looks all good
#help-27
vernal solar
devout snowBOT
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fair coral
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craggy fossil
Help please
devout snowBOT
Help please
craggy fossil
teal perch
What is the problem?
devout snowBOT
@craggy fossil Has your question been resolved?
flat ermine
Please help with the following question:
It asks to find the value of each expression, in this case sin 𝛳.
Here, I have found b through the pythagorean theorem but I am also confused because it asks to find sin 𝛳. If sin is opposite/hypotenuse, it would be sqrt (-23/3) over 2 (sqrt 3)/3?
devout snowBOT
Please help with the following question:
It asks to find the value of each exp...
@flat ermine Has your question been resolved?
flat ermine
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safe sphinx
for the sequence, find the limit points, for each of the limit points, find the subsequence...am I right in my approach..? Thanks for helping
devout snowBOT
for the sequence, find the limit points, for each of the limit points, find the ...
faint gorge
for the sequence, find the limit points, for each of the limit points, find the ...
yes
nice work
safe sphinx
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idle bloom
devout snowBOT
idle bloom
Please help
frosty cradle
What are your thoughts on those choices
idle bloom
i was thinking B
frosty cradle
Yup
idle bloom
ayy W
okay appreciate it
@frosty cradle
this one is question 5 still havent gotten it yet
this one has really stumped me i gave up on it
versed raven
I don't understand what this question is asking me to do. (I haven't done a problem like this before.) Can someone please explain what to do step by step?
devout snowBOT
I don't understand what this question is asking me to do. (I haven't done a prob...
tame palm
I don't understand what this question is asking me to do. (I haven't done a prob...
cos(theta) is associated with the x variable.
versed raven
cos(theta) is associated with the **x** variable.
So how do I create the line?
tame palm
On a Cartesian plane, if x = c, you draw a vertical line at x = c.
versed raven
On a Cartesian plane, if **x = c**, you draw a vertical line at **x = c**.
I have no idea what that is...
tame palm
The vertical line implies that any point on that line is equal to x.
versed raven
The vertical line implies that any point on that line is equal to **x**.
Where would I put the line?
tame palm
I don't think the line has to be exactly at -0.58.
versed raven
I don't think the line has to be exactly at -0.58.
Does this look right?
tame palm
Looks close enough.
versed raven
Looks close enough.
What do I put here?
tame palm
There are two values of theta that result in cos(theta) being equal to -0.58. Those two angles can be determined by the intersection of the vertical line and the unit circle.
versed raven
There are two values of theta that result in cos(theta) being equal to -0.58. T...
Can you explain how to find the angles?
tame palm
arccos(-0.58) on a calculator will find the angles.
versed raven
arccos(-0.58) on a calculator will find the angles.
I got 125.45
tame palm
,calc arccos(-0.58)
woven radishBOT
The following error occured while calculating:
Error: Undefined function arccos
tame palm
,calc cos^-1(-0.58)
woven radishBOT
The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)
tame palm
,wolf cos^-1(-0.58)
woven radishBOT
versed raven
versed raven
That's in radians
tame palm
With that angle, you can use the x-axis as a reference angle to find the other angle.
125.45 is in degrees.
versed raven
Okay
versed raven
With that angle, you can use the x-axis as a reference angle to find the other a...
How would I find the other angle?
tame palm
Note that the other angle is an equal distance from the x-axis.
versed raven
Ok
tame palm
The point on the unit circle where x=-1, the angle there is 180 degrees, or pi radians.
Find the difference between 180 and 125.45 and add that difference to 180.
versed raven
Find the difference between 180 and 125.45 and add that difference to 180.
180 - 125.45 = 54.55
180 + 54.55 = 234.55
Like this?
tame palm
Yes.
tame palm
versed raven
It says something is incorrect.
tame palm
Post a screen capture of the entire question.
tame palm
,calc 360-125.45054
woven radishBOT
Result:
234.54946
So 234.5, not 234.6
tame palm
Yeah.
tame palm
Sure.
versed raven
Sure.
How do you know if the line is vertical, horizontal, diagonal, etc.?
Is it because of cos? Along the x axis?
tame palm
Yes. We associate cos() with an x-value and sin() with a y-value.
versed raven
Yes. We associate cos() with an x-value and sin() with a y-value.
To find the angle, can I do 360-138.59?
tame palm
The second angle, yes.
versed raven
The second angle, yes.
How do I find the first angle?
versed raven
Oh yeah I forgot about that lol oops.
tame palm
Sure.
tame palm
Have you ever seen the hand trick for the basic angles 0, 30, 45, 60, and 90 degrees?
versed raven
No I haven't.
tame palm
Assuming you have all five fingers on your right hand, hold your right hand in front of you with your palm facing towards you and thumb pointed upwards.
Fingers spread out.
Your thumb is zero degrees, forefinger is 30 degrees, middle finger is 45 degrees, ring finger is 60 degrees, and your pinky is 90 degrees.
versed raven
Okay.
tame palm
If you pull in your forefinger reprsenting 30 degrees, you will have one finger above it(thumb) and three fingers below it.
sin(30) is sqrt(1)/2.
cos(30) is sqrt(3)/2.
