#help-13
cedar kilnBOT
crimson sedge
need help finding y
thin roost
Find x first
crimson sedge
oh wait i already did
grand forge
Find x first
?
grand forge
why is that q13
crimson sedge
i need help with this one
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
bright rampart
"Evaluate the integral as a geometric power series"
cedar kilnBOT
"Evaluate the integral as a geometric power series"
bright rampart
I feel like I went wrong because in the last equation it no longer looks like a simple power series
cedar kilnBOT
@bright rampart Has your question been resolved?
delicate atlas
what did i mess up on
cedar kilnBOT
what did i mess up on
delicate atlas
the solution is 0, trying to see where i messed up on the negatives signs or something but i don't spot anything
hollow trail
that's supposed to be 1⁸/8 - (-1)⁸/8
i think you wrote the exponents so big they looked like they're multiplying instead
delicate atlas
holy shit you're right
delicate atlas
thats never happened to me before damn my brain fried 😭
buoyant latch
Those lines are for words not math
They are not tall enough for fractions and the like
delicate atlas
start using double lines for math equations?
buoyant latch
Just ignore them
Or double line if you like it being neat like that
I personally use blank paper so it’s really up to you
frank bronze
i wrote a related rates problem and was wondering how to solve this?
frank bronze
im assuming start with deriving the equations of both shapes?
cedar kilnBOT
@frank bronze Has your question been resolved?
frank bronze
<@&286206848099549185>
quaint quiver
You just should know how much water we need to make the height from 7m to 14m
And then divide this volume by the water increasing speed.
quaint quiver
The change of height is piecewise
But the change of volume is even
So it can be divided directly
frank bronze
You just should know how much water we need to make the height from 7m to 14m
and how would i solve for this? would i differentiate both equations with the height of 12m anf radius of 4?
gritty viper
This isn't really a related rates problem
The water is filling at 4m^3 per hour
You calculate the remaining volume, then divide by 4
Calculating the remaining volume will be very hard but still not a related rates problem
frank bronze
This isn't really a related rates problem
hmmm, how could i change this problem to better make it a realted rates problem?
gritty viper
Related rates would be like
The water is currently flowing in at 4 m^3 per hour
How fast is the water height changing right now
frank bronze
oh, so i would have to be directly solving for a derivative for it to be rates.
gritty viper
Yeah
The rate of volume change and the rate of height change are the related rates here
frank bronze
How fast is the water height changing right now
also what did you mean by "right now"
uhh what would that imply as in what im solving fore
gritty viper
When the current height is 7
if it was higher, height would be increasing slower right
because wider
frank bronze
well yes
frank bronze
agreed.
yeah i was just trying to figure out a way i can reword this now
would i have to give an amount of hours to then be able to solve for the rate the height is changing say when h = 14
gritty viper
you don't necessarily need number of hours
though if it's filling up at a constant rate you can figure out number of hours from height
frank bronze
i see
An upside right cone with a hemisphere on top are shown. Height of cone is 12m and diameter is 8m. Water is comming. into structure at a rate of 6m/1^3 Hour. The bottom of the cone is leaking the water at a rate of 2m/1^3 Hour. How fast is the waters height changing when the height is 14m
cedar kilnBOT
@frank bronze Has your question been resolved?
crimson sedge
cedar kilnBOT
crimson sedge
so 30 each hour
tender cipher
cedar kilnBOT
tender cipher
,rotate
wraith daggerBOT
tender cipher
I’m trying to prove this and I don’t think I’m doing it right
versed fulcrum
Where did this matrix come from?
true violet
Where did this matrix come from?
i think it's binomial expansions not matrices
green prairie
I think its binomial coefficients
versed fulcrum
Ohhh okay
royal loom
I think it's binomial coefficients
green prairie
I think it's binomial coefficients
I think it's binomial coefficients
versed fulcrum
Side-effects of linear algebra 😅
cedar kilnBOT
@tender cipher Has your question been resolved?
cedar kilnBOT
@tender cipher Has your question been resolved?
pure tulip
check the terms in red - they don't look right
velvet juniper
I’m trying to prove this and I don’t think I’m doing it right
.
tender cipher
check the terms in red - they don't look right
would it be something like this?
pure tulip
yep, now just simplify what you have in the square brackets in the last expression
this will work, you can also do what Ethereal said above, if you are allowed to use that formula.
pure tulip
just expand (n+h+1)(n-h+2)
tender cipher
oh ok
pure tulip
multiply it all out
wraith daggerBOT
pure tulip
yep 👍 Also look at Ethereal's suggestion
tender cipher
what do i do with that formula? do i sub it in where nCk is in the original question?
pure tulip
hmm, actually that's not the formula I was thinking of... hang on
I was thinking you could use this one, if you are familiar with this formula?
