Yah
Local
#help-13
carmine whale
quick fulcrum
Yah
*Local*
whats local
carmine whale
whats local
Local means in the surrounding i.e. it is the highest or lowest value of f(x) in its surroundings
quick fulcrum
Local means in the surrounding i.e. it is the highest or lowest value of f(x) in...
ok
so that one
how to see if this things are wrong or true if the graph is f(x)
carmine whale
how to see if this things are wrong or true if the graph is f(x)
So in this graph f(-1), f(3) are the local minimas and f(1) is local maxima
So now do u know the points where f'(x)=0 ?
carmine whale
So in this graph f(-1), f(3) are the local minimas and f(1) is local maxima
Do u get why is this so
quick fulcrum
Ok ?
you still here?
How to see if f''(x) is true or wrong here if the graph is f(x)?
crimson sedge
f’’x is the second derivative
quick fulcrum
f’’x is the second derivative
Ye
clear flame
How to see if f''(x) is true or wrong here if the graph is f(x)?
B, F is false and E is true
quick fulcrum
why
crimson sedge
what does the second derivative mean
quick fulcrum
It means that its the second derivative of the function I guess
or what do u mean?
crimson sedge
The second derivative tells you if the tangent to the slope is increasing or decreasing
quick fulcrum
The second derivative tells you if the tangent to the slope is increasing or dec...
whats a slope?
clear flame
whats a slope?
the slope of the tangent line at any point on the function
quick fulcrum
the slope of the tangent line at any point on the function
ok
And how do I see if theyre true and wrong?
clear flame
And how do I see if theyre true and wrong?
Check this video out, it explains nicely the concept that your problem uses
its nice and short
crimson sedge
f”x < 0 means the tangent is decreasing, > 0 means its increasing, = 0 means its an inflection point
Inflection point is where it changes from decreasing to increasing
or increasing to decreasing
quick fulcrum
f”x < 0 means the tangent is decreasing, > 0 means its increasing, = 0 means its...
Would B be true then since 3 is the point where the graph changes from decreasing to increasing?
crimson sedge
Would B be true then since 3 is the point where the graph changes from decreasin...
No, The second derivative is about the tangent to the curve
The tangent before that point was already increasing
You can see as the graph is curving, so there is a change in the gradient of the tangent to the curve
The second derivative at 3 is > 0
quick fulcrum
Ill watch the video
clear flame
Ill watch the video
promise u itll make sense once u watch it
clear flame
ye thanks I understood it now
cedar kilnBOT
mortal hemlock
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cedar kilnBOT
clear flame
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cedar kilnBOT
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limber wing
I'm reading Discrete Mathematical Structures by Bernad Kolman and I'm at the chapter 1 "Addition Principles" (page 10) and it's written that if two sets A and B are disjoints then | A ∪ B | = | A | + | B |, and I was wondering, is that still the case if A and B are not disjoint sets? Even if some elements in the sets repeat, are addition and union the same thing? I'd appreciate if someone could help me understand, thank you.
split pike
Ok
limber wing
?
dawn junco
I'm reading Discrete Mathematical Structures by Bernad Kolman and I'm at the cha...
it's not the case
take A = {1, 2} and B = {2, 3} for example
split pike
here is an image
the a intersection b is added twice
so we need to subtract
a intersection b
Does this help?
limber wing
Oh ok so it does matter if it repeats in an addition, but not in an union*
Yes it does help thank you
split pike
Oh ok so it does matter if it repeats in an addition, but not in an union*
i didnt get that
in union we add a and b
but they have a common part
common to both a and b
so it gets added twice
we just subtract the common part
limber wing
wait hold on
split pike
from the addition
limber wing
if we subtract the common part, some numbers are then missing no?
astral bay
|A| + |B| counts the common part twice
if we subtract it, |A| + |B| - |A \cap B|, then now we only count it once
split pike
if we subtract the common part, some numbers are then missing no?
no the common part appears twice
so subtract it once
a and b have common part x suppose so, a+b = a+x+b+x
so we have a+b+2x
limber wing
oh yeah sry
split pike
so there is an extra x
limber wing
i didn't understand
limber wing
yeah there are two numbers repeating in the addition and we subtract one time the repeating numbers to get them once
split pike
yes
rustic verge
Can someone pls calculate the inverse of:
cedar kilnBOT
Can someone pls calculate the inverse of:
rustic verge
Wolfram calculator says no solution found in standard mathematical functions
cedar kilnBOT
@rustic verge Has your question been resolved?
sand cradle
Wolfram calculator says no solution found in standard mathematical functions
We need to restrict the domain
crimson sedge
Can someone help me?
cedar kilnBOT
Can someone help me?
gray blade
crimson sedge
Show me
cedar kilnBOT
Available help channel!
