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#help-38
simple panther
27th question
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27th question
undone gorge
Try rationalising the terms
simple panther
$x=\frac{1}{\sqrt{17}+\sqrt{16}}$
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Suika
simple panther
Like this?
radiant portal
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red mountain
radiant portal
red mountain
hahahahahaha
frail heron
underrated XD
red mountain
I got 2 values for p
which two values?
radiant portal
2 and -2
red mountain
red mountain
🙂
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red mountain
🙂
radiant portal
Losing easy marks 😂
red mountain
yup
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marsh forum
Trying to paramatrize this surface
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Trying to paramatrize this surface
marsh forum
so to start I probably want to parametrize a parboloid in general
that would probably be $(r \cos(t), r\sin(t), r^2); 1≤r≤2; 0≤t≤2π$
solid kilnBOT
What a wonderful world !
marsh forum
so I suppose $(r \cos(t), r\sin(t), r^2); 1≤r≤2; 0≤t≤2π$ works in this case?
solid kilnBOT
What a wonderful world !
marsh forum
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formal raven
Hi,
Can I please have help on the following?
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Hi,
Can I please have help on the following?
formal raven
$\lim_{x\rightarrow \infty}\frac{x^5-2\log x}{2e^x -x}$
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user.not.found
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formal raven
So far, I split the fractions:
$\frac1{2e^x -x}\left( x^5-2\log x \right)$\
Then, I use solve each part separately:
$\frac1{2e^x -x} = \frac{\frac1{e^x}}{2\frac{e^x}{e^x} -\frac x{e^x}} = \frac{\frac1{e^x}}{2-0} = \frac1{2e^x}$
And,
$x^5 -2\log x = \frac{x^5}{x^5} -2\frac{log x}{x^5} = 1- 2 \times 0 = 1$
solid kilnBOT
user.not.found
formal raven
Am I using the correct method?
1/2e^x times 1= 1/2e^x
Then I have to find the lomit of 1/2e^x?
trim lichen
kinda vague... what does 1/(2e^x) approach then?
and uhhh
your numerator is just mega suspicious
formal raven
What does that mean 😭😭
trim lichen
the equality
x^5 - 2log(x) = x^5/x^5 - 2log(x)/x^5
simply isn't true
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It's 0
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
trim lichen
wrong message replied-to?
formal raven
Yeah sorry
uncut pewter
As a helper, please do not give out answers that could be copied as a homework s...
Oh alright my bad
uncut pewter
Yeah sorry
Jus use L hospital until you eliminate all the x terms in the numerator
formal raven
Can't do that
Isn't covered in thay unit
I can only use what's given in that unit
trim lichen
there is no need for that either... all you need to know is x^n/e^x approaches 0 at infinity
for any constant n
formal raven
**user.not.found**
Sooo is not correct 😭😭
uncut pewter
**user.not.found**
It isn't...
formal raven
Can I use the same method but correct it
trim lichen
your method is bad and i told you exactly why.
trim lichen
Can I use the same method but correct it
if you do that you get infinity over infinity which is useless as is
formal raven
Oh
uncut pewter
Can I use the same method but correct it
Yes it's basically taking out e^x
X^5/e^x-2log(x)/e^x
Would be your numerator
uncut pewter
there is no need for that either... all you need to know is x^n/e^x approaches 0...
This
formal raven
Could I use the squeeze Rule in that case?
uncut pewter
Could I use the squeeze Rule in that case?
Sandwitch theorem?
trim lichen
Could I use the squeeze Rule in that case?
if you can find two things to squeeze WITH
formal raven
Yeah
chilly bobcat
i mean
trim lichen
then nobody can stop you
chilly bobcat
x⁵ expands way slower than e^x
uncut pewter
Could I use the squeeze Rule in that case?
You are overcomplicating it
chilly bobcat
i don't see the problem
formal raven
Thanks for your help everyone
eager eagle
I need someone to help me with my discrete math tomorrow
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I need someone to help me with my discrete math tomorrow
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
trim lichen
I need someone to help me with my discrete math tomorrow
why tomorrow
do you have a test tomorrow that you are zero percent prepared for
eager eagle
Yes
eager eagle
do you have a test tomorrow that you are zero percent prepared for
Permutations, combinations and probability
dull pilot
okay
so 'discrete math' means..... 'combinatorics'?
with some set theory for good measure
trim lichen
so 'discrete math' means..... 'combinatorics'?
in this particular case, it seems to
eager eagle
Combinatorics?
dull pilot
,w define combinatorics
trim lichen
Permutations, combinations and probability
solid kilnBOT
trim lichen
@eager eagle give that playlist a watch
dull pilot
ask if you have specific questions 
eager eagle
Okay
trim lichen
I have around 2 hours before my sleep time
ok then go to sleep and take the L
trim lichen
you are cooked either way so might as well be cooked and well rested instead of cooked AND sleep deprived
eager eagle
I also have programinng test tomorrow morning. Im so cooked
dull pilot
definitely do know what basic permutations and basic combinations are
unkempt oriole
I also have programinng test tomorrow morning. Im so cooked
U r Deep fried
trim lichen
yes, cooked you are indeed. all the more reason to go to sleep and not destroy yourself
eager eagle
PIE?
dull pilot
principle of inclusion-exclusion
trim lichen
these tests won't ruin your life even if you bomb them to a zero, but the sleep deprivation can and will
unkempt oriole
these tests won't ruin your life even if you bomb them to a zero, but the sleep ...
