#help-17
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gentle umbra
i can have a cheat sheet filled with this kind of stuff but once the variation changes (ie. asks for water in a cylinder or something) i will completely blank out
so i want to know how to generalize all of these types of problems into one formula hopefully…
like 3d work problems
what should i look for that is the same for all variations?
…
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edgy sapphire
yea the thing about pyramids/cones is that the area is scaling linearly from the point to the base
here it goes from 0 (point) to a side of 100 over a height of 0-60, so the side length formula is (100/60)*y
volume is area*height though so you need the area of that changing square, so (100y/60)^2, plus you multiply by the density for the weight
for cones it's the same but you want the radius which is like that 50 you found, then pi*r^2
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gentle umbra
yea the thing about pyramids/cones is that the area is scaling linearly from the...
so i just keep in mind about the similar triangle and applies to everything shaped like this?
i got started a little bit on it but got stuck after setting the ratios up
edgy sapphire
so i just keep in mind about the similar triangle and applies to everything shap...
right, since those 3d shapes are a point transforming into a full base at a steady rate
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vital loom
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late reef
Hello
late reef
How am I supposed to know if the function is wide or narrow? , the function is:
a +(x + p)² +k
The a affects whether it will be narrow or wide, but how will I know?
fervent wasp
How am I supposed to know if the function is wide or narrow? , the function is:
It depends on the absolute value of a
late reef
Lets say its 2.
fervent wasp
The greater |a| is, the narrower it is
late reef
And if its -1 its upside down ?
late reef
Ok thx let mr chek it
fervent wasp
If a>0, it faces upward
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finite hatch
how come
finite hatch
they get this
173 MeV
i though to get to MeV u need to multiply the eV by 10^8
so its 1.73 x 10^18
oh
um.
bye guys
.close
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neon kernel
Given are the common densety functions of the 'accidental' variables X and Y:
Consider following statements:
vocal sleetBOT
Given are the common densety functions of the 'accidental' variables X and Y:
Co...
neon kernel
how many are correct
Does anyone know how to find the last one
I think it would be Pi/4
als = if and elders = elsewhere
found it
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quartz beacon
would this question: Denote in the complex plane all the numbers z = a + bi for which Im(conjugated of z)² = 1, be equal to y=-1/2x?
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would this question: Denote in the complex plane all the numbers z = a + bi for ...
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sharp perch
would this question: Denote in the complex plane all the numbers z = a + bi for ...
If z = x + iy then yes
xy = -1/2
quartz beacon
what am i supposed to do w the a+bi
sharp perch
what am i supposed to do w the a+bi
Nothing
Im((a - bi)²) = -2ab = 1
But you considered x and y
Doesn't matter really
quartz beacon
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thick vessel
I understand how to find key features when graphing rational functions, however I do not understand certain problems when they are in this format
vocal sleetBOT
I understand how to find key features when graphing rational functions, however ...
thick vessel
Should I divide first?
mental falcon
remember that division by a fraction you can treat as multiplication by the reciprocal
thick vessel
Also I wondering if for all problems like this I should put both the numerator and denom in factored form
mental falcon
so you can rewrite it as $\frac{(x^2-4x)(x+4)}{(4x-8)(x+2)}$
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Soosh
mental falcon
well i mean if you're trying to find key features
why? it's easier to work with a factored form
or what would be your purpose in distributing exactly?
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fast imp
really struggling with this, i honestly have no idea where to even begin
fast imp
i guess i could try like doing something in base 99 but i dont think thats it
or no it would be base 100
and i still dont think that would work
hollow raptor
Choose primes, you'll be given a linear combination so you can factorize it and get the unknowns
inner osprey
or no it would be base 100
doesn't it?
fast imp
Choose primes, you'll be given a linear combination so you can factorize it and ...
but theyll all be added together
inner osprey
there aren't any restrictions on the numbers Berris can name
fast imp
i think base like 200 might actually do something
hollow raptor
there aren't any restrictions on the numbers Berris can name
Ah yes, I'm assuming integers
inner osprey
it doesn't matter integer or not
the fact that Harris can only use secret 2-digit numbers is already extremely restrictive
fast imp
its assumed to be across the integers, this is a number theory book
id be very surprised it it wasnt across the integers
inner osprey
that's fine but my point is this problem need not be confined to the integers as it does not heavily affect the solving process
you can solve it using integers as a restriction if you wish
fast imp
well i cant solve it, thats why im asking for help lol
crimson shell
The base for expansion of abc would be 100 as a, b and c are 2 digit numbers
fast imp
The base for expansion of abc would be 100 as a, b and c are 2 digit numbers
im still not sure how that would help though
since any integer that large has tons of ways of making it from adding 3 smaller numbers
hard atlas
make up three numbers x,y,z. and then tell me 10000x+100y+z
hollow raptor
The two digit restriction is what makes it work
hard atlas
you are overthinking probably
hard atlas
make up three numbers x,y,z. and then tell me 10000x+100y+z
it might help if you just do it
crimson shell
im still not sure how that would help though
Would give you (100^2)a + 100b +1c so that a, b and c still remain visible in the sum as abc, acb, bac, bca etc.
