i'm an engineering student so my live rn is basically math
#help-27
pulsar oracle
pulsar oracle
K.E. is kinetic energy i assume?
cyan flame
yup
pulsar oracle
how high up is the pendulum?
pulsar oracle
erg is that some kind of derivative of Joules?
cyan flame
i guess 1 J = 10^7 ergs
pulsar oracle
I got it imma write it down
cyan flame
ok
cyan flame
ok
i am too trying to solve
By law of Conservation Of Mass
le me try
by the way
i have one recommendation for you
try solving IIT Questions once
pulsar oracle
what is that
pulsar oracle
for what grade is it?
pulsar oracle
yea
cyan flame
Are you there
pulsar oracle
i am
cyan flame
I got this one
pulsar oracle
with power do they mean Watt?
cyan flame
plz check mine
pulsar oracle
alr but then i have to go
cyan flame
with power do they mean Watt?
yes
cyan flame
alr but then i have to go
ok
cyan flame
plz check mine
2 mins i am sending
pulsar oracle
47040 W
cyan flame
check it once
pulsar oracle
?
cyan flame
..
pulsar oracle
fast
pulsar oracle
0.84J = 84 * 10^5 erg
cyan flame
i mean i took approx upto 2 decimal places
pulsar oracle
I see but still
cyan flame
ok 84.7 * 10^4 erg
pulsar oracle
im not very familiar with the conversion rate but u said 1J = 10^-7 erg
cyan flame
1 J = 10^7 ergs
pulsar oracle
it basically says 84 * 10^4 * 10^(-7) J and that is 84 * 10^(-3) J or 0.084J
not 0.84
but anyways your methods are right
pulsar oracle
ask your teacher I'm pretty sure your book is wrong
charred frigate
devout snowBOT
charred frigate
how do i approach this question
dry oxide
!status
devout snowBOT
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
is it a because it is an equilateral triangle and the premeter is the addition of a b and c
lyric hornet
the area of a equilateral triange given one side is $A=\frac{s^2\sqrt{3}}{4}$
woven radishBOT
PajamaMamaLlama
charred frigate
i assume it would be 16sqrt3 +16sqrt3+16sqrt3
wait
if its that equation: is it 16sqrt3=(s^2 sqrt3)/4
what is s?
charred frigate
ok let me try to write it on paper and ill show it
do you think this equation would be given in a standardized exam
or is it just known
also i got 24 as an answer
hence 32 is greater
what exactly is s?
restive river
I think s is one side of the equilateral triangle
charred frigate
ok ty!
restive river
also beautiful bird 💕
charred frigate
tysm ❤️
oh i never asked my question lol
could you help me with this
i know the diameter is 180
a triangle has to be 180 in total
restive river
I think you might need to post this question in “math help available” because I think the people helping assume your question has been answered 💕
charred frigate
oh okay ty!!
charred frigate
.close
charred frigate
devout snowBOT
charred frigate
ok so here is what i know about it so far
AB is a diameter of a circle
the diameter is 180 degrees
dry oxide
the diameter is 180 degrees
thats not gonna help anyway
dry oxide
do you have any about this theorem
charred frigate
i havent taken geometry in over 6 years so i am really iffy on these topics.
i know P would go to O
so we could have one at <POA and <OB P
dry oxide
okay so theres a theorem which says that angle subtented by diameter on the circumference of the circle is 90 degree
so you have 2 angles now, work for the 3rd and then give your answer accordingly
charred frigate
i apologize, what is subtented?
charred frigate
so you have 2 angles now, work for the 3rd and then give your answer accordingly
what are the two angles?
dry oxide
like "makes"
charred frigate
is it this? <POA and <OB P
dry oxide
what are the two angles?
one is 90 deg and another is given in the question itself
charred frigate
OH
okay
so 70 degrees
IM SO SORRY
i confused it with a different word lol
apologiez for the poor hangwriting i did it using a trackpad
i dont think the 10 degrees part is correct
charred frigate
oh? how do we know this?
dry oxide
i think you need to understand this first https://www.cut-the-knot.org/Outline/Geometry/AngleOnDiameter.shtml
charred frigate
ok give me a second. ill ping you when im done wih it
@dry oxide im confuse on this
oh its because its an isosclees and share a line together
<aop is equal to <bop
dry oxide
its really problematic as you dont know the theorems, you can maybe learn this for now, and now work further
charred frigate
i just need a little refresher, give me a second to continue
charred frigate
its really problematic as you dont know the theorems, you can maybe learn this f...
ok i finished with the website
dry oxide
can you find angle CBA now
charred frigate
so <cba=<cao+<bao
so we have to find the angle of <cao and <bao
and <cao=<bop as they are both isoscele triangle
is this correct so far
so cba is 20 degrees?
