<@&286206848099549185>
#help-36
hearty zephyr
how would you solve 3k+8 = 26?
hearty zephyr
charred fulcrum
idkdkdkdkkdd
is this taiko
plucky umbra
how would you solve 3k+8 = 26?
ivfce tried k = 6 but that not the answer
hearty zephyr
because the question isn't asking for an equality
plucky umbra
wheere do i get the answer then
?
hearty zephyr
since the original is asking for >=, and you didn't multiply or divide by a negative, the sign doesn't change.
the method for solving it is, otherwise, the same as solving an equality.
but the answer maintains the original inequality sign
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
hello!
why are multiples of dx ignored ?
eg. $\frac{d}{dx}x^2= \frac{2(dx \cdot x) + dx^2}{dx} = 2x + dx = 2x$
why does the dx in $2x + dx$ dissapear ?
i know that it is an "infinitely small" value, and that it is infinitely small compared to any number - but still, it is not zero, thus it should still count
soft zealotBOT
trololol !
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
<@&286206848099549185>
final saddleBOT
@tranquil pine Has your question been resolved?
pine garden
I don't understand how to solve this
final saddleBOT
I don't understand how to solve this
@pine garden Has your question been resolved?
pine garden
<@&286206848099549185> hi
pine garden
<@&286206848099549185>
open oxide
look at unit circle
oak arrow
could someone please help me with 16
final saddleBOT
could someone please help me with 16
oak arrow
i just dont really know how to find the directional vector
because (6,1,3) when dotted with v is not 0
what if i add the vector (0,-1,0). adding those two dot products together would yield 0
would that work?
pine root
the vector equation of a plane is usually its normal vector
and thats just v by the definition
final saddleBOT
@oak arrow Has your question been resolved?
oak arrow
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eager trellis
Direction: write a rule for g described by the transformations of the graph of f f(x) = x^2; vertical stretch by the factor of 2 and a reflection in the x axis , followed by a translation 3 units down
final saddleBOT
Direction: write a rule for g described by the transformations of the graph of f...
eager trellis
I’m stuck on everything
rare halo
final saddleBOT
eager trellis
.reopen
final saddleBOT
✅
eager trellis
Direction: write a rule for g described by the transformations of the graph of f f(x) = x^2; vertical shrink by a factor of 1/2, followed by a translation 3 units left
now im confused on this question
where would I put the parentheses?
eager trellis
so plus 3
hot patrol
so y= 1/2(x+3)^2
raven bridge
how can i calculate rank of this matrix?
final saddleBOT
how can i calculate rank of this matrix?
raven bridge
<@&286206848099549185>
raven bridge
Find the number of linearly independent columns
what does is mean that columns or rows are linearly independent?
worldly vale
Do you know what linear independence means?
raven bridge
no
raven bridge
well, lastly i didn't pay much attention to university due to depression
and now i'm trying to make it up
soo, i'm figuring it out now
worldly vale
And your first port of call was calculating the rank of a matrix? You should cover some background first
raven bridge
soo, i'm figuring it out now
i know two methods
worldly vale
Okay then use one of them
raven bridge
but those methods don't really work in this case
worldly vale
Show your work
raven bridge
And your first port of call was calculating the rank of a matrix? You should cov...
i mean, this is already transformed
worldly vale
Okay and so...
Whats the point of doing the row reduction? (Its the correct thing to do but you need to recall the point of doing it)
raven bridge
the point of this is to get Identity matrix
the longest possible one
but i don't see the way how to get one longer than 3x3
<@&286206848099549185>
mellow cedar
could you give us the original matrix ?
raven bridge
could you give us the original matrix ?
mellow cedar
you can reduce it to
$\begin{bmatrix}
1 & 0 & 0 & 0 \
1 & 5 & 0 & 6 \
1 & 0 & 7 & 0 \
1 & 8 & 0 & 9 \
1 & 0 & 0 & 0 \
\end{bmatrix}$
soft zealotBOT
Mehdi_Moulati
mellow cedar
since the colmun 0 is the same as the 2 ,4 and 6
mellow cedar
i didn't know about this
let me verifier
yeah it's true
let a and b vectors :
if vector a = K * b where K integer you can delete it
in general :
if i could get a vector using other vectors i could delete it
raven bridge
ok, with this knowledge the rest of this problem is trivial
thanks for help
.close
final saddleBOT
mellow cedar
@raven bridge you can delete the first and last row also
final saddleBOT
Available help channel!
raven bridge
<@354970469323243523> you can delete the first and last row also
you mean the first or the last row, right?
final saddleBOT
you mean the first or the last row, right?
mellow cedar
you mean the first or the last row, right?
