i got (-inf, -4] U {2/7, inf]
#help-27
faint zinc
can you show your work?
faint zinc
so were you entering this into some automated grading system?
faint zinc
did you enter in exactly "(-inf, -4] U {2/7, inf]"
because technically, this is wrong in 2 ways
even though it is morally correct
both I thought were typos
zenith forge
faint zinc
inf is always non-inclusive
zenith forge
ah okay
do you know why this would be wrong?
should one of the circles be open?
faint zinc
that looks correct to me.
zenith forge
its still all showing as wrong
faint zinc
is this another inf] vs inf) thing?
faint zinc
positive
faint zinc
truuuuu
devout snowBOT
@zenith forge Has your question been resolved?
restive river
How to calculate the combined transformation of 3 matrices?
devout snowBOT
How to calculate the combined transformation of 3 matrices?
small jackal
How to calculate the combined transformation of 3 matrices?
Try doing each separately in the order they appear
polar wharf
Depends on the situation but in general calculate the matrix of transformation for each one then multiply them in order to the object you're transforming iirc
woven radishBOT
polar wharf
Basically multiply those 3 matrices in that order iirc
lean grove
Hiiii I'm new here
devout snowBOT
Hiiii I'm new here
eager nova
Do you have a specific question?
lean grove
not yet
eager nova
These channels are for specific questions, for unrelated or offtopic you can talk here #chill or here #discussion
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bright tangle
Where did I go wrong here
devout snowBOT
Where did I go wrong here
lunar harbor
Where did I go wrong here
Dividing by $2 \cos x-1$ means you lose the solutions where $2 \cos x-1=0$
woven radishBOT
Civil Service Pigeon
bright tangle
Okay is there any way to not devide?
lunar harbor
factor ... ?
lunar harbor
$(2 \cos x-1)(\cot x+1)=0$
woven radishBOT
Civil Service Pigeon
lunar harbor
I got that the answer is d
you forgot about periodicity
bright tangle
**Civil Service Pigeon**
Where did the one with cot come from
lunar harbor
$\cot x (2 \cos x-1)=-(2 \cos x-1)$
woven radishBOT
Civil Service Pigeon
lunar harbor
$\cot x (2 \cos x-1)+(2 \cos x-1)=0$
woven radishBOT
Civil Service Pigeon
lunar harbor
$(2 \cos x-1)(\cot x+1)=0$
woven radishBOT
Civil Service Pigeon
lunar harbor
just add the periods on and you're done
lunar harbor
for cos, yes
lunar harbor
yeah
bright tangle
Answer choice A?
lunar harbor
,w 2 cos x cot x - cot x = 1 - 2 cos x, 0 \leq x <2pi
woven radishBOT
lunar harbor
I got that the answer is d
nvm I missed the [0, 2pi) part earlier
you were right originally
I was gonna say what the solution set would be if they wanted the general solution
but neither A nor C are right
bright tangle
😭
lunar harbor
I was gonna say what the solution set would be if they wanted the general soluti...
it would be $\frac{\pi}{3}+2k \pi, \frac{5\pi}{3}+2k \pi, \frac{3\pi}{4}+k\pi$
woven radishBOT
Civil Service Pigeon
bright tangle
nvm I missed the [0, 2pi) part earlier
Yes I saw that which is why I was confused there would be no k if we were limited to just 2pi
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latent sundial
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supple knot
I'm stuck on this problem. Does anyone know how to proceed?
your f'(x) is wrong
$\frac{d}{dx} (x-1)^n = n(x-1)^{n-1}$
woven radishBOT
riemann
devout snowBOT
@latent sundial Has your question been resolved?
latent sundial
thank you! I'll try again
rough hatch
devout snowBOT
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rough hatch
How do u do th8s
devout snowBOT
@rough hatch Has your question been resolved?
ocean shale
Not sure if this is the correct way to do this but it was wrong
devout snowBOT
Not sure if this is the correct way to do this but it was wrong
hasty forge
grim anvil
You've chosen the right answer
eager nova
!occupied
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eager nova
You did the wrong order
It would be 8/24-1/24
But anyways, if you don’t want to think too much about it just do it absolute value, cause area is always positive
ocean shale
You did the wrong order
i did? I thought its upper - lower?
eager nova
But the function is decreasing
ocean shale
But the function is decreasing
so when the function is decreasing, its lower - upper?
eager nova
Oh mbo
No
U missunderstood me
Your integral is -1/3x^3 right?
-1/24 -(-8/24)
That should solve your problem
I meant you did the opposite cause i thought u simplified
ocean shale
Your integral is -1/3x^3 right?
