#help-10
obtuse pebbleBOT
median dome
!status
obtuse pebbleBOT
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
median dome
try doing u substitution
slender nebula
it didnt get me anywhere
median dome
what did you get
median dome
what if you add and subtract something to the numerator?
to get the derivative of the bottom
slender nebula
I tried adding and subtracting cos x
median dome
yes
slender nebula
but then i get 1 - cosx/(cosx + sinx)
slender nebula
okay then I'm not sure how to proceed
median dome
$\frac{sin(\theta)-cos(\theta)}{sin(\theta)+cos(\theta)} + \frac{cos(\theta)}{sin(\theta)+cos(\theta)}$
warm shaleBOT
kheerii
slender nebula
ah so I can solve the first one by substitution
slender nebula
but the second fraction is similar to what I already have
median dome
**kheerii**
somehow in this expression you want the numerator to be the same as the denominator
in the second fraction
right?
median dome
okay
median dome
yep
pale shore
Can you tell me how to solve this
obtuse pebbleBOT
Can you tell me how to solve this
median dome
?
median dome
= x -1/1+x
knotty crow
e^(2x)/(1+e^x) = e^x + 1/(e^x+1) - 1
thick gyro
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
rapid relic
for this question does it denote a vector
obtuse pebbleBOT
for this question does it denote a vector
rapid relic
like what does it denote
frigid prism
Yeah they’re all vectors
twin spire
9
obtuse pebbleBOT
@rapid relic Has your question been resolved?
granite eagle
Greetings, how to calculate this?
2^25 * 3^8?
obtuse pebbleBOT
Greetings, how to calculate this?
2^25 * 3^8?
warm shaleBOT
granite eagle
STOP
wooden cipher
why did you ask
median dome
are you giving an exam right now?
wooden cipher
this is an exam
median dome
LMFAO
wooden cipher
still sus
median dome
not if you're in an exam
granite eagle
So i need to multipliy 222*… (15 2’s?)
wooden cipher
prove youre not in an exam (figure it out) and then we will help
we take academic integrity seriously
wheat seal
factor 12 as 2^2•3
obtuse pebbleBOT
@granite eagle Has your question been resolved?
obtuse pebbleBOT
@granite eagle Has your question been resolved?
obtuse pebbleBOT
@granite eagle Has your question been resolved?
daring salmon
i got -295/228
granite eagle
i got -295/228
No
obtuse pebbleBOT
@granite eagle Has your question been resolved?
true breach
I need to have it as simple answer as it can be.
Expand the integers with exponent
Then multiply the numerators together
Then factor
azure anchor
$f(x)=\frac{x}{1-3x}$ find $f^{-1}$
obtuse pebbleBOT
$f(x)=\frac{x}{1-3x}$ find $f^{-1}$
warm shaleBOT
b0ngl0rd
sacred root
$y=\frac{x}{1-3x}$
warm shaleBOT
Basudev
warm shaleBOT
Basudev
azure anchor
im stuck on how to manipulate it here though, i would usually start by moving the denom to the left
then i got x(1-3y)=y
not sure after that
dark stirrup
Distribute the multiplication on the left side
azure anchor
x=y(3x+1)?
sacred root
Yes
azure anchor
1=y(3x+1)/x ?
warm shaleBOT
Basudev
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hasty tinsel
guys why is these 2 ways giving me opposite answer
obtuse pebbleBOT
guys why is these 2 ways giving me opposite answer
hasty tinsel
what is the correct answer?
nocturne minnow
guys why is these 2 ways giving me opposite answer
On the right side, all you did was take the reciprocal, why did you flip the sign?
obtuse pebbleBOT
@hasty tinsel Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
frosty widget
I'm trying to find out how to integrate the u variable into the equation can you guys help me with this?
obtuse pebbleBOT
I'm trying to find out how to integrate the u variable into the equation can y...
thick gyro
I'm trying to find out how to integrate the u variable into the equation can y...
chain rule
frigid prism
and quotient rule
solve for y'(u)
then plug in u(x)
make sure to use chain rule for u(x) since its a function of x
frosty widget
okok I'll try 
frigid prism
gl
tardy abyss
The Air Force receives 40% of its parachutes from Company C1, and the rest from Company C2. The probability that a parachute will fail to open is .0025 given it is from C1 and .002 given it is from C2, respectively. If a random parachute fails to open, what is the probability that it is from C2?
obtuse pebbleBOT
The Air Force receives 40% of its parachutes from Company C1, and the rest from ...
tardy abyss
I have a tree diagram describing all possible outcomes.
I know that P of C1 is .4, and P of C2 is (therefore) .6.
I also know that P(F|C1) = .0025, and P(F|C2) = .002.