You count how many fingers are above the degree finger and take the square root of that and divide by 2.
versed raven
I see. What about for cos?
tame palm
sin(45) is your middle finger with two fingers above it. sin(45) is sqrt(2)/2.
You count the fingers below the degree finger for cosine.
cos(30) = sqrt(3)/2. There are three fingers below your forefinger that represents 30 degrees.
versed raven
Okay.
tame palm
Now here is the relevant part to the last question.
tan = sin/cos
So for any degree, you just square the number of fingers above and below the degree finger.
versed raven
Isn't - sqrt 3 equal to 1/sqrt 3?
tame palm
-sqrt(3) = -sqrt(3)/1 = -sqrt(3)/sqrt(1)
versed raven
Oh
tame palm
Which finger is equivalent to sqrt(3)/sqrt(1)?
Three fingers above and one finger below.
versed raven
Three fingers above and one finger below.
How did you get that? Do you pull away your ring finger?
tame palm
Curl it inwards, wiggle it, or any other method that works for you to indicate it is the degree finger.
versed raven
I meant for sqrt 3 / sqrt 1, you should have 1 finger below the degree and 3 above the degree?
tame palm
Yes.
versed raven
How do you know what function that applies to?
tame palm
Assuming you have five fingers, there are three fingers above the ring finger and one below it.
Above is sine, below is cosine, the combination of the two is tangent = sine/cosine.
versed raven
I see.
tame palm
What is cos(45)?
versed raven
sqrt 2 / sqrt 2
tame palm
sqrt(2)/2
versed raven
Oh
tame palm
tan(45) is sqrt(2)/sqrt(2) though which is the same as 1.
tan(45) = sin(45)/cos(45)
The division by 2 cancels out.
versed raven
The division by 2 cancels out.
How would I use this to get tan -sqrt 3?
versed raven
Which degree finger is that equivalent too?
30?
tame palm
30 degrees is which finger?
versed raven
Forefinger
tame palm
And how many fingers are above your forefinger?
versed raven
One
tame palm
Which is not 3.
versed raven
60
tame palm
Ok.
But there is one other thing to consider before answering this question and that is the negative sign.
versed raven
Yeah
tame palm
The tangent line goes diagonally through the origin.
tame palm
Sine is horizontal, cosine is vertical, and tangent is diagonal through the origin.
versed raven
I see.
tame palm
Now the significant of the - comes into play here.
versed raven
Okay
tame palm
The sign of x and the sign of y where the line intersects the unit circle is dependent on the quadrant the line goes through.
versed raven
Ok
tame palm
If the diagonal line goes through Q1 and Q3, the sign of x and y will be either both positive or both negative.
versed raven
Ok
versed raven
If the diagonal line goes through Q1 and Q3, the sign of **x** and **y** will be...
I don't get what to do with the negative sign?
tame palm
The points of intersection results in either (-x,+y) or (+x,-y).
When you divide +y/-x or -y/+x, you get a negative value.
versed raven
The points of intersection results in either (-x,+y) or (+x,-y).
I see.
tame palm
The points of intersection here results in either (+x,+y) or (-x,-y).
+y/+x is positive and -y/-x is also positive.
Now, you are given tan(theta) = -sqrt(3).
versed raven
Yeah.
versed raven
Which quadrants does the line go through?
Q1 and Q3
tame palm
No.
Q1 and Q3 are +y/+x or -y/-x which result in a positive value.
You are asked to find theta for tan(theta) = **-**sqrt(3).
tame palm
Correct.
And the reference angle is 60 degrees above the x-axis in Q2.
And 60 degrees below the x-axis in Q4.
versed raven
And the reference angle is 60 degrees above the x-axis in Q2.
What do you mean 60 degrees above the x-axis in Q2? Isn't Q2 past 90 degrees? I know you said Q2 and Q4 are negative, which is what the degree needs to be,
tame palm
tame palm
No, the reference angle is 60 degrees. You need to find the actual angle CCW from the x-axis.
versed raven
No, the reference angle is 60 degrees. You need to find the actual angle CCW fr...
180-60?
tame palm
Yes.
devout snowBOT
@versed raven Has your question been resolved?
tame palm
Is 120 the only answer?
No, there is the angle in Q4 as well.
versed raven
No, there is the angle in Q4 as well.
What is that angle?
tame palm
60 degrees relative to the x-axis.
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Available help channel!
fair ruin
How was the first line drawn
devout snowBOT
How was the first line drawn
rocky ice
I understand the second lin eon the graph but not the first
What do you mean by the first line? The asymptote or the curve?
fair ruin
the solid line
not dotted
undertsnad?
<@&286206848099549185>
bro just logged off
rocky ice
The original graph of log base 2 x was drawn, then translated 3 units left and 4 units up as the equation is log base 2 (x + 3) + 4
restive river
given curve
rocky ice
No problem 
fair ruin
.close
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fallow forum
devout snowBOT
fallow forum
am i going crazy? why doesn’t this work
why do i have to distribute the root into each component instead of just doing chain rule
wait no it does work
i guess i’m just crazy
regal moat
Seem correct
orchid charm
restive river
I have a question isn't it
= 1/2 (xy)^-1/2 (y+xdy/dx)
humble fulcrum
Did I do something wrong on the calculator? It doesn't seem to match the values of Y shown in the other picture
devout snowBOT
Did I do something wrong on the calculator? It doesn't seem to match the values ...
tawdry torrent
Did I do something wrong on the calculator? It doesn't seem to match the values ...