fast imp
so like the idea is to pick the numbers 10000, 100, and 1, and then berris converts the number harris gives to base 100?
or something like that
hard atlas
you dont specifically need to frame this in terms of base 100
hard atlas
you can already read off the numbers from the result
base 100 is just base 10 but two digits at the same time
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lyric raptor
Let $f$ be a function from a finite set $A$ to itself. Prove that $f$ is injective if and only if $f$ is surjective. Does this remain true if the finiteness assumption on $A$ is dropped?
I understand why this must be true. in the direction injectivity implies surjectivity:
Assume the function is not surjective. This means $|f(A)| < |A|$.
The codomain and domain are the same set, so $| \text{codom} f | = |A|$. Since injectivity implies that $|f(A)| \ge |A|$ and $f(A) \subseteq A$, we know $|f(A)| \le |A|$. Consequently, $|f(A)| = |A|$. This contradicts with $|f(A)| < |A|$, and thus $f$ must be surjective.
I qualitativly understand the reverse, but am even less sure how to write it out.
Is my reaosning ocrrect, and how can I turn it into a proof? Thanks!!
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Nameless
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quasi roost
Discrete Math
Q: Prove A ∩ (B ⊕ C) = (A ∩ B) ⊕ (A ∩ C)
I showed my work so far, but I've hit a wall since adding X and Y back in doesn't lead to what I'm looking for
quasi roost
This was my first answer but I'm not sure if this would be valid as it seems too simple for the assignment
Ping me if you reply to the message
edgy gulch
Ping me if you reply to the message
seems like its easier if you work with the right side
quasi roost
Alright I'll try that
quasi roost
seems like its easier if you work with the right side
I did the right side and I got a statement that would always be false, did I miss a step or is this on the right track still?
Since it proves the right side is false, however the left side may still be true or false, not sure how I could do that
unless 1 side being false means the entire statement is false
edgy gulch
lemme see
edgy gulch
I did the right side and I got a statement that would always be false, did I mis...
how did you get that it will always be false?
quasi roost
Oh wait I saw it wrong, in my head I saw that it would need A and A^c to be true which would always be false i read that really wrong woops
even then I'm till kind of lost what to do after the last line and what law I could apply
edgy gulch
its gonna be a lot of distributive laws
quasi roost
its gonna be a lot of distributive laws
ok i'll try that, also is watson amelia your top 5
edgy gulch
hmm i would have to think about that
quasi roost
ok and you're sure distributive laws is the only way to go about this cause looking at it, it looks like its gonna get super messy idk
edgy gulch
yes it will get super messy
quasi roost
edgy gulch
<@281970066764070912> how do I know which way to distribute it? Or it doesn't ma...
take A intersect B as your entire A
and distribute it that way
quasi roost
take A intersect B as your entire A
so something like this and then distribute it ok ill try that
edgy gulch
yeah
gosh i hate using set operations to do boolean algebra
using addition as OR and multiplication as AND is so much easier to keep track of stuff
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quasi roost
@edgy gulch i've been staring at this for awhile im mad confused, i could do distribution again but at that point there is no way i'll even see how it'd simplify
i did notice that these have to cancel out and be forced as false though, unless im reading that wrong
edgy gulch
yes indeed
so you can just get rid of them
since they'll just be empty sets
then what you have left is (A∩B∩C') ∪ (A∩C∩B')
reverse the distribution law
A∩((B∩C') ∪ (B'∩C))
A∩(B⊕C)
and boom we done
quasi roost
o ok thank you im just gonna write it all out with the laws i used, have you been doing discrete math for awhile?
at what point can u just look at something and know how to do it
cause every new question i look at i just get so confused
quasi roost
edgy gulch
at what point can u just look at something and know how to do it
if its still boolean algebra then yeah i suppose
quasi roost
if its still boolean algebra then yeah i suppose
Thank you for the help, makes sense to me now
I have 1 more question, I got this answer for another set problem with my work already shown, does this look alright or did I miss something midway
edgy gulch
yeah looks good
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fathom hedge
doing comp sci, trying to understand union find, not understanding dot points 3 and 4
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doing comp sci, trying to understand union find, not understanding dot points 3 ...