1/3x^3
ocean shale
The antidirevative of 1/x^4 is 1/3x^3 right?
ocean shale
reverse power rule
eager nova
1/x^4 = x^(-4)
.
ocean shale
Yeah 1/x^4 = x^-4, and the antidirevative of x^-4 = x^-3/3 which is equal to 1/3x^3
oh wait
eager nova
Why do u divide by 3?
ocean shale
divide by neg 3
eager nova
Yes
ocean shale
okay so its still upper - lower
eager nova
Yes yes
ocean shale
i just messed up the reverse power rule
eager nova
Correct
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solid osprey
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solid osprey
how can i explain it with using pigeon hole principle?
like i know its baaically floor(10000/7)-1000 but how can i explain how i got the numbers
placid minnow
by doing it
solid osprey
??
placid minnow
by doing it
solid osprey
what?
placid minnow
idk set the pigeons to like the 1000 sets S1, S2, ..., S1000.
and the holes to the 7 possible remainders when an integer is divided by 7: 0, 1, 2, 3, 4, 5, 6.
there must be at least one hole containing at least ⌈1000/7⌉ or 143 pigeons
actually i should probably floor instead of round
142 pigeons
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ashen dagger
whats another word for velocity decreasing
or rather just change in velocity
yeah
so you have vi = 0.5 m/s
a = -0.05 m/s^2
remember you need 3 pieces of information for the big 5
whats the last piece of info you have
yeah
and what are you looking for
yeah so you dont need distance
whats the one equation without distance
yeah
can you solve for t from there
np
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ashen dagger
yeah exactly
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tropic sinew
Does anybody know how I can practice computing Eigenvalues and Eigenvectors? (Is there a website where they give me the correct solution? Sometimes I have a problem finding the Eigenvalues after calculating the determinant :c I would like to practice that)
devout snowBOT
Does anybody know how I can practice computing Eigenvalues and Eigenvectors? (Is...
solar goblet
i recommend using erdman
they have exercises for linear algebra, including eigeneverything
devout snowBOT
@tropic sinew Has your question been resolved?
tropic sinew
i recommend using erdman
thanksss !!
summer igloo
Im done mentioning the pain this problem causes me often shrug unless its in a critical or inquisitive context shrug.
1. They divided the entire problem by A to remove A. Doing so would appear to divide the overall functions output and affect everything, how is this still equivalent?
2. Are B/A and C/A division or fractions (though theyre probably the same thing).
3. What was the purpose and explanation behind moving C/A to the right of the equation?```
devout snowBOT
> ```lua
> Im done mentioning the pain this problem causes me often shrug unless...
lyric hornet
> ```lua
> Im done mentioning the pain this problem causes me often shrug unless...
-
Diving by constants changes nothing about the equality (unless it's 0, 0 is tricky)
-
Treat b/a and c/a the same way you would treat b and c normally, just constants.
-
we move c/a to the right side to prepare for completing the square. :)
summer igloo
I do not believe your response encapsulated any of the information I requested beyond requesting that I simply understand already which I failed to do despite trying at 100% for hours to understand even the first one.
lyric hornet
summer igloo
e.g., how this response does not actually answer the question, and instead, focuses on a logical truth rather than the explanation behind why that is the case or the steps taken to arrive at that conclusion and how to make said steps.
lyric hornet
dividing by a constant does not change the output for the same input because you are changing the output congruent to how much you are changing the input
if both you and I have 2 pizzas
and we both half our supplies
we both have an equal number of pizzas
smoky nimbus
They divided the entire problem by A to remove A. Doing so would appear to divide the overall functions output and affect everything, how is this still equivalent?
Try it yourself
3x + 6 = 9
Dividing by 3, you get (3/3)x + 6/3 = 9/3 or x + 2 = 3
Both are equivalent
restive river
> ```lua
> Im done mentioning the pain this problem causes me often shrug unless...
1- you want to get the value of X which will hold two values because it's a quadratic equation so you need to get rid of A
2- you could say so
3- to make both sides equal
summer igloo
also a little off topic but thank you for actually trying because earlier alot of people were just being toxic to the point even a mod asked me to close the post because they thought i was trolling due to how many ppl were attacking me due to my confusion over a question.
and then after all that 1 guy came along and answered almost everything so yea
summer igloo
https://tenor.com/view/walter-white-breaking-bad-falling-pain-sad-gif-20448687
me when i did not realise they were dividing X and that X was the input value:
alr thank you
.close
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lyric hornet
> also a little off topic but thank you for actually trying because earlier alot...
there's no such thing as a bad question :) was just a little confused on your wording sorry 😅 esp if my answers weren't the best
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summer igloo
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meager carbon
I need help getting past this point. I’ve replaced f(x) with x^3 but I can’t see how I could simplify this further.
devout snowBOT
I need help getting past this point. I’ve replaced f(x) with x^3 but I can’t see...
lapis sparrow
I need help getting past this point. I’ve replaced f(x) with x^3 but I can’t see...
