bc u have all the elements
#help-0
astral grove
lyric stream
you are meant to solve for how long it takes to double
astral grove
oh sorry
thats right
so it starts at 100
ends at 4500 in 12 hours
what rate it is increasing?
bc it has to get from 100 to 4500
lyric stream
I think you just put x/12 instead of 12/x
astral grove
it doesnt say what rate it is increasing
is it a flat rate
like 4400/12
or is it exponential
dusky igloo
as an example, the answer could be: It doubles every 0.79 hours
lyric stream
I think you just put x/12 instead of 12/x
@dusky igloo
dusky igloo
got it now, it took me a bit to understand why that worked
lone heartBOT
@dusky igloo Has your question been resolved?
astral grove
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torn isle
lone heartBOT
lyric stream
-2x--x should be -x I think
carmine reef
Probably common denominators are the way to go
serene junco
So that when you multiply (1/A)(Ax+1) you get a leading coefficient of 1 to match your current remainder
torn isle
So that when you multiply (1/A)(Ax+1) you get a leading coefficient of 1 to matc...
I don’t understand
Like this with a constant, then I don’t know how to do😅
rigid bough
anyone can help me for my math exam?
torn isle
-2x--x should be -x I think
Yea, this I will change
serene junco
Notice how your coefficients here don't match
They always should. This term should always cancel out when you do the subtraction step
torn isle
They always should. This term should always cancel out when you do the subtracti...
That means I do another part?
serene junco
No, it means you made the wrong choice when you put 1 up here
You should have done 1/A
serene junco
Did it work out this time?
lone heartBOT
@torn isle Has your question been resolved?
alpine sable
hi
lyric stream
hi
alpine sable
so working on this project & have a sequence that i made into a series
but having trouble finding for what values of certian variables it converges
i'll send an ss rn
having problem on part five (maybe i did part 4 wrong)?
rose sigil
this feels like it could be the wrong idea
alpine sable
ya i think im missing some information or something
but even if i had a value for C0 ("initial value"), could i still determine convergence if i have two unknowns?
lyric stream
you could find the values of k*L that it converges for
alpine sable
if i had C0 right?
lyric stream
yea
alpine sable
hmm
rose sigil
the questions and answers seem weird to me :c
alpine sable
also the series in the ss is off
i think it should be n=1 to inf
forgot to change that part
yeah i'm also pretty confused ;p
lone heartBOT
@alpine sable Has your question been resolved?
warm frigate
hi
lone heartBOT
warm frigate
.close
lone heartBOT
Available help channel!
lone heartBOT
prime badge
the position function doesn't let you do this alone
true sandal
you already have position function
the position function can give me the displacement
not total distance
true sandal
the position function doesn't let you do this alone
how would I do this properly with derivatives?
prime badge
when the derivative is zero, that's the point where the particle changes direction
prime badge
it really only change direction at x=6
true sandal
so now that I know this what do I do next?
prime badge
now you can just add up two displacements
0 to 6 and 6 to 10
i've never seen this problem, I don't know what the solution is supposed to actually look like
yeah
prime badge
i get 472
true sandal
hmm
true sandal
s(6) = -160
s(0) = 56
s(6) - s(0) = -160-56
prime badge
interesting that it gets it so wrong
i guess it's not supposed to be the same number
true sandal
what did you use for this
true sandal
hmm are we wrong or is wolfram wrong? but it's close though
prime badge
i assume we're both right
it's the actual length of curve, but length of curve is not what we're looking for
true sandal
I think we are looking for the area under the curve right?
prime badge
can someone confirm?
true sandal
wait a minute, should I use second derivative test to show that it changes direction?
hmm
I did but my point of inflection is x = 3
hmmm
covert pollen
how do i solve 2a and 2b
lone heartBOT
how do i solve 2a and 2b
vague mirage
how do i solve 2a and 2b
Bro why this messy calculate on another paper
covert pollen
my teacher makes us do it like that
sorry
i can clarify anything if not legible
i just don’t understand how to solve a and b
vague mirage
And don't mark that much point on linear equations
Just mark 2 points
Nd make a line with it
vague mirage
they need to
I meant it will save time
latent basin
no like thats what the teacher is asking for in the question no?
vague mirage
Yess but I was saying that It will still be accurate if we just take two points
Am I right
vague mirage
how do i solve 2a and 2b
And let me guess this is from ncert class 9 ?
covert pollen
And let me guess this is from ncert class 9 ?
what?
covert pollen
And don't mark that much point on linear equations
our teacher makes us do this way
covert pollen
You are from india?
no i’m from the us
karmic solstice
Are u allowed a calculator
covert pollen
yes
vague mirage
Your answers are right
covert pollen
yes but how do i solve b through ii
covert pollen
yeah don’t need to write down the working
i didn’t realize until after yea
she always gets mad at us if we don’t show work and so i did and then realized at the end
karmic solstice
ah
covert pollen
but i don’t get how to solve b-ii
karmic solstice
okay I understand
vague mirage
how do i solve 2a and 2b
Wait you already solved 2a and 2b
covert pollen
Wait you already solved 2a and 2b
i meant b-ii
karmic solstice
look at every 20 degrees C increment
how much is F increasing
and get that ratio
vague mirage
i meant b-ii
C-ii
covert pollen
sorry i’m trying to understand
karmic solstice
look at every 20 degrees C increment
every 10**
covert pollen
C-ii
no need to correct me on something as simple as that and criticize the work, it’s 2AM lol
vague mirage
no need to correct me on something as simple as that and criticize the work, it’...