Ann what's ur screen time (just asking politely 🐭 )
trim lichen
nope.
unkempt oriole
i was just wondering cuz u r always online
trim lichen
illusions are a powerful thing
frail heron
Its just tonight soo
There’s nothing you can do to change the result.
trim lichen
in either case this has nothing to do with op's question
unkempt oriole
alr
trim lichen
the place to ask me this sort of thing would have been #discussion
eager eagle
Hm
eager eagle
Here
eager eagle
🙂
iron pier
nah this is totally crammable
it's all combinatorics
make sure to have a strong understand of permutations and combinations and you'll be chilling
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timid bear
How big of N do I need to reach
2^(-B) error
where B = 120
for the formula on step 3a
timid bear
where
0.1 <= t < 1
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pure sand
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safe talon
Need help with a geometry question
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Need help with a geometry question
undone forge
Yea
safe talon
Can someone explain the geometric argument made here: https://youtu.be/ufKWQXL_E2I?t=194
his claim is you can determine whether or not two rectangles are equal by joining them as shown and seeing if you can enclose them between two parallel lines as shown
but he kind of handwaves the proof of it
ionic pendant
if they have the same area then
A = xy = ab
so rearranging
b/x = y/a
but b/x and y/a are the slopes connecting the corners, so if the slopes are equal then the two connecting lines are parallel
safe talon
ah ok, that makes perfect sense
in the video he cuts the thing up into 2 triangles and a prallelogram and slides them around, i didnt realize it was so simple
is there an argument that can be made that doesnt rely on analytic geometry?
fair bison
is there an argument that can be made that doesnt rely on analytic geometry?
you mean an argument that the two rectangles have equal area that doesn't rely on coordinates?
safe talon
you mean an argument that the two rectangles have equal area that doesn't rely o...
yes
fair bison
you can observe that the two triangles here are similar bc the two lines being parallel causes the angles to be equal
that should be equivalent to the areas of the rectangles being equal
safe talon
so you're saying triangle xbo is similar to ayo
fair bison
sorry, pic loading slowly
these two triangles
the angles are congruent since the two lines are parallel, and alternating angles formed by a traversal line intersecting two parallel lines are congruent
so since those two triangles are similar, x/b = a/y, so xy = ab
safe talon
ah, yea i like that one
am i correct in thinking it would also be possible to skew rectangle xy horizontally and skew ab vertically so that they share a base
and then maybe they can be skewed along the parallel line such that they overlap
fair bison
you could do that without changing the areas yea, by cavilieri's principle, idk how helpful it is
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slim eagle
fair bison
!occupied
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wanton scaffold
yooo
wraith hinge
transposing
wanton scaffold
ive never heard of cross multiplying
or transposing
(yes im aware im stupid af)
wraith hinge
basically when u bring the denominator from lhs to rhs it becomes the numerator
wanton scaffold
from the what to the what
wraith hinge
gimme a min
wraith hinge
yes
wanton scaffold
ok so
5x + 60 = 12x
so
that means
-5x -5x
60 = 7x right?
which would be liike 8 & 4/7
=
x
right?
wraith hinge
wraith hinge
its helpful in a lot of cases
wraith hinge
basically its like how division becomes multiplication when u switch sides
wanton scaffold
cuz ima forget otherwise
wraith hinge
mind if i copy paste that ss?
sure
wanton scaffold
YAYYYY TYSMMM
wraith hinge
👍
sterile hearth
Difficulty lvl SAT
rose needle
hi is this the right channel i hope it is
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hi is this the right channel i hope it is
rose needle
i just have a question, i have to determine the zeros and the maximum or minimum value for each function, i just need this one so i can carry on:
f(x) = x^2+2x-15
lowkey just forgetting everything 😝
damn, bad time to ask💀🙏
bleak echo
i just have a question, i have to determine the zeros and the maximum or minimum...
Maximum and minimum occur when slope/derivative is 0
So take derivative and find when it equals 0
Then do the first derivative test (testing numbers before and after your critical points) to see whether or not it’s a maximum or minimum
If it goes from a negative to positive slope/derivative it’s a minimum
If it goes from a positive to negative it’s a maximum
rose needle
can you do an example bc lowkey i have no clue what you just said sorry
rose needle
thanks
bleak echo
Sometimes you’ll get multiple critical points
In this case I didn’t
You know how to take derivatives right?
bleak echo
You know how to take derivatives right?
@rose needle
rose needle
You know how to take derivatives right?
i have bad memory
i should probably ask my teacher
i’m cooked
rose needle
yep i’m cooked
bleak echo
watch YouTube
rose needle
ax^n goes to n•a•x^n-1
umm i’ll try to comprehend this
rose needle
watch YouTube
i shoudlved asked earlier
bleak echo
umm i’ll try to comprehend this
A video will say it better
bleak echo
umm i’ll try to comprehend this
An example is 6x²
You multiply the 2 by 6 and then subtract 1 from the exponent (2)
bleak echo
i have 13 questions to do
Goodluck
rose needle
thanks..
