple choice so like I need to do this under 30 seconds
unique vortex
owh i thought like everything in beside X in the modulus is the y-intercept
but ofcourse calculate the one outside due to PEMDAS right?
trim swan
The y-intercept of any graph is the point where x=0. So just plug x=0 and find y
toxic stratus
owh i thought like everything in beside X in the modulus is the y-intercept
what is this supposed to mean
foggy salmon
The y-intercept of any graph is the point where x=0. So just plug x=0 and find y
yasss
just do that
foggy salmon
what is this supposed to mean
gogo
toxic stratus
y intercept is always always at x=0
unique vortex
like for example if y = |x + 1| then the y intercept would be 1 and so on
trim swan
Yes
toxic stratus
that's because you plug in x=0
foggy salmon
when u do x=0 u get that
trim swan
Because that means the point (0,1) is on the graph, and of course (0,1) falls on the y-axis
toxic stratus
and you get |1|
unique vortex
because the x in the modulus andf beside the x will always be the y intercept right?
foggy salmon
NOOO
toxic stratus
no
foggy salmon
like
toxic stratus
just plug in x=0
foggy salmon
,w graph y=|x|+1
flat frigateBOT
foggy salmon
here thrs nothing in the mod
well except x
toxic stratus
,w plot y=|-x-2|+3
flat frigateBOT
unique vortex
welp ok then, I just wanna clarify if that is an illegal method
toxic stratus
y intercept is 5
trim swan
It is not unique to the modulus. To find the y-intercept of any function, just let x=0. That's all
unique vortex
the one I said before
foggy salmon
which 1
unique vortex
because the x in the modulus andf beside the x will always be the y intercept ri...
this one is illegal
right then I'll stick with substitusion then
right then thnx everyone!!!
.close
safe radishBOT
foggy salmon
❤️
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Available help channel!
unique vortex
Evaluate: log3(1)
safe radishBOT
Evaluate: log3(1)
flat frigateBOT
foggy salmon
o well its just 0 for both
foggy salmon
how did u get inf
unique vortex
i put in in(1) / in(3)
trim swan
That's definitely 0, not infinity
foggy salmon
,w ln1/ln3
flat frigateBOT
foggy salmon
see
trim swan
Any log of 1 is 0
flat frigateBOT
idle sage
0 is infinity confirmed
foggy salmon
thats inf
idle sage
,, 0 = \inf
foggy salmon
other
flat frigateBOT
swaggofishballs
foggy salmon
person
idle sage
..
unique vortex
right I see
foggy salmon
i mean
unique vortex
**swaggofishballs**
???
idle sage
Any log of 1 is 0
^^
unique vortex
i know
foggy salmon
here
idle sage
yep
unique vortex
cuz infinity is any number
idle sage
0 divided by anything is 0
unique vortex
whilst in 0 is only 0 as a whole
foggy salmon
cuz infinity is any number
wait wait
no
we got some
big
misconceptions here to fix
idle sage
infinity isn’t a number
unique vortex
oh wait
unique vortex
is exponential form like the base power to something?
opaque sorrel
logayrithms
foggy salmon
wdym base power
opaque sorrel
hi goddess
foggy salmon
hiii
unique vortex
like 3 to the power of 2
opaque sorrel
do u mean $log_3n$
unique vortex
something like that
unique vortex
is that exponential form?
opaque sorrel
yes
elfin yew
flat frigateBOT
foggy salmon
thats exponential form
idle sage
is exponential form like the base power to something?
if $a= log_b(x)$ then $b^a = x$
pls work
flat frigateBOT
swaggofishballs
idle sage
^^ this pic is better
opaque sorrel
$\lnot (b^a = x) => \lnot (a = log_b(x))$
flat frigateBOT
HellO
idle sage
move the numbers to the other side
elfin yew
• While asking questions, make sure to mention all relevant details, including what you have tried and what you're stuck at. Do not expect others to simply solve your questions for you.
toxic stratus
whats actually going on here
idle sage
whats actually going on here
logarithms 🥳
unique vortex
well nevermind I also remembered I could do that too
toxic stratus
were we not calculating log3(1)
toxic stratus
is exponential form like the base power to something?
this?
