oops I put an extra 1 in the picture lol
#help-33
elder ridge
neon lagoon
So I understand 1 = 2 and the 0 equal to the power, but how do you determine what 1111 is? Since theres no 0 to determine the power
neon lagoon
2 to the power of -1 is .5 though?
elder ridge
wait
you misinterpreted what i said
It's (2 to the power) - 1
because when you added one it became the one with the zeros after it
which is 2 to a power
It's 430am here so I'll get to the point
Try to understand this
Then note how this is essentially the same as your sum
neon lagoon
I will say you’ve been a TON of help, and that picture helps. Thank you very much!
elder ridge
No worries at all
elder ridge
I've been waiting for my question to be answered so this has passed the time lol
Feel free to pm if you have any problems!
peak lotus
hi
a. Gavin has nickels, dimes, and quarters in the ratio of 8 : 1 : 2. If 30 of Gavin's coins are
quarters, how many nickels and dimes does Gavin have?
this is my question
marsh citrusBOT
hi
a. Gavin has nickels, dimes, and quarters in the ratio of 8 : 1 : 2. If 30 of...
peak lotus
hi
ik this question is ez but im in gr7
Gavin has nickels, dimes, and quarters in the ratio of 8 : 1 : 2. If 30 of Gavin's coins are
quarters, how many nickels and dimes does Gavin have?
this is my question
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
How would I do question 11?
marsh citrusBOT
How would I do question 11?
proud ice
,rotate
elfin berryBOT
still temple
rotated my image and skedaddled😢
marsh citrusBOT
@still temple Has your question been resolved?
still temple
marsh citrusBOT
marsh peak
!status
marsh citrusBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
5
Well I answered it
it's just im not sure if it's right
which is why I want someone else to solve it
marsh peak
Show your work
still temple
I ended up getting a quadratic
but I don't have my work saved anywhere
I can start from the beginning ig
wait
marsh peak
Alright I'll just show you how I (and anyone else probably) would solve it
marsh peak
Did you forget to mention 0 as an extremum point?
marsh peak
The rest is fine yeah
still temple
can I ask another question or do I have to start in a new channel?
marsh peak
You can
marsh peak
Yes
marsh peak
Yes
still temple
I got one more sorry
marsh peak
That doesn't seem like how average velocity is generally calculated
It should be $\frac{\int_0^3v(t)dt}{3}$
elfin berryBOT
A Lonely Bean
marsh peak
Which is 90, in this case
marsh peak
Right, and simplify the fraction
lofty anvil
f'(x) = e^-x + (x+2) * (-e^-x)
For the second derivation I should need u' * v + u * v' ?
So u = e^-x + (x+2) and v = (-e^-x) ?
high pine
rather u = (x+2)
leaden monolith
f'(x) = e^-x + (x+2) * (-e^-x)
For the second derivation I should need u' * v ...
The way you set up your equation is more like
$\frac{d}{dx}[(e^{-x}+(x+2))\cdot (-e^{-x})]$
elfin berryBOT
Frosst
lofty anvil
My school never explaiend this thing with d/dx . Where is the difference between yours and mine?
leaden monolith
Pretty much the same
Just a notation difference and it’s easier to express certain things with each notation
high pine
Leibniz vs Lagrange
high pine
for (x+2) * (-e^-x) you can use it
elfin berryBOT
Frosst
leaden monolith
This is your question right?
lofty anvil
yeah f''(x)
leaden monolith
$\frac{d}{dx}[e^{-x}]+\frac{d}{dx}[(x+2)\cdot (-e^{-x})]$
elfin berryBOT
Frosst
leaden monolith
Split it up like this
lofty anvil
Ah so basically split it into two functions
leaden monolith
The second part will need product rule
lofty anvil
-e^-x + product rule
leaden monolith
Yep
lofty anvil
so u = (x+2) and v= -e^-x
leaden monolith
Yep
You can even expand it first
$\frac{d}{dx}[e^{-x}]+\frac{d}{dx}[-xe^{-x}] + \frac{d}{dx}[-2e^{-x}]$
elfin berryBOT
Frosst
lofty anvil
so u = (x+2) and v= -e^-x
but this is also possible right?
leaden monolith
Yes
lofty anvil
And second question for extrem values of f= (x+2) * e^-x
I need to do f'(x) = 0 with term of zero product?
f'(x) = e^-x + (x+2) * (-e^-x) = 0 ?
leaden monolith
Yes
lofty anvil
so I move on like this e^-x = 0 no solution ?