Coefficient of y is negative
In the quadratic formula it will be -(-b)
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smoky mason
x= 1 , p = 17 satisfies by trial and error; but that doesn't help with number of solutions
smoky mason
brb in 10 min
devout snowBOT
@smoky mason Has your question been resolved?
timid solstice
x= 1 , p = 17 satisfies by trial and error; but that doesn't help with number ...
I think the only solution is where it is one, because when x > 1 you will be adding to consonant numbers which will be non prime.
and zero is not possible because it will be 2 power even number which is also a consonant
smoky mason
im sorry but what do you mean by consonant numbers?
timid solstice
consonant meaning non prime number, my bad
timid solstice
ya
smoky mason
I don't think there's such a rule that adding composite numbers yields only composite numbers
for eg. 20+9 = 29
timid solstice
I don't think there's such a rule that adding composite numbers yields only comp...
ya fair point
devout snowBOT
@smoky mason Has your question been resolved?
little totem
its really tricky because even the factorization of x=5 is highly nontrivial as far as i can see
obviously you can rule out even x values but i dont see a way to divide and conquer the odd values
dense lynx
x= 1 , p = 17 satisfies by trial and error; but that doesn't help with number ...
there is very nice and simple trick that solves this problem (though it may be hard to come up with if you have never seen it before)
first you take out the 2^2 in the exponent so you have 4 * 2^2^x
and does the resulting expression look familiar to you
smoky mason
I mean I did reach that step before but don't know how to proceed after that
dense lynx
i see
for 2^2^x and x > 1, the expression is divisible by 2^4
consider ||a^4 + 4 * b^4||
smoky mason
I still dont get what to do :x
that 2exponential term will give units place = 4 for x>1
and the only possible candidate for primes will be when x^8 ends in 5, so when x has units digit 5
do i end it there and call it infinite solutions or can i restrict it more
dense lynx
I still dont get what to do :x
the key idea here is that the expression i posted is factorable
it probably doesn't make much sense if you didn't know about the factorization beforehand but yes it's a famous identity that is good to be familiar with
smoky mason
unfortunately I don't get what you mean. could you do it and send the solution? no worries if not
hidden vortex
devout snowBOT
@smoky mason Has your question been resolved?
little totem
and does the resulting expression look familiar to you
i cant believe i didnt see that
omfg
i knew there had to be a factorization somewhere
devout snowBOT
@smoky mason Has your question been resolved?
smoky mason
spoiler: ||https://artofproblemsolving.com/wiki/index.php/Sophie_Germain_Identit...
Thank you for this
sonic sphinx
how much is -1^ infinite
devout snowBOT
how much is -1^ infinite
sonic sphinx
none, you cant determine
safe fractal
We know that -1 to an odd power is -1, but to an even power is 1
stone stump
why do you think -1^infinite should have a value to begin with
you are thinking of (-1)^infinite aki
safe fractal
Since infinity can't be defined as either odd or even, the answer to this can't be defined
Wait, op, are you asking for (-1)^infinite or -(1^infinite)?
sonic sphinx
(-1)^infnite
safe fractal
ye
stone stump
why do you think -1^infinite should have a value to begin with
this still applies
safe fractal
It boils down to the limit of (-1)^x as x approaches inifinity, but this doesn't converge so it doesn't have a value pretty much
sonic sphinx
so in sequences should i write the answer cant be defined or should i write two possibilities where infinite odd and even?
sonic sphinx
stone stump
is that (-1)^n + n or (-1)^n * n
sonic sphinx
is that (-1)^n + n or (-1)^n * n
(-1)^n * n
safe fractal
I swear I've never seen someone write * for times irl
sonic sphinx
lmao
wicked apex
its n/n which you can just think of 1
sonic sphinx
so its diverge?
wicked apex
- 4 doesn't matter
alt series test
its limit doesn't go to 0
it goes to 1
since its n/n
sonic sphinx
its n/n which you can just think of 1
cant it be -n/n and n/n?
wicked apex
in alt series
safe fractal
wicked apex
you think of bn which does not contain the (-1)^n
safe fractal
It doesn't converge but it does bounce :d
wicked apex
it is (-1)^n * bn
safe fractal
you can found the boundaries in which it bounces (if they exist)
wicked apex
seems like it goes to inf tho?
safe fractal
Does it?
