but that's for another day 🙂
#help-36
sweet summit
fathom walrus
But doesn’t that mean u go from R^2 to something else
sweet summit
well to go to something else we would have to make our matrix from 2 x n to (not 2 x n), so something like 3 x 2
that would be R^3
for example, say we had a function
$f : \mathbb{R}^2 \rightarrow \mathbb{R}^3$ such that $f(<x, y>) = <x, y, x + y>$
soft zealotBOT
MellowDramaLlama
sweet summit
then that would take 2d Vectors and push them onto the 3d plane
fathom walrus
How does that make sense logically tho
sweet summit
what do you mean?
fathom walrus
How am I allowed to make a line I draw on a page into a line that exists in 3D
Man that sounds terribly phrased
Idk how to ask it lol
sweet summit
well keep in mind that the 3D plane is nothing more than us look at the x, y plane from straight above
hold on let me draw some visual aids
fathom walrus
Thanks
fathom walrus
Yes
fathom walrus
Sure
fathom walrus
well keep in mind that the 3D plane is nothing more than us look at the x, y pla...
I think I understand this more clearly thinking about it now
The nature of the vector being <2,3> doesn’t change
It’s just popping out of the page now
sweet summit
yep!
well almost lol
it's still on a flat plane
oh wait
for our function, it would be <2, 3, 5>
yes that would be popping out of the page
but <2, 3, 0> would be flat on the xy plane
fathom walrus
Ah i c
sweet summit
see? not so bad 🙂
now when you get to dimensions >= 4, then it's really hard to visualize
but the math checks out
fathom walrus
see? not so bad 🙂
yea, thats true. its hard to just understand from the textbook cuz unfortunately my college only offered the online course and its asychronous with no lectures, just textbook, webassigns, and tests, so its a bit tough to learn
fathom walrus
now when you get to dimensions >= 4, then it's really hard to visualize
oh boy
isnt 4d time
fathom walrus
thanks so much man, i really appreciate the explanations
sweet summit
of course, happy to help 🙂
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Available help channel!
gleaming mantle
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gleaming mantle
Can i get tips or advice to solve c
wary python
How can I learn Graph Theory step by step?
gleaming mantle
?
wary python
Didn't you understand?
gleaming mantle
Its my question
wary python
No, I just asked something to people to help me.
gleaming mantle
Yah but ure taking my space
opal needle
Can i get tips or advice to solve c
its like the question you had earlier
final tangle
split the shaded region into smaller regions
parts a,b) will be helpful in calculating areas of those smaller regions
gleaming mantle
How about the small semis
opal needle
you shouldnt look at it like that i think
seperate it into two pieces, DOA and AOB
since you know the angles of each of the triangles, you can calculate their area and take away the shaded parts
by treating them as smaller triangles
final tangle
wdym by small semis
final tangle
what unshaded quad on the left
if quad was short for quadrilateral, the unshaded part isn't a quadrilateral
gleaming mantle
@final tangle how to find that
final tangle
applying the appropriate formulae for areas of sectors, triangles,segments
the radius / relevant sides are known
you've pretty much already determined the angles you need as well in parts a,b
feral pivot
Normally wouldn't we say 400$ on a win, because we paid 100 and won 500, hence 400
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Normally wouldn't we say 400$ on a win, because we paid 100 and won 500, hence 4...
feral pivot
and thus the expected value would be 0
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@feral pivot Has your question been resolved?
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@feral pivot Has your question been resolved?
fossil geyser
The wording is kind of vague, but I agree with you.
@feral pivot
Maybe they meant that if she wins, she profits $500
final saddleBOT
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Available help channel!
barren saffron
Hey
Today we talked about sets but i didn't understand this:
let A be a set, then what is supA and infA?
final saddleBOT
Hey
Today we talked about sets but i didn't understand this:
let A be a set, the...
fossil geyser
If A is a subset of some ordered set, for example the real numbers
Then sup(A) is the smallest element of the larger set, which is greater than every element of A
For example if A is the set of all real numbers less than 2,
$A = {x \in \R: x < 2}$, then $\sup(A) = 2$
soft zealotBOT
tatpoj
fossil geyser
inf is the same, but on the lower end instead
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bitter orbit
can anyone explain to me how to determine if a relation is a function
bitter orbit
I still dont understand it
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@bitter orbit Has your question been resolved?
eager stirrup
Heracles needs to fight the Lernean Hydra for one of his labors. A Hydra has many heads, and to defeat it, you must remove them all.