@dry oxide
ok i understand it now ty
.clos
.close
west tinsel
Hi
west tinsel
Translation:
"Imagine a vector c in R^4 which holds that u, v, w and c are linearly independent. Show, that the vector C cannot be written as a linear combination of u, v and w"
I do not know how to start on such a proof
dapper tiger
it comes from the definition of linearly independent itself
if c = au+bv+dw, for some scalars a, b, d which are not all zeros
then au+bv+dw-c = 0, where coeff are not all zero
it obviously contradicts the definition of linearly independent
and that's simply bc linearly independent exactly means you can't write one as a linear combination of the others
west tinsel
and that's simply bc linearly independent exactly means you can't write one as a...
can you say it in a simpler way?x)
dapper tiger
I quote the definition of linearly independent vectors, and it contradicts the idea that c could be written as a linear combination of u, v and w
west tinsel
yeah okay
so because c is also independent with those
there cannot exist a combination of them together where subtracting c equals 0
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scenic surge
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scenic surge
ABC is the only one that dont make sense right coz A has 2 column and B has 3 rows so it dont match
4A, C^T C for sure make sense
(B^T A)C
B^T is gonna have 3 columns and A has 3 rows.
B^T A = is gonna be 3 x 2 right. 2 columns and C has 2 columns so that makes sense too
(A - 3B) makes sense so (A - 3B)^T should make sense too
C(A^T - 4B^T )
A^T - 4B^T = 3 x 2
it has 2 columns and C has 2 rows so that should make sense too
so that means only ABC doesnt make sense right
.close
still dawn
devout snowBOT
lament cradle
similar triangles
lament cradle
when two triangles share the same angles, they are similar, this also means that the ratios between the sides are the same no matter how big/small they become.
look at that equation and the triangles carefully
it should pop out that they are just "comparing" the similar triangles' sides to the ratio of the two known corresponding sides.
still dawn
ohh
lament cradle
just like 15 is the bigger side, and 6 is the smaller
lament cradle
np
lament cradle
did you try drawing it out
devout snowBOT
@still dawn Has your question been resolved?
lament cradle
now write out what we are given and what is unknown
i don't have much time. but you have to find a way to relate the distance to the ship positions
faint drift
help
faint drift
Is this proof correct. Its about convergenc of a function
this is the function
<@&286206848099549185>
devout snowBOT
@faint drift Has your question been resolved?
devout snowBOT
@faint drift Has your question been resolved?
dapper tiger
a lot of ways to do it, you could see A from the point of view of the linear map from R^3 to R^3, x->Ax, which has R^3 as range since the column space is of dim 3, it's injective so A has an inverse
you could also, look for the inverse and find it, which is also quite efficient if the matrix is small and you're quick ig
dapper tiger
that's essentially the same argument as the injective thing
the determinant is non zero so the column space is of dim 3
so it has an inverse
and you even have an expression for the inverse with the determinant and the transpose of Idk how it's called in english
smoky nimbus
Isn't this channel taken by @tron?
west tinsel
the determinant is non zero so the column space is of dim 3
wdym with dim 3?
west tinsel
Isn't this channel taken by `@tron`?
it showed up as accessible
west tinsel
Under the available panel
thats why I typed in it
So what you are saying is that if the determinant is not 0 then it has an inverse? @dapper tiger
dapper tiger
yes
west tinsel
Great!
And for the inverse I wanna set up the rank 3 next to the matrix? @dapper tiger
Or how do I calc the inverse?
west tinsel
interesting
can you take a row and divide it by 2 ? is that a permitted row operation? @dapper tiger
dapper tiger
row operation for ?
west tinsel
matrix
dapper tiger
yeah I know we are talking about matrices I think
the question is why you're doing this operation for, and what do you hope it doesn't change
dapper tiger
if you divide a matrix A by 2 you get A/2 which is also invertible if that's your question
but obviously the inverse of A/2 is twice the inverse of A
dapper tiger
but for what purpose ?
dapper tiger
when you're doing a pivot you can multiply any line by any scalar yes
west tinsel
nice
btw there is a rule to define if a system of linear equations has an answer. something about p(A) = p(AIb)
How does that work?
west tinsel
rank
b is the coefficient matrix
like when you turn a system of linear equations into a matrix, then b would be on the right side of =
dapper tiger
ok so you have Ax = b for some matrix A
and then if the determinant is non 0, A is invertible
so there is a unique solution
bc x = A^-1 b
the determinant being non 0 is equivalent to the rank being equal to the dimension
west tinsel
it was something about if the rank of the AIb matrix is hgiher than the matrix A then theres no answer to the system
dapper tiger
Idk what AIb has to do with anything here
west tinsel
Idk what AIb has to do with anything here
lemme send you
like idk what is meant by this
dapper tiger
[A | b] is the matrix A where you add b as a last column to A
west tinsel
yes
dapper tiger
then the theorem is crystal clear, if A and [A | b] don't have the same rank, there is no solution
dapper tiger
where what is not the case ?
dapper tiger
take the coefficient matrix A
1 0 1
0 1 1
0 0 0
and b = 0
0
1
A is of rank 2, [A | b] is of rank 3
devout snowBOT
@faint drift Has your question been resolved?
fair wyvern
I have the following question:
Problem context: I have two channels, wave 1 (w_1) and wave 2 (w_2), both of functions of t, which have entries for the amplitude of a sound wave at time t.