crimson sedge
I wanted to convert 2 radians to degrees
cedar kilnBOT
I wanted to convert 2 radians to degrees
crimson sedge
my thought process was this
I multiplied 2 rad/1 by 180 degrees/pi radians
radians cancel
360 degrees/pi
I just wanted to ask if there's anything that can be done in steps, without directly calculating from here
feral juniper
2pi radians are 360 degrees
crimson sedge
yeah thanks, figured that only real way to simplify is just
plugging exact value of pi and dividing
which is
not ideal lol
.close
crimson sedge
cedar kilnBOT
storm abyss
well you see in the formula the angle is in radians rather than degrees
round turret
did u use radians instead of degrees
remote yoke
please could someone give me a more in depth explanation about this:
idle tusk
please could someone give me a more in depth explanation about this:
which part specifically?
the way log_2(n)+1 is created is by rounding the denominators to the nearest power of two
try n=2
or more
log_2(n)+1 is expanded as adding 1/power of 2
remote yoke
this is meant to be programming
I have only done differentiation and a bit of integration in calculus
remote yoke
well I'm learning data structures and algorithms
so I need to be able to understand each section
idle tusk
mhm
remote yoke
All i know is that log base 2 refers to the input as a power of 10
idle tusk
...you mean power of 2?
crimson sedge
how do you calculate the derivative of Abs(x) at 0? left and right, I now how limits work, I just don't know what approaching from one side changes...
round turret
You can write abs(x) differently
crimson sedge
square root of square x
wraith daggerBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
round turret
f -> {y = x if x > 0 and y = -x if x < 0 }
You can use these 2 functions to determen the limit
limit x->0, x > 0, you would use the fist function
hollow minnow
how do you calculate the derivative of Abs(x) at 0? left and right, I now how li...
If you’re trying to calculate the derivative just use the first principle.
crimson sedge
thanks @round turret I got the solution for that one
but now what if I'm trying to evaluate abs(cos(x)) at pi/2 ?
i assume it's a similar process but' I can't get it to work
round turret
f -> { cos(x) , for x = [-pi/2,pi/2]; -cos(x), for x = ] pi/2, 1,5*pi]
oops should be pi/2
grim yacht
how do you calculate the derivative of Abs(x) at 0? left and right, I now how li...
You can't
crimson sedge
... left and right
grim yacht
I wouldnt call it the derivative at 0 but a one sided limit of the derivative at 0
crimson sedge
@round turret thanks bro you're the man
crimson sedge
I wouldnt call it the derivative at 0 but a one sided limit of the derivative at...
mb you're right
shell smelt
When the digit '1' at the beginning is moved to the end, what is the minimum positive integer that becomes three times larger?
shell smelt
It was translated from Turkish*
tropic oxide
"An integer begins with the digit 1. Moving the 1 to the back makes it exactly 3 times larger. Find the smallest integer with this property."
this?
shell smelt
"An integer begins with the digit 1. Moving the 1 to the back makes it exactly 3...
Like, 1234 becomes 2341, and the second number (2341) should be the 3x of the first number (1234)
cedar kilnBOT
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
Then yes
1A and 1AB as 2 and 3 digit numbers, didn't work and the variables just get more and more complicated when I continue to 4+ digits
tropic oxide
try reconstructing the number digit by digit without worrying about its length
start like this perhaps:
n = ...___
3n = ...__1
what must be the last digit of n so that 3n ends in a 1?
shell smelt
7?
tropic oxide
right
shell smelt
Yeah I think that's the only one working
tropic oxide
so now
n = ...__7
3n = ..._71
Hmm
tropic oxide
what must the tens digit of n be so that 3n ends in the digits 71?
shell smelt
5 I think
tropic oxide
yes
shell smelt
So that 5*3 + 2 = 17
tropic oxide
so keep going like that
shell smelt
Let me try that
tropic oxide
until you hit a 1 for n
wraith daggerBOT
General_Jacob
mortal hemlock
!status
cedar kilnBOT
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
at what point does the cube stop sinking
thats not what i asked
when does the cube stop sinking
tulip gorge
does this assume snow is a fluid
mortal hemlock
snow isnt a fluid
tulip gorge
no it isn't
taking this condition then I'd use density and the volume of the shaft of snow below the cube
mortal hemlock
i am tryihng to help you
tulip gorge
since if it can't be more than 200 kg/m^3, and the shaft's top surface area remains the same since the cube isn't changing shape, a height can be ascertained
tulip gorge
what is being used for the snow pressure
time isn't necessary if it asks for just a height
tulip gorge
since if it can't be more than 200 kg/m^3, and the shaft's top surface area rema...