Is this calculus 1? Or is it pre calc?
meager carbon
pre calc
lapis sparrow
Okay so you have (x+h)^3 - x^3
I'm going to use h in place delta x
You can multiply (x+h) (x+h) (x+h)
In other words, expland the cubed term
does that make sense?
meager carbon
it does but how would i go about multiplying them together
lapis sparrow
Okay so if you have x^2 - 1 right?
Y'know how you can factor it into (x-1)(x+1)?
Then if you multiply them together you get x^2 - 1?
meager carbon
yes
lapis sparrow
Okay so esseentially you have the factorized form of your cubed function here
Where you have (x + deltax)^3
So if something is cubed, what does that mean?
like if I have 2^3 what does that mean?
meager carbon
it multiplies by its self twice?
lapis sparrow
Close, three times
so you'd have 2 * 2 * 2
Waiit
Yeah you explained it right I think
I think you had the right idea I just interpreted it wrong
You meant what I had put right?
meager carbon
yea
lapis sparrow
ok so think about that same idea but multiplying that binomial twice
So (x+h) * (x+h) * (x+h)
Does that make sense now?
meager carbon
yes
lapis sparrow
Alright work that out quickly at let me know what you get
meager carbon
So doing that I got
meager carbon
yea
lapis sparrow
Okay so for thee numerator, you can cancel some terms out
meager carbon
is it the x^3's
lapis sparrow
Yep!
meager carbon
and so i just divide it by the h at the bottom?
lapis sparrow
Well yes
but I would just factor the h
So you have h(3x^2 + 3xh + h^2)/h
Then the h's cancel out
lapis sparrow
Youre all good
meager carbon
.close
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west wing
this is driving me crazy
devout snowBOT
this is driving me crazy
polar wharf
Can help to start with the diagram
Also... what unit are you in? In your class
The method to get this answer could vary slightly depending on the tools they gave you (also what class you're in)
west wing
Also... what unit are you in? In your class
this is mechanics (physics) first semester
polar wharf
So you're doing this like a vector problem?
west wing
Yeah exactly
polar wharf
Ok great that's a bit easier than the algebra ii way
So let's come up with vectors to describe the movements
We'll make different vectors for each leg of the journey
East and North we will orient as "right" and "up"
west wing
Okay okay
west wing
Ax = 41 km
Ay = 0 km
polar wharf
Yes you could write it
< 41, 0 >
Or sometimes with square brackets
How about leg 2
25 km north
west wing
(0i + 25j)
west wing
Ofcourse
polar wharf
Ok cool
Then finally the 3rd leg
This one is trickier
Because it isn't straight north, south etc
west wing
Yeahh ikik
polar wharf
Ok so based on the description you gotta figure out the angle
west wing
it's <22,05i + 13,78j >, that's what I got for the 3rd movement
polar wharf
What was the angle you used
west wing
32 deg
west wing
oh shit
polar wharf
They didnt give you standard position
They gave you the bearing
Which you have to convert to the standard position first
Then you can do the rest normally
west wing
Okay okay, how do I convert it to the standard position?
polar wharf
So standard position is where pointing straight right is 0
And straight up is 90 degree etc
west wing
Okay yeah
west wing
isn,t east of north in the first quadrant
polar wharf
Then rotate eastward (to the right) by 32 degree
It is in 1st quadrant but so is the correct angle
west wing
Okayy so technically it's 90-32 deg
polar wharf
Yessss
Exa6
Exactly
So that's the tricky thing about these bearing problems
You have to first translate them to the usual angles
west wing
Yeah it's really weird and annoying since I'm always confused by the angles
polar wharf
Just remember those words east from north, west from south etc
Those are bearings your "real" angle is the one where right is 0
west wing
now I add them up and find the magnitude
west wing
71,46 km
now for (b)
I got 41,18 deg after using the magnitude of the sum
is that exactly the answer or am I going to need to subs 180 or do some extra steps
Oh it's correct
thank you so much I appreciate it
west wing
ofcourse it was incredibly helpful
polar wharf
The final answer was the magnitude because the magnitude of that sum would represent the overall length of the movement from the 3 vectors
west wing
Simple, it's just every summer is like an amnesia phase for me and I forget everything
polar wharf
Lol yes can relate
devout snowBOT
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rancid flax
Would X^-4 also be correct here? I flipped X^-5, and X^1 to make the -5 positive. Then it would be X^1/X^-5. Which would be X^-4
devout snowBOT
Would X^-4 also be correct here? I flipped X^-5, and X^1 to make the -5 positive...
supple knot
Would X^-4 also be correct here? I flipped X^-5, and X^1 to make the -5 positive...