Basically, each channel is represented as a vector. So, I have two vectors, w_1(t) = <x1,x2,x3,...,xn> and w_2(t) = <y1,y2,y3,..,yn> where each vector is of equal size. All entries in w_1 and w_2 are random (because they are amplitudes from a microphone).
Here is the problem...
I want to take the sum of the difference of all elements inside the two vectors, and minimize it by multiplying one vector by some constant scalar B.
I need to choose a B such that the thing is minimized.
fair wyvern
basically, to put it into latex terms.... where N is the size of the two vectors,
\sum_{t=0}^{N}(w_1(t) - B*w_2(t) ) should be minimized through picking a value for B
supple knot
` \sum_{t=0}^{N}(w_1(t) - B*w_2(t) )` should be minimized through picking a valu...
Do you know how to find B for N=1? N=2?
fair wyvern
Do you know how to find B for N=1? N=2?
For N=1, I just do
w(1) - B*w(2) = 0
so B = w(1)/w(2)
but this doesnt scale because i would need like
a weighted average
fair wyvern
Yes
supple knot
Write out an equation for N=2
supple knot
` \sum_{t=0}^{N}(w_1(t) - B*w_2(t) )` should be minimized through picking a valu...
Are you missing absolute value signs here
fair wyvern
wait
I think they can be negative
and I do not believe so
Here is the broader context
supple knot
Then your minimum can be negative as possible?
Yea you're missing a square
Instead of absolute value
fair wyvern
yeah
I am trying to maximize gamma so I want to minimize the square of the thing in the denominator
mb
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fair wyvern
.close
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Available help channel!
spark hound
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spark hound
dont know what to do, do i solve w/ arc lenght, bc i did that n i dont get any answers on the list
then i tried cos= a/h , n going from there to find angle
no avail
dim knot
s = rtheta
s = the arc (AB) = 87cm
2pier = 2.5 m
=> r = ?
hence theta= ?
remember the theta u get using s =rtheta is in radians
convert it to degrees
devout snowBOT
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restive river
How does one simplify the terms of the sum \sum_{i=0}^{log(n)-1} (2^i)(i+1)
restive river
?
devout snowBOT
@restive river Has your question been resolved?
livid geyser
Um
The log(n) - 1 doesn't make sense as an upper bound for the sum
It should be an integer
restive river
Yeah, sorry. This is on a recurrence relation with the stated assumption that n is a power of 2.
livid geyser
Oh bet
restive river
I'm fairly certain the answer is 1 + log(n/2) * n, but I don't know how to show it.
restive river
Sure
livid geyser
I've seen it b4 but I don't have the derivation off the top of my head like with arithmetic or geometric sums 
, gotta figure it out first
restive river
Thanks, I appreciate the help.
I think I have sth which might be useful.
So, let's ignore the log(n)-1 as the upper bound. Just say the upper bound is n.
And let's just move out the first term, which is 1.
Then we get terms like this: 2(2) + 4(3) + 8(4) + 16(5) + ... + 2^n(n+1)
Nevermind, this isn't a good approach.
The sum from 1 to log_2(n)-1 is basically 2(2) + 4(3) + 8(4) + ... + (n/2)(n+1). I just need a good way of proving that this is nlog(n/2)
livid geyser
OK I got u now, I haven't fully simplified it but
In general if u have a sequence that's like $(b_n) = ((a_0 + nd)r^n)$
woven radishBOT
992qqoloy
livid geyser
In ur case $a_0 = 1$, $d = 1$, $r = 2$
woven radishBOT
992qqoloy
livid geyser
Then $\sum_{k = 1}^n b_k$ is
woven radishBOT
992qqoloy
livid geyser
$\frac{a_0(1 - r^{n + 1})}{1 - r} + d(\frac{\frac{r(1 - r^n)}{1 - r} - nr^{n + 1}}{1-r})$
woven radishBOT
992qqoloy
restive river
You mind if I show you the recurrence directly? It seems like this is pretty far beyond what we've been taught in class, so I think I may have taken a wrong turn here. I was trying to solve this with a recurrence tree, but there may be a simpler solution using telescoping. (I tried that, but didn't get anything.
livid geyser
hmm ok
restive river
My work so far is basically this:
I suspect this is all correct, but there may be an easier way?
woven radishBOT
livid geyser
And then if u plug in for m = log(n) - 1
$2^{\log(n)-1 +1}(\log(n) - 1) + 1 = n\log(n) + 1 - n$
woven radishBOT
992qqoloy
restive river
Thanks, I appreciate the help.