In my book they rewrite f'(x) = e^-x + (x+2) * (-e^-x) to ==> - 1+x / e^x
leaden monolith
What?
lofty anvil
then it makes sense for me because 1+x = 0
lofty anvil
I don't understand this step : f'(x) = e^-x + (x+2) * (-e^-x) simplified to ==> - 1+x / e^x
leaden monolith
Change the negative indicies into fraction
lofty anvil
I am so confused with this step
leaden monolith
Change e^-x to a fraction
lofty anvil
= 1/e^x
marsh citrusBOT
@lofty anvil Has your question been resolved?
long cape
marsh citrusBOT
long cape
I don’t understand how sin(theta/2) can be in quadrant 2
Wouldn’t half of an angle still be in the same quadrant?
long cape
Right OK
That makes sense
But how do you find out if unknown size half angle is or is not in same quadrant?
tribal jungle
it is if it's between 90 and -90, it's not if not
if you don't know the angle, you surely don't know what half of it is 😄
tribal jungle
Your question doesn't really make sense, we have to know about something
long cape
-Sqrt(5)/5
Do you just type this into calculator to see if it’s between 90 and -90?
tribal jungle
-Sqrt(5)/5
cos(x) = sqrt(5)/5?
long cape
tribal jungle
Sin is negative on the 2nd and 3rd quadrant, there is a theta satisfying that in each of those
Half of any angle in the 2nd is definitely in the first quadrant
Half of any angle in the 3rd is definitely in the 2nd
Think about it in terms of inequalities
long cape
Oh I thought the angle starts at where I draw the triangle.
tribal jungle
No, we are always talking about the angle starting from the positive side of the x-axis
long cape
Oh I thought the angle starts at where I draw the triangle.
We always start every angle at 0/2pi?
tribal jungle
We start at 0, we go counter clockwise, always
long cape
Ohhhh
I was thinking the triangle was the angle
How we get theta
From the angle of the triangle
tribal jungle
Do you know how to use the unit circle? I find it very useful when thinking about these
long cape
But it’s a combination of quadrants (90 degrees each) leading up to it too
long cape
Do you know how to use the unit circle? I find it very useful when thinking abou...
Yes.. I just forgot when drawing the triangles but now I understand. If I drew it correctly theta would not be so small and inside the triangle only
Theta must include all prior quadrants, unless it’s a full cycle 360 degrees then it can restart again at 0
I’m always seeing theta being drawn inside the triangle, never highlighting all prior quadrants too
Is theta supposed to be drawn like that? Smaller inside the triangle
I will show you an example
tribal jungle
Think of it like this
long cape
tribal jungle
yellow is theta
long cape
tribal jungle
yep or as in your second image
long cape
I always see it illustrated like this
But I guess it’s implied prior quadrants are included if you understand how theta and the unit circle works
long cape
yep or as in your second image
What about reverse?
Theta never goes in this direction? For problems that give -3/pi or something..
tribal jungle
That is a negative theta yeah
long cape
That is a negative theta yeah
It’s OK to do that for negative?
tribal jungle
Sure, and notice you can also add 2pi to it to get a positive angle, going the other way around
https://www.desmos.com/calculator/kxy8odj8q3 you can mess around with this if you'd like
orange is how I like to think about theta
play with alpha on the left to change the angle
In the unit circle the nice thing is that the side of the triangle on the x axis is cos and the side on the y axis is sin
long cape
play with alpha on the left to change the angle
Thanks. That’s quite interesting, What is the “a” slider representing on this graph?
tribal jungle
Thanks. That’s quite interesting, What is the “a” slider representing on this gr...
a is theta, desmos doesn't like me using theta so I had to change the name
tribal jungle
you can also increase the limit to see why we can always subtract or add 2pi to angles
it just starts over
tribal jungle
polar graphs are fun to mess around with 😄
tribal jungle
https://youtu.be/snHKEpCv0Hk
Yeah, watched this a while back, very interesting
long cape
polar graphs are fun to mess around with 😄
I will be learning this next
How r can be a negative value with polar
But I don’t know if I will need to use or understand this for Calculus 1
tribal jungle
It depends on how you define your polar coordinates. I don't allow mine to have negative r
However, you lose a bit of the beauty of polar plots when you do so, the cool flower like curves all use that 😄
tribal jungle
How r can be a negative value with polar
When plotting negative r you just add pi/2 to theta btw
median breach
Hello
somber pier
well
if you consider 1/x divided by ln2 then it'd be 1/x times the reciprocal of ln2
which would end up being 1/x times 1/ln2= 1/x*ln2
somber pier
1/ln2 yes
median breach
But what about
1 / 1/x ?
