And after figuring out both solutions what
#help-23
hard crest
figure out when it's above 100 and when it's below 100
couple ways to do that, one is to just test points in between the solutions
that's probably the simplest
would recommend a sketch
obtuse folio
oh and is the equation for solving the suplementary sine like this $\frac{\pi}{15}x+\frac{3\pi}{2}=\pi-\sin^-1 \frac{30.5}{67.5} + 2\pi n$
flat frigateBOT
N1x1T4
hard crest
yeah that'll work
obtuse folio
And after that I plug in the smallest n values for the equations and then calculate the difference between them
lean otter
Product of all Even divisors of 1000
safe radishBOT
Product of all Even divisors of 1000
upbeat ridge
Huh?
lean otter
Huh?
Yeah
Subjective question
Find the product of all Even divisors of the number N = 1000
upbeat ridge
Even divisors?
misty coral
Product of all Even divisors of 1000
fundamental theorem of arithmetic
misty coral
consider the prime factorization of 1000 and all the factors that make it up
a grid can help visualize it
lean otter
Uhh
misty coral
(i+1)(j+1) ?
lean otter
Okay
I guess
Yeah
Must have forgotten
Then?
Next step
So there are 16 factors yes
hard crest
if you just list them all and multiply them together
that will give you your answer
all of the even ones anyway
lean otter
if you just list them all and multiply them together
I have answers in powers of 2 and 10
I'll have to factor all the factors
misty coral
I have answers in powers of 2 and 10
thats fine
lean otter
Yet like a faster way pr something
We typically get 45 seconds or so to solve this
Without calculator
hard crest
i mean you can just generate the factors without multiplying them out
factors are (some number of 2s) times (some number of 5s)
flat frigateBOT
hayley!
lean otter
Oh (2+2²+2³)(5⁰+5¹+5²+5³)
This will give me all factors of 1000 divisible by 2
hard crest
if you systematically list them out, it's clear how to multiply them all together
lean otter
I mean I wanted a better method, if that exists, but yeah okay nvm
lean otter
Oh (2+2²+2³)(5⁰+5¹+5²+5³)
One by one multiplication of first bracket into second
There's no other method tho?
misty coral
I mean I wanted a better method, if that exists, but yeah okay nvm
this honestly takes 30 seconds after you've done it once
safe radishBOT
hard crest
really any nested structure
those are common ones but like if you have sin(x²) you need it
you'd use the chain rule here
yes
well no
yes
glacial mesa
Is there a way to calculate the temperature after t units of time with only the item’s temperature and temperature?
safe radishBOT
Is there a way to calculate the temperature after t units of time with only the ...
wise saddle
If you know how fast temperature "travels" between the object and the exterior
glacial mesa
So do I need another piece of info after t units of time
wise saddle
What you often have is
-supposing outside temp is constant
-how much energy is required to heat up the object by 1 degree
-starting temperature of the object and the outside
wise saddle
Well if the object is 1kg of water it wont heat up the same if it were 1kg of cement
For example
So youll need that info
desert pasture
Is there a way to calculate the temperature after t units of time with only the ...
Imo you'll also need to know how conductive the substance is, and probably the dimensions too
wise saddle
Yes
glacial mesa
I’m doing calc right now and the practice gives me the temperature of the exterior, the item’s temperature before being put into the exterior temperature, and the item’s temperature after t units of time inside the exterior temperature
And I’m usually told to find after t units of time
wise saddle
So how does the thermal energy travel ("how fast")
How much thermal energy is needed to warm up the object by a certain amount
wise saddle
I’m doing calc right now and the practice gives me the temperature of the exteri...