Heracles has two swords, and he can only use one of them at a time. The smaller sword will sever 21 of the Hydra’s heads with a single stroke. The larger one will sever 100 heads with each stroke, but then the Hydra (unless it has just been killed) will grow 2023 new heads! If the Hydra initially has 101 heads, is it possible for Heracles to defeat it with his present swords or does he need to procure another sword?
NOTE: A sword can only remove a particular number of heads, no fewer and no more. If, for example, the Hydra has just 5 heads, they cannot be cut off with either of the swords.
final saddleBOT
Heracles needs to fight the Lernean Hydra for one of his labors. A Hydra has man...
eager stirrup
is this an invariant question?
if so, whats the invariant
also, i dont think its possible, because every time he severs some heads, they increase by 2023
with is much larger than the largest amount taken away
so it will always be larger
unless im missing smth
crisp plover
The heads only grow if you use the larger sword.
crude lagoon
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stoic mural
no
crude lagoon
sorry
stoic mural
you are not
crude lagoon
ooh
stoic mural
@outer storm get to your channel pls
thanks
we have
4,12,36,...
do you see what sequence this is?
crude lagoon
so my way of thinking was: 4 x 3 = 12, 12 x 3 = 16, so i thought it was like multiples of 3 so i divided the 708 number by 3 and got that n = but its wrong
yes i think the sequence is times 3
not sure
crude lagoon
right
stoic mural
so 4*3^2=36
in general we see that
4 * 3^0 = 4
4 * 3^1 = 12
4 * 3^2= 36
so in general
crude lagoon
right
stoic mural
4*3^(n-1)
stoic mural
the n-1 is because our first element of the sequence has exponent of 0 in this notation
but we want to start n from 1
crude lagoon
yes that makes sense
crude lagoon
it says that n isnt defined
stoic mural
n=1 means we look at the first element
stoic mural
it is given that 708588 is an element of the sequence
so we can set them equal
4*3^(n-1)=708588
3^(n-1)=177147
log_3(177147)=n-1
n=log_3(177147)+1
,w log_3(177147)+1
soft zealotBOT
soft zealotBOT
stoic mural
looks good
stoic mural
log_3(177147)=n-1
does this step make sense to you?
stoic mural
great
stoic mural
$a^{b}=c \ log_{a}(c)=b$
soft zealotBOT
~Martin
stoic mural
i always read the log as
a equals c if taken to the power of b
base equals () if taken to power of result
stoic mural
oh no
stoic mural
n=log_3(177147)+1
this is what we have
however
we can calculate this
,w log_3(177147)+1
soft zealotBOT
stoic mural
you spooked me for a second haha
crude lagoon
spooky season
fr
idk if i can continue using this channel but heres the next (if i can)
stoic mural
sure thing
what do they mean with common ratio?
im not used to english terms here
but a_n are easy
stoic mural
$a_{1}=\frac{9^{1+3}}{6}=\frac{9^{4}}{6}=\frac{6561}{6}=1093.5$
soft zealotBOT
~Martin
crude lagoon
i think its 3
soft zealotBOT
crude lagoon
because they are all divisible by 3
ok 3 is not correct
lol
i have unlimited tries btw so
stoic mural
i think with common ratio they mean a_n/a_n-1
or something like that
oh great
$\frac{9^{n+3}}{6}:\frac{9^{n+4}}{6}=1:9$
soft zealotBOT
~Martin
stoic mural
so it is either 9 or 1/9
crude lagoon
9 is correct
stoic mural
,w (9^(1+3))/6
soft zealotBOT
stoic mural
,w (9^(2+3))/6
soft zealotBOT
stoic mural
,w 9*1093.5
soft zealotBOT
crude lagoon
got that correct!! thank you!!
crude lagoon
crude lagoon
and for each a_n after that we just multiply by 9
this is what i did
lol
great stuff
so 5 more questions left!! almost there
stoic mural
we start with 2.5
stoic mural
multiply by 7 each time
stoic mural
multiply
crude lagoon
2.5 n x 7
crude lagoon
why would u multiply twice?
stoic mural
so 2.5*7^(n-1) should work
btw
we could avoid this (n-1)
this comes up often
we can avoid this if we say the sequence starts with the 0th term
but in math that is uncommon
that is a programming thing though
there this is usual
stoic mural
lets start with the first sequence
we can split it up into 2 sequences
the sequence of nominators and the sequeence of denominators
3,4,5,6,...