Then its 1 times
Reciprocal of 1/x which is x/1 no?
OH
This is opposite
somber pier
exactly
worn nimbus
yes
somber pier
yes it is
worn nimbus
,calc (1/3) / ln2
elfin berryBOT
The following error occured while calculating:
Error: Undefined symbol ln2
worn nimbus
,calc 1 / (3/log(2))
median breach
Ah okay , thats why it cannot be
1 * ln2/3
elfin berryBOT
Result:
0.23104906018665
,calc (1/3) / log(2)
elfin berryBOT
Result:
0.48089834696299
Because this is not the same
Ah yeah!
Thank u very much guys for clearing my confusion!
So for these fractions they gotta be in order
Unlike multiplication
somber pier
i guess? don't understand your statement though
median breach
Oh like
(1/3) / ln2
U do 1/3 first
Then divide by ln2
Cant just do 1 over 3/ln2
Gotta divide in their respective orders
somber pier
yes yes
marsh citrusBOT
marsh citrusBOT
Available help channel!
gilded iron
Can someone help me with this Descartes rule of signs question? I’m confused as to why it’s not a).
marsh citrusBOT
Can someone help me with this Descartes rule of signs question? I’m confused as ...
@gilded iron Has your question been resolved?
gilded iron
<@&286206848099549185> pls help
still temple
ok step one collect like terms
gilded iron
ok step one collect like terms
wdym they all differ by a power of x
gilded iron
x^ and x arn't like terms
but I can't add or subtract any of the terms
may you clarify what you mean by collecting like terms
still temple
is this equations idk
collecting like terms is basically simplifying the equation
@gilded iron
gilded iron
if you don't know, it's okay
I can always for help from someone else
<@&286206848099549185>
can anyone else help
I'm still confused with this question
.close
still temple
how do i evaluate the intergral
marsh citrusBOT
how do i evaluate the intergral
still temple
tan^3(x) sec^7(x)
craggy needle
i think u need to do u sub
if i remember correctly
also u need to sub in a trig identity for tan
thats how id do
still temple
uh how would you do intergral of 2 arctan(5y)
crimson perch
lmao
craggy needle
uh how would you do intergral of 2 arctan(5y)
arctan i think there is a trick with 1
same as when u integrate ln(x)
like, u have to do integration by parts
and then one of the functions will be arctan
and one function will be 1
if that makes sense
fathom ridge
Yup it's done easily by parts
still temple
I SUCK AT CALC 2
mystic minnow
factor out sec(x)tan(x),
use a trig identity on tan^2(x)
then u-sub with u = sec(x)
marsh citrusBOT
@still temple Has your question been resolved?
sweet pagoda
im not sure where to go with this without using a calculator and I want to know if its possible to do without just plugging in two small numbers on the left and right of 0
marsh citrusBOT
im not sure where to go with this without using a calculator and I want to know ...
fathom ridge
Well start with taking the log
nova totem
L'Hopitalssssss
sweet pagoda
log of the entire funtion?
sweet pagoda
L'Hopitalssssss
if i do l'hopital wont the exponent still have x on the bottom so when i plug in 0 its divding by 0?
nova totem
Maybe
sweet pagoda
im not sure if i derived it right but i got 1/x((e^x) +1)((e^x)+ x)^((1-x)/x)
which still has diving by 0
marsh citrusBOT
@sweet pagoda Has your question been resolved?
sweet pagoda
<@&286206848099549185>
fathom ridge
$\ln L = \lim_{x \to 0} \frac{1}{x}\ln (e^x + x)$
elfin berryBOT
NEONPerseus
fathom ridge
Now you can L'Hospital
smoky epoch
I can’t figure out my problem
marsh citrusBOT
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.
nocturne fiber
by the way
smoky epoch
This is my third ticket
Also sure
Graph orthocenter L(4,6), M(-3,2), N(-2,-6)
Idk what I’m doing wrong
smoky epoch
I can’t figure out my problem
.
nocturne fiber
Ok do you know what the definition of an orthocenter is
nocturne fiber
ok draw a diagram
nocturne fiber
sorry it's really hard to decipher your handwriting
smoky epoch
Could you tell me how you would do it?
smoky epoch
I don’t know where tho
main idol
try typing out your work here and explain it since your work is hard to read
nocturne fiber
you still haven't typed it
smoky epoch
Which part do you need me to type??
@nocturne fiber
?