Oh ok
covert pollen
yea
covert pollen
yes
covert pollen
yes
covert pollen
i’m sorry i don’t get it
covert pollen
yes
covert pollen
20
covert pollen
36
karmic solstice
yeah
so when C increases by 20
F increases by 36
so when C increases by 10
F increases by?
covert pollen
18
karmic solstice
yep
covert pollen
i don’t know how to apply it to the problem
covert pollen
oh i was looking at i
vague mirage
When c=0°
F = 32°{F=9/5c+32 , therefore y intercept is 32 so f is 32 when c is 0}.......(1)
Now,
C=10°
9/5×10+32
9×2+32
18+32...........(2)
Substracting (2) by (1)
(18+32)-32
18+32-32
18
Therefore F increase by 18 when celcius increases by 10
This is your work
karmic solstice
thank you but i am looking at i
what
karmic solstice
i meant b-ii
??
covert pollen
question i
vague mirage
By that equation
F=(9/5)c +32
karmic solstice
he’s a beast
vague mirage
he’s a beast
My god when does that happen
karmic solstice
i needed help w ii too
look at my explanation or arnab’s work
covert pollen
i’m saying that c-ii means problems c through ii
covert pollen
look at my explanation or arnab’s work
yes i did
karmic solstice
i’m saying that c-ii means problems c through ii
OH HAHAH
covert pollen
but i don’t understand what ‘bruh’ was in response to
karmic solstice
i’m saying that c-ii means problems c through ii
sry bro I thought this just meant c ii
covert pollen
it’s ok don’t worry
vague mirage
By that equation
F=(9/5)c +32
So we know that F =90 then substitute 90 in that equation and solve it you will get the value of c
90=(9/5)c+32
$90=\frac{9}{5}c+32$
ocean sealBOT
𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛
vague mirage
By solving this equation
You will get the Value of c and that's it
@covert pollen got it?
covert pollen
how do i find c
vague mirage
i don’t need to refer to the graph?
Nope you don't you can solve some graph question by algebra
covert pollen
do i divide both sides by 9:5
vague mirage
And I am pretty sure the answer will be in decimals
vague mirage
do i divide both sides by 9:5
Yes or multiplying both sides by 5/9
Both are same
You could do anything
covert pollen
tysm
vague mirage
What's your answer?
ocean sealBOT
vague mirage
,w 90=(9/5)c+32
ocean sealBOT
vague mirage
,w 290/9
ocean sealBOT
vague mirage
Your answer verify when you have done it
The approx answer according to the question is 32.2°c
You could write
C≈32.2°
lone heartBOT
@covert pollen Has your question been resolved?
wooden mantle
lone heartBOT
wooden mantle
is the nullity of this matrice 0?
also the ref is correct right?
Or am I missing something
vale wigeon
the REF is correct assuming a, b, c are not all zero as well as d ≠ 0
and no, the nullity (i.e. dimension of the kernel) of this matrix is not 0. it is either 2 or 3 depending on whether this matrix is in fact the zero matrix or not.
vale wigeon
matrix*
lone heartBOT
lone heartBOT
Available help channel!
celest sapphire
Hey Guys I have a doubt in parabola section of coordinate geometry
Suppose we have an equation y^2 - 2x=0
we are supposed to make a pair of tangent to this equation from point (-4,0)
I found the equation to be x^2-8y^2+8x+16=0
Now how can I use this equation of pair of straight line to find a circle which also have same pair of tangent as the given parbola?
lone heartBOT
Hey Guys I have a doubt in parabola section of coordinate geometry
Suppose we ha...
celest sapphire
.close
sick ice
Why can the i just be removed out of nothing my problems is where the red ? Is
alpine sable
Why can the i just be removed out of nothing my problems is where the red ? Is
i is never zero?
alpine sable
Why can the i just be removed out of nothing my problems is where the red ? Is
Yeah so I is not zero so you can move it to rhs
And 2 for that matter too
sick ice
Could you call for a second?
When you move something to the other side if its + it becomes - on the other side and for * it become /
alpine sable
When you move something to the other side if its + it becomes - on the other sid...