pure tulip
yes it is although I didn't know it's name until now lol
it can be proved the same way you proved this problem...
anywho, if you could use pascal's identity then this problem becomes easy, do you see how?
tender cipher
nope
pure tulip
just apply it on the RHS multiple times
tender cipher
rn i got (n+1)choose k - n choose(k-1)
pure tulip
RHS is ${n\choose k} + 2 \times {n\choose k-1} + {n\choose k-2}$\
$= ({n\choose k} + {n\choose k-1}) + ({n\choose k-1} + {n\choose k-2})$
wraith daggerBOT
JS
pure tulip
if you apply pascal's to each of the stuff within brackets what do you get?
tender cipher
${n+1\choose k} + {n+1\choose k-1}$
wraith daggerBOT
BOHO
pure tulip
right 👍 and can you use Pascal's on this again?
pure tulip
yes indeed, so this would be an easier way to prove this, so long as you are allowed to use Pascal's
otherwise, your proof is also fine, just requires more work.
tender cipher
yeah i made mistakes when combining the fractions
and unrolling the factorials
alr, tysm for helping me
.close
stiff gyro
i need help again hahah
cedar kilnBOT
i need help again hahah
spice kraken
make the right side 1
stiff gyro
make the right side 1
why 1?
stiff gyro
umm hold on is it gonna be.....1 = 5/2x - 3/2y + 2/2z?
spice kraken
yes
stiff gyro
alright thanks!
cedar kilnBOT
Available help channel!
nova snow
how does part B work? im still confused
cedar kilnBOT
how does part B work? im still confused
rustic siren
would it be the min and the max?
vapid edge
you don't actually, simply set the cosine term to 1 to get the maximum high and -1 to get its minimum
nova snow
oh? why does this work?
vapid edge
you don't actually, simply set the cosine term to 1 to get the maximum high and ...
wait, it's the opposite. Set cos to -1 to get maximum and 1 to get minimum
vapid edge
oh? why does this work?
you can ask yourself how to make d maximum or minimum. For it to be maximum, the cosine term has to be negative, since it will turn positive because of the minus sign in front of cosine. We don't need t for that.
nova snow
you can ask yourself how to make d maximum or minimum. For it to be maximum, the...
doesnt that differ because theres a change in amplitude and a vertical shift so its not your standard y=cosx
why wouldnt t =1 be max
and t= -1 be min
vapid edge
what made you think of that?
nova snow
wait, it's the opposite. Set cos to -1 to get maximum and 1 to get minimum
well you said -1 is a max but y=cosx at y=-1 is a minimum
vapid edge
the cos x is the key here, so pay attention to it. we know the maximum value of cos x is 1 and its minimum is -1
nova snow
oh will 1 be a max because
cosine is reflected across the x-axis
because of the - term
vapid edge
try putting the d function into graph
vapid edge
you'll see that it should reach its maximum at t = -25/4 (physically it doesn't make sense to have negative time, but I just want you to see that the value of the cosine term is -1)
vapid edge
what do you think? try substituting it
nova snow
im really lost
vapid edge
uhm, how do I put it
I'll try summarizing my points
Here is our function
it's 1,3 minus something, and that something is governed by the cosine(4pi/25 t)
nova snow
yeah
vapid edge
what could you do to maximize d?
maybe you get rid of that something, that is by making the right term zero
but there is a better way
nova snow
hm.
vapid edge
you make that something negative, because the negative would cancel and now, instead of 1,3 minus something, it is now 1,3 plus something
right?
nova snow
so we are trying to make d really big?
vapid edge
yes
nova snow
why not plug in a giant number like 1000 or something then
vapid edge
that's a nice question, but here we are dealing with periodic function, that is they repeat themselves and fluctuate between certain values, and those values are not infinite
the maximum value of cosine is +1, and its minimum is -1
you can't get beyond that
even if you substitute t equals infinity
nova snow
oh okay
vapid edge
you can see them here
try zooming out, see whether the cosine function ever approach 1.1 value
ok, got it?
let's back to our original function
vapid edge
Here is our function
Here, there is a number before the cosine function. It's just an amplification, it doesn't change the behavior of the cosine function.
vapid edge
so we are trying to make d really big?
since we're trying making d as high as possible, what would the value of the consine(4pi/25 t) be? Two options, -1 or +1 since these are the extreme value
vapid edge
since we're trying making d as high as possible, what would the value of the con...
to make d high, cos(4pi/25 t) has to be -1. Again, we don't yet care about t, all I want is that it should equal to -1 so that d = 1.3 + 0.6 = 1.9
to minimize d, simply substitute cos(4pi/25 t) = 1, so d = 1.3 - 0.6 = 0.7
can you get it?
nova snow
so we sub in -1 and 1 for the cos function?
vapid edge
yes
that's my approach. Idk if you have studied about finding optimum values, but I prefer this intuitive approach
vapid edge
you'll see that it should reach its maximum at t = -25/4 (physically it doesn't ...
actually I made a fatal mistake here, it should be 25/4, no pi and no minus
sorry if that confuses you
nova snow
hm
cedar kilnBOT
@nova snow Has your question been resolved?
stiff gyro
can i ask something? my teacher asked me to make a simple racing car game using vectors but how to apply when i add or subtract vectors for that?
cedar kilnBOT
can i ask something? my teacher asked me to make a simple racing car game using ...