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i dont get question b
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scenic ravine
If the two decks are shuffled together
scenic ravine
in how many ways can you arrange them>?
finite hatch
idk
finite hatch
104
scenic ravine
ok, in how many ways can you arrange 104 cards
scenic ravine
remember , so cards are repeated
scenic ravine
some cards
scenic ravine
yes
finite hatch
104!/2!?
wait ok i skipped that one
how does the n! turn into an n
in the third line
ionic owl
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orchid pier
Is this worked out correctly?
vocal sleetBOT
Is this worked out correctly?
twin meteorBOT
orchid pier
in the solutions they used comparison test but is my method correct aswel?
or does 6^n / 3^n +4^n not equal (6/3+4)^n
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karmic oar
can someone give me a trick to remeber the radians of the unit circle(I have memorised the angles(convert them from radians) as well as the coordinates)
vocal sleetBOT
can someone give me a trick to remeber the radians of the unit circle(I have mem...
wraith python
can someone give me a trick to remeber the radians of the unit circle(I have mem...
Look up the Hand Trick on Youtube.
karmic oar
k lemme check
this does not answer my querstion
I am asking how to memorize the pi/6, pi/4, pi/3, pi/2 so and so forth
wraith python
You're only interested in memorizing the radian measure?
wraith python
What are you trying to understand about radian measures? That will help me explain whatever it is you are trying to learn.
karmic oar
how do I memorize it
wraith python
Just the values themselves? Their relation to degrees? Their position on a unit circle?
karmic oar
the vals themeself
wraith python
,calc pi/2
twin meteorBOT
Result:
1.5707963267949
okay...
wraith python
So the numerical values?
wraith python
You named all of the important radians aside from pi and 2pi.
wraith python
After that, it's really just learning how to apply them to reference angles.
wraith python
7pi/6 is just 7pi/6 - pi = pi/6. From there, you can see that the difference in values are just negative signs from pi/6.
karmic oar
I am confused man
wraith python
One moment, let me make a graph.
karmic oar
okay
wraith python
You should read about reference angles.
https://www.cuemath.com/geometry/reference-angle/
karmic oar
ik what ref angles are
wraith python
So what's the problem?
karmic oar
i dont know how to remmevber the unit circle radians
wraith python
Like 7pi/6 or 3pi/2?
wraith python
You don't need to remember every single radian in a unit circle. Just do the conversion as needed to pi/2, pi/3, pi/4, or pi/6 as needed.
karmic oar
the pi/6, pi/4, pi/3, pi/2, 2pi/3, 3pi/4, 5pi/6, pi, 7pi/6, 5pi/4, 4pi/3, 3pi/2, 5pi/3, 7pi/4, 11pi/6, 0
wraith python
After that, it's just a matter of remembering the signage.
karmic oar
the pi/6, pi/4, pi/3, pi/2, 2pi/3, 3pi/4, 5pi/6, pi, 7pi/6, 5pi/4, 4pi/3, 3pi/2,...
^^^
how to memorize what I said above
karmic oar
My mind is not working rn
wraith python
The other is just adding pi/6.
karmic oar
ic the pattern for quad 1 and quad 2 its for the denomitoers: 6, 4, 3, 2, then for quad 2 its 2, 3, 4, 6
but the numerator tho
wait
for quad 2 5pi/6 becomes 7pi/6
its 2pi increment for numerator
and that applies to all
so all I have to do is memeorize quad 1 and not 2
then I got the rest
wraith python
In 2Q, just add pi/2.
karmic oar
and the sign chamghe is self explantaroy
wraith python
In 3Q just add pi
wraith python
In 4Q, add 3pi/2.
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tawny shadow
if you can find the perpendicular line of a linear function by finding the negative reciprocal of the gradient then how do you find the perpendicular line of a quadratic function?
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if you can find the perpendicular line of a linear function by finding the negat...
tawny shadow
if you can find the perpendicular line of a linear function by finding the negat...
do i need to find the negative derivative of x^2 or smthing
y = mx +c , m is the gradient and a perpendicular line would be y = -(1/m)+c
wait what
m = gradient
i have no idea
uhhh
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quasi roost
Discrete Math
Q If g : A → B is surjective and f : B → C is injective, then g ◦ f is surjective
Showed my work so far, but I'm confused on how to prove g ◦ f is surjective or if I missed a step in between, hit a wall
vocal sleetBOT
# Discrete Math
## Q If g : A → B is surjective and f : B → C is injective, then...
quasi roost
ping me if you reply to this please
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quasi roost
made it more clear
safe sable
made it more clear
Surjective does not mean that two different values in the domain map to the same value in the codomain, it means that each value in the codomain has an element in the domain that maps to it
quasi roost
Surjective does not mean that two different values in the domain map to the same...
Yes but I wanted to put an example that I could use for the proof, so the example I used had two distinct values map to one
but I should reword it with "Let" thank you, unless I shouldn't be using this example at all
safe sable
Oh, is the question asking you to just find an example of functions satisfying that property?
Or to prove it is true for all functions f,g satisfying the assumptions?
quasi roost
Oh, is the question asking you to just find an example of functions satisfying t...
This is the question
safe sable
Ah okay. So do you think it is true or false?