😢
that’s all ig
i’ll try harder next time
thanks anyways!
have good day
.close
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bold sandal
ok i need help
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ok i need help
bold sandal
so basically I have an exam that is 2 classes long. So I just finished the 1st class and I'm at a roadblock. I tried to recreate from memory and most of the information that i have is shown in the picture
If i know the area of the triangle that has an arrow pointing at it (forgot what it was), can I get any information on the red triangle?
Ask any info if you need
I actually have no clue to get the red one, pretty much the only one i have no clue
Im in 10th grade, so pretty much only triganomatry(sin, cos, tan, metric relations, sin and cos laws) and stuff
ionic pendant
can you try resending the image?
bold sandal
ok
frail heron
bold sandal
frail heron
It’s still a file
bold sandal
oh
frail heron
I’ve sent it up there, no worries
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bold sandal
ill be back in 5min
bold sandal
back
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molten comet
Hello
zinc ginkgo
Why do you have a Jacobian on the left
grim sparrow
Why do you have a Jacobian on the left
wait, what's wrong with that?
the det of Jacobian evals to rho, and x^2 evals to the thing inside brackets
zinc ginkgo
I didn't say it was wrong per se. Just depends on the original integral
molten comet
Why do you have a Jacobian on the left
Does it have to be after the dxdydz?
molten comet
😭
zinc ginkgo
You inserted a Jacobian on the left out of nowhere
ionic pendant
the jacobian only appears in the cylindrical integral because it came from the change of coordinates
zinc ginkgo
In two dimensions, for polar coordinates
dx dy = r dr dtheta
molten comet
What's the difference with this one...
Every day I come to realize to look highly on Gauss
ionic pendant
notice that the jacobian appears in the new du dv integral, not the original dx dy integral
zinc ginkgo
Also this is absolutely abuse of notation
molten comet
notice that the jacobian appears in the new du dv integral, not the original dx ...
Ohhhh
Yess
zinc ginkgo
y/x^5 should be expressed in terms of u and v on the right
molten comet
How can I fix this then?
zinc ginkgo
In two dimensions, for polar coordinates
dx dy = r dr dtheta
So it's just this with dz tacked onto both sides
molten comet
dxdydz = |Jacobian| dpdthetadphi
Ohhh wait I see
That replaces the \rho
I have another question
Since this integral started with dzdydx
Should the partial(x, y, z) be partial(z, y, x) also?
ionic pendant
the order of coordinates in the jacobian relates to the arrangement of the partial derivatives in the matrix. you don't need to swap the order in the jacobian to swap integration order
molten comet
Ohhh okay
zinc ginkgo
I think also swapping variables doesn't affect the absolute value of the Jacobian
ionic pendant
yeah it only affects the sign, so the absolute value washes it out
molten comet
Notation wise
ionic pendant
for cylindrical i think it makes sense to always have it in the order (rho, phi, z) regardless of the order of integration since z keeps its position
but ultimately it doesn't matter which order you use
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daring sandal
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austere shard
!status
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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
1
trim lichen
do you know how the distance formula is derived in 2D
daring sandal
I do not
trim lichen
start with that first then
draw up a coordinate plane, place two points on it labelled (x1, y1) and (x2, y2) and think about how you can express the distance between them via Pythagoras
daring sandal
okay so with pythagorean theorem it would be (x1, y1)^2+(x2, y2)^2 right?
hidden dew
okay so with pythagorean theorem it would be (x1, y1)^2+(x2, y2)^2 right?
don't forget the sqrt
daring sandal
so it would be d=√(x1, y1)^2+(x2, y2)^2
hidden dew
okay so with pythagorean theorem it would be (x1, y1)^2+(x2, y2)^2 right?
oh wait from the way you wrote it the core is wrong
my brain was a little off
austere shard
okay so with pythagorean theorem it would be (x1, y1)^2+(x2, y2)^2 right?
Why are u squaring a point
Also can u show which triangle u used to get that
daring sandal
if you're referring to this then this is what I only have for the problem because its from a photo of a text book
daring sandal
okay so if were to see if it has a 4d space we would js habve to add another point?
hidden dew
for the 3d proof try first finding the distance between (x1,y1,z1) and (x2,y2,z1)
then using that again between
(x2,y2,z1) and (x2,y2,z2) you'll find that
c^2=d^2+(z2-z1)^2 (c being a different distance)
jolly saffron
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jolly saffron
How would I determine the limits on varphi?
