which one should i plug into?
#help-23
delicate sphinx
Start with one of the functions, plot it then do the other one
delicate sphinx
And y equals?
kindred violet
sine of pi?
delicate sphinx
You stated this
kindred violet
thats not right
yes
ohhhh omg
OH
wait wait
since y = sin pi
and sin = y/r
its
pi?
delicate sphinx
Not quite
Sin = y/r, in the unit circle r = 1, because the radius of the unit circle is one, so basically sin = y, what is the y coordinate at sin pi, using the unit circle?
delicate sphinx
Where is pi on that?
kindred violet
ahhhhhhhhhhhh okay
i was getting confused because
actually i don’t know why i was confused
just too many numbers
anyways
and then for cos
its
y= cos pi
cos of pi is -1
delicate sphinx
Yes
kindred violet
there we go
delicate sphinx
You're probably just checking if you understand that process with cos, but I suggest plotting one at a time, Plot y = sin x first then y = cos x
kindred violet
You're probably just checking if you understand that process with cos, but I sug...
yes
i will for sure keep that in mind
thank you
.close
dusky harbor
Hello. This question got me stuck.
"Find the limit value". \ $L = \lim_{x \rightarrow 0} \frac{1}{x}-\frac{1}{xe^{2x}}$
flat frigateBOT
HqppyFeet
dusky harbor
I made an attempt to use L'Hoptials, but x was still in the denominator
How should I approach this?
thin bridge
combine into a single fraction, separate the factor of 1/(e^(2x))
as that →1 as x→0
and apply definition of the deriviative for the remaining component
dusky harbor
combine into a single fraction, separate the factor of 1/(e^(2x))
hmm, I ended up with \ $$L = \lim_{x \rightarrow 0} \frac{e^{2x]-1}{xe^{2x}}$$
what
flat frigateBOT
HqppyFeet
hmm, I ended up with \\ $$L = \lim_{x \rightarrow 0} \frac{e^{2x]-1}{xe^{2x}}$$
```Compilation error:```! File ended while scanning use of \frac .
<inserted text>
\par
<*> 458335985567137792.tex
I suspect you have forgotten a `}', causing me
to read past where you wanted me to stop.
I'll try to recover; but if the error is serious,
you'd better type `E' or `X' now and fix your file.```
dusky harbor
I hope you are able to read Tex math : P
thin bridge
i am able to yes
dusky harbor
(e^{2x}-1) / (xe^{2x})
flat frigateBOT
ℝαμΩℕωⅤ
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
dusky harbor
bad day for tex lol
thin bridge
first limit can be evaluated from direct sub
and apply definition of the derivative for the remaining component
dusky harbor
Approach using product rule I assume?
thin bridge
don't resort to lhop
dusky harbor
don't resort to lhop
xd I should stop doing that
thin bridge
if you want to incorporate derivatives here
and apply definition of the derivative for the remaining component
$$f'(a) = \lim_{x\to a} \frac{f(x) - f(a)}{x-a}$$
here your: \
$$f(x) = e^{2x}, a = 0$$
flat frigateBOT
ℝαμΩℕωⅤ
dusky harbor
**ℝαμΩℕωⅤ**
The correct answer is 2, but I got 0 in this approach: $\frac{(e^{2x}) - (1)}{e^{2x}-0}$
flat frigateBOT
HqppyFeet
dusky harbor
if f(x) = e^2x and a=0 here.
dusky harbor
I feel like I am missing a concept.
$\frac{(e^{2x}) - (e^{2(0)})}{e^{2(0)}-0}$
woop
flat frigateBOT
HqppyFeet
dusky harbor
**ℝαμΩℕωⅤ**
your idea here- 🫠 if f(x) = e^2x, when f(0) = e^2(0)
thin bridge
yes
recognising your limit is in that form,
that limit is the derivative of e^(2x) evaluated at x=0
i.e. with
f(x) = e^(2x)
that limit is the value of
f'(0)
so start with differentiating e^(2x) to get f'(x)
dusky harbor
f'(x) would then be 2e^2x...
thin bridge
and then f'(0)?
dusky harbor
2 😮
thin bridge
yes
safe radishBOT
@dusky harbor Has your question been resolved?
dusky harbor
Found the solution <3<33<
devout vault
I’ve got viets formula. How do I form quadratic equation now?
safe radishBOT
I’ve got viets formula. How do I form quadratic equation now?
fickle pendant
are these simultaneous equations?
devout vault
Just look x like x1 and y like x2
fickle pendant
if so, make the first one into x = stuff with y
and then substitute y in the second equation
devout vault
split fulcrum
!nogpt
safe radishBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
lean otter
The number of automobiles that arrive at a certain intersection per minute has a Poisson distribution with a mean of 5. Interest centers around the time that elapses before 10 automobiles appear at the intersection.
