Yup !
#help-36
sand portal
Or more like
A property of its curve representation
The function is a process, not a curve
The curve is just a certain representation of the function itself
And in order to interpret it geometrically, a geometrical representation is needed
Which is why we talk about the graph of the function
rare marlin
so how would i obtain a geometrical representation of say this function?
sand portal
It's defined analytically, with a function, but the object is the set of points (x,c(x)) in the plane constituted of all the (x,y) points
sand portal
so how would i obtain a geometrical representation of say this function?
Hmmmmmm
Plotting ?
It would not be accurate for sure
rare marlin
Ah alright
rare marlin
Yeah i guess i could just use the fact that c(x) = c(-x)
sand portal
"explain this geometrically" is basically "explain how this relation translates in a geometrical level on the curve of the function c"
So if you talk about a reflection along the y axis, I think you get all the points
rare marlin
Which in this case would be a reflection which was proved by the fact that c(x) = c(-x)
Right?
sand portal
Yup
If you want to compare it with the general case
The curve of a function f has an axis of symmetry of equation x=a iff for all x, f(a-x)=f(a+x)
rare marlin
So the general idea is that if a function c(x) is equal to c(-x) that proves that the function is symmetrical and it can be reflected over x=0
sand portal
So the general idea is that if a function c(x) is equal to c(-x) that proves tha...
I'm gonna accept this one but x and c(x) are numbers, c is a function,
sand portal
So the general idea is that if a function c(x) is equal to c(-x) that proves tha...
Other than what I mentioned this is perfect you know
Good job !
rare marlin
But im just a bit confused on this part, isnt the "looks identical part" the important part because can't any function be reflected across the y axis? Is there more specific terms?
Sorry u may have answered this before im unsure could u explain it one more time?
sand portal
But im just a bit confused on this part, isnt the "looks identical part" the imp...
Reflection. That's the specific term. And not every function f have the property f(x)=f(-x), thus not every function has a reflection along the y axis. For example, f(x)=(x-1)² is centered at x=1, and not at x=0
rare marlin
Oh so "has a reflection" essentially says that it looks identical when reflected.
sand portal
The function f(x)=x doesn't even follow that property anywhere
sand portal
Oh so "has a reflection" essentially says that it looks identical when reflected...
Don't take "has a reflection"
Apart from
The actual reflection
"a reflection along the x axis"
That's the actual reflection
rare marlin
Yep
sand portal
Now
Let's say, we can see "looks identical" as an undefined term in maths basically
It is either identical or not
rare marlin
Oh okay sure, ill just use reflection across x=0
sand portal
Yes, that's the geometric property of ... what already ?
What is reflected across x=0 ?
rare marlin
C(x)?
sand portal
It's still a number, has always been
rare marlin
isn't c(x) reflected across x=0?
sand portal
"Isn't 3 reflected across x=0 ?", that's an equivalent of what you just said
What you are saying doesn't make sense
c(x) is a number, not a geometric object
rare marlin
Then the geometric representation of c(x) has reflection over the line x=0?
sand portal
Almost there YES !
c(x) is a number
I still don't know what is the representation of a number in a plane
A point, sure
A number, no
rare marlin
Oh wait
sand portal
It's just that tiny bitty thing you have to change
Really, just 3 characters that have to be deleted
rare marlin
Is it the geometric representation of the function C has a reflection over the lime x=0?
sand portal
Np np 
rare marlin
Helped me a lot hahah
sand portal
Is it the geometric representation of the function C has a reflection over the l...
"the line of equation x=0"
But you did the hardest
sand portal
Yeeeeeeeessssssssss
It's such a thing students hardly understand
I'm actually so glad you did
rare marlin
Yeah ur a great helper ngl
rare marlin
Just curious what r u studying in math?
final saddleBOT
@rare marlin Has your question been resolved?
misty hemlock
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shadow aspen
i think we use the discriminant formula to find it
Yeah
When discriminant = 0 it has "1" root
final saddleBOT
misty hemlock
.reopen
final saddleBOT
✅
misty hemlock
.close
charred tiger
im not sure how to do B
final saddleBOT
im not sure how to do B
rotund citrus
same thing but you plug in (1+h) where x goes.
charred tiger
same thing but you plug in (1+h) where x goes.
wait so the x is 1 and then i plug the x into the h?
rotund citrus
what?
so for example you did f(2) = 7 - (2)^2 for the first part for f(2)
same exact thing, but instead of 2, you plug in (1+h).
charred tiger
ohhhhh ok
rotund citrus
its okay to have h in the answer if they don't notate a limit. if its still wrong then they expect you to find it when h = 0.
generally, you never want to just make h = 0 until after you've found the simplified expression.
blissful pelican
hellp
vital crag
!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/
blissful pelican
huh?
vital crag
No need to ask "Can I ask...?" or "Does anyone know about...?"—it's faster for e...
this
final saddleBOT
@blissful pelican Has your question been resolved?