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jolly saffron
how do you determine the limits though
nova spire
how do you determine the limits though
to fully describe the hyperball, the limit values (integral bounds) of the angles theta, phi, psi are written
then you just have to find the values of r that we run through
jolly saffron
is there a pattern to it for higher dimensions?
nova spire
yes
if you had 5 dims
x_0,x_1,x_2 same as 4 dims
x_3 = r sin(psi)sin(theta)sin(phi)cos(xi)
jolly saffron
yeah the coordinates are alright
nova spire
x_4 = rsin(psi)sin(theta)sin(phi)sin(xi)
jolly saffron
I get that
I'm talking about the values of the new parameters
Is it always the first angular parameter runs from 0 to 2pi and the rest from 0 to pi?
nova spire
it's always the last introduced angle that runs between 0 and 2pi
jolly saffron
ah okay
nova spire
it's a choice
jolly saffron
so in this case varphi goes to 2pi?
nova spire
any one angle can be chosen to range between 0 and 2pi
and the others to range between 0 and pi
just to make sure
jolly saffron
any one angle can be chosen to range between 0 and 2pi
but doesn't the Jacobian affect it
nova spire
I would pick the last angle
nova spire
but doesn't the Jacobian affect it
yes I'm wondering
jolly saffron
because it's not symmetric
nova spire
just to make sure pick the last angle
serene summit
How am i supposed to prove that gef and fob are complementary?
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How am i supposed to prove that gef and fob are complementary?
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
Idk where to begin
trim lichen
How am i supposed to prove that gef and fob are complementary?
what do those arrows mean
trim lichen
you're the one who saw the original diagram and sent us a reproduction :P
but if they are meant as parallel then this question can actually be solved
if you run a line from F to the left and parallel to both EG and OB...
serene summit
if you run a line from F to the *left* and parallel to both EG and OB...
I just did that right now the moment you were typing 😭
trim lichen
well, it is good that you had the same idea
serene summit
Doesnt that only prove their congruence tho?
trim lichen
whose
steep knot
Doesnt that only prove their congruence tho?
the angles made are equal to GEF and FOB
serene summit
the angles made are equal to GEF and FOB
Yeah
Oh
ohhh
Because it splits the 90
I understand thank you
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solemn zealot
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dusty sleet
Hint: draw a (suitable) right triangle
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true vigil
A line passes through the vertex of a right angle and forms angles of 45° and 60° with its sides. What is the angle between this line and the plane in which the angle lies?
orchid wagon
,rccw
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true vigil
<@&286206848099549185>
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<@&286206848099549185>
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oak knot
In a tetrahedral, say SABC, from multiple points M1, M2, ... in SA, are altitudes made from those points parallel to each other?
oak knot
Visualization if possible please, thanks!
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opaque ledge
In a tetrahedral, say SABC, from multiple points M1, M2, ... in SA, are altitude...
i dont think altitudes can be made from arbitrary points, if i understand your question
there is only one altitude for each face
(and one for each side of each face)
oak knot
hmmm ye I get it just that one source says that they actually aren't
opaque ledge
oh, really?
oak knot
they said that the directions are different
lines that are perpendicular to a surface will be parrarel only if the lines are the same direction and the starting points aren't restricted
they said
dont quite understand T.T
unique sonnet
Show source that says they're different
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opaque ledge
lol its okay
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dark sandal
I'm trying something a bit out of my comfort zone here
I'm trying to create a functioning variable that shifts the [chance] weight to favor rarer outcomes with respect to the variable.
In this case, let's say we have a random roll with 5 outcomes.
We are guaranteed to get an outcome that isn't null, meaning the 5 outcomes have a total weight of 1.0
Let's just assume our set looks like this
A = 0.05 B = 0.10 C = 0.18 D = 0.22 E = 0.45
This variable, call it L, is equal to 50, and functions like "luck" or something of similar essence, so in a vacuum it would be a 1 + L / 100 = 1.5 times increase to any outcome - but this doesn't exactly strictly apply in this case, since you can't have a total weight of 1.5 for a single outcome. I was told about a "bias" factor, which could respect this L variable.
I'm just trying to work out how i would go about this.
I expect a behavior that would increase the outcome weight of the more rare outcomes, while the more common outcome weights would be decreased
any help is appreciated
vagrant prism
I'm trying something a bit out of my comfort zone here
I'm trying to create a fu...
if you want to bias, say, event A, can't you just set new A to be 1.5*A, and then rescale everything to add up to 1 again?
i may be terribly misunderstanding though
lament reef
i think they're wondering how to do the rescaling
but i might be misunderstanding too 😅
vagrant prism
in that case you can find the sum and then divide every probability by it, that will guarantee that the new sum will be 1
there are also things like softmax but that may be overkill for these purposes
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dark sandal
if you want to bias, say, event A, can't you just set new A to be 1.5*A, and the...
oh yeah sorry i should probably clarify.
it's a leveling redisribution
it will favor the lower outcomes, but will more or less equalize and gradually shift the total weight towards the rarer outcomes.
i'm just gonna spit some completely arbitrary numbers now
but I would imagine a new set would look somewhat like so:
A = 0.07
B = 0.13
C = 0.20
D = 0.20
E = 0.40
not sure how to word it exactly, but it would redistribute the total weight more equally, based on the L variable.
if this variable is high enough, A or B might even become higher than D or E
that make somewhat sense?