yeah
raven bridge
kk
mellow cedar
$\begin{bmatrix}
1 & 0 & 0 & 0 \
1 & 5 & 0 & 6 \
1 & 0 & 7 & 0 \
1 & 8 & 0 & 9 \
\end{bmatrix}$
soft zealotBOT
Mehdi_Moulati
raven bridge
I knew that I can delete rows, but i just didn't know that I also can delete columns
mellow cedar
also the column
you just need to prove that the the vectors are all independent
the rank is number of independent vectors
i guess you will find the rank = 4
raven bridge
you just need to prove that the the vectors are all independent
i don't really know how to do this
raven bridge
i guess you will find the rank = 4
yes
wait, one column or one row is a vector, right?
mellow cedar
wait, one column or one row is a vector, right?
yeah
mellow cedar
two columns an test them if they are independent
or
two rows an test them if they are independent
if two vectors (A and B) are dependent when
AX = B
like
$\begin{bmatrix}
1 \
1\
1\
\end{bmatrix}$
X = $\begin{bmatrix}
3 \
3\
3\
\end{bmatrix}$
raven bridge
if two vectors (A and B) are dependent when
AX = B
what is X?
soft zealotBOT
Mehdi_Moulati
mellow cedar
what is X?
a variable
mellow cedar
is it a real, whole or literally random number?
if this system of equations is true then the two vectors are dependent
mellow cedar
**Mehdi\_Moulati**
in this case , X = 3
raven bridge
yes, but i mean, can X be for example a complex number?
mellow cedar
$\begin{bmatrix}
1 \
1\
1\
\end{bmatrix}$
X = $\begin{bmatrix}
1 * X \
1 * X\
1 * X\
\end{bmatrix}$
$\begin{bmatrix}
3 \
3\
3\
\end{bmatrix}$
soft zealotBOT
Mehdi_Moulati
mellow cedar
it's like a system of equations where
$\begin{cases}
1 * X = 3 \
1 * X = 3 \
1 * X = 3 \
\end{cases}$
soft zealotBOT
Mehdi_Moulati
mellow cedar
and you trying to find the value of the X
if you find a solution then the vectors are dependent
mellow cedar
**Mehdi\_Moulati**
in this case X = 3 so the vectors are dependent
so i could remove one of them
raven bridge
ok, so for example if
$\begin{bmatrix}
1 \
1\
1\
\end{bmatrix}$
X = $\begin{bmatrix}
1 * X \
1 * X\
1 * X\
\end{bmatrix}$
$\begin{bmatrix}
3i \
3i\
3i\
\end{bmatrix}$
soft zealotBOT
Trenek
raven bridge
then X=3i
mellow cedar
yeah
$\begin{bmatrix}
1 \
2\
3\
\end{bmatrix}
X
\begin{bmatrix}
5\
10\
15\
\end{bmatrix}$
find the X in this example
soft zealotBOT
Mehdi_Moulati
mellow cedar
that right so the vector (1,2,3) and (5,10,15) are dependent
raven bridge
thanks a lot 😊
raven bridge
huh, okay
mellow cedar
sometime you need to prove that
A = BX + CY + DZ
where
A ,B ,C and D are vectors
and X,Y and Y are variables
$\begin{bmatrix}
1\
1\
0\
\end{bmatrix}
X
+
\begin{bmatrix}
1\
0\
1\
\end{bmatrix}
Y
+
\begin{bmatrix}
0\
1\
1\
\end{bmatrix}
Z
\begin{bmatrix}
8\
8\
8\
\end{bmatrix}$
soft zealotBOT
Mehdi_Moulati
mellow cedar
**Mehdi\_Moulati**
like this example
the vectors (1,1,0) (1,0,1) (0,1,1) and (8,8,8) are not independent if you find a solution to this system of equations
raven bridge
ok, so we've got
$\begin{bmatrix}
X+Y\
X+Z\
Y+Z\
\end{bmatrix}
\begin{bmatrix}
8\
8\
8\
\end{bmatrix}$
soft zealotBOT
Trenek
mellow cedar
**Trenek**
and you need to find the value of X,Y and Z
raven bridge
ok, so it seems that X=Y=Z=4
mellow cedar
ok, so it seems that X=Y=Z=4
correct!
then the vectors (1,1,0) (1,0,1) (0,1,1) and (8,8,8) are not independent
raven bridge
indeed
mellow cedar
but those vectors (1,1,0) (1,0,1) (0,1,1) are independent
and you can prove it by the same method
$\begin{bmatrix}
1\
1\
0
\end{bmatrix}
X
+
\begin{bmatrix}
1\
0\
1
\end{bmatrix}
Y
=
\begin{bmatrix}
0\
1\
1
\end{bmatrix}$
soft zealotBOT
Mehdi_Moulati
$\begin{bmatrix}
1\\
1\\
0
\end{bmatrix}
X
+
\begin{bmatrix}
1\\
0\\
1
\end{bmatrix}
Y
=
\begin{bmatrix}
0\\
1\\
1
\end{bmatrix}$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.78
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```
raven bridge
ok, so
$\begin{bmatrix}
X+Y\
X\
Y\
\end{bmatrix}
\begin{bmatrix}
0\
1\
1\
\end{bmatrix}$
soft zealotBOT
Trenek
raven bridge
and this has no solutions
mellow cedar
and this has no solutions
correct
raven bridge
so those vectors are independent
mellow cedar
so those vectors are independent
correct
which means that the rank is equal to 3 (number of independent vectors)
mellow cedar
thanks a lot for your help 😊
anytime mate
raven bridge
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final saddleBOT
final saddleBOT
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tranquil bone
If $a_0 = 0, a_n = a_{n-1} + 3 \ \text{or} \ a_{n-1} -2$ what are the possible values of a_{100}
final saddleBOT
If $a_0 = 0, a_n = a_{n-1} + 3 \ \text{or} \ a_{n-1} -2$ what are the possible v...