It's not clear if you're trying to prove or disprove it
quasi roost
Ah okay. So do you think it is true or false?
I believe it's true so I'm trying to prove it
safe sable
Got it. To prove something is true, you can't just use an example, you actually need to show that the conclusion follows from the assumptions. To disprove something, you can just use a counterexample
Also, I think it should be f ○ g, not g ○ f
quasi roost
Also, I think it should be f ○ g, not g ○ f
I thought this too, but in the questions it is labelled as this
ill check emails my teacher sent just incase but this is mostly what confused me a lot
safe sable
I mean, the codomain of f is C, but g takes A as it's domain, so g ○ f isn't well defined
Unless the notation they're using is supposed to be read left to right, not right to left, which is quite uncommon but not unheard of
In any case, g is first, then f, for it to make sense
quasi roost
Unless the notation they're using is supposed to be read left to right, not righ...
Found no email, but I found this
This is from the lectures from the same teacher, the [X] is supposed to be ◦, and in this case it does not look reversed, but I think the teacher intended on the assingment for it to be reversed since it does say at the bottom that the reverse is not well defined
quasi roost
In any case, g is first, then f, for it to make sense
So I need to use f(g(x)) for it to make sense
quasi roost
Got it. To prove something is true, you can't just use an example, you actually ...
How would I go about doing this then, since I'm not sure how else to do the problem
for now i have it like this
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queen crest
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edgy gulch
This is what I’ve done so far
draw the graphs of those straight lines
queen crest
Yeah, I did
edgy gulch
then find the intersection points between them
novel wedge
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novel wedge
How do I do this
regal bane
Note that x is the upper limit of that integral. What happens to that integral as x approaches 0?
Keeping in mind the lower limit is 0, ofc.
regal bane
Right. The numerator approaches 0 here.
novel wedge
How would I do that tho
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raven owl
Is it like g’(x) = the integral
$\frac{d}{dx}\int_0^xf(x)=f(x)-f(0)$
novel wedge
$\frac{d}{dx}\int_0^xf(x)=f(x)-f(0)$
So do I have to find the anti derivative?and then evaluate ?
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Sora Harewataru
raven owl
I mistyped
vocal sleetBOT
raven owl
the good thing about ftc2 is u dont have to find the antiderivative
novel wedge
the good thing about ftc2 is u dont have to find the antiderivative
How do I know when to apply ftc2 rather than just integrating
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novel wedge
Hi
raven owl
How do I know when to apply ftc2 rather than just integrating
when you take the derivative of an integral
that is when you will use ftc2
novel wedge
Oh alr
raven owl
because derivatives and integrals are like inverses they cancel nicely
novel wedge
And derivative of integral cancels out bc it’s just derivative of anti derivative rigjt
Yea
raven owl
yeah thats even better
raven owl
Looks like it has an answer. You might need to do L'Hopital multiple times
and its not 0
raven owl
did you remember to chain rule sin(3x^2)
first L'Hopital gets sin(3x^2)-sin(0)=sin(3x^2) in numerator
raven owl
sin(3(0)^2)=sin(0)=0
novel wedge
i thought sin(0) was 0
novel wedge
sin(3(0)^2)=sin(0)=0
Is this after doing hosptial once
raven owl
yeah
novel wedge
oh yeah i meant 24x sorry
raven owl
Oh yeah that might work
novel wedge
Cause if i hospital one more time id get 0
raven owl
cancel out the x's?
yeah you can
novel wedge
so i get 1/4
raven owl
yeah
novel wedge
yeah you can
did u hospital it an additional time?
raven owl
yeah it still gives 1/4
novel wedge
Wait how
raven owl
you get like 6*sin(3x^2)-6xcos(3x^2)/24 = 6-0/24 = 1/4
novel wedge
Oh my days
raven owl
maybe sin and cos are switched
novel wedge
i forgot abt the product rule
raven owl
yeah
raven owl
np
mental falcon
$\lim_{x\to0}(\csc^2-x^{-2})$
vocal sleetBOT
$\lim_{x\to0}(\csc^2-x^{-2})$
twin meteorBOT
Soosh
mental falcon
to do this limit, i wrote it as 1/sin^2 - 1/x^2 then found a common denominator, then it became indeterminate form 0/0 then had to apply lhopitals like 4 times until it finally worked out, which was rather painful and long, is there an easier way to do this limit?