Since I have these given values, I can assume that P(F^c|C1) = .9975, and P(F^c|C2) = .998.
It is asking me the probability of (C2|F). I thought that the way this would be solved is by using the formula
P(A|B) = P(A&B) / P(B)
distant lantern
I also know that P(F|C1) = .0025, and P(F|C2) = .002.
That’s the correct train of thought
Ignore the reply^, I meant to say that to your last text
In this case P(B) would represent the probability that any parachute fails, right?
tardy abyss
Yes.
Which would be the accumulative sum of all probabilities of failure; .002 + .0025 = .0045
distant lantern
Which would be the accumulative sum of all probabilities of failure; .002 + .002...
It would be the sun of the respective probabilities of each company multiplied by the probability of the parachutes failing for each company
I think this is a bayes theorem question
So 0.4(0.0025) + (0.6)(0.002)
tardy abyss
When searching up this theorem this is what shows up.
Is this what you are referring to?
distant lantern
Yes
tardy abyss
This is essentially, P(A|B)= P(A&B) / P(B), no?
distant lantern
It’s really just an extension of your original
Yes, correct
But it serves to highlight more how you calculate each component since it places more emphasis on conditional probabilities
tardy abyss
So 0.4(0.0025) + (0.6)(0.002)
So how would I get to this?
distant lantern
In this case, the probability that a parachute fails is given by the P(F|C1)P(C1) + P(F|C2)P(C2)
This might be a better equation to follow for bayes theorem
tardy abyss
Ohhh, I see. Yes, I finally found one of the answers that is actually a choice on my homework lol
How do I know when to use Bayes' Theorem instead of the normal P(B|A)?
distant lantern
You are technically using the normal P(B|A) whenever you use bayes theorem
tardy abyss
Or is it simply because B depends upon A and therefore demands Bayes' Theorem?
distant lantern
You can think of it like that
Basically within this scope, it’s safe to connect conditional probabilities -> bayes theorem
Given the correct type of problem, of course
tardy abyss
I see I see.
Thank you so much. I will add this theorem to my notes.
The correct answer should be .5455 I believe.
As it would be .0012 / .0022.
distant lantern
👍
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
.
timid silo
<@&286206848099549185>
royal basin
<@&286206848099549185>
!15m
obtuse pebbleBOT
<@&286206848099549185>
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.
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.
royal basin
!status
obtuse pebbleBOT
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
So I’m doing the cylinders first so I’m doing py x 4 squared x 5
There’s 2 of them
So I times that by 2
Then find the volume by doing
10x8x5
royal basin
pi, not py. and don't use the letter x for multiplication.
pi * 4^2 * 5 would give you the volume of a cylinder with radius 4 cm and height 5 cm.
you do not have 2 such cylinders in your solid
instead, you have two halves of such a cylinder on either side.
timid silo
I got 251.327
timid silo
instead, you have two **halves** of such a cylinder on either side.
So now would I get the volume of the cube by doing 10 * 8 * 5 ?
timid silo
the middle part isn't a cube and shouldn't be called one
Ok
But is the calculation correct?
warm shaleBOT
Result:
251.32741228718
checks out.
timid silo
So now would I get the volume of the cube by doing 10 * 8 * 5 ?
Then do I do this ? @royal basin
Then add them together and that’s the answer
royal basin
yes
timid silo
,calc 10 * 8 * 5
warm shaleBOT
Result:
400
,calc 251.327 pi + 400
warm shaleBOT
Result:
1189.5670568488
@royal basin any idea why?
Gave me a new question now
So I would do pi * 3^2 * 4
Then 6 * 4 * 10
Then add them all together
royal basin
ah, perhaps it is because you rounded to 3 decimal places instead of 3 significant figures as they told you to.
my bad for not catching that immediately.
timid silo
my bad for not catching that immediately.
No worries
timid silo
ah, perhaps it is because you rounded to 3 _decimal places_ instead of 3 _signif...
Ah ok I’ll try again now
,calc pi * 3^2 * 10
warm shaleBOT
Result:
282.74333882308
Result:
240
,calc 283 + 240
warm shaleBOT
Result:
523
@royal basin what you think
royal basin
in the future you should do all rounding AFTER all calculations, not in the middle...
though i suppose in this particular case your mistake doesn't affect anything
royal basin
ah, of course, you're putting the wrong measurements in the wrong places again
10 isnt the height of the cylinders
the height is 4
warm shaleBOT
Result:
113.09733552923
,calc pi * 3^2 * 4 + 10 * 6 * 4
warm shaleBOT
Result:
353.09733552923
Result:
240
,calc 113 + 240
warm shaleBOT
Result:
353
yes
obtuse pebbleBOT
@timid silo Has your question been resolved?
past walrus
obtuse pebbleBOT
thorn kernel
How did you solve it?