soft zealotBOT
Faq
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
hybrid heath
Can you fix your tex?
tranquil bone
Wait why?
boreal bluff
$a_0 = 0 \text{ and } a_n = a_{n-1} + 3 \text{ or } a_n = a_{n-1} - 2$
soft zealotBOT
Doggo
tranquil bone
Yeah that’s what I said
hybrid heath
Oh I only saw the compile error. I didn't know the bot allowed fixing it
boreal bluff
so I believe you have 100 different "slots" each of which are either 3 or -2
if it's all 3, then you have 300
all -2, you have -200
tranquil bone
Yep
boreal bluff
so if a is the number of 3's, b is the number of -2's, you're solving for a + b = 100 right?
grim nebula
you can trade them in multiples of 5
robust mulch
Yeah
robust mulch
If you switch one from -2 to +3, its like adding 5
robust mulch
Ye
tranquil bone
Inclusive
boreal bluff
I guess that's one way of doing it too
with a + b = 100 you can think of 100 balls separated by a line, and there are 101 slots the line can go in
think a + b = 5, you have balls (O) separated by line (/)
/ O O O O O
O / O O O O
...
O O O O O /
the no. of balls to the left of the line is a, no. of balls to the right is b
grim nebula
3a - 2b given the constraint a + b = 100 is 5a - 200
tranquil bone
Tbh I have no clue what you’re talking about
I think I’ll leave it here
Thanks
.close
final saddleBOT
final saddleBOT
Available help channel!
trim jolt
Small follow up question, i posted a question earlier and received answer:
Q: Im trying to show a row given by b_n = (3n+1)/(n+2) converges. I know the definition and how to apply it when the limit is already known. But we havent done an example in class for when the limit is unknown. Im not sure how to tackle this
A: plug large values of n into a calc and guess the limit
I was wondering whether i could guess the limit by defining a function from R-->R given by b(n) = (3n+1)/(n+2) and applying the limit as defined in calculus to guess the limit for my row.
final saddleBOT
Small follow up question, i posted a question earlier and received answer:
Q: I...
trim jolt
I think it should be okey since "guessing" isnt all that formal so yk why not use calc, but i cant show that the limit of the function is always a good guess for the limit of the row
dusty harbor
just look at the largest powers of n
worldly vale
are you required to use an epsilon-N proof?
trim jolt
are you *required* to use an epsilon-N proof?
Yes i am
dusty harbor
for large n its practically 3n/n = 3
trim jolt
wait nvm
im not sure if do? Im supposed to apply the definition of the limit of a row
which is an epsilon definition
i can type it out if thats necessary
worldly vale
not sure what you mean by "of a row"
dusty harbor
sequence
trim jolt
Oh sorry in english its a sequence
worldly vale
ah gotcha
dusty harbor
in dutch a direct translation would also be row
worldly vale
well if you have to use epsilon-N then you need to figure out the limit by other means (algebra of limits) or long term behaviour like what Gijs said and then do an epsilon-N proof with that value
trim jolt
So calculus wont suffice for a guess for a candidate limit
worldly vale
well you need to know what the limit is to use the definition
so im not sure how you'd use the definition to guess a limit
trim jolt
just take the limit for n to infinity of the function b(n). b(n) being a function from R to R given by b(n) = (3n+1)/(n+2)
then you have a candidate limit and can prove it using epsilon-N
worldly vale
theres no need to consider it as a function
just find the limit of the sequence in any way you know how
for example dividing the top and bottom by n
trim jolt
Hmm okey, that follows from the algebra of limits then?
specifically that the limit of the qoutient of two sequences is the limit of the dividend divided by the limit of the divisor
worldly vale
yes as long as everything converges
limit of quotient is quotient of limit
limit of sum is sum of limit
trim jolt
But then dont i have to prove that the numerator and denominator are sequences aswell
trim jolt
yes as long as everything converges
they dont both converge tho, the denominator diverges
worldly vale
for example dividing the top and bottom by n
did you do this or not
trim jolt
No but thats not the issue, i can see and i know that the limit is 3. Im just asking about how to guess that as a candidate.
Where im stuck is that, if i divide the top and bottom by n, im implying that both the numerator and denominator are sequences. Dont i have to prove that before i can divide by n?
worldly vale
why would you have to prove anything before dividing by n?