so then you use this
mortal hemlock
and what are the two forces
tulip gorge
gravitational force on block and reaction force from snow
tulip gorge
gravitational force on block and reaction force from snow
although these aren't needed considering the density maximum
mortal hemlock
lets start with the first one, what is $F_g$
wraith daggerBOT
Flappie
tulip gorge
the exact forces are unnecessary
the maximum density of 200 kg/m^3 with an initial snow height of 1m
can be used as then just a ratio of initial and final maximum densities for the same column of snow and same mass
therefore all that is going to change will be the volume of the shaft itself
it should be
no other parameters change presumably
but you calculate just a height
not a time
$H_f = H_i\frac{\rho_i}{\rho_f} = 1m\frac{50kg/m^3}{200kg/m^3} = 0.25m$
wraith daggerBOT
Fjörðe
tulip gorge
the mass is 100% irrelevant if im not mistaken
the snow has a maximum compressibility so since no equation for its internal pressure is assumed or given we just work with height and density
the final height will just be the initial height multiplied by the ratio of the initial and final/maximum densities
because when the snow reaches the maximum density then the reaction force applied back onto the block is equal to the gravitational force of the block downwards that is compressing the snow
with what equation
if the snow stops compressing, therefore assuming the block stops moving, $\Sigma F = 0$, therefore $F_g = F_S$
wraith daggerBOT
Fjörðe
tulip gorge
snow is compressible so it can't be a liquid
and snow is not a gas because it has an initial set volume without a fixed container
internal pressure here if im not mistaken would only apply if the snow is a fluid, which we have already ascertained it is not
$H_i = 0.25m$ qed.
wraith daggerBOT
Fjörðe
tulip gorge
that's not what the question is asking
if anything, the pressure of the cube can be used, which is then 1 Pa
no
the final height of the snow for the cube sinking into the snow is 0.25 m
here yes
because nothing else is given
yes
what is the answer given
how is the answer known to be wrong then
as far as I can tell, the mathematical logic is working
and since nothing else is given
yes
there is no other way to figure it out im pretty sure besides that
how would the cube be included
which pressure
what equation
how do you calculate the pressure
that is the pressure
not internal pressure
yes
because you need more information
something with the snow's compressibility
yes
which means it can compress to 1/4 times its current size
so it can be 4 times as compact
therefore it can have 1/4 the height
so the cube will sink 0.75m and rest on a shaft of snow 0.25m high
qed
why not
yes
you don't need to calculate a force
you can rely solely on the geometry
yes
except here it's an idealised condition
no
not when
at what height
which can be done geometrically and with density
mortal hemlock
my guess is that it sinks 2 cm
tulip gorge
how would you figure that out
oh I see my fallacy with density
still though forces aren't required per se
or shouldn't be
mortal hemlock
the force the snow pushes back up, is the amount that the cube displaces
the cube displaces 10N worth of snow
but its compressable
you have to squish the snow down
if youre trying to squish anything
it will push back
everything is a spring
just a very tough spring in most cases
it wont push back
so the force it exerts on the cube is 0
but the gravity on the cube is 10N
so the netto force is 10N down
thus the cube moves down
thats when it compresses the snow
yes youre right
but in this case the area is 1m^2
so i removed it
but in general, yes you should keep taht in
cedar kilnBOT
@crimson sedge Has your question been resolved?
tulip gorge
there is a change in density
cedar kilnBOT
cedar kilnBOT
Available help channel!
gritty prairie
cedar kilnBOT
gritty prairie
How does this equal to 1/8 pi x^2
mortal hemlock
$\frac24 \pi x^2 - \frac14 \pi x^2 = \frac14 \pi x^2$
mortal hemlock
wdym?
mortal hemlock
then it just becomes:
wraith daggerBOT
Flappie
wispy talon
cedar kilnBOT
wispy talon
is 0/0 equal to 0?
wispy talon
??
wispy talon
yes
wispy talon
huh
mortal hemlock
see the contradiction?
wispy talon
so it's not undefined?
wispy talon
but desmos is saying 0
wraith daggerBOT
wispy talon
is desmos wrong?
cosmic steppe
but desmos is saying 0
That's more of a limit. ln(0) also isn't 0
mortal hemlock
so im not sure why youre saying that desmos is giving 0/0 = 0
cosmic steppe
Limits doesn't mean the function is defined there. But desmos likes to put a point at limits anyways because why not
wispy talon
Limits doesn't mean the function is defined there. But desmos likes to put a po...
oh..
desmos moment
💀
cosmic steppe
,w limit as x -> 0 for x/ln(x)
mortal hemlock
the function you put in x/ln(x) has a limit at x->0
wraith daggerBOT
mortal hemlock
but if you plug in 0/ln(0) then its undefined
wispy talon
yeah i get this
mortal hemlock
but if you plug in 0/ln(0) then its undefined
important distinction
wispy talon
the limit of (x/log(x)) as x approches 0 is equal to zero
because 0.00000000001
and -0.0000000001
will tell you
but i still don't like
how desmos
says it's 0
kinda annoying but ok
whatever
well thanks guys!
👍
mortal hemlock
Limits doesn't mean the function is defined there. But desmos likes to put a po...
@wispy talon
What happens when you plug in (x+1)(x-1)/(x+1) into desmos?