unique vortex
yea but then I got confused with another question
but no worries I now know what I done wrong
foggy salmon
ive no idea what that Q was even
unique vortex
and another question
foggy salmon
another 1
unique vortex
P(x) = 2x^3 + ax^2 − 36x + b , where a and b are real numbers. P(x) has a remainder of −12 when divided by x + 1 and a remainder of 7when divided by x +2. Find a and b.
foggy salmon
this
idle sage
have u learnt simultaneous
foggy salmon
is a totally diff tangent
idle sage
use remainder theorem
toxic stratus
remainder theorem yes
unique vortex
was just asking if it would end with simultaneuos equation
toxic stratus
it would
idle sage
was just asking if it would end with simultaneuos equation
yepp!
foggy salmon
is that the
foggy salmon
icant type
toxic stratus
it ends up as linear simultaneous
elfin yew
are u guys still solving the problems for them
toxic stratus
u can find the residues of P
just isnt helpful
unique vortex
which is the the faster way? substituting the equation with the factors? for example x+1 -> x = -1 so sub -1 to all x, or dividing them normally?
foggy salmon
if you do synthetic division
what is
unique vortex
since this is a multiple choice I need to do it under 30 sec ish
unique vortex
another question again
Solve for the point of intersection of the curve
y = x^2 + 5x − 2 and the line y = x + 3.
is there a quick way to solve this? or I assume I'll just use substitusion again?
unique vortex
equate the 2 lines
what do you mean by equate the 2 lines
idle sage
equate ur 2 equations
unique vortex
so like x^2 + 5x − 2 = x + 3
idle sage
yesh
idle sage
so u can find the common point
foggy salmon
so like x^2 + 5x − 2 = x + 3
yesss
idle sage
that lies on both the lines
foggy salmon
so like x^2 + 5x − 2 = x + 3
then
grp like terms
make it into a qudratic
then u can just apply the formula
unique vortex
I got x = -5 and 1
unique vortex
is that the final answer?
idle sage
did u find ur y-coordinates?
unique vortex
uhh
idle sage
so far you have $(-5, ) and (1, )$
flat frigateBOT
swaggofishballs
idle sage
u need to find the y coordinates
so u sub the x values back into either eqn
to find y
so when x = -5 what is y
and when x= 1 what’s y
unique vortex
so there will be 4 points of intercept?
flat frigateBOT
swaggofishballs
unique vortex
so like x^2 + 5x − 2 = x + 3
so I apply it to this equation only then?
idle sage
either equation
u can plug x=-5 and x=-1 into the first eqn or the second one
preferably the x+3
since it’s easier
so u have $y=x+3$
flat frigateBOT
swaggofishballs
idle sage
what is y when x =-5
unique vortex
another question again
Use factor theorem to show that b = 2 when P x = bx^3 − 11x^2 − 22x + 15 is divided by (x + 5).
do I apply the b variable in the equation or divide it with x+5 first?
idle sage
is x+5 a factor?
unique vortex
yes
unique vortex
I ended up with 125b = 150
idle sage
I didn’t work it out HAHA
I trust that ur calculations are right
so just solve for b
u won’t get 2 tho
u might’ve gone wrong somewhere when calculating
unique vortex
its 125b - 275 + 110 + 15 = 0
lean otter
?
idle sage
,w -275 +110 +15
flat frigateBOT
unique vortex
hmm might be the question thats wrong
idle sage
wait u said x+5 is a factor of P(x) tho
idle sage
did the question say that
unique vortex
its not said to be a factor
unique vortex
Use factor theorem to show that b = 2 when P x = bx^3 − 11x^2 − 22x + 15 is divi...
this one
its the whole question
well
thats that I guess
idle sage
oh alrighty then u can try long div
idle sage
is the 3 and 9 bases
unique vortex
solve for ab
idle sage
oki so u have $log_3(a) + 2log_9(b) = 3$
flat frigateBOT
swaggofishballs
idle sage
change of base
idle sage
wait
unique vortex
but with that method it'll be long
idle sage
so u changed the base 9 to 3
idle sage
ok
idle sage
do u have a pic
unique vortex
nope
but I can work it out in my mind directly
just wanna know if there is a fast method to do this
idle sage
but I can work it out in my mind directly
HAHAHA
idle sage
just wanna know if there is a fast method to do this
change of base yes
unique vortex
just saying this is in multiple choice so I need to do it under 30 sec ish
idle sage
it’s a method
unique vortex
ab = 27
hmm
well ok then seems to be a fine and quick method to me I'll just stick with the change of base rule then
well thnx @idle sage for the help and the other people that helped!!!