What is the probability that more than 10 automobiles appear at the intersection during any given minute of time?
safe radishBOT
The number of automobiles that arrive at a certain intersection per minute has a...
lean otter
The number of automobiles that arrive at a certain intersection per minute has a...
not sure what to do with the given information
.close
coarse kelp
can someone explain to me how they jumped from that to the last line?
safe radishBOT
can someone explain to me how they jumped from that to the last line?
@coarse kelp Has your question been resolved?
lean otter
Function: f(x) = 0.5x^2 + 2x + 6
Domain [-2, 7] We can use x from -2 to 7 in this function
8 is the maximum point of the parabola
What is the domain for f(x)?
I solved f(7) which is -4.5
I solved f(-2) which is 0
Why isn't the domain for f(x) = [-4.5 , 0] ?
According to the book the answer is [-4.5 , 8]
safe radishBOT
Function: f(x) = 0.5x^2 + 2x + 6
Domain [-2, 7] We can use x from -2 to 7 in thi...
plucky elk
Function: f(x) = 0.5x^2 + 2x + 6
Domain [-2, 7] We can use x from -2 to 7 in thi...
You're given the domain of f
Why do you think it's something different from what you're told
safe radishBOT
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tacit moth
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plucky elk
<@&286206848099549185>
!15m
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
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solar needle
whycan you say U^T ui = ei
safe radishBOT
whycan you say U^T ui = ei
peak estuary
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warm patio
In the opposite figure, a circular disc weighing 4 Newtons resting on a vertical wall and a horizontal ground with the same coefficient of friction was applied to it by a horizontal force tangential to the disc of 15 Newtons until the disc was about to rotate in the direction of the force, so the coefficient of friction = ? (Note that the vertical reaction to the ground is twice the vertical reaction to the wall)
safe radishBOT
In the opposite figure, a circular disc weighing 4 Newtons resting on a vertical...
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warm patio
<@&286206848099549185>
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warm patio
<@&286206848099549185> any help please?
snow bear
Bro I can t solve this sorry
safe radishBOT
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granite cape
Could someone help me out with this?
safe radishBOT
Could someone help me out with this?
safe radishBOT
@granite cape Has your question been resolved?
flat frigateBOT
Mycobacterium
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Available help channel!
pine geyser
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pine geyser
I really have no idea what's being asked of me here
The only idea I have to to just write it out?
Like for X
0-by
Sine to get X you'd flip the equation
X = 0 - by
pine geyser
Yeah but there's no system to solve
pine geyser
Then what's X,Y
drowsy karma
let em write it to you in latex, moemnt
pine geyser
It's just a bunch of arbitrary gibber jabber so I can't exactly calculate it. This system feels like a thought experiment rather than a math problem
drowsy karma
$\left{ \begin{array}{l}
ax + by = 0\
x + y = 6
\end{array} \right. \Leftrightarrow \left{ \begin{array}{l}
x = \frac{{ - 6b}}{{a - b}}\
y = \frac{{6a}}{{a - b}}
\end{array} \right. \Leftrightarrow \left( {x,y} \right) = \left( {\frac{{ - 6b}}{{a - b}},\frac{{6a}}{{a - b}}} \right)$
flat frigateBOT
Joanna Angel
pine geyser
I...what am I looking at?
pine geyser
I can't comprehend how I was ever expected to get this correct
drowsy karma
wel, you need to learn how to sue their interface
safe radishBOT
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safe radishBOT
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Available help channel!
gloomy cliff
IM currently studying about PMI ( Pointwise Mutual Information) and I don't really understand a part of this topic.
So the question was:
Theres 10.000 documents. 200 of them contained the word statistics, 10 of them the word translation. 40 of them contained both words.
What is the association of Statistics,translation?
The association would be:
https://imgur.com/a/Gicdxbk
Now to my quesiton however: Why does the size of the documents increase the association between the 2 words?
For example: Lets say the association in the 10.000 documents is pmi(statistics,translation)=5
If I copy the 10.000 documents and add them together, id get a higher association even though P(st) P(s) P(t) stays the same.
How does this logically follow?
safe radishBOT
IM currently studying about PMI ( Pointwise Mutual Information) and I don't real...
@gloomy cliff Has your question been resolved?
gloomy cliff
<@&286206848099549185> been a while and rlly require help on this one^^
safe radishBOT
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tacit cosmos
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tacit cosmos
So for (c) only
I can parametrize the line to <2t, 0> 0<=t<=1
Or
<t, 0> 0<= t <= 2
And for both situations I get different answers
Can anyone explain why and what method might be wrong here?
wind stream
can you show your work for both approach that you used?
tacit cosmos
There's not really work I can show here
wind stream
both parameterisation are correct and should give the same answer
tacit cosmos
uhh
int (0 to 1 ) 6t dt
int (0 to 2) 3t dt
Aren't they different?
