claimed it lol sorry
#help-0
wheat saffron
proud mortar
Sorry
wheat saffron
its fin e
Provide a trigonometric equation. Considering only the space between š„ = 0 ššš 2š, the
equation must only have solutions at š„ = 1 and š„ = 2. Explain your thought process and
the work you did to create the equation. You may round decimal values to 3 places.
I've tried using desmos just to visualize what equation works but i cant find anything as changing the variables of a transformed sin function or cosine function allows me to just have zeros at x=1 and x=2
midnight wharf
@wheat saffron you can try solving for it
er i mean
you can write your guess equation like
A cos(k x + phi) = 0
this should be true with x = 1 or 2
then you can solve for the "unknowns" in your guesses - the variables A, k, and phi
you could also put the guess equation in desmos to see how it works
wheat saffron
thanks i will try it
ornate schooner
is it acceptable to rewrite $\lim{x \to 2^+} e^{3/(2-x)}$ as $e^{\lim{x \to 2^+} 3/(2-x)}$
ornate schooner
is it acceptable to rewrite $\lim_{x \to 2^+} e^{3/(2-x)}$ as $e^{\lim_{x \to 2^+} 3/(2-x)}$
ocean sealBOT
Noah
ornate schooner
guess latex doesnt wanna format it correctly
but yeah, question still stands. is there a property in which a limit can be moved to the power
limber widget
$$\lim_{x\to2^+} e^{3 / (2 - x)} = e^{\lim_{x\to2^+} 3/(2 - x)}$$
ornate schooner
kekw
limber widget
puts on glasses Oh actually it did, it did the inline notation
Also:
I'm 80% sure that it's correct to do that, but I'm currently trying to see if I can track down justification for it
I recall doing it in school, at least
ornate schooner
I know the limit evaluates to 0, I'm just struggling to understand how to justify this. Currently I'm doing something like:
Let k = 3/(2-x)
Since lim_(x->2^+) (3/(2-x) = -inf, the original limit can be rewritten as
lim_(k-> -inf) (e^k) = 0
oh, yeah so i just did a google search. apparently that's similar to how some dude on math exchange solved it
I don't think the multiplication by 2 really matters here lol
limber widget
Let me see how I remember...
The way we did this I believe is to set your limit equal to something, say L. We then take the log of both sides. Giving you $log(L) = \lim_{x -> 2^+} \frac{3}{2 - x}$
You then solve the limit, and then solve for L.
Your way should be equivalent, though.
ocean sealBOT
SpiderString
ornate schooner
yeah it seems about the same. I appreciate the help š
viral loom
How do i make :
a^4 - 7a^2 + 2ab - 10a + 2b^2 - 16b + 56 as sum of squares ?
lone heartBOT
@viral loom Has your question been resolved?
vital grove
IF h=12 and p= 45 and b=66 then what is the value of 4h/p x 78p/h / bb
vital grove
Anyone here to solve??
jagged cobalt
i dont get what the last part is meant to be, brackets save lives
but this seems like a simple sub in the numbers no?
vital grove
Yh but somehow my book answer and my answer is not matching
tacit arch
Yh but somehow my book answer and my answer is not matching
Show your answer and the book answer
fresh wedge
there may be some mistake
Maybe show your original question, without brackets it's difficult to understand the substitution
vital grove
its 4h divided by p mutiplied by 78p divided by h and also divided by bb means b x b
fresh wedge
its 4h divided by p mutiplied by 78p divided by h and also divided by bb means b...
(4h/p) x (78p/h)/bxb
Is this correct?
lusty token
My answer is 78 and book answer is 75
hmmm you sure you copied the question correctly? 75 doesn't make sense given the numbers
vital grove
may my book has got mistaked
lusty token
not very likely
vital grove
This is the answer i got
fresh wedge
lusty token
This is the answer i got
the x for multiplication confuses calculators
you need to be precise in your typing
usually * is used instead
vital grove
lusty token
it also confuses us, so it'd be great if you could use that too
oh you actually meant x
vital grove
yh wht did i typed then
vital grove
bro i am new here i dont know wht to dooo
lusty token
consider ((4h)/(px * 78p))/(h/(bb)) instead
fresh wedge
No worries @vital grove , from next time just paste a screenshot of your original question
vital grove
ok
vital grove
then is it a correct answer
lusty token
that's a very odd answer though
vital grove
Gauth ai is telling that
lusty token
i doubt it's interpreting it correctly, i don't see why a textbook would give that as an answer
vital grove
ok then i am going for my school its late now
i will ask with my teacher
thank everyone
.close
lone heartBOT
lone heartBOT
Available help channel!
chilly zephyr
Can somebody explain pythagoras theorem
lone heartBOT
Can somebody explain pythagoras theorem
chilly zephyr
:/
ocean sealBOT
wtr.on
chilly zephyr
This
Idk how to find e value like I found the hypotenuse of the triangle with the values given which is 106
limpid heart
chilly zephyr
Arent both the sides the same
Can you tell the answer I'll understand from it
Yes
Idk š
Ohh
Alright
Is the answer 9.4
I don't got a pic but it's like this
4Ā²+eĀ²=106
16+eĀ²=106
eĀ²=106-16
eĀ²=90
And then you just use square root
Oh no worries
Ohh
Don't we already have the base for thw triangle?