(3n+1)/(n+2) on its own is just an expression, we can do what we want to it
trim jolt
Can i claim its still the same sequence then?... We've never really defined operations on sequences in class.
But ig we defined them as functions so that works
But still, then id have to plug in large values to estimate the limit. Imagine i had a differrent sequence say a_n given by 1/a. Then i cant use the algebra of limits to guess a limit.
Using calculus for the function a: R-->R: a-->1/a i can guess a limit tho
Okey i think im just going to far with this. I'll rethink it tommorow when im not so sleepy haha
thanks for the help!
.close
final saddleBOT
final saddleBOT
Available help channel!
rare glen
final saddleBOT
fallen reef
这是什么
final saddleBOT
@rare glen Has your question been resolved?
rare glen
.close
vestal kestrel
hi
vestal kestrel
how to go from top to the bottom one?O.o
vestal kestrel
thats the way i understand
no idea how the other one i supposed to work though :(!
also thank you
paper zodiac
You can do L'hopitals rule but this checks out
paper zodiac
since he tried to factor out x^2, he was able to cancel it
Then it produced an equation with x as a denominator and anything divided by infinity is 0
So this one also checks out
final saddleBOT
@vestal kestrel Has your question been resolved?
heavy laurel
final saddleBOT
vital crag
,w diff sqrt(x) sin(x)
soft zealotBOT
heavy laurel
,w diff sqrt(x) sin(x)
So the way I did it on the blackboard is incorrect?
hearty zephyr
it's the same
heavy laurel
So for a problem like this, I’d use chain rule?
hearty zephyr
yes
heavy laurel
For a problem like this, I know my f(x) and thus also my f’(x), but how do I get my g(x)..?
Anyone?
heavy laurel
For a problem like this, I know my f(x) and thus also my f’(x), but how do I get...
Like how would I apply the chain rule here?
heavy laurel
So 5x^2+4x+2? is the g of x?
hearty zephyr
yes
hearty zephyr
f(x) is root(g(x))
heavy laurel
🤔
heavy laurel
f(x) is root(g(x))
So f(x) is g( ) except it’s under a radical?
heavy laurel
f(x) is root(x)
What is root x here, isn’t it radical (5x^2+4x+2)?
hearty zephyr
to do chain rule you have an inside function and an outside function.
you have root(g(x))
the root( ) is the outside function
so when you take the derivative, you'll take the derivative of the root( ), leaving the inside function alone.
and then multiply by the derivative of the inside
heavy laurel
so when you take the derivative, you'll take the derivative of the root( ), leav...
So I’d multiply 5x^2+4x+2 by 10x+4?
heavy laurel
look through some of the worked examples there
Don’t understand. I understand how g(z)=5z-8, but how is f(z)= radical z?
Why do we decide that it’s radical z?
heavy laurel
it's the function 5z-8 was plugged into
So in my case for this problem my f(x)=(radical (x))?
hearty zephyr
yes
hearty zephyr
yes
heavy laurel
So it would be something like this?:
So it would be like this right?
Like, I’d my process here correct?
As in, I’d get 5x+2/(radical (5x^2+4x+2))?
final saddleBOT
@heavy laurel Has your question been resolved?
heavy laurel
<@&286206848099549185>
vital crag
,w diff sqrt(5x^2+4x+2)
soft zealotBOT
vital crag
yup
final saddleBOT
@heavy laurel Has your question been resolved?
heavy laurel
How would I solve this?
final saddleBOT
How would I solve this?
surreal elbow
so here
it gives you f(0) = 0
and its asking for the derivative of the total composition derivatigve
try substituting 0 in for x in the composition and see what you get
so you'll have f(3f(4f(0)))
final saddleBOT
@heavy laurel Has your question been resolved?
heavy laurel
so you'll have f(3f(4f(0)))
Right?
heavy laurel
and then you have f(3f(0))
Then we get f(3(0)..
surreal elbow
and then.. ?
heavy laurel
and then.. ?
F(0)=0..
surreal elbow
and you are given the derivative at x = 0
heavy laurel
and you are given the derivative at x = 0
So the answer is -2?
final saddleBOT
final saddleBOT
Available help channel!
half marsh
hey i need help
final saddleBOT
hey i need help
grim badger
hey i need help
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.```4 8/8 - 9 8/8 =
grim badger
That's terribly typed. Can you present the question better?
remote cargo
I need help
south vine
asking for help in every channel wont help
half marsh
That's terribly typed. Can you present the question better?
sorry
grim badger
I need help
half marsh
<#488120190538743810>
two quaters minus two eights
final tangle
eights or eighths
half marsh
eights]
half marsh
eights or eighths
are u the one helping me
final tangle
several people are attempting to assist by getting clarification of your question
eight: 8
eighth: 1/8
which one is you question saying
half marsh
eight
grim badger
Can you post an image of the question you are asking?
half marsh
6/2 - 1/2
grim badger
You just presented 3 different expressions when people were asking you for clarification
final tangle
are you spamming us with multiple questions
final saddleBOT
@half marsh Has your question been resolved?