You need to have a forula that tells how fast the warmth travels
For example
With f(t) giving the sarmth of the object
F'(t) = (t exterior - t object) * a certain factor
safe radishBOT
@glacial mesa Has your question been resolved?
hard crest
I’m doing calc right now and the practice gives me the temperature of the exteri...
i think you assume it's an exponential curve and use the given points to find the coefficients
safe radishBOT
safe radishBOT
Available help channel!
past birch
how would i do q5? im not sure where to start
safe radishBOT
how would i do q5? im not sure where to start
split ether
I would try substituting for 2x-1
split ether
Yes
So it becomes 1/2 the integral of (u + 1)^4/u^2 from 1 to 3
Now you can just expand the nominator, divide each term by u^2 and apply power rule for integration
split ether
Really weird
past birch
this is the farthest substitution can get you?
past birch
So it becomes 1/2 the integral of (u + 1)^4/u^2 from 1 to 3
like i cant make another substitution to simplify this?
split ether
Hmm
past birch
yeah
split ether
No, I think expanding is inevitable
Even if you don't know binomial theorem you could just square (u^2 + 2u + 1)
past birch
Looking at wolfram did it though, it seems expanding is inevitable
,w integrate 16x^4/(2x-1)^2
flat frigateBOT
past birch
huh?
calm bridge
hmm
flat frigateBOT
Dyssrupt
calm bridge
apply difference of squares two times
flat frigateBOT
Dyssrupt
past birch
oh
calm bridge
see if you get something useful
past birch
hold on
calm bridge
past birch
there is still a +1 tho
calm bridge
who's a?
past birch
a "+1"
calm bridge
yeah
flat frigateBOT
Dyssrupt
past birch
yup
flat frigateBOT
Dyssrupt
calm bridge
i think you can do this multiplication, this one's not too difficult
and then use long division
and show what you get
past birch
and then use long division
shouldnt the brackets be at the bottom for this though?
calm bridge
wdym
past birch
im not sure how to long divide that
past birch
i havent learnt that yet unfortunately 😭
past birch
cant i express it in the form of A/u-1 + B/u+1
calm bridge
cant i express it in the form of A/u-1 + B/u+1
you can, but when above's degree is less than bottom
past birch
8
calm bridge
and integration?
past birch
yes
calm bridge
past birch
😭
calm bridge
i learnt integration a month ago
calm bridge
neither lol
calm bridge
well you cant proceed without division
its actually simple
maybe try an online source to learn how to do one.
calm bridge
yeah
past birch
oh i see
past birch
do i need to use tangent half angle substitution to evaluate integrals such as csc and cot?
safe radishBOT
@past birch Has your question been resolved?
robust ether
do i need to use tangent half angle substitution to evaluate integrals such as c...
what exactly do you mean by this?
(what's the integral that includes csc and cot)
past birch
simply integrate csc^2x
calm bridge
hint : whats the derivative of cotx?
past birch
-csc^2x?
calm bridge
you got your answer.
low galleon
im not really sure what this is asking
safe radishBOT
im not really sure what this is asking
wise saddle
You can write f as x times v +something perpendicular to v right ?
What they ask you is what that perpendicular to v thing is
low galleon
What they ask you is what that perpendicular to v thing is
but dont they ask for the asnwer as a vector
is it asking for the coefficient of i?
obsidian oracle
but dont they ask for the asnwer as a vector
The first thing you need to do is to find a vector perpendicular to v
Let's name it w
And then you have to write F = av + bw
The component parallel to v will be av
And the component perpendicular to v will be bw
So first question : can you find any vector w perpendicular to v ?
obsidian oracle
This one is much too complicated
low galleon
am i wrong
obsidian oracle
No, but you will regret using fractional coefficients
low galleon
and for parallel, 28,-16
im still unsure what it means by component tho
if i entered those would they be the right answer?
obsidian oracle
What are you trying to do right now ?
obsidian oracle
i think -64/7,-16
If I add those vectors
low galleon
is that how it works
obsidian oracle
So those are not the parallel/perpendicular components of F
Ok, do you know about the dot product ?