lament reef
the best idea i can think of is to choose a function that prioritizes higher values and then renormalize it so it's a valid probability distribution
like if your probabilities are x, calculate 1/x for each value. then add those up and divide by the new total
this skews it in the opposite direction
1/x makes it very heavily skewed, but you can mess around with different functions and see what works
and you should ofc make your transformation function rely on L so your luck factor plays a role
dark sandal
i was given something like this:
new_weight = weight × bias_factor```
where
```bias_strength = L / 50
weight_rank = 1 - weight / highest_weight```
whereafter you would just normalize the weight with ``normalized_weight = new_weight × (1 / new_weight)`` since the all the new weights combined would be less than 1.0the constant in L / 50 would be adjustable based on how high you'd want bias_strength to be
dark sandal
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wraith raft
i take good notes but are confused with this
like im stuck on 7 other similar problems, i either get nonsense answers or something that makes sense, check the answer key, then im so far off
12x=144
x=12
answer key: 7.4```
???????????????
wraith raft
like visually it doesnt make sense but with the formula my teacher gave me like
dull pilot
i take good notes but are confused with this
like im stuck on 7 other similar p...
power of a point
wraith raft
?
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frosty canopy
You have a bag with n > 1 M&Ms, m > 0 are green
and n − m > 0 are red. One at a time, you randomly pull candies out of
the bag and eat them until you pick one of the other color. (That is, you
stop eating candies if you started with a green one and then picked a red
one, or started with the red one and then pick a green one.) When you
get to a candy of the other color, you put it back in the bag, and start
picking candies again using the same rule. You keep going until you have
eaten all n M&Ms. What is the probability that the last candy you eat is
a red M&M?
I've thought about this question for a while -- it seems "intuitive" that the answer should be simply (n-m)/n, but i'm having trouble coming up with a rigorous proof.
frosty canopy
its also not obvious to me that the answer is not 1/2
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echo dove
I fucking swear I can't do it because the machine won't let me plop the line the way I want
echo dove
so this
has a horizontal asymptote at y=-1
and a vertical asymptote at y=2
but the little widget won't let me graph it the way I want to
help
ionic pendant
judging from the picture it seems like you are supposed to drag the red dots around
echo dove
yeah but I won't flip the lines
it's supposed to curve up at one and approach two
and the the other line is supposed to curve down twoards two as a vertical asymptote
echo dove
judging from the picture it seems like you are supposed to drag the red dots aro...
help pls
ionic pendant
can you move the red dot that is at the intersection of the two green lines?
echo dove
mhmm
ionic pendant
so i would move that so that the two green lines are at the correct asymptotes
echo dove
lemme try
echo dove
so i would move that so that the two green lines are at the correct asymptotes
like this?
ionic pendant
didn't you say that the horizontal asymptote is y = -1?
echo dove
mhmm
ionic pendant
but on the graph the horizontal asymptote you placed is y = 1
echo dove
fixed
ionic pendant
ok so now you need to find a known coordinate on the graph of your funciton, and move the red dot on the blue curve to that known coordinate
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heavy light
How do I solve???
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How do I solve???
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vapid tartan
I might be slow, but what is part b asking me to do? 
any help would be appreciated by a sleep deprived student that chose to procrastinate and leave all their work for the last minute! Hah… (save me)
opaque ledge
I might be slow, but what is part b asking me to do? <:splendo:13483546575962112...
i think its just asking when is P(x) positive
vapid tartan
i think its just asking when is P(x) positive
So it’s asking what x is when y is greater than 0?
opaque ledge
yep
vapid tartan
Alright, tysm
opaque ledge
well it wants the domain
vapid tartan
?
opaque ledge
it says between the numbers so that means it wants the lowest value of x and the highest value of x for which y is positive
assuming that x is nonnegative because it wouldnt make sense to have a negative number of units i assume
opaque ledge
np
vapid tartan
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rotund reef
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rotund reef
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vestal oyster
hello guys I need help with this quesistionfor calc AB
i get part A but somehow not able to do part B
trim lichen
so you did part a) as $\pi \int (y_2^2 - y_1^2) \dd{x}$, yes?
solid kilnBOT
Ann
vestal oyster
so you did part a) as $\pi \int (y_2^2 - y_1^2) \dd{x}$, yes?
yup
trim lichen
yeah so now you need to do $\pi \int ((y_2 - 10)^2 - (y_1 - 10)^2) \dd{x}$ instead
solid kilnBOT
Ann
trim lichen
perhaps swapping those around too cause i think the whole region lies below y=10, so the top one becomes the smaller radius
solid kilnBOT
Ansh
trim lichen
ok looks good
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full dock
using gauss jordan to solve the system of equations but my last row are all zeroes which means infinite solutions so do i just write this system has infinite solutions as my answer or something?
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trim lichen
using gauss jordan to solve the system of equations but my last row are all zero...
no, you keep going until RREF and then declare all variables corresponding to non pivot columns as parameters
full dock
should i assign the last column a parameter now or wait until everything is in RREF
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limpid dawn
wb
you dont need necessarily rref, you can already write down the two equations and choose two free variables
full dock
you dont need necessarily rref, you can already write down the two equations and...
oh but the exercise wants me to get it into RREF first
trim lichen
oh but the exercise wants me to get it into RREF first
then do as it says lol
full dock
should i assign the last column a parameter now or wait until everything is in R...
yeah but this is my question
trim lichen
i would say if you are remotely unsure then just keep going until RREF.
and only then assign.
but if you are ballsy enough, you can observe that your matrix already is in REF and so assignment can be made even now
if you want it
full dock
but if you are ballsy enough, you can observe that your matrix already is in REF...
wait so since its in REF does that mean i can stop doing row operations now and keep this matrix as is?
trim lichen
well you will need to do a few row ops in all but name still
full dock
well you will need to do a few row ops in all but name still
is this because i need at least one 1 in a row and the rest with zero's so i can back substitute?