Does it have a perforation at x=1?
cedar kilnBOT
@wispy talon Has your question been resolved?
wispy talon
Does it have a perforation at x=1?
at 1?
you mean -1?
at -1 it should
because we are diving by 0
another thing to add, i don't like this phenomenon either
calculator moment
💀
they just rounded it down to 0
yeah but now i know how calculators and demos interepret limit as
interesting
thanks guys
.close
split pier
cedar kilnBOT
split pier
I can show by definition that
| |f(x)| - |l| | </= |f(x) - l| < ε whenever 0 < |x - c| < δ
If i choose ε = |l|/2 then
|l|/2 < |f(x)| < 3|l|/2 whenever 0 < |x - c| < some delta that depends on the given epsilon
I can't find that delta since f(x) isn't given, or can i? The question tells me to show that a δ>0 for which this happens, but how can i find that delta
dull oxide
Grammatically, I cannot understand this question
split pier
Grammatically, I cannot understand this question
- i think it meant to find an epsilon for which that statement holds water
- 0<|x-a|<delta is clearly a printing mistake, it should be c not a
wild verge
cedar kilnBOT
wild verge
Why in the last step is it minus 6sqrt(3) - 5sqirt(2)
Oh it it because the forces are pushing against each other?
Because it’s in the x direction
.close
dark jackal
cedar kilnBOT
dark jackal
can I get any hints how to start solving this one? I only know that |sinx| will be wavy above x axis
cedar kilnBOT
@dark jackal Has your question been resolved?
crimson sedge
Abs[Sin[x]] is going to match Sin[x] when Sin[x] is positive.
shut tapir
You don't have to calculate the value of the integral, use comparison test to check the nature of the integral
Is that JAM's paper's question?
cedar kilnBOT
@dark jackal Has your question been resolved?
plucky merlin
what are you looking for exactly? @dark jackal
But what are you solving?
No
So, converges means the integral from 1 to infinity approaches 0
Diverges means the integral from 1 to infinity approaches a finite number
0 in this case is not a finite number, I'm assuming
This may help more than I can. But, For something to be 'not absolutely convergent' it has to be convergent in it's base form and divergent in it's absolute form
royal finch
Is there extra information on this problem? The phrasing in that screenshot doesn't make sense.
plucky merlin
Sin(x) is convergent |sin(x)| is divergent
royal finch
The integral without the absolute value sign is conditionally convergent, but as written that is obviously wrong
plucky merlin
The integral without the absolute value sign is conditionally convergent, but as...
That is the part that is confusing me too
royal finch
Well that integral as written is not convergent. It isn't conditionally convergent.
plucky merlin
Either the question was supposed to be sin(x)/x or the 'correct' answer is wrong
royal finch
The intuition is that unlike sin(x)/x, |sin(x)|/x is O(x^3) and always positive on 0 to infinity, so asymptotically it is similar to integrating x^3 from 0 to infinity which diverges. If you want write an inequality in terms of an integral, it's a lot more technical work.
uneven matrix
The intuition is that unlike sin(x)/x, |sin(x)|/x is O(x^3) and always positive ...
where did you get x^3
plucky merlin
See if sin(x)/x diverges or converges set up an integral (or sigma notation) than if no calculator available plug and chug, if available set number from 1 to (approaching infinity) and see what happens. Then make the equation absolute and do the same thing. If they are different it is 'not absolutely convergant' (is this a correct way of denoting it JessicaK?)
uneven matrix
my intuition is that |sin(x)| = O(c)
royal finch
Sorry x^2
uneven matrix
and integral of 1/x diverges
royal finch
You can compare it to a harmonic too yes
uneven matrix
i just dont know how to exactly formalize the fact that |sin(x)|>epsilon>0 except for like measureless points
royal finch
You would use the fact that $\int_{n\pi}^{(n+1)\pi} |\sin(x)|/x dx \geq \frac{1}{(n+1)\pi} \int_{n\pi}^{(n+1)\pi } |sin(x)| dx = 2/(n+1)\pi$ and then sum over all the intervals and do a comparison to a harmonic series.
The key is that the integral of |sin(x)| is constant
wraith daggerBOT
JessicaK
royal finch
shrug it's your solution
You would have gotten it from where you were at with a bit of thinking
cedar kilnBOT
@dark jackal Has your question been resolved?
atomic valley
Please explain.
In first equation why he used x^3+2 as f(-6), however in second equation he used right side of the equation “4x+1/x-5”, why did he write f^-1=4x+1/x-5, but not 2x-1/x+3 like in previous equation??
crimson delta
well in the first he asks for f(6) and in the second for f^-1(3)
atomic valley
yes what is the difference
crimson delta
well the ^-1
atomic valley
if ^-1 we should use the right side?
crimson delta
yes
atomic valley
why?
crimson delta
f^-1(3) asks what you have to put into f to get 3
so f(what you want)=3
so the 3 is on the right side
crimson delta
yes
crimson sedge
cedar kilnBOT
crimson sedge
can someone explain the third condition for a first order approximation for me? I don't understand what it says that isn't already being said by the first two
tropic oxide
is this in the context of multivar or single var?