low galleon
yea
low galleon
wait what is the numerator
obsidian oracle
Oh different notation
flat frigateBOT
rafilou2003
obsidian oracle
And the perpendicular component will be the difference between F and its parallel component :
It will be $F - \frac{F\cdot v}{|v|²}v$
flat frigateBOT
rafilou2003
low galleon
The parallel component of F will be $\frac{F\cdot v}{\|v\|²}v$
is this right for the perpendicular component
i mean parallel
obsidian oracle
Yes
low galleon
bruh i got it wrong
obsidian oracle
Np 👍
low galleon
.close
safe radishBOT
safe radishBOT
Available help channel!
indigo wharf
indigo wharf
ok
pallid nymph
perhaps try a base 10 expansion of each of the numbers
indigo wharf
perhaps try a base 10 expansion of each of the numbers
what does that mean
what i've tried so far:
simplifying to:
300a+21b+11c=998d
pallid nymph
yes, this
pallid nymph
Try each case: what happens once you set a = 1?
pallid nymph
Suppose you want to make this hold, for nonzero digits. If d=1, can there be values for b or c?
indigo wharf
alright
pallid nymph
I believe you should consider rerunning the logic you used to restrain a
indigo wharf
so 21b+11c = 698
indigo wharf
I believe you should consider rerunning the logic you used to restrain a
o
ok so what should our next step be
pallid nymph
It seems that putting a restraint on d may be easier
pallid nymph
Since it has the largest coefficient, it will the your first step
indigo wharf
and constrain d value from that
pallid nymph
Yes, this is a good idea
Once d is set, you can redo that process for the next largest coefficient and check all the cases
pallid nymph
Indeed, so what can d be?
indigo wharf
1 or 2
pallid nymph
Precisely; what happens when d=1, now?
pallid nymph
Yes
pallid nymph
Such is life sometimes. Let's explore this a little bit: if a = 1 and d = 1, then we have that 21b + 11c = 98. Do you know about linear combinations of natural numbers or Euclid's algrotihm?
indigo wharf
no but i know factoring of diophantine equations
tiny wraith
Overall
indigo wharf
alr
now what
wait
i can solve this via system
huh?
this doesnt make sense b became negative
or maybe this case doesn't work
pallid nymph
Indeed. I think you have 6 systems to solve: if the solutions do not make sense, that case will not lead to a solution; if they do that is a solution.
Not all cases will have solutions, all that we have done is narrowed down the search
You should also consider what happens if a = b = c
pallid nymph
what i've tried so far:
simplifying to:
300a+21b+11c=998d
I am realizing this expansion is not correct
100a + 10b + c + 100a + 10c + b + 100a + 10b + d = 111d
Each value of d will lead to a unique solution here
indigo wharf
oops
pallid nymph
d = 1, d = 2 will have a = 0
d = 3, d = 4, d = 5 will have a = 1
d = 6, d = 7, d = 8 will have a = 2
d = 9 will have a = 3
indigo wharf
whats the right expansion
pallid nymph
You should recreate what we have, just with this equation
indigo wharf
100a + 10b + c + 100a + 10c + b + 100a + 10b + d = 111d
so this is the right one?
pallid nymph
100a + 10b + c + 100a + 10c + b + 100a + 10b + d = 111d
this one: i am not sure how you got to 998d
indigo wharf
oopsie
indigo wharf
this one: i am not sure how you got to 998d
ok but then d could be anything
<@&286206848099549185>
tiny wraith
Try carrying it out as a normal addition first
c + b + d gives d, so c + b must be 10 and you have to carry 1
pallid nymph
ok but then d could be anything
Indeed it can be
safe radishBOT
@indigo wharf Has your question been resolved?