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final saddleBOT
Available help channel!
west plover
how can i solve this
jovial spoke
help
final saddleBOT
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Available help channel!
charred tiger
im not sure how to do this
final saddleBOT
im not sure how to do this
astral grotto
are you familiar with properties of logarithms
charred tiger
yea kinda
astral grotto
how would you simplify $y \log_b x$ or $\log_b x + \log_b z$
soft zealotBOT
LordNwahs
charred tiger
umm i think wouldnt it be like logb^(x * z)?
astral grotto
how about $y \log_b x$
soft zealotBOT
LordNwahs
astral grotto
yep
just apply those properties to get the RHS to some expression $log_b (something)$
soft zealotBOT
LordNwahs
charred tiger
wait then do u multiply the 2/3 and 1/2 together then?
astral grotto
no?
charred tiger
wut
astral grotto
how do you simplify $2/3 \log 27$
soft zealotBOT
LordNwahs
charred tiger
charred tiger
logb27^2/3
astral grotto
yes... and what is 27^(2/3)?
charred tiger
3^2
charred tiger
o
astral grotto
yep!
charred tiger
okeee thanks :D
astral grotto
cheers
astral grotto
yep looks good to me
charred tiger
.close
charred tiger
is this right?
final saddleBOT
is this right?
final saddleBOT
final saddleBOT
Available help channel!
gritty matrix
Factor 3xy + my - 6nx - 2mn
final saddleBOT
Factor 3xy + my - 6nx - 2mn
tranquil pine
Factor 3xy + my - 6nx - 2mn
what have you tried
cedar cove
Factor 3xy + my - 6nx - 2mn
if you can't find a common variable in all the terms, try finding commons in two or more terms
gritty matrix
I'll try grouping them
cedar cove
yeah, that should help
small zodiac
I'll try grouping them
ye
gritty matrix
So I came up with the answer y(3x + m) - 2n(3x - m), is that right?
cedar cove
So I came up with the answer y(3x + m) - 2n(3x - m), is that right?
That's one way to factorize it, but it is not fully factorized, right?
See if you can group them differently, while still being able to have commons and factorize
final saddleBOT
@gritty matrix Has your question been resolved?
final saddleBOT
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Available help channel!
rugged sigil
What actually is this red line?
final saddleBOT
What actually is this red line?
rugged sigil
In Line Integration
jagged cosmos
The space curve or the path?
final saddleBOT
@rugged sigil Has your question been resolved?
rugged sigil
The space curve or the path?
Sorry I didn't see.
I might've been misunderstanding
Is the red line the curve and the blue line just follows the surface and we're finding the area between the curve and surface?
quiet garden
Domain is so confusing
quiet garden
I need help
warm ether
in your first one youre saying x cant be 6, when in reality x cant be -6
so you need to fix that
quiet garden
in your first one youre saying x cant be 6, when in reality x cant be -6
Ok I changed that
What about the rest
final saddleBOT
@quiet garden Has your question been resolved?
shell hatch
Hello everyone, I solved a rational inequality and ended up with
X³-7X²+7X+15<0
I have to factor this polynomial, but I don't know how to rewrite some terms (as example -7X=-9X+2X) is there a rule?
neat sable
try subbing in values for x?
shell hatch
Randomly?
neat sable
yes
shell hatch
And how would that help?
neat sable
i think if u sub in x = 1 the polynomial should equal 0
then make x = 1 into a factor and divide it into the polynomial
to get a quadratic and then solve the quadratic to get remaining two factors
echo needle
1 is not a solution
shell hatch
Intresting, but If I have to be honest it doesn't look efficent.
Some zeroes could be irrational, and i would just waste time.