stoic mural
3
3+1
3+1+1=3+2
and so on
so we get
3+n
16,25,36,49,...
do you notice something with these numbers?
stoic mural
25+9=34 which is not 36
crude lagoon
like +1 for numerator and +9 for derminator
stoic mural
so nope
stoic mural
is starts with 16
crude lagoon
perfect squares
stoic mural
try to get a formula
crude lagoon
hiya
stoic mural
lets call this rule f
f(12)=81
f(6)=9
f(8)=25
f(10)=49
and so on
notice that 81,9,25,49 and so on are all perfect squares
f(12)=9^2
f(6)=3^2
f(8)=5^2
f(10)=7^2
notice something else here?
final saddleBOT
@crude lagoon Has your question been resolved?
stoic mural
not quite
12^9 and 9^2
6^2 and 3^2
8^2 and 5^2
there is a pattern
f(x)=(x-3)^2
crude lagoon
f(x)=(x-3)^2
so i jus leave it like this?
crude lagoon
.close
dry light
Is there an easier way to do this?
Basically, I was given this stupid problem:
For Triangle ABC, $\frac{\sin(0.5(A-B))}{\cos(0.5C)} = \frac{12}{15}$. Sides $BC$ and $AB$ are 40 and 50, respectively. Find the exact length of AC
final saddleBOT
Is there an easier way to do this?
Basically, I was given this stupid problem:
...
soft zealotBOT
Umbraleviathan
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@dry light Has your question been resolved?
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@dry light Has your question been resolved?
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Available help channel!
tired oyster
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ℝamonov
final tangle
that's not what the question says
tired oyster
it says to find the asymptote, but it says to factor it out
and in the video he says 2x - 2 factors into 2x * (x - 1)
final tangle
note that the x^2+x was factored too
final tangle
I'm pretty sure they don't say that
tired oyster
because it doesn't make sense to me why that is true
final tangle
factoring is the reverse of expanding
it's still the application of the distributive property
are you able to expand
a(b+c)?
final tangle
yes
tired oyster
cause I am distributing a
final tangle
missing ()
tired oyster
yea i'm writing it fast
final tangle
write slow and properly
tired oyster
but ok that helps so much because in the video he just says oh yea that factors into that
without explaining what it means
final tangle
otherwise the default assumption is misunderstanding
2x-2 = 2(x-1)
x^2+x = x(x+1)
overall (2x-2)(x^2+x) = 2 * (x-1) * x * (x+1)
= 2x(x-1)(x+1)
tired oyster
otherwise the default assumption is misunderstanding
Here he cancels out a -x and gets 1/2x (x + 1), and he says replace the denominator, which in this case is 2x (x + 1) to 0
so that would just make it 1/0? how does he arrive that both x are either 0 or -1
final tangle
by solving
2x(x+1) = 0
tired oyster
oh wait
he set to 0
ok not replacing the whole equation to 0
I got confused
.close
wicked skiff
No clue on how to start
final saddleBOT
@wicked skiff Has your question been resolved?
wicked skiff
After that you can reduce and you should get tan
so i would use the second formula?
restive falcon
no the first one and the fourth one: sin(6x) + sin(4x) = 2 sin(6x + 4x / 2) cos(6x-4x / 2)
do the same of the denominator
wicked skiff
how would i do it for the denominator if its 2
restive falcon
no I mean the cos(6x) + cos(4x)
wicked skiff
so im using 2 different formulas
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wicked skiff
.reopen
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✅
wicked skiff
ok 2cos(6x+4x/2)cos(6x-4x/2)
gleaming bramble
ok 2cos(6x+4x/2)cos(6x-4x/2)
U need to simplify this?
wicked skiff
2cos(8x)cos(4x)
gleaming bramble
yeah thats it
wicked skiff
2 sin(6x + 4x / 2) cos(6x-4x / 2)= 2sin(8x)cos(4x)
olive bramble
U need to simplify this?
Need to write it in terms of tangents
restive falcon
now plug it into the original equation and reduce you see the numerator and denominator have both cos(4x)
gleaming bramble
mmk
olive bramble
If you expand this all the way you should end up@with a simple term tan(__)
restive falcon
how do you get sin8x + sin4x?
and no it is not one
write it down and show it to me your paper
wicked skiff
restive falcon
the denominator too
okay
now take 2sin(5x)cos(x) / 2 cos(5x) cos(x)
reduce it what do you get
wicked skiff
tan(5x)
restive falcon
there is your answer
vague gull
Hello
vague gull
I’m doing a question on related rates and it’s asking me to find how the fast the angle of a triangle is changing
I tried to do it on my own and this is what I got
Does this seem correct?