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wide grotto
I'm doing Solving Systems by Substitution: Part 2, and I know how to do it but I can't remember the order it goes.
zinc ginkgo
I'm doing Solving Systems by Substitution: Part 2, and I know how to do it but I...
just show a problem and your attempt at the problem
wide grotto
dull pilot
I'm doing Solving Systems by Substitution: Part 2, and I know how to do it but I...
you first substitute and then you solve
wide grotto
you first substitute and then you solve
When I substitute do I put the the "9x" to the y or both the 2y?
cause in my lesson video it show me the 2y
dull pilot
When I substitute do I put the the "9x" to the y or both the 2y?
you substiute x or y
wide grotto
did I do something wrong, causse this is what I got. and if I divide it, it's 1.3636?
dull pilot
did I do something wrong, causse this is what I got. and if I divide it, it's 1....
....yeah
everything here is wrong
cobalt karma
Good arithmetic. However, y does not equal 9x - 3, 3y does. To avoid extra operations, I would simply advise for you to isolate y in the second equation, and provide the correct statement of what y equals.
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main sigil
<@&268886789983436800>
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dapper kayak
translated the question is
The figure below shows the graph of the function f(x) with a solid line and the graph of the function g(x) with a dotted line. Which of the following statements is valid?
According to the book the answer is D
f(x) = g(x-b) + a
I understand the + a but not the -b. As seen in my second image if we remove the "a" for a second wouldn't f(×) = g(x-b) simply be to the left of f(x)?
red mountain
,rccw
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red mountain
translated the question is
The figure below shows the graph of the function f(x...
als je een grafiek naar rechts verschuift dan moet je (x-x_0) doen (met x_0 je verschuiving naar rechts)
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dapper kayak
als je een grafiek naar rechts verschuift dan moet je (x-x_0) doen (met x_0 je v...
omg... ben je Nederlands? of Belgisch?
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red mountain
omg... ben je Nederlands? of Belgisch?
belgisch? ieuw
dapper kayak
belgisch? ieuw
ik Ben Belg:'(
red mountain
als je een grafiek naar rechts verschuift dan moet je (x-x_0) doen (met x_0 je v...
hoe ik dit meestal voor mezelf bijhoud is dat ik 0 volg
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red mountain
als ik een grafiek naar rechts verschuif met 5, dan moet mijn 0 naar 5 gaan
red mountain
en dat kan ik controleren door 5 in te vullen in de nieuwe functie en dat te controleren met 0 in de oude functie
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red mountain
ik Ben Belg:'(
oh oeps, haha
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latent holly
I need help
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latent holly
Hey so I got a few questions
red mountain
!da2a
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@latent holly Has your question been resolved?
red sentinel
could someone please help me understand turning points for functions?
red sentinel
i know a turning point is the point on the graph where the function turns (in parabolas i think?) but i don't know how to calculate them
from something like this
royal drift
what definition of turning points have you got in class?
red sentinel
what definition of turning points have you got in class?
i cant find one anywhere
red mountain
-# derivative
opaque ledge
i know a turning point is the point on the graph where the function turns (in pa...
for a parabola, the turning point is simply the vertex, which you can find by converting the equation into vertex form or using a formula. in general, though, the turning point of a function is a local extremum, which is where the derivative = 0 or does not exist
red sentinel
okay
opaque ledge
btw the formula i think is -b/2a for the x coordinate of the vertex (in y = ax^2 + bx + c)
red sentinel
alrighty ill try it
red sentinel
btw the formula i think is -b/2a for the x coordinate of the vertex (in y = ax^2...
if my b value is already negative, does it turn positive or stay negative?
opaque ledge
if my b value is already negative, does it turn positive or stay negative?
it turns positive
opaque ledge
right so 5/6 is the x coordinate which we wouldve gotten from -(-5) / (2*3)
red sentinel
mhm
opaque ledge
to get the y coordinate you just plug in 5/6 into the equation
red sentinel
:-)
opaque ledge
and then boom
red sentinel
as x?
opaque ledge
yea
red sentinel
ohh!! right that makes sense
opaque ledge
i think theres also a direct formula for it but theres no reason to remember it
royal drift
is there any other way to find TP?