tranquil pine
this is gonna make me seem stupid but can someone please explain calculus to me
tranquil pine
so like
supple copper
I’m taking calc rn
tranquil pine
i dont know anything about calc
im not really a jock
but also yeah
i dont understand the concept
supple copper
oh
well the first unit is limits
so it may be a good idea to start learning that from khanacademy or something
if you’re trying to self learn
supple copper
yeah np
final saddleBOT
@tranquil pine Has your question been resolved?
quick bronze
Ok one more question I swear
final saddleBOT
Ok one more question I swear
quick bronze
(56)I'm pretty sure it's right but if it's not I'm screwed
violet widget
dark crest
help
dark crest
quick bronze
Ok so m is parallel to m
dark crest
okok
quick bronze
And they are being intercepted by the same line
So a good way to start would be to find the angle like to the right yk right next to the one which is 142°
(It's been so long I forgot the names)
raw adder
can someone check me on this adjacent angle of 142 is 180-142 = 38 since they are linear pair
raw adder
x = 38 because alternate angle
raw adder
and again solving for y we get 180-38(linear pair) = 142
dark crest
can someone check me on this adjacent angle of 142 is 180-142 = 38 since they ar...
OHHH
i thought u were asking for someone elses herlp here
sry
quick bronze
Oh well u got it?
quick bronze
Ok so same process as the other, because they are parallel and being intercepted by the same line
They are like corresponding angles or whatever they are called
Y is a vertical angle to 59° so that will be the same
x is a special angle and will also be the same as angle 59°
tranquil pine
An upside down conical container has 1L of water in it, the water is 15cm deep in the container.
How high will the water level be if another 1L is added to the container?
final saddleBOT
An upside down conical container has 1L of water in it, the water is 15cm deep i...
@tranquil pine Has your question been resolved?
tranquil pine
.close
whole ermine
final saddleBOT
stoic mural
what have you tried?
@whole ermine
which step are you struggling with
also dont ping helpers before 15 minutes
and if you do, only ping once
@whole ermine
you there?
alright, i got to go
before i go let me give you some hints:
1)
rewrite the left hand side as a sum
2)
prove it for n=1
3)
now look at n+1
on the left we will have a sum from i=1 up to n+1
rewrite this sum by pulling out the last term, the one with i=n+1
that will give you a sum from i=1 up to n, for which we already proved it, thus we can substitute something in
then show equality by rearranging
final saddleBOT
@whole ermine Has your question been resolved?
stark apex
Determine the exact values of the six trig function values for the angle Ø where the terminal arm of Ø in standard position extends through (-7,1)
final saddleBOT
Determine the exact values of the six trig function values for the angle Ø where...
lethal totem
kinda dumb question
final saddleBOT
kinda dumb question
lethal totem
let's say you have 4 teams in a tournament and you want each team to play each other team exactly once
how do you approach this from a combinatorics perspective
lethal totem
is the correct calculation just:
(4-1) + (4-2) + (4-3) + (4-4)
lethal totem
Matches for A: B,C,D
Matches for B excluding A: C,D
Matches for C excluding A and B: D
Matches for D: (none)
yeah that checks out
so in general we could just say
flint mist
lethal totem
ooh
thanks for that that's actually very helpful
it did not occur to me to treat this geometrically
flint mist
does it answer ur question
lethal totem
so now we have transformed the combinatorics problem into a geometry problem. so just the number of side lengths of an n sided polygon plus the number of diagonals
flint mist
im not sure what ur tryna calculate rn lmao
lethal totem
so now the question is just how many diagonals a polygon has
i'm just trying to generalize here
lethal totem
$\sum_{k=1}^n (n-k) = n^2 - \frac{1}{2}(n)(n+1)$
soft zealotBOT
Mr. Gamer
lethal totem
ok there we go that's the formula
final saddleBOT
@lethal totem Has your question been resolved?
whole ermine
final saddleBOT
finite hound
induction looks reasonable
whole ermine
can you explain how to do the step?
finite hound
well what do you have so far?
finite hound
can you be more specific on what you don't understand?
whole ermine
the questions
finite hound
do you know what induction is? is there another method you're being asked to use to prove it?
whole ermine
my madam said we need to do the calculation, but idk how
can you explain to me or not?
finite hound
i mean it doesn't really look like you've thought about this problem much so far
i am happy to explain, but you have not given me much context on what you do know or what you think you may need to do to prove it
whole ermine
assume that P(k) was true, then would proceed to show that P(k+1) must also be true too?
like that or how
finite hound
yes, that is induction
whole ermine
.closed
vital crag
.close
west brook
Can someone tell me how this can be a one-one function?
final saddleBOT
Can someone tell me how this can be a one-one function?
tranquil pine
if g(x1) = g(x2) implies x1=x2 only then g(x) will be one-one
final saddleBOT
@west brook Has your question been resolved?
west brook
if g(x1) = g(x2) implies x1=x2 only then g(x) will be one-one
Yea, but how do I solve the equation. Cross multiplication, I assume. But do I change the X’s in the equation with X1 and X2?