obtuse folio
$\sin{x}+\sin{\frac{\pi}{2}}=0 \parallel \sin{}^-1 \
\begin{cases}
x+\frac{\pi}{2}=2\pi n \
\
x+\frac{\pi}{2}=\pi+2\pi n
\end{cases} \parallel -\frac{\pi}{2} \
\text{here are the x values :}
\begin{cases}
x=-\frac{\pi}{2}+2\pi n \
x=\frac{\pi}{2}+2\pi n
\end{cases} \
\text{let's say} \ \ \ n=0 \
\begin{cases}
x=- \frac{\pi}{2}+2\pi \times 0 \
x=\frac{\pi}{2}+2\pi \times 0
\end{cases} \
\
\begin{cases}
x=-\frac{\pi}{2} \
x=\frac{\pi}{2}
\end{cases} \
\
\text{Since we now} \ \ \ \sin{\frac{\pi}{2}}=1 \ \ \ \text{We can rewrite the original function like this :}\
\
\sin{x}+1=0 \to \sin{x}=-1 \
\
\text{Let's plug in in our x values to see if they're right} \
\
\begin{cases}
\sin{-\frac{\pi}{2}}=-1 \
\sin{\frac{\pi}{2}}=-1
\end{cases}\
\begin{cases}
-1=-1 \
1=-1
\end{cases}\
\
1 \neq -1 \
$
safe radishBOT
$\sin{x}+\sin{\frac{\pi}{2}}=0 \parallel \sin{}^-1 \\
\begin{cases}
x+\frac{\pi}...
flat frigateBOT
N1x1T4
gentle oak
$x+\dfrac{\pi}2=\pi +2\pi n\iff x=-\dfrac{\pi}2+2\pi n+\pi$
obtuse folio
What's this?
flat frigateBOT
Joseph.P
sleek ingot
x+ pi/2 = pi + 2pi*n is not correct
gentle oak
In your second system you wrote $x=\dfrac{\pi}2+2\pi n$
flat frigateBOT
Joseph.P
obtuse folio
yes
gentle oak
For the second equation
sleek ingot
so did you get your two equations by applying inverse sine to the original problem?
flat frigateBOT
N1x1T4
obtuse folio
then I took the inverse sine
sleek ingot
so I don't think you can distribute that
obtuse folio
so I don't think you can distribute that
what does distribute mean?
so one of these is wrong or? $\begin{cases} x+\frac{\pi}{2}=2\pi n \ \ x+\frac{\pi}{2}=\pi+2\pi n \end{cases}$
flat frigateBOT
N1x1T4
obtuse folio
what does that mean?
safe radishBOT
@obtuse folio Has your question been resolved?
obtuse folio
<@599643194850017320> Has your question been resolved?
Well guess Botty, has it?
lament quartz
Could someone help me derive this, by the definition method plzz
stable inlet
from the start, you can factor a difference of two squares
then $\frac{\sqrt[3]{x+h}-\sqrt[3]x}{h} = \frac{\sqrt[3]{x+h}-\sqrt[3]x}{h} \cdot \frac{\sqrt[3]{x+h}^2+\sqrt[3]{x+h}\sqrt[3]x+\sqrt[3]x^2}{\sqrt[3]{x+h}^2+\sqrt[3]{x+h}\sqrt[3]x+\sqrt[3]x^2}$
flat frigateBOT
Toblerone
stable inlet
multiplying by cuberoot(x+h) + cuberoot(x) won't work because that's not the correct conjugate
stable inlet
Wouldn't this be for x^1/3 not x^2/3?
if you complete the square at the start, the ^2/3 becomes ^1/3
stable inlet
**Toblerone**
you could modify this to be the correct conjugate for ^2/3, but it becomes messier
safe radishBOT
@lament quartz Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
golden umbra
safe radishBOT
golden umbra
Need help for this section step by step !
Don’t tell me the answer because I wanna learn how to figure it out but yeah I’m kinda confused and it would be best to see if I can get support
flat frigateBOT
tall crow
Dyk what the y intercept, c is?
golden umbra
Yeah
golden umbra
Dyk what the y intercept, c is?
Wdym c
golden umbra
Ohh okay
tall crow
So what is it?
golden umbra
So it would be y=mx + 1
And the slope would be
Y=-2+1
Right?