Ohhh
Tysm
Wait what
Wait wdym
Alright I understand
Tysm
orchid gate
Hey so I have this question right
lone heartBOT
Hey so I have this question right
orchid gate
i multiplied by (a^2-ax) and by 4(a-x)
orchid gate
Hey so I have this question right
ignore the extra + in the middle my bad on that
orchid gate
i multiplied by (a^2-ax) and by 4(a-x)
ended up with
from here i got to
no clue what to do from this point
verbal blaze
shouldn't that be (4a+x) Ā· 4(a-x) = ...?
fair parcel
nono
orchid gate
shouldn't that be `(4a+x) Ā· 4(a-x) = ...`?
??
i just separated the steps of multiplying the denominator
orchid gate
and i ended up with this
which idk what I can do with as if i try to root it, then the equation breaks right
cuz at this point on the second half (xa^2 - ax^2) only the a and x are squared and not the first number
ie its x*(a^2) - a*(x^2) so i cant root
verbal blaze
you have 4(a+x), not (4a+x)
orchid gate
you have `4(a+x)`, not `(4a+x)`
quick question about what i wrote
when i have something like xa^2 only the a is squared
IE i cant connect these two right?
verbal blaze
IE i cant connect these two right?
you can factor out a ax from both terms
or, what would be better is to move them to the LHS of the equation, and get a quadratic ...x^2 + ...x + ... = 0
orchid gate
or, what would be better is to move them to the LHS of the equation, and get a q...
but i have here like 6 different things
a's on their own, squared a's, (same for x's) and ax^2 and xa^2
which was my question
they're not interchangeable or are they
(this specifically: ax^2 and xa^2)
verbal blaze
pick one, doesn't matter, and make a quadratic in terms of it.#
e.g. (...) x^2 + (...) x + (...) = 0 for a quadratic in terms of x.
orchid gate
i understand what you mean but i dont see how it can be done here
orchid gate
but i have here like 6 different things
due to this
verbal blaze
what do you have when you put all terms on the LHS?
orchid gate
right but i still have 5 different parameters
verbal blaze
so you can refactor it into a quadratic
verbal blaze
right but i still have 5 different parameters
yep
2 terms: ax + bx
1 term: (a+b) x
you need to refactor it into a quadratic
orchid gate
you need to refactor it into a quadratic
which i've tried doing 20 times
I dont know how
in this specific case
verbal blaze
what are the x^2 terms?
what are the x terms?
what are the constant terms?
orchid gate
this is the closest i could get
verbal blaze
you can reorder the terms
verbal blaze
hint:
ax^2 + 3a + 2x^2 = ax^2 + 2x^2 + 3a = (a+2) x^2 + 3a
orchid gate
hint:
`ax^2 + 3a + 2x^2 = ax^2 + 2x^2 + 3a = (a+2) x^2 + 3a`
all good mate i moved to the next one its fine
wicked tree
lone heartBOT
wicked tree
So I know I can do x'=concentration(in)rate(in) - concentration(out)rate(out), with concentration(out) equalling x/volume, then plugging in volume from v=volume(initial)+(rate(in)-rate(out))*t
finding an integration factor, multipling then dividing by it etc etc
then plugging in x(0) = 0 with the formula I found to find C
but then, I assume that will give me the formula for the amount of plutonium itself, not its concentration?
so can I just divide that whole formula by 2000 to get the formula for concentration?
vale crag
So I know I can do x'=concentration(in)rate(in) - concentration(out)rate(out), w...
well the volume isn't constant as you noted here
so no you don't just divide by 2000
wicked tree
so where does 2000 enter the equation?
vale crag
v=volume(initial)+(rate(in)-rate(out))*t
what do you think the initial volume of water is
@wicked tree
vale crag
not by itself no
vale crag
so can I just divide that whole formula by 2000 to get the formula for concentra...
what I'm saying is that the volume isn't constant, so just saying "oh yeah the concentration is x(t)/2000" is incorrect
if anything it's x(t)/v(t) whatever the volume ends up being
and v(t) isn't 2000 for all t
wicked tree
hmm, so how do I find v(t)?
vale crag
v=volume(initial)+(rate(in)-rate(out))*t you just wrote the equation right here
just plug in the numbers
wicked tree
v=2000+(4-2)t=2000+2t
vale crag
yeah
wicked tree
then I do all the integration stuff for x(t) and then divide that by 2000+2t
vale crag
yes
wicked tree
I guess that makes sense
feels weird dividing formulas like that lol
but alright ill just do that then, thx
vale crag
you can keep the channel open if you want your work checked afterwards
dawn quail
lone heartBOT
dawn quail
I am confused with row 9 the conditional proof
Itās saying take the first statement and imply that to the 8th statement
Why are we allowed to just put an arrow between both statements like that?
If we are allowed to do that couldnāt we do it at any row? Row 1 implies row 7 for example
lusty token
so basically, we're assuming statement 1 is true right?
given that statement 1 is true, we know that statement 8 is true
dawn quail
Yes we are assuming all statements are true
lusty token
thus 1 implies 8
dawn quail
But with that logic canāt we say row 1 implies row 2 implies row 3 etc etc
lusty token
you can
dawn quail
Just keep going down in any order and with any statement
Wth lol
Thatās so weird
I thought proof is about extracting true statements
Equivalency is comparing two expressions for being the same
Each of these rows is a single statement that is true from the original expression
So any row above can imply any row below?
lusty token
But with that logic canāt we say row 1 implies row 2 implies row 3 etc etc
1 implies 2 implies 3
by hypothetical syllogism
1 implies 3
dawn quail
Hmmm
So thatās the idea with proof
Each step is implication
Thatās always how proof works?
lusty token
pretty much, given premise is true, some statement is true
if premise isn't true, who cares about the statement
dawn quail
I thought we are just taking true statements from expression but not necessarily in relationship to one another
What if we have two expressions using equality?
lusty token
I thought we are just taking true statements from expression but not necessarily...
you have to assume some statement is true, this is your hypothesis or premise
but assuming this is itself an implication, rather, any result you obtain is implied by the premise
dawn quail
What if we have two expressions using equality?