Its divided
Eg 2x = y
X = y/2
For 2x = 0 we divide 2 on both sides
2x/2 = 0/2
X= 0
sick ice
Thanks
lone heartBOT
@sick ice Has your question been resolved?
gilded elk
hi
gilded elk
i don’t understand wat is asked here
alpine sable
hi i dont understand why when i integrate in respect to y i should treat x as a constant
waxen plinth
hi i dont understand why when i integrate in respect to y i should treat x as a ...
(you might need to open another channel)
gilded elk
and then?
lament glen
$\frac{A + B}{C} = \frac{A}{C} + \frac{B}{C}$
ocean sealBOT
Doggo
lament glen
this is the next step
alpine sable
I am having trouble understanding limits and continuity.
A function $f$ is said to be continuous at a point $c$ if and only if
$$\lim_{x \to c} f(x) = f(c)$$
Based on this definition, the floor function should be continuous at any point, including the integers, which is obviously wrong.
I assume that my calculation of the limit caused the trouble. However, I don't understand what I did wrong. According to the discontinuity of the floor function, the following statement should be false:
$$\lim_{x \to c} \lfloor x \rfloor = \lfloor c \rfloor$$
(where $c \in \mathbb{Z}$).
However, if we replace (in the previous equation), $x$ with $c$, then yes, $\lfloor x \rfloor = \lfloor c \rfloor$. What did I get wrong about limits ?
Any help would be appreciated. Thanks in advance!
ocean sealBOT
trololol !
peak bough
The limit as x approaches any integer for the floor function doesn't exist since the left-hand-side and right-hand-side limits will be different
So the floor function does not fit the limit-definition of a continous function since the limits at several defined points don't exist
alpine sable
The limit as x approaches any integer for the floor function doesn't exist since...
Hmm, so a limit is said to exist only if it has the same value no matter where the "argument" comes from (as in, if we have a limit as x approaches 0, the limit is the same even if x comes, for example, from a positive number and approaches zero, and if it comes from a negative number and approaches zero).
Is that what you meant by left-hand-side and right-hand-side limit ?
peak bough
Yeah, that is:
$\lim_{x\rightarrow c^{+}} f(x) \neq \lim_{x\rightarrow c^{-}} f(x) \Longrightarrow \lim_{x\rightarrow c} f(x) = DNE$
ocean sealBOT
Mikkel
peak bough
A lot of times when we evaluate limits, we are working with functions already assumed to be continous in which we don't have to check the limits from both positive and negative
alpine sable
A lot of times when we evaluate limits, we are working with functions already as...
Alright. One more question, though:
In the case of the floor function, how are the left-side limit and the right-side limit different ?
Let's take an example, $c$ = 0. If $x$ comes from $-1$ towards $c$, then yes, $\lfloor x \rfloor = -1 \neq 0$, meanwhile, if $x$ comes from $1$ towards $c$, $\lfloor x \rfloor = 0 \neq -1$. These are different values. But, they are different if $x$ is any number other than $c$. It will, however, reach $c$ itself "one day", in which case, the left-side limit will also be $0$, and thus, be equal to the right-side limit.
What am I getting wrong?
By the way, thanks for answering me!
ocean sealBOT
trololol !
peak bough
We are not really interested in what the function's value actually is at the value we are approaching when evaluating limits. The left-hand-sided limit of your example will not approach 0 just because the functional value is 0.
If it helps you can kind of think of the limit as x -> c of f(x) as the function's value "right next to" f(c)
It's not as rigorous, but I find it helps with an intuitive understanding some times
alpine sable
If it helps you can kind of think of the limit as x -> c of f(x) as the function...
Ahhh, I see, so kind-of like the last element of a closed interval.
peak bough
If it helps you can kind of think of the limit as x -> c of f(x) as the function...
To add on to this: "right next to" can be interpretated as both on the left and on the right, which is why we are evaluating limits from both sides and say that the limit only exists if both interpretations give an equal value
peak bough
Ahhh, I see, so kind-of like the last element of a closed interval.
Open interval, but yeah
Kind of
alpine sable
Open interval, but yeah
Sorry, yeah, I meant open interval.
peak bough
It's a good analogy, so I think you get the idea
alpine sable
But, if we have a function $f(x) = x + 1$ (which is obviously continuous), and a point $c$, then the left-side limit (which is analogous to $(-\infty, c)$, and the right-side limit (which is analogous to $(c, \infty)$ shouldn't, somehow, be different ?
Or the limit kind-of analyzes where the function tends to go based on the values that $x$ already went through.
As in, in the case of the $f(x)$ function I defined earlier in this message, we all know that if we went just a number further, the two limits would be equal (to $f(c)$), because we already saw the "pattern".
Meanwhile, in the case of the floor function, if $x$ goes from $[-1, 0)$, all we see is that it is constant at $-1$, so the left-side limit would assume that it actually approaches $-1$.
ocean sealBOT
trololol !
peak bough
There you have to take into account the properties of the Real numbers that there aren't any "gaps". You might be familiar with the famous equation 0.999... = 1
It's kind of similar to this here
When we approach something like x = 0 for x + 1 you could kind of imagine the function's value right next to f(1) to be 2.00000... and then a 1 and the end (not at all rigorous but it might help give an understanding) or 1.99999... depending on the side you take the limit from. But if the Real number's can't have gaps, 1.99999... = 2 = "2.00000...1" and the limit is then evaluated to be 2.