3t^2 (1, 0) -> 3- 0 = 3
3/2 t^2 (2, 0) = 6- 0 = 6
wind stream
hmm strange, they technically should give the same answer, lemme check once again
oh right, oops i forgot how to multiply
for the parameterisation (2t, 0), you didn't substitute correctly. You should have the integral of 12t instead
safe radishBOT
@tacit cosmos Has your question been resolved?
tacit cosmos
for the parameterisation (2t, 0), you didn't substitute correctly. You should ha...
12t?? how?
wind stream
because...2*2*3=12...
I can't really say where you messed up but probably somewhere along the line of calculating the derivative, or calculating the dot product of F(r)*r'
safe radishBOT
safe radishBOT
Available help channel!
dapper nest
Helloo
dapper nest
Do you guys know any website or dc group that has chegg and course hero unlocks for free? And when i mean free like FREE because others was such a b
final halo
That's not the kind of thing we endorse here sorry
dapper nest
Okay thank you because like i joined a gc here already before but since the update, it's not legit anymore
safe radishBOT
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teal finch
is 2nlogn same as 2nlogn^2?
safe radishBOT
is 2nlogn same as 2nlogn^2?
azure cobalt
We need help with this question. I found surface integral of the curve using cylindrical co-ordinates but don't know how to define the two linear sides in cylindrical
safe radishBOT
We need help with this question. I found surface integral of the curve using cyl...
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azure cobalt
<@&286206848099549185>
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@azure cobalt Has your question been resolved?
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@azure cobalt Has your question been resolved?
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@azure cobalt Has your question been resolved?
edgy osprey
Hi. I have to find the limit of following sequence:
safe radishBOT
Hi. I have to find the limit of following sequence:
edgy osprey
i tried to expand with the conjugate of the bracket
\frac{\sqrt{n}}{\sqrt{n+1} + \sqrt{n}}
I mean sqrt(n)/(sqrt(n+1)+sqrt(n))
here the limit is still infinity
or 0? 😄
how can I simplify this more?
i know its a half
empty gyro
$\frac{1}{\left(\frac{\sqrt{n+1}+\sqrt{n}}{\sqrt{n}}\right)}$
flat frigateBOT
SWR
lean otter
How do I solve $70+(190-70)e^{-k(30)}=170$
safe radishBOT
How do I solve $70+(190-70)e^{-k(30)}=170$
flat frigateBOT
Matt
lean otter
First I subtract 70 from both sides, simplifiy whats in the paranthesis and divide 120 on both sides but then i get stuck
lean otter
Just divide by 30
because there is a negative infrontn of the k
safe radishBOT
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Available help channel!
strange orchid
safe radishBOT
strange orchid
Yeah
strange orchid
<@1126563012094996500> What are you trying to take the derivative of?
Sry if its messy
crimson matrix
you can write it as 2|x|. so derivative is 2 if x>0 and -2 if x<0
or like write it as 2 sqrt(x^2) and have u(x)=x^2
Then use chain rule and u'll get 2x/root(x^2)
crimson matrix
Is this correct ?
Derivatives
they are equivalent
you can take out the root(4) in ur solution
so its
4x / 2 root(x^2)
which simplies to
2x / root(x^2)
crimson matrix
what does big mean
strange orchid
it means that it is just something that is not simple X , stuff like 1+x , 3*x ,x+x
crimson matrix
root(func of x) = (func of x)^1/2
derivative of (func of x)^1/2
=
1/2 * (func of x)^(-1/2) * derivative of func of x
so yeah
strange orchid
is this method correct ?
okay if following this is a possible way to solve it
strange orchid
where did I mess up when I tried that
strange orchid
ohh
interesting tnx
you seem to solve it in a more logical way I will take a look at how you are solving it so I dont have to memorise stuff like I do
I think
THANKS AGAIN !
.close
safe radishBOT
crimson matrix
np
fickle thicket
.close
dusky harbor
Hello. I'm still trying to get familiar with integration techniques. ... writing the example in TeX, bare with me--
safe radishBOT
Hello. I'm still trying to get familiar with integration techniques. ... writing...
flat frigateBOT
HqppyFeet
dusky harbor
there
First of all..