No it's right on the screenshot
jagged harbor
Would X^-4 also be correct here? I flipped X^-5, and X^1 to make the -5 positive...
x^1 / x^(-5) is not x^(-4)
and x^1 / x^(-5) is not equivalent to the given expression
rancid flax
why is that wrong? I thought you were supposed to flip the equation to get a positive number, then when it's divisible you subtract the exponents
jagged harbor
you also had said you flipped the x^(-5) down to make it positive, but then wrote it as negative again anyway
if you had really flipped everything it should be x^(-1) / x^5
devout snowBOT
@rancid flax Has your question been resolved?
vivid estuary
Does my answers look ok? Want to make sure I got the defintions down correctly
jagged harbor
your solution for (c) is too wordy for the wrong reasons. we don't care about these infinitely many solutions to some system, especially if we never use it. it's the linear dependency that asserts that perhaps C is a linear combination of A and B. your solution should justify why C = A+B as you claim
(d) is uninspiring and poorly worded, but the choice for D is acceptable and requires no computation. saying D = A+B+C suffices
vivid estuary
your solution for (c) is too wordy for the wrong reasons. we don't care about th...
So more like this?
jagged harbor
much nicer and to the point, cool
since it's all just a calculation you can throw in words. like, "we assert/see that C = a_1A + a_2B with a_1=a_2=1. indeed, [calculation on second line]" but like, whatever lol
or like, "we verify that C = a_1A + a_2B with a_1=a_2=1 in the following: [calculation]"
some words to show you're human, not too many to get to the point 🤷
but like
it's fine
uninspiring questions get uninspiring answers 
love that you're indicating where the solution goes in italics by the way
good presentation
devout snowBOT
@vivid estuary Has your question been resolved?
frosty cipher
I'm so confused 😕 would love some help!!!
devout snowBOT
I'm so confused 😕 would love some help!!!
@frosty cipher Has your question been resolved?
polar niche
Triangle ABO is isosceles
B is 50 degrees because 180-130=50
A is also 50 degrees because it is opposite to a side that is congruent to the side opposite B
Triangle interior angles sum to 180, so 180-50-50=30, which is x
D is 130 because if you notice, the line through DE is parallel to the line through BA
Then 180-130=50 for y
frosty cipher
ohhh tysm thats so easy thxx!!!
polar niche
Np
frosty cipher
.close
robust drift
devout snowBOT
robust drift
Stuck on d
storm gyro
if P takes B to E and Q takes E to F, and N takes B to F, then it stands to reason that N=QP (edit: corrected order of P and Q
You have both P and Q so that's just a simple matrix multiplication
and maybe there's one more piece of information that determines k
robust drift
It says the determinant of N is 2
storm gyro
it does indeed say that
storm gyro
and maybe there's one more piece of information that determines k
hint hint this part is why they tell you that |N|=2
robust drift
Yes
Thanks I found k
But how do I find the vertices now
Oh nvm got it
Thanks a lot
storm gyro
no worries
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full nymph
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full nymph
So how do i solve this
faint gorge
I would do polynomial division to see if it gets to a nicer expression
full nymph
it has a reminder
timid violet
So how do i solve this
This is a case of improper function means you need to divide to divide this
full nymph
Ok
timid violet
how did the quotiant came in fraction?
full nymph
huh?
timid violet
I think you need to recheck your division
timid violet
Yeah that great now intergration of Q is done easily using formulas
faint gorge
The remainder prob some with log or arctan
timid violet
Ok there you go since now everything is simplied it's easy now
timid violet
why are itegrals such a pain
It's called calculas
weak cove
i hate itegrals calculas
faint gorge
i hate itegrals calculas
weak cove
<:bnuuy:1270384601654886580>
😓
timid violet
<@799929153319075861>
its easy
just mutiply the brackets and done now its x^n formula
full nymph
Ohhh ok
faint gorge
,,- \frac{1}{27} \cdot \frac{287x - 183 }{3x^2+5x-3}
woven radishBOT
bacc
faint gorge
partial fraction decomp is also an option but ugly numbers
full nymph
just mutiply the brackets and done now its x^n formula
I will just use this method
faint gorge
What is this method
timid violet
Omg mistake in calculas can cost you a lot
faint gorge
One log two arctan
mystic scarab
Wasn't arctan for irreducible denominators?