if single var, c ensures g has the same slope as f near x=a
crimson sedge
thank you
cedar kilnBOT
Available help channel!
near aurora
Need help with 13.10 (8)
cedar kilnBOT
Need help with 13.10 (8)
idle tusk
$1-4\cos^2 (x) = 2\sin(x)\cdot\cos(x)$
wraith daggerBOT
artemetra
idle tusk
this one?
near aurora
yes
near aurora
its a identity?
idle tusk
yeah my bad
near aurora
??
near aurora
do i write is as that?
idle tusk
$4\sin^2(x) - 3 = 2\sin(x)\cdot\cos(x)$
wraith daggerBOT
artemetra
near aurora
ok now what?
wary anchor
sin^2x = 1-cos^2x
idle tusk
sin^2x = 1-cos^2x
we just came from there lmao
torpid shard
$sin^2x = 1-cos^2x
wary anchor
oh lol
raw gulch
I don't want to interrupt, but maybe you'd better think of a way to get sin2x and cos2x and then combine them together
minor crystal
oh yeah
torpid shard
<@&286206848099549185> what should i do?
where is the problem
near aurora
**artemetra**
this
torpid shard
Uhm
cedar kilnBOT
@near aurora Has your question been resolved?
cerulean harness
**artemetra**
try to isolate the cos(x) in RHS by dividing the both equations by cos(x) and sqaure both sides
@near aurora
near aurora
Ok ill try
cerulean harness
Continuing the calculation would end up having a quadratic eqaution of cos^2 (x)
near aurora
do i divide everything by cos?
cerulean harness
do i divide everything by cos?
yes in first step
near aurora
Is this correct?
cerulean harness
Is this correct?
I won't prefer breaking into two different fraction in LHs
Keeping that together would be of help
also in RHS it should be just 2sin(x)
near aurora
2sinx/cosx is tg no?
cerulean harness
2sinx/cosx is tg no?
tg? wdym?
cerulean harness
alr 👏
near aurora
so the left side should be together too?
cerulean harness
so the left side should be together too?
Yes it'd be better if u do so
near aurora
so it would be 1-4cos^2x/cosx
cerulean harness
so it would be 1-4cos^2x/cosx
yes
near aurora
so RHS is 4sin^2x
cerulean harness
so RHS is 4sin^2x
exactly
near aurora
i just gotta square the LFH right?
cerulean harness
yes
cerulean harness
i just gotta square the LFH right?
both sides u mean?
near aurora
yea
cerulean harness
(a-b)^2 = a^2 - 2ab + b^2
near aurora
yea 4cos^2x would be 16cos^4x no?
cerulean harness
yea 4cos^2x would be 16cos^4x no?
u have (1-4cos^2(x) )
cerulean harness
no that's perfect!
near aurora
ok
cerulean harness
since we have cos in majority we'd like to form an equation ONLY conataining cos
since u have sin in RHS ,
Apply sin^2 (x) = 1 -cos^2 (x)
then muliply both sides by cos^2(x) , that would cancel out the denominator
Then continue simplifing untill a qadratic eqaution comes up
near aurora
do i bring everything to the left?
cerulean harness
do i bring everything to the left?
sure u can
whatever u do, form a quadratic eqaution
near aurora
Like this?
cerulean harness
oh that's nice
u have those values for cos^2 (x)
Sqare rooting them will help u to get the values of x
cerulean harness
Like this
ah let's say yes
I mean is there any inerval for x given in the question?
near aurora
no i just need to find x
near aurora
no intervals are given
cerulean harness
okay then
then solve for [0, 2pie]
do u know how to solve trig angles using unit circle?
near aurora
not rylly
crimson sedge
There are 100 numbers in a number set. If you remove one number from a set, then the median of the remaining numbers will be 78. If you remove another number, then the median of the remaining numbers will be 66. Find the median of the entire set
help
@cedar kiln
There are 100 numbers in a number set. If you remove one number from a set, then the median of the remaining numbers will be 78. If you remove another number, then the median of the remaining numbers will be 66. Find the median of the entire set
cedar kilnBOT
There are 100 numbers in a number set. If you remove one number from a set, then...
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crimson sedge
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cedar kilnBOT
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crimson sedge
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cedar kilnBOT
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cedar kilnBOT
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granite knoll
cedar kilnBOT
Available help channel!
crimson sedge
hello
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
cedar kilnBOT
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crimson sedge
<@&286206848099549185>
cedar kilnBOT
@crimson sedge Has your question been resolved?
dull oxide
I'm just wondering why z+x/2 and z-x/2 are coprime
Because you're only considering primitive triples
If they were not coprime, then z and x would not be coprime, and -by extension- y would share that same factor, so the triple would not be primitive
@crimson sedge hope that helps
crimson sedge
If they were not coprime, then z and x would not be coprime, and -by extension- ...
thx man ^_^
.close
harsh dove
hey,
an enemy has health and heals health every turn
allies deal damage every turn
how do i figure out how many turns to kill the enemy?