Solve for limit of n/(n+4) and -n/(n+4) as n goes to infinity
to get the boundaries it bounces between
safe fractal
?
sonic sphinx
alright thanks
sonic sphinx
ima take series in couple days when im done with sequences
thanks tho for the link
.close
devout snowBOT
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Available help channel!
alpine vapor
Number 10 I forgot how to solve these type of questions
devout snowBOT
Number 10 I forgot how to solve these type of questions <:catking:81238636129786...
oblique rover
why is domain of function f(x,y)=(xy)^{1/3} R^2 when sgn(x) has to equal sgn(y)?
oblique rover
i can not have x=-5 and y=2
safe fractal
Define sgn?
safe fractal
So the pair of (x,y) mustn't be (-3, 3) for example?
devout snowBOT
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narrow cradle
how to tell fast if this diverges or not?
devout snowBOT
how to tell fast if this diverges or not?
viral rapids
how to tell fast if this diverges or not?
ratio test
or just know that polynomial/exponential always converges
devout snowBOT
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long trout
im trying to do the part (b) but im not sure of my solution i did it as integrating the joint density function over possible values of x for a given y, is that correct
devout snowBOT
im trying to do the part (b) but im not sure of my solution i did it as integrat...
long trout
<@&286206848099549185>
versed badger
what kind of math is this?
half haven
what kind of math is this?
fr
@versed badger i think my problem is better and ez
1+1
ez
tall knoll
!noping
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long trout
.close
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oblique rover
find partial derivatives at the origin for f(x,y)=(x^5+y^5)^1/5
devout snowBOT
find partial derivatives at the origin for f(x,y)=(x^5+y^5)^1/5
oblique rover
how should i do this?
d f(x,y)/dx =x^4/(x^5+y^5)^(4/5) and d f(x,y)/dy =y^4/(x^5+y^5)^(4/5)
but i can not just plug in (0,0) can i?
pls help
wicked apex
<@&286206848099549185>
hollow blaze
You need to prove that the limit exists
try polar coordinates
then as r->0, the limit shouldnt depend on the angle theta
wicked apex
so ve lim x,y -> 0,0 on the partials?
hollow blaze
yup
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Available help channel!
bleak crest
$$x=\pi r\cos((t-\pi)/2)\cos(bt)$$
$$y=\pi r\sin((t-\pi)/2)$$
is it possible to write x in terms of y and eliminate t, b and r are constant
devout snowBOT
$$x=\pi r\cos((t-\pi)/2)\cos(bt)$$
$$y=\pi r\sin((t-\pi)/2)$$
is it possible to ...
woven radishBOT
mavizasyon
bleak crest
yes
safe fractal
Sure, you could express t from the second expression and then plug it into the first one
bleak crest
I stuck at some point and now all messed up
bleak crest
yes but it should be
this is just random function and I want to convert it into quadratic formula which I need
true geode
If you square both and add the equations it could make it a lot less messy
safe fractal
In order to get this curve in form y(x) you'd have to split it up into multiple functions
Since this curve itself isn't a function of x so to speak
This will probably come out as a result of quadrants for sin and cos as different cases
So pay mind to that
safe fractal
If you square both and add the equations it could make it a lot less messy
Would that eliminate t though?
true geode
Oh that cosbt is multiplying
Then it won't help at all
You could still try but its gonna end up being the same amount of work
safe fractal
This is it basically
So expressing t from the second and plugging in the first gives you the green part
then the negative is the purple part
Why negative? Probably has to do with the angles for sin and cos, not sure exactly where the angle has to be changed, but yeah that's it
This function is periodic with a period of 4pi
is there a cleaner way to write this, probably, maybe try to simplify it
bleak crest
Let me send it original
safe fractal
You can chain these together to make em look all cool
safe fractal
can you send the original function directly
I don't really have time to read through the whole article
bleak crest
I am trying to take screen shot
bleak crest
safe fractal
Ok so you set z to be 0 and did what else?
safe fractal
Well, by setting z to be 0 you're essentiall getting the projection of the spiral
the new z I mean
bleak crest
Yes that was my intention
safe fractal
so what we have here is the spiral viewed from the side
bleak crest
Yes
safe fractal
I simplified the expressions a bit, I don't think it gets any more simple though
you get 2 expressions for the same reason that you can't graph a circle with 1 expression as a function
Note that not all parametric given functions can be cleanly expressed as y(x) or x(y), it's often a mess
bleak crest
I understand, anyway then
safe fractal
bleak crest
I thought it would convert y(x) somehow, looked easy because of trigonometric functions
safe fractal
Oh and for some reason if b isn't a whole number it breaks
bleak crest
Should I close it
safe fractal
ah because the period changes
this function is really funky
if you want to yeah, if you don't have any more questions
bleak crest
Yeah it is all random, not prepared by teacher
I dont have more, I just wanted to see if it is possible, shouldn't blame chat gpt being for dumb lol
safe fractal
Aight, good luck
devout snowBOT
@bleak crest Has your question been resolved?
proud perch
Prove Fermat's Little Theorem.
devout snowBOT
Prove Fermat's Little Theorem.
proud perch
Let's proceed by induction.
weak cove
Unrelated, solve Navier-Stokes
prove P=NP
proud perch
stop memeing
safe fractal
Sorry
sand dove
yeah induction will give you a handful
proud perch
uh
proud perch
I know we can use Lagrange's theorem and that implies FLT but idk how to prove Lagrange's theorem
sand dove
Lagrange theorem is simple
if H is a subgroup of G
then you look at G/H
since the classes of G/H make a partition of G
and each class has |H| elements
|G| = |G/H| |H|
proof finished
so now with Lagrange you can maybe prove FLT...
sand dove
why would it feel like cheating?
proud perch
because we used a really powerful theorem
sand dove
do you perhaps want to go through $(k+1)^p \equiv k^p + 1 [p]$?
woven radishBOT
rafilou2003
sand dove
how do we prove that identity
expand
proud perch
oh right!
pascals triangle
all prime rows have binomial coeffs divisible by primes
devout snowBOT
@proud perch Has your question been resolved?
safe fractal
You need the work for it? Define "work"
Ok, so how do you calculate work?
what's delta?