dawn kestrel
Unfortunately I don’t think so
Sometimes just have to grind out a bit of lhopitals
There might be something slightly easier by playing around with the common denominator and maybe some trig identities, but it’s negligible I assume
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cinder mulch
Find the value of the expression 20x^2y^4, if 4xy^2 = - 6
vocal sleetBOT
Find the value of the expression 20x^2y^4, if 4xy^2 = - 6
drifting terrace
try squaring both sides of 4xy^2=-6
cinder mulch
sullen notch
try change of variables xy^2 = a in both expressions
wide sundial
4xy^2 = -6 so xy^2 = -6/4
mild raven
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mild raven
ok
this seems silly
this is a calc 2 problem
but for some reason im having trouble taking the derivative of that y =
its not nessecairly that i cannot do it
I have the derivative
but simplifying it to a point where when i use SA formula
im getting tripped up on the part where i Use the property sqrt a * sqrt b to simplify the integrand
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timid leaf
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worthy citrus
yep looks good, your work before the first bold line is not needed as they just want you to verify they are inverse to each other which is what the rest of your work does
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native heath
Proof by induction
native heath
<@&286206848099549185>
obsidian vigil
Proof by induction
Expand brackets and use the formulae
For sum of squares and sum of a variable
native heath
Im trying to solve it but im having problems with both sides of the equation when im solving for n=k+1
obsidian vigil
Can I see your work?
native heath
idk what to add on which side and the sigma notation is just messing me up
native heath
Can I see your work?
1 sec
I tried removing the sigma notation to make it easier
But i just dont get it, ive watched a thousands of videos and AI couldnt explain it properly
obsidian vigil
Do you know the standard formulas for the sigma notation
We learn this here with Sigma notation idk bout u
native heath
No ive never seen smth like this
I mean i know what sigma is
i understand what it is but when using it in induction its just making things complicated
ruby vapor
When you have k^2(k+1)+(3k+2)(k+1), factor out the (k+1) to get (k+1)(k^3+3k+2) and it's easier to work with
native heath
I never factored anything before
so im pretty lost in factoring
Can you solve it and show me your work? Maybe that will help me somehow
ruby vapor
Can you solve it and show me your work? Maybe that will help me somehow
Not having factored anything before will make problems like this a lot harder. There's only one more step to go after I wrote, but here it is: $k^2(k+1)+(3k+2)(k+1)=(k+1)(k^2+3k+2)=(k+1)(k+1)(k+2)=(k+1)^2(k+2)$ You're allowed to factor out a (k+1) the exact same way you can factor out a 2 (for example) if all the terms have a 2. When you get $(k^2+3k+2)$, that's a quadratic you can figure out a few different ways, it depends on how you were taught/are comfortable with.
twin meteorBOT
DonDoesMath
ruby vapor
And the goal of this induction is to get to show that $\sum\limits_{k=1}^{n+1}(3k-1)(n+1)=(n+1)^2(n+2)$, so the last step I reached proved that
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ruby vapor
No problem!
native heath
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wheat drum
How will I move on? I think I messes up somewhere
vocal sleetBOT
How will I move on? I think I messes up somewhere
wheat drum
this is practice problem for the main question and this is how the textbook does it
sharp perch
Why did you substitute $x$ as zero when the condition given is $y\left(\frac{\pi}{3}\right) = 7c$
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Kappa
wheat drum
Why did you substitute $x$ as zero when the condition given is $y\left(\frac{\pi...
so i drop the absolute value bc x is between 0 and pi/2; therefore making x positive?
sharp perch
so i drop the absolute value bc x is between 0 and pi/2; therefore making x posi...
x is positive, but the absolute value is on sin
It's dropped because sin is positive
wheat drum
For this question how would I proceed or are there any errors?
sharp perch
Should be $-e^{-z}=-2e^{t}+C$
twin meteorBOT
Kappa
wheat drum
Should be $-e^{-z}=-2e^{t}+C$
why?
sharp perch
$\int \frac{1}{e^z};dz = \int e^{-z};dz = -e^{-z} + C$
twin meteorBOT
Kappa
sharp perch
Does that make sense?
wheat drum
Does that make sense?
no I thought you could not take the integral if n=-1
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worldly badger
Really bad at math, the fraction kind of screwed me up, keep getting a different answer compared to the answer key, any help?
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Really bad at math, the fraction kind of screwed me up, keep getting a different...
subtle blaze
Could you show us what you did? Maybe we could see where you went wrong
worldly badger
Could you show us what you did? Maybe we could see where you went wrong
im on my computer right now, i wrote it in a notebook so i cant share it
but i did most of the steps right
used this formula
the 3/8 fraction keeps messing me up, i dont really know how to solve the questions with the fraction like that
<@&286206848099549185> sorry for the ping, need help asap, exams in 2 hours
outer dune
Can you show what you did
vast shale
coefficient of x^7 is 12C7 (3/8)^5(4)^7
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@worldly badger Has your question been resolved?
worldly badger
Can you show what you did
I got it now
worldly badger
coefficient of x^7 is 12C7 *(3/8)^5*(4)^7
thanks, this kind of helped
worldly badger
does op know why
rugged nacelle
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rugged nacelle
I need help with this limit
I'm stuck here (honestly idek if im on the right path but yea)
I'm assuming I have to create a bunch of limits I alrdy know (tan(x)/x when x approaches 0 is 1 and tan(ax)/x when x approaches 0 is a)
<@&286206848099549185>
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vast moth
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vast moth
the answer is supposed to be
x + y3 - 11 = 0
not
x + y3 - 10 = 0
i went through it a couple times and i keep getting the same answer
can someone help ?