past walrus
I first put -1 and 1 and it said it was wrong
it says that the answer is -1.2 and -.4 so Im not sure how
eternal flare
Did you calculate the projection of a onto b, or b onto a?
thorn kernel
Why did you divide by (-2^2 +2^2)?
past walrus
thats what the example says u must do
eternal flare
If you're using this notation, note that it's dot product of a,b divided by dot product of b,b multiplied by b
past walrus
Why did you divide by (-2^2 +2^2)?
past walrus
If you're using this notation, note that it's dot product of a,b divided by dot ...
this is how Im supposed to follow it tho
and that is what I did but I ended up with -1, and 1 for my answer for this prblm
\
thorn kernel
You did your projection wrong
Look at your solution again and see on what vector you projected
@past walrus did you see your mistake?
past walrus
no
I mean I followed all the steps and got this so I rlly cant see where its wrong
thorn kernel
You found a projection on b
past walrus
Ok?
eternal flare
If these were the vectors, you would've calculated how vector a looks projected onto vector b. When instead you wanted the opposite like francis said
These two are entirely different projections. See which one you did and choose the correct one
torpid narwhal
what is the largest 4 digit palindrome whose digits are prime numbers and the total of its digits is 16?
obtuse pebbleBOT
what is the largest 4 digit palindrome whose digits are prime numbers and the to...
royal basin
!15m
obtuse pebbleBOT
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.
royal basin
what's troubling you?
rich plume
what is the largest 4 digit palindrome whose digits are prime numbers and the to...
Notice there are only 4 single digit primes
2,3,5,7
torpid narwhal
okay
rich plume
The number is a palindrome so atmost 2 of these 4 digits can be used
royal basin
what the answer 😭
we don't give answers here
also you should say what confuses you
in words
maybe there are some parts of the problem that you don't understand
we can clear those up but only if you tell us
torpid narwhal
what’s a palindrome
rich plume
So it is clear that only 2 out of the 4 numbers 2,3,5,7 will be used
because the 2 numbers will repeat itself
torpid narwhal
2662
rich plume
to make a palindrome
rich plume
2662
That is for sure a palindrome but not the one you are looking for
Since your palindrome has only prime digits
But 6 is composite
royal basin
2662
this is a palindrome and it has four digits and they sum to 16 but not all digits are prime
obtuse pebbleBOT
@torpid narwhal Has your question been resolved?
umbral crest
obtuse pebbleBOT
obtuse pebbleBOT
@umbral crest Has your question been resolved?
umbral crest
.close
rain canopy
25(a)
mellow glacier
!status
obtuse pebbleBOT
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
2
mellow glacier
Show work
rain canopy
mellow glacier
Ok, you have to make 2 linear equations with 2 variables
rain canopy
plsss thank you
mellow glacier
Nah nvm i cant
obtuse pebbleBOT
<@&286206848099549185>
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.
obtuse pebbleBOT
warm shaleBOT
Onkel.Lars
obtuse pebbleBOT
prime sandal
.reopen
That's my question
I think I can get the point if that would just mean there exists a set with the same elements
glacial obsidian
I think I can get the point if that would just mean there exists a set with the ...
No, B can have any elements
prime sandal
No, B can have any elements
I was just stuck between "no elements" or "same elements", but I understand now
obtuse pebbleBOT
Available help channel!
latent jasper
can you only do partial fraction if the degree between numerator and denominator is 1
obtuse pebbleBOT
can you only do partial fraction if the degree between numerator and denominator...
latent jasper
How do I integrate this $\int \frac{1}{x(1+x^6)}dx$
warm shaleBOT
afeAlway
royal basin
"degree between numerator and denominator"?
do you mean to ask "Is a partial fraction decomposition legal to perform ONLY when the denominator's degree is EXACTLY 1 more than that of the numerator"?
latent jasper
do you mean to ask "Is a partial fraction decomposition legal to perform ONLY wh...
yes that is what I meant to say
royal basin
then the answer is no.
you can perform a partial fraction decomposition on any proper rational function, meaning deg(num) < deg(denom)
it is not necessary that the difference in degrees be exactly 1
as for that integral you posted? it looks painful.
you would probably need to factor x^6 + 1
as (x^2+1)(x^4-x^2+1)
and then that quartic too
latent jasper
$1 = A(1+x^6) + Bx$
warm shaleBOT
afeAlway
royal basin
no. you skip a dozen steps and you land in the mud.
do not skip steps. do not speedrun.
latent jasper
This is what I end up tho when I tried to do partial fraction. I didn't skip it on my paper. I just didn't wanna write everything here
royal basin
IF you wanted to use x and 1+x^6 as your denominator,
(which you shouldn't, because 1+x^6 is factorable,)
THEN over the denominator 1+x^6 you would need to put a generic fifth-degree polynomial
latent jasper
(which you shouldn't, because 1+x^6 is factorable,)
how I can I factorize it
royal basin
as (x^2+1)(x^4-x^2+1)
.