.close
safe radishBOT
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proven wren
What exactly is the purpose of having parametric equations? and where can they be used?
Let's say
x = t^2
y = t+1
safe radishBOT
What exactly is the purpose of having parametric equations? and where can they b...
proven wren
What does all of this mean? I know that x and y are independent, but what would this try to explain for example?
wind stream
who says that x and y are independent? They are still very much dependent on each other
proven wren
who says that x and y are independent? They are still very much dependent on eac...
In a parametric equation no
right?
wind stream
no, not really
proven wren
I thought they both depend on the t
wind stream
yes, but they are still dependent on each other
proven wren
They're the dependent var and t is the independent
wind stream
yes
wind stream
no
a simple judgement of this is because as x varies, y varies
for example, as x increases, y may increase or decrease, depending on how x and y are defined
proven wren
I don't think x and y always have to be dependent on each other
Sure, they're related, but there can be instances where they work independently from each other
wind stream
they dont in general, but in this case, they do
proven wren
They don't in general what? Like depend on each other?
wind stream
yes, they dont have to depend on each other in the general sense. That is when talking about them as two random variables
proven wren
Right
So what does this mean in a parametric equation tho
Like what would x = t^2
y = t+1 signify or explain
wind stream
well im not sure how to answer this really, because there are a lot of uses. The most important meaning of this would be that parameterisation help simplifies down on how an implicit curves, or in other cases, explicit curves can be represented using x and y
for example, take the equation of a circle
proven wren
right
wind stream
having it as x^2+y^2=1 may be hard for us to solve for the coordinates (though this is subjective)
parameterising it would allow for simpler calculation
or say you want to find a tangent line to this curve
parameterising it will allow for simpler calculation of the derivative at a point on this curve
which allows you to find the slope of the tangent
perhaps a better example of this would be a rotated parabola, or rotated ellipses, or even vertical and horizontal ellipse that are in the form of x^2/a+y^2/b=c
these curves are absolutely ugly when represented in polar coordinates, as well as cartesian
but with some simple parameterisation, these can be represented as a simultaneous equation that involves two different function of t (or any variables you like)
lapis cove
is dividing x^2 +6x -2 = 0 by 2 the same thing as factoring out the two and dividing? Dividing right away makes the process faster right?
safe radishBOT
is dividing x^2 +6x -2 = 0 by 2 the same thing as factoring out the two and divi...
wind stream
well the process of factoring involves dividing
to answer it, they are pretty much the same thing
burnt bloom
Wow waler ur a helper now
lapis cove
yea but when i factor out the 2 and divide then im left with 2 (x + 4)^2 = 21/2
wind stream
i guess, it's the new role stuff
thin bridge
whut
wind stream
yea but when i factor out the 2 and divide then im left with 2 (x + 4)^2 = 21/2
im not sure what you are getting at here
thin bridge
that's a completely different equation
thin bridge
where's that coming from
thin bridge
show full work
cosmic summit
hey can anyone help
foggy salmon
.close
safe radishBOT
foggy salmon
bye
safe radishBOT
Available help channel!
dire fjord
Hi
final sail
safe radishBOT
final sail
I have no clue how to solve this equation or what this specific equation is even called
plucky elk
you're solving for x?
final sail
Yes, sir.
plucky elk
do you know how to clear denominators
plucky elk
you multiply the whole equation by the lowest common denominator of all your fractions
e.g. 4 is one factor that's in the denominator of some terms, so multiply the whole equation by that.
plucky elk
yes
plucky elk
uh you multiplied the second term's denominator by 4
$a \cdot \frac{b}{c} \neq \frac{ab}{ac}$
flat frigateBOT
riemann
plucky elk
what now exactly?
repeat for everything that appears in denominators until you don't have anymore denominators
plucky elk
try simplifying before proceeding
plucky elk
the first term isn't legible
final sail
its -4
plucky elk
repeat for everything that appears in denominators until you don't have anymore ...