Do you see any better ways of solving the recurrence I sent, though?
woven radishBOT
Pat M
restive river
$T(2) = 1$
woven radishBOT
Pat M
restive river
Btw, I'm not expecting a full solution, obviously. I just want to know if there's a better way using telescoping or something, or whether I should stick on my current path.
livid geyser
well at least telescoping isnt feasible cus the 2 in front of T(2) prevents terms from canceling out
But I found other neat solutions here: https://math.stackexchange.com/questions/206733/solving-recurrences-using-telescoping-backwards-substitution
Well actually
Hmm 1 isn't the same as nlog(n) cus it doesn't depend on n, so that won't work
restive river
Actually, looking into it, it seems like there's an answer for a very similar equation: https://math.stackexchange.com/questions/159720/how-to-solve-this-recurrence-tn-2tn-2-n-log-n
livid geyser
I think this specific one https://math.stackexchange.com/a/207075/126569 is most applicable. Says you can solve it by solving homogeneous linear recurrence relation (which is super ez) and finding a guess (less ez)
Noice
Yeah p much the same
restive river
The n/2 in the log shouldn't make telescoping unusable, right?
livid geyser
Then u only have like T(4)- 2T(2)
Then T(8) - 2T(4)
So when u add them together for example u still have -T(4)
restive river
I suppose I could just rewrite nlog(n/2) as n(log(n) - log(2)) = nlog(n) - n
livid geyser
Oh wait hmm
I gués could do 1/2T(8) - T(4) = n/2log(n/2)
Then 1/4T(16) - 1/2T(8) = n/4log(n/2)
So telescoping could totally work 
restive river
Thanks, would you mind if I ask you to look over my work in ~5 min, once I've worked it out?
livid geyser
Ok
restive river
Sorry, just typing it up.
restive river
Ok
Does this solution look correct to you? I'm not 100% sure I got the boundaries right on the sum.
Wait, hold on, I notice an error in my sum.
You know, this is taking longer than I thought, I think I'll just yield the channel. Thanks for all the help.
./close
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undone crystal
So this is about solving for X. And its about geometric sums
devout snowBOT
So this is about solving for X. And its about geometric sums
undone crystal
I understand everything except when that -1 shows up
Where does it come from? 🤔
It just randomly shows up after taking the root square of both sides?
I see. tyvm for clarifying it! ❤️ How do we know that they have started to calculate from i=0?
Is it just geometric sum formula that dictates it from 0
Ahh, so we have overcounted with i=0 thus needs to adjust it.
Again, tyvm! 😁
.close
karmic spindle
quick question: when using point slop form at the end of this problem, do I use f'(x) as the slope (m)?
devout snowBOT
quick question: when using point slop form at the end of this problem, do I use ...
haughty glacier
for ii and the rest, do I have to substitue both values iof each pair nto the limit?
devout snowBOT
for ii and the rest, do I have to substitue both values iof each pair nto the li...
@haughty glacier Has your question been resolved?
devout snowBOT
@haughty glacier Has your question been resolved?
prime hollow
In ii), you first find the limit for the path $x=0$, then you find it for the path $x=y$
woven radishBOT
Ivar Ängquist
prime hollow
for ii and the rest, do I have to substitue both values iof each pair nto the li...
Did that answer your question?
prime hollow
Yes. If you set both equations to be true at once, then you are left with a point, rather than a curve.
It also applies to i)
prime hollow
np
haughty glacier
.close
urban hornet
devout snowBOT
livid geyser
Might be useful? I haven't checked yet https://math.stackexchange.com/questions/390899/proving-that-x-fracx33-sin-x-x-for-all-x0
urban hornet
Might be useful? I haven't checked yet https://math.stackexchange.com/questions/...
This is just the taylor expansion.
Doesn't help much on this question
livid geyser
not the full Taylor expansion
Just first term or two
And it would help by making upper and lower bounds
cus if h(x) <= f(x) <= g(x)
Then same for the integrals
And having x's on the numerator would make appropriate h(x) and g(x) ezier to integrate
urban hornet
The answer is option (3). How can root(2) come using this formula
livid geyser
ok
Actually
if ur willing to estimate sqrt(2) as 1.4 or w/e, then u can probably make it work
So yeah it's actually worth a shot
but this is probably the intended way https://math.stackexchange.com/questions/1694019/prove-that-frac-sqrt38-int-frac-pi4-frac-pi3-frac-sin-x
devout snowBOT
@urban hornet Has your question been resolved?
urban hornet
but this is probably the intended way https://math.stackexchange.com/questions/1...
This only gives sqrt 2
Pi is gone 
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restive river
Write a function with the following characteristics: Degree 4. Root multiplicty at x = 4, and a root of multiplicty of 1 at x = 1 and x = -2. Vertical intercept at (0, -3)
devout snowBOT
Write a function with the following characteristics: Degree 4. Root multiplicty ...
restive river
Currently I got f(x)=(x-4)^2(x-1)(x+2)
I know that (x-1) and (x+2) should be there cause it says they should have a multiplicty of 1
and I know the first first one needs to be squared so the function has a degree of 4
I guess wshat Im asking is how would I make the y intercept -3
rugged sparrow
well you'll have f(x)=k(x-4)^2(x-1)(x+2)
since intercept is (0,-3), f(0)=-3. This would allow you to find the value of k
restive river
since intercept is (0,-3), f(0)=-3. This would allow you to find the value of k
Wait so would I find the answer just by plugging 0 in?
im confused
rugged sparrow
plug in x=0
woven radishBOT
Matt
rugged sparrow
You forgot the k
charred token
-4-8=
rugged sparrow
f(0)=-32k
restive river
$-32k=-3$
woven radishBOT
Matt
restive river
?