Also dx/dt and dy/dt are given
X is 6 and y is 8 too
I thought it would be easier to just leave them as variables so that’s what I did
<@&286206848099549185>
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void crest
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void crest
f - f(x+z0) + C1 + C2 = sum of residues
thats what i got but idk what theorem to apply to do this
like idk how we can find C1, C2 or show they vanish
final saddleBOT
@void crest Has your question been resolved?
void crest
yeshh
grim nebula
the first choice is wrong lol
void crest
it was a random
grim nebula
ok
grim nebula
nice
void crest
the first choice is wrong lol
whats it tho
grim nebula
should be last one i think
grim nebula
should be 3rd not last
grim nebula
void crest
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void crest
ty
grim nebula
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barren saffron
inf is the same, but on the lower end instead
So it's like a upper and lower limit of a set?
And in the example provided, the infA should be 0 right?
final saddleBOT
So it's like a upper and lower limit of a set?
And in the example provided, the ...
tired walrus
no, the infimum of {x ∈ R : x < 2} is not 0. it either doesn't have an infimum at all or its infimum is -∞ depending on who you ask
final saddleBOT
@barren saffron Has your question been resolved?
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Available help channel!
normal hill
final saddleBOT
https://gyazo.com/0afe361c3930c5bb66b2616330233537
hallow sail
How do I get better at math
final saddleBOT
How do I get better at math
hallow sail
I'm in college algebra, yet I'm behind by years because I was lazy and my high school was shit
summer vale
hallow sail
ok
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signal ginkgo
can anyone help me
final saddleBOT
can anyone help me
vital crag
how old are you?
vital crag
what grade are you in ?
signal ginkgo
7th
vital crag
use this rule
signal ginkgo
i did
vital crag
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regal vector
Anyone tell me about, how can I PDE by solve neural network?
final saddleBOT
Anyone tell me about, how can I PDE by solve neural network?
@regal vector Has your question been resolved?
keen frigate
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fleet rain
We toss coin until either the sequence of HHT appears, or HTH. WHat is probability that HHT appears first. How about unfair coin with probability p
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```We toss coin until either the sequence of HHT appears, or HTH. WHat is probab...
sturdy cypress
first why it's 2/3
fleet rain
did you use the abracadbra theorem?
sturdy cypress
never heard of it
sounds mildly interesting
i win if hht comes first
skip the Ts at the start however many
then
HHT: i win
HTH: i lose
HHH: i win
HTT: we start over
there's 2 ways for me to win and 1 to lose, the fourth option doesn;t change my odds
it probably works the same for arbitrary p
$\frac{p²(1-p) + p³}{p²(1-p) + p²(1-p) + p³}$
sturdy cypress
hm
fleet rain
we start all over at HTT since we didn't get either options we're looking for?
sturdy cypress
that's too short it scares me
sturdy cypress
like it's the same procedure to determine who wins from that point
because it ends with T we have the same chances as in the beginning from that point
fleet rain
so itll be a waste of a turn?
thats why we start all over at that turn?
@sturdy cypress
fleet rain
im just tryna understand why we start all over when we get HTT
<@&286206848099549185>
fleet rain
im just tryna understand why we start all over when we get HTT
like why did you say that?
sturdy cypress
the probability doesn't change from the initial
htt helps neither of us to win later
it doesn't start with H
fleet rain
htt helps neither of us to win later
thats why we start all over?
sturdy cypress
i don't understand what you mean
fleet rain
since HTT helps neither of us win, thats why we would start all over if any of us flip that sequence HTT right?
sturdy cypress
we read the text from the beginning
fleet rain
why would you lose if you flip HTH?
sturdy cypress
what
it's in the text of the problem
HTH is the sequence that keeps HHT from appearing first if it appears first
i'm sorry i couldn't help, srsly
fleet rain
its okay at least you tried, ty
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tranquil pine
whats 2 plus 2 and 1 divided by 2
final saddleBOT
whats 2 plus 2 and 1 divided by 2
dreamy shadow
quaint sail
Type .close
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Available help channel!
dull dirge
do any of you know how to find an optimal curve based on certain parameters?