Because we are given 2 points on the graph
Oh whoops
y=-2x+1
So moving to the next question it says “the shading is <blank> the line, and the boundary is <blank>”
The shading would be a solution of some sort and the non shading is not. How can I fill in the blank?
tall crow
y=-2x+1
Uhm no
How’d you get this?
you have 2 points you need to do the regular $y2-y1/x2-x1$
flat frigateBOT
𝕏
golden umbra
you have 2 points you need to do the regular $y2-y1/x2-x1$
ohh
Okay so the 2 points are (-2,0) and (0,1)
tall crow
Yeah
golden umbra
Okay so now I can apply it to the equation
tall crow
The next one I do not know what the first blank is but the second is Solid
Strict or Slack
golden umbra
Ah okay
tall crow
Third one
golden umbra
The inequality would be X + y = 1/2 correct?
tall crow
We have not determined the inequality sign yet
tall crow
Are you ready for the thirdv
golden umbra
No wait
Ah nvm okay yeah
How can I find the inequality?
OH NVM
figured it out
tall crow
You have technically you just need to find the sign
golden umbra
Ah okay
tall crow
So that makes number 3?
golden umbra
Thank you so much man! You’re such a life saver fr🙏🏼
safe radishBOT
Available help channel!
lean otter
what is that $a_{r} : and : b_{r}$ ?
safe radishBOT
what is that $a_{r} \: and \: b_{r}$ ?
flat frigateBOT
bearcw
devout shale
Arbitrary finite sequences
lean otter
Arbitrary finite sequences
like "a "and "b" is from different sequence and they are the same nth term in those two sequence?
devout shale
Yes
velvet kelp
hi idk how to do this but is this right? and for part b would i just input the answer that i got (304908.9721) ?
safe radishBOT
hi idk how to do this but is this right? and for part b would i just input the a...
@velvet kelp Has your question been resolved?
velvet kelp
<@&286206848099549185>
i got another answer which was 436804.0599 but idk if that's right either
earnest rapids
hi idk how to do this but is this right? and for part b would i just input the a...
Well you know the general term of gp is Tn = (a) (r^(n-1)) ?
You are asked to write a general term and put sigma before it to get sum
But you directly put n=20
Remember n is variable here you put n=1,2,3... and sum all terms
earnest rapids
i got another answer which was 436804.0599 but idk if that's right either
Yeah this is correct
So you knew all that, nvm
earnest rapids
hi idk how to do this but is this right? and for part b would i just input the a...
0.965^(n-1) **
slate spade
hi not sure why my answer is wrong
safe radishBOT
hi not sure why my answer is wrong
slate spade
hi not sure why my answer is wrong
this is what the computer says the correct answer is
my answer is this
wait never mind
.close
safe radishBOT
safe radishBOT
Available help channel!
brazen galleon
determine lim f(x) when x->0 Deduce the equation of an asymptote to the curve.
flat frigateBOT
frank valley
Determine the radius of convergence of $\sum _{k=1}^{\infty }\left(\sqrt{k^2+1}-\sqrt{k^2-1}\right)x^k$.
safe radishBOT
Determine the radius of convergence of $\sum _{k=1}^{\infty }\left(\sqrt{k^2+1}-...
flat frigateBOT
sunside
frank valley
$R=1/\limsup_{k\to\infty}|a_k|^{1/k}$, where $a_k=\sqrt{k^2+1}-\sqrt{k^2-1}$, however, how to evaluate that limsup?
flat frigateBOT
sunside
feral linden
**sunside**
This time this method might not work
Try radius = lim a(k)/a(k+1) method
(divide by k both above and below in a(k)/a(k+1))
frank valley
Try radius = lim a(k)/a(k+1) method
I will try, thanks for replying
feral linden
Np
And also rewrite sqrt()-sqrt() as 2/(sqrt()+sqrt()) by the way
For both a(k) and a(k+1)
feral linden
I will try, thanks for replying
Got it?
feral linden
Okay
frank valley
Okay
$$\begin{align}\frac{2}{\sqrt{k^2+1}+\sqrt{k^2-1}}\frac{\sqrt{(k+1)^2+1}+\sqrt{(k+1)^2-1}}{2} \ =\frac{\sqrt{1+\frac2{k}+\frac2{k^2}}+\sqrt{1+\frac2{k}}}{\sqrt{1+\frac1{k^2}}+\sqrt{1-\frac1{k^2}}} \end{align}$$
frank valley
let me edit
flat frigateBOT
sunside
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
feral linden
Correct
frank valley
ok, so this clearly tends to 1
feral linden
Yeah
frank valley
cool, thank you
feral linden
Np
frank valley
.close
brazen galleon
safe radishBOT
brazen galleon
how do i find the root 0.7472...