We can take statements from both expressions and use them simultaneously in same chart for proof?
high cargo
Thatās always how proof works?
You can also introduce assumptions and disprove them to show theyāre false
But youāll learn about that some point later if you havenāt already
dawn quail
How do you know where to begin with the very first step: assumption
Just trial and error?
lusty token
usually given
dawn quail
usually given
So this one why did they start with row 1
lusty token
i don't know where they got the first statement
lusty token
it'd be kind of weird to find the assumption?
dawn quail
This is uni first year discrete math for me btw
lusty token
cuz you can just assume the result
dawn quail
Yeah exactly, this example is proving tautology
Always true
So maybe thatās why he started at answer and worked backwards for first assumption
I believe just using de Morganās law to go backwards if Iām not mistaken
lusty token
why would you have to go backwards?
lusty token
are you trying to prove biimplication?
dawn quail
You were saying you donāt know how they got assumption, Iām saying itās working backwards from answer
Prove tautology
lusty token
that doesn't make sense as a proof, they're in order
dawn quail
are you trying to prove biimplication?
Not sure if thatās same thing as tautology for proof
lusty token
tautology is a statement that is always true
dawn quail
They are in order yes, one sec lemme send video
This will explain it better, how the first step was derived
lusty token
yup im wrong it's just true
dawn quail
yup im wrong it's just true
So for that first assumption
Row 1
Do you absolutely need to start there? To show this proof
Or could you start at a completely different assumption and still get same result in the end
lusty token
I guess you can just take contrapositive and start with a different assumption if u wanted to
dawn quail
Thatās where I am confused the most. Where or how to find the very first assumption
Assumption feels like bad idea with math, but i guess I have to remind myself itās human assumption and only for proof, not Computer assumption
Computers cannot make assumptions
(Maybe AI is changing that now tho)
lusty token
I think I sort of get it
you're assuming A then proving A implies B, this statement, A implies B is always true, then you can manipulate A implies B and still get a statement that is always true
dawn quail
Oh because A being true can never imply B to be false
Is that the idea here?
So we know with A being true there is only one true statement for B. It also must be true to satisfy implication
lusty token
assume A is true, then it proves B is true, thus B is true if A true, or A -> B
lusty token
Oh because A being true can never imply B to be false
i guess so
dawn quail
assume A is true, then it proves B is true, thus B is true if A true, or A -> B
We can also get so many more statements from this too
Contrapositive
Or material implication
lusty token
yea, very cool indeed
dawn quail
We can manipulate until we get it to where we need it
Kinda crazy
But also overwhelming if a lot going on
Trying to find like a needle in a haystack sometimes
lusty token
for sure
dawn quail
But at least there are many ways to solve a proof so maybe there are many assumptions that can be made a lot of times too
Depends on the expression I guess
Hopefully first year they will not make them super complicated
lusty token
i think condition proof u just want to get the tautology to an implication cuz then you can make an assumption
dawn quail
Computers are so much better at this lol, we are like 0.000001 MHz processor single threaded
lusty token
yea we operate at 10 Hz
lusty token
daily dose of the overclocking juice
dawn quail
I feel like we are living through the birth of an evolution thoughā¦ especially with web and AI.. maybe it felt like in the 50s with ENIAC and whatnot too. I know itās a bit off topic to original question, but dang who know what our clock cycle will be in another 100 years
Prob the exact same 10 Hz but āriced outā as the modding community puts it
I mean.. single celled organism > fish > monkey > reptile it just makes sense it will keep growing, but it kinda feels like we are on the cusp of speeding up the process from the million year pathways of nature in some ways
Haha this discrete math has got me thinking all philosophical now, which is what the Greeks were all about, still using their philosophy terms
Alright I will close this now
.close
lone heartBOT
lone heartBOT
Available help channel!
fleet dagger
Is it reasonable to assume you can gain a "sense" for trigonometry like you can with other fields of mathematics? I struggle to remember alot of the identities (I am in calculus 2).
fleet dagger
If anyone has any tips for studying or has an intuitive way to think about trig and its trig functions that would be super appreciated.
remote heron
most all of the identities can be derived from scratch without too much trouble
so if you are worried to not remember something, its possible to convince yourself on the fly provided you remember some base identities from which to work
alternatively there are pretty powerful mnemonics for trig
for example
fleet dagger
Which base identities should i try to remember?
remote heron
pythagorean, sum and difference for sure
shift identities are obvious and sometimes helpful
fleet dagger
https://www.mathsisfun.com/algebra/trig-magic-hexagon.html
Oh wow that is pretty clever
remote heron
sum and difference gets you very many
fleet dagger
What about trig derivatives and integrals? Is there any good way to remember those?
remote heron
honestly that might be all id remember
remote heron
What about trig derivatives and integrals? Is there any good way to remember tho...