faint gorge
**bacc**
The idea is here to split the fraction
And modify the numerator
So that we can apply natural log and arctan
woven radishBOT
bacc
faint gorge
In the first term we want 6x + 5 in the numerator
And for the second we would complete the square
of the quadratic in the denominator
full nymph
Ok i am back
faint gorge
,,- \frac{287}{27 \cdot 6} \cdot \frac{6x + 5}{3x^2+5x-3} + \frac{287}{27 \cdot 6} \cdot \frac{5}{3x^2+5x-3} + \frac{183}{27} \cdot \frac{1}{3x^2+5x-3}
Only thing left is to complete the square of 3x²+5x-3
And write it in the form of 1 + y²
where y = ax
woven radishBOT
bacc
faint gorge
I hope this helps
full nymph
Hopefully i will make something out of this
gilded zealot
just wanted to know if youre allowed to use the double angle identity for cos like this
devout snowBOT
just wanted to know if youre allowed to use the double angle identity for cos li...
gilded zealot
the first line is the equation i have and, i tried to simplify it using the double angle identity and squred cosine rule
crude wasp
yeah that's valid
devout snowBOT
cold bough
walk like a boss
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whole hemlock
Please could I ask if someone could double check my b and c, I believe I’ve done it right but I’m not 100%.
devout snowBOT
Please could I ask if someone could double check my b and c, I believe I’ve done...
gusty nexus
multiply both sides by e^x and let k = e^x
whole hemlock
multiply both sides by e^x and let k = e^x
I believe that’s what I did
I made it = to y
And then solved from there
gusty nexus
so it is solved?
gusty nexus
btw you find solutions for y, not x
don't forget to do y = e^x at the end
charred frigate
can someone here explain to me how to get from equation 3 to 4?
devout snowBOT
can someone here explain to me how to get from equation 3 to 4?
charred frigate
im doing it based on my own work.. but that one line confuses me
honestly im just confused on 6.26 and so on..
equation 6.26
devout snowBOT
@charred frigate Has your question been resolved?
devout snowBOT
@charred frigate Has your question been resolved?
charred frigate
wait lemme really explain this
so essentially i have a question that uses this work, but diffrrent values
i am trying to integrate my work with the book process
here is what i have so far
all that is highlighted is what matches the book
devout snowBOT
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charred frigate
.close
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compact blaze
Is dividing x by 2 under modulo 2^n with n > 0 undefined?
Or is it ok to divide by 2 in a usual sense if x is even?
Or maybe it depends on the context/field that's being worked?
devout snowBOT
Is dividing x by 2 under modulo 2^n with n > 0 undefined?
Or is it ok to divide ...
rotund umbra
$$\frac{x}{2} (\mbox{modulo}; 2^n) = r \iff \exists; s \in \mathbb{Z} .; \frac{x}{2} = s 2^n + r$$
It works the same as any modulo group.
bright lagoon
it is totelly okey if i the mod deletes this but i was wondering how to get better at math. I i dont understand the math at all. is there youtube chanels, websites whatever that helps me get better in math.
woven radishBOT
Shuba
compact blaze
It works the same as any modulo group.
Does it? Usual pairs of the integer you want to divide by and the modulo are coprime
In this case it isn't so it doesn't have a multiplicative inverse, no?
rotund umbra
Does it? Usual pairs of the integer you want to divide by and the modulo are cop...
if you're looking for integer solutions, then no because you can't divide in the ring of integers.
If you're looking for solutions in a field, then it works the same.
By which I mean, if x is an integer, then x / 2 is not a valid operation.
compact blaze
Umm
rotund umbra
And you can't say x (mod 2^n) = 2r either because we might have 2r > 2^n
compact blaze
By which I mean, if `x` is an integer, then `x / 2` is not a valid operation.
Under what modulus?
I don't quite get it
rotund umbra
In the ring of integers modulo $2^n$, you can't do $x/2$ because that's not an integer.
