#help-33
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and if you change your minutes its exponential
this is gonna be a differential equation isnt it
yea it's exonential all right, tho i still think using series is our best bet
two things that can either increase or decrease
yea you are probably right
we should say that we always either run it for 4 minutes or start with 2 cows
to make it easy
or we can try including both
but it's a start
ok give me a sec
I divided the two lists and the the longer it gets the closer it gets to two
but the longer it gets the less exact two's I get
If we can get an exact formula or suite converting X baby cows to Y adult cows
then we only have one suite
meaning I can solve the recursive equation
thats fine tho still thank you for trying, do you have an Idea of to whom I can ask?
you can ping helpers
they might know where to start
also maybe re posting your q is a good idea because we kind of clogged the channel

yea good idea 
<@&286206848099549185> Lately I have been interested in converting coding problems into mathematical functions, and this is one of them :
You start with X adult cows and 0 baby cows. Once per minute, for every pair of adult cows, one baby cow will be bred. A baby cow takes 2 minutes to become an adult. So with X starting adult cows, how many of them will there be in Y minutes.
With Z being the final number of adult cows, your equation should only be expressed using X, Y and Z as variables. With f(X, Y) = Z
the code is:
<@&286206848099549185>
OOps


are these ints? just input your sequence of integers to oeis
oeis?
ok let me try this
nope
doesn't work
I THINK I FOUND IT!
@deft apex
this might just work
@deft apex ok I just came back, let me try it out
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was trying to optimise for this using theta = arctan(15/x) - arctan(4/x) as the equation, then solving for x. but this was incorrect
got 15 cuz 15 = (11 + 9) - 4
got 4 cuz 4 = 8 - 4
@vapid nexus Has your question been resolved?
@vapid nexus your equation looks correct
But read the directions. The first blank is expecting theta as a function of x
Also, I didn't do the calculation so I'm not exactly sure how you got 35.38, but that number suggests you used degrees. You should be using radians
@vapid nexus Has your question been resolved?
derivative of arctan(15/x)-arctan(4/x) = (see image)
i set this equal to zero and got x = 7.74596
then plugged this into arctan(15/x)-arctan(4/x) and got that number
where did i go wrong?
@trim quest
If you're going to round to five decimal places, the last digit should actually be 7
But, are you sure you're supposed to round it, instead of the exact value?
not sure
I'd wager you're meant to use exact values. That's usually the case in a math class unless the directions say otherwise
Do you know what the exact value is?
7.74596669241
That's not exact either
How did you get that?
I mean specifically, just back up one step. What did you do to get that number
Yeah, 2sqrt(15) is the exact value
Any decimal is approximate
Do you have a way to input square roots?
yes
Then 2sqrt(15) should work for the bottom one
ok
Oh yeah, that's right
and was it correct to sub 2*15^.5 in for x
There's no reason to do that.
That would get you the angle, but that's not what the first blank is asking for
It wants the function in terms of x
Do you have an actual sqrt symbol you can use?
Like do they provide you with symbols like that?
It is but sometimes programs like this aren't that smart
its worked with this before
so it'd be 19 and 11
Nah 15 and 7, it's like this
The cow's eyes are 4 feet above the ground, the bottom of the screen is 11 feet above the ground
And the screen is 8 feet tall
oh i c
plugged in the new values, and worked smoothly
thanks for the help
.closse
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How do i factor this expression
i believe the question is wrong just leave it or recheck the question
no it is right
or change the 24 to 25
wth bro?
which grade are you in?
?????
I need to learn how to do this
this was given to me by the teacher. I can’t leave it out.
u do know how to factorize at all right?
if u can solve the quadratic substitute the x in the general form with k^3
then solving should give you something if any form is fine
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<@&286206848099549185>
@still temple Has your question been resolved?
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
@still temple Has your question been resolved?
no
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what is the general way of solving these types of (diagonal) determinants?