numbers:
63 max health (cannot heal above this)
heals up to 2 health every turn an ally takes (after damage dealt)
allies deal 8 damage each turn
also im making a table in sheets with a bunch of different health/heal/damage number combos so im looking for a math formula i can turn into a sheets formula to put into each cell
harsh dove
also technically the enemy heals 4 health every other turn an ally takes, but im going by average damage dealt by all allies
cause simplicity is better here to cover all ally team combos, but id still like an exact number of hits based on those averages
cedar kilnBOT
@harsh dove Has your question been resolved?
harsh dove
<@&286206848099549185>
cedar kilnBOT
@harsh dove Has your question been resolved?
upper abyss
So the enemy loses 6 health per turn? Then it would take 11 turns to deal 63 damage
crimson delta
as long as you dont make the classic mistake of the enemy dying before he "heals" again and needs another turn. tho that doesnt happen here at least. close tho
cedar kilnBOT
@harsh dove Has your question been resolved?
harsh dove
What about
(Max health - damage) / (damage - healing)
I know it will be wrong for practically every combo of health/heal/damage because im using averages but it will be close right?
I had a hunch I was supposed to use fractal exponents somehow, like
X^1.(damage)
Or something
crimson delta
What about
(Max health - damage) / (damage - healing)
that rounded up and then +1 works. at least in the above case. but really with combos etc it will only be an approximation
harsh dove
Why + 1 at the end?
gloomy bough
I tried to did on my own and I figured out 2^a/2^b = 64
= a-b = 6
so I know its A but I tried figuring out (3^a)(3^b) = 9
and I got 9^a+b = 9 which gives 1
am I doing something wrong?
hollow trail
,tex .exp rules
wraith daggerBOT
cloud
hollow trail
that was incorrect, yes
minor stone
how do i start this problem?
cedar kilnBOT
how do i start this problem?
ancient lodge
Consider the zeros and turning points
gloomy bough
How do I do this
cedar kilnBOT
How do I do this
split pike
How do I do this
assuming your answer y = x-2/x^2 is correct
then
option h is the correct ansswer
split pike
assuming your answer y = x-2/x^2 is correct
.
gloomy bough
.
I was just trying to solve each one of the options 💀
to see which one gives me undefined
cedar kilnBOT
@gloomy bough Has your question been resolved?
cedar kilnBOT
@gloomy bough Has your question been resolved?
cerulean sail
Note that with yours, if you put in x=2, your function would be undefined there - but the graph shows that it is defined there
Moreover you'd want the values close to x=2 to be nonzero, but with your one it would be
They get J because cancelling out the (x+2) factors gets you the 1/x^2 graph as you'd want, but you want that when x = -2 that you can't take that value
cedar kilnBOT
@gloomy bough Has your question been resolved?
minor crystal
hii @solid juniper , btw i meant the derivative of b^(1/b)
minor crystal
,w derivative of b^(1/b)
wraith daggerBOT
minor crystal
-b^(1/(b-2)) can't ever be 0 so that's out of the picture for a maxima point
log(b) - 1 = 0 can work but doesn't this depend on the base?
,, \log_{10} b - 1 = 0
wraith daggerBOT
kanna
minor crystal
would give 10 as the maxima point
but ln(b) - 1 = 0 would give e as the maxima point
at least those are the two familiar bases
btw sorry for the ping 
I was just responding to what u asked me
glossy inlet
log(b) - 1 = 0 can work but doesn't this depend on the base?
its base e by default
minor crystal
its base e by default
yeah but where does that follow from?
glossy inlet
well do you know how to do that derivative by hand
$b^{1/b} = e^{\frac{1}{b}\ln b}$
wraith daggerBOT
jewels!
glossy inlet
now you just apply the chain and product rule
minor crystal
yes that's one way
but i can just log both sides
and i'm not forced to use ln then
glossy inlet
sure
but then when you differentiate a base 10 logarithm
you get an additional factor of log_10(e)
slate lintel
you need a very strong reason to use log base anything but e in math
minor crystal
hmm fair enough
i've seen people using log instead of ln but your point makes sense
slate lintel
log is assumed to mean loge in math
glossy inlet
its just implied in calculus that its base e
minor crystal
you need a very strong reason to use log base anything but e in math
:V then why is log anything else relevant?
slate lintel
log2 is useful in CS
glossy inlet
log 10 is used in pH, the Richter scale and stuff
slate lintel
log10 is nice if you're using a slide rule or something
minor crystal
log10 for digit counting too ig
glossy inlet
decibels as well
slate lintel
since they're just a scale factor away from each other
it often doesn't really matter
minor crystal
also can i ask a (not related) trig question or do i have to make a new channel for that?
minor crystal
since they're just a scale factor away from each other
mhm i get it now, thanks~
glossy inlet
I could give it a shot
ask right here
spending my Christmas morning doing math is not what I expected
minor crystal
spending my Christmas morning doing math is not what I expected
😭 same-
i'm sorry
it's a personal question btw
but this relation can only ever be satisfied when the triangle is a 30-60-90 right?