If so, how do I solve the equation with that
tranquil pine
Yea, but how do I solve the equation. Cross multiplication, I assume. But do I c...
yes obviously
tranquil pine
If so, how do I solve the equation with that
multiply and open brackets
some terms will get cancelled
like x1x2
west brook
(4x1 - 7) x (2x2 + 3) right?
tranquil pine
maybe we can simplify the function
g(x) = 2 -13/(2x+3)
2-13/(2x1+3)= 2-13/(2x2+3)
then you get
2x2+3 = 2x1+3
x1=x2
hard mist
How does this derivative get 'simplified' ? Where does the 8 suddenly come from?
worn mortar
do you know all the derivative rules?
hybrid heath
Have you tried working out the derivative at all?
hard mist
Ah, I see now, the ^3 gets distributed between num and denom
hybrid heath
Are you familiar with chain rule, product and quotient rules?
wanton sentinel
does taking a derivative here affect the 1/2?
final saddleBOT
does taking a derivative here affect the 1/2?
final saddleBOT
@wanton sentinel Has your question been resolved?
worldly vale
Differentiation is a linear operation, it doesn't matter if you times by a constant before or after differentiating
You can "pull the constant out" of the derivative
wanton sentinel
You can "pull the constant out" of the derivative
is it cuz its a ln?
wanton sentinel
What's the derivative of 5x²?
10x
ah i seee
constants are zero if they are alone?
worldly vale
Yes which is 5(2x)
wanton sentinel
1+x for example
worldly vale
Yes the derivative of a constant is zero
But obviously 5x² is not a constant
Nor is a constant times ln(2x+1)
wanton sentinel
yes yes i got it now
so whenever there is a constant multiplied i can just put it out of the differentiation
worldly vale
You can indeed
wanton sentinel
Alright thanks
final saddleBOT
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worldly vale
.close
tiny forge
$\int \frac{2x+1}{x^2-1}$
final saddleBOT
$\int \frac{2x+1}{x^2-1}$
soft zealotBOT
Derek ♡
slow tapir
split numerator
2x/x^2-1 is f'(x)/f(x) = log(f(x))
1/x^2-1 is direct formula 1/2(log(x-1)/(x+1))
tiny forge
why on sloving partial fraction and doing simply give diffrent answers
tiny forge
split numerator
i did this
tiny forge
ohh
final tangle
expressions may differ by a constant
tranquil pine
Rational exponent anyone
tiny forge
i think they are diffrent
final tangle
show work
slow tapir
ah they did by partial frac
tiny forge
and i am getting log |x^2 -1 | + 1/2 log (x-1)/(x+1)
tiny forge
ah they did by partial frac
mhm
final tangle
solution shouldn't have that x^2/2 in there
final tangle
and then log laws should get something equivalent
tiny forge
i tried
final tangle
prod to sum
and quotient to difference
tranquil pine
I was wondering what topic is that
tiny forge
yeah ik that
coefficient goes to power
and that stuff
but if i solve just by splitting terms is my answer right?
why to overthink 
.close
final saddleBOT
final saddleBOT
Available help channel!
heavy lichen
Hello, can someone please help me understand why this result is true ?
heavy lichen
tranquil pine
can you translate this?
heavy lichen
Sure
heavy lichen
can you translate this?
Doesn’t say much, just asks us to "define" g’(t) using the partial derivatives of f
"Définie par" means defined on
I’m fairly sure i have the right expression but i don’t really understand the logic behind it.
tranquil pine
well this is just chain rule isn't it
heavy lichen
well this is just chain rule isn't it
I guessed it must be linked to that yes, but i can’t quite see which composition we’re talking about ?
Oh shit i think i got it
Yeah got it lets goooo
.close
keen haven
I am once again asking for help
final saddleBOT
I am once again asking for help
wise crescent
yo @keen haven
jack can read 5 novels in 1 month
so the number of novels = N
number of months = M
so we get N = 5M
final saddleBOT
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keen haven
Kariok
final saddleBOT
keen haven
Thank you
final saddleBOT
Available help channel!
tranquil pine
where did they get tan60 from the equation? i recognize that tan60 = sqrt3 but im not sure how i can get to that
final saddleBOT
where did they get tan60 from the equation? i recognize that tan60 = sqrt3 but i...
unique aspen
@tranquil pine
tranquil pine
hi
unique aspen
you need to post the question or we don't know what's going on
tranquil pine
tranquil pine
uh huh
unique aspen
yes
tranquil pine
how do you go from sqrt3 to tan60
unique aspen
BC = 12sqrt(3)
AC = 12
BC/AC = sqrt(3)
so tan(BAC) = sqrt(3)
then if tan of an angle is sqrt(3) and the angle is less than 180, the angle has to be 60 degrees
this is just a fact
tranquil pine
i see so i just need to know it
final saddleBOT
tranquil pine
Integration of e^4x
final saddleBOT
Integration of e^4x
ashen shadow
Oh sry it was integration
cloud zephyr
Oh sry it was integration
i was trying to read that
tranquil pine
It's right
I see ma notes are incorrect so confused
ashen shadow
i was trying to read that
What that paper?
cloud zephyr
i was trying to read that
with head turned demon mode
tranquil pine
Thank u
ashen shadow
with head turned demon mode
💀
tranquil pine
.close
humble jay
Help
humble jay
How would you write the prove to this?