I factored the denominator to become (x+3)(x+4)
Then I want to split it into A/(x+3) + B/(x+4) ... But I don't think that's the correct approach, because the degree on the numerator is greater... or am I overthinking?
mossy bobcat
try to factor the above?
burnt nest
**HqppyFeet**
mossy bobcat
usually with these you can probably cancel out some factors between the numerator and the denominator
dusky harbor
hmmm.. I tried x(x^2 + 11x + 40) + 45
median vigil
partial fraction decomp requires the degree of the denominator to be higher than the numerator
dusky harbor
but that quadratic in the centre leads to b^2 -4ac <0
hasty falcon
what is the source of this question?
median vigil
partial fraction decomp requires the degree of the denominator to be higher than...
you can bypass this by doing polynomial long division first
dusky harbor
what is the source of this question?
Canvas. University course question (Calculus)
burnt nest
That good question 🤔
dusky harbor
you can bypass this by doing polynomial long division first
polynomial long division? woop new territory
i know simple long division
but i didnt know that works for polynomials?
mossy bobcat
it does
mossy bobcat
mossy bobcat
our king, king
median vigil
after doing polynomial long division you should end up with
(quotient) + (remainder)/(denominator)
quotient is just a polynomial, remainder/denominator can be done with partial fraction decomposition
hasty falcon
after doing polynomial long division you should end up with
(quotient) + (remain...
yep this would do
safe radishBOT
@dusky harbor Has your question been resolved?
dusky harbor
Alright so... This is the "accepted" correct answer: \ $I = \frac{x^{2}}{2} + 4x - 3\ln(|x+3|)+3\ln(|x+4|)$ \ ... I also got the first two terms, but instead I have 7 in the denominator under both "ln()"'s... hmm
I'll show my process, wait a sec
flat frigateBOT
HqppyFeet
dusky harbor
So through polynomial long division... Then factoring the denominator, I have \ $I = \int x+4-\frac{3}{(x+3)(x+4)} dx$
flat frigateBOT
HqppyFeet
dusky harbor
This became $I = \frac{x^{2}}{2} + 4x -\int\frac{3}{(x+3)(x+4)} dx$
flat frigateBOT
HqppyFeet
dusky harbor
Through partial fraction, $\int\frac{3}{(x+3)(x+4)} dx$ became \ $\int\frac{A}{(x+3)} dx + \int\frac{B}{(x+4)} dx$
flat frigateBOT
HqppyFeet
dusky harbor
I eventually found A = (3/7) and B = (-3/7)
So... $\int \frac{3}{7}\cdot \frac{1}{(x+3)} dx + \int -\frac{3}{7}\cdot \frac{1}{(x+4)} dx$
flat frigateBOT
HqppyFeet
dusky harbor
I assumed that both of those fractions were "constants", right... so I put it on the outside of the integral...
then I simply did integration on both sides to get ln|x+3| and ln|x+4|... 3 on the numerator and 7 on the denomintaor..
what did I do wrong?
median vigil
i think you probably solved for A and B wrong
safe radishBOT
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gloomy light
safe radishBOT
gloomy light
Sorry lol you take this one
gloomy light
No it's cool
lean otter
its cool
gloomy light
Lol l
gloomy light
Trying to figure out why (P)(1+rt) gives me an answer so different
According to my answer key I have all the correct answers but when I try it all in one formula I get a different answer
Shouldn't there be a way to do compound interst without a chart ? Or am I using the formula incorrectly ?
safe radishBOT
@gloomy light Has your question been resolved?
subtle kettle
help
tough spruce
subtle kettle
yep keep getting it wrong
please give me the answer
for my own mental
2pi x 15 x 4
2pi x 4 squared
376.9
100.530964915
477.5220833
@lean otter
still not working
if u show me how u solve it ill understand
delicate sphinx
still not working
Did you round to 1 dp like it says?
subtle kettle
yes
subtle kettle
151.9
delicate sphinx
Why did you type in that?
subtle kettle
becuase thats what i got
delicate sphinx
477.5220833
This is what you got, correct?
subtle kettle
yes then i put it to 1d.p then divided it by pi
delicate sphinx
Why did you divide by pi?
subtle kettle
somebody told me to divide the final answer by pi
delicate sphinx
No one said that
You don't do that
You do that if you wanted it in terms of pi
But you don't need it in terms of pi
delicate sphinx
477.5220833
This is what you got as the surface area of the can
Round it to 1 dp
delicate sphinx
Did you try it yet
subtle kettle
oh dam
it worked
Thanks bro
@lean otter thanks as well ur explanation was jsut a bit too complicated
bye
.close
safe radishBOT
delicate sphinx
<@456226577798135808> thanks as well ur explanation was jsut a bit too complicat...
There was nothing confusing with the explantion
You just needed to apply the formula
You just divided by pi when you didn't need to
safe radishBOT
Available help channel!
tidal atlas
Hey I got a quadrilateral test tomorrow and I’m kinda confused on how to remember the relations between the shapes as in how do I remember if a square is a trapezoid or a square is a rhombus but a rectangle isn’t a square?
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Hey I got a quadrilateral test tomorrow and I’m kinda confused on how to remembe...