I want to make it extra clear that 2.00000...1 is not at all proper notation and shouldn't be used in a serious context
But it kind of gives an understanding of the number "right next to 2 on the right side"
alpine sable
oooooooooooooooooooooooooooooh
I see now...
and the floor function wasn't continuous because there is an obvious gap between $-1$ and $0$, unlike $-0.000000...1$ and $0$
ocean sealBOT
trololol !
alpine sable
Thank you so much!
peak bough
Yeah, here we can talk about a gap, which mean they are different numbers
hidden sparrow
can anyone help me
lone heartBOT
can anyone help me
lone heartBOT
@hidden sparrow Has your question been resolved?
lone heartBOT
@hidden sparrow Has your question been resolved?
wicked tree
lone heartBOT
alpine sable
Is that the 11th square root
wicked tree
yup
I did the test and got this
so then if you take lim n -> infinity of that, you get 1/2
peak bough
Is that the 11th square root
11th square root
wicked tree
but i'm not sure where to go from there
i'm assuming since the limit is 1/2 which is less than 1, it converges for all values of x
but apparently that's incorrect
alpine sable
>11th square root
<:thinkies:827642567775748163> <:thinkies:827642567775748163>
Wdym smh
proper tangle
you may search for "ratio test" and try to apply the techniques
wicked tree
that's what I did
if you take the limit of that, it's 1/2 * x
<@&286206848099549185>
lone heartBOT
@wicked tree Has your question been resolved?
wicked tree
.close
past socket
How do I find cos(theta) = -5/12 with the first quadrant of the Unit Circle
tacit arch
but for the test we'll only be given the first quadrant
use trig identities to find the rest
past socket
use trig identities to find the rest
so sin^2theta + cos^2theta=1?
tacit arch
no. these
torn forge
use the fact cos theta is an odd function
lone heartBOT
@past socket Has your question been resolved?
tacit arch
i dont get it
try plugging in angles from 90 <= theta < 360
past socket
i still don't get it
lone heartBOT
lone heartBOT
Available help channel!
gaunt sky
Anyone can explain how to get to to this result?
lone heartBOT
Anyone can explain how to get to to this result?
keen hornet
I am not sure but I believe that the two A's cancel one another and then the s is just placed in front instead at the end
gaunt sky
I am not sure but I believe that the two A's cancel one another and then the s i...
Forgot to say these are matrixes, A x B isn't the same as B x A
keen hornet
ohh, yeah can't help you then.
mortal trellis
well WA probably doesn't know they are matrices
given that they divided by A
which is a big nono for matrices
gaunt sky
But here, they say `(As)^T * A^-1 * (As) = s^T * A * s`.
is that correct?
mortal trellis
if A is symmetric
did you send the correct image?
$(As)^T A^{-1} (As) = s^T A^T (A^{-1} A) s = s^T A^T s$
ocean sealBOT
Denascite
gaunt sky
@mortal trellis is (A * s)^T = s^T * A^T a rule that's always true?
mortal trellis
in general $(AB)^T = B^T A^T$, yes
ocean sealBOT
Denascite
mortal trellis
for all matrices A, B
idle stone
Research has shown that 62% percent of teenagers pass the G2 driver’s test on their first try. Ten teenagers who take the test are randomly surveyed.
What is the probability that at least two (2) teenagers passed the G2 test on their first try? Give your answer as a percent rounded to two decimal places.
idle stone
can someone please provide me assistance on this question
@mortal trellis
<@&286206848099549185>
lone heartBOT
@idle stone Has your question been resolved?
lone heartBOT
@idle stone Has your question been resolved?
idle stone
.close
crude jungle
say i have (x/3)^n
lone heartBOT
say i have (x/3)^n
abstract fractal
Yes
alpine sable
lone heartBOT
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
zealous wagon
What is this notation? I've never seen it before, I don't know what it means, and I can't find reference to it in any material I have.
brave solar
real part and imaginary part i suppose
zealous wagon
real part and imaginary part i suppose
Maybe. Such a weird script.
brave solar
i think they are $\mathfrak{R}$ and $\mathfrak{I}$
ocean sealBOT
PROnoob
brave solar
yes
alpine sable
Help me
alpine sable
Can @brave solar u help me with parallelograms
brave solar
you need to post the question in a separate available help channel
zealous wagon
Can <@656147982177271818> u help me with parallelograms
Look under "MATH HELP (AVAILABLE)" and post in one of those forums, not under "MATH HELP (OCCUPIED)".
digital walrus
How do I prove, that a space is complete?
lone heartBOT
How do I prove, that a space is complete?