im not aware of anything fantastic unfortunately
im sure it exists
fleet dagger
Ah thats okay, I'll keep looking arround. Thank you!
remote heron
i think being aware of the techniques is pretty powerful
like power of sine integrals, power of cosine integrals
when to use trig sub, inverse trig sub
etc
fleet dagger
Power of sine?
remote heron
im not aware of anything like the magic hexagon though
yea like $I_n := \int \sin ^n x \dd x$
ocean sealBOT
jan Niku
fleet dagger
Ah okay
remote heron
or sometimes people look at ones like $I_{m,n} := \int \sin ^n (x) \cos ^m (x) \dd x$
or things like that
ocean sealBOT
jan Niku
remote heron
you can sometimes work these out in general
but just knowing how theyre approached is pretty good IMHo
fleet dagger
Trig substitution is probably the thing I am struggling with the most right now. Do you have any resources or videos i could watch to help me gain a better intuition when it comes to trig substitution? Practice problems would be great too if you know where I could find some.
remote heron
I'm in love with this guy, michel van biezen
here is one of his playlists
i love his format of short, results focused videos
but you may find some other format more helpful
fleet dagger
Hmm okay I'll check out his stuff, thanks.
lone heartBOT
Available help channel!
lavish smelt
I need help figuring this one out please
lone heartBOT
I need help figuring this one out please
knotty schooner
uhh i kinda forgot how this works but
the filled circle means its closed
so its more "defined"? meaning you use the [] bracket
lavish smelt
yes
knotty schooner
hollow circles are open so it would be ()
you would go from left to right for domain
wait
its whatever was less to more
lavish smelt
its whatever was less to more
isn't that for the range?
lavish smelt
yea
knotty schooner
im kind of rusty but im PRETTY sure you take the highest value for the range in this
because theres no defined point, you would use )
lavish smelt
I need to find both the range and domain for this problem
i would have assumed the domain is (-infi,2]
but its wrong
sharp trail
uhh i kinda forgot how this works but
the domain is the lowest to highest points of a line on the horizontal axis
the range is the lowest to highest point of a line on the vertical axis
For this problem.
The line to the left goes towards -x indefinitely while ending at a x of 2 however that is a hole making it (-infiinty, 2)
The range would be [-5, 4] because the lowest value gets to -5 with a close hole therefore inclusive and it goes to 4
oh shoot i replied to wrong person
lavish smelt
i got the domain correct but the range is not
lavish smelt
[-5,4]
lavish smelt
shouldn't it be correct since those are the lowest and highest points?
knotty schooner
it should but
4 isnt defined
as a closed point
closed point would mean it literally is 4 on the graph
lavish smelt
so it should be 2?
knotty schooner
what no
sharp trail
so it should be 2?
your either choices are 4) or 4] lol
lavish smelt
your either choices are 4) or 4] lol
both options didnt work
lavish smelt
lavish smelt
im going to need to try another problem now
sharp trail
its right
its infinite
the arrow on the left side of the graph
is always going up
knotty schooner
oh lol
sharp trail
so it can go above the 4
lavish smelt
this is the new graph
sharp trail
this is the new graph
is the left side of the graph an arrow or a close point?
lavish smelt
so domain is (-infi,3)
lavish smelt
is the left side of the graph an arrow or a close point?
arrow
sharp trail
ok
sharp trail
so domain is (-infi,3)
yep sounds right
sharp trail
nope
sharp trail
and range [-5,infi)?
look at very bottom point, is it a closed hole or open hole
lavish smelt
open
sharp trail
you should use a parantheses
because it means
it doesnt include the -5
it just goes down to -5
so (-5, infi)
lavish smelt
correct thanks
sharp trail
np
lavish smelt
this one just broke my brain
sharp trail
this one just broke my brain
Ah, some functions create graphs with asymptotes. That just means that the lines dont connect/are not continuous together.
Basically, look at them as different lines
and combine them with U which means union
lavish smelt
how do i figure out the interval notation tho?
lavish smelt
ok
lavish smelt
ok
sharp trail
where does that line start from
lavish smelt
no sure because it seems to be continuous
sharp trail
well when it doesnt end. it would mean (-infi
lavish smelt
ok
sharp trail
most lines approach the asymptote but it never reaches it
so its kind of like a open hole
lavish smelt
the other end of the line seems to be reaching towards -10 but it isnt for certain
sharp trail
the other end of the line seems to be reaching towards -10 but it isnt for certa...
do domain first not range
lavish smelt
so -2?
sharp trail
nop
it approaches 0
thats where the asymptote is at
so it would be
(-infinity, 0)
lavish smelt
ahhh your right
i was thinking of the x-axis
so then for the other part of the interval notation i would need to find the range?
lavish smelt
ah
lavish smelt
didnt we just do the left side and it was (-infi,0)
sharp trail
ye
so, so far we have domain = (-infi, 0) U ???
we gotta find the ??? which is the other part of the domain
sharp trail
it appears so
lavish smelt
now i need to find the range of K
sharp trail
yep
lavish smelt
ahhh ok isee where this is going
sharp trail
now i need to find the range of K
just to make sure, did you get the domain as (-infi, 0) U (0, infi)
lavish smelt
yes its correct
sharp trail
good
lavish smelt
we do lowest to highest or highest to lowest? for range
sharp trail
lowest to highest
lavish smelt
ok walk me through this
sharp trail
ok walk me through this
do you see a horizontal asymptote that separates the lines apart
lavish smelt
yes
sharp trail
where
lavish smelt
in the middle
sharp trail
nuh uh
lavish smelt
the red line im assuming no?