@stiff gyro Has your question been resolved?
safe ermine
can i ask something? my teacher asked me to make a simple racing car game using ...
you have to check if the vectors are tail to tail i think
because this determines whether you gotta make one vector positive/negative in order to “add or subtract”
untold mulch
im making some drawing stuff in maple using the geometry package, and i was wondering if its possible to assign a dynamic value as a name
like if i had "x := 10"
and i wanted a "y10 := 89"
i would think to do something like "yx := 89" or "y+x := 89" but none work/are allowed
any ideas?
cedar kilnBOT
im making some drawing stuff in maple using the geometry package, and i was wond...
@untold mulch Has your question been resolved?
cedar kilnBOT
@untold mulch Has your question been resolved?
untold mulch
<@&286206848099549185>
untold mulch
.close
marsh pond
cedar kilnBOT
marsh pond
what is the objective to solve? REF or RREF?
what am I trying to find? if i get no solution, w is not in span of v1,v2,v3?
if I get 1 or infinite solutions, w is in span of v1,v2,v3?
floral arrow
If v1, v2, v3 are linearly independent, then getting a row of 0 here would mean w is a linear combination of the others
But that's a given since if v1, v2, v3 are linearly independent you can form any other vector in the same space
marsh pond
marsh pond
If v1, v2, v3 are linearly independent, then getting a row of 0 here would mean ...
does this help at all? or waste of time
marsh pond
But that's a given since if v1, v2, v3 are linearly independent you can form any...
how do you know v1,v2,v3 are linearly independent?
floral arrow
I don't
marsh pond
OK
floral arrow
That's why I said "if"
marsh pond
well, I am stumped..
floral arrow
The goal is to find if there exist a,b,c such that
a{-5,4,1} + b{-10,9,2} + c{-31,26,6} = {2,8,10}
marsh pond
oh so I should make this an augmented matrix
also, I wrote these down wrong didn't i?
i used a transpose I think
floral arrow
Yeah I mean it would work with a transpose if you transpose all the operations too
floral arrow
I guess so
marsh pond
now I just solve for the last column
floral arrow
Btw the way to find out if v1,v2,v3 are linearly independent is to do the same but with w = {0,0,0}
If you find that the solution is a=b=c=0 then they are
marsh pond
Btw the way to find out if v1,v2,v3 are linearly independent is to do the same b...
so we have solutions for all, this means w fits within the span of v1,v2,v3?
floral arrow
,w a{-5,4,1}+ b{-10,9,2}+ c{-31,26,6}= {2,8,10}
wraith daggerBOT
floral arrow
Yep
marsh pond
does this indicate if w is linearly independent? or that's a different question
to say it fits within the span of 3 other vectors
floral arrow
linearly independent from what?
marsh pond
i'm not sure
if it asked for that
"is w linearly independent" lol
dunno if that even makes sense
floral arrow
2 vectors can be linearly independent
marsh pond
yeah
floral arrow
n vectors for n > 1
marsh pond
so could it ask: "is w linearly independent in the span of {v1,v2,v3}?"
floral arrow
That make no sense
floral arrow
If w is not in {v1,v2,v3} then w is linearly independent from v1,v2,v3
Which does not mean that w,v1,v2,v3 are all linearly independent
marsh pond
OK, so for the "how many vectors are in" question, are we still asking in regards to w tagged onto the end for the augmented matrix?
floral arrow
That feels like such an obvious question I'm not sure what they mean by "in {v1,v2,v3}" anymore
marsh pond
there are 4 questios in total actually
here they are, for context
- how many vectors
- how many vectors in span
floral arrow
Ok so that's just a trick question
{v1,v2,v3} is a set of 3 vectors
w is different from all 3, so it's obviously not in that set
marsh pond
yeah
floral arrow
It is however in the subspace they form
marsh pond
so for question 2
the answer would be 3
floral arrow
Yeah and for 1 it would be no
marsh pond
i thought we determined w is in the span
floral arrow
Yes, that's not what is written in (1)
marsh pond
it is what we worked on here tho
marsh pond
I don't get it
floral arrow
w is different from all 3, so it's obviously not in that set
.
marsh pond
with more context this question makes more sense?
in terms of how to answer question 1
1 is no
4 is yes?