i was in fact about to say how x^4-x^2+1 factors
because factor it does
but in a mildly unpleasant way
latent jasper
how did you factorize it
royal basin
"it"?
royal basin
you could have asked more clearly, "How did you factor x^6 + 1 as (x^2+1)(x^4-x^2+1)?"
to which i say, i treated x^6 + 1 as a sum of cubes.
latent jasper
Still doesn't explain how it got factorized to (x^2+1)(x^4-x^2+1)?
At least for me it doesn't make sense
royal basin
do you know the sum of cubes identity?
latent jasper
do you know the sum of cubes identity?
nope
royal basin
that's what i used
latent jasper
alright then
royal basin
x^4 - x^2 + 1 can be written as x^4 + 2x^2 + 1 - 3x^2 and this can then be factored as a difference of squares
(x^2+1)^2 - (sqrt(3)x)^2
latent jasper
thanks for the help!
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
x+y+z=0
x, y, z belong to set of real numbers,
then this equation has infinite number of solutions, right?
We could write all solutions of such equation by set notation:
{ (x, y, z) | z = - (x + y) }
solution is a set of tuples, where the given condition is satisfied, and where x and y are independent variables (that belong to set R).
If so, then I have a question about geometric representation of solutions for this equation. Is the solution a single plane (all points on one plane) or infinite number of planes?
obtuse pebbleBOT
x+y+z=0
x, y, z belong to set of real numbers,
then this equation has infinite ...
kind hawk
one plane
grizzled shore
Ayo I’ve learned just enough LA to help here
The points on your solution is (x, y, -x-y), which if you turned them into vectors would span a plane in 3D space
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
In these equations x, y and z are specific points, x is a coordinate on x axis (x, 0, 0), y is a point (0, y, 0), z (0, 0, z).
And one specific plane will have only one specific combination of x, y, z.
but if I write the plane as
x + y + z = 0
or
z = -(x+y)
then if I say that x=1 and y=1, then z = - 2
one plane (1,1,-2)
but if I say x=2, y=2 then z= - 4
different plane (2,2,-4)
So, my solution for x+y+z=0 is infinite number of planes..
grizzled shore
A plane is described using 2 vectors that are linearly independent scaled to any length within ℝ
In your case it’s a(1,0,-1) + b(0,1,-1), a,b ∈ ℝ
(I hope I’m doing this right, please tell me off if I say anything wrong)
timid silo
can't say it is clear.. am pretty much confused trying to visualize it and combine it with algebra..
I'll try again a bit later
Appreciate your help @grizzled shore @kind hawk
I'll have in mind your answers.
Thanks!
grizzled shore
,w graph x+y+z=0
warm shaleBOT
mental cosmos
whats the probability function of 4 independent events with different probabilities?
i mean the distribution of the random variable of the number of successes of those 4 events
obtuse pebbleBOT
whats the probability function of 4 independent events with different probabilit...
@mental cosmos Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
left grove
obtuse pebbleBOT
left grove
can anyone help me understand the notation of the second line
latent walrus
f_x is the partial derivative of f with respect to x
f_y is the partial derivative of f with respect to y
i believe you are just multiplying them by x and y respectively
left grove
ok thank you i think it’s cause we haven’t gone over partial derivatives yet in class so i’m not sure on the notation
.close
shy agate
i have no idea
obtuse pebbleBOT
i have no idea
shy agate
ok
median dome
tell me what you get
median dome
you always have to use the chain rule
shy agate
but how do i chain this
median dome
what
shy agate
3x^2 h(x^2) + h(x^2)x^3
median dome
you're on the right track
but you have to use the chain rule
for the second term
when you differentiate h(x^2)
you will get h'(x^2)
but you have to multiply it by the derivative of the inside function
shy agate
ok
median dome
so what will you get
shy agate
why not the first term tho
median dome
why not the first term tho
because you are not differentiating h in the first term
median dome
why h?
shy agate
i thought its h(x^2) 2x
median dome
when you differentiate h, will it not become h'?
median dome
what?
shy agate
wait im confused
median dome
what will you get after differentiating h(x)
shy agate
uh
shy agate
yea
median dome
so you can just calculate g'(2) directly
median dome
3x^2 h(x^2) + 2x h'(x^2)(x^3)
by putting x = 2 in this equation
vale lion
For question #2 is it right I feel like it’s wrong
obtuse pebbleBOT
For question #2 is it right I feel like it’s wrong
@vale lion Has your question been resolved?