lavish smelt
ok
sharp trail
do you see a horizontal asymptote that separates the lines apart
let me rephrase this
do you see a y value where there wont be an x value
lavish smelt
yes i guess based on assumption
because i cant scroll down or up on the graph so it cant be for certain
sharp trail
true, since it doesnt really say lets say no and make them infinite
lavish smelt
ok
sharp trail
or is it -infi
this is right
lavish smelt
ok
sharp trail
now you know that, whats the highest y value the graph goes up to
lavish smelt
also -infi
lavish smelt
2?
sharp trail
no it owuld be infinity
lavish smelt
ok
lavish smelt
ahhh ok
sharp trail
lavish smelt
so (-infi,infi)
sharp trail
see it goes up forever
sharp trail
so (-infi,infi)
yes
lavish smelt
yes i got it thanks
fervent lichen
lone heartBOT
low ermine
if i got a question do i sent it here?
low ermine
okok
fervent lichen
I tried doing it, may anyone tell me if there is anything correct in it
Sorry for bad english
lone heartBOT
@fervent lichen Has your question been resolved?
fervent lichen
Anyone?
lone heartBOT
@fervent lichen Has your question been resolved?
proud zealot
the question is from 1962, has math changed since then?
lone heartBOT
@fervent lichen Has your question been resolved?
fervent lichen
the question is from 1962, has math changed since then?
I dont know what answer you want...
proud zealot
such task cannot be solved by the rules of mathematics that we know today
fervent lichen
Why?
lilac jolt
convert the equation of an ellipse into standard form: x^2 + 2x + 100yĀ² - 1000y + 2401 = 0
lone heartBOT
convert the equation of an ellipse into standard form: x^2 + 2x + 100yĀ² - 1000y ...
lilac jolt
i have
((x+1)Ā²/100) + ((y-5)^2) = 1
is that correct
$\frac{(x+1)^2}{100} + \frac{(y-5)^2}{1} = 1$
ocean sealBOT
sterling
alpine sable
you can check if it is correct by simply calculating the squares and simplifying
if the expression you get is the same to the initial expression then is correct
as long you followed the method of completing the square it should be correct
lone heartBOT
@lilac jolt Has your question been resolved?
deft ledge
you can check if it is correct by simply calculating the squares and simplifying
if the expression you get is the same to the initial expression then is correct
as long you followed the method of completing the square it should be correct
alpine sable
you can check if it is correct by simply calculating the squares and simplifying...
lol wtf
alpine sable
you can check if it is correct by simply calculating the squares and simplifying...
you just copied what I said
alpine sable
you can check if it is correct by simply calculating the squares and simplifying...
why?
deft ledge
why?
Because it was good advice
And clearly needed to be reiterated
Because OP did not read it
alpine sable
ok (my english writing is not that bad then lol)
deft ledge
No worries, what you said made sense
lone heartBOT
@lilac jolt Has your question been resolved?
lilac jolt
sorry, I was giving the bot the x reaction so it doesn't close yet ToT
but yes, thank you
my problem is
is that my answer doesn't match the answer of wolfram alpha
idk how u use the command for wolfram here
lone heartBOT
@lilac jolt Has your question been resolved?
pseudo ice
idk how u use the command for wolfram here
,w e^pi
ocean sealBOT
pseudo ice
Put whatever you want after the ,w
indigo anchor
hey lol i need someone to explain the explanation
lone heartBOT
hey lol i need someone to explain the explanation
indigo anchor
so i understand the f'(x) = 0 , < 0 , > 0 stuff
but from that i dont understand how they got the derivative graph
uneven isle
but from that i dont understand how they got the derivative graph
it kinda is just 'looking' at it, we will go through graph a as an example
we know the turning point (stationary point), so f'(x) will = 0 at that point
we know its decreasing for x<3, so it will be negative gradient = negative in derivative graph
we know its increasing for x>3, which is positive gradient = positive in derivative graph
indigo anchor
yup
uneven isle
as in why its a straight line
i think its bad practise for the textbook to not actually include the function since a lot of functions might look parabolic
but it seems they just assumed you will treat the graph (a) as a parabola
indigo anchor
ahh i think i get that
uneven isle
which takes form of ax^2
the derivative of that will be a straight line
for the second graph
indigo anchor
so its increasing after 3 and decreasing before 3
uneven isle
yep
indigo anchor
ok yeah
im just a bit stuck on the single line one
ok so its just constantly positive
so always above the axis ok i get it
thank you
.close
lone heartBOT
uneven isle
im just a bit stuck on the single line one
for that one
if you think about a straight line of the form y=mx+b
we know the derivative of gradienti s just m
regardless of what value x is
so the derivative is constant value
which means its just y = m for all values of x for the derivative
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safe vine
can anyone help me do simultaneous of these three equations? i can rewrite in terms of a but im not sure how to get rid of the rest of the constants
white marsh
can anyone help me do simultaneous of these three equations? i can rewrite in te...
try sin(A+B), I don't think there's anything else you can do (at least to proceed). rigorous calculations though
white marsh
wdym take out -a
white marsh
there is no way to factor out anything from these equations
lone heartBOT
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devout helm
Why is 3150000 the nearest million 3000000
lone heartBOT
Why is 3150000 the nearest million 3000000
hushed locust
maybe you left out a 0?