I would try finding a recurrence relation
interesting
but this is material from second semester and i need to solve these without recurrence relation
you could try solving the first few by hand and checking if you find a pattern
and in the end, 8 is not that bad, you could do it by hand
with row reducing
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thanks
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$16 + 2^x = 2^{x+1}\$
$16 = 2^{x+1} - 2^x\$
$16 = 2^x(2 - 1)\$
$16 = 2^x\$
MellowDramaLlama
I think you can get it from there 🙂
just isolate y and u get y=16
just the same as llama
So what he's saying is this:
Let $y = 2^x$. Then $16 + 2^x = 2^{x+1}$ turns into $16 + y = 2y \implies y = 16$. But $y = 2^x$ so $2^x = 16$.
MellowDramaLlama
it's just using substitution to get rid of the 2^x
which sometimes makes it easier to see 🙂


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completing the square
Yeah okay what have you done so far
excuse the Messines
I'm wondering do I subtract the two fractions or add them
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hey i need some help with chain rule
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Why wont I get the lowpoint in sin(bx), with the formula 1/b * 3pi/2 + 2pi* 1/b
It isnt the lowPOINT, i know, but it should still give me the x-value. The left side of the plus is the first lowpoint and the right is for the period.
With the k I should be able to decide, which lowpoint I want to get if k is element of Z.
Wait a minute.
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Can anyone help me to solve this equation?
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Need some big help lmao
Post your question
Screenshot?
Given is the family of functions fa(x)=3x-a^2*x^3 ( a>0 )
a) Determine the zeros and the extrema of the family depending on a
b) Show that all family functions have a common tangent
t have .
c) determine the locus of high points of the set fa(x)
d) Investigate which family curve fa has a high point with the ordinate y = 4.
e) For which family curve fa applies: The distance from the high point and low point = square root of 5
Its german so yall probably cant read it
functions mmmmm
I only know a bit
^Well
I might be asking this question too yk
yeah
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I did l'hopital's rule and got e/1. Good?
yes
,w plot (e^x-e)/log(x) for 0<x<2
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how did they remove the denominator?
They just multiplied both sides by both denominators
as in
they multiplied both sides by t(3t^2+100)
no problem 👍
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how do i do this question
so if $a$ and $b$ are the roots of $f(x) = x^2 - mx + 2$ what does this tell us about how $f(x)$ factors?
moonside
uhhh not too sure
hmm
like if i tell you a polynomial of degree two has roots 1 and 3
can you tell me the polynomial?
yes
good
now if i tell you a and b are the roots
tell me hte polynomial in terms of a and b
like (x - a)(x - b)
yes
now foil that out and set it equal to what they tell you the polynomial is
and compare the coefficients
so like x^2 -xb - ab - ax?
yes can you simplify it a bit more
there arent like terms???
yes there are
wait hold on
so q = (a + 1/b) (b + 1/a)
so we have ab + 1 + 1 + 1/(ab)
we know that ab = 2
so we have 2 + 1 + 1 + 1/2
4 + 1/2
yes
so 8/2 + 1/2 = 9/2
you jumped some steps lol but yeah
wdym
idk, you went from not understanding how to simplify $(x-a)(x-b) = x^2 -mx + 2$ to solving the problem
moonside
but i guess you only needed that ab = 2
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✅
oh yeah the reason is that
i forgot that the product of 2 roots is -b/ a
so like -b is -m and a is 1
so a + b = m
-m
product of 2 roots is c/a
so 2/1
and then you distributed (a + 1/b) and (b + 1/a)
uh
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Quick question, but what would you give a geometric interpretation to the pair of equations: $x^2+y^2 = 49, z = x$?
kind of confused on the z = x
♡LexQa♡
so it is going to be a circular shape, in the octane z = x
really hard to visualise
but...ellipse?
it cannot have a uniform radius...can it?
oh wait is it like going to be a circle with centre at the origin stretched out diagonally or something?
both of these equations have to be simultaneously true ? or the graphs are to be superimposed
the former
well ig the graph will be of two circles with their planes perpendicular to each other
hm
not sure
apparently the answer is "The ellipse formed by the intersection of the cylinder x^2+y^2=49 and the plane z=x"
not sure how they got to that answer though
oh wait yes that's true
i was imagining x=z to be a line
stupid me
oh dw im still mentally 3 steps behind you with this

and the x^2 + y^2 = 49
will obviously form a cylinder
thought it would be a circle
gotta stay in touch with 3-D
why would it obviously be a cylinder?