floral arrow
Yes because I thought "in {v1,v2,v3}" meant "in the subspace formed by {v1,v2,v3}"
floral arrow
Right
marsh pond
ummm
marsh pond
does this answer question 3?
floral arrow
Not really
marsh pond
or is question 3 kinda asking: how many columns are there
the answer for question 3 would be 4?
floral arrow
No
marsh pond
"how many vectors are in span"
floral arrow
How many vectors can you make with a linear combination of v1, v2, and v3?
floral arrow
Yes
marsh pond
using scalars it could be anything really
floral arrow
Even without row operations
marsh pond
marsh pond
Even without row operations
how so?
floral arrow
At least one of v1,v2,v3 is not zero, so you can scale it with any real
The span of a single non-zero vector contains an infinite number of vectors
floral arrow
So the answer is kind of infinity cubed, but that's just infinity
marsh pond
Even without row operations
so I'm not sure I'm following
floral arrow
Oh right if you count it like that
marsh pond
OK
marsh pond
OK, yeah when it comes to upper or lower triangular matrices to find determinant, I try to avoid scalars
since the diagonal does not need to be 1, so no scalar is necessary
and it reduces the math in the end by not using scalars, then multiplying by reciprocal of scalar and messing up somewhere
but for REF/RREF I still count scalar as row operation
floral arrow
opaque valve
Hi , if I have ln(x^(sqrt(x))). Why isnt that the same as expressing it as (x/2) * ln(x) using arithmetic laws for exponential?
opaque valve
south tundra
Who told you that?
wraith garnet
south tundra
Ah wait I thought you were asking "Why is it the same"
Alright, why do you think it should be (x/2) * ln(x)?
opaque valve
Because sqrt(x) can be written as x^(1/2) right?
south tundra
Right
opaque valve
Ok, so. ln(x^(x)^(1/2))
And by rules a^(b^c) = a^(b*c) right?
south tundra
No
You are confusing it with (a^b)^c = a^(b * c)
There's no such rule as a^(b^c) = a^(b * c)
opaque valve
How are (a^b)^c not equal to a^(b^c) ? So you´re saying that its not equal to a^b^c?
south tundra
(a^b)^c is different from a^(b^c)
Let me demonstrate
If a = 2, b = 3 and c = 2, we have
(a^b)^c = (2^3)^2 = 8^2 = 64
2^(3^2) = 2^9 = 512
64 and 512 are not equal
opaque valve
Alright, that clears things up. Then, If I have ln(x^(sqrt(x)) How do I then know if
a) Its ln(x^((x)^(1/2))
b) its ln((x^x^(1/2)) ?
floral arrow
Too many parentheses
south tundra
It's $\ln\left(x^{\left(x^\frac12\right)}\right)$
wraith daggerBOT
A Lonely Bean
south tundra
And you may bring the $\left(x^{\frac12}\right)$ to the front of the $\ln$
wraith daggerBOT
A Lonely Bean
opaque valve
But by using exponential laws. Say we have sqrt(x) / 1. That is equal to ((x) / 1) ^ (1/2) And by this manipulation Ive extracted (1/2) Outside of the parentheses?
south tundra
That is valid, yes
opaque valve
I get the example you did before with actual numbers to prove why im wrong. Im not understanding entirerly why I cant do the same manipulation here.
Alright, thanks for the help anyways. Found the issue
.close
dull plover
alright this time i promise its a tricky one
cedar kilnBOT
alright this time i promise its a tricky one
dull plover
i tried multiplying with the conjugate
simplified it to (1+cosx)/sinx
could not go further
crystal raptor
try splitting the fraction now
dull plover
lim (1/sinx) + lim cosx/sinx
crystal raptor
now you're going to want to study the behaviour as you approach 0 from the left versus from the right
(you probably could have done this without splitting but this is probably easier to think about)
crystal raptor
if we are approaching 0 from the left, is sin(x) positive or negative?
dull plover
negative?
crystal raptor
yeah
dull plover
and positive from the right
dull plover
positive from both sides
crystal raptor
great
so from the left, sin(x) is negative, so 1/sin(x) is negative and so is cos(x)/sin(x)
dull plover
right
crystal raptor
so as we let x go to zero from the left, both the terms are getting very very negative (going to -inf)
crystal raptor
great, so the whole thing is going to -inf
what about if we approach 0 from the right?
crystal raptor
yes
what conclusion can you draw?
if we approach from the left we get -inf and if we approach from the right we get +inf
what does this mean for the limit
dull plover
its non existent
crystal raptor
Yep!
dull plover
right?
;DD
thanks
so when i cant factor it anymore i can just substitute it like that?
crystal raptor
Well like in general you should be checking whether the behaviour of the function changes depending on which side you approach your limit point from
dull plover
alright
sorry ive asked u so many times today but im practicing by solving equations since im new to this
golden finch
Given A,B square matrices:
If A^13 = B, and B is invertible, then A is invertible.