prime badge
makes sense
hushed locust
round to the nearest million means that everything after the millions place should be 0
devout helm
So for 2539836000 the nearest million is 254 0000000
hushed locust
yes
devout helm
Ok thanks bro
raw jetty
is there a polyhydron where its made with 12 triangles and 8 squares that are identical?
raw jetty
it came out in an exam yesterday and i want to know whats its called
or maybe its 12 squares and 8 triangles idr
the thing is, it was named a "cuboctahedron" in the exam but that thing has 8 triangles and 6 squares
white marsh
have heard 6 squares and 8 triangles (cuboctahedron). maybe there is some nomenclature that you can name all the polyhedrons I am not sure
raw jetty
huh ok i remember copying the drawing and when i looked at it again it was a cuboctahedron, wierd
.close maybe my teacher swapped it with verticies and edges
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fossil pelican
a
lone heartBOT
a
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
@fossil pelican Has your question been resolved?
dusk moth
ive been trying to solve this thing where i need to find their intersection points, theres a rule that it cant be negative but it keeps coming out negative on my end.
Had to use only elimination method on this one. what am i doing wrong
ocean whale
,rotate
ocean sealBOT
ocean whale
ive been trying to solve this thing where i need to find their intersection poi...
Who said it can't be negative?
I think you misheard something
dusk moth
ocean whale
I'm not sure what a decision variable is but you can have negative solutions. The intersection is where the two lines meet, so are you saying that line can only intersect in quadrant 1?
Because that's where the values are only positive
charred jewel
!xy
lone heartBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
ocean whale
i tried putting it up in desmos to graph it out and it does show negative too
Yes the intersection can be negative as I stated
I think you should ask your teacher on what they meant by decision variable
Because I'm not sure what that means
But you can have negative solutions
As I mentioned, the intersection is where the two lines meet, and what you are saying, it's only bounded in quadrant 1 which is not true, it has 3 other quadrants that it can be in
dusk moth
yea i might have misunderstood the rules and such. ill redo it maybe it would help
Thanks!
oh wait im an idiot
i messed up the givens
its supposed to be 18 and not 8
.close
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devout helm
Why is this a minimum point plus I need help with qn 5b (ii)
charred jewel
Why is this a minimum point plus I need help with qn 5b (ii)
is the xĀ² term positive or negative
devout helm
Positive
charred jewel
do you know what a positive quadratic graph looks like?
devout helm
No
mossy jasper
Alternatively, if you don't know the shape of the graph, you can differentiate it twice, if d^2y/dx^2 >0 then you have a minimum
devout helm
Thatās a minimum point right?
charred jewel
yes
devout helm
Since the curve is at the bottom
mossy jasper
if d^2y/dx^2 < 0, you have a maximum, and if it = 0 then it's a POI
devout helm
Why is this a minimum point plus I need help with qn 5b (ii)
But in this case the graph is not quadratic
mossy jasper
?
Okay, so, you know that if you differentiate once, and make it = to 0, you get a stationary point, right?
so dy/dx = 0 is a stationary point
devout helm
Are you using gradient formula?
mossy jasper
No, differentiation, have you not learnt that? If not then yeah I don't know how you're gonna get the 2nd one
devout helm
No, differentiation, have you not learnt that? If not then yeah I don't know how...
I didnāt learn that can you explain to me
mossy jasper
Honestly, if you haven't learnt it then they probably just expected you to plot the graph
devout helm
Honestly, if you haven't learnt it then they probably just expected you to plot ...
Wait how do we identify if the graph is a minimum or maximum point?
mossy jasper
Differentiation's got a lot to it, you're better of waiting for once it's taught
mossy jasper
Wait how do we identify if the graph is a minimum or maximum point?
You can look at the shape of it. So if you plot the graph, look at the points where it changes from going up to down and vice versa
charred jewel
Alternatively, if you don't know the shape of the graph, you can differentiate i...
(i think if u dont know how a quadratic graph looks like you got some problems)
mossy jasper
Tbf, it's (x+4)^2 + 12, that can be a lot harder for people to imagine than just x^2, hence plotting can help with that
devout helm
You can look at the shape of it. So if you plot the graph, look at the points wh...
So are you trying to say that if the graph is ascending, its a miminum point and if its descending its a maximum point?
mossy jasper
no, if it looks like this, it's a minimum, if it looks like the image is flipped upside down, it's a maximum, you probably don't care about POI yet so you can just ignore that for now
devout helm
Tbf, it's (x+4)^2 + 12, that can be a lot harder for people to imagine than just...
Maybe I just have to plot because I donāt think theyāre teaching differentiation anytime soon
charred jewel
Tbf, it's (x+4)^2 + 12, that can be a lot harder for people to imagine than just...
true but if you're just asked if that has a min or max a regular xĀ² suffices
mossy jasper
If I had to put it into words, if you look at the graph from left to right, the minimum is the point at which it goes from going down to going up, and vice versa for maximum
mossy jasper
true but if you're just asked if that has a min or max a regular xĀ² suffices
Yeah that's fair
devout helm
If I had to put it into words, if you look at the graph from left to right, the ...
So if the graph is at the right side going from down to up, itās a minimum point?
mossy jasper
wdym by at the right side?
Okay, how about this, a minimum point looks like a u, a maximum point looks like an n
devout helm
Okay, how about this, a minimum point looks like a u, a maximum point looks like...