rugged sparrow
yes
rugged sparrow
k=3/32 YES
rugged sparrow
welcome 
restive river
.close
restive river
Please can you help me evaluate this indefinite integral using power series representation ?
devout snowBOT
Please can you help me evaluate this indefinite integral using power series repr...
restive river
Here's my scratch work
Maybe there is a hint
Perphaps I need to substitute tan(u) for x in the integral ?
devout snowBOT
@restive river Has your question been resolved?
bleak bay
devout snowBOT
bleak bay
i have no idea what im doing wrong. the derivative of the function is secxtanx + 2sinx
when i plug in pi/3 i get 3sqrt3/2 so i mught be formatrting something wrong? idk
.close
hearty yoke
shape is correct points are wrong
hollow urchin
👍
winter patrol
it also looks like you're connecting the two pieces with a vertical line (Which would be wrong)
cobalt wraith
whats the right way to do it?
winter patrol
not connect your pieces,
use open/closed circle to indicate whether a point is included
show your work and reasoning for the piece where
f(x) = (x-2)^2 if x>=0
cobalt wraith
@winter patrol
cobalt wraith
im confused :/
winter patrol
show your work and reasoning for the piece where
f(x) = (x-2)^2 if x>=0
winter patrol
yes
cobalt wraith
it opens upwards because the coefficent is positive
winter patrol
yes
cobalt wraith
and the other part would be like y = -x?
winter patrol
you didn't finish /provide sufficient reasoning
what you've said so far is true, however,
that doesn't mean that you can draw any upwards facing parabola
cobalt wraith
so i took the same line and re-drew it
winter patrol
forget about the |x|, that part was pretty much fine
cobalt wraith
oh so this part is correct?
cobalt wraith
forget about the |x|, that part was pretty much fine
ok
winter patrol
what were your calculations for the specific points
y = (x-2)^2
will pass through?
cobalt wraith
what were your calculations for the specific points
y = (x-2)^2
will pass throug...
i asked gpt code interpreter
winter patrol
!nogpt
devout snowBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
cobalt wraith
ok
cobalt wraith
ok ill try and do that
do you think i should re-do this one as well
with a table of values
winter patrol
knowing the definition,
table for that isn't really needed,
but you do need to be more careful about how you draw you axis,scale,lines
cobalt wraith
ok
winter patrol
slope of that left piece is wrong
cobalt wraith
on this one?
winter patrol
yes
that looks like you line is passing through stuff like
(-1,1.5), (-2,3), (-3,4.5)
i.e. like y =-1.5x
instead of y = -x
devout snowBOT
@cobalt wraith Has your question been resolved?
devout snowBOT
@cobalt wraith Has your question been resolved?
random ice
winter patrol
!noping
devout snowBOT
Please do not ping individual helpers unprompted.
winter patrol
!noadvert
devout snowBOT
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cobalt wraith
now do work for the parabola
i tried watching a lot of youtube videos to understand it but i am still struggling. do you have any recommendations for specific videos on how to solve it? thanks
pulsar relic
is this the right way to think about solving this problem? (i had to simplify to just one exponent, and got stuck around the red arrow area for a bit. is there a different way to think about solving this that would be easier?
devout snowBOT
is this the right way to think about solving this problem? (i had to simplify to...
wheat pawn
you do a lot of unnecessary steps, but it is correctly simplified
pulsar relic
you do a lot of unnecessary steps, but it is correctly simplified
can you point out whats unnecessary and where i should just try to skip to the next step to save time. sort of trying to understand how other people think about these problems
wheat pawn
i'm gonna try to tex it, gimme a bit of time (and a few tries)
$\frac{3^{x+1}}{2^{2x-3}} = \frac{3\cdot3^x}{2^{-3}\cdot2^{2x}} = 24\cdot\frac{3^x}{(2^2)^x} = 24\cdot(\frac{3}{4})^x$
woven radishBOT
LordFelix
pulsar relic
thanks, what would you say i'd have to work on. or basically just more problems like these with exponents...exponent laws
wheat pawn
well it really depends on how detailed you're asked to do it
pulsar relic
i dont know how detailed i will be asked to do anything. im trying to self learn
wheat pawn
then what i would recommend is doing the few first as painstakenly detailed as possible using exclusively the rules that you have as is, and start taking shortcuts each time you have a rule completely down
For example, first step uses the rule of:
$a^b\cdot a^c=a^{b+c}$
woven radishBOT
LordFelix
wheat pawn
2nd step is chaining several rules, so it would be "cheating" if going on full detail
you'd first need to apply:
$\frac{1}{2^{-3}} = \frac{1}{\frac{1}{2^3}} = 2^3$
woven radishBOT
LordFelix
wheat pawn
which are two steps
pulsar relic
thanks for typing/texting it all out btw, it seems to take a lot of time.
wheat pawn
depends on how much experience you got typing all these things. I'm pretty new at tex
pulsar relic
2nd step is chaining several rules, so it would be "cheating" if going on full d...
what do you mean by 'cheating if going full detail'
wheat pawn
if you go only by the formal definitions and properties
for example, if you were to make a proof completely rigourously
however, if the steps are obvious enough you can daisy-chain them. Like i did from 2nd to 3rd in the equality
sure, "formally" it would take several steps, but they are very obvious steps that no one is gonna have trouble following
pulsar relic
ok, so i guess teachers are looking for only so much detail
wheat pawn
not really. I do teach the absolute maximum detail, demonstrate a couple of times, and then start showing where shorcuts can be taken with what is done still being obvious
pulsar relic
this type of question, the original, is sort of relating to exponential equations / graphs. is there something i can search online specifically for more problem sets that deal with i guess simplifying ______? into exponential graphing functions?
wheat pawn
**LordFelix**
for example, here, you could go directly from first to last.