grim dawn
you have a slope of 1/3 instead of -1/3 for the normal
and also your 1/6 dissapears and isnt added
oh
vast moth
oh shit, alr lemme try
grim dawn
unless 3.5-1/6 is 10/3 and i made a mistake
let me check
ah yea no u did do that part correctly
just the sign then
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viral steeple
A regular hexagon whose center is at the origin has one vertex on the positive y-axis at a distance of 3.5 feet from the center. Find the polar coordinates (using radians) of the vertices and find the distance between 2 consecutive vertices. (round the distance to 2 decimals places)
I've tried muliple things like finding (0, 3.5), I tried to get the vertices which I thought was: (3.5, pi/6), (3.5, pi/2), (3.5, 5pi/6), (3.5, 7pi/6), (3.5, 7pi/6), (3.5, 3pi/2), (3.5, 11pi/6). and the distance: 3.5ft.
I think this is wrong though, can some one please help thanks!!!
vocal sleetBOT
A regular hexagon whose center is at the origin has one vertex on the positive y...
viral steeple
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terse forum
I need help
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I need help
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proud zealot
you can calculate the area of the right triangle displayed
and then multiply that area by the number of triangles there would be in the shape
so in this case 10 triangles
proud zealot
you can calculate the area of the right triangle displayed
1/2 base * height
so in this case $\frac{1}{2}(5.1/2)*3.5$ is one triangle
twin meteorBOT
sabllamas
proud zealot
@viral steeple does that make sense??
proud zealot
oh! my bad
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stoic patrol
bro I joined this server yesterday and got freaking 245 pings
vocal sleetBOT
bro I joined this server yesterday and got freaking 245 pings
stoic patrol
<@&286206848099549185> I joined this server a day ago and why did I have 245 pings
explain yall
tough hedge
Exactly
tight sonnet
💀
tough hedge
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
tough hedge
HAHAHAH
tight sonnet
remove the "helpers" role youd get much less ping
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vapid lion
someone help w this math question pls
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someone help w this math question pls
lime gorge
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pearl juniper
So im doing sinusoidal functions, and somehow I keep messing up the phase shift. The distance between pi, and pi/4 is 5pi/4 and I cannot understand as to how.
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So im doing sinusoidal functions, and somehow I keep messing up the phase shift....
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rancid sky
“y varies inversely as the square root of x, y equals to √6/6, when x = 24”
here’s my solution so far I’m new to the topic and unsure if it’s correct or not
rancid sky
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vocal sleetBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2, 4
livid horizon
You don't need to add the ± while taking sqrt(24)
rancid sky
okayyy
livid horizon
Also in step 2, won't sqrt(24)= 2sqrt(6)?
rancid sky
Yes the 2 isn’t as clear
livid horizon
Oh kk
timber wagon
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meager talon
Can anyone explain how the 2nd step or I say x³-1/x-1 come?
vocal sleetBOT
Can anyone explain how the 2nd step or I say x³-1/x-1 come?
strong grove
$$(x^3 - 1^3) = (x-1)(x^2 + x + 1)$$
$$\frac{(x^3 - 1^3)}{x-1} = \frac{\cancel{(x-1)}(x^2 + x + 1)}{\cancel{x-1}} = x^2+x+1$$
twin meteorBOT
JustToPro
meager talon
$$(x^3 - 1^3) = (x-1)(x^2 + x + 1)$$
$$\frac{(x^3 - 1^3)}{x-1} = \frac{\cancel{(...
Ah, Got it.
Thanks brother.
.close
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ornate birch
can anyone guide me through the process of answering this?
vocal sleetBOT
can anyone guide me through the process of answering this?
ornate birch
yes okay wait
karmic forge
g' is 4
ornate birch
oh right my bad
ornate birch
im not familiar in using that on quotient rule
we only use that in chain rule
is it ok that i stick to what ik how to use but still do the process
karmic forge
We have to find f'
karmic forge
And we can use chain rule for that
karmic forge
You know gof(x) rule
ornate birch
yes
karmic forge
product rule
And use u(x) and v(x) or other then f(x) ,g(x) you willget confuse
ornate birch
how do i continue the last line?
should i get lcd and add them or that's the derivative of f(x)?
karmic forge
Ya that's the value of f'
karmic forge
Here f'
ornate birch
i dont need to add through lcd?