vale lion
.close
vernal flower
coral epoch
!status
obtuse pebbleBOT
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
3
We can write N as:
N = 111...111 (2*n times) = (10^(2n) - 1)/9
Taking the square root of N, we get:
sqrt(N) = sqrt[(10^(2n) - 1)/9]
We can simplify this expression as follows:
sqrt(N) = sqrt[(10^(2n) - 1)/9] = sqrt[(10^n + 1)*(10^n - 1)/9]
sqrt(N) = (10^n + 1)/3 * sqrt[(10^n - 1)/(10^n + 1)]
Let's focus on the second term in the expression above:
sqrt[(10^n - 1)/(10^n + 1)]
We can express this as a continued fraction as follows:
sqrt[(10^n - 1)/(10^n + 1)] = [1/(1 + (10^n - 2)/(10^n + 1))] = [1/(1 + 1/(10^n + 1)/(10^n - 2))]
We can truncate the continued fraction after a certain number of terms to obtain an approximation for the square root. For example, if we truncate the continued fraction after two terms, we get:
sqrt[(10^n - 1)/(10^n + 1)] ≈ [1/(1 + 1/(10^n - 1))] = [(10^n - 1)/(10^n + 1)]
Therefore, we can approximate sqrt(N) as:
sqrt(N) ≈ (10^n + 1)/3 * (10^n - 1)/(10^n + 1) = (10^n - 1)/3
The (n+1)st digit after the decimal point in sqrt(N) is the digit in the (n+1)st position after the decimal point in (10^n - 1)/3. We can write (10^n - 1)/3 as:
(10^n - 1)/3 = 333...332 (n times) + 1/3
Therefore, the (n+1)st digit after the decimal point in sqrt(N) is the (n mod 3 + 1)st digit of 333...332. We can compute this digit as follows:
If n mod 3 = 0, the (n+1)st digit after the decimal point is 3.
If n mod 3 = 1, the (n+1)st digit after the decimal point is 3.
If n mod 3 = 2, the (n+1)st digit after the decimal point is 2.
Therefore, the digit in the (n+1)st position after the decimal point in sqrt(N) is:
If n mod 3 = 0 or 1, the digit is 3.
If n mod 3 = 2, the digit is 2.
Note that the result above holds for n >= 1
IS IT TRUE ??
obtuse pebbleBOT
@vernal flower Has your question been resolved?
coral epoch
well im not gonna read through that but look at when n =1, we have sqrt(11) = 3.3166247903554
so the n+1th digit here is 1
which isnt what ur proof says
obtuse pebbleBOT
@vernal flower Has your question been resolved?
vernal flower
well im not gonna read through that but look at when n =1, we have sqrt(11) = 3....
True
Any ideas to prove it ?
coral epoch
True
not sure but you can try using my counterexample to see where your proof falls wrong
also try for other values of n
silver plover
hey
silver plover
im trying to do this but a bit stuck
i wanna say its an elliptic paraboloid
but that 1 is not making that the case
neon eagle
Take cross sections of the surface it’ll help
silver plover
Take cross sections of the surface it’ll help
wdym by cross sections?
neon eagle
Like set z=k and see what type of 2D thing it is
silver plover
Like set z=k and see what type of 2D thing it is
like this?
would this be an elliptic parabloid
<@&286206848099549185>
hidden spindle
How would you calculate this? (Stats)
obtuse pebbleBOT
How would you calculate this? (Stats)
hidden spindle
i know the multiplication rule and the addition rule and stuff
i just dont know what the steps would be to solve this
also this
radiant palm
If the prizes are equivalent, then you need to find out how many ways there are of picking three tickets out of the 62 sold, do you agree?
hidden spindle
yes but how would i do that
radiant palm
Have you learned about permutations and combinations?
hidden spindle
yes but i dont understand how to do them
how would i apply that in this situation?
radiant palm
One of these questions is asking you the number of 3-permutations and the other one is asking you to for the number of 3-combinations of 62 objects.
I don't mean to be harsh, but if you don't see which one to apply to which problem, you should take a minute to relearn permutations and combinations (from your textbook or maybe KhanAcademy) and then come back to these questions later.
obtuse pebbleBOT
@hidden spindle Has your question been resolved?
obtuse pebbleBOT
@hidden spindle Has your question been resolved?
obtuse pebbleBOT
@hidden spindle Has your question been resolved?
obtuse pebbleBOT
@hidden spindle Has your question been resolved?
gloomy hill
Quadrants on a graph
obtuse pebbleBOT
Quadrants on a graph
gloomy hill
I was just wondering of what the quadrants on a graph
tardy epoch
high heath
gloomy hill
What does it mean if an angle is coterminal
obtuse pebbleBOT
What does it mean if an angle is coterminal
gloomy hill
I did and I dont understand it
how is 390 even on there
if its a circle
thats why im asking
high heath
gloomy hill
i still dont get it
keen jetty
how is 390 even on there
so you know a circle has 360 degrees right? and you also understand ow quadrants work?