But thatās a curve
devout helm
Why is this a minimum point plus I need help with qn 5b (ii)
Iām talking about this
mossy jasper
Yes, and the stationary point is the exact point at which the direction changes
mossy jasper
Iām talking about this
Yes, and Shioshi discussed that earlier
mossy jasper
^
mossy jasper
true but if you're just asked if that has a min or max a regular xĀ² suffices
^
The actual graph of y = (x+4)^2 + 12 is pretty similar to x^2, which, as they showed, x^2 has a minimum
charred jewel
But in this case the graph is not quadratic
?
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Available help channel!
ember mango
any hint to answer this?
lone heartBOT
any hint to answer this?
tight pier
any hint to answer this?
inspect the triangle and try to assign r and h accordingly
to its length
ember mango
inspect the triangle and try to assign r and h accordingly
length^2=r^2+h^2
tight pier
ok good
ember mango
so r^2=length^2-h^2
tight pier
thanks for asking
ember mango
equilateral meaning same side length?
subtle light
yep
tight pier
comon alan you got this almost
ember mango
r^2=h^2-(2r)^2 ?
subtle light
bingo
subtle light
so r^2=length^2-h^2
but itās (2r)^2-h^2=r^2 from what you have here
just rearrange and solve for r^2 and you should be fine
tight pier
you need to solve for r^2
tight pier
just rearrange and solve for r^2 and you should be fine
.
tight pier
nice work
ember mango
.close
ember mango
lone heartBOT
verbal blaze
what's the formula for the area under the ladder?
ember mango
lone heartBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
tight pier
ok bro
left isle
my bad
tight pier
š
verbal blaze
yep
Now, the question is asking you to find the rate of chage in A wrt t, knowing the rate of change in x wrt t.
ocean sealBOT
Shuba
tight pier
why would you use partials btw
verbal blaze
just habit
because, if A is a multivariate function, then you need partial derivatives
makes no difference in your particular case, where A only depends on x
tight pier
I see A = A(x(t)) but sure
ember mango
tight pier
ye
tight pier
ember mango
<:hmmcat:831508801646755850>
do I substitute t to x in this case?
ember mango
sry what deos x(t) mean?
tight pier
the distance x depends on time t
I think x = 1
Basically dA/dt denotes the change in area when x = 1 I think
tight pier
and now i am up
lone heartBOT
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wispy nebula
I'm doing basic fluid dynamics and I struggle to plot streamfunctions when they are in polar coordinates. For example:
wispy nebula
$r = \frac{\psi}{Usin\theta}$
ocean sealBOT
trayan_b
wispy nebula
Psi and U can be anything
I need to plot the whole family of functions
But I notice there's gonna be singularities because of the denominator
Also why is there no fluid dynamics channel?
even if you could help me plot $\frac{1}{sin\theta}$ it would be helpful
ocean sealBOT
trayan_b
zealous ingot
first identify the areas where 1/sin(theta) is not defined, i.e. when sin(theta)=0
lost badger
Also why is there no fluid dynamics channel?
Wouldnāt it be #dynamical-systems ?
zealous ingot
those give you the vertical asymptotes
lavish cave
**trayan\_b**
if you want to plot $r = \frac{k}{\sin \theta}$, just note that $r \sin \theta = k$
so $y = k$
and $k = \frac{\psi}{U}$ in your case
ocean sealBOT
higher's secret twin brother
lavish cave
(r cos theta, r sin theta) if you scale everything here by a factor of r
and yes this is undefined for sin theta = 0 or when theta = k pi, k is an integer
lone heartBOT
@wispy nebula Has your question been resolved?
smoky river
I need help creating a quantitative death curve for wolfs.
For context I am working on a project to model the wolfpopulation in Europe. With different sources I found useful information, such as the lifespan, and so also my domain [0,13].
What I need for the deathcurve is that the area under the curve equals 1(, or is approximately equal) as logically speaking eventually every individual dies once.
Now the difficult part, I want the distribution to begin at a value somewhere between 0 and 1, than at x=6 half of the population died. The minimum shoudl be somewhere between x=0 and x=6, here the wolf is independent and can survive.
I found a graph of this sort for humans in a work from Murray (2011), I added a screenshot of this graph.
Now finally my question, what kind of equation or distribution can I use to create my deathcurve, which has the form of the graph in the screenshot?
lone heartBOT
I need help creating a quantitative death curve for wolfs.
For context I am wor...
@smoky river Has your question been resolved?
smoky river
<@&286206848099549185>
lone heartBOT
@smoky river Has your question been resolved?
tired sail
smoky river
Wrong chat my friend
lone heartBOT
@smoky river Has your question been resolved?
alpine sable
anyone knows about basic logical functions?
rugged schooner
hello
smoky river
<@&286206848099549185>
lone heartBOT
@smoky river Has your question been resolved?
lapis pelican
what is 19 * 2
lone heartBOT
what is 19 * 2
lapis pelican
how
cedar kelp
<@809691997672964096>
And don't ping individual helpers
lapis pelican
bruh why
mint flare
And don't ping individual helpers
tbf it does say in your bio
cedar kelp
it also has some rules
cedar kelp
tbf it does say in your bio
for those whom I am already helping
cedar kelp
how do you get the helper role
lapis pelican
use the generic method or just use a calculator
this is what i got
but my algebra teacher said it was wrong
cedar kelp
,w 19*2
ocean sealBOT
cedar kelp
,calc 19*2
ocean sealBOT
Result:
38
how did you get 38
cedar kelp
,calc 19*2
by using calculator here
cedar kelp
this is what i got
this calculator isn't legit
lapis pelican
my math teacher said to not use calculators or its ceating
cedar kelp
my math teacher said to not use calculators or its ceating
okay then think multiplication as repititive addition
19*2 is 19 added to itself 2 times
so 19+19
=38
cedar kelp
like i need a proof for it
that's how multiplication is defined
lapis pelican
ill post a screen shot of the question
lone heartBOT
@lapis pelican Has your question been resolved?