@main idol @nocturne fiber ```Finding Altitude of M
m=y-y/x-x
mMN=2+6/-3+2
mMN=8/1
mMN=8
M⊥=-1/8
y-2=-1/8(x+3)
y-2=-1/8x-3/8
y-16/8=-1/8x-3/8
y=-1/8x-13/8
Finding Altitude of N
mLN=6+6/4+2
mLN=12/6
mLN=2
m⊥=-1/2
y+6=-1/2(x+2)
y+6=-1/2x-1
y=-1/2x+5
System Of Equations
y=-1/2x+5
y=-1/8x-13/8
-1/8x-13/8=-1/2x+5
(-1/8x-13/8=-1/2x+5)8
-x-104=-4x+40
3x=144
x=48
y=-1/8(48)-13/8
y=-6-13/8
y=-48/8-13/8
y=-61/8```
But that's wrong
and idk why
L=(4,6)
M=(-3,2)
N=(-2,-6)
<@&286206848099549185>
Bro i luv this server
holy
This is hilarious
I figured it out before y'all helped me the tiniest bit
Great Help lmfao
God damn formatted it even for y'all
.close
hidden nacelle
why is there this discrepancy?
marsh citrusBOT
why is there this discrepancy?
hidden nacelle
why not
crystal wraith
For the AM-GM inequality, for equality to hold, your numbers should be equal.
In this case that doesn't happen.\
$\cos^2x = 4\sec^2(x) \implies \cos^2(x) = 4$\
Which doesn't happen. So yeah.
elfin berryBOT
What the hell am I doing here?
marsh citrusBOT
marsh citrusBOT
Available help channel!
keen plover
how do i solve the problem 3sin(2x+30)=tan(2x+30)
-180<x<180
marsh citrusBOT
how do i solve the problem 3sin(2x+30)=tan(2x+30)
-180<x<180
rotund narwhal
I suck at trigo so it might be wrong
rotund narwhal
oh i know why
keen plover
rotund narwhal
you welcome
keen plover
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
long cape
marsh citrusBOT
long cape
Why does law of sines work on oblique triangles?
Doesn’t sin require knowing what opposite and hypotenuse are?
stoic saddle
the "opp" and "hyp" you are talking about are nowhere to be found.
at least not on your diagram...
also did you mean obtuse triangles perhaps?
long cape
also did you mean obtuse triangles perhaps?
No, oblique
Acute triangle in this case
All angles smaller than 90 degrees
long cape
the "opp" and "hyp" you are talking about are nowhere to be found.
But that’s how sin is defined: opposite/hypotenuse
stoic saddle
the sine of an angle as seen in a right triangle, sure.
stoic saddle
it is, it just isn't applicable on the diagram as drawn. yet.
you're gonna need to draw some altitudes to make sine appear as a ratio.
lucid hinge
stoic saddle
<:probability:1068623046312722462>
shoo.
long cape
P(x)?
long cape
Oh I see. I’m making two right triangles out of one oblique triangle
lucid hinge
Oh I see. I’m making two right triangles out of one oblique triangle
^
and then just represent all those angles
divide some, and u get the formula
long cape
Clever!
lucid hinge
while Ann is still drawing her diagram
stoic saddle
not forever, no. i've seen them ask about other precalc shit here not more than a month ago.
long cape
Angles A*C = length b?
stoic saddle
no
if i wanted to write $\angle A \cdot \angle C = b$, i would've done that. but i didn't.
elfin berryBOT
Ann
long cape
avidrunner has been learning trig forever
Only about a week
stoic saddle
are you going to attack my failure to put an overbar on the segment $AC$ to clarify that i was referring to its length and not the segment-per-se, or, god forbid, the product of two angles?
elfin berryBOT
Ann
stoic saddle
i chose not to place the b length-mark on the diagram in case i would need to label the lengths of AH and HC separately (even though, in the end, i ended up not needing to do so).
your misinterpretation of AC as meaning the product of two angles (something very rarely considered in geometry) feels deliberate.
long cape
This refers to where the length of b starts (angle A) and where it ends (angle B)?
stoic saddle
you're seriously overthinking it.
long cape
are you going to attack my failure to put an overbar on the segment $AC$ to clar...
Not attack, no. Just understand
stoic saddle
AC = b means the length of the segment AC is labeled with the letter b.
nothing more nothing less
don't tell me you've never seen people write shit like "XY = 10cm" when talking about a geometric diagram.
this is much the same
long cape
I normally see variables together as multiplication. You are saying there should be an overbar for referring to length?
lucid hinge
capital letter is like angle, and lower case is its opposite side
stoic saddle
capital letters in geometry are used for names of points.
and when a particular point has only one angle depicted that has it as a vertex, the point's name can also refer to that angle.