True or false
golden finch
I'm not sure how I can determine this.
cedar kilnBOT
@golden finch Has your question been resolved?
golden finch
<@&286206848099549185>
sonic cradle
Given A,B square matrices:
If A^13 = B, and B is invertible, then A is invertib...
how much do you know about determinants?
golden finch
mmm I know how to calculate them
sonic cradle
have you learned their properties
golden finch
and I know that if det != 0, then the matrix is invertible
golden finch
det(B) != 0
sonic cradle
right
golden finch
then? 😄
sonic cradle
what else do you know about determinants
golden finch
det(XY) = det(X) * det(Y)?
golden finch
I don't remember seeing it
golden finch
but doesn't this mean that det(A) != 0?
sonic cradle
it does but i wouldnt use that without proof
golden finch
if det(B) is not 0, then det(A) must also be != 0, otherwise in the multiplication it would equal 0? Or am I going in the wrong direction
maybe we can multiply both ends by B^-1, so that we get B^-1 * A^13 = I ?
which means that A^13 must be equal to B?
but that's where we started...
tribal verge
Question: The math faculty of Pythagoras College uses this logo. All four triangles are right triangles, the whole logo is a square, and the inner quadrilateral is also a square. Prove that the right triangles are all congruent.
crimson sedge
Question: The math faculty of Pythagoras College uses this logo. All four triang...
is this an AMC question?
crimson sedge
Question: The math faculty of Pythagoras College uses this logo. All four triang...
ok so umm here is my logic explanation
right triangles are all congruent
😁
crimson sedge
where the diagram?
fair geyser
tribal verge
Yes thats it
fair geyser
i know
crimson sedge
yes
tribal verge
I know that the hypotenuses are congruent since thats the definition of a square
But I need something else to prove its congruence
crimson sedge
the opp side to the angle closest to the square is congruent
tribal verge
Proof?
tribal verge
alr thx
fair geyser
you said the same thing
crimson sedge
yes
fair geyser
but what angle
tribal verge
the angle in the corners
because they form a supplementary angle, and since its a square (90 degree corners) it bisects the angles and forms two congruent 45 degrees angles
fair geyser
?
tribal verge
the angles in the corners are congruent
crimson sedge
i shall demo it
in a square all angles sum up to 360
so if you sum the angles in the diragram it should = 360
tribal verge
yeah
tribal verge
So even if the angles in the corners arent congruent, all the angles would still add up to 360
But they are congruent
crimson sedge
yes
tribal verge
should I close this channel?
crimson sedge
wait
fair geyser
i didn't understand what you're talking about
crimson sedge
i didn't understand what you're talking about
look
all the yellow angles sum up to 360
fair geyser
sure
tribal verge
and put whiskers on the hypotenuses
fair geyser
okay
crimson sedge
and all the red angles also sum up to 360
fair geyser
they are visibly not equal
crimson sedge
cause its 90 times 4
crimson sedge
they are visibly not equal
i didnt line them up
tribal verge
and all the red angles also sum up to 360
because they're all 90 degrees
fair geyser
there's no logic
you;re just saying actually they are equal and this line is a bisector
tribal verge
It is a bisector because the red angles are 90 degrees
and the yellow angle is 90 degrees
crimson sedge
yes
fair geyser
well i don;t mind if you close
fair geyser
we can't
like i'm not convinced
and i don;t understand whart you mean
i literally don;t see how it could be settled
crimson sedge
crimson sedge
i guess if you have an account you do
yeah 💀
Each side of the big square is also the hypotenuse of its associated right triangle. Therefore, all hypotenuses are congruent.
that makes sense
crimson sedge
i only see one of them
fair geyser
you absolutely lined everything up correctly, it's a proof that these angles aren't equal as far as i;m concerned
they add up to 90 which you can prove in two ways, and you;re just saying they are also equal because of that
there's no logic
crimson sedge
we know the side opp to the hyp is equal to the rest because it draws out a square
tribal verge
Wait
fair geyser
wait i can't because i trust what it looks
tribal verge
If we drew an imaginary line and formed an exterior angle, that could prove that they're congruent
since the bisector is 90 degrees
crimson sedge
what happens when we put a squere in the middle of a square and turned it 45 degrees
fair geyser
crimson sedge
wait i can't because i trust what it looks
ik i just didn't line them up properly
fair geyser
you did though
tribal verge
I think they are lined up properly...
fair geyser
angles 3 + 2 = 90°
angles 1 + 2 = 90°
proves that 1 = 3
crimson sedge
no the angle of the triangles i had no con over
tribal verge
angles 3 + 2 = 90°
angles 1 + 2 = 90°
proves that 1 = 3
true
fair geyser
that's a proof, you can keep showing that 2 angles are equal, you can't show that it's secretly a bisector and those are isosceles
tribal verge
by substitution
fair geyser
yours i don;t even understand what you;re saying
maiden lintel
cedar kilnBOT
maiden lintel
How do you do this?
maiden lintel
Ok
mild fern
then move terms that contain y or yx on the left and terms that contain only x or constants on the right
maiden lintel
then move terms that contain y or yx on the left and terms that contain only x o...