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twilit nebula
safe radishBOT
muted sapphire
What don't you understand?
versed wave
it is a-s-a case
you have 2 pairs of congruent angles and both triangles share a side, which is in the middle of the congruent angles
twilit nebula
you have 2 pairs of congruent angles and both triangles share a side, which is i...
how do i prove that the angles are congeuent
versed wave
how do i prove that the angles are congeuent
you dont need to
because its already given
twilit nebula
thanks
safe radishBOT
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strong bison
safe radishBOT
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Available help channel!
atomic pulsar
The homogeneous system, Ax = 0, has a unique trivial solution if and only if
λ=/=0 is an eigenvalue of A.
why is this statement true?
safe radishBOT
The homogeneous system, Ax = 0, has a unique trivial solution if and only if
λ=...
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neon arrow
Hey
fleet condor
KK RGW N NIDDHTHE YRTMS CVAMVE; PIT
rotund river
There is a (-1/(n-1)) term in the "..."
neon arrow
i don't understand, can you explain a bit more?
neon arrow
you end up with 1/4
icy lance
such violent cancelling
neon arrow
I need to see the work on how you end up with 1/2
bc i don't get it
(3/1) + (1/(n-1) - 1/n)
no?
fleet condor
you end up with 1/4
nope i cancelled it with the 1/4 in the next term
neon arrow
nope i cancelled it with the 1/4 in the next term
u still have left 1/2 and 1/5
fleet condor
u still have left 1/2 and 1/5
ya but i cancelled the 1/5 with the 1/5 in the next term
fleet condor
fleet condor
why can't they write all the numbers up to infinite
might take a while
pallid wadi
safe radishBOT
pallid wadi
How would I find maximum point if i was only able to find minimum point from cn and number line
my work is above
fleet condor
when finding min and max on a range you have to check endpoints AND critical points
check x = 0, x = 29, and x = 30
pallid wadi
ohhh
fleet condor
one of those has to be the max on [0, 30]
fleet condor
why are you checking f'(x) when checking the value of f(x)
pallid wadi
i apolgoize lmao
fleet condor
out of { f(0), f(29), f(30) }, one is the minimum and one of the maximum on [0, 30]
pallid wadi
out of { f(0), f(29), f(30) }, one is the minimum and one of the maximum on [0, ...
f(0)
is the maximum
i get it now
so the answer is x = 0 y = 30
let me try one more question
fleet condor
thats right
pallid wadi
thats right
hey can i get some help solving this one
nvm
i see my mistake
oh wait
i need help
If its negative before the cn and positive after then what is it? a max or a min
fleet condor
neither
pallid wadi
so there is no max or min
flat frigateBOT
pallid wadi
yeah
how would i continute then
would i just assume that length and width are both 9
fleet condor
wait why are you doing negatives and positives?
oh if it goes from negative to positive it's a minimum
since you are doing f'(x)
the slope goes from decreasing to increasint
pallid wadi
oh if it goes from negative to positive it's a minimum
yeah if it goes from negative to positive to negative its a max
and if it goes from positive to negative to positive its a min
.close
inner cradle
safe radishBOT
inner cradle
can anyone help
Find the equation for the graph of the hyperbola in the figure below.
safe radishBOT
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tidal burrow
Find an explicit solution to $2xy+(x^2-y)y'=0$
safe radishBOT
Find an explicit solution to $2xy+(x^2-y)y'=0$
flat frigateBOT
rkwilli2
tidal burrow
My ODE instructor hasn't gone over how to do things like this so I'm not entirely sure how to go about finding any solution for this
I know that $-2x^2 y + y^2=1$ is an implicit solution
flat frigateBOT
rkwilli2
safe radishBOT
@tidal burrow Has your question been resolved?
tidal burrow
<@&286206848099549185>
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@tidal burrow Has your question been resolved?
safe radishBOT
@tidal burrow Has your question been resolved?
spice furnace
<@&286206848099549185>
do you know the type of differential equation wolfram alpha can help
tidal burrow
First order nonlinear ODE
spice furnace
**rkwilli2**
Why don't you complete the sqaure?
safe radishBOT
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primal birch
let's say we have a group of points, they go like this, (1,1),(2,2),(3,3),... and we have to find the rule that all the points follow.
safe radishBOT
let's say we have a group of points, they go like this, (1,1),(2,2),(3,3),... an...
prime nacelle
let's say we have a group of points, they go like this, (1,1),(2,2),(3,3),... an...
this seems like a linear relationship
primal birch
I think so, there linear, and there related so I think it is
prime nacelle
what linear could it be
primal birch
linear diagonal ig
vague shell
wrong chat
prime nacelle
linear diagonal ig
i mean liek eq
safe radishBOT
@primal birch Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
merry lintel
Yo, probably a really dumb question, but anyway, here:
So i had X - 3Y = 6 and i needed it to be in the y = mx + b format
So i transferred 6 to the other side, and the same with -3y.