because in the x-y plane the eqn will be of a circle but since no info has been given about z therefore the eqn will be true for any value of z the constraints are only on x and y and so you can strech the graph along the y-axis
okay give me a second
visualising 3D is so HARD
so let my ooga booga brain try and understand this, so if we had something of the form x^2+y^2 = 49, z= 3 thats just going to be the plane perpendicular to the z axis at point 3, and it is going to form a circle
now, if you very z with x, meaning z =x, it is not going to be only the plane of z = 3
but multiple planes kind of added up together
because now z can be anything
forget the z=x while visualising the cylinder
i kind of understand why it would be a cylinder
because it is just multiple layers of circles, if u think about it
yes the centre will be (0,0,3)
yes
so that makes sense, but i dont get the ellipse
well we know that since both the equations have to be simultaneously true we'll have to take the common (intersecting) part of both the graphs
intersection point... so the origin?
because z = x is is just some weirdly diagonaled plane and the other is just going to be a cylindar
no it's an ellipse
okay so
i dont really know how to make them simultaneously true in this program
but that looks...funky
also how the hell is that a cylindar haha
you can see the ellipse
it's the common portion
yeah i figured now
3-D diagram yumm
what program is this
i want it
it is math3d.org
just searched like
"3d grapher"
ok thnx
got this
alrighty ty
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Hi guys I badly need help right now, I didn't get to understand at learn our lesson since I was asleep because i slept late doing so many projects, I'm struggling how do I solve this rational function
I have examples here but I forgot how sir did it
Lemme show brb
Here
Can someone mind willingly teach me
Please 🙏
what were you ask to do
unclear image
i can help
Yes please
We were told to answer
this may sound strange, but i use an analogy to explain this
This one
are you familiar with famous war battles? specifically, the battle at the beach of normandy?
d-day, world war 2? it's the opening battle for the movie Saving Private Ryan
okdoke, great
so during that battle, the germans had the land, and the allies were attacking from sea. the germans had the domain
they had the beach
I bet this will sound interesting
the germans had their machine guns and mortars and whatnot as their ranged attacks, trying to take out the allies as the allies tried to land on the beach
well, when you think of the cartesian coordinate, the domain is the left and right directions, like how you'd see a beach. the range is how far you can see or reach
you follow that so far?
Wait, is the land and the domain are the same?
yep
Rightt
so we can look to verify the domain of the first question, B(x) in your assignment
Wait also, you mind telling me what Cartesian coordinate is? Maybe Im familiar with it but not exactly that i know it
Alright alright
ah, ok, sorry, wanted to make sure i wasn't missing anything
No no it's fine, it's actually cool coz Its way easier to understand
so what i like to do first is find the domain. to do that, we're basically verifying if there are any specific numbers that we might plug in for x that won't give a valid number as output
the value of the output would be the range
it's like putting a mortar shell in and firing it
Ohhh
you put in the input, and after it's fired and landed, you can see the range
so for the first problem, B(x), the key thing that i like to keep in mind is that we cannot divide by zero
i do that for all problems like this
right!
we can't even do 0/0
so is there any number that we could plug in for x that would cause us to be dividing by zero?
nice!
yep
EUIRIEKDKK RIGHT
that means that our domain is restricted, 12 is not within our domain
Because i remember sir saying about the LCD
Right!
Also while we're discussing do you mind helping me like teaching me whole showing how the illustration of the solution looks like?
that's why your notes have the "find the domain" bit
They turned off the light so I'm gonna just right it here lol and gonna copy it tomorrow
Right
Oh right! I get it
B(x) = x+12
(-12) (-12)
x = -12?
Ohh Soo B(x) = x+12
(-12) (-12)
x = -12?
that's how we find where our domain is restricted
you'll see that your notes have something similar:
Ohh so therefore -12 is the restricted value?
that bit at the bottom is basically saying that the domain can be any value of x except the restricted value
yep!
if you're ready 🙂
YEP I AM
ok, remember that cartesian coordinate pic i uploaded?
Yep
B(x) = x-6/x+12, let x = 0?
B(0) = 0-6/0+12 ?
yep! i was going to say, you may notice that where the red line passes through the y-axis, x is equal to zero
Ohhh
this is how you find the y-intercept. you just plug in 0 for x
Ohhhhhh
OMG
It's so cool that what you're teaching me is what I actually can somehow understand 😁
Alsoo what's next about the 0-6/0+12?
you're doing the hard part, the learning 🙂 it's good effort!