(otherwise you would have to use three point-name letters to unambiguously refer to an angle)
long cape
OK
Btw, I’ve seen sin cos tan written so many times without brackets now that I’m just kinda used to it
stoic saddle
for shame.
long cape
For things like squaring I know it comes before theta and not after
It’s messy but all too common
stoic saddle
it comes before the parentheses too if you put them (like you should)
i.e. $\sin^2(\theta)$
elfin berryBOT
Ann
lucid hinge
this is empty set
stoic saddle
did you post this deliberately to provoke a reaction in me @lucid hinge
lucid hinge
possibly, my apology
stoic saddle
i'm going to take this to DMs.
marsh citrusBOT
@long cape Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
lean monolith
Let's say we have n students, and k buses.
If a student has another student as a friend, they both know each other, or they don't know each other.
We have to assign students a bus so that no friends remain in one bus.
Show that number of ways to assign buses is divisible by k.
marsh citrusBOT
Let's say we have n students, and k buses.
If a student has another student as ...
lean monolith
What I tried to do is
Construct a k-partite graph
I do have an algorithm for that which works given that the student who has maximum number of friends, has friends less than or equal to k
But I am having trouble counting the number of ways we can do that
All students are distinct (can't believe I said this)
marsh citrusBOT
@lean monolith Has your question been resolved?
wary bluff
marsh citrusBOT
wary bluff
How
This is what I got
and I used u = arctan(3x)
how they get thatt
our ans r diff too
marsh citrusBOT
@wary bluff Has your question been resolved?
tardy monolith
@wary bluff Yours is correct, keep going, they probably used another substitution
marsh citrusBOT
dapper phoenix
wrong question
worthy trellis
Yes
dapper phoenix
is 2^p always congurent to 0 mod 4
marsh citrusBOT
gilded cape
what? is every number a power of two?
marsh peak
Isn't that the same?
dapper phoenix
yes
gilded cape
2^p = 2^2 * 2(p-2)
dapper phoenix
yeah yeah
marsh peak
Yes
marsh peak
x = 0 mod m is equivalent to saying x is divisible by m
knotty trellis
every prime is bigger than 2, therefore 2^p will have at least 2 2s in it's prime factorization, 2 2s means, it's divisible by 4
dapper phoenix
Yeah i know that but okay nvm thank u
.close
How do i solve 3^(p-1) = 1 (mod 4)
dapper phoenix
thank u
marsh citrusBOT
Available help channel!
teal kernel
This is grade 9 math, please show steps or explanation 💖
marsh citrusBOT
This is grade 9 math, please show steps or explanation 💖
marsh citrusBOT
@teal kernel Has your question been resolved?
teal kernel
hello?
marsh citrusBOT
@teal kernel Has your question been resolved?
teal kernel
.close
thorny jetty
May I ask how do you get 210 in this Circle?
marsh citrusBOT
May I ask how do you get 210 in this Circle?
dapper phoenix
Do numbers in the form n^p were p is prime have any special properties? (and n is natural)
marsh citrusBOT
Do numbers in the form n^p were p is prime have any special properties? (and n i...
knotty trellis
Do numbers in the form n^p were p is prime have any special properties? (and n i...
They are divisible by n, and n^2
dapper phoenix
Yeah that is like logical but any fancy shmancy stuff that you wouldnt see straight away?
still temple
?
knotty trellis
For what properties are you looking for?
fathom ridge
35^3 has 4 divisors?
knotty trellis
the question is find every prime were that thing is a square number
for any n or for every natural n?
dapper phoenix
for every integer
knotty trellis
okay
dapper phoenix
i got to this point
3^(p-2) - 2 ^ (p-2) + 3^(p-3) - 2^(p-3) + .... + 3 - 2 = (k+1)^2 + k^2
i noticed that n has to be odd and substituted n = 2k+1
I know a property that (k+1)^2 + k^2 has to be a difference of cubes but idk if that means anything in this case
I also found that 3, 5 have to be solutions
idk what else
devout mauve
as p is odd, 3^(p-1) is a perfect square. so then 2^p has to be the sum of consecutive odd integers (it's actually easy to find sums like that). maybe an approach like this helps
dapper phoenix
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
desert prairie
Why don’t all the solution work?
marsh citrusBOT
Why don’t all the solution work?