My question is: is it going to be -6 • X = 3y or -6 + X = 3y?
safe radishBOT
Yo, probably a really dumb question, but anyway, here:
So i had X - 3Y = 6 and i...
merry lintel
I forgot how it works soo yea
lavish urchin
Yo, probably a really dumb question, but anyway, here:
So i had X - 3Y = 6 and i...
X - 6 = 3y
merry lintel
I see, thank you
How do i continue from here?
Pretty sure i need to get rid of the 3 in 3y but idk how because of the X
merry lintel
Can I? I thought i couldnt since Y isnt a defined number
So it’d be X -6/3 = y?
Which would be X - 2 = y?
Ohh that makes way more sense
flat frigateBOT
1401
merry lintel
why -2?
lavish urchin
because 6 ccan be simplified
merry lintel
Oh i divide both the X and -6 by 3?
wide raft
yes
merry lintel
I see
lavish urchin
yea
merry lintel
Thank you both
wide raft
aight
merry lintel
.close
coarse kelp
$\frac{50}{s^2 + 5000s + 100,000}$ how to make this easier to partial fraction decompose
safe radishBOT
$\frac{50}{s^2 + 5000s + 100,000}$ how to make this easier to partial fraction d...
flat frigateBOT
LeGM
lean otter
Is this for finding the inverse laplace? If it is, show the original question
lean otter
u the Heaviside function of what?
coarse kelp
u is supposed to be micro
flat frigateBOT
LeGM
lean otter
micro? 
coarse kelp
micro? <:thonk:406575732563902485>
here
lean otter
okay i think you are forced to use the quadratic formula here probably
find the roots and plug them into a form of (s-a)(s-b)
flat frigateBOT
LeGM
coarse kelp
find the roots and plug them into a form of (s-a)(s-b)
damnn okay
pls dont close this thanks
coarse kelp
find the roots and plug them into a form of (s-a)(s-b)
you mean (s-a)(s+a)?
lean otter
whatever gets you your original expression of the quadratic
coarse kelp
okay
coarse kelp
whatever gets you your original expression of the quadratic
omg the values really suck
lofty geyser
how is there not p if there always is p
safe radishBOT
how is there not p if there always is p
@lofty geyser Has your question been resolved?
frozen gulch
how is there not p if there always is p
not quite understand your question,but isn't the 4th column not right
safe radishBOT
@lofty geyser Has your question been resolved?
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Available help channel!
gloomy knot
Hi
fleet condor
lhopital
fleet condor
lhopital doesnt even work well, it was an impulse reaction
gloomy knot
you dont even need lhopital
like putting
f(x)=e^sqrt(x)
finding f'(x) and replace x with 0 ?
cosmic grove
$\lim_{x \to a} \frac{f(x) - f(a)}{x-a} = f'(a)$
flat frigateBOT
Herels
cosmic grove
use this ^
gloomy knot
i found f'(x)= 1/2*sqrt(x) * e^sqrt(x)
fleet condor
cant you just argue that the limit from the left is in C\R and limit from the right is strictly real so there is no two sided limit?
gloomy knot
which is impossible right?
The question was "that limit shoud be equal to 1 or 0 or infinete"
so no?
cosmic grove
i found f'(x)= 1/2*sqrt(x) * e^sqrt(x)
yea there is a problem at 0, we need something else
if sqrt isnt even differentiable at 0
cosmic grove
**Herels**
then we cant use this
gloomy knot
indeed we cannot use it 😢
cosmic grove
hmm
gloomy knot
got any other ideas to try?
fleet condor
I'm not asserting it as fact, but does my argument not work?
cosmic grove
cant you just argue that the limit from the left is in C\R and limit from the ri...
what does C/R means ?
fleet condor
complex not including reals
gloomy knot
complex not including reals
this sounds too complex for my level so i dont think it's the thing x)
fleet condor
oh good point
cosmic grove
and its not really possible to jump from a function defined in R\{0} to C
well we need to do smthing else
gloomy knot
hmmm
fleet condor
and how would you prouve the limit is complex
it wouldnt be that hard I think, but also probably not the right approach
cosmic grove
$\frac{\exp(\frac{1}{2} \sqrt{x}) \left( \exp(\frac{1}{2} \sqrt{x}) - \exp(-\frac{1}{2} \sqrt{x}) \right)}{x}$
gloomy knot
huh?
flat frigateBOT
Herels
gloomy knot
oh oki oki!