previously i did that
and there was this question
after
- calculate g(1)
- deduce the sign of g(x) on the interval 0; +infinity
so i thought it was guiding us to the thing that its negative between 0 and 1 and positive between 1 and +infinity
(which i think its what its expecting to see)
but i found out there was also that 0.7472
so what do you think about that
maybe its bcs its nearly not negative so they dont count it ?
.close
compact fossil
how can i find an exponential equation that relatively passes through these points
safe radishBOT
how can i find an exponential equation that relatively passes through these poin...
obtuse jackal
a function is exponential iff its logarithm is a line
you know how to find the best line
obtuse jackal
a function is exponential iff its logarithm is a line
just use this to bring it back to a linear problem
I'm not sure the exponential you get is guaranteed to be the best fit (by the same criteria as the line) but it ought to be a good fit
compact fossil
is there a way to do it without logarithms cause we haven't learned that yet
obtuse jackal
i tried using geometric sequences
in this case it does work nicely
you can take the average ratio to be the base of your exponential
and that should be a decent fit
(with a good initial value of course)
compact fossil
so i did r^54-1= 5.750/0.001
and r= 1.177
so would the exponential be y=0.001 * 1.117^x
obtuse jackal
,w 1.117^6
flat frigateBOT
obtuse jackal
it's just that it introduces a ratio of 6 when the other ones are between 1.5 and 2
so it's quite strongly offputting
but I mean ... Data is data
safe radishBOT
safe radishBOT
Available help channel!
coarse cove
hello
cold aurora
Hello
naive lagoon
^
coarse cove
something like this
how doi work it out
hello?
: (
@cold aurora
are u here
cold aurora
Yes
coarse cove
from the answer from 16 x 8
its not really a question information type
it just says what isthe diameter
no what is the are of the circle
area
.close
fallen notch
Hi, could someone help me with this? Whenever I try to use substitution and try to calculate the new integral limits I get integral from 0 to 0... But that cant be as the result isnt 0
safe radishBOT
Hi, could someone help me with this? Whenever I try to use substitution and try...
Show your work, and if possible, explain where you are stuck.
obtuse jackal
what substitution are you trying to make ?
fallen notch
I tried to do sqrt(x) as z
fallen notch
so I am stuck because I get 0 for the integral borders and idk why
and also, i am not sure if I substituted the right thing
calm bridge
how are you getting limits 0 to 0
fallen notch
sin(pi)/pi = 0/pi = 0
obtuse jackal
the new bounds are the image of the previous bounds by the substitution function
fallen notch
Could someone help me with my solution? for this integral I get the result I am about to send in. But chatgpt and integral calculator say different solution, and I dont know what I did wrong.
safe radishBOT
Could someone help me with my solution? for this integral I get the result I am ...
fallen notch
cold aurora
Mistake is in the last line.
You forgot to change the sign after opening the bracket.
sonic storm
safe radishBOT
sonic storm
supposed to use the parametric function arc length formula(L = integral)
but where is t in this situation
oh wait
nvm im slow
how do i unoccupied this channel
.close
safe radishBOT
safe radishBOT
Available help channel!
keen sequoia
safe radishBOT
lean otter
Do you know the definition of a limit? Not being condescending, but it’s important conceptually
If not I will explain:
L is a limit of f as x -> a if we can get f arbitrarily close to L as x gets arbitrarily close to a
Meaning that you can get your function as close to your suspected value as you want
At -6, you can only ever get your function to within two units of the black dot, while you can get your function as close as you want to the white dot
So choosing the black dot as your limit value would be a poor choice. You’re already picking up on this in your previous two answers with -4
safe radishBOT
@keen sequoia Has your question been resolved?
lean otter
Instead of responding to the bot, ask questions @keen sequoia
deep musk
Trying to understand what this means, can anyone explain it for me😭
deep musk
The underlined part
craggy eagle
so f is a function right
and if you sub in any value from -4 to inf you'll get a negative value
craggy eagle
nah that's not right bro but it's close
stoic dune
What numbers are in (-4, inf)?