@digital walrus Has your question been resolved?
lone heartBOT
@digital walrus Has your question been resolved?
lone heartBOT
@digital walrus Has your question been resolved?
digital walrus
Going to sleep. Do not close it pls
lone heartBOT
@digital walrus Has your question been resolved?
green obsidian
hello can someone show me the basics in one to one function involving rational functions and inverse
dim sail
do you have a particular example? That always helps
alpine sable
Started learning about the integral test for infinite series, and on the first problem of the integral test handout, f is cont and positive, but not decreasing, which is a requirement for the integral test, what would I do from here?
alpine sable
continuous and positive for x >= N, but not decreasing for x >= N*
f is (2n)/(2n+7) also
knotty spire
An infinite series converges only if $\lim_{n\to\infty} |a_n| = 0$, where $a_n$ is the n-th member of the series.
ocean sealBOT
Remavas
knotty spire
(This is a necessary, but not sufficient condition for convergence)
alpine sable
So would I take the limit of f, and find if it equals 0? (Sorry for my lack of understanding, I was sick for the introduction for this and have been trying to use the online resources he posted but I'm using any source I can now ;-;)
knotty spire
So would I take the limit of f, and find if it equals 0? (Sorry for my lack of u...
Yes, take the limit as n approaches infinity.
If you get something non-zero, then you know it's impossible for this series to converge.
And no other tests are needed.
In English literature, this test is called the divergence test if I recall correctly.
alpine sable
So after taking the limit as n approaches infinity, i got inf over inf so I applied L'hopitals, which gave me 2/2, which equals 1, so it doesn't converge?
ocean sealBOT
alpine sable
When I learn about more theorems like the comparison test, is taking the limit and seeing if it equals 0 or not the first thing i do no matter what or is there more to it than that?
knotty spire
It's an easy enough test in most cases, and it can tell you immediately when a series does not converge. So if you suspect that the limit is non-zero, yes.
If you get 0, then you must do some other test.
alpine sable
Oooo okay, is the limit being 0 super common or no?
knotty spire
I mean, in problem sets it is heh
Or else people wouldn't use the more advanced tests now would they.
alpine sable
Yeahhh so for learning about it, my professor would have a lot of the limits for each problem be 0 just so we can apply all the tests I think
knotty spire
Just as an example $\sum_{n=1}^\infty \frac{1}{n}$ does not converge, but $\lim_{n\to\infty} \frac{1}{n} = 0$.
ocean sealBOT
Remavas
alpine sable
ooooo okay, if this is only the beginning of inf series im probably gonna be here a lot T_T
knotty spire
When I learn about more theorems like the comparison test, is taking the limit a...
I'd say most people do it in their heads if it's an easy enough case.
But it won't hurt you if you check.
alpine sable
Oooo alr, but it's quick so I'll barely waste time doing it
knotty spire
Here's also a resource I highly recommend: https://tutorial.math.lamar.edu/classes/calcii/convergenceofseries.aspx
alpine sable
ahhh thank you so much, ill close this channel and try to learn a bit more on my own before asking a bunch of questions
thank you once again
.close
vestal hawk
help
vestal hawk
not sure how to find homogenous solution
dim sail
you can use a characteristic equation to get the homogenous solution
vestal hawk
you can use a characteristic equation to get the homogenous solution
how
c1x^2+c2x^2lnx?
@dim sail
<@&286206848099549185>
tacit arch
Google the definition of homogeneous equation
vestal hawk
what is lnx * lnx
tacit arch
Nothing special
vestal hawk
what do u mean
vestal hawk
what is (x^2)(ln^3(x)) + (x^2)(ln^3(x))
lone heartBOT
@vestal hawk Has your question been resolved?
amber pawn
lone heartBOT
amber pawn
sorry its a bit blurry but i only got one picture 
i have to find the derivative but there are just a lot of different rules to memorize and i'm not sure where to start or what to use 
placid zinc
No need to Sad Omori. It's pretty easy to read
amber pawn
is it the product rule??
placid zinc
Ye. You can read this as a product of two things, so product rule makes sense to use here
boreal verge
id use the product rule then exponential for the 2nd bit
placid zinc
After employing the product rule, use your memorized derivatives for t² and 2^t, yeah
boreal verge
a to the u
because a is any number
e is natural exponential and doesnt apply here
boreal verge
t²?
oh the derivative of t²
well use the product rule
too lazy to write it so here u go
for here replace f(x) and g(x) with t² and 2^t
boreal verge
send a pic
lament glen
write $2^t$ as $e^{t\ln(2)}$
ocean sealBOT
Doggo
amber pawn
instead of what i have now or next?? i'm confused where is that coming from
lament glen
for the second part of the product rule, you need to differentiate 2^t
so you can write $2^t$ as a power of e then chain rule and some simplifying to get $2^t \ln(2)$
ocean sealBOT
Doggo
lament glen
I believe things get circular depending on how you define log and e though
lament glen
how do i know which one to use <:kel_welp:815116561240293407>
oh you already have the rule here
you just apply the second rule for 2^t
amber pawn
OH yes i know to do that rule for that part, i meant the 2t in the front,, do i just leave it be or does it disappear or something??