cosmic grove
$$\frac{\exp(\frac{1}{2} \sqrt{x}) \left( \exp(\frac{1}{2} \sqrt{x}) - \exp(-\frac{1}{2} \sqrt{x}) \right)}{x} = 2\frac{\sinh(\frac{1}{2} \sqrt{x})}{x} \exp(\frac{1}{2} \sqrt{x})$$
fleet condor
what level of math is this supposed to be?
flat frigateBOT
Herels
fleet condor
im still psuedo convinced you are supposed to say you cant take sqrt(a) for a < 0 and claim the limits cant be equal - even though its not as rigorous
cosmic grove
im still psuedo convinced you are supposed to say you cant take sqrt(a) for a < ...
well yea, the main problem is with the sqrt
gloomy knot
what level of math is this supposed to be?
last year of highschool maths 🤔
cosmic grove
last year of highschool maths 🤔
hmm
gloomy knot
im still psuedo convinced you are supposed to say you cant take sqrt(a) for a < ...
nope, because i gotta choose between 3 answers which are 0, 1 and infinite
and it didnt say limits from the left and the right
gloomy knot
what does DNE mean?
fleet condor
does not exist
gloomy knot
oh
fleet condor
at least im like 99% sure
cosmic grove
does not exist
are you sure ?
fleet condor
,w limit a to 0 of (e^(sqrt(a))-1)/a
flat frigateBOT
cosmic grove
well when you take the limit of smthing with sqrt at 0, its always at the right
well they didnt specify tho
gloomy knot
well when you take the limit of smthing with sqrt at 0, its always at the right
Hm that's right!
fleet condor
oh i definitely did not learn that
so really you are trying to solve $\lim_{a\to0^+} ...$
flat frigateBOT
cosmic grove
we all know the limit at the left of sqrt doesnt exist anyway
fleet condor
well yes, but high schoolers have problems that require them to realize that limit at left and limit at right being unequal means limit DNE
i didnt know about this implicit assumption though, so my bad
cosmic grove
well yes, but high schoolers have problems that require them to realize that lim...
you are right but sqrt isnt defined at the left so its pointless
fleet condor
the problem as written above is DNE, and could easily have been a trick question, but fair enough
in which case, is the argument not just as simple as lhopital, then 2sqrt(x) -> 0 and e^(sqrt(x)) -> 1 so lim -> inf
again not rigourious but easily jumps to the right answer
safe radishBOT
@gloomy knot Has your question been resolved?
fresh vessel
Does sin^2 theta become theta in small angle approximation
fresh vessel
Or theta squared
zinc hornet
theta^2
fresh vessel
What about (sintheta)^2
What does theta become
empty gyro
$\sin^2{\theta}=(\sin{\theta})^2$
flat frigateBOT
SWR
safe radishBOT
@fresh vessel Has your question been resolved?
fresh vessel
.close
spare copper
Help me write this in mathematical way
safe radishBOT
Help me write this in mathematical way
spare copper
So the solutions are:
x1 = 2, x2 = 5, x3 = 0
x1 = 3, x2 = 3, x3 = 1 etc
but i need to find a way to write this mathematically
if i increase x1 by 1, x2 gets decreased by 2 and x3 gets also increased by 1
neon pewter
if i increase x1 by 1, x2 gets decreased by 2 and x3 gets also increased by 1
Call the amount that you are increasing x1 by the variable t
neon pewter
In which case from what you are saying x2 decreases by 3t and x3 decreases by t
neon pewter
if i increase x1 by 1, x2 gets decreased by 2 and x3 gets also increased by 1
But the values you are claiming here don’t line up with the two solutions you gave
spare copper
why not
neon pewter
The values that you gave have when x1 increased by 1, x2 decreases by 2 and x3 increases by 1
spare copper
no it decreases by 3
neon pewter
Going from 5 to 3 is a decrease by 2
spare copper
oh yeah true
but thats not the problem
the problem is that i cant write it in mathematical
like how do i find all solutions
neon pewter
Yeah, so let the amount you increase x1 by be denoted by t, then we have that our solutions are given by $(2,5,0)+t(1,-2,1)$
flat frigateBOT
Willow
neon pewter
That would be one common way to notate it
spare copper
oh my god thanks
neon pewter
Or if you want one vector $(2+t,5-2t,t)$ for $t\in\mathbb{R}$
flat frigateBOT
Willow
worldly fiber
Maybe a little explanation on how to solve this one.
safe radishBOT
Maybe a little explanation on how to solve this one.
worldly fiber
What i know so far is this:
Or I assume.
T1 stands for triangle 1
Triangle 1's two triangles inside probably has same angles, meaning that i can allow myself to put a Phi/x on the one side of my T1's triangle.