Also, as said above, 1 isn't a solution
echo needle
can you do a rational root test?
shell hatch
Sorry, what is?
echo needle
hm, look it up then, it gives us the options what to try as a guess
basically you have two sets A,B
shell hatch
Oh okay I just searched on wikipedia
shell hatch
So basically i get some numbers, and within them there are zeroes of the polynomial, right?
echo needle
and then try every b/a where b is in B and i is in A
yes
if you have rational roots
it will find it
and now you have 3 nice roots so its gonna work
the guessing should work in this case too cuz - 1 will be a hit already
echo needle
with this method, no
but i doubt they give you one where every root is irrational
you would need the solving formula then i guess
which is far from your topic i think
shell hatch
but i doubt they give you one where every root is irrational
Yeah you are right
echo needle
and if you have one nice root, you are left with a quadratic which is easy at that point
shell hatch
So I find the root, as example x=1. Then I know my A(x)=(x-1)(usually a quadratic) and I just have to factor x-1 out of the terms until i find this quadratic, right?
echo needle
yea
shell hatch
I have this inequality
(X²-1)²>9/4
I would like to avoid to solve this quadratic term
But idk if I can take the root from both terms
shell hatch
X²-1>3/2 looks wrong, since the first term can be negative, while in the original form it cannot
echo needle
also you could just substitute in y=x^2
and then you have a quadratic
just at the end you need to substitute back
shell hatch
X²-1>3/2 looks wrong, since the first term can be negative, while in the origina...
Is there a way to solve it in that way?
Oh do i have to use absolute value?
Like |x²-1|>3/2?
echo needle
since we are just searching for the roots i think both are okay
it will give us the intervals between them anyway
and if you are unsure at that point try a random number from every interval
shell hatch
Like |x²-1|>3/2?
In that case what should I do?
Do i have to rewrite it as
X²-1=±3/2 to find roots?
And then take the exterior intervals
soft zealotBOT
echo needle
,w X²-1>3/2
soft zealotBOT
echo needle
,w (X²-1)² > 9/4
soft zealotBOT
shell hatch
How is that possible? Doesn't taking the root from both members change things?
echo needle
it does, the first has 4 solution to begin with
but we lost the 2 complex one
i wont try this now, but i think if you follow the y=x^2 line
which i really recommend
you would end up with 2 scenarios and one would be something like: negative number =x^2
shell hatch
The only thing i don't understand is how can
|x²-1|>3/2 ("correct" form i think)
be equal to
x²-1>3/2
echo needle
so that would be the dead end which we lost
echo needle
The only thing i don't understand is how can
|x²-1|>3/2 ("correct" form i think...
ahh
we have this
the || only flips our graph between -1 and 1
the roots stay
did you try the y=X^2 substitution?
it will help you in the future too
shell hatch
Intresting, is that a coincidence? Take as example the vertex , what if its y coordinate was bigger in module?
echo needle
i dont understand the question
shell hatch
did you try the y=X^2 substitution?
Yeah I already used it with polynomials in the form of x^(2n)+x^(n)+c=0
echo needle
but we are sidetracking now i think
okay, then you can solve this in that way too
and we dont need to think about anything that could go wrong
cuz maybe there could be sth just we dont see it in this case
shell hatch
i dont understand the question
Thing "under" x axis get reflected. So if the vertex had coordinates as (0, -2) with the absolute value it would have been (0,2), therefore i would have 4 solutions
shell hatch
okay, then you can solve this in that way too
Yeah I asked cause i am studying a chapter about absolute values and maybe in the test i will have to do in that specific way
Wait give me a second
You can see that the red equation is bigger than y=14.1 for different intervals
Red equation > y=k has this region in which it is verified, while blue doesn't
@echo needle i tried with desmos and found out that absolute value is necessary
Anyways, thank you very much for all the help
.close
trim lance
final saddleBOT
trim lance
how do i proceed with this
final saddleBOT
@trim lance Has your question been resolved?
trim lance
how do i proceed with the integral on the bottom
final saddleBOT
how do i proceed with the integral on the bottom
vital crag
Try cancelling and sub maybe?
Or use a trig identity once you get to only sines and cosines
trim lance
Or use a trig identity once you get to only sines and cosines
I tried on the top
I don’t see anything that appears evident
vital crag
I tried on the top
!show
final saddleBOT
I tried on the top
Show your work, and if possible, explain where you are stuck.
vital crag
Oh wait I see it
trim lance
Oh wait I see it
Is this right ?
final saddleBOT
@trim lance Has your question been resolved?
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@tranquil pine Has your question been resolved?
plush stag
final saddleBOT
plush stag
I don't understand what these are asking
final saddleBOT
@plush stag Has your question been resolved?
plush stag
<@&286206848099549185>
robust trellis
<@&286206848099549185>
Amplitude means (max-min)/2
So what are the max and min for -sin(2x)
plush stag
Is it just the -pi/2 and pi/2?
robust trellis
Is it just the -pi/2 and pi/2?
No
I mean like
Minimum output maximum output
What is the most -sin(2x) can be
And what is the least
plush stag
1 and -1?
robust trellis
Yeah
So (1—1)/2
Amplitude is 1
Now what are the minimum and maximum of -tan(x-pi/2)
plush stag
-tan gives me an error
robust trellis
And what about periods and phase shifts?
Ok
Do you know the period of just sin(x)
plush stag
Idk
robust trellis
Idk
So
There’s 2pi radians in a circle right
So no matter where I pick on the unit circle
If I turn 2pi radius clockwise or counter clockwise
I will get back to where I was
And if I get back to where I was I will have the same length opposite the angle (definition of sine)
So we say for all x
sin(x)=sin(x+2pi)
Which means every sine value will repeat after 2pi
And the definition of period is basically how long it takes to repeat
So the period of sin(x) is 2pi
plush stag
So does it work that way for 2x as well?
robust trellis
So does it work that way for 2x as well?
Well
plush stag
Except multiply by 2?
robust trellis
No
If you thing about it
With sin(2x)
You’re gonna reach values twice as fast
So it takes half as long to repeat
So the period is pi
In general
If you have sin(ax)
The period is 2pi/a
robust trellis
And then for -sin, the answer just becomes negative, right?
No
Cuz think about it
If you have -sinx
It’s gonna take the same amount of time to repeat
Period is always positive
robust trellis
Yeah
robust trellis
So then what about phase shifts?
Ok
So phase shift is how far it goes from the parent function
So if we have sin(x-1)
The phase shift is 1
final saddleBOT
@plush stag Has your question been resolved?
tranquil pine
You can factor out the x in the denominator
final tangle
limit exists because you have a hole there
doesn't matter if the function isn't defined there
tranquil pine
$\lim_{x\to 7} \frac{x-7}{x^2-7x}=\lim_{x\to 7} \frac{x-7}{x(x-7)}=\frac{1}{x}=\frac{1}{7}$
soft zealotBOT
bla
tulip gyro
final saddleBOT
Commands:
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consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
final saddleBOT
Available help channel!
dusky vigil
Can not solve this stupid question
final saddleBOT
Can not solve this stupid question
dusky vigil
final saddleBOT
@dusky vigil Has your question been resolved?
robust trellis
So
V=4/3pir^3
If you take the derivative with respect to t
You get
90=4pir^2*dr/dt
Then solve form there
I think you got a similar thing but kinda did it in reverse or smth
Cuz the pi should be in the denominator in the final answer
final saddleBOT
@dusky vigil Has your question been resolved?
winter sky
help
static crypt
hi i tried before in a different channel to no success could someone check over this integration question please?
final saddleBOT
hi i tried before in a different channel to no success could someone check over ...
static crypt
@tiny gorge i couldnt type in that other one for some reason
tiny gorge
what is your question?
no point opening and closing channels without actually showing the question
static crypt
tiny gorge
horrifying numbers
static crypt
legit
ive been trying so long
cant spot the error/s
bungo brother are you looking or...?
final saddleBOT
@static crypt Has your question been resolved?
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@static crypt Has your question been resolved?
tardy ridge
final saddleBOT
tardy ridge
what does the red thing mean in this equation
tiny gorge
it's hard to read, does it say m_tan ?
tardy ridge
it's hard to read, does it say m_tan ?
yes
tiny gorge
i guess "slope of tangent line"
dreamy gull
could someone look over my work to see if i did this right?
final saddleBOT
could someone look over my work to see if i did this right?
dreamy gull
finding the determinant of a 4x4 matrix
tired walrus
,w determinant {{2,-3,0,1},{5,4,2,0},{1,-1,0,3},{-2,1,0,0}}
soft zealotBOT
tired walrus
ok so apparently you fucked up somewhere
dreamy gull
yeah i just dont know where
tired walrus
btw all these [] should be | | instead
dreamy gull
it looks right
gotcha
i used the first line to calculate these
does it matter which line
dry light
dreamy gull
so i did the first line as required
tired walrus
does it matter which line
it doesn't matter
dreamy gull
oh okay
dreamy gull
oh shit
tired walrus
could someone look over my work to see if i did this right?
in the last 3 by 3 thing, 1(1) - (-1)(-2) = 1 - 2 = -1 not -2
not that this would fix the apparent discrepancy still
fuck i can't see where else you fucked up lol
dreamy gull
yeah.... its strange
is there maybe just a way i can redo it but get the right answer?
tired walrus
ok hang on lemme try to reproduce...
dreamy gull
also would getting the determinant of a 5x5 matrix be the same as this just like repeating the steps over again but adding another step to it
if that makes sense
tired walrus
yes determinants can be calculated recursively like that
dreamy gull
ok thought so
tired walrus
dreamy gull
omg
tired walrus
yeah you need to be super careful with copying
a missed minus sign can REALLY screw you over like this
dreamy gull
i see that
wow
lol
thanks for noticing my problem
i have another question with this real quick
,w determinant {{2,-3,1,0,4},{0,3,2,5,7},{0,0,1,6,0},{0,0,0,5,2},{0,0,0,0,-1}}
soft zealotBOT
frigid drift
90% - 99% - 112
80% - 89% - 66
69% - 79% - 19
how to find the median of the given data if the mean is 89.69%
tired walrus
gonna need a bit more context to these chief
frigid drift
gonna need a bit more context to these chief
its ok if its not accurate
just an estimated value
i asked ChatGPT its giving me 74 which litrally isnt possible
it has to lie between 90 and 99
i just want an estimate
final saddleBOT
@frigid drift Has your question been resolved?
vital crag
i asked ChatGPT its giving me 74 which litrally isnt possible
yea don't' use chatgpt for math
eternal wharf
final saddleBOT
eternal wharf
Why are they not taking phi as common?
tight void
Cuz each & every set belonging in the universe already has null set as common
Morever, null set (phi) isn't considered as an element
@eternal wharf
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@eternal wharf Has your question been resolved?
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@eternal wharf Has your question been resolved?
final saddleBOT
@eternal wharf Has your question been resolved?
scarlet sequoia
This is one of the cases where I think the solution is wrong
The empty set will always be an element of any power set
So if you take the intersection of two power sets, it will ALWAYS have the empty set in it, which is a valid element
So emptyset and {-7} constitute 2 common elements of P(A) and P(B)
eternal wharf
Morever, null set (phi) isn't considered as an element
See@scarlet sequoia
<@&286206848099549185>
scarlet sequoia
Empty set IS an element... that's where I disagree with the first helper
$\mathcal{P}(A)\cap\mathcal{P}(B) = {\emptyset, {-7}}$, thus $|\mathcal{P}(A)\cap\mathcal{P}(B)| = 2$
soft zealotBOT
rafilou2003
scarlet sequoia
The argument "$\emptyset$ is not counted as an element" is invalid. If it were true, then the set ${\emptyset}$ would be a set with no elements, ie. the empty set itself. However $\emptyset \neq {\emptyset}$
soft zealotBOT
rafilou2003
scarlet sequoia
I suggest you take the matter to your teacher if you're still unsure
sonic crystal
thats a cool font
eternal wharf
I suggest you take the matter to your teacher if you're still unsure
For your concern. There is no teacher. I am graduated poorly
And i am learning all the things through online sources and discord(maths,english)
eternal wharf
Empty set IS an element... that's where I disagree with the first helper
Thanks
final saddleBOT
@eternal wharf Has your question been resolved?
eternal wharf
.close
unkempt fern
hello
unkempt fern
how do i find the domaine of Arctan((x-1)/(1+x)) ?
i need to do -∞<x-1/1+x <+∞ and x =/= -1 so domf = R/{-1} ?
<@&286206848099549185>
final saddleBOT
@unkempt fern Has your question been resolved?
unkempt fern
<@&286206848099549185>
tranquil pine
<@&286206848099549185>
Yes sir!
unkempt fern
look up
unkempt fern
how do i find the domaine of Arctan((x-1)/(1+x)) ?
this @tranquil pine
tranquil pine
this <@456226577798135808>
Ay Ay Captain!
unkempt fern
what ay ay
tranquil pine
what ay ay
I mean yes sir
tranquil pine
yeah i need help for this
no problem sir
i will do this for u
but it will take some time coz I am pc so can just do it and take pic and send you
unkempt fern
ok
final saddleBOT
@unkempt fern Has your question been resolved?
tranquil pine
i need to do -∞<x-1/1+x <+∞ and x =/= -1 so domf = R/{-1} ?
Okay, we're dealing with the function, (arctan(u)), which works for all real numbers, but here's the thing - we can't divide by zero.
In this case, the problem is in the denominator, (1 + x), so we solve for when that's zero:
[1 + x = 0]
Solving for (x), we get (x = -1). That's the issue; we can't have (x = -1) because it makes the denominator zero.
So, the domain of f(x)= ((x-1)/(1+x)) is all real numbers, except for (x = -1). Think of it as covering every real number except -1, it goes from negative infinity right up to -1 (but not including -1), and from just after -1 to positive infinity. Avoid -1, and you're good to go homie. 😛
unkempt fern
Ok
but
@tranquil pine -∞<x-1/1+x <+∞ how we can prove it with that
we cant have x = -1
so -∞<x<+∞
with x =/= -1 ?
tranquil pine
we cant have x = -1
ttyl gotta go
final saddleBOT
@unkempt fern Has your question been resolved?
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Available help channel!
oblique turret
would the answer for a) be 6 years?
final saddleBOT
would the answer for a) be 6 years?
candid hull
,calc log(0.25)/log(0.8)
soft zealotBOT
Result:
6.2125674390108
so would it round up or down? or stay as 6.2
id assume it would eb 6 years
as she is gonna sell it one it becomes over 6.2
@candid hull
candid hull
some kind of rounding above probably
"she wants to keep it until its value is less than 25% blablabla"
i.e. if it's not less than 25% I don't sell this kind of deal
that's how I interpret that at least
@oblique turret
oblique turret
that's how I interpret that at least
so u would round up?
but your looking at how long she wants to keep it for @candid hull
oblique turret
isn't that what the question is asking
yes
so she would keep it for 6years?
@candid hull did u use the value of a to be 1 or 0.1?
candid hull
re I was disconnected for some reason
oblique turret
oh
candid hull
<@177516015033384960> did u use the value of a to be 1 or 0.1?
wdym a ?
candid hull
0.8^n <0.25
yeah
oblique turret
when you work it our did u use ar^n <0.25
waht happened to the value of a?
candid hull
just supposing the original value of the car is 1
if we start at 1, then 1/4 of the orig value is 0.25
candid hull
does it matter
mortal bison
Find m so that there is a unique solution to the system
final saddleBOT
Find m so that there is a unique solution to the system
mortal bison
in the sec eq?
thorn grotto
Yes
thorn grotto
If you have something like a^2 + b^2 = 0, then you can solve for a and b
Would there be any way of getting to there
mortal bison
is that a rhetoric question
thorn grotto
Try completing the square on x and y independently to get the sum of two squares
mortal bison
with 1 for example? to get something like (x+1)^2+(y+1)^2?
thorn grotto
You want to get rid of the x as well, so try 1/2
frosty vector
final saddleBOT
https://gyazo.com/e7a0f45bf9ee0dea7b91e0f7daff8cd7
frosty vector
need help understanding how to plot the x<1
x>1 thing
like why is it 1,2 and 1,-4?
this is piecewise
stuff
final saddleBOT
@frosty vector Has your question been resolved?
frosty vector
.close
rain star
can someone please tell me how to continue or if I used the wrong method while solving the problem?
final saddleBOT
can someone please tell me how to continue or if I used the wrong method while s...
@rain star Has your question been resolved?
final saddleBOT
@rain star Has your question been resolved?
red leaf
how do i make formulas for non geometric and arithmetic sequences
final saddleBOT
how do i make formulas for non geometric and arithmetic sequences
@red leaf Has your question been resolved?
vital crag
how do i make formulas for non geometric and arithmetic sequences
if you're working on a problem, just show its original form
red leaf
if you're working on a problem, just show its original form
3,12,27,48
red leaf
try factoring that out and find a pattern
their seccond difference is 6?
1,4,9,16
+3 +5 +7
their secoond difference is 2
so ur gone?
vital crag
so ur gone?
now you're gone?
red leaf
now you're gone?
im here
red leaf
this is a pattern
their second difference is the same
vital crag
uh huh
red leaf
the next term is 25
yea
red leaf
nth term is ?
like a formula?
vital crag
yes
like 2,4,6,8,10, ... the general term is 2n
or 1, 2, 4, 8, 16, .... the general term is 2^n
red leaf
or 1, 2, 4, 8, 16, .... the general term is 2^n
so the equation is 3n^2?
vital crag
yes
vital crag
why
red leaf
if i had a number like
2 6 12
vital crag
plug into your calculator
red leaf
do i find second difference
red leaf
so how did u do it?
vital crag
do what
red leaf
,calc 2^3
soft zealotBOT
Result:
8
,calc 2^2
soft zealotBOT
Result:
4
@red leaf Has your question been resolved?
deft crater
Can anyone help with this
final saddleBOT
Can anyone help with this
warm ether
do you have an idea of what the average rate of change would mean?
deft crater
yes its slope right
warm ether
yeah, how would you get an average
warm ether
it would basically be the slope of a straight line joining those points
warm ether
yup
warm ether
youre gonna have to estimate the y values by eye roughly
deft crater
ohh
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@deft crater Has your question been resolved?
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@deft crater Has your question been resolved?
deft crater
.close
pseudo kite
a
pseudo kite
i understand why 4x4 matrices are mathematically used to transform 3d points, but i dont understand why you wouldnt just directly add to the components one by one
rather than having to do unnecessary matrix multiplication
like if you want to move (0,0,0) to (5,5,10)
why not just add 5 to x 5 to y and 10 to z
vital crag
what is the context
pseudo kite
well im rendering 3d shapes onto a canvas
and im implementing a setPosition function
to move them around
but my question is more general
i just dont see the reason to use a matrix over basic addition
vs
x+a, y+b, z+c
no one knows?
pov every channel gets help but you even though linear algebra is a 100 level college class
eternal lichen
Try to think about transformations that are more complicated than translation
Can you stretch an object in one direction and squeeze it in another using basic addition?
pseudo kite
Can you stretch an object in one direction and squeeze it in another using basic...
oh true true :)
final saddleBOT
@pseudo kite Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
rotund warren
final saddleBOT
tight void
!show
final saddleBOT
Show your work, and if possible, explain where you are stuck.
rotund warren
i dont know where to start, i tried a method but i dont know if its correct
3 tan^2A – sec^2A + tan^2A = 0
= 4tan^2A-sec^2A = 0
= (4*sin^2A-1)/cos^2A = 0
fathom walrus
Just isolate tan A in left eqn and find A
rotund warren
Just isolate tan A in left eqn and find A
got that as 1/√3
fathom walrus
Yea
rotund warren
ah alr got it
final saddleBOT
final saddleBOT
Available help channel!
candid loom
Can someone help me with a math problem?
final saddleBOT
Can someone help me with a math problem?
sleek token
post it
candid loom
Can someone explain to me how to find the area of this parallelogram?
sleek token
do you know the area formula?
candid loom
Yes
B x H right?
Do I just multiply the numbers by each other?
Like 16 x 22 x 14?
candid loom
Yes
ember flicker
so u have to multiply 14 * 16
candid loom
224?
ember flicker
yes
candid loom
So that is the answer?
candid loom
Why did I not multiply 22?
ember flicker
take the parallelogram and put it horizontally, with the base of 22 inches on the floor.
ok?
candid loom
Ok
ember flicker
So, the 14 inches is not the H, because it's not perpendicular to the base of 22 inches
right?
ember flicker
The same thing happens when you put it vertically.
22 inches isn't the H, but it's 16/sin(angle)
so it's 224
because the H is 16
The H is always perpendicular to the Base
candid loom
Oh ok
ember flicker
If it's not perpendicular, it's not the H
candid loom
So with this would the 14 feet not be multiplied?
ember flicker
Look at the picture.
14 feet is the Base, right?
candid loom
Yes
ember flicker
Which measure segment isn't perpendicular to the Base?
10 feet or 8 feet?
candid loom
8
tranquil pine
perpendicular to the base means it forms a 90 degree angle with the base
does 8 do that?
ember flicker
Perpendicular means that forms an angle of 90° with the Base.
A 90° angle is like the angle of the letter "L"
10 feet forms an angle < 90°
with the base
ember flicker
yes, so u have to multiply 14 times 8 and u get the answer
ember flicker
I get it, thank you for the help!
You're welcome
final saddleBOT
@candid loom Has your question been resolved?
royal fractal
Anyone know how to do this?
royal fractal
Or this:
hallow topaz
the radius and height of the smaller cone and original cone are proportional
royal fractal
Oh yeah so for that its 5 but what about the other question?
royal fractal
Anyone know how to do this?
This
hallow topaz
u can write out the formula of the volume of a cylinder = 8, and surface area of cylinder = 24
multiply the volume by 3 and solve for radius
royal fractal
u can write out the formula of the volume of a cylinder = 8, and surface area of...
Thanks
I thought year 16 is university..?
year 13 is the final year of a levels isn't it
oh so you should be in year 12 which is final year of GCSE
no lol
no.
/close
final saddleBOT
Available help channel!
final saddleBOT
ancient zodiac
We think its d but we dont know how to do e
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Available help channel!
quasi plinth
final saddleBOT
final saddleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
grizzled tusk
it's just a system you have to work with, you won't find the solution just by looking, write some stuff
like 5^(b/a) = 2 so 5^b = 2*5^a
then square it and 25^b = 4*25^a
work with the equations until you find some things
the exponents are the variables of interest too, so you may need to use log
especially on the first equation
quasi plinth
is this even solvable?
grizzled tusk
you don't need to actually solve it
only to work with it until you can deduce 25^b/a²
grizzled tusk
I just squared it
quasi plinth
alright , understood
grizzled tusk
and that was just an example
Idk if the smartest is trying to get rid of some a or b to get to the answer
or smt else
just write things and deduce stuff
quasi plinth
when is log being used though?
grizzled tusk
since you need a² on denom
I was thinking of writing something like
(a+1)/b log(4) = 3log(5)
so (a+1) = b*3log(5)/log(4)
grizzled tusk
this is from olympiads right ? it's meant to take time
and it's indeed not nice
you're supposed to try stuff until the good way to work with the equations pops out
final saddleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
yes
in fact you can already solve the system
you got a/b = log(5)/log(2) and (a+1)/b = 3log(5)/2log(2) so 1/b = log(5)/2log(2)
so b = 2log(2)/log(5)
so a*log(5)/2log(2) = log(5)/log(2)
and a = 2
grizzled tusk
I'm too lazy to check I didn't make any mistake but I think it's right
,w 4^((a+1)/b) = 125, 5^(b/a) = 2
soft zealotBOT
Requested by not_melo
grizzled tusk
why you doin' this to me wolfram
then I'll check my sol by hand I guess uuuuuuuuh
64 = 125*4^b and 5^b = 50
and it's supposed to not be a contradiction
gosh
I did something wrong at some point
I hate calculations so much
grizzled tusk
ok so this is true
this is too
then a/b = log(5)/log(2) = log(25)/log(4)
and (a+1)/b = log(125)/log(4)
so 1/b = log(5)/log(4)
b = log(4)/log(5)
then a = log(25)/log(5) = 2
it's supposed to be the solution
quasi plinth
then a = log(25)/log(5) = 2
🤔
I solved for a but I think we maybe can still simplify further
grizzled tusk
log(4) = 2log(2)
you'll find a = 2
but what my brain is too lazy to check is if it's coherent with the first equation
like, what happens when I plug back a and b in it
I get 3/b = 3log(5)/log(4)
so b = log(4)/log(5)
it is coherent
that should be the answer
so 25^b/a² is 25^(log(4)/log(5))/4
quasi plinth
k, let me solve for b, but this is manageable
oh yes
I see what you said earlier goddess
can you check if what i did is legal? @grizzled tusk
wow this seems illegal
<@&286206848099549185>
grizzled tusk
too lazy to check everything but you found the same answers as me
final saddleBOT
@quasi plinth Has your question been resolved?