desert prairie
Aka why don’t I get all the solution
elfin berryBOT
high pine
Solution to:
$$\sin x = a, \ a \in [-1,1]$$
is given by:
$$x = \arcsin a +2\pi n \vee x = \pi -\arcsin a + 2\pi n, \ n \in \mathbb{Z}$$
elfin berryBOT
Modus
high pine
you did only arcsin(0.4) + 360
and you're missing 180 - arcsin(0.4) + 360n
this is why
desert prairie
Oh ok
desert prairie
0< or equal to 360
high pine
ok
desert prairie
and you're missing 180 - arcsin(0.4) + 360n
Do u mean 360n not +180n
Since that what u wrote before
desert prairie
Ok thanks
still temple
hello
still temple
im not sure where the 8 is coming from lol
i understand -7, but i thought it would be +5, not +8
worthy trellis
Ya there you go
still temple
Thanks
worthy trellis
Np:)
still temple
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
viscid birch
Hi can anyone here help me figuring out this math problem?
marsh citrusBOT
Hi can anyone here help me figuring out this math problem?
spring kestrel
I just don't know whether you have to draw continous functions or discrete
like because you can't but 4.5 t-shirts should you not draw graph between integral values
I guess, you are most likely asked to draw continous graph
marsh citrusBOT
@viscid birch Has your question been resolved?
jolly sigil
I'm stuck rn. Would appreciate a push in a direction on how to continue
jolly sigil
Can I omit the 1/n and summation for now? Since I need it in the end?
marsh citrusBOT
@jolly sigil Has your question been resolved?
plucky trout
can i get assistance on this problem?
marsh citrusBOT
can i get assistance on this problem?
plucky trout
so i got $5 + sqrt(164)$
elfin berryBOT
Harp
proud ice
plucky trout
how ever the answer is wrong. the correct answer is nota (none of the above)
plucky trout
<:badtex:924222207251582996>
i know
proud ice
Use \sqrt{164}
proud ice
how ever the answer is wrong. the correct answer is nota (none of the above)
Show how you got your answer
plucky trout
ok so
the point (10, 5) is 5 units away from the x axis
and i got to point (10, 0).
now i calculated the distance between the points (10, 0) and (2, 10)
and i got $\sqrt{164}$
elfin berryBOT
Harp
proud ice
That's shortest path to x axis but that makes a longer path to the stable
plucky trout
oh*
so
do i calculate the distance from (10, 5) to (2, 10)
and thats my answer?
plucky trout
That's shortest path to x axis but that makes a longer path to the stable
and i did that because they told me that he went to the x-axis and then to the point (2, 10)
proud ice
and i did that because they told me that he went to the x-axis and then to the p...
Yeah but he can go anywhere on the x axis in order to minimize his total path traveled
plucky trout
ohhh
proud ice
do i calculate the distance from (10, 5) to (2, 10)
Nah this path want take you to the x axis
Okay here's how I think about the problem
The shortest distance between any two points is a straight line
But you need to touch the x axis then turn back
plucky trout
yes
proud ice
But what if, instead of turning back, I kept going forward
What if I reflected the stable to the other side of the river
plucky trout
same distance?
plucky trout
ohh
proud ice
Seeing the picture now?
plucky trout
mhm
plucky trout
so do i reflect by the x-axis?
proud ice
Now just find the distance between this and your home coordinate
plucky trout
so do i just find the distance between my current point and to the reflected point?
i got the answer of 17
so the answer is E!
thank you so much@proud ice
.close
ivory laurel
Is there any issues with my proof?
marsh citrusBOT
Is there any issues with my proof?
ivory laurel
The question is to prove if f(x)=g(x) for all x in the rationals then f=g
stoic saddle
The question is to prove if f(x)=g(x) for all x in the rationals then f=g
assuming continuity of f and g?
marsh citrusBOT
@ivory laurel Has your question been resolved?
ivory laurel
Are there any issues?
marsh citrusBOT
@ivory laurel Has your question been resolved?
marsh citrusBOT
@ivory laurel Has your question been resolved?
short wadi
Hey guys, so I understand the parallel axis theorm, and I also understand the second moment of area about a rectangles own centroid is 1/12 b*H^3, but I dont understand what the teacher did in this exercise. Can someone please elaborate?
marsh citrusBOT
Hey guys, so I understand the parallel axis theorm, and I also understand the se...