I can maybe use pythagoras theorem to find the other side
<@&286206848099549185>
hazy roost
Since it is a right triangle, there is a thought there
hazy roost
I am not opposed to that notion
worldly fiber
meaning?
hazy roost
Yeah, that is a good ideam
worldly fiber
I'm thinking like this:
hazy roost
Okay so you said you can use the phi/x to fill in. Can you explain why that is?
worldly fiber
Well let me show:
I believe they have the same angles
just different sizes
meaning:
This bottom side divided by an unknown number
hazy roost
Your logic makes sense. Say if top angle is 80 and bottom angle is 100, then the cut from the rectangle makes the supplements
hazy roost
I'm saying the angles are correct. I just threw in numbers to help visualize
hazy roost
A triangle make s 180. I meant to say compliment.
hazy roost
We do not know what x is. How can we utilize the second graph?
worldly fiber
worldly fiber
We do not know what x is. How can we utilize the second graph?
Oh
well
I have an idea
Let me find c^2 first
hazy roost
Yes
hazy roost
Yes I like that
worldly fiber
Maybe we can isolate x??
hazy roost
And we can simplify with a denom of 2x^2
worldly fiber
Hmm, can you show?
hazy roost
So (3+sqrt(5))/(2x^2) + 1 = c^2
hazy roost
Okay, let me ask why you say that is 1 * y?
hazy roost
Not saying it is wrong, just asking you to justiy
hazy roost
May I propose a step
worldly fiber
UH
hazy roost
hazy roost
This is the angle relations for the second triangle. Do you believe we can do anything with these?
Yes, because they are the same triangle and same rectangle
hazy roost
And justify your reasoning
worldly fiber
Well, i could use maybe the same pythagora-rule and apply it to this one.
But then we have 2 unknowns.
Hmm wait
It sayts
specify the area of the triangle when there's two
so they have the same area
hazy roost
Exactly
hazy roost
It is the same rectangle, yes
hazy roost
So the 3 small triangles on the right have the same area as the two medium triangles on the left
worldly fiber
Hmmm
Wait the other big triangle right?
just to clarify, i don't study english math, i study it in danish. So i translate a lot of the math terms/words
hazy roost
Okay. Thank you for saying that
Yes they are both the same triangles golding the same rectangle. So the remaining triangles are the same
hazy roost
worldly fiber
The area of a triangle is expressed like this i remember: 1/2 * height * bottom
hazy roost
Yes
worldly fiber
OH
I assume this means i will have to find all areas 😭
no problem
no wasting time
wait no
it doesnt
i only have to find the area of one big triangle
if i know all the small triangles and rectangle's area in one big triangle
i can put it together
is this somewhat right you think?
oh snap wait
it's a golden rectangle
could it possibly have some unique features that'll help me?
I saw a quick video about it
and it had some features
but i don't think they'll help
worldly fiber
Ok, finding the area of triangle 2
now i pray that this is right
and move onto comparing triangle 2 with triangle 1
I know that the length of the side "a" in triangle 2 is shorter that the "a" in triangle 1
because rectangles dont got same sidelengths
yes
but
same angles, meaning:
Ok time to translate a word
scale ratio
it can be determined
hazy roost
I'm sorry, but I have to leave. You seem to be getting the idea well. Feel free to ask another helper if needed
worldly fiber
Thank you very much Master
I apreciate your help and tips!
enjoy your night/day
OH
😮
The scale ratio
is x
I KNEW IT
OOOH
SO c^2 HERE MUST ME Sqrt(phi^2+x^2)
worldly fiber
SO c^2 HERE MUST ME Sqrt(phi^2+x^2)
and i think we know phi^2+x^2 from before
without the +1
Ohh thats cool
seriously
okokok
c^2 here would be this
but wait i didnt have the need to find this
Wait so
We can find the area for the whole triangle now
Area for triangle = 1/2 * h * b
OOOO
SO THE WHOLE THING IS LIKE THIS
wait what
ok ok ok
its fine
let me calculate
uh
ok
WAIT
IS THIS IT
HOLY SCHNITZEL
no
it cant be
I need some expert checking <@&286206848099549185>
Hello guys!
You can check pinned messages and see all my problem solving
novel pasture
Whats this?
worldly fiber
I just need help proofreading this.
Ah.
So this is the area of:
This triangle
I hope so
I just need someone to help proofread my calculations.
novel pasture
Ur saying that the area of the big triangle is sqrt5 + 3 /4?
novel pasture
No
worldly fiber
not even a little?
novel pasture
Whats the area of the rectangle
worldly fiber
novel pasture
Yea so ..
worldly fiber
One side is 1 and the other is that
novel pasture
Right
worldly fiber
The left big triangle
Triangle 1
I found my area for it
by using this equation: 1/2 * height * bottom
my height is
and my bottom is
novel pasture
The base is 1+x
worldly fiber
oh my actual good