Well how is this half cylinder oriented?
How is the pump pumping?
restive river
Is it calculus
pale terrace
oh this
wdym finding the work?
so it has volume 250pi
so like find the rate of change?
so what is it filled with
idk about the density of water though
thats about 15625 pounds of water
like a limit in calculus?
oh ok ima think about that
limit as x approaches 0 of pi(r)^2*h is the limit
so if you turn that into an integral
pale terrace
limit as x approaches 0 of pi(r)^2*h is the limit
nvm that doesnt even contain x im stupid
do u know the limit function?
bc i can convert limit to integral
k
im thinking of it as the limit as x approaches 5 from 0 of pi(x)^2 * 20 * density of water
but i think im wrong
isn't the length just a constant 20
you don't really need the width though right?
k
oh ok
maybe integral from 0 to 5 of pi(x^2)* 20 * density of water, so 500pi*density of water
but i think im wrong
k
but volume of a cylinder formula is y=pi(x)^2*10 where x is any value and y is the volume of the cone i think
idk
ill check
what unit is J?
k
i think that you're right
equilateral or not?
k
with side length 5?
k
i think so
i gtg now sry
yw
bye
devout snowBOT
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lament schooner
||||||||||||||||||||||||||||||||||||||||||||KLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLVB 1xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxdc,L
devout snowBOT
||||||||||||||||||||||||||||||||||||||||||||KLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL...
sullen island
@lament schooner it's time to fix your keyboard
safe fractal
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
I hope it's her cat
lmao
upper schooner
||||||||||||||||||||||||||||||||||||||||||||KLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL...
Very interesting question 
sullen island
her cat got suddenly interested in KL divergence or something
safe fractal
I'm still giggling about this
sullen island
it's the start of the new ARG
dense lynx
||||||||||||||||||||||||||||||||||||||||||||KLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL...
hello!
here is an analysis of the frequency of every character in your message
hope you find this information useful and thank you for your patronage :3
sullen island
good bot
lament schooner
omfg
lament schooner
||||||||||||||||||||||||||||||||||||||||||||KLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLL...
ofmg
omg
my cat
lament schooner
her cat got suddenly interested in KL divergence or something
yes
my cat spewed seizure on my keyboard
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safe fractal
@upper schooner lmaooo
dense lynx
LOL
upper schooner
<@788085606483361802> lmaooo
.Very good guess 
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plucky kernel
hi
plucky kernel
would what the range of the inverse of the function y=1/x^2 be?
also its monotomic increasing
question h
nvm
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restive wigeon
Need help with question B. For question B, I come up with a dot product of -38 between vectors B and C (final number is all numbers in the dot product added). And for the magnitude, for B i get sqrt(225) and then for vector C i get sqrt(25). The final answer is -38/75 (sqrt(225) and sqrt(25) are 75 when multiplied). However the answer given by my lecturer is apparently -9/sqrt(225). I don't know how they got that answer
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Need help with question B. For question B, I come up with a dot product of -38 b...
restive wigeon
This is the formula I use
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winter torrent
$A(-3, 2\sqrt{30})$, $E(-4, \frac{12}{7}\sqrt{30})$, and $F(x_3,y_3)$
woven radishBOT
hayley table
restive river
What is at the same py
Same point, u meant circumcenter
Is this jee math
Pt *
This is a damn lengthy question
U know in circumcircle, distance of vertices from circumcenter are equal
U need to use this
Measure the distance of these line segments, AE=EF
EF=AF
Use distance formula, u will then find pt F
@long trout
Oh wait I meant from circumcenter (let x,y) to vertex
See if that works
That's all I said
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pale terrace
what is the question?
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hearty sable
Can anyone talk me through b)?
The answer to a is P=16a/y^2
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Can anyone talk me through b)?
The answer to a is P=16a/y^2
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k = 16a
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
hearty sable
oh, is k constant even when it is a sub-question?
vestal oyster
yes
hearty sable
I see, let me try that
vestal oyster
basically, you first have to find k based on the conditions given in the question and then plug k back in the equation
hearty sable
Here is the mark scheme
vestal oyster
yes p = 4a^2/x
hearty sable
Oops do you mind talking me through it? Idk why but my brain refuse to understand it
hearty sable
np
hearty sable
sure
vestal oyster
hearty sable
Allow me a minute to process it
hearty sable
I see
hearty sable
How did you get to this step ?