amber pawn
okay okay i think i found what i'm missing out on,,
where did that part after t^2 come from??
thats the only thing i don't have right
lament glen
we first differentiate t^2 and keep 2^t as is
then we keep t^2 as is and differentiate 2^t
and finally add the two up
the part after t^2 is the derivative of 2^t
amber pawn
so to the left of the plus sign is t^2 and the right is 2t?
did i mess up in the product rule part??
no bc the derivative of 2t would be 2 right
so, you start with the product rule, and then you get this right?
and then you use the rules n stuff
lament glen
amber pawn
what rule did you use to get the g' at the end?? i don't know if i'm just not seeing it or i haven't gotten that one yet
lament glen
how do i know which one to use <:kel_welp:815116561240293407>
g' is the second rule here
a = 2, u = t
so u' = 1
maybe the order is confusing you, since you wrote ln first there and I wrote ln after
amber pawn
so i could also write it as ln2(2^t)
ohhhh okay i see it now i'm sure
and then i just add them together
lament glen
so i could also write it as ln2(2^t)
yeah it's multiplication so you can switch things around
amber pawn
how do i add them together 
how do i get to that ending that you got 
and also does it just end there?? is there nothing else after that
amber pawn
ohhh okay okay
thank you!! to all three of the people that help i understand a lot more 
.close
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still coral
in (-inf,9] is 9 a valid test value
lone heartBOT
in (-inf,9] is 9 a valid test value
still coral
for rational inequalities
echo socket
9 is included in (-inf, 9], yes
alpine sable
What is Degree of "xy=0"
still coral
instead of 8.5 or 10
this is the full image
if i were to use 9 in the (8,9] then it would equate to 0, so that interval would be correct instead of wrong.
echo socket
Yeah you can pick x = 9 and the original inequality will work
still coral
then why does the interval (8,9] not work if we can use 9
still coral
the + there is to represent the value of the function if u substitute the test value
so let’s take the 8.5 if u substitute it to -x+9/ x-8 you get .5/.5 which is 1
so it’s positive
but the inequality has to be less than or equal to 0 so its wrong and everything in that interval is entirely wrong except for 9 which equates to 0
so is teacher’s teaching wrong
or is his given wrong
srry im asking so much im just dumbfounded
final viper
we know that if a determinant has two rows/col same the value will be 0 , but is the converse always true?
final viper
or in other words, if a det = 0 can it always be simplified in a way where it will have 2 rows/col same
speaking of 3x3 det
rose sigil
https://mathworld.wolfram.com/InvertibleMatrixTheorem.html check this out 🙂
final viper
oh okay 👍
rose sigil
but to answer, yes, those are equivalent
cinder rain
How do you work out the height of a triangle without the area?
cinder rain
Question 11
alpine sable
,rotate
ocean sealBOT
lyric stream
area = base * height / 2
area = (1.1*base) * (0.9 * height) / 2
cinder rain
Oh
lyric stream
its asking for the percentage increase in area
cinder rain
So increase by 1 percent?
lyric stream
whats 1.1 * 0.9
opaque plaza
Hello I'm new here..Can anyone tell me how to solve this?
cinder rain
0.99
cinder rain
so is that an increase or decrease
Decrease by 0.01 percent
cinder rain
Wait no
cinder rain
decreased by 10 percent
ocean sealBOT
lyric stream
how much did it decrease by
cinder rain
99 so decrease by 1 percent
lyric stream
yes
orchid mulch
Can someone help me to solve this question?
lone heartBOT
Can someone help me to solve this question?
orchid mulch
Yes
shut pewter
Can someone help me to solve this question?
Try to square both sides
alpine sable
thats gonna be
shut pewter
And maybe let x^3 and 3x be their own variable?
alpine sable
a bit rough
ornate condor
lol
wanton nova
Lmao
alpine sable
yeah good luck finding the zeros to that monstrosity ig
ornate condor
use appx algs
lone heartBOT
@orchid mulch Has your question been resolved?
ocean sealBOT
shut pewter
Can anyone check it?
lone heartBOT
Available help channel!
alpine sable
I need to describe the roots, but the brackets are confusing me:
f(x)= 2(x-1)^2+5
echo socket
In this case you'd need to solve 2(x - 1)^2 + 5 = 0
But that means that 2(x - 1)^2 = -5 which is impossible for all real numbers x
Since (x - 1)^2 can't be negative
alpine sable
So what would I do for that
echo socket
Just write that there are no solutions
scarlet echo
zes
scarlet echo
question
I am watching this video
and the teacher gave y=-3x as a direct proportion
but doesnt "direct proportion" mean both variables will kind of like.. go the same way? as in if x decreases so will y. but in this equation thats not the case. if y is -6 then x is 2. if y is -3 then x is 1. so if y decreases then x increases. that seems more like a inverse proportion to me
is that not what it is
<@&286206848099549185>
<@&286206848099549185>
civic willow
Well, that's not really the best way to think about them. Think about direct proportionality being y=kx and inverse being y=x/x
civic willow
Yeah, it's just not quite right to say going the same way.