how*
obtuse pebbleBOT
@gloomy hill Has your question been resolved?
supple quest
If x,y and z are three positive integers, such that $x^n+y^n=z^n$ where $n>1$, then prove that x,y,z are greater than n.
obtuse pebbleBOT
If x,y and z are three positive integers, such that $x^n+y^n=z^n$ where $n>1$, t...
warm shaleBOT
SirLance013
obtuse pebbleBOT
frigid prism
.reopen
obtuse pebbleBOT
Available help channel!
true breach
How do you do this question
obtuse pebbleBOT
How do you do this question
obtuse pebbleBOT
How do you do this question
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
the topmost row contains exactly 1 log
true breach
So n would be 21?
royal basin
i don't know what the letter n is. you have not introduced it.
i was going to ask you to write the number of logs in the pile as a summation with a term for each row
royal basin
yuck
but yes, perhaps that would be so.
would prefer you write down the summation itself though
true breach
What is summation
royal basin
sum
true breach
So the answer?
royal basin
as in, i want you to write out what it is that we wish to add together
without calculating it
before plunging into any formulaic bullshit
royal basin
yes, that
you could have recognized this as the 21st triangular number (and the problem even mentioned the word "triangular") but you didn't
if you wish to use that formula you talked about then i can't exactly stop you
even though imo it would be a bit circular
true breach
What is imo
royal basin
in my opinion
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Hmm can someone remind me why we can optimise x^2 + y^2 +z^2 instead of sqrt(x^2 + y^2 +z^2) to find the shortest distance between something and its constraints 
obtuse pebbleBOT
Hmm can someone remind me why we can optimise x^2 + y^2 +z^2 instead of sqrt(x^2...
timid silo
Is it because both y = x and y = sqrt(x) are monotonic
royal basin
the squaring function is monotone
timid silo
Yeah right okay, so technically any equivalent monotonic function could also be viable in this case right 
Like what about an exponential function for example
timid silo
Let's say we are masochistic and want to replace x^2 +y^2 + z^2 with e^(x^2 +y^2 + z^2)
Oh okay okay cool
The more you know
Ty
.close
past walrus
obtuse pebbleBOT
past walrus
can someone help me pls
frigid prism
dot product
past walrus
I know
frigid prism
draw it out
past walrus
but I keep getting it wrong
frigid prism
draw the two vectors and the projection
past walrus
draw the two vectors and the projection
That I wasn't taught
frigid prism
That I wasn't taught
it becomes very important once you start talking about distances
get into a habit of drawing them
or learn how first
past walrus
In the example video It doesnt do that tho
and I've followed the same steps carefully and still ended up missing it
obtuse pebbleBOT
@past walrus Has your question been resolved?
past walrus
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lost summit
obtuse pebbleBOT
gleaming ridge
,w int 1/(25 - x^2)^(3/2)
warm shaleBOT
obtuse pebbleBOT
@lost summit Has your question been resolved?
lost summit
,w int 1/(25 - x^2)^(3/2)
I can look up the answer but I wanna know where I messed up thats what
lost summit
huh
It was (25-25sin^2)^(3/2)
I took out the 25 by rooting then cubing = 125
and the 5cos is on top
so its 5/125 = 25
gleaming ridge
oh you directly changed so I got a bit confused
proud coral
can someone help me here
gleaming ridge
won't that cosx above cancel the cos^3x below
obtuse pebbleBOT
can someone help me here
Please read #❓how-to-get-help
lost summit
won't that cosx above cancel the cos^3x below
OHH THATAS WHY
gleaming ridge
can someone help me here
get your own help channel
lost summit
Im solving for 1/25 integral of 1/cos^2
which is sec^2x
1/25 tan(theta) then just do pythagorean theorem
gleaming ridge
yep
lost summit
bruh how did I forget to subtract a power
At least I got a lot of practice for solving 1/sec^3x..
gleaming ridge
yee
lost summit
ty
gleaming ridge
use .close to close the channel
lost summit
.close
dense lodge
For the last part I understand that the maximum is 3 for the new range, but I don’t understand why it’s greater than zero
obtuse pebbleBOT
For the last part I understand that the maximum is 3 for the new range, but I do...
gleaming ridge
For the last part I understand that the maximum is 3 for the new range, but I do...