(also, you can calculate the derivative, find where its value is 0 and then calculate the y value on that point)
red sentinel
yeah this seems like the easier way
exotic saffron
this was the answer for it
why is the answer in mixed numbers
red sentinel
(also, you can calculate the derivative, find where its value is 0 and then calc...
how would you calculate the derivative?
exotic saffron
makes me unhappy 😦
red sentinel
makes me unhappy 😦
my teachers feeling a little goofy
opaque ledge
why is the answer in mixed numbers
ew i just realized that
royal drift
how would you calculate the derivative?
if you haven't been taught that in class, it's better not to use it
red sentinel
if you haven't been taught that in class, it's better not to use it
okay haha
exotic saffron
how would you calculate the derivative?
someones gonna give u a 2 hour lecture about it
red sentinel
methods is not my strong suit 🫡
exotic saffron
most important thing of ur life
exotic saffron
12 i reckon
red sentinel
can't be worse than polynomial long division
exotic saffron
in some cases it is worse
sour lagoon
for this solution can someone explain why you multiply everything by secx, and how it becomes (secxy)^1, is this the integrating factor?
sour lagoon
(im still new to linear DE)
zinc ginkgo
for this solution can someone explain why you multiply everything by secx, and h...
product rule
zinc ginkgo
,tex .product rule
solid kilnBOT
riemann
sour lagoon
also can someoen tell me a way to know if a DE is seperable vs linear, ik theres an equation but sometimes im unable to tell but my prof says its obvious
like this for example
that P is first order no?
gaunt wave
Separable can be easily identifiable by the fact that you can pull all (in this case) Ps to one side and ts to the other (more generally all dependent variables to one side and independent variables to other). If both are present they have to be either cancel-able or multiplied together (in this case only the dependent variable is present)
sour lagoon
oh okay so like for b) here, the answer is not seperable is it because both the independ and dependent variables are present?
gaunt wave
You will include dP and dt as parts of it
sour lagoon
like i couldnt do dy + y = x(dx)?
wait no
nvm
you would also multiply the y by dx
gaunt wave
yep
empty orchid
for this solution can someone explain why you multiply everything by secx, and h...
(Its not sec(xy)^1, it’s (sec(xy))’, represents the derivative of sec(xy))
plush crow
can smone help me here?
gaunt wave
I don't think it's sec(xy) either, I believe it's sec(x) * y
gaunt wave
can smone help me here?
!occupied
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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
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vocal ocean
Why is the answer -pi/2 and not 3pi/ 2
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Why is the answer -pi/2 and not 3pi/ 2
scenic basin
Why is the answer -pi/2 and not 3pi/ 2
domain restriction of arcsin
remember the arcsin only has a domain of [0,pi] because that is where it is a one to one function
vocal ocean
i’m not seeing that here
vocal ocean
remember the arcsin only has a domain of [0,pi] because that is where it is a on...
the notes from class only show that for arccos or am i misunderstanding
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vocal ocean
<@&286206848099549185>
latent wave
Why is the answer -pi/2 and not 3pi/ 2
While sin (-pi/2) and sin (3pi/2) are both -1, arcsine is a function and can only give one answer
If arcsin(-1) gave 3pi/2, then arcsine would either have to be discontinuous or not include arcsin(0) = 0
vocal ocean
i understand that there can only be one answer but i don’t understand why it’s -pi/2
vocal ocean
While sin (-pi/2) and sin (3pi/2) are both -1, arcsine is a function and can onl...
forgot to ping
latent wave
It's the only value where sin(x)=-1 for x in [-pi/2, pi/2]
vocal ocean
It's the only value where sin(x)=-1 for x in [-pi/2, pi/2]
ok i think i get tysm
latent wave
You're welcome
vocal ocean
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strange ledge
My answer is x=3 so the shaded area is 49cm². Is it correct?
exotic saffron
My answer is x=3 so the shaded area is 49cm². Is it correct?
mhm
strange ledge
Our paths cross again
exotic saffron
ok
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strong finch
My answer is x=3 so the shaded area is 49cm². Is it correct?
Correct
burnt topaz
can someone explain why my answer is wrong? it looks correct to me. This is the problem Find |𝘂|, |𝘃|, |2𝘂|, 1/2𝘃, |𝘂 + 𝘃|, |𝘂 − 𝘃|, and |𝘂| − |𝘃|.
𝘂 = −8, 8, 𝘃 = −3, −1
exotic saffron
can someone explain why my answer is wrong? it looks correct to me. This is the ...
dont see why theyre wrong
burnt topaz
apparently (-11, 7) and (-5, 9) is incorrect
exotic saffron
apparently (-11, 7) and (-5, 9) is incorrect
what were the answers
frail heron
exotic saffron
cuz unless im screwing up addition i think theyre right
burnt topaz
it didnt show nor did it explain why it was wrong. I already submitted my answer but I can't go back and change it
exotic saffron
im certain it was the right answers
maybe u didnt type it in the right format idk
like missing a comma or smth
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timber crescent
I need help solving this and sketching and labeling v(t) and a(t) pleaseeee
gaunt wave
Are you aware that the derivative of a position function with respect to time is velocity and the derivative of a velocity function with respect to time is acceleration?
timber crescent
yea
gaunt wave
And the given function and graph represents position, so how would you figure out the velocity graph?