keep doing this
$\frac{4x}{4x-1} \neq -4$
flat frigateBOT
riemann
plucky elk
e.g. x=1: 4/3
final sail
what is the relevance of that picture?
plucky elk
i'm telling you that you can't simplify that way
plucky elk
**riemann**
this is your original left hand side. you simplified it to -4 and i'm saying it's incorrect
final sail
oh
then how are you supposed to simplify this picture
WAIT
STOP
I think I got it
plucky elk
cool. .close when you're done
plucky elk
yea, but you can still simplify the first term
final sail
how do you simplify 4x?
plucky elk
$\frac{ax}{ay-az} = \frac{ax}{a(y-z)} = \frac{a}{a} \frac{x}{y-z}$
flat frigateBOT
riemann
final sail
.close
safe radishBOT
tardy copper
i thought about cubing everything but there must be something more simple
rotund valley
which class/grade are u?
tardy copper
wdym
rotund valley
like 9th or 8th
rotund valley
hs?
tardy copper
high school
toxic stratus
just cube everything
spice grove
There should be neat stuff involving a^3 + b^3 + c^3 - 3abc shit I think
tardy copper
hmm
toxic stratus
you really want to solve that
spice grove
Lol.
toxic stratus
somehow magic up the a b c from the cbrt(2) - 1?
idle parrot
use cubert 2 = x or something like that
tardy copper
i tried
spice grove
Cubing everything works, everyone knows. I think op is looking for alternatives. That's what we're doing here.
lean otter
you stull got the cbrt(9) to deal with then
toxic stratus
like
spice grove
alternatives require much more thought
True that
lean otter
alternatives require much more thought
thoughts is math 
idle parrot
eh?
spice grove
" Thoughts" the word is plural
lean otter
math is about the thinking
toxic stratus
if you had to do this for general n
lean otter
if I wasent clear
idle parrot
maths is plural
toxic stratus
maybe you might want to consider giving it more thought
spice grove
It's not
lean otter
maybe you can get somthing good
tardy copper
yeah, ill just continue brainstorming, thnx
pretty sad if the task is just to cube
but im sure there is something cleaner
.close
safe radishBOT
lean otter
I think I am getting something nice
lean otter
using a^3-b^3 and a^3+b^3+c^3-3abc
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Available help channel!
mortal wave
e
whole acorn
what have you tried
and this looks like a discrete mathematics question ( #discrete-math )
safe radishBOT
@mortal wave Has your question been resolved?
lean otter
safe radishBOT
grave flint
whats the range of cosine function
just by itself
cos(x) whats the range @lean otter
lean otter
i dont know what that means
lean otter
thats not given i think
grave flint
..
it shouldnt need to be
whats the largest number that cos(x) can give @lean otter
and whats the smallest number it can give
lean otter
how would i find that
lean otter
sorry im new to this
grave flint
yeah
which is the output
it wouldnt be the y-vlaue
its the smallest output that the expression can give
and since we trying to find minimum we get the smalles
safe radishBOT
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Available help channel!
vivid fern
Give an example of a function whose domain is the interval [0, 1] and whose range is the interval (0,1)
obsidian oracle
hello, what conditions do you need on your function ? because if you don't have any then just take f(x) = x if x in (0,1), and f(x) = 1/2 if x = 0 or x = 1
vivid fern
oh i see, there doesnt seem to be any conditions, thank you
Give an example of a function F whose domain is the
interval [0, 2] and such that F(0) = 0 and F(2) = 2 but 1
is not in the range of F
vivid fern
Give an example of a function F whose domain is the
interval [0, 2] and such tha...
I'd like to ask this as well
obsidian oracle
alright. let's work out together on what function we could take for this
first of all : do you think F can be continuous ?
vivid fern
no
obsidian oracle
correct, this is because of the intermediate value theorem
So, since we only have the condition that the values for F in 0 and 2 are themselves, might as well take the easiest function
That is, take F a function that only takes its values in {0,2}
for example, F(x) = 2 if x = 2, else F(x) = 0
vivid fern
do we do f(x)=x when x is 0 or 2?
obsidian oracle
yes, that works too
but then you have to define F(x) for x neither 0 or 2
and you have no restrictions on what that can be except F(x) != 1
vivid fern
nothing else other than what is written in the question
obsidian oracle
Give an example of a function F whose domain is the
interval [0, 2] and such tha...