Also about the 0-6 do I have to put like parenthesis?
Thanks! 😁
Oh rightt
can you see how we can simplify this fraction?
6/12?
yep!
😁
and we can even simplify it further
it's not a mixed fraction, don't worry
is there a number that can go into 6 and also go into 12?
that works, yeah. but you can simplify it even further 🙂
X_X
what number goes into both 3 and 6?
naw, but here, it may help if i provide a visual way to see it
Alright
Oh it's a negative
or, actually, a better way might be:
I prefer this one 😁
lol, okdoke
Sooo 0-6/0+12 = -6/12 = - 2x3/2x2x3
negative sign, but yeah
Oh right
but here we can reduce the fraction
Alrightt
see how there's a 2 in the numerator and a 2 in the denominator?
LCD is lowest common denominator, which is something different, but i think you're thinking the right idea, just using the wrong words
since there's a 2 in both the numerator and a 2 in the denominator, we can just cross each one of those out:
3/6??
you may notice that this means we can also do this with the 3 in the numerator and the 3 in the denominator
Yee
so we do it with those
negative sign 🙂
yep! and remember that graph i posted above, with the red line?
After the -1/1x2 do i have to put -1/2 at last or i can turn it -1/2 immediately instead of -1/1x2?
you can just turn it to -1/2
Alrighttt
if you look at where the red line crosses the y-axis of that graph, what is the value of y?
KSKKSKDKSKKDKEKDJ I'm so happy I managed to understand lol
Wait lemme check again
1/2?
negative sign 🙂
yep!
you wanna try the g(x) in your assignment?
Alsoo about this one, if LCD was not the right name, do you mind telling me what is it?
greatest common factor
So that i could easily explain it to my classmates because, I'm gonna try answering it at the board
OH RIGHT
it's the largest number that can go into each number
Gcf
Righttt
OMG
Now for the other one, I'm gonna do it but can you check if I was right?
i'd love to 🙂
OMG
Alright
Lemme look at it again skkfkdkd
Okay Soo there's g(x) = x-2/2x+1
2x+1
(-2) (-2)
x=-2?
Am I right that -2 is the restriction?
Actually, I'm still a bit confused how did they solved it
so in this case, the denominator is what?
2x+1
and we want to get x by itself, so that we can see what x is equal to, yeah?
Can you also tell me how did they manage to solve like what was in my notes?
0 rifht
I forgot
Is it 0?
2x+1 = 0
that's the right first step 🙂
Ohh right
so what can we do now?
Then (-2) and (-2)?
what do you mean, "Then (-2) and (-2)"?
To be honest im confused how did they solve that in that arrow arrow thing in my notes
it's okay, i can explain what they did
I'm referring to my notes 😅
Yes please
i'll use the problem in your notes to explain it
Wait
Soo in the current problem that i am going to solve, i subtract 1 with the (-2)?
in the notes, the (-5) and (-5) is where the person was subtracting 5 from both sides
Yea
Since my problem is 2x+1, because of the 2 is positive so I'm gonna turn it into negative right?
Ah yesyes
so in your case, what number are we going to subtract from both sides?
2x+1
(-2)(-2)
nope
the 2 is "attached" to the x
2x-2*
just like the 3 is "attached" to the x in the notes
Sooo
but what isn't attached to the x?
1
yep, just like the 5 isn't attached to the x in the problem in the notes
I subtract 2x-2 right Soo it's gonna be only x
nope
in the notes, we basically "moved" the 5 over to the other side, yeah?
i'm afraid not
Wait lemme check
Awss
That's why
What should be the number?
Is it -1?
-2 and -1?
in the 3x + 5 = 0, which number isn't attached to the x?
5
yep!
Where do we move it??
so let's move that to the other side. to do that, we subtract it from both sides
Oh
notice that it was a positive 5 on the left, yeah? so we have to do the opposite function, therefore, subtracting it from both sides
yep!
Righttt
perfect!
2x=-1????
excellent work 🙂
no worries at all, i've done this before, i had to learn it once, too
so now we want to get that x by itself still, yeah?