I thought it will be P=16a/(k'sqr.x)^2
hearty sable
Oh right
vestal oyster
hope you understood
hearty sable
Oh I am stupid
hearty sable
I am non native speaker so pardon my grammar
No your grammar is perfect
hearty sable
I don't really get how do you put k'=2/sqta lmao
I am usually very good at maths idk what is wrong with me on this question
vestal oyster
where
hearty sable
The 2nd to last line
vestal oyster
bro can you plz point it for me
hearty sable
vestal oyster
like are you asking how did I get k' = 2/sqrt(a) ?
hearty sable
like are you asking how did I get k' = 2/sqrt(a) ?
Nope, I got that. The step after that
vestal oyster
ok just put k' in 1
sorry I have removed some steps
I should have written clearly
k' = 2/sqrt(a)
=> k'^2 = 4/a
and now put it in 1
hearty sable
give me a second.. I sort of get it
hearty sable
This question is like asking about everything little things that I understood wrong with the algebraric concept
vestal oyster
from which topic is it
hearty sable
from which topic is it
Basic algebra lmao. I always get silver/gold in the national challenges but I can't go basic algebra
💀
Anyways, thanks and have a nice day
vestal oyster
welcome! have a nice day too!
hearty sable
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thorn wigeon
I found out for example that:
1 throw: ø
2 throw: 2 chances sur 36 (2/36) = 5.56%
3 throw: 30 chances sur 216 (30/216) = 13.89%
4 throw: 270 chances sur 1296
(270/1296) = 20.83%
5 throw: 2070 chances sur 7776
(2070/7776) = 26.62%
Maybe i am wrong
thorn wigeon
I have a problem with a specific situation (my english might be bad since it's not my native language):
I have a dice with 6 faces which behave normally.
I want to know if there is an equation that allows someone to know when he get 1 and 2 after an amount x of times someone throw a dice [x≥2] and get the general equation for that case and in a second time, with number that can be triggered more times than other faces and making another general equation for that.
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thorn wigeon
@modest dagger may you help me please?
It is said above that i can ping so that's why.
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thorn wigeon
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pale terrace
what
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willow ember
Are you asking the chance of getting a one followed by a two or the chance of getting one and two with 2 dice?
@thorn wigeon
uncut crow
I have a problem with a specific situation (my english might be bad since it's n...
this is very confusing. can you give an example?
brisk panther
I have a problem with a specific situation (my english might be bad since it's n...
the chance of getting a 1 and then a 2 is 1/6
if you throw the dice enough times
willow ember
the chance of getting a 1 and then a 2 is 1/6
1/36*
p(1 and 2) = P(1) * P(2)
P(1 and 2) = (1/6) * (1/6) = 1/36
thorn wigeon
Are you asking the chance of getting a one followed by a two or the chance of ge...
One and two or two and one to start of with 2 throws
Here i found there 2/36 possibilites
But i want to found out for not 2 throws of dice, but x throws
For exemple how many possibilites there is to get an 1 and 2 with 6⁸ possibilities (8 = throws)
thorn wigeon
Yeah, in a x amount of throws of dice
thorn wigeon
so for example 1 1 1 1 1 1 1 2 is ok?
Yes
uncut crow
5 1 5 5 2 5 5 5 also ok?
thorn wigeon
Yes
uncut crow
so one way to look at this is
just for 8, but it will generalize easily
you can find the number of strings of 8 numbers between 1 and 6 that have a 1 and a 2
so like 5 1 5 5 2 5 5 5 is a good string, 5 6 3 4 1 5 4 6 is a bad string
and there are 6^8 total strings
thorn wigeon
Yeah that's the situation
uncut crow
if there are no 1s and 2s
4^8 possibilities for that right
now how about if there are 1s but not 2s? and 2s but not 1s?
if you count those up, that's all the bad strings
all the other ones have a 1 and 2
thorn wigeon
I'm not sure to follow where we are going with this
uncut crow
good strings have a 1 and a 2
bad strings are missing a 1 or a 2. i suggest you can count them up by counting
- the strings that have no 1s and no 2s
- the strings that have a 1 but no 2s
- the strings that have a 2 but no 1s
and adding them up
if there are N bad strings, then there are 6^8 - N good strings
and the probability of a good string is then (6^8 - N)/6^8
thorn wigeon
I can do that, but it would take an eternity to count
uncut crow
lolll well yea we don't actually want to count them
more like make a formula that counts them
thorn wigeon
Yeah that's right
willow ember
Could you use the indirect method for this?
uncut crow
good strings have a 1 and a 2
bad strings are missing a 1 or a 2. i suggest you ...
for 1, there are 4^8 right?
thorn wigeon
and the probability of a good string is then (6^8 - N)/6^8
But on that case don't we need to count N which need us to counts every cases that don't work?
thorn wigeon
Hmm, if now i take 8 throws and replace it with 2 throws to get 4^2 = 16, i won't get 34 which is the amount of possibilites that i won't get 1 or 2 and after a 2nd throw to get the other number.