What is a derivative?
gaunt wave
If the slope is increasing it is speeding up and if the slope is decreasing it is slowing down
gaunt wave
I feel like I should point that the slope just has to be increasing, direction (positive or negative) doesn't matter as long as it is going to a more vertical slope it is increasing (same but horizontal slope for slowing down)
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ivory rock
how to inorder traversal if the root is at the left side
ivory rock
this is discrete math
trim lichen
how to inorder traversal if the root is at the left side
can you show the full problem
just so we know there's some order disambiguation or something
ivory rock
im doing quetion 4 b
trim lichen
otherwise you can probably just rotate the entire thing 90° if you feel it easier to construct an inorder reversal that way?
... universal address system?
ivory rock
yea?
ivory rock
otherwise you can probably just rotate the entire thing 90° if you feel it easie...
if you do that then for the preorder the asnwer wont be the same though
<@&286206848099549185>
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nimble charm
can someone help.
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can someone help.
spiral ocean
(ax+c)(x^2 + px + 1) = ax^3 + bx + c
ax^3 + (c+ap)x^2 + (a+cp)x + c
c + ap = 0 and c + ap = b
nimble charm
(ax+c)(x^2 + px + 1) = ax^3 + bx + c
why did u multiple (ax+c)
spiral ocean
because by eyeballing
the 1 must be multiplied by c
and x^2 must be multiplied by a
cuz its missing
spiral ocean
c + ap = 0 and c + ap = b
i think u can work from here
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loud bobcat
can someone explain to me this diagram?
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can someone explain to me this diagram?
loud bobcat
what does it mean when bx has been used in yh?
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livid dune
for question likne number 14 do we have to graph to find the limits of integration of can we just tell by the inequalities given
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whole coral
(Are you allowed to change coordinate types to do the integrals?) [ignore, misread question number]
whole coral
Hi 
for what you’ve asked, I mean, at least for me, I would sketch it out, as I can’t tell instantly (and there’s no harm in doing so!)
As for it being “possible”, it might be, but not for me 
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wraith hinge
can someone explain to me this diagram?
bx means the power (exponent) as in Ae^bx
and that's not yh it is Yp
nova pumice
Can someone explain to me what this means
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Can someone explain to me what this means
ionic pendant
find f'(x) and show that it's equal to f(x)
nova pumice
so do i find derivative of the series wiht respect to n
ionic pendant
whenever you're asked to show that a function is a solution to a differential equation, you just need to plug in the function and its derivatives to both sides and show they're equal
ionic pendant
so do i find derivative of the series wiht respect to n
no, with respect to x
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cunning cliff
f'(x) is the derivative of f with respec to the parameter, x
fringe gust
Hey can someone help me with these?
fringe gust
No
fringe gust
Hey can someone help me with these?
<@&286206848099549185>
high heron
<@&286206848099549185>
Try ask in one of the more advanced channels, though I don't know which is most relevant / most likely to get you a response (I mean I would guess#advanced-pdes from reading "PDE" but this is not something I studied). You can give yourself the Undergraduate or Postgraduate roles (depending on which is relevant) in #info if you can't see those
fringe gust
Try ask in one of the more advanced channels, though I don't know which is most ...
I see thank you!
high heron
it might take a while to get an answer there as well especially in the less active ones, but these help channels tend to be for more high school / earlier undergrad questions, so some of the people who might be able to help at a higher level don't really look in these
fringe gust
it might take a while to get an answer there as well especially in the less acti...
Okay I applied for it
knotty shuttle
We can rewrite this to be 12*(2/3)^n, why is it that when We rewrite it in this way the first term changes to 12 instead of 4. (Sequences and series)
knotty shuttle
oh I see my mistake
i think it comes out to be 4(4/3)^n-1
thank you for your help
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vast egret
$\int_0^2 \frac{t^2 \cdot e^t}{(t + 2)^2}$ dt
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$\int_0^2 \frac{t^2 \cdot e^t}{(t + 2)^2}$ dt
solid kilnBOT
╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮
austere cedar
u = t + 2
austere cedar
I'm suggesting a u-sub, sorry if I was unclear
IBP might come in at some point haha
vast egret
I'm suggesting a u-sub, sorry if I was unclear
What is u-sub?
Integral by parts?
@austere cedar
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real herald
Hey, im trying to verify this theorem but ran into an issue. Am i doing somethign wrong?
real herald
the $c_3,c_4$ does not match, but im confident i did this properly
solid kilnBOT
BOSS
whole coral
the $c_3,c_4$ does not match, but im confident i did this properly
a3 and b3 are [assumed to be] zero, from their absense in how you did your polynomials (and the note they made)
real herald
@whole coral oh what, thats a really pooly written note
but yeah that makes sense
aah
first problem of the day
tyty
bro where do u get ur cat emojis
i need more
either way tyty
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whole coral
bro where do u get ur cat emojis
.there's a cats server that has them 
https://discord.gg/cats
real herald
@whole coral w tysm i was thinking of getting a cat too
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real herald
Why is it that $(q'-q)b \< b$ ?
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Why is it that $(q'-q)b \\< b$ ?
solid kilnBOT
BOSS
real herald
note : a and b are positive integers. This is a proof of the division algo
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real herald
@spare orchid wait so
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<@329749386315956225> wait so
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spare orchid
no worries lol👍
real herald
.reopen
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