ornate birch
ok wait
is this correct
<@&286206848099549185> sorry for the ping
<@&286206848099549185>
lucid zinc
dw about the ping gimme a second to answer you
i am struggling to understand how u derived sqrt(x³-1)
the derivative of sqrt(u) is simply u'/2sqrt(u)
meaning 3x²/2sqrt(x³-1)
oh my bad
i didn't notice the x
shits so unnecessarily complicated it hurts my brain
i need paper
lucid zinc
f'(x)=sqrt(x³-1)+3x³/2sqrt(x³-1)
ornate birch
how did u get that
vocal sleetBOT
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lucid zinc
how did u get that
derivative of x times the square root + x times the derivative of the square root
and like i said to derive the square root you can use the chain rule
just as (sqrt(x))' = 1/2sqrtx
(sqrt(u))'=u'/2sqrt(u)
ornate birch
i dont get it
ornate birch
no, i cant visualize what you said
primal mauve
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primal mauve
at a given time, vector (1 | 2 | -4) is modeling the direction of the falling sunlight
Calculate the angle of which the sunlight hits the ground (x1 ,x2)
the solution is:
sin alpha = |(1|2|-4) * (0|0|1)| all divided by square 21 = 4 / square 21 = alpha = 60.8°
where do I get the normal vector ( 0|0|1) or square 21 from ??
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@primal mauve Has your question been resolved?
vast citrus
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zinc quail
where are you stuck
vast citrus
where are you stuck
its asking me choose all the shapes below that you could get by cutting some of the edges of a cube and unfolding it
zinc quail
its asking me choose all the shapes below that you could get by cutting some of ...
am aware
vast citrus
ive tried everything i know and still stuck
zinc quail
try to do it in reverse
can you fold A into a cube?
yes :)
likewise you do so for the others
vast citrus
wait how
zinc quail
you can imagine to fold it back into a cube
vast citrus
you can imagine to fold it back into a cube
so am i looking for the ones that fold into a cube or the ones that dont
im confused
zinc quail
so am i looking for the ones that fold into a cube or the ones that dont
if you can fold them back into a cube
then obv you can cut a cube such that it unfolds that way
vast citrus
so im looking for the ones that fold into a cube
zinc quail
sure
zinc quail
legitly the last 2 question are about shapes
but you just need to fold them backwards
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primal mauve
but you just need to fold them backwards
can you by any chance help me out too? on my previous one
primal mauve
this
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rare viper
How do you divide a whole number between a ratio? Like, you know 21 must be divided in two with a ratio of 4/3
vocal sleetBOT
How do you divide a whole number between a ratio? Like, you know 21 must be divi...
dark kiln
divide in 7
rare viper
which equals three
dark kiln
so 12 and 9
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leaden sail
I have an img
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I have an img
leaden sail
cobalt ocean
what have you tried
cobalt ocean
idk i tried joining the lines
try and write EF and EH and FG and HG in terms of the vectors a, b, c
leaden sail
try and write EF and EH and FG and HG in terms of the vectors a, b, c
alr
wait i dont get what BC will be
HE will be -a + b
HG will be a + c
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unreal sage
Just need some clarification for this question, and my working so far, the only thing I don't understand is for the x,y values, I was told by my lecturer it's just t but I wanna know why
vocal sleetBOT
Just need some clarification for this question, and my working so far, the only ...
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pliant portal
On a n*m matrix there are non-intersecting(they do not attack each other) rooks that cover all the squares. How many squares are hit twice if n=7 and m=13
lyric fossil
what have you tried
vocal sleetBOT
@pliant portal Has your question been resolved?
lyric fossil
where did that number come from
pliant portal
Every rook hits 6 squares in the same collumns and 12 in the same row
I meant *7
18*7
lyric fossil
right but you just counted all the squares each of the rooks see
each square is seen twice
so you counted every square twice
pliant portal
My options are a)42 b)21 c)56 d)37 e)91 f)28
So even if i divide by 2 i dont get the right answer
lyric fossil
oh because of the extra squares that aren't seen twice
lyric fossil
well not quite
think of it as
you have 13 columns, but only 7 rooks
so although the rooks see 12 squares horizontally, only 6 of those are seen by another rook
so you actually want (6 + 6) * 7 / 2
rather than (6 + 12) * 7 / 2
you basically just want a 7x7 grid
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tidal knoll
I'd like to integrate what's in the box, I thought I'd do that by parts but I don't know the indefinite integral of exp(-ax²)...
Substitution doesn't seem good, because it's exp(-ax²) not exp(-ax³),
and Wolfram doesn't give any explanation. I wouldn't like anything with the error function either since I'm not that familiar with it. Does anyone know the integration trick ?
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I'd like to integrate what's in the box, I thought I'd do that by parts but I do...
unborn coral
The integral of exp(x^2) is a result you may memorize! Or you use tricks to get it (e.g. converting it to a polar integral). What class is this for?
gentle oriole
I'd like to integrate what's in the box, I thought I'd do that by parts but I do...
exp(-a^x^2) = e^x^2?
tidal knoll
The integral of exp(x^2) is a result you may memorize! Or you use tricks to get ...