slate lintel
no, you've only constrained two sides
crimson sedge
no not necessarily
minor crystal
i mean i thought that too but i couldn't find a counterexample
glossy inlet
if you go by the sine rule multiple triangles are possible
minor crystal
,w 2* sin(54 degrees)/sin(108 degrees)
wraith daggerBOT
minor crystal
doesn't work with 54 or 108 or anyhting like that
the best i got to was when z = 1 and y = 0.5
but that's a wolfram issue
,w 2 * sin(0.5 degrees)/ sin(1 degrees)
wraith daggerBOT
minor crystal
it just rounds to 1 but it's not really 1
slate lintel
there's a ton of options https://www.desmos.com/geometry/csxwxnovz4
minor crystal
there's a ton of options https://www.desmos.com/geometry/csxwxnovz4
can you give one?
I'm not sure how to use desmos geometry
slate lintel
you can click and drag those points
everything that is visible is a valid triangle
with one side twice the length of the other
crimson sedge
i mean i thought that too but i couldn't find a counterexample
let $z = 60\degrees$ for example, with the third side being $y$ then by the law of cosines: [
4x^2 = x^2 + y^2 - 2xy\m\cos{60\degrees}
]
so [
y^2 - xy -3x^2 = 0 \[1ex]
y = \f{x+\s{x^2+12x^2}}{2} = \f{1+\s{13}}2x
]
By what you were going for, $y$ should be the hypotenuse and [
x^2 +(2x)^2 = y^2
]
but thats not true by what we derived
wraith daggerBOT
minor crystal
but hmm it isn't 2 though?
slate lintel
yes, 52.3º is an approximation
the real value will be irrational
if you wanted both of those angles to be integers then that's harder and might indeed only be 30-60-90
crimson sedge
last equation being Pythagorean theorem to be clear
minor crystal
if you wanted both of those angles to be integers then that's harder and might i...
but how do you know it's possible if the angles aren't integers
would u just assume an irrational degree
slate lintel
wdym
minor crystal
would allow for the ratio to be exactly 2?
slate lintel
yeah i just constructed a triangle with one side exactly twice as long as the other
as in your diagram
solid juniper
thanks hayley
crimson sedge
😭
there might be an easier and more convincing method 
mess around with the usual trig equations to convince yourself
broken monolith
Hi can anyone help me with my trig geometrical prove? 🙃
crimson sedge
Hi can anyone help me with my trig geometrical prove? 🙃
!occupied
cedar kilnBOT
Hi can anyone help me with my trig geometrical prove? 🙃
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
broken monolith
Sorry
minor crystal
thanks hayley
omg kanna!! 
minor crystal
mess around with the usual trig equations to convince yourself
trig isn't allowed ig 😭
solid juniper
minor crystal
sin(z)/2x = sin(y)/x
sin(z)/sin(y) = 2
sin(z) = 2sin(y)
-1 < cos(y) < 1 but cos(y) is never 0 unless it's 0 degrees or 180 degrees:
sin(z) > 2sin(y) cos(y)
sin(z) > sin(2y)
z > 2y over the monotonically increasing interval
dull oxide
Hi can anyone help me with my trig geometrical prove? 🙃
If the sum is obtuse can you use $\sin(A+B)=\sin(\pi-(A+B))$?
wraith daggerBOT
SWR
solid juniper
yay
dull oxide
Ack in in the wrong channel
minor crystal
crimson sedge
geometry proofs aren't for me
I introduce: two column proofs
just kidding please no
dull oxide
too hard for me
Where's the question?
minor crystal
This
minor crystal
but this relation can only ever be satisfied when the triangle is a 30-60-90 rig...
and this is the actual question using the above pic as reference
dull oxide
idle tusk
recall the definition of the derivative
$f'(x) = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)-f(x)}{\Delta x}$
wraith daggerBOT
artemetra
idle tusk
what you are talking about is the same thing but if we just delta x to be 1
in general, derivative is a better approach for marginal costs
it's faster and it scales to continuous units
for example you wouldn't been able to do this if instead of radiators you had, say, kilograms of rice, it's not a discrete unit
yes
idle tusk
**artemetra**
^
which is where the derivative comes from
the cost of producing one more good (for discrete units, like radiators) OR the cost of producing infinitesimally more of a good (for continuous goods, like gallons of sth.)
well i can produce 3 gallons of water
or 3.1
or 3.0001
it's not discrete
there is half a gallon but there is no half a radiator
the f(x+1) - f(x) does work for discrete units but not continuous
derivative works for both
what f are you referring to?
c'(10)
as it says there :)
I'm not sure what you are asking here
"about how much extra will it cost to produce one more radiator"
we use the derivative to approximate f(11)-f(10)
cedar kilnBOT
@crimson sedge Has your question been resolved?
crude gale
cedar kilnBOT
crude gale
Could anyone help check my work?