I calculated that i get 2/36 which respect this case
And 34/36 which don't
uncut crow
well there are 16 ways to roll no 2s and no 1s
but you can also roll
a 2 and not a 1
or 1 and not a 2
uncut crow
a 2 and not a 1
possibilities here are
2 then one of 2,3,4,5,6 (5 possibilities)
or one of 3,4,5,6 then 2 (4 possibilities)
so 9 total
uncut crow
or 1 and not a 2
this one is similar
uncut crow
good strings have a 1 and a 2
bad strings are missing a 1 or a 2. i suggest you ...
so this would say 16 + 9 + 9 bad cases for 2 rolls
which agrees with your 34
thorn wigeon
Ok so 4^x is a part of the answer, but about the 9 and 9 on that case?
uncut crow
yea, the other 2 are tricker
uncut crow
good strings have a 1 and a 2
bad strings are missing a 1 or a 2. i suggest you ...
let's call these values A B and C
so we know A = 4^x
and we wanna compute A + B + C
well one thing to note is B and C are the same
so we really just want A + 2B
thorn wigeon
Yes
uncut crow
for computing B...
let's say x = 8 for concreteness for right now
are you familiar with the binomial distribution?
thorn wigeon
No i'm not
uncut crow
aw darn that gives a formula that computes the value B we want
thorn wigeon
Can i still see it? I'll try to comprehend
uncut crow
yea sure
so we can have either one, two, ... or up to eight 1s right
and the rest just need to not be 2s
for an arbitrary $k$ ones, there are ${8 \choose k}\cdot 4^{8-k}$ strings we can make with no twos
woven radishBOT
slayla
uncut crow
familar with the 8 choose k thingy?
uncut crow
**slayla**
but summing this up over each possible k gives us B
thorn wigeon
Not really, does it work like that?
uncut crow
yep
uncut crow
**slayla**
you can change the 8 to x here and it will work the same
so the probability of getting at least one 1 and at least one 2 in x rolls is $$\frac{6^x - \left(4^x + 2\sum_{k=1}^x {x \choose k}\cdot 4^{x-k}\right)}{6^x}$$ me thinks
wait
woven radishBOT
slayla
uncut crow
this is (6^x - (A+2B))/6^x if i haven't messed up anything
thorn wigeon
I'll need to familiary myself with this
Thanks!
This work for others cases too?
uncut crow
yea i think it should work for any x >= 2
thorn wigeon
I mean if it's not a dice but for exemple calcuting this with a set of 52 card
uncut crow
o
numbers need careful changing but yea similar idea
if you are putting cards back each time
if not it would be different
thorn wigeon
numbers need careful changing but yea similar idea
Alright! Thanks for your time!
Have a nice evening.
uncut crow
:3
thorn wigeon
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odd abyss
Find all integer solutions $(p,a)$ with $p$ being a prime number that satisfy $p^p-p=a!$
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BeeReallyYum
odd abyss
I’ve managed to show that for $p\geq5,$ there are no solutions if $p\equiv1\pmod4$ but I couldn’t prove it for $p\equiv3\pmod4.$
woven radishBOT
BeeReallyYum
odd abyss
Could anyone help me with this case?
shut pagoda
i dont think thats the way to do it
i think its more helpful to notice that p^p-p = 0 mod q for every prime q<p
and that p<=a
odd abyss
i think its more helpful to notice that p^p-p = 0 mod q for every prime q<p
Why would this be true
shut pagoda
because p^p-p = 0 mod a!
shut pagoda
do you know eulers totient thm
i forgot the name
but it says something like p^q=p mod q
for relatively prime p, q
odd abyss
Yeah that’s fermat
shut pagoda
so you can get that p-1=0 mod q-1
odd abyss
Okay, I will try this out
Actually I just stumbled into a method to solve it for $p\equiv3\pmod4$
woven radishBOT
BeeReallyYum
odd abyss
I just had to set $q=p+2$ and use LTE
woven radishBOT
BeeReallyYum
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livid mantle
How do you calculate the derivative of g: t \mapsto \int_{(0,\infty)} e^{-tx}((Sin x)/x)^3 \lambda(dx) in (0,\infty)
I know the derivative is \int_{(0,\infty)} -xe^{-tx}((Sin x)/x)^3 \lambda(dx) But how you even go about solving this in a reasonable time span?
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livid mantle
lebesgue integral btw
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shrewd lion
Hello, how do you find the range and domain of a parabola
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Hello, how do you find the range and domain of a parabola
shrewd lion
Please ping me if i don't respond
devout snowBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
limber finch
Please ping me if i don't respond
domain is always all real numbers
range depends on the direction of the parabola
obtuse flower
It seems to have vertical asymptote at around x = 2 and -2, so domain is -2<=x<=2 (roughly) and range is all real numbers
To show that the domain is such you would have to find the equation of the curve itself
shrewd lion
To show that the domain is such you would have to find the equation of the curve...
y = 2x^2
obtuse flower
I'm not sure if that is the graph of y=2x^2...
Here's what I got on a graphing calculator (desmos):
In this case, the domain is all real numbers, while range is y>=0
shrewd lion
Here's what I got on a graphing calculator (desmos):
Looks right to me. Mine just has more squares
obtuse flower
The y value shouldn't be negative in the graph
Like, the graph shouldn't go below the x axis
Ohhh, you drew a second graph of y=-2x^2, sorry.
obtuse flower
In this case, the domain is all real numbers, while range is y>=0
No yeah this is the domain & range. For y = -2x^2 domain is the same while range is y<=0
shrewd lion
No yeah this is the domain & range. For y = -2x^2 domain is the same while range...