smoky shore
smoky shore
i need to find the quadratic that best fits some parameters
Well, what parameters are you trying to have it best fit?
dull dirge
one sec
its hard to explain
essentially i am doing a model, where i have 675.46cm^2 of surface area (material)
and i need to make a curve that gives me the highest maximum, with the volume of revolution from 0-that maximum being 750cm^3
heres a picture
smoky shore
ah i get it now
dull dirge
and im changing the curve accordingly
if u want the bigger picture, I have to model a wine jug, where 750ml of wine has the biggest surface area touching air, where i have 675.46cm^2 of glass for the bottom part
smoky shore
so do you know the equation for the surface area of a solid of revolution?
dull dirge
yes i do, I have the equations all down
one sec
first one is SA of a solid of revolution, the second one is volume of revolution and the third is an expression for how "tall" (y component) the jug is
smoky shore
so really what you want to do here is make a system of equations to solve for a and b, right? that's what it looks like at first glance
dull dirge
yes
but would that output the widest possible r? or just any r?
my teacher said i could use optimization as in using differentiation but i dont see how
i wanna find the values of a and b that make r the largest
smoky shore
hm that's a tough question, but you should probably try solving the equations for a and b to start off
If a and b are variable, then maybe you can model an equation to show how the r changes with respect to a and b and then differentiate that to find the maxima?
smoky shore
that's not right
dull dirge
smoky shore
https://i.imgur.com/fTYgyON.png
how did you get this?
dull dirge
and yeah a and b are variable so maybe i can think of something there?
i equalled the two eqn
dull dirge
https://i.imgur.com/Q3ESdcV.png
.
dull dirge
https://i.imgur.com/CSSmtRH.png
.
and started simplifying
but idk it doesnt seem to be very nice
or doable
smoky shore
i equalled the two eqn
maybe a better option would be to solve the second (easier) integral for a or b by integrating it, and then plug that value into the first integral so you only have one of them
hm
dull dirge
i solved them both, and yeah the first one is simpler
but i dont know if i can solve for either a or b
one second
smoky shore
it looks like you can solve it for a
dull dirge
$-\frac{b^3}{24a^2}+\frac{b^3}{8a^2}-\frac{2.61155b}{a}$
soft zealotBOT
lawl
smoky shore
yeah i got that too, so you can just multiply both sides by a^2 and then use the quadratic formula?
soft zealotBOT
lawl
smoky shore
$a=\frac{-\left(12\left(5.2231\right)b\right)\pm\sqrt{\left(12\left(5.2231\right)b\right)^{2}-4\left(\frac{18000}{\pi}\right)\left(2b^{3}\right)}}{2\left(\frac{18000}{\pi}\right)}$
soft zealotBOT
demaw
dull dirge
but apply the quadratic formula to what
dull dirge
yeah but theres an a on the oter side too...
smoky shore
move them all to one side
smoky shore
i just did that to preserve the 5.2231, if you simplify my expression you should get the same thing that you would get by doing the quadratic formula on the expression you got
smoky shore
i would assume after solving for a like this, you can probably plug it in to the equation for the radius? and then just find the maxima by differentiating with respect to change in b?
smoky shore
yeah i suppose so
dull dirge
well here goes nothing
ill try rq so ill leave this open
for now tho tysm u saved my adhd ass
smoky shore
hah i hope it works man. i have no idea if it will but it should i think
dull dirge
i hope it will
if not ill turn this in and figure it out with my teacher
its only a first draft so
smoky shore
hm, you might be right about that, if you think it's supposed to be negative just make it negative ill double check my work
dull dirge
ill redo mine too xD
fleet rain
sorry
final saddleBOT
@dull dirge Has your question been resolved?