Oh right
but there's a 3 attached to it
What am I gonna do next?
the function that's happening between the 3 and the x is multiplication, yeah?
Yea
it's "3 times x is equal to -5"
Yee
so we need to do the "opposite" of multiplication with that 3
what's the reverse of multiplication?
Subtract?
one way to get better!
Let me know dkkdkdkkd
lol, to practice
Right right MMDMDKKDKDKS
I just kept forgotting it
Alright soo
What are we gonna do now?
We're gonna use division??
are you guessing?
I mean -1
guessing isn't effort 😉
😅
Was it the -1?
Like, lately we moved it right,
Then it becomes 2x=-1
Oh
Are we gonna move 2x?
To make it like 2x-1?
Am I still wrong?
one sec, in a meeting
Oh sorry sure sure take your time
I think I slowly get it
2x=-1 = 2x/2 = -1/2 ?
2x/2 = x
-1/2 = 1?
{x|x≠1}?
you had it right up to here
this is where you made your mistake
not just 1/2
yep!
ALRIGHT so therefore, {x|x≠-½}
negative sign
AH I FORGOT
FDKGDGDGDHLDDDH
Now for the y Intercept, g(x)= x-2/2x+1, let x = 0
Soo 0-2/2(0)+1?
Alright! OMG I'm sorry for disturbing you
Now for the y Intercept, g(x)= x-2/2x+1, let x = 0
Soo 0-2/2(0)+1 = 2/2+1 = 2/3?
Or 2/2? Or 2/4?
Which one is correct?
You seem to be busy x_x i guess this will end here
sorry, ya, at work, this is what i do for a hobby when i'm not busy
OMG, You still tryna help me even when you're busy
Thank you very much!
This will all end here now, thank you so much really! Now i need to sleep lol it's already 12:44 am, önce again thank you!
And also! I hope you'll have a great day! Like always!
Cya!
have a great day!
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can someone help me find polar form of (1+sqrt(3)i)^10
so first we get R=2 and tan o=sqrt(3) or o = pi/3
R=2^10
(1024)e^(ipi/3)
to find the angle, we say tano= sqrt(3)/1 which is sqrt(3) but how do we get pi/3 from that
bruh trigonometry
what is sin(pi/3)
sqrt(3)/2
not like what is but do you know how do you get that
no I dont really remember learning that but i might be forgetting.
opp/hypo
yea i get that
but I guess my question is why is tan sqrt(3)/1 = pi/3. i know that tan is sinx/cosx but i feel like im missing something
tan(pi/3) is sqrt(3)
thats a neat picture, just gotta burn it into my mind
@smoky marsh
https://www.youtube.com/watch?v=zfUs6iV455o
watch this video before it
Using some simple geometry, Pythagoras' Theorem and laws of trigonometry, we can easily derive the exact values for sine, cosine and tangent of the angles of 30˚, 45˚ and 60˚.
You may have been expected to remember values such as sin(30˚) = 1/2, sin(45˚) = √2/2, sin(60˚) = √3/2. Unfortunately, this is pretty boring stuff to try and remember.
W...
and remember tanx = sinx/cosx , you will only be required to remember sinx and cosx values the rest would take seconds to figure out if you know the identities
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Hello, very general question that I want to confirm.
Let A = the set of x where f_1(x) > c, let B = the set of x where f_2(x) > c, A - B = A interset B complement, what would thislook like?
ultimately im trying to get that f_1(x) > f_2(x)
idk if subtracting the two sets would be the way to go
how is this a general question
?
it doesn't matter just, it's a regular question I was expecting something "general"
$\begin{aligned}A=\left{ x,f_{1}\left( x\right) >C\right} ;B=\left{ x,f_{2}\left( x\right) >C\right} \ A-B=A\cap \overline{B}=A\backslash B\ A\cap \overline{B}=\left{ x,f_{1}\left( x\right) >C ,and, f_{2}\left( x\right) \leq C\right} \end{aligned}$
Zamarus
So it's interesting if f1 is always >c and f2 always <=c for other cases we don't know if f1>f2
If the set is empty then f2>f1 so maybe it's better to consider B-A and check if it's empty for f1>f2 but it doesn't looks like a good idea in the first place
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Can i have some help with this
c looks pretty tasty to me
so negative gradient on f(x) translates to under the graph for f'(x) to me, and it will approach the same thingy majigy
ikr
dude
you see how positive f(x) gradient means above the graph
right
also stationary points become roots
so
dude this is my chat
ok
so thats why I think C
k
interesting
just reposting for someone else
<@&286206848099549185> can you help me please
@oak bough Has your question been resolved?