The text is saying that if x is in (-4, inf), then f(x) is negative
safe radishBOT
@deep musk Has your question been resolved?
deep musk
What numbers are in (-4, inf)?
-4 to infinity
But the infinity is positive so i drew the graph like that
stoic dune
Well, 0 is in (-4,inf)
But it looks like f(0) is positive on your graph
fiery valley
I'm trying to understand the green text, I use n = 36, a = 9 and b = 4, but it's not true 9 <= sqrt(36) and 4 <= sqrt(36). I'm lost :c
safe radishBOT
I'm trying to understand the green text, I use n = 36, a = 9 and b = 4, but it's...
solar hazel
it just says a prime divisor less than or equal to sqrt(n)
doesn't say every prime divisor is less than equal to sqrt(n)
fiery valley
I don't understand
solar hazel
oh
let me reread i might not have paid attention to the parts you highlighted
ok still tho
it says a <= sqrt(n) or b <= sqrt(n)
not a <= sqrt(n) and b <= sqrt(n)
safe radishBOT
Please read #❓how-to-get-help
solar hazel
9 <= sqrt(36) or 4 <= sqrt(36) is true
solar hazel
sure thing 🙂
solar hazel
every positive integer is prime or has a prime divisor
so we might have either a is prime or has a prime divisor
and a <= sqrt(n)
so if a is prime, a is a prime divisor of n less than or equal to sqrt(n)
if a has a prime divisor, that's a prime divisor of n less than or equal to sqrt(n)
that whole thing i just typed holds for either a or b
solar hazel
yay!
solar hazel
fiery valley
.close
split fulcrum
Question 3 I know this is more physics but I was wondering if this question was even possible. I asked around my teacher and classmates and they also believe it’s impossible because we aren’t given enough information to find the length of the solenoid
safe radishBOT
**Question 3** I know this is more physics but I was wondering if this question ...
split fulcrum
I was wondering if we could use any formulas for the height of a cylinder to find the length but I’d need other information like volume for that wouldn’t I
By the way the word cut off on the right is “what is the”
obtuse plover
Googled it
Diameter might be a diversion
Majority of the sources I checked agreed with the image I posted
split fulcrum
Here’s my thinking if I could somehow find the thickness of one coil using the diameter and multiply that by how many turns there are maybe it’s possible?
split fulcrum
Diameter might be a diversion
Possibly but how could we do a question like this without Length
obtuse plover
Hmm oops I didn’t see it didn’t give length, misread lol
Lemme look into this a little more
split fulcrum
Yeah sure
split fulcrum
right
flat frigateBOT
Stephen
obtuse plover
Permeability of free space
Turns/unit length
Current
n = N/L as provided by the first formula
@split fulcrum
U don’t need length as it gives turns/unit length
safe radishBOT
@split fulcrum Has your question been resolved?
safe radishBOT
safe radishBOT
Available help channel!
lean otter
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lean otter
Pay,ent means new added amount and receipt means taken away money
On second day
We got +284?
Or 84?