Ok
ebon pulsar
hint:
2x = 2x - 1 + 1
wraith daggerBOT
~ ℂ𝕣𝕒𝕗𝕥𝕒𝕥𝕠𝔻𝕦𝕕𝕖𝕤 ~
maiden lintel
So now do we just simplify?
mild fern
i mean you should have gotten
mild fern
$2x + 6xy = y - 2xy$
wraith daggerBOT
Scythed
mild fern
then $y-8xy = 2x$
wraith daggerBOT
Scythed
ebon pulsar
also works
mild fern
and just $y(1 - 8x) = 2x$
wraith daggerBOT
Scythed
crimson sedge
hi what rule was used here
cedar kilnBOT
hi what rule was used here
cedar kilnBOT
cedar kilnBOT
Available help channel!
neon salmon
cedar kilnBOT
neon salmon
Need help please
austere hull
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
queen marlin
id start with reading your notes
its just about learning what different types of triangles are called
cedar kilnBOT
@neon salmon Has your question been resolved?
neon salmon
If it dosent have anything is it just a regular triangle?
earnest cobalt
hi
earnest cobalt
i need help
what is this "Amanda made 3 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 3 necklaces was $17.10. If the beads cost a total of $10.20, how much did each pendant cost?"
south pine
start by subtracting the cost of the beads from the total cost of the beads and pendants for all 3 necklaces. Then, divide the total cost of the pendants by the number of necklaces (3)
hollow minnow
south pine
@hollow minnow it's back
wraith daggerBOT
Pure2
cedar kilnBOT
@earnest cobalt Has your question been resolved?
earnest cobalt
start by subtracting the cost of the beads from the total cost of the beads and ...
ok thanks
sour hollow
The question is "In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?" and i got 336. So we have sibling pairs $A_1,A_2,$ $B_1,B_2,$ and $C_1,C_2,$ and say the first row is in form ABC, when $A_1$ is in the front we have 8 possibilities of $(A_1, B_1, C_1), (A_1, B_1, C_2), (A_1, B_2, C_1), (A_1, B_2, C_2), (A_1, C_1, B_1)$
$(A_1, C_1, B_2), (A_1, C_2, B_1), (A_1, C_2, B_2)$ and for each of these there are 6 possible endings due to the remaining people so we have 48, but then multiply by 6 because we have 6 possible starting people $A_1,A_2, B_1,B_2, C_1,C_2,$ so 288, then Now we consider if it was in the form ABA if so, say we start with $A_1,$ we can have $(A_1, B_1, A_2), (A_1, B_2, A_2), (A_1, C_1, A_2), (A_1, C_2, A_2)$ and again each of these only have 2 possible endings so 8, but then there are 6 possible people to start the row, $A_1,A_2, B_1,B_2, C_1,C_2,$ so then 8*6=48 and then 48+288=336. But i feel like im wrong, can someone check my work?
wraith daggerBOT
ilegosking
south pine
i think 366 is too big
answer is smaller
When the first row is in the form ABC:
6*8
When the first row is in the form ABA:
4 * 4 = 16
sour hollow
yea, but a different person can start each row
for example say its in the form ABC, where A1 starts we have 8 ways, and then we have 6 ways to start, A1 A2 B1 B2 C1 C2, so times 6 possible starting rows
sour hollow
ye again if we start with A1 we have 4 possible ways and 6 possible starting people so 24, then each way only has 2 possible endings say we have first row, A1 B1 A2, then we can only have C1 B2 C2 or C2 B2 C1 in order to confide by the rules, so 24*2=48
.close
stable stump
Howdy! I'm having some trouble with a question in my "Sampling distributions for means" unit (See screenshot 1). I have access to statcrunch, but I'm having trouble navigating to the section that would help me put this together. I also haven't had much luck finding a formula for this sort of thing. Anyone got any tips or tricks?
cedar kilnBOT
Howdy! I'm having some trouble with a question in my "Sampling distributions fo...
@stable stump Has your question been resolved?
crimson sedge
cedar kilnBOT
royal loom
!15mins
cedar kilnBOT
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 loom
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
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3. I got an answer but I was told that it's wrong.
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5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@gleaming path need help solving these two
royal loom
<@397068881362944011> need help solving these two
Don't tag random users, also only tag helpers once, as stated above, and it still has not been 15 minutes.