Let's work out on this example
take the first function that comes to mind that could work, for example F(x) = x
then look at where the problems with this function are
(here, the problem is F(1) = 1 and that doesn't work)
then tweak the problematic values
vivid fern
wait, there's no definition for what the range is, so what should i pretend "not in the range" as
obsidian oracle
the range has no restrictions, except from the fact that 1 is not in the range
as in "you can't have F(x) = 1 for any x"
vivid fern
can't think of anything that makes f(1) completely destroy itself like how f(0) could be made into
obsidian oracle
let's look back at this way of finding a function that fits
obsidian oracle
then tweak the problematic values
this way
So, let's say we look at F(x) = x for all x, and we look at why it doesn't work
it doesn't work because F(1) = 1, and that's not allowed
obsidian oracle
So we change F(1) to be anything else
So our new function is F(1) = [insert any value different than 1] ; else F(x) = x
vivid fern
-x, 0, anything?
obsidian oracle
and that works
obsidian oracle
yeah
vivid fern
I was extremely confused on what not in the range is
obsidian oracle
by definition, for f : A->B any function, range(f) = {f(x) for x in A}
so "y not in the range" is the same as "f(x) != y for all x"
vivid fern
cuz if its saying f(0) then i know to say 1/x so that f(0) doesnt make sense so its not in range
vivid fern
so "y not in the range" is the same as "f(x) != y for all x"
ah i see
thank you for your help @obsidian oracle
.close
lean otter
what is multiplicative inverse?? How do you find it
safe radishBOT
what is multiplicative inverse?? How do you find it
crisp wraith
ahhhhhhhhhh helpp we have to finish this puzzle - or we die in 15 minutes--
is it hexadecimal? how do find the solution
pliant pendant
what is multiplicative inverse?? How do you find it
It's the number such that [multiplicative inverse of x] • [x] = 1.
Rearranging we get [multiplicative inverse of x] = 1/x
safe radishBOT
@lean otter Has your question been resolved?
visual patio
is it hexadecimal? how do find the solution
this is a help channel..
and its taken 🙃
toxic stratus
@sand stratus if you're done close this channel
since your other channel already has been closed
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Available help channel!
golden stirrup
After finding the length of a parameterized curve via integration, I've achieved a negative number for my length. I was wondering if anyone could explain if this means I am incorrect, or if it simply means the direction of travel along that length is negative?
safe radishBOT
After finding the length of a parameterized curve via integration, I've achieved...
obsidian oracle
Can you show your work if possible ?
obsidian oracle
First of all, you wrote that 4 -16t + 16t² = 4(2t²-1)², and the factor 2 disappears
golden stirrup
why 2t^2 -1?
but I'd imagine not?
yeah because, I removed the square root
and 2 squared is 4
obsidian oracle
no but you wrote sqrt((2t²-1)²) = t²-1
golden stirrup
oh there
obsidian oracle
no but you wrote sqrt((2t²-1)²) = t²-1
Why did the "2" here disappear ?
golden stirrup
i didn't notice that
obsidian oracle
Ok so thats the first mistake, which is no big deal
golden stirrup
obsidian oracle
Then... you write that sqrt(a²) = a, but is that always the case ?
golden stirrup
yes?
stray socket
sqrt(a^2) := |a|
obsidian oracle
Even when a is any real number ?
obsidian oracle
sqrt(a^2) := |a|
Thank you, I was about to write that
golden stirrup
I'm not understanding
obsidian oracle
sqrt((-3)²) = 3
golden stirrup
oh okay, yeah..alright I follow
obsidian oracle
Then, depending on the value of t, sqrt(4(2t²-1)²) is either 2(2t²-1) or 2(1-2t²)
Find which values of t corresponds to which value of sqrt(...)
dim smelt
this should be a + sign, the - goes inside parenthesis
obsidian oracle
Right, I didn't even see that
golden stirrup
okay...