Hint: 2x^2 + 4x + 9 = 2(x^2 + 2x + 1) + 7
dense lodge
i assume tho if the graph is inverted/turned upside down it would go below zero on the y axis?
sage geode
2x^2 + 4x + 9 is always positive, so is 21/(2x^2 + 4x + 9)
gleaming ridge
because of +7?😂
yeah
dense lodge
hmm
gleaming ridge
i assume tho if the graph is inverted/turned upside down it would go below zero ...
it would be squished towards 0 but not below 0
dense lodge
i thought that only tells u that max is 3
dense lodge
it would be squished towards 0 but not below 0
oh okay yeah i learn visually so was struggling to see it😂
thanks so much guys
dense lodge
yeee
i feel like most would just plot in their graphical calc
but anyways ill use that
thx
.close
trim swallow
float2 EvaluateBezier(float2 P0, float2 P1, float2 P2, float2 P3, float t)
{
float2 p = float2(0, 0);
p = pow(1.0f - t, 3) * P0;
p += 3 * t * pow(1.0f - t, 2) * P1;
p += 3 * pow(t, 2) * (1.0f - t) * P2;
p += pow(t, 3) * P3;
return p;
}
This is the math for the equation, incase you can't read what I wrote
queen sand
can someone help me with a visual of every step to solve this question?
obtuse pebbleBOT
can someone help me with a visual of every step to solve this question?
gleaming ridge
can someone help me with a visual of every step to solve this question?
That looks like linear equation in 1 variable. Just simplify and solve it directly.
gleaming ridge
can someone help me with a visual of every step to solve this question?
What exactly do you need help with?
gleaming ridge
Multiply by 2 everywhere
queen sand
both sides?
gleaming ridge
Yeah
bold glade
How did he come to the conclusion that e^x is always bigger than 0? (Thus removing the negative at the last line).
obtuse pebbleBOT
How did he come to the conclusion that e^x is always bigger than 0? (Thus removi...
trim swallow
I think it's because of derivatives, like if you reduce the x by one it can never be zero
bold glade
just general knowledge about e^x
Can you elaborate?
sage geode
It is generally true
kind hawk
bot is down I guess
bold glade
Ah right no matter what I plug in, it'll be above 0
sage geode
e > 0 -> e^x > 0
kind hawk
e^x = (e^(x/2))^2 is a square and therefore not negative
sage geode
Ah right no matter what I plug in, it'll be above 0
Unless the base is negative or 0 itself
obtuse pebbleBOT
trim swallow
Does someone know how I can draw a bezier curve inside geogebra?
obtuse pebbleBOT
Available help channel!
vivid pagoda
If there is a condition for a binary string: "can have at most one occurrence of 000"
Would you say that 0000 and 00000 both have multiple occurences (since there is overlap)
Or are those examples fine?
obtuse pebbleBOT
If there is a condition for a binary string: "can have at most one occurrence of...
delicate junco
if that statement as such is given correctly, then 0000 has exactly 2 occurrences of 000
but you should check if that is given correctly, for formatting of binary files for example it searches for the first occurrence of the word, then searches again afterwards, meaning if you search for 'ababa' in ccababababcc you will find the ababa, and the search again afterwards with the remaining babcc, so there it's only once
obtuse pebbleBOT
@vivid pagoda Has your question been resolved?
vivid pagoda
if that statement as such is given correctly, then 0000 has exactly 2 occurrence...
Hmm this specific question is only asking what I said. It is stemming from Finite Automata/CFG/RE classes.
So it sounds like 0000 and 00000 would not be accepted?
delicate junco
Hmm this specific question is only asking what I said. It is stemming from Finit...
yes
vivid pagoda
Thanks!
gaunt raven
can someone help
obtuse pebbleBOT
can someone help
delicate junco
Start filling out angles you can find and the solution should present itself
You will also have to consider sums of angles
gaunt raven
yeah?
delicate junco
so the top part is 40
whats this number? 30?
gaunt raven
20
delicate junco
so the top part is 40
then thats correct
gaunt raven
then how can i found the right part
delicate junco
whats their sum?
gaunt raven
240
delicate junco
now you have to use some bigger equation
say that a and b are the angles in the top, and b is the one you want to find
use information you have to make an equation system
delicate junco
well, you have more information given other than a+b=40
gaunt raven
where?
gaunt raven
hum
delicate junco
hum
the second line could've been the middle like:
240=360-a-b-50-30
which just becomes 40=a+b too
then the equation system gives a=a or 0=0, meaning all a work
but we know angles must be atleast some number, so a>0, which also implies b>0, and thus a<40 and b<40 or a+b=40
obtuse pebbleBOT
delicate junco
but why 30
obtuse pebbleBOT
Available help channel!
frosty valve
obtuse pebbleBOT
frosty valve
is this right?
royal basin
good enough, though you are signing yourself up for a lot of minus-management.
timid silo
missing x for the -2sqrt(6) i am guessing?