However, i would at least show the 2nd
pulsar relic
this type of question, the original, is sort of relating to exponential equation...
i dont know the terminology
wheat pawn
power simplification exercises maybe?
i usually dont really pay much attention to repetitive exercises that are just "apply this property with this number. do it again 20 more times with 20 different numbers"
the only reason to do that is if you wanna go faster for some reason
pulsar relic
a lot of the power simplification exercises are basically just single expnents, without variables which trips me up sometimes
wheat pawn
it doesnt really matter that you have numbers and letters tbh
you just need to memorize the properties making sure you dont mix them up, and use them as needed.
If possible, also learn why those properties hold.
also if possible, get to prove them yourself
wheat pawn
**LordFelix**
For example, this one is very easy to prove by yourself, assuming the exponents are natural numbers, just by expanding the expression
static berry
Hello everyone,
As I am in grade 10, I'm determined to elevate my math skills to new heights. While I currently don't feel entirely confident in my math abilities, I'm eager to change that. My aim is to become adept at mental math, tackle challenging problems well above my current level, and build a solid foundation for advanced learning.
I'm reaching out to this community for guides, resources, and tips that can help me achieve my goal. I'm particularly interested in eventually delving into calculus ahead of schedule. If you have any recommendations – whether it's strategies for enhancing mental math, book suggestions, online courses, or other resources – I'd be grateful for your insights.
My aspiration is to not just catch up but to forge ahead, and excel in math beyond what's expected at my level. Thank you for your time and any support you can provide. I'm excited to learn from your experiences and knowledge as I work towards my goal.
These are also 2 books I found after research. Would they be good?
-
"Discrete Mathematics with Applications" by Susanna Epp
-
"Concrete Mathematics" by Donald Knu
Also to add, the cut off for my knowledge is algebra, my math teacher last year did not teach us much, so I am even not that good at algebra
glad kindle
how do you do this
devout snowBOT
how do you do this
pale bolt
how do you do this
(x-a) is a factor of f(x) iff a is a root
turbid steeple
I need help understanding what this question means
devout snowBOT
I need help understanding what this question means
restive river
I need help understanding what this question means
what value would c need to be for the function to be continous
jade oak
I need help understanding what this question means
If you plot that function, you will see there is a jump for most values of c at x=2
you want to find c so there is no jump
devout snowBOT
@turbid steeple Has your question been resolved?
turbid steeple
one sec
devout snowBOT
Available help channel!
teal bramble
why did they flip the sign here, wouldnt that make x into -x?
devout snowBOT
why did they flip the sign here, wouldnt that make x into -x?
supple knot
why did they flip the sign here, wouldnt that make x into -x?
Not if you flip it in both numerator and denominator
umbral spindle
devout snowBOT
umbral spindle
simple question: I am struggling with taking the derivative of T(t) here
for i^ I understand
however, I cannot figure out j^
I am doing a product rule for each unit vector
.close
median quest
devout snowBOT
small nest
!spam
median quest
what are u saying
small nest
Maybe, what have you tried, @median quest ?
median quest
can u just help me :/
im stressing already
instead of asking me what i did, and what i have done, cuz none of that matters, since it's not the answer
nvm i got it
its 0
thanks for nothing
.close
elfin cosmos
Show that, $\frac {2cos2^n \theta + 1} {2cos\theta +1} = (2cos\theta - 1) (2cos2\theta - 1) (2cos2^2 \theta - 1) ...... (2cos2^{n-1} \theta -1)$
devout snowBOT
Show that, $\frac {2cos2^n \theta + 1} {2cos\theta +1} = (2cos\theta - 1) (2cos2...
woven radishBOT
SubZero
elfin cosmos
I have 0 clue what to do
livid geyser
Just keep dividing both sides by the frontmost term remaining on the right side 
elfin cosmos
W h a t
livid geyser
do u know ur double angle formula
elfin cosmos
Cos2A one?
livid geyser
ye
elfin cosmos
Yeah
livid geyser
If u divide both sides by the frontmost cos(whatever) - 1 term ull see why it works
I mean why it helps
livid geyser
Um I was thinking just make a note that all steps are reversible at the end. Which you'll have to justify also, I haven't actually figured out that part yet but it shouldn't be bad basically just amounts to showing that if L. H. S is 0, then so is R. H. S. If L. H. S. not 0, steps are reversible cus theres no division by 0
Divide both sides
As in like just keep dividing both sides until you get 1 = 1
Wait hold up im udmb there's a better way
elfin cosmos
I can do that????