I've been making a few mistakes like this lately
it's getting towards the end of the semester
obsidian oracle
So actually you're looking at 4+ 16t² + 16t⁴ = 4(2t²+1)²
dim smelt
So actually you're looking at 4+ 16t² + 16t⁴ = 4(2t²+1)²
^ this
obsidian oracle
Careful, int(0,1)[2t²] = ...
golden stirrup
yeah we're all good I think
almost every time I have trouble, I've made some stupid mistake like misplaced a negative sign
just can't find it
dim smelt
always check if what's inside sqrt is never negative
obsidian oracle
Careful, int(0,1)[2t²] = ...
dim smelt
and in this case it never will be, because this is always positive
obsidian oracle
Careful, int(0,1)[2t²] = ...
How did you calculate this integral @golden stirrup ?
golden stirrup
...
wrongly
i took the derivative
it's like 1 am... okay... i think i see why this is so wrong now lmao
obsidian oracle
You shouldnt be doing maths so late xd
golden stirrup
THERE we go... mistakes fixed
I knew something was up, I shouldn't have been getting a negative length
just didn't realise I'd made so many
obsidian oracle
Np :)
naive idol
I need help with this still, Redstone helped me before but I had to go halfway through and I can't figure it out with the advice I got then
safe radishBOT
I need help with this still, Redstone helped me before but I had to go halfway t...
naive idol
I've looked at how to use quotient rule to derivate the functions but I don't know how this leads to a new limit?
I'm also kind of stuck in a huge mess of rational numbers here..
burnt bloom
- apply lhopital
- evaluate limit
- sub in -8 in all x
- simplify
naive idol
Right, so that second step. What does that mean?
burnt bloom
move terms, split limit
naive idol
split limit?
burnt bloom
naive idol
Okay, but the case here is f(x)/g(x) so how does that work?
burnt bloom
I've looked at how to use quotient rule to derivate the functions but I don't kn...
ok i will show you with this method instead
proper crypt
$$\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)}$$
If $\lim_{x \to a} f(x) = \lim_{x \to a} g(x) = 0$ and the limit $\lim_{x \to a} \frac{f'(x)}{g'(x)}$ exists
flat frigateBOT
RedstonePlayz09
proper crypt
It's pretty clear that both f(x) and g(x) (in your case) are approaching 0. You can see that by just plugging in -8 to the x and you will get 0/0
naive idol
Okay, so if I understand this right I need to calculate f'(x) and g'(x), then use quotient rule thing and somehow then find a new limit?
proper crypt
Okay, so if I understand this right I need to calculate f'(x) and g'(x), then us...
Yes. You write it like this:
$$\lim_{x \to -8} \frac{\sqrt{1 - x} - 3}{2 + \sqrt[3]{x}} = \lim_{x \to -8} \frac{\left(\sqrt{1 - x} - 3\right)'}{\left(2 + \sqrt[3]{x}\right)'}$$
Give me a sec... lol
burnt bloom
flat frigateBOT
RedstonePlayz09
proper crypt
Finally.
burnt bloom
=-2 at the end
proper crypt
Now just continues the = and simplify
Shouldn't it be 2 at the end?
Oh no
My bad it's -2
naive idol
Yeah it is for sure, but I am not following your calculation at all...
What even happens at the first step?
naive idol
Ah right, same as I got before..
burnt bloom
And simplified a little
good eye
naive idol
I tried to look up quotient rule and I got a very long formula that I must've messed up somewhere. Clearly this is simpler..
naive idol
Right..
Have to look that up too
Alright, thanks I totally get it now!
just gotta figure out how to say all this in my language...
.close
trail cliff
can someone help me with this part of the explanation
safe radishBOT
can someone help me with this part of the explanation
lean otter
the radius of the circles is d/2
trail cliff
ok
how do we know that this little part in the middle assigned d/2
is the radius of the circle
isnt that incorrect ?
lean otter
it is the distance between two parallel line segments
the distances between both ends of the shorter segment and the longer segment is equal to d/2, so the distance between segments (between every point of the shorter one and the whole longer one) is d/2
trail cliff
ooooh
i didnt see that the arrow was between the inner square and the outer one
🤦♂️
i was so confused xD
thought it was the distance between the circle's outline
from the shortest route between the other circle's
lean otter
oh
safe radishBOT