dull dirge
wait but @smoky shore this is still a in terms of b
smoky shore
wait but <@766866943566938134> this is still a in terms of b
yeah, my thought was that you can replace all substitute all instances of a so you can find the maxima of b and then solve backwards for a
dull dirge
confusion
oh
i get it
oh nooo
thats gonna be pain
dont i need to integrate the other eqn then too
oh noooo
$\frac{\pi \left(5.2231\left(-0.5b\sqrt{b^2+1}-0.5\ln \left|b+\sqrt{b^2+1}\right|\right)+\frac{b\sqrt{b^2+1}+\ln \left|b+\sqrt{b^2+1}\right|-2b\left(b^2+1\right)^{\frac{3}{2}}-4b^2\left(-b\sqrt{b^2+1}-\ln \left|b+\sqrt{b^2+1}\right|\right)}{32\cdot \frac{-12\cdot :5.2231b\pm \sqrt{\left(12\cdot :5.2231b\right)^2-4\cdot \frac{18000}{\pi }\left(-2b^3\right)}}{2\cdot \frac{18000}{\pi }}}\right)}{\frac{-12\cdot :5.2231b\pm \sqrt{\left(12\cdot :5.2231b\right)^2-4\cdot \frac{18000}{\pi }\left(-2b^3\right)}}{2\cdot \frac{18000}{\pi }}}$
soft zealotBOT
lawl
dull dirge
hmm
delicious
<@&286206848099549185> anyone know a site that can find b for me from this soup?
solar swift
.w $\frac{\pi \left(5.2231\left(-0.5b\sqrt{b^2+1}-0.5\ln \left|b+\sqrt{b^2+1}\right|\right)+\frac{b\sqrt{b^2+1}+\ln \left|b+\sqrt{b^2+1}\right|-2b\left(b^2+1\right)^{\frac{3}{2}}-4b^2\left(-b\sqrt{b^2+1}-\ln \left|b+\sqrt{b^2+1}\right|\right)}{32\cdot \frac{-12\cdot :5.2231b\pm \sqrt{\left(12\cdot :5.2231b\right)^2-4\cdot \frac{18000}{\pi }\left(-2b^3\right)}}{2\cdot \frac{18000}{\pi }}}\right)}{\frac{-12\cdot :5.2231b\pm \sqrt{\left(12\cdot :5.2231b\right)^2-4\cdot \frac{18000}{\pi }\left(-2b^3\right)}}{2\cdot \frac{18000}{\pi }}}$
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solar swift
yikes
dull dirge
hmm
solar swift
wolfram alpha lol
dull dirge
does wolfram take latex
solar swift
oh wait its past the max chars
dull dirge
i havent been able to
no... fffffffffffffffff
can i DL a wolfram alpha with more max chars
dull dirge
yeah symbolab is just deding on this
idk what the problem is
its just b with a bunch of things around it
solve!
@solar swift can u think of another way to put this
into that
solar swift
id have to see the original expression
dull dirge
https://i.imgur.com/CSSmtRH.png
this
@solar swift
i did the integration, rearranged it and did a quadratic formula
now i need to put it into that other integral
but symbolab and wolfram just die if i try
solar swift
https://i.imgur.com/CSSmtRH.png
you can literally plug this into wolfram alpha to find what a and b are
dull dirge
you can literally plug this into wolfram alpha to find what a and b are
<@&286206848099549185>
dull dirge
wait what is this?
dull dirge
no but the way ur writing in wolfram
solar swift
the int stuff is latex but the rest is just words
dull dirge
well shit
this absolutely doesnt give me the right answer
could u help me out from the start? i am hopeless at this point
solar swift
depends on what it is tbh
dull dirge
essentially i am doing a model, where i have 675.46cm^2 of surface area (material), and i need to make a curve that gives me the highest maximum, with the volume of revolution from 0-that maximum being 750cm^3. The y intercept is fixed at 5.2231.
so what i did is make 3 equations
and im adjusting a and b to get the highest r, but they need to follow the two equations so the parameters are followed
this is a drawing i made of it
if u want the bigger picture, I have to model a wine jug, where 750ml of wine has the biggest surface area touching air, where i have 675.46cm^2 of glass for the bottom part
solar swift
yeah ngl i dont really know revolution stuff, it doesnt get taught until 3rd year uni where i live
dull dirge
the revolution stuff is chill, idk how to do the optimization
its just 2 equations
<@&286206848099549185>
solar swift
https://i.imgur.com/6UGNGko.png
you didnt square f
solar swift
yeah i mean i check wolframalpha for the first one and the a,b values never make the SA equation equal to what you want
i think it might either be the curve of the interval points
dull dirge
yeah
im fucked
theres no way im gonna solve this
i dont even know how i could possibly create an equation for r out of this
cos thats what i need really
a way to express r that incorporates the volume and SA
solar swift
also the r equation is wrong
dull dirge
wym how
solar swift
nvm no it isnt
dull dirge
<@&286206848099549185>
coarse yacht
What can I do for you?