More to say that they both have the same factor applied to them
I know what you mean though it's confusing
scarlet echo
like in math problems they will ask us questions about direct proportions like, for example the more days go by the more work you get done so these things are directly proportional. but for inverse proportions the question will be more like the more workers there are the less time it takes to get the work done
so its hard to not think of it that way because these are how the questions are presented
so if direct proportions have the same factor applied to them, what do inverse proportions have
civic willow
That's true, let me think if I can find a way of presenting it.
Inverse proportions have the opposite factor applied.
That's the best way I think to explain it
Like for y=2x and y =2/x
Being an example of direct and inverse
If we multiply the direct by 3, the x is multiplied by 3
But for the inverse if we multiply the y by 3, the x is divided by the same factor
So it doesn't have anything to do with increasing or decreasing its just to do with same factor or inverse factor
But I 100% agree that since all worded problems work with positive values, it gives the illusion that direct always means both values increase and inverse means y increases x decreases
scarlet echo
so its only because problems ask about real life most of the time and in real life negative numbers dont exist you cant have -3 workers etc thats why direct proportion always works that way
scarlet echo
can we think of direct proportion as their ratio is always constant even tho variables, well, vary
civic willow
Yes, the k value being their ratio
scarlet echo
why is this important in maths besides real life problems then? why do mathematicians need this
civic willow
Hm well I'm sure there's a few examples. Maybe in debt which is one example of negative numbers applied to real mathematics.
Something like a company that is losing money, every one computer they lose 3x that in money. It's direct proportionality even though the money is going down as the computer amount goes up.
scarlet echo
so the main difference between inverse and direct isnt the fact x increases so does y yada yada but its the fact that in direct the ratio is constant whereas in inverse the multiplication of the variables is and not the ratio
im sorry for the way i worded this i hope you understood regardless
because for direct proportions we divide the both variables as a way to compare two things
and it always equals to k
civic willow
I think I do.
scarlet echo
but in diverse we multiply these two things
like 2 workers, each worker lays 30 bricks a day, 60 bricks in total which is the sum of the work
and it applies since more workers you have the less time it takes to finish the work yada yada
does that make sense
civic willow
Well here's how I would say it
Just much more simply
Direct: change factor in y = change factor in x
Inverse change factor in y = divided by the change factor of x
Although honestly that is a bit hard to comprehend too
scarlet echo
yes
civic willow
I think you get the idea overall it is hard to understand but I think you understand.
scarlet echo
i think also cuz i dont learn maths in english 💀
civic willow
Mhm
scarlet echo
whats a change factor
civic willow
Like
Y=2x
2y=4x
Change factor I'm defining as the number multiplied to both sides being 2
civic willow
Okay I'm really sorry if I explained this bad but you seem pretty confident with it now in your examples so you all good?
scarlet echo
so very very basically if something is directly proportional by 2 that means i divide it
this is my last question
so like the thing being x
civic willow
Let me just comprehend that lol
scarlet echo
x/2 = k
x = 2k
x is directly proportional with 2
the change factor ur talking about
civic willow
Yeah it means as y is multiplied by the change factor, x is divided by the change factor yes.
civic willow
Np 😊
lone heartBOT
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Available help channel!
acoustic mirage
how did they go to the next step ?
lone heartBOT
how did they go to the next step ?
acoustic mirage
(not the log part)
alpine sable
the one where they included the x in the square root?
acoustic mirage
yesss
alpine sable
basically they made it (x^8)^1/2 which is equivalent to x^4
you can conjoin the square roots then, and then they split up the the x^8 to x^6 and x^2
x^6/2 is just x^3 so it goes out of the square root
idk the point tho
to make it look nicer?
alpine sable
ahhh makes sense
acoustic mirage
.close
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Available help channel!
proud kestrel
lone heartBOT
proud kestrel
Quick sanity check, is this correct?
vale wigeon
yeah should be
bright jay
The distance between Exeter and London is 175 miles. At 10:00 on Tuesday Sam left Exeter for London and Morgan left London for Exeter They travelled on the same road. Up to the time when they met, Sam's average speed was 25 miles per hour, and Morgan's average speed was 35 miles an hour.how far away from exeter when sam and Morgan met?
bright jay
pls i need the answer urgent
the question is
The distance between Exeter and London is 175 miles. At 10:00 on Tuesday Sam left Exeter for London and Morgan left London for Exeter They travelled on the same road. Up to the time when they met, Sam's average speed was 25 miles per hour, and Morgan's average speed was 35 miles an hour.how far away from exeter when sam and Morgan met?