Im also not too sure how to evaluate the final sum
tepid ginkgo
Praying for people to help lil bro 🙏🏻😭
cedar kilnBOT
@crude gale Has your question been resolved?
cedar kilnBOT
dire geode
well 1^3 = 1
Factor w^3 - 1
If w is a root, plug in w^2 to this equation and verify w^2 is also a root
crimson sedge
hint (A-B)^3
good
yes
what do you mean
yes you can express
that
w^9
(w^3)^3
yes
either (w-1) = 0
or w^2+w+1 = 0
you welcome ^^
crimson sedge
translate?
i thought there is more okay
use distance formula
the distance formula between a point (x,y) and the origin(0,0) is given by
$r=\sqrt{x^2+y^2}$
wraith daggerBOT
snow
twin panther
By using 2,7 and 9 we create numbers and put them in growing order : 2, 7, 9, 22, 27, 29, 72, 77, 79, 92, 97, 99, ...
twin panther
in this order what place "72297" is ?
nimble mountain
seems isomorphic to base 3
cedar kilnBOT
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
3
nimble mountain
yea, slightly different my bad
twin panther
i got 208 but the answer is 209
tropic oxide
show how you got 208
twin panther
1 ,2,3,4,5 shows the how many number are there like with 1 digit all has 1 way so total 3 way
2 digit each has 3 way so total 9 ways
3 digit each has 9 way total 27
and so on
tropic oxide
what is the "total" column?
twin panther
i got there is 120 number until 5 digit
wraith daggerBOT
Result:
121
121, not 120
that's how many numbers there are with 4 or fewer digits
wait hold on ok
twin panther
yes
tropic oxide
what is that 1 at the beginning anyway
tropic oxide
the more i look at this, the more confused i get
"total" is not the cumulative total of the left column. what do those roman numerals mean.
literally wtf lol
twin panther
roman numerals shows how many digits they have
then other column show for example , with 2 digits each has 3 way to make number 22, 27, 29 or 72,77,79
surreal karma
twin panther
so total column is 3* second column cus if each has 3 way and there is 3 numbers 3 * 3 is the total number they can make with 2 digits
tropic oxide
roman numerals shows how many digits they have
ok then why does I correspond to 1 and not to 3
twin panther
ok then why does `I` correspond to 1 and not to 3
cus each can make 1 number that have 1 digit
tropic oxide
....
?????
there are 3 single-digit numbers that you can make, not 1...
sorry @twin panther i don't understand ANY of your work at all
twin panther
there are **3** single-digit numbers that you can make, not 1...
that is what i say
each can make 1 total 3 * 1 = 3
tropic oxide
"each"?
twin panther
yes 2 ,7 ,9
twin panther
just english is my fourth language )
tropic oxide
what are the other 3?
twin panther
my own russian and turkish
cedar kilnBOT
@twin panther Has your question been resolved?
cedar kilnBOT
@twin panther Has your question been resolved?
cedar kilnBOT
@twin panther Has your question been resolved?
twin panther
<@&286206848099549185>
raw gulch
<@&286206848099549185>
I give you initial hint for you, look and read it carefully:
raw gulch
<@&286206848099549185>
$\square \longleftarrow 3\\square \square \longleftarrow 3\cdot 3\\square \square \square \longleftarrow 3\cdot 3\cdot 3\\square \square \square \square \longleftarrow 3\cdot 3\cdot 3\cdot 3\\overset{2}{\square }\square \square \square \square \longleftarrow 3\cdot 3\cdot 3\cdot 3\\overset{3}{\square }\square \square \square \square \longleftarrow 3\cdot 3\cdot 3\cdot 3$
wraith daggerBOT
Joanna Angel
raw gulch
I consider that rest should be easy for you to estimate and summarise it
cedar kilnBOT
@twin panther Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
cedar kilnBOT
@crimson sedge Has your question been resolved?
polar holly
all I've really heard from derivatives in word problems is that it mostly brings affect when finding the amount of someting in respects to time
kindred storm
The derivative tells the (instantaneous) rate of change in cost per part.
The exact answer is the average rate of change in cost per part from x = 10 to x = 11, but the instantaneous rate is close to that.
So they use it as an estimate.
To find the slope between those points, you have to calculate the cost of 11 using a cubic polynomial and then subtract the cost of 10.
It's more work than just using the derivative, which is a quadratic polynomial.
I mean the error will be low.
Because both are slopes.
We don't care about between points.
When it's getting near a local maximum, the slope is close to zero.
Which is what you'd expect.
The point is that it's an estimate, and saying that the slopes have different signs doesn't make it not an estimate.
kindred storm
<@&268886789983436800>
opaque harbor
you've not seen a limit definition?
kindred storm
That's not very likely when x increases by 1.
opaque harbor
cool
so
when $h$ is small, we can say
$$f'(x)\approx {f(x+h)-f(x)\over h}$$
and so $$f(x+h)-f(x)\approx f'(x)\cdot h$$
wraith daggerBOT
Edward II