@short wadi Has your question been resolved?
short wadi
In fact, if I do it the way I think it works, it comes out to be 127/12a^4
I actually do understand what the teacher did now, but I still dont understand how our solutions can be different if we both did the right thing
he multiplied the second moment of area of the flange by 2. Which makes sense because there is 2flanges, however he didnt take into account the parallel axis theorm. So I would really apreciate if someone gave their opinion on this
marsh citrusBOT
@short wadi Has your question been resolved?
short wadi
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
shut oyster
marsh citrusBOT
leaden monolith
send through the working out you’ve done
marsh citrusBOT
Show your work, and if possible, explain where you are stuck.
shut oyster
work: -3x + 21 + 6 = -4x + 4
pallid pine
hol up
shut oyster
im holding
leaden monolith
Expand 3(x+7)
Do this
shut oyster
wdym expand?
shut oyster
3x + 21 + 6 = -4x + 4
elfin berryBOT
Frosst
pallid pine
do the same with -4(x+1)
shut oyster
3x + 21 + 6
leaden monolith
Ok fantastic
leaden monolith
work: -3x + 21 + 6 = -4x + 4
Why is the 3x negative here
shut oyster
i accidentally did that
shut oyster
= -4x + 4
leaden monolith
It was a different example
leaden monolith
Ok what is a*b
shut oyster
-4x?
elfin berryBOT
Frosst
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
leaden monolith
Dammit it was supposed to be a + not a \cdot
shut oyster
i said that lmao
leaden monolith
Ok now what’s a*c
shut oyster
4
leaden monolith
What is a
shut oyster
yeah so its 4?
shut oyster
-4
shut oyster
-4x -4
leaden monolith
Show your working
shut oyster
3x + 27 = -4x - 4
-3x
+4
27 + 4 is 31
3x is zero'd out
-4x = 3x is -1x
so its -31
but where does the 7 come from?
i dont get it at all
i get it now
but my questions is @leaden monolith why do we subtract the 27 from the -4 why dont we just add to the -4?
leaden monolith
Show your working on paper
Every step please
Hard to see what you are struggling with when I can’t see where you’re making the mistakes
shut oyster
i know what i did wrong already
i canceled the -4 instead of the 27
but i dont get why we do the 27 instead of the -4 is all
leaden monolith
but i dont get why we do the 27 instead of the -4 is all
And I don’t get what you’re asking here
Can you write it out
Like the math steps
shut oyster
what im asking is why do we subtract the 27 from both sides and not add the 4 to both sides
leaden monolith
what im asking is why do we subtract the 27 from both sides and not add the 4 to...
They both work
leaden monolith
That’s why writing out all the working steps is good
shut oyster
but why do we add 4x to both sides
instead of just subtracting 3x from both
nevermind
im dumb dont answer that
it works both ways
i just did it really wrong
marsh citrusBOT
Available help channel!
marsh citrusBOT
marsh citrusBOT
@lucid hinge Has your question been resolved?
marsh citrusBOT
@lucid hinge Has your question been resolved?
marsh citrusBOT
@lucid hinge Has your question been resolved?
proper zodiac
💫 c o n t e x t 💫
lucid hinge
💫 c o n t e x t 💫
no context, trynna ask for people to identify possible context for my notes
lucid hinge
.close
vestal mist
any hints for this?
marsh citrusBOT
any hints for this?
vestal mist
i just have to prove that M and H are equally distanced from K
marsh citrusBOT
@vestal mist Has your question been resolved?
vestal mist
anyone??
marsh citrusBOT
marsh citrusBOT
Available help channel!
analog pier
$\frac{1}{2}\int _0^{2\pi }\left(7+cos\left(2x\right)\right)^2dx:$
marsh citrusBOT
$\frac{1}{2}\int _0^{2\pi }\left(7+cos\left(2x\right)\right)^2dx\:$
elfin berryBOT
spetnaz
unreal oxide
expand it
analog pier
expand it
$\frac{1}{2}\int _0^{2\pi :}\left(49+14cos\left(2x\right)+cos^2\left(2x\right)\right)dx:$
elfin berryBOT
spetnaz
unreal oxide
now break it up into a sum of integrals
use the double angle formula with cos^2(2x)
analog pier
use the double angle formula with cos^2(2x)
$\frac{1}{2}\left(\int _0^{2\pi ::}49dx+\int _0^{2\pi ::}14cos\left(2x\right)dx+\int _0^{2\pi ::}cos^2\left(2x\right)dx\right):$
elfin berryBOT
spetnaz
analog pier
Whats the double angle formula?
unreal oxide
do u know a formula for cos(2A) ?
i know im just asking u this
unreal oxide
yeah this is one formula
analog pier
Is that good?
unreal oxide
u mean this one?
use this
analog pier
and find cos2A = in terms of cos^2 only
ok so my first would be $\cos^{2}2x=1-\sin^{2}\left(2x\right)$
elfin berryBOT
spetnaz
analog pier
I am inputting 2x into the formula because of $cos^2(2x)$
elfin berryBOT
spetnaz
unreal oxide
well no im asking u to find cos2A in terms of cos^2(A) only, forget abt the x, we'll get there later
unreal oxide
u already know this
and coz im asking u to use cos^2(A) only, u r gonna hve to replace the sin^2(A) with something else
unreal oxide
u mean this one?