frosty valve
i have the answer but multiplying this did not give me the answer
royal basin
wait, hold on.
frosty valve
missing x for the -2sqrt(6) i am guessing?
right sorry
royal basin
something sus
timid silo
truly is
frosty valve
i did get the answer right
on my calculator
but how do i do the working for the last part
royal basin
what is your question
royal basin
,rccw
warm shaleBOT
timid silo
,w (-(-2sqrt(6)) +sqrt((2sqrt(6))^2 - 4(5)))/(2)
royal basin
fucked up parentheses
timid silo
warm shaleBOT
timid silo
yeah thats fine
frosty valve
i got the right answer when i pressed this into the calculator but the working is giving me other answers
royal basin
i have the answer but multiplying this did not give me the answer
to translate this into human readable language, "I have the answer key in my book, but when I did it on paper, I got something different."
royal basin
i got the right answer when i pressed this into the calculator but the working i...
share the working with us
frosty valve
to translate this into human readable language, "I have the answer key in my boo...
in my book?
frosty valve
.
royal basin
i should probably disengage before i get overly irritated sorry
frosty valve
im just stuck at the circled part
timid silo
[
\f{1+\s6}{-1+\s6} \cdot \f{-1-\s6}{-1-\s6}
]
warm shaleBOT
timid silo
we need to simplify this
this is more or less just FOIl
and difference of squares
do you have any idea what either of those terms mean? @frosty valve
frosty valve
this is more or less just FOIl
never seen this b4
warm shaleBOT
timid silo
does this help
timid silo
okay
so you are basically doing this for both the numerator and denominator
try it out
timid silo
uhm
timid silo
but which part went wrong
how did u magically
summon the -7 on the right
you are multiplying the square roots right?
timid silo
yes
frosty valve
sorry
frosty valve
why tho
timid silo
wdym 'why'
frosty valve
how do i know when to cancel the negatives
timid silo
when...you can?
frosty valve
oh
timid silo
like you have [
\f{-7-2\s6}{-5} ]
you can factor the negative sign from the numerator and cancel it with the one in the denominator
warm shaleBOT
frosty valve
only when the numerator and denominator has negatives?
then we can cancel it off?
@timid silo
timid silo
obtuse pebbleBOT
sage geode
What's your question?
sage geode
,w 1.38 * 273 * 1.414 * 3.14 * 1.01
warm shaleBOT
sage geode
Let's call this number k
timid silo
Ok
sage geode
So we have 70 = kd^2 * 10^-18
Here you simply need to divide both sides by k and multiply both sides by 10^18
So that it becomes d^2 = 70/k * 10^18
And d will simply be plus or minus the root of that
By any chance, is the definition of d also given?
For example is it a length/distance?
timid silo
Yup it's physics chapter and the d is diameter of mole
timid silo
Yea
sage geode
,w sqrt(10^18 * 70/(1.38 * 273 * 1.414 * 3.14 * 1.01))
warm shaleBOT
sage geode
Approximately 2 * 10^8
timid silo
But as I know in last my teacher said answer would be something like 4.313 I can't remember but it's something 4.
@sage geode
sage geode
Graphing calculator is providing this as well
The teacher is wrong then I suppose
Or you plugged a value incorrectly
sage geode
It says 70nm, not 70m
And the right hand side should be inverted
Hm, still doesn't give 4
timid silo
Okh
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
whole salmon
obtuse pebbleBOT
whole salmon
Need to find p(A) can't seem to get a start looks like it shouldn't be too hard
But really stuck
keen sandal
p(a) should be 0.3
P(A|B) * P(B) = 0.1 * 0.6 = 0.06
P(B|A) = P(A and B) / P(A)
so P(A) = P(A and B) / P(B|A) = 0.06 / 0.2 = 0.3
obtuse pebbleBOT
@whole salmon Has your question been resolved?
whole salmon
.close
obtuse pebbleBOT
whole salmon
.reopen
obtuse pebbleBOT
✅
keen sandal
P(B|A) = P(A|B) * P(B) / P(A)
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A) [use the law of total probability]
P(A) + P(not A) = 1 => P(A) = 1 - P(not A)
So, P(B) = P(B|A) * (1 - P(not A)) + P(B|not A) * P(not A)
Now, P(B|A) = (P(A|B) * P(B)) / P(A)
P(B|A) = (P(A|B) * [P(B|A) * (1 - P(not A)) + P(B|not A) * P(not A)]) / [1 - P(not A)]
whole salmon
.close
zinc spruce
hello
zinc spruce
I had a question regarding 3d equilibrium problems
Can anyone explain why they are taking the perpendicular distance to calculate moment in a 3d problem?
werent we suppose to take the cross product when calculating moment in 3d
i would really appreciate the help, i have an exam tomorrow.