Like dont I have to like prove that one is equal to the other
livid geyser
I can do that????
Like dont I have to like prove that one is equal to the other
As long as all steps are reversible
But instead what you can do is
Multiply both sides by denominator of L. H. S.
And from there simply the R. H. S. by spamming double angle identity
livid geyser
Yeah lol plus that way you don't even have to justify reversibility
elfin cosmos
What is this justify reversibility and why have I never heard of it
livid geyser
It's just like
For instance say you had 0< a <b
Then you can conclude a^2 < b^2
Buuut
From a^2 < b^2
You cant conclude a< b
For instance if b= -3 and a = - 2
elfin cosmos
Makes sense
livid geyser
So for example if you want to prove an inequality (e +f)^2 < (c + d)^2 you can't just square root both sides then rearrange and arrive at something like 0< 1
Only if you can reverse every step that you took
Can you do that
Here the problem I was thinking of is if you divided then you couldn't reverse the steps if any terms were equal to 0
elfin cosmos
I might sound stupid but how modify $4cos^2\theta -1$
woven radishBOT
SubZero
elfin cosmos
I know its cos2A somehow but how
livid geyser
Cos(2theta) = 2cos^2 - 1 so 2cos(2theta)= 4cos^2(theta) - 2 so 2cos(2theta)+1 = 4cos^2(theta) - 1
elfin cosmos
11th grade (I am 9th grader)
livid geyser
nice yeah that's a hard problem for a pre-calc class then XD
if I'd been thrown into it from just having learned those identities I wouldn't have gotten it in ages
elfin cosmos
Smh 10th grade problems were so much easier
Wtf is this
Ive been doing trig for god knows how long and I have 0 clue wtf I am even doing at this point
winter torrent
elfin cosmos
Ok but thanks tho lol
Yeah so you just repeat the same thing upto like cos 2^n-1 theta + 1
Then spam identity one last time
livid geyser
yeah I think so, I didn't do the whole thing xd
I was just thinking induction would work except for a few basse cases or something
livid geyser
np
elfin cosmos
.close
clever girder
i need help with this homework proof
devout snowBOT
i need help with this homework proof
pseudo basin
hazy yarrow
spiral shell
im confused on what the bounds should be
devout snowBOT
im confused on what the bounds should be
devout snowBOT
@spiral shell Has your question been resolved?
restive river
So for example lets say your given a logrithm or exponential GRAPH. You will have to derive an equation given that graph. How will this be acheived?
devout snowBOT
So for example lets say your given a logrithm or exponential GRAPH. You will hav...
restive river
So for example lets say your given a logrithm or exponential GRAPH. You will have to derive an equation given that graph. How will this be acheived?
restive river
i see so its impossible to determine really
river gorge
So for example lets say your given a logrithm or exponential GRAPH. You will hav...
can you show a graph as an example so i can explain it using that example?
devout snowBOT
@restive river Has your question been resolved?
restive river
@river gorge @topaz axle that is the graph your given 3+ points but heres 2 (0,-9) (8,-1)
topaz axle
−8, −1 you mean?
restive river
yes
topaz axle
yeah ok
polar chasm
I have 2 questions bout this, first of them is regarding the part a), I managed to show it by showing that any model of it's negation must be infinite, the negation turned out to be $\forall x\left( Pxfx\wedge \neg Pxx\wedge \forall y\forall z\left( Pxy\Rightarrow Pyz\Rightarrow Pxz \right)) \right)$, however then I proceeded by showing that $x \not = fx \not = ffx \not = fffx \dots$ which is true by irreflexivity and $\forall x Pxfx$. And by the previous statement, it cant have a finite model because it would soon run out of elements in the universe, and the statement would break. However, in this proof I didnt use transitivity at all, so I think there might be some flaw
devout snowBOT
I have 2 questions bout this, first of them is regarding the part a), I managed ...
rugged jewel
(complex numbers)
I have this:
z^2 − 4z + 13 = 0
And the answer I need to find is this:
z1,z2 = 2+-sqrt{4-13} OR z1,z2 = 2+-3j
But how do I find any of these 2 answers?
rugged jewel
Im guessing using the quadratic equation formula, but idk how that works with complex numbers
winter patrol
Im guessing using the quadratic equation formula,
pretty much the same way
with $\frac{-b\pm \sqrt{-k}}{2a} = \frac{-b\pm i\sqrt{k}}{2a}$ when you have a negative value under the root
woven radishBOT
ℝαμΩℕωⅤ
rugged jewel
Oh i see
Yeah I get 2+-3j as a final answer
But how about this z1,z2 = 2+-sqrt{4-13}
How did they find that?
devout snowBOT
@rugged jewel Has your question been resolved?
daring nebula
Determine the number of all six-digit numbers in the decimal system that are divisible by 9 and contain the digits 2, 0, 2, 3 in exactly this order in immediate succession.
devout snowBOT
Determine the number of all six-digit numbers in the decimal system that are div...