Respond to the status prompt if you need help
cedar kilnBOT
@crimson sedge Has your question been resolved?
fervent saffron
what really is a congruence class
cedar kilnBOT
what really is a congruence class
fervent saffron
like what is it
fervent saffron
is there like
a less complex explanation
like i get the definitino
but like
cedar kilnBOT
@fervent saffron Has your question been resolved?
cedar kilnBOT
@fervent saffron Has your question been resolved?
cedar kilnBOT
@fervent saffron Has your question been resolved?
cedar kilnBOT
@fervent saffron Has your question been resolved?
cedar kilnBOT
@fervent saffron Has your question been resolved?
weak python
when will this happen (a, b are positive intergers)
cedar kilnBOT
when will this happen (a, b are positive intergers)
@weak python Has your question been resolved?
dire geode
Take the log of both sides
weak python
hmm like what
dire geode
hmm like what
What's your question
dire geode
Try it
weak python
bro pls im in a rush 💀
dire geode
bro pls im in a rush 💀
?
dire geode
log(log(a)) == log(log(b)) or sth ?
You have it here why can't you do it
dire geode
Taking the log twice
If x=y then yes log(log(x))=log(log(y))
Apply that to your expression
weak python
when will this happen (a, b are positive intergers)
no like if i have this can i have sth more simple ?
dire geode
I don't know what you're asking
weak python
uhhh
dire geode
You want to have something more simple?
weak python
ye
cedar kilnBOT
weak python
😭
cedar kilnBOT
Available help channel!
drowsy egret
hey how do i integrate secx again?
cedar kilnBOT
hey how do i integrate secx again?
meager jungle
cos(x)/cos²(x)
cedar kilnBOT
cedar kilnBOT
Available help channel!
ripe steppe
how to find derivative of f(x) = x ln (x^2) ?
cedar kilnBOT
how to find derivative of f(x) = x ln (x^2) ?
ripe steppe
i got f'(x) = 2 ln x + 2 but my process of getting there was wrong
i dont think i am allowed to move the ^2 down in front of the x ln because its in a parenthesis
crimson sedge
f’g+fg’
broken mist
How familiar are you with the product rule?
crimson sedge
f’=1
fair mortar
i dont think i am allowed to move the ^2 down in front of the x ln because its i...
you still can
crimson sedge
g’=2
fair mortar
$f(x) = 2x\log x$
wraith daggerBOT
Bettim
fair mortar
now prod rule
ripe steppe
the way i did it was
i moved the 2 from the (x^2) infront of the x ln and got 2x ln(x)
and then did the product rule
fair mortar
even if you didnt move the 2 you should get the same answer
ripe steppe
is that allowed though
fair mortar
yes
ripe steppe
is x ln the same as ln x
fair mortar
no
ln is a function
the arguement to the function comes after the function itself
its like saying $\sin \theta$ and $\theta \sin$
wraith daggerBOT
Bettim
fair mortar
second one is not right
ripe steppe
yeah thast what i thought
ripe steppe
ooooh
fair mortar
ln(x^2) = 2ln(x)
check the original ques
gritty viper
I did
ripe steppe
i thought it was the other way around
ripe steppe
i thought if the exponent was on the outside you could move it to the front
gritty viper
Yes, it is
fair mortar
yea thanks great
gritty viper
np
fair mortar
and i thought if it was on the inside you cant
lol yw
ripe steppe
if it were ln(x)^2 what would i have done
fair mortar
if it were ln(x)^2 what would i have done
chain rule
fair mortar
(2lnx)/x
gritty viper
ln(x^2) = ln(x * x) = ln(x) + ln(x) = 2ln(x)
ripe steppe
ln(x^2) = ln(x * x) = ln(x) + ln(x) = 2ln(x)
this is what i just did
was the exponent inside the parenthesis
gritty viper
ye I was just mentioning why it's true even the exponent is in the parentheses
for ln(x)^2 you could do chain rule
ripe steppe
oh thank you
gritty viper
or product rule ln(x)*ln(x)
ripe steppe
for the chain rule on ln(x)^2
would i do
would i get f'(x) = lnx * 2x
did i do that chain rule right
the chainrule is still new to me and it confuses me sometimes
gritty viper
not quite
ripe steppe
oh wait so
gritty viper
Did u learn chain rule as (f(u))' = f'(u) * u'
ripe steppe
1/x * x
ripe steppe
f would be the ln and g is (x)^2?
gritty viper
ln(x)^2 is the whole thing
gritty viper
is the squared on the outside or the ln function on the outside
ripe steppe
its on the outside of the (x)
gritty viper
what's ln(e)^2
ripe steppe
1
gritty viper
the outside is the one you did last
when you do f(g(x)), first you apply g to x
then you apply f
ripe steppe
ahh so the outside would be ^2?
ripe steppe
so the derivative would be 2x * ln(x)
ripe steppe
ughhh
alright so the outside in x^2
inside is ln(x)
so with the chain rule = lnx * 2x * 1/x?
and then simplify
so its 2 lnx?