However, if you want to define a ``$\mbox{mod}$'' operation on a group containing the integers such that
$$x ;\mbox{mod}; n = r \iff \exists; s \in \mathbb{Z} .; x = sn + r$$
$x ;\mbox{mod}; n$ in the ring of integers determines the representative in the ring of integers modulo $n$, i.e. it functions the same as a modulus, but can be applied to bigger groups, like the reals where you can divide, and therefore $x / 2 ;\mbox{mod}; 2^n$ is a perfectly fine operation.
woven radishBOT
Shuba
rotund umbra
Let me give you an example. Consider the real number $x = 25$ and $n=3$. Then
$$\frac{x}{2} ;\mbox{mod}; 2^n = 12.5 ;\mbox{mod}; 8 = 4.5$$ because $12.5 = 8*1 + 4.5$
woven radishBOT
Shuba
stone stump
well there are two options, either there is no x with 2x=y mod 2^n for whatever y you want to divide by 2
or there are actually two different values of x with 2x=y mod 2^n
either way, dividing y by 2 makes no sense
rotund umbra
well there are two options, either there is no x with 2x=y mod 2^n for whatever ...
you can't say x/2 mod 2^n = r <=> x mod 2^n = 2r because 2r might be bigger than 2^n.
stone stump
and this will always be the case when the number you want to divide by is not coprime
either there is no possible x or there are several possible x
compact blaze
and this will always be the case when the number you want to divide by is not co...
Yeah, so that's what I was asking
So if they're not coprime it doesn't make sense
stone stump
a similar question which would make sense is considering the function f(x)=2x and then asking for the preimage f^-1(y)
which would then either be empty or all the possible x
just in case you want a formalism which somewhat allows this idea
devout snowBOT
@compact blaze Has your question been resolved?
devout snowBOT
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hidden pier
devout snowBOT
hidden pier
can someone check my answers
7.5 or -7.5
0 or -1.25
1.5 or -6.5
i think theyre all wrong but i dont even know
solid osprey
what are you trying to find here? x?
placid minnow
7.5 or -7.5
0 or -1.25
1.5 or -6.5
first one is right
second one you have the 0 correct
third one you have all wrong
hidden pier
yes
placid minnow
what are you trying to find here? x?
it would be quite weird if they werent solving for x
hidden pier
first one is right
second one you have the 0 correct
third one you have all wr...
elaborate
?
tropic dune
How first one right
placid minnow
How first one right
let me ask you this: how would it not be right?
tropic dune
My fault I’m slow
hidden pier
i kinda need specifics
on how to get the other ones right
placid minnow
on how to get the other ones right
you told me to elaborate, what do you want me to elaborate on
hidden pier
to elaborate on what i did wrong on the other ones to get them right
polar dagger
3rd one is x = 0 or x = -5/2
placid minnow
3rd one is x = 0 or x = -5/2
dont just give them the answer without the process lol
placid minnow
to elaborate on what i did wrong on the other ones to get them right
you have:
2|4x+5| - 3 = 7
polar dagger
My bad I can send the process too :))
placid minnow
what is the first operation in opposite of PEMDAS on the lhs?
hidden pier
what is the first operation in opposite of PEMDAS on the lhs?
the 3
placid minnow
-3* but yeah
hidden pier
-5 and 5
wtf
isn't you make the thing it eqals negative and positive
that sounds wrong
placid minnow
isn't you make the thing it eqals negative and positive
You make the lhs equal to either plus or minus the rhs
idk what escanor is on lol
hidden pier
cant the answer not be a negative though?
placid minnow
the x is inside the absolute value
hidden pier
what does that mean exactly
placid minnow
absolute value means:
|-x| = x
placid minnow
yes i know
then how come you dont get why it can be negative
hidden pier
because in the videos i was watching it was saying the answer cant be a negative
idk
something about it cant be a negative
alr bet lets do the next 1
placid minnow
because in the videos i was watching it was saying the answer cant be a negative
probably heard it wrong
placid minnow
alr bet lets do the next 1
i mean its kind of self expanatory after the last one
if you still get it wrong ask me
hidden pier
if you still get it wrong ask me
is it 10 and -2
placid minnow
is it 10 and -2
you swapped the negative signs somehow
hidden pier
i just saw it
placid minnow
so got it?
hidden pier
yes
placid minnow
great you can .close now
devout snowBOT
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Available help channel!
placid mortar
how do i approach this problem
devout snowBOT
how do i approach this problem
placid mortar
my trig is like a 2/10
placid minnow
how do i approach this problem
i mean just evaluate the left and right hand limits
placid mortar
i mean just evaluate the left and right hand limits
what
placid minnow
what is the limit of that as theta approaches a little less than 0 and a little over 0
placid mortar
what is the limit of that as theta approaches a little less than 0 and a little ...