A EQUIVALENT A
Equivalent being denoted by the three line equals
worldly vale
What are you even asking
humble jay
How would you write the mathematical prove for this statement
A|=A
Im assuming this. I say if A equivalent to itself then it can be said that A is a logical consequence of it self. 🤔
desert mantle
well on what level are you doing logic
this is either trivial or might be pretty hard
humble jay
I think it's trivial I'm probably over thinking it and just confusing myself
. Close
.close
south prawn
can someone help me with this please
final saddleBOT
can someone help me with this please
south prawn
To carry out a repair on the fifth floor, a plumber wants to bring up a 3 m pipe with the elevator.
The lift is 1.5 m by 1.75 m and 2.2 m high. Will the plumber succeed?
Make a drawing on paper and write the dimensions.
they want me too do something like this
any help please
alpine yacht
so basically they are asking if the diagonal of a rectangular prism with side lengths 1.5, 1.75, and 2.2 is greater or equal to 3 or not.
The formula for the length of the diagonal $d$ of a prism with side lengths a,b,c is $d=\sqrt{a^2+b^2+c^2}$ (3D distance formula)
soft zealotBOT
FireBlazer
alpine yacht
@south prawn Do you know how to continue?
south prawn
uhm
final saddleBOT
@south prawn Has your question been resolved?
cloud zephyr
ye
final saddleBOT
@south prawn Has your question been resolved?
tranquil pine
final saddleBOT
tranquil pine
for part b
i could to -2i +4j + 7k + lambda(AB) or -1i +3j + 8k + lambda(AB), right? (where lambda is just a scalar)
the answer only gives the latter
tranquil pine
i could to -2i +4j + 7k + lambda(AB) or -1i +3j + 8k + lambda(AB), right? (where...
this seems obvious to me
just wantot make sure
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
.close
final saddleBOT
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Available help channel!
vagrant wigeon
Can anyonw help me
final saddleBOT
Can anyonw help me
final saddleBOT
@vagrant wigeon Has your question been resolved?
vagrant wigeon
<@&286206848099549185>
final saddleBOT
@vagrant wigeon Has your question been resolved?
vagrant wigeon
, , \frac {sin\alpha + sin\beta} {sin\alpha} = tan\alpha + 2tan\beta
soft zealotBOT
ytboy
vagrant wigeon
<@&286206848099549185>
vital crag
Plug in beta = 90-alpha and use sum/difference formula
vital crag
Prove it when a + b = 90°
Solve for beta first
vagrant wigeon
sin(beta) = sin(90-alpha)
, , \frac {sin\alpha + cos\alpha} {sin\alpha} = tan\alpha + 2tan\beta
soft zealotBOT
ytboy
vagrant wigeon
what after it
vital crag
I'd work on the right side actually
vagrant wigeon
hmm then
vagrant wigeon
I'd work on the right side actually
, , \frac {sin\alpha + sin\beta} {sin\alpha} = tan\alpha + 2tan (90 -\alpha)
?
soft zealotBOT
ytboy
vital crag
Right. You just need to express tan in terms of sine and cosine and then use difference angle formula
vagrant wigeon
wait lemme do
, , \frac {sin\alpha + sin\beta} {sin\alpha} = \frac { sin\alpha } { cos\alpha} + 2cot\alpha
soft zealotBOT
ytboy
vagrant wigeon
see @vital crag
, , \frac {sin\alpha + sin\beta} {sin\alpha} = \frac { sin\alpha } { cos\alpha} + 2 \frac { cos\alpha } { sin\alpha}
soft zealotBOT
ytboy
vagrant wigeon
now ?
final saddleBOT
@vagrant wigeon Has your question been resolved?
merry ridge
Given that P(A)=0.8 , P(B)=0.6 and P(AANDB)=0.40 . Are the events A and B independent?
trail lance
Given that P(A)=0.8 , P(B)=0.6 and P(AANDB)=0.40 . Are the events A and ...
Context not clear enough
Because I got 0.48 for P(A and B)
merry ridge
trail lance
so they’re dependent
trail lance
If they independent, then the probability would’ve been 0.48
But the question gave 0.4
merry ridge
ohhhh
one more question
this would be dependent right
since its 1/20 then 1/19
or wait
it would be independent since its replaced right?
trail lance
it would be independent since its replaced right?
yes
the probability for each turn would be the same
because it’s teplaced
white rock
final saddleBOT
white rock
can i get help please i dont understand this
final saddleBOT
@white rock Has your question been resolved?
final saddleBOT
white rock
.reopen
final saddleBOT
✅
white rock
please help me
final saddleBOT
@white rock Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
twilit brook
Hi
twilit brook
In the picture i got a math solution for finding a impedance i wanna know why they used z1 =Xc//Xl and Z3 =Z2//xc i know what these letters stand for but can someone explain why they use this?