for that u can use this
cos^2(A) = 1 - sin^2(A)
find sin^2(A) using this one and replcae the sin^2(A) in cos(2A) = 1 - 2sin^2(A) with that
and tell me what u get
analog pier
and tell me what u get
I just looked it up and I knew it, I had to use a trig identity
unreal oxide
so do u know what happened here
analog pier
Nope
But I know it's probably some obscure formula I need to spend 10 years to memorize
unreal oxide
well no im asking u to find cos2A in terms of cos^2(A) only, forget abt the x, w...
thats why im asking u to do that
unreal oxide
But I know it's probably some obscure formula I need to spend 10 years to memori...
its not obscure
analog pier
.close
harsh dew
I need to put the equation: 1 = 3sin(2θ) into cartesian form from polar
harsh dew
Im stuck in that, i can't seem to figure out, where "r" falls in this equation
To me it already does seem to be in cartesian
full tree
It must want you to solve for theta and then give the equations of those rays.
harsh dew
Heres the exact wording, it might have been a typo, because thats all i can think of
"Write the following Polar equation in terms of x and y. Be sure to
simplify!: 1 = 3sin(2θ)
full tree
I think it means what I said. Solve for theta and you can write these as y as a function of x, or x as a function of y potentially. For example, if you determine theta = theta_0 is a solution, then the ray would be represented by y = tan(theta_0)x.
still temple
this question is about the philosophy of mathematics: is it astonishing that "so little knowledge gives us so much power?" in the field of mathematics specifically, what can make that surprising, or not surprising as well? anyfactors of the study of mathematics?
marsh citrusBOT
this question is about the philosophy of mathematics: is it astonishing that "so...
nova totem
1/0
fathom ridge
Fascinating 
Perhaps unifying topics?
If you know what I mean
Representing shapes with algebraic equations
still temple
I'm sorry, I don't think I do
fathom ridge
If you're in for basic stuff
still temple
right
fathom ridge
Surprising how simply these concepts connect
And the use of complex numbers in places you wouldn't expect them to be
still temple
like in the fourier transform?
fathom ridge
Since many are still under the assumption that they're "theoretical"
still temple
right
fathom ridge
like in the fourier transform?
That could be one
still temple
okay so you're talking about the link between different pieces of little knowledge?
fathom ridge
And in quantum physics, I'm pretty sure complex numbers are used to encode positions of particles and stuff
fathom ridge
okay so you're talking about the link between different pieces of little knowled...
Yup
still temple
and so then power comes from their ability to interact with other such pieces of knowledge
fathom ridge
The link between complex numbers and coordinates in general
fathom ridge
and so then power comes from their ability to interact with other such pieces of...
You could say that
still temple
so what could make it unsurprising?
fathom ridge
Life would be a lot harder without complex numbers
nova totem
Ngl this seems more like a #discussion thing
fathom ridge
so what could make it unsurprising?
nova totem
We're down to 4 vacant help channels ://
still temple
Ngl this seems more like a <#268882317391429632> thing
I don't see that channel
trim quest
Just click it here: #discussion
nocturne fiber
We're down to 4 vacant help channels ://
oh god
trim quest
We're down to 4 vacant help channels ://
There's like 15 at the bottom lol
but yes you are right
silk flame
We consider simple and connected graphs, is graph isomorphism a equivalence relation and if so how many equivalence classes exist and what's their cardinality?
marsh citrusBOT
We consider simple and connected graphs, is graph isomorphism a equivalence rela...
nocturne fiber
$\original$
elfin berryBOT
active mental mutilation liker
silk flame
its in a another language will try my best
nocturne fiber
that's fine
silk flame
Consider graphs (simple, connected). Is isomorphism of the graphs a equivalence relation and if yes how many equivalence classes exist and what cardinality do they have
I know they are an equivalence relation but fail to prove their number
nocturne fiber
the cardinality of the equivalence classes?
silk flame
could be of the graphs?
nocturne fiber
um cardinality of the graph?
silk flame
the cardinality of the equivalence classes?
but i guess this?
which makes more sense idk
nocturne fiber
!show
marsh citrusBOT
Show your work, and if possible, explain where you are stuck.
silk flame
i dont have any
nocturne fiber
I know they are an equivalence relation but fail to prove their number
then how would you know they are an equivalence relation
if you say something is an equivalence relation I would expect some proof
nocturne fiber
you posted the question on MSE already?
silk flame
not mine
nocturne fiber
I specifically want to see your proof