idk
0.001
-0.001
?
placid minnow
have you learned the unit circle yet
placid mortar
uhh
i was supposed to in math analysis but i didnt do the class with trig
so i dont know it
placid minnow
so you somehow ended up here without learning trig?
placid mortar
yes
placid minnow
well thats weird
placid mortar
am i cooked
placid minnow
kind of
you need a very strong understanding of basic trig
if this isnt urgent then I suggest first studying that
placid mortar
if this isnt urgent then I suggest first studying that
its due tomorrow
placid minnow
well dang
placid minnow
its due tomorrow
so like
you learned absolutely no trig
do you at least know the trig identities
placid mortar
a bit
restive river
csc and cot confuse me. I'll just use sin, cos. Using those, the expression is $(\frac{1}{\sin x} - \frac{\cos x}{\sin x})/(\frac{x}{\sin x})$
You can just multiply numerator and denominator with sin x to get
$\frac{1 - \cos x}{x}$ if I'm not mistaken
woven radishBOT
gautamdb
restive river
Then to calculate limit as x->0, because numerator and denominator approach zero, use l'Hospital, so differentiate numerator and denominator, to get $\frac{\sin x}{1}$. Limit as $x\rightarrow 0$ is then just $\sin 0 = 0$.
woven radishBOT
gautamdb
devout snowBOT
@placid mortar Has your question been resolved?
woven radishBOT
gautamdb
placid mortar
Then multiply all with sin theta
wha
restive river
You can multiply numerator and denominator by the same thing
placid mortar
oh to get a common demoninator right
restive river
So multiply numerator and denominator by sin theta
restive river
oh to get a common demoninator right
No, to simplify
placid mortar
restive river
Yes
restive river
**gautamdb**
Then this
restive river
$\frac{1 - \cos \theta}{\theta}$
woven radishBOT
gautamdb
placid mortar
$\frac{1 - \cos \theta}{\theta}$
how does it simplify to that
is it cause the bottom cancels
gusty nexus
yes
placid mortar
.close
potent pike
devout snowBOT
potent pike
How am i supposed to find this
topaz axle
it says the tokens are worth 5 and 45
devout snowBOT
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Available help channel!
ebon belfry
devout snowBOT
ebon belfry
im stuck at
r/5 + 0.3 = c/a
0 clue how we got c=a(r/5+0.3)
ok nvm
i had brain fart i forgot im solving for c and that i legit just needed to multiply by A 😭
.close
devout snowBOT
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ember patrol
I have elementary matrices $E_1$ through $E_4$ and I am asked to do left multiplication. Does this mean I’m starting at $E_1$ and working my way down or am I starting at $E_4$ and working up?
devout snowBOT
I have elementary matrices $E_1$ through $E_4$ and I am asked to do left multipl...
woven radishBOT
KySquared
ember patrol
<@&286206848099549185>
devout snowBOT
@ember patrol Has your question been resolved?
dapper quail
I need to check if this boolean simplification is correct
devout snowBOT
I need to check if this boolean simplification is correct
woven radishBOT
severe sparrow
wolfram will not rotate it for you
it might
dapper quail
So could you help me with boolean algebra
severe sparrow
im not sure I understand your work
dapper quail
For the problem
dapper quail
i don't understand your algebra though
The lines are ones if that helps make sense
dapper quail
I don't think so either
severe sparrow
yea probably not
severe sparrow
The lines are ones if that helps make sense
nope, still utterly confused and don't understand the algebra
oh wait are you simplifying from truth table
dapper quail
Yeah I turned it to dnf form then tried to simplify
severe sparrow
you can just demorgan and get the answer
severe sparrow
Yeah I turned it to dnf form then tried to simplify
that looks like cnf to me
dapper quail
Ohh wait
I think I've fixed it
, rotate
,rotate
No that's wrong again
Guys idk what to do
My final result requires more than 5 gates
How can I reduce gates
@severe sparrow
severe sparrow
My final result requires more than 5 gates
the algebra?
severe sparrow
yea? what's your result?
severe sparrow
I can only use 5 gates NANR and inverters
3 nand 2 inverter, ur circuit is right u just need to change some of the inverters
severe sparrow
$(p\land \lnot q) \lor (\lnot p\land r)$
woven radishBOT
someone1010
severe sparrow
do u know how to make or gate with nand?
dapper quail
**someone1010**
How did you get that?
severe sparrow
How did you get that?
literally the equation given
dapper quail
do u know how to make or gate with nand?