Oof
+close
.close
desert arch
please help me ;-;
safe radishBOT
please help me ;-;
stray socket
What have you tried
obtuse plover
There’s ur first problem
desert arch
i know I got my adhd over here trying to learn how to do this
lean otter
please help me ;-;
have you tried isolating p?
flat frigateBOT
Free Geoffrey
desert arch
yeah that ;-;
lean otter
-14 does not equal 15
isolate p as in make it so its the only thing on one side of the equation
like
this
stray socket
There’s ur first problem
Damn okay Stephen
lean otter
$$p = \text{everything else}$$
flat frigateBOT
Free Geoffrey
desert arch
so what if you subtract 14 and cancel it out then subrat 15 - -14 which would equal 1?
desert arch
no no i meant -14 - -14
lean otter
??
desert arch
p is equal to one though
lean otter
no
lean otter
$$p -14 = 15$$
flat frigateBOT
Free Geoffrey
lean otter
how do you remove the -14 from the left side
desert arch
switching it to the right..?
lean otter
how
desert arch
15 = 14 - p ?
desert arch
MANNN
desert arch
eat them
desert arch
yeah
flat frigateBOT
Free Geoffrey
desert arch
plus 14
desert arch
im so smart
desert arch
14
lean otter
no
desert arch
14p
lean otter
turn the -14 into a zero
desert arch
MANNNNNNNNN
desert arch
Yeah
flat frigateBOT
Free Geoffrey
lean otter
what is p
desert arch
29
lean otter
desert arch
IM SO SMART
lean otter
Now do that to the other 4 equations
safe radishBOT
@desert arch Has your question been resolved?
obtuse plover
Damn okay Stephen
I speak from experience lol
7:30 am calc bc classes had the same effect on me
stray socket
Fair enough
safe radishBOT
safe radishBOT
Available help channel!
wraith prism
safe radishBOT
dull sequoia
I’d probably separate it into 2 parts
For the left half of the red oval I’d just half the area of an ellipse
For the other half I’d just integrate the blue function
wraith prism
How to find an equation of a circle which touches to x=-1, x=3 and y=3
sly field
try drawing a rough diagram.. it helps
sly field
How to find an equation of a circle which touches to x=-1, x=3 and y=3
like it touch 3 points
?
wraith prism
like it touch 3 points
Yes
sly field
do you have diagram
wraith prism
safe radishBOT
wraith prism
.reopen
safe radishBOT
✅
sly field
Do you mean by three points
nothing..i just read the question wrong
wraith prism
(0,3) (-1,0) (3,0)
sly field
(0,3) (-1,0) (3,0)
what is this?
feral linden
These are not the three points the cycle touches with three lines…
You already have the x-coordinate of the center, y-coordinate plus r is 3 you know radius r too…
sly field
Do you mean by these three points?
see you know the two end points of diameter are (-1,y) (3,y)
wraith prism
I got it
Here we see that radius is 2
So the center will be 2 points away from y=3
Y coordinates of center is (y=1)
And same 2 away from x coordination
(-1+2) (3-2) so it is 1
Center will be (1,1)
But there can 2 circles
Outer circle
feral linden
Just similarly
wraith prism
2 points up from y axis
wraith prism
(h,k) = (1,5)
feral linden
Correct
wraith prism
2 more
feral linden
What two more
wraith prism
2 cm up+y axis
feral linden
They should touch all three lines
feral linden
(h,k) = (1,5)
You already solved it, this is the center of it
feral linden
We already solved two, touching all three lines. How many did you expect there are?
wraith prism
feral linden
Yeah, 2
wraith prism
.close
lean otter
safe radishBOT
lean otter
is this okey?
whole acorn
how did the top become n^2n + n^2n
wraith prism
is this okey?
No
lean otter
is that the same as this
whole acorn
and no it's not okay
wraith prism
Try log
feral linden
Divide by 3^n both above and below
lean otter
we never used log for infinite
feral linden
And you know that n^r/a^n ->0 for any positive integers a,r right
lean otter
oke i will try someting
can i add 1?
1+expression-1?
we had similar example just was n+5
feral linden
No reason to do that, just divide by 3^n
feral linden
is that the same as this
I was replying to this
feral linden
So this is your original question
lean otter
yea
flat frigateBOT
Cogwheels of the mind
feral linden
$=(\frac{n+3}{n+2})^{-4}((1+\frac{1}{n+2})^{n+2})^{2}$
flat frigateBOT
Cogwheels of the mind
lean otter
oke I will have a solution, so I will attach it later
feral linden
Okay
feral linden
Not really
lean otter
oh