Sorry what's the symbol in between x and R for domain
I don't understand what it means
Is this right?
obtuse flower
R is the set of all real numbers
That notation means x is a real number
so it could be any number from negative to positive infinity
shrewd lion
That notation means x is a real number
oh okay
yeah that makes sense
So range can't go into the negatives? Is that correct
obtuse flower
If it is just a x^2 function yes
if it is ax^2-b then it will go into negatives
for instance, 2x^2-3 will have a range of x>=-3
shrewd lion
for instance, 2x^2-3 will have a range of x>=-3
so b is the range?
obtuse flower
but it is just an x^2 function
If the concave is down, then it would be y<=0
obtuse flower
so b is the range?
b is the y intercept, which, if the concave is up, is the minimum aka lowest point, and vice versa
shrewd lion
If the concave is down, then it would be y<=0
Ahh
shrewd lion
b is the y intercept, which, if the concave is up, is the minimum aka lowest poi...
yeah that makes sense
obtuse flower
Great!
shrewd lion
Great!
Sorry to bother you but how do I answer this
As far as I can tell. 4 is the y-intercept. Vertex is 0,0
I understand the domain
obtuse flower
vertex would not be 0,0 because the graph never touches the x axis
vertex is 0,4 I'm fairly certain
Range is y>=4
obtuse flower
Solve the equation supposing y is 0
So in this case, 0=x^2+4, or -4=x^2
but we know that no x satisfies -4=x^2
because all numbers after squared are positive
so x doesn't exist as a real number
so the graph doesn't intersect with the x intercept
you will learn later that there are imaginary solutions to this
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restive river
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restive river
need help for (v)
i wanted to use induction
so we say
for r = 1
$\sum_{n=0}^1 s(1,n) = s(1,0) + s(1,1) = 0 + 1 = 1 = 1!$
woven radishBOT
Derivative
restive river
now, assume this holds for case $k$ Therefore we have: \
$\sum_{n=0}^k s(k,n) = s(k,0) + s(k,1) + s(k,2) + \dots + s(k,k-1) + s(k,k) = k! $
woven radishBOT
Derivative
restive river
Now we check for case r = k+1
In other words, we need to arrange at most k+1 objects around n circles (0<n<k+1) such that no circle is empty
So we need to check that
$\sum_{n=0}^{k+1} s(k+1,n) = (k+1)!$
woven radishBOT
Derivative
restive river
this is where i am stuck
i do not know how to show this (using the assumption i made)
frosty cradle
split up the sum
restive river
split up the sum
how?
frosty cradle
how do you think you could? you want to use the induction hypothesis
restive river
isnt r = k+1 fixed?
i want to make my thing into a sum of s(k,n)
and then just add s(k+1,k) or something
frosty cradle
ah, right. let me think about it
restive river
ok thanks
its very difficult problem
been thinking about it for couple days haha
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unborn cedar
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unborn cedar
do i need to put abs around something
shut sentinel
do i need to put abs around something
you know they are all positive
so no need for abs
cause positive * positive * positive = positive and negative * negative * negative = negative
if you mix the two you will also get a negative, unless two are negative.
unborn cedar
ok ok
shut sentinel
but since all are positive, it's certain the answer is positive
so you did it correct
topaz beacon
"simplest form" has always been kinda weird wording
shut sentinel
"simplest form" has always been kinda weird wording
deadass
topaz beacon
maybe they want you to keep any fractional parts in the cbrt
unborn cedar
nvm i needed to put all the simplified stuff outside the radical
shut sentinel
oh
shut sentinel
so just 5s^3 * cbrt(r^4*t^7)
topaz beacon
no, you can still take out some r and t
fallow flax
How could I calculate the point where the line intersects with the circle?
grand hearth
What info were u given
winter patrol
get equation of line,
sub into equation of circle,
solve the resultant quadratic equation
choose the large solution
ivory void
that
fallow flax
get equation of line,
sub into equation of circle,
solve the resultant quadratic...
how would i get the y int for equation of a line
winter patrol
i'd just apply two-point formula directly and manipulate as required
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fallow flax
get equation of line,
sub into equation of circle,
solve the resultant quadratic...
is there a way to just have a formula and plug in both points to get answer?
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static kite
I can't proof this statement. How to solve it?
the following function is a open map.
f: (0,∞)×(0,2π) → ℝ
f(r,θ)=r cosθ
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I can't proof this statement. How to solve it?
the following function is a open...
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static kite
<@&286206848099549185>
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pallid zephyr
I can't proof this statement. How to solve it?
the following function is a open...
TAG ME WHEN SOMEONE ANSWERS U
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hoary anvil
I can't proof this statement. How to solve it?
the following function is a open...
I'm not sure how formal the proof needs to be but f is just a plane in 3-space (note that x = r cosθ). Open "wedges" on the rθ plane correspond to open wedges on f.
grave tusk
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safe sphinx
does any one know how to do this
grave tusk
my question is why is B1= <a2,-a1> instead of <-a2,a1>