I think it's OR inverted
severe sparrow
I think it's OR inverted
?
dapper quail
That's nand
severe sparrow
$\lnot (A \lor B)$ is the same as $\lnot A \land \lnot B$
severe sparrow
OR with inverted inputs is nand
yea
woven radishBOT
someone1010
severe sparrow
magically 3 nand gates 💀
or maybe im wrong
am i wrong wait im wrong am i not
yup i should just \lnot exist myself
severe sparrow
yup
woven radishBOT
someone1010
severe sparrow
$\lnot(\lnot(p\land \lnot q) \land \lnot (\lnot p\land r))$
woven radishBOT
someone1010
severe sparrow
ok, I was 💀, that's cool
severe sparrow
But how else do you check ur right
i mean, boolean algebra is valid
dapper quail
Gotta make sure we didn't make a mistae
severe sparrow
make a truth table ig?
grand siren
a truth table is the most obvious general algorithm, but you can also just like
dapper quail
**someone1010**
How would I draw this with less than 5 gates
grand siren
a truth table is the most obvious general algorithm, but you can also just like
put in p = true and see what it simplifies to
put in p = false and see what it simplifies to
severe sparrow
How would I draw this with less than 5 gates
i mean, the expression is literally 2 inverter 3 nand
grand siren
put in p = true and see what it simplifies to
put in p = false and see what it s...
and then compare the results of that to doing the same thing to the original expression
severe sparrow
brute forcing SAT ;-;
dapper quail
@severe sparrow
Giys
I think your example fails for the case 0 1 1
Ok maybe I just ran the logic thru my head wrong
Also how do you guys suggest I learn latex so that I can type up my work and make it easy to grade
It would probably be good for all my math related classes
I wanna use it for notes too
Give me all the resources ❤️ 🙏
devout snowBOT
@dapper quail Has your question been resolved?
severe sparrow
overleaf
don't try to use a local latex editor
trust me, the man who installed like 8 gb to try to do it
you can use a note taking app like obsidian for notes, u can write latex straight on the page
devout snowBOT
agile elbow
ocean trench
.close
placid roost
what is g(f)(3))?
what is f(4)g(4)?
devout snowBOT
what is g(f)(3))?
what is f(4)g(4)?
solid osprey
for number 6 find f(3), then find the g(the f(3))
devout snowBOT
@placid roost Has your question been resolved?
torpid prairie
For dN/dt=k(N-B), N=B+Ae^(kt). What does each variable represent, I know t is time and k is rate of change and N is amount made but what is A and B
devout snowBOT
For dN/dt=k(N-B), N=B+Ae^(kt). What does each variable represent, I know t is ti...
feral agate
The B is present in your original differential equation
And the A is an integration constant
Meaning A can take whatever value and that function for N will still satisfy the differential equation
torpid prairie
we haven't done differential equations or integration yet, we are doing exponential growth. I understnad N=Ae^(kt) for dN/dt=kN, A is the initial value but apparently B is the initial value for the other form? Then what is A?
feral agate
we haven't done differential equations or integration yet, we are doing exponent...
The difference between this differential equation and the above one is just that N has been replaced by N-B
It's just a linear shift
Think of it like shifting the graph of N vs t to the right B units
torpid prairie
ok, but is A or B the initial valiue
flint spire
torpid prairie
if I graph it tho it asymptotes to B so how is it the final value
devout snowBOT
@torpid prairie Has your question been resolved?
restive swan
hello! I just want to ask if this is correct?
f(x) = 1/x
domain : (-∞, 0) (0, ∞)
range : 0>1
winter torrent
i don't understand what you mean by range but the domain is correct
devout snowBOT
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Available help channel!
copper prairie
helo
copper prairie
Just need someone to explain this
where did the sqrt go
if its (x^2 - 1)^1/2 wouldnt the sqrt just cancel the square on the x? and the 1 would remain the same?
So it would just be x - 1
also here
where did the 2x come from
severe sparrow
log rules
sand dove
if its
d/dx 2lnx + d/dx ln(x^2 -1 )
shouldnt that be
2/x + 1/x^2 - 1
no, chain rule
sand dove
d/dx f(g(x))
copper prairie
d/dx f(g(x))
elaborate further?
sand dove
severe sparrow
d/dx f(g(x))
= f'(g(x))g'(x)
severe sparrow
of course
copper prairie
ic
copper prairie
log rules
canu specify which one
Ohwait nvm itsokay
dw
i understood
thank u tho
.close
devout snowBOT
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dull cairn
Can someone