It's for a quantum physics class, I was calculating the expectation value of x² for a given wave function
unborn coral
I see, in that case yea you may need to use the classic result! See here https://en.m.wikipedia.org/wiki/Gaussian_integral
tidal knoll
ok, but I need the indefinite integral of that for my particular problem, don't I ?
like
and even if it was ok to use directly the "integrated between -inf and inf" version, I'd get something that is not convergent:
Maybe I just have to memorize some integrals like the error function related ones
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tidal knoll
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timber scaffold
hello i want to develop a diffential equaition to prict price of asset based on no. of factors. as time passes the eqation evolves into chaos
vocal sleetBOT
hello i want to develop a diffential equaition to prict price of asset based on ...
@timber scaffold Has your question been resolved?
timber scaffold
no
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onyx swallow
I can't solve this
vocal sleetBOT
I can't solve this
onyx swallow
it's confusing to me
onyx swallow
I think it's sum of all numbers/total amount of numbers or something
vast shale
I think it's sum of all numbers/total amount of numbers or something
right can u try writing an equation to represent that for both classes individually
the mean score for class A and class B
onyx swallow
Class A:
Mean score= sum of all scores/ number of students
75= sum of all scores/28
vast shale
yuh
onyx swallow
Class B:
Mean score = sum of all scores/ 32
i'm not sure what the sum here is
it mentions the sum of the mean but idk if that counts
vast shale
Class A:
Mean score= sum of all scores/ number of students
75= sum of all scores...
right this is fine. Now, try multiplying both sides of that equation by 28
vast shale
i'm not sure what the sum here is
u will find that out soon dw
onyx swallow
right this is fine. Now, try multiplying both sides of that equation by 28
mean score=2100
vast shale
no
onyx swallow
wait I mean sum
vast shale
it's not thr mean wcore
yeah
so sum of all scores of class A = 2100
now
what would be the average for BOTH class A and B together?
can u write that out mathematically
onyx swallow
what do I find the average of exactly?
vast shale
the average score of both class A and class B considered together
onyx swallow
Average score= 2100+ (Mean score * 32)
vast shale
well you have to be careful here
okay lets backtrack
first things first
we want to find
mean of class A and B = (sum of all scores from class A and B)/(amount of students in class A and B)
agreed?
@onyx swallow
onyx swallow
yes
vast shale
yes
ok
sum of grades from A & B = Sum of grades from A + sum of grades from B
agreed?
onyx swallow
yes
onyx swallow
60
vast shale
ok
fantastic
now
solve for "sum of grades from class B"
you have
75 = (sum of A + sum of B)/60
vast shale
mean score=2100
you know sum of A to be this
vast shale
you should take a break then. Don't pressure yourself too much
onyx swallow
the problem is that my homework is due tomorrow-
I have like 6 other questions I don't know how to solve
vast shale
to encourage you our problem is almost finished if you want to keep pushing a bit more
oh i see
hmm cant ask for a deadline extension?
calm ore
can someone help me with grade 12 calc
vast shale
can someone help me with grade 12 calc
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can someone help me with grade 12 calc
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calm ore
mb
onyx swallow
hmm cant ask for a deadline extension?
she gave us that hwk 4 days ago but I had to study for 2 exams so I didn't start it til now
she's strict so she'll probably just take a graduation point away from me ;-;
vast shale
awww that's really unfortunate man
well the choice is up to you. I can continue helping you with this if you are still able to
onyx swallow
i'll try writing everything u mentioned here
maybe seeing all the info at once is easier
vast shale
aight
your goal is to find the mean score of class B, which written would be:
mean B = (sum of grades of B)/(num of students in B)
you know num of students in B, so u just need to find sum of grades of B. You also know that:
mean A & B = (sum of grades of A + sum of grades of B)/(num of students in A & B)
You can try solving for "sum of grades of B" in the aboce and then plug it in into your first equation above, ans thats the answef
@onyx swallow
i summarised what u need to do if that helps
vast shale
that helped me a lot, I think I got my answer now
ayee thats good
onyx swallow
here is my working
vast shale
here is my working
ah
vast shale
I can't solve this
ur procedure is totally fine but like it says 72.6 for both actually
i may have miswrotr that
do the same stuff but replace 75 with 72.6
onyx swallow
new answer is 70.5
onyx swallow
I thought I wouldn't be able to get it without coffee ;-;
onyx swallow
(this is one of the topics I dislike)
vast shale
aight do u have any ideas
onyx swallow
I know that there are two sum formulas that I don't know the difference of (when to use each one)
vast shale
I know that there are two sum formulas that I don't know the difference of (when...
ok i think this one might take a bit longer to do so you need to bear with me for my explanation
anyways lets start
onyx swallow
I think my basic understanding in this topic is also bad ;-;