<@&286206848099549185> please help me on this
@oak bough Has your question been resolved?
@oak bough Has your question been resolved?
at this point the gradient is negative, because it is going down
K
that means the asnwer has to be C or D, they are the only two graphs with negative gradients at that point
at this point the slop is going up, therefore the gradient must be positive
correct
i mean i dont think the graph is actually -1/x
but youre right that the answer is C
yeah i get what you mean
Yh
at that region its similar enough that the graident would work the same
this region?
Yea
the graph value is increasing, so the gradient must be positive, at the gradient is slowly getting steeper, so the gradient must be getting larger
Ah ok
As a general rule, if the graph is going down its a negative gradient and if its going up its a positive gradient, and the steeper the graph the larger the gradient would be (think rise over run)
Tysm for that tip
all good :)
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Event = ✅ or ❌
Outcomes = 10
Example:
✅❌❌✅✅❌✅✅✅❌ [Fail]
✅✅✅✅✅✅✅✅✅✅ [Win]
The probabilities of win are:
1/(10^2) also 1/100
or?
10/2
and i want to get it in percentage so
"and i want to get it in percentage so":
%0.01
or?
%5
@median aspen Has your question been resolved?
@median aspen Has your question been resolved?
percentage = 100 * probability
@median aspen Has your question been resolved?
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"A car is worth 180000 and drops by 12% each year" how would you graph this?
Norwegian numbers so the value of the car might be bit weird to you
It's a linear function
It's supposed to be an exponential
Oh it compounds ig
it's exponential
Makes sense
Any suggestions?
I would think something like 180000(1-3/25)^t
Just graph it as any exponential decay Function with intercept at 180000 ig
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How did they get this answer? did they Divide? Multiply? Subtract? add?
yes
they just did basic multiplication and division to isolate a (make it the new subject)
@quiet quartz do you understand now?
Like this?
Do i Multiply the Sin20?
Am i doing it correctly?
no
you want a/1
you divided by sin 20 on the left side, and multipliedon the right side
you have to do the same thing to both sides to keep the equality
yes
so you'd have to divide by sin20 on both sides@quiet quartz
do it correct and show me
if this is correct, then how come the answer has the denominator and numerator reversed?
Am i wrong?
.close
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Hello, i have trouble with a geometry problem about areas, it is known that BD/CD=CE/EA, I am to prove that Area[EPDC]=Area[ABP]
all i can really think of is you just do a lot of similarities between triangles
then derive their area factor as k²
then play with the areas
id probsbly need some paper for this
@tired ore Has your question been resolved?
I cant find any similar triangles without adding new segments and that seems to make it more complicated
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How can I solve #17
I took the derivative and got -1, but im not sure what to do after that
you also have to check the endpoints because the function does not have a derivative at those points
What do you mean how do I check that
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whats wrong with using n = 2k + 1 for any n integer n adding it twice
since an odd is usually represent by 2k + 1 for e.g.
why is there k n l here?
you wanna show it holds for any odd integers. if you just add n to itself it doesnt necessarily hold for all odd numbers
Meaning if you use the same letter, say k for both integers
They are the same integer
You can’t have say 3= 2 * k+1 and 5 = 2 * k+1
k can’t be 1 and 2 at the same time
@limber void Has your question been resolved?
oh right thanks
how doi know when to use contra+ or contradiction in a proof q?
or can i use any types of proof?
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NightHorn — Today at 22:20
Q. Sets of data are summarised by the information given. For each set of information find the standard deviation.
a) i) Σ(x - x̄)^2 = 42.9 n = 10
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A mouse wheel is 16cm in diameter and the base of the wheel is 2cm off the ground. If the hamster spins the wheel 4 times each second, determine the cosine function that describes the movement of the wheel if it starts at lowest point
Anyone please
Been working on this for a week now
Seems like no one knows the answer or how to solve it
@solar nimbus Has your question been resolved?
Anyone know?
?