dull dirge
hey
I'm working on an optimization question, where I am trying to find the optimal quadratic maximizing the y component of the maximum, with 2 parameters
The surface area of the solid of revolution = 675.46cm^2, and the volume of revolution from 0-maximum =750cm^3
The y intercept must = 5.2231
i did a fancy illustration
i can show u what ive done already
i somehow need to combine these i think, though im not really sure
@coarse yacht u got any idea?
coarse yacht
https://i.imgur.com/f4uHf3B.png
I would advise to compute this integral
In function of a and b
coarse yacht
https://i.imgur.com/yExl4gf.png
And plug it here
coarse yacht
https://i.imgur.com/Ip7zmGT.png
You can express $ax^2 + bx + c $ using $r$ in the canonical form
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black_couscous
coarse yacht
Yes
coarse yacht
You know you can express it that way $y = (x- \frac{b}{2a})^2 + smthg$
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black_couscous
dull dirge
really?
soft zealotBOT
black_couscous
dull dirge
wait but how would i find that lol
coarse yacht
wait but how would i find that lol
$(b/2a)^{2}= r +5,2231$
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black_couscous
dull dirge
okay, now that i have that how can i incorporate the other 2 eqns?
coarse yacht
Yup
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lawl
coarse yacht
You can express b/2a as a function of r
coarse yacht
**black\_couscous**
Here
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lawl
dull dirge
@coarse yacht can u explain pls
coarse yacht
Yes
coarse yacht
Yes
dull dirge
ok i will try
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@dull dirge Has your question been resolved?
tranquil pine
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tranquil pine
I got the first part
But not sure how to do the second one without multiplying and making the factors of f(x)
Is there some other approach?
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@tranquil pine Has your question been resolved?
grim nebula
@tranquil pine possibly symmetry?
you know f is symmetric in x=6
so the roots should add to that maybe
,w (x-1)(x-3)(x-5)(x-7)+15=0
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grim nebula
void crest
twerk
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tranquil pine
.close
gleaming mantle
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gleaming mantle
Need help with b
cold gorge
Anything you've tried
thorny tendon
@gleaming mantle ^
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@gleaming mantle Has your question been resolved?
dull orchid
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dull orchid
ak is ksin(1/k)
so how is the limt of ak =1 as k goes to inf?
cuz it woul be inf *0
vital crag
where's the question
vital crag
so how is the limt of ak =1 as k goes to inf?
are you just trying to show each term converges?
instead of the series?
dull orchid
where's the question
vital crag
cuz it woul be inf *0
that's indeterminate form. you should have learned something about l'hopital or something else
dull orchid
that's indeterminate form. you should have learned something about l'hopital or ...
oh right i totaly forgot about lhopital xd
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@dull orchid Has your question been resolved?
solid lance
I need help with my math. So the topic is, Finding the equation of a quadratic function. How to find the quotation of a quadratic function given: (a) table of value, (b) graph, (c) zeros; y= ax² + bx + c, is determined by 3 points. Point is named by its ordered pair (x,y). Find the value of a,b and c. To get the answer substitute 3 ordered pairs (x,y) in y=ax²+ bx + c.
I've already got the a and c now I can't get the value of b
final saddleBOT
I need help with my math. So the topic is, Finding the equation of a quadratic f...
solid lance
final tangle
show work
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limpid orchid
Can you ask more clearly
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@outer storm Has your question been resolved?
lime bison
oh hey its you again!
placid bobcat
these would be θ/2 as well
limpid orchid
Use trig only for right triangles
placid bobcat
you have to find the base and height values for the area right
so you use the shaded right triangle and find those values using trigonometry
you have to have a right triangle to write those things you know
yeh sorry but i was just trying to say you have to use the same right triangle for the second case as well
so it would be θ/2 only
can u tell me the length of red line?
are you sure
ah yeh
no no
first
before using trigonometry u need to have a right triangle
can you outline the right triangle on it?
right
now do you see what x is
yep
similarly the perpendicular would be rsin(θ/2)
now is it fine?
i get that but
that second triangle you wont have cosθ and sinθ right
those would be cosθ/2 and sinθ/2 no
ah its fine then i will stop
dull dirge
im bacl
dull dirge
i got a problem
where this turns into 0...
which idk i think it should be impossible
or better said i have to do simultaneous eqn of these 3 things
<@&286206848099549185>
<@&286206848099549185>
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@dull dirge Has your question been resolved?
dull dirge
<@&286206848099549185>
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.close
trail osprey
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vestal frigate
,rccw
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