The Z1=Xc//Xl for example is shortened for (Xc*Xl)/Xc+Xl)
final saddleBOT
@twilit brook Has your question been resolved?
twilit brook
<@&286206848099549185>
jovial wigeon
A connected graph with N nodes has at least N-1 edges. Does that imply that a non-connected graph with N nodes has at most N-1 edges?
final saddleBOT
A connected graph with N nodes has at least N-1 edges. Does that imply that a no...
jovial wigeon
my brain isn't braining anymore
hearty zephyr
it doesn't tell you anything about a disconnected graph
cobalt lodge
degenerate example: 3 nodes, and 50 edges between the same 2 nodes
jovial wigeon
i see, what if we restrict ourselves to simple graphs (no multiple edges)?
cobalt lodge
or a less stupid example for simple graphs: 5 nodes, 4 of the nodes form a complete graph K4 with 6 edges
agile tangle
Heyy.
agile tangle
So I came to show my work for a answer, I know I could just calculate but I don’t have a calculator on my phone plus I can’t download it since don’t remember my AppStore password but here is my work.
Is this true?
soft zealotBOT
magic gyro
yeah
agile tangle
oh mk ty
grim badger
So I came to show my work for a answer, I know I could just calculate but I don’...
You can use google, google is a calculator
agile tangle
You can use google, google is a calculator
oh yeah i forgot but i still need to show my work.
grim badger
Yes, and?
agile tangle
I have a milestone benchmark practice next week.
grim badger
You do the problem like what you did and use google to check your answer
grim badger
Yes, and? Like I stated, you can do the work on your own, get some answer, then use a calculator to check
If you get what the calculator gets, then the work is correct
If it's different, either you typed it into the calculator wrong or you did the math wrong
agile tangle
Sorry, I don’t do that plus like I said I have a millestone benchmark graded practice next week and I can’t just calculate it I rather show my real work. discussion ended.
grim badger
Yes, and?
frigid sierra
what dldh is saying is that u can do ur own work
but to check if ur answer is right or not
use a calculator
it’s just for checking
agile tangle
k I’ll do that.
frigid sierra
grim badger
Sorry, I don’t do that plus like I said I have a millestone benchmark graded pra...
You can do the work yourself, and you can check your final answer using a calculator instead of relying on others to do it for you
agile tangle
You can do the work yourself, and you can check your final answer using a calcul...
k tyy
final saddleBOT
@agile tangle Has your question been resolved?
timid tulip
Need a alternative to differntiation
final saddleBOT
Need a alternative to differntiation
vital crag
why can't you use derivatives
oh number of turning points
what's a turning point? local min/max?
timid tulip
both
also its coz i need to work it out to check if the roots of the derivative are real so
there's a lot of time thats wasted
final saddleBOT
@timid tulip Has your question been resolved?
final saddleBOT
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Available help channel!
tawdry cloak
hey
tawdry cloak
if for a poission random variable Xn, the parater is lambda, what is the parameter for X^2 n l
final saddleBOT
@tawdry cloak Has your question been resolved?
jade shale
dry light
I was just gonna reply to your tangent line question but then you closed it
And then it locked me out
dry light
This one here I'm pretty sure you can find dp/dq and then raise everything to the -1 power
jade shale
This one here I'm pretty sure you can find dp/dq and then raise everything to th...
i found dp/dq
do i just
inverse it
jade shale
oh thx
dry light
Not inverse it
jade shale
never thought of that
dry light
Take the reciprocal
jade shale
yeah thats what I meant
jade shale
Find dy/dx
Idk how to implicit e^(x/y)
jade shale
sec lemme try
dry light
Lmk what you got when you differentiate only e^(x/y)
jade shale
e^(x/y)(y-xy')/y^2
dry light
Yeah
jade shale
and on the other side i have 1-y'
dry light
Yes
jade shale
2
y=2x-1
yeah thats the answer
Thanks for the hel
help
appreciate it
.close
final saddleBOT
final saddleBOT
Available help channel!
ashen shadow
How many solutions a polynomial will have if it's degree is -1
final saddleBOT
How many solutions a polynomial will have if it's degree is -1
amber holly
You mean the amount of solutions to a + b/x = 0?
ashen shadow
Yes you could say but not specifically a+b/x I was talking about any type of polynomial with highest power 1 and unique power -1
amber holly
So ax + b + c/x = 0?
ashen shadow
1/x=0
amber holly
1/x = 0 has no solutions
ashen shadow
But why?
soft zealotBOT
amber holly
1/x = 0 has no solutions
Let's assume there is a solution
ashen shadow
If we see the graph
ashen shadow
Let's assume there is a solution
Ok
ashen shadow
Hm