daring nebula
i got 31 but i dont know if thats correct
mild comet
How did you get that?
daring nebula
i just added numbers to the end and start of the number 2023 that would equal 9 or 18 if we added all of the digits
for example: 112023, 202311, 120231, 202023, 202302... etc
mild comet
Can you send your list?
daring nebula
sure!! wait a second
topaz axle
computer says 31
rich summit
Consider 892023
topaz axle
that's divisible by 3, but not 9
mild comet
Consider 892023
,calc 892023/9
woven radishBOT
Result:
99113.666666667
202311
120231
112023
202023
202302
202320
220230
202383
202338
382023
832023
320238
820233
202374
202347
742023
472023
420237
720234
202356
202365
562023
652023
620235
520236
202392
202329
292023
922023
920232
220239
topaz axle
yeah, 31 is right, so it's probably right
feral bobcat
devout snowBOT
stuck prairie
remind me again what the mean value theorem states?
feral bobcat
Suppose that y = ƒ(x) is continuous over the closed interval [a,b] and differentiable at every point of its interior (a, b). If ƒ(a) = ƒ(b), then there is at least one
number c in (a, b) at which ƒ′(c) = 0
rare mantle
can someone tell me why i cant apply mvt here
the function isn’t differentiable at x=1.25 because it’s an absolute function
feral bobcat
the function isn’t differentiable at x=1.25 because it’s an absolute function
that doesnt make snese to me
its continou s
rare mantle
continuous doesn’t always mean differentiable
sullen island
Suppose that y = ƒ(x) is continuous over the closed interval [a,b] and differentiable at every point of its interior (a, b). Then...
you said it yourself
sullen island
there is a point in the interior, namely x=1.25, where f is not differentiable
so the hypotheses of MVT do not hold
feral bobcat
why its not differentiable
how did we know
( i havent studied calculus for a year)
rare mantle
feral bobcat
and just cam eback to it
rare mantle
this is a good explanation
sullen island
have you studied derivatives ?
stuck prairie
able to be differentiated lol
sullen island
yeah
rare mantle
but what means differentiable
that there is a line tangent to the point that you can take the slope of
feral bobcat
https://math.stackexchange.com/questions/991475/why-is-the-absolute-value-functi...
ill read it
but i want a quick explanation
rare mantle
the main thing here is that there is an abrupt change in the slope
vs something like x^2 where, at the vertex, the slope changes gradually
feral bobcat
What question?
this
feral bobcat
this
rare mantle
what part?
feral bobcat
what part?
soom in thing
feral bobcat
Because derivative doesn't exist at corners
can u show me if possible please
abstract skiff
Go to a web called flippedmath calculus 1
feral bobcat
then
mild comet
that means it is differentiable?
no, it means a differentiable function is continuous
mild comet
so if have a continious function
|x| is continuous, but not differentiable at the origin
feral bobcat
or vice versa?
like if the function is differentiable then it must be continous
feral bobcat
|x| is continuous, but not differentiable at the origin
i still do not understand this
mild comet
or vice versa?
like if the function is differentiable then it must be continous
if the function is differentiable, then it must be continuous
but if a function is continuous, it may not be differentiable
mild comet
i still do not understand this
What don’t you understand
feral bobcat
what means not differentiable at origin
i do not understand what a differentiable function is
rare mantle
what does a derivative mean to you?
abstract skiff
so if have a continious function
@feral bobcat no if the function is continuous then it's differentiable
If its* differentiable then it's continuous
Sorry I had a mistake
Slope means derivative
rare mantle
i know it means finding the slop
so how could you find the slope at the bottom of an absolute function
feral bobcat
making a tangent line
oh at origin the tangent line will be horizontal?
so its = 0?
feral bobcat
then what
rare mantle
there is the abrupt change in slope as I was talking about
unlike x^2 where it is gradual, and therefore there is a point when the slope is 0
rare mantle
there is the abrupt change in slope as I was talking about
which means there is no derivative at the corner
pine pilot
Easy integration question.
I have an equation, $f'(x)=5-\left(x-2\right)^{2}$
Looks like image.png when graphed
I want to find the area under this curve between when x = 0 to when x = 4. At those x-values, f'(x) = 1.
woven radishBOT
AlexanderJ
pine pilot
The indefinite integral of f'(x) = $x - \frac{x^3}{3} + 2x^2 + C$ .
How do I find what C is here?
woven radishBOT
AlexanderJ
rich summit
It can be anything, but the area is F(4) - F(0) and C cancels out
pine pilot
Oh, so the area is $(4 - \frac{4^3}{3} + 2\cdot4^2 + C) - (0 - \frac{0^3}{3} + 2\cdot0^2 + C)$ ?
woven radishBOT
AlexanderJ
rich summit
Yes
hexed ocean
Can someone tell me what I did wrong here?
devout snowBOT
Can someone tell me what I did wrong here?
winter patrol
how are you getting 3pi/2 for the second argument
hexed ocean
how are you getting 3pi/2 for the second argument
tan^-1( 1/SQRT(3) )
winter patrol
is not 3pi/2
winter patrol
missing pi