lapis pelican
<@&286206848099549185>
lone heartBOT
@lapis pelican Has your question been resolved?
lapis pelican
<@&286206848099549185> i need help
lone heartBOT
@lapis pelican Has your question been resolved?
lone heartBOT
@lapis pelican Has your question been resolved?
lone heartBOT
@lapis pelican Has your question been resolved?
spring dawn
Help me in precal I forgot how to solve quadratic equation
lone heartBOT
Help me in precal I forgot how to solve quadratic equation
spring dawn
Wait lemme take a pic of it
spring dawn
Or like complete the square
Yeah but it isn't a complete square
Anyways it's linear equation
manic wyvern
Can you send the pic I'll take a look
alpine sable
solve by how? factoristaion or quadratic formula
spring dawn
So basically quadratic formula it will be written as this wait lemme write it
alpine sable
where are you confused
spring dawn
solve by how? factoristaion or quadratic formula
Can it be solve by factorisation?
alpine sable
let me see
spring dawn
Our teacher made us solve it by quadratic since we thought it wasn't factorable
alpine sable
ig no
spring dawn
And I forgor how to solve quadratic equations
alpine sable
wait i ll show you
spring dawn
Thank you!
And also how to write it in quadratic formula... Like which number do I put... Is it the 3, 2 or -17
spring dawn
Oki thank you
spring dawn
b^2 - 4ac = D (discriminant)
What's a discriminant again šššš
alpine sable
What's a discriminant again šššš
the formula i mentioned
alpine sable
Then we solve the ones inside the radical first right?
do you know how to make perfect square?
spring dawn
Thank you š
spring dawn
let me show you something
Btw where do I solve first?
alpine sable
alpine sable
Btw where do I solve first?
i derived the quadratic formula see
using perfect square
(x+a)^2 identity
spring dawn
Oh
spring dawn
Looks complicated but familiar I think we did this before
spring dawn
you can solve your quadratic using this methood too
Which method is easier in your opinion?
alpine sable
Which method is easier in your opinion?
i prefer perfect square method
alpine sable
Which method is easier in your opinion?
check if it can be factorised
if you are having difficulty then try either perfect square methohd or quadratic formula
spring dawn
check if it can be factorised
if you are having difficulty then try either perf...
Wait
Will the answer be the same w quadratic?
Can you teach me that one too?
alpine sable
Will the answer be the same w quadratic?
Yes bro ofcourse
see above
i derived quadratic formula using perfect square method only
lol
alpine sable
...
spring dawn
I am confused š
alpine sable
I am confused š
where
spring dawn
Oh
spring dawn
where
Can you just help me solve quadratic equation first then I'll try doing the perfect square method after
alpine sable
heres the way using quadratic formula
see
and below is the one for general terms, a,b,c
spring dawn
heres the way using quadratic formula
What do I solve here first tho? -4(3) or (3)(-17)?
alpine sable
What do I solve here first tho? -4(3) or (3)(-17)?
a x b x c = (axb) x c = a x (bxc)
theyre all mutliplied bro
you can solve in any order
alpine sable
solved?
spring dawn
Since idk what to do here
alpine sable
shhow
spring dawn
Idk what to do next š„²
spring dawn
Oki
spring dawn
I don't get how you got that answer š
spring dawn
a+-b = a+b or a-b
I get this part tho
spring dawn
(-1+2root(13))/3 is one ans
Yeah but I don't get how he got that answer
spring dawn
Oh
proven depot
splitting them because denominator is the same
spring dawn
Okay
proven depot
and then you can merge those both
spring dawn
Ok thanks
spring dawn
.close
lone heartBOT
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stuck otter
Hi guys, have a big question abt this mathematical problem, dont rly know to witch kind of math capitol it suppouse to fit.
So the problem is: in isolated square or rectangle by size m*x meters and lays only on x,y axis, on this x,y axis somewhere is a satelite (cant be in a corner), witch can move inside of this area and bounce from "walls", also size of satelit is matter and angel "a" is in range (0deg, equal or bigger then "a" < 360 deg.)
and here is to quesions what i have left with
1.
We have a specified maximum distance D that the satellite can travel. Depending on D, determine
how many different pairs of (d, Ī±) exist, where d ā¤ D denotes the distance traveled by the satellite and Ī±
the angle at which it starts to move, such that the satellite stops exactly in one of the corners
rectangle?
2. We have specified the maximum number of satellite reflections N . Let's assume that the reflection by the corner of the rectangle counts
for two bounces. How many different pairs of (n, Ī±) exist, where n ā¤ N denotes the number of satellite reflections
o the edge of the rectangle and Ī± the angle at which it starts to move, such that the satellite moves exactly n
will the reflections stop just at the corner of the rectangle?
I will be glad for any help or tip/trick how to get what i need to do.
Thanks ā¤ļø
trim plinth
didn't the other person tell you a trick already?