@gritty viper sorry
gritty viper
No
gritty viper
yes
gritty viper
yeah
ripe steppe
2lnx * 1/x?
gritty viper
Yeah that's correct
ripe steppe
finally
gritty viper
Nice
gritty viper
you're welcome
ripe steppe
.close
cedar kilnBOT
ripe steppe
thank u very much
cedar kilnBOT
Available help channel!
ancient oak
i saw the figure and gave up someone send help
cedar kilnBOT
i saw the figure and gave up someone send help
ancient oak
so i was able to sketch it on my own aswell but i have no idea how to continue from here
valid yacht
what's y = x doing there
but beside that, what methods have you studied for finding volumes by revolution like this
ancient oak
what's y = x doing there
y = x+5 is the line about which the parobola needs to be rotated
ancient oak
but beside that, what methods have you studied for finding volumes by revolution...
integrals
ancient oak
but doesn't the question say its revolved around x + 5 = 0
uh i though that is what you meant
where is y = x
valid yacht
line equation is x + 5 = 0
valid yacht
the poc you sent
valid yacht
haha
ancient oak
mb mb
valid yacht
no worries
so what i thought of is using cylindrical shells but it seems u haven't learn abt it yet
ancient oak
so what i thought of is using cylindrical shells but it seems u haven't learn ab...
we have only learnt about discs
valid yacht
ah okay
for some reason i find the shells method easier to understand and apply, although it's supposed to be more complicated
valid yacht
so.... if you take shells perpendicular to y axis i think it'll be better?
ancient oak
i have no clue how to do it with shells
valid yacht
honestly I've forgot too. Let me have a look back at my textbook
ancient oak
but i'm guess the radius for disc would be the equation of parabola-equation of line right?
valid yacht
disks perpendicular to y axis should have this much radius... R^2 - r^2
valid yacht
valid yacht
disks perpendicular to y axis should have this much radius... R^2 - r^2
not helpful i guess
ancient oak
and the limits?
valid yacht
-9 to 0
valid yacht
but the x value
actually both are x values of parabola
so we will have to use vertex of parabola and do something there. i guess its not the right methodology
ancient oak
but how do we write the equation of the parabola in terms of y?
coz the intergation will be in terms of dy
valid yacht
yeah that's the issue
ancient oak
this question is cursed
i hope i don't get stuff like this on my finals that is gonna start in like 2 weeks 💀
valid yacht
so this is what we've been thinking so far. and i dont think this approach is gonna take us anywhere pleasurable
x axis supposed to be at the top most part* drew at centre by mistake
and honestly i cant even draw the other way.
i dont think I'll be able to help here any further. my recommendation is to close this channel and remake a new one so someone else can look at the problem. good question, but i think i proposed a wrong method. i need to learn more about volumes by revolutions and alike
@ancient oak ^^
cedar kilnBOT
@ancient oak Has your question been resolved?
ancient oak
i dont think I'll be able to help here any further. my recommendation is to clos...
thanks a lot it is okay :)
meager finch
Can someone tell me where I went wrong
cedar kilnBOT
Can someone tell me where I went wrong
meager finch
sharp lotus
hushed urchin
cedar kilnBOT
hushed urchin
find the area of the region of the red outside of the blue
why is my answer wrong
the area is clearly greater than 1.57
floral arrow
Why do you have a square in there?
floral arrow
In that case the 1 should be included in the square
hushed urchin
In that case the 1 should be included in the square
1^2 is 1.....
floral arrow
Not that 1
hushed urchin
oh shoot
minor crystal
(1 + sin(theta))^2
floral arrow
Read the formula again
hushed urchin
why am i stupid
floral arrow
floral arrow
Looks right to me
hushed urchin
oh nvm
evaluating these dumb integrals is so annoying
cause i need the exact answer
cedar kilnBOT
@hushed urchin Has your question been resolved?
cedar kilnBOT
Available help channel!
fluid rivet
I'm currently a bit confused on how I should proceed on this diophantine equation. The part that mostly puzzles me is how I should proceed in calculating the remainder of:
195x+42y=12
195x+42y=1 (I was told to use 1 as a GCF for every diophantine equation in this class to make it easier for us)
The part that confuses me is when you start applying the euclidean theorim on the process to get X and Y because when I start with 195÷42 it then leads to 4.6 as the quotient, However, I was told to round up/down my quotients so I rounded it up to 5.
Now it's 195÷42=5. Should I consider the 5 when I'm calculating for the remainder I.e. 42x5=Ans-195 or should I instead do 42x4=Ans-195?
fluid rivet
Apologies for the scribbly handwriting, It's mostly cus I don't really write much with my course.