so this
pls
urgent
<@&286206848099549185> 15 mins overs
plss
help
lone heartBOT
@bright jay Has your question been resolved?
bright jay
<@&286206848099549185>
vale wigeon
pls i need the answer urgent
we don't give answers here
bright jay
we don't give answers here
.
vale wigeon
well you're asked to say where the two friends meet (i.e. how far away from Exeter)
maybe you could try instead finding when they meet? i.e. the time it takes them to meet
you know both of their speeds, after all.
lone heartBOT
@bright jay Has your question been resolved?
alpine sable
hi
alpine sable
I think I already know this
but I just need someone to clear it up
so when it comes to x^n
if I for example want to subtract x^2-x^2 I am allowed to do so am I not?
but what about x with different values for n? For example x^4-x^3?
<@&286206848099549185>
keen mason
but what about x with different values for n? For example x^4-x^3?
??
how old are you
alpine sable
how old are you
wym
tf does that gotta do with anything
I said I'm confused
what's x^4 = x * x * x * x
but you surely cannot subtract x * x * x * x - x * x * x right?
keen mason
???
alpine sable
???
either answer the question or just let someone do it man
no need to fucking insult me
alpine sable
just answer the question...
alpine sable
its agaisnt the rules too answer questions
bro how is this an exam question
fine make it x^50 - x ^49
I don't give a shit
this is clearly a conceptual question
and not some homework...
keen mason
ok now give x a value
alpine sable
2
ocean sealBOT
Result:
1.1258999068426e+15
Result:
5.6294995342131e+14
.calc 1.1258999068426e+15 - 5.6294995342131e+14
,calc 1.1258999068426e+15 - 5.6294995342131e+14
ocean sealBOT
Result:
5.6294995342129e+14
???
alpine sable
alright, so no
keen mason
does that seem like 2^1?
alpine sable
you could've just fucking told me that
keen mason
if u ask me its a bit big
alpine sable
if u ask me its a bit big
why the fuck are you such a self centered egoist
nobody gives a shit if you know some basic math
yeah you're better than me, well done
the fuck you want, a medal?
keen mason
ahh you see
alpine sable
holy shit people like you
make learning so much more annoying
the whole point of this damn server is helping people
keen mason
Yea 'help' not 'spoon feed'
alpine sable
not fucking provoking them
alpine sable
Yea 'help' not 'spoon feed'
spoon feed my ass
I'm asking for some goddamn rules and that's it
you aren't spoon feeding shit
I didn't ask with numbers, I asked with variables
it's clearly conceptual
keen mason
???
but u can literally plug in numbers to check any algebraic expression
u just were too lazy too
i guess
alpine sable
yea aight bro...
or maybe I just wanted some fucking reassuring
either way, you're one fucking asshole
long axle
Woah woah guys chill out
keen mason
Nice u use humans as re-assurance (Even tho we all lie like 90% of the time) but u dont trust numbers
10/10 bro
alpine sable
Woah woah guys chill out
this dude just started insulting me for no damn reason
long axle
Mortta the method of plugging in numbers isn’t always accurate
long axle
However, I see what u were trying to communicate
alpine sable
0^50 = 0
keen mason
Yea
alpine sable
0 ^ 49 = 0
keen mason
YEa
alpine sable
this shit doesn't help me
overall I appreciate your answer
but you didn't have to say it like that
keen mason
u need to learn to trust yourself
alpine sable
just fucking answer the question normally without using each and every chance you get to provoke the other side
because that's really besides the point
alpine sable
u need to learn to trust yourself
well guess what, I don't
which is why I'm here
too fucking bad
keen mason
??? than u should work on that first
keen mason
I can tell what type of person u are already
alpine sable
I can tell what type of person u are already
oh yeah?
how about a straight A+ student who fucked up the first couple of exams of the year
so now I don't trust myself with shit
how's that?
that's the fucking reason I'm here
keen mason
Oh yea u got that side
but u also got the side of properly easily angered
low temper
alpine sable
just wanted to make sure I had the fucking fundamentals inside
alpine sable
but u also got the side of properly easily angered
easily angered?
bro it's a discord server
and you're a fucking asshole
there's no me getting angered here
alpine sable
there's you being a sadistic person feeding off of others getting pissed lmao
which I have no respect for
but you do you
.close
lone heartBOT
keen mason
mhm
lone heartBOT
Available help channel!
rocky summit
If I want to prove that a set of matrices spans M2x2
lone heartBOT
If I want to prove that a set of matrices spans M2x2
rocky summit
Would I enter the matrices as 4-entry columns in a matrix and reduce to REF?
Assuming there's 4 pivots, I'd know that the columns span R4 (and by extension, M2x2)?
mortal trellis
yes that would be the process
lone heartBOT
@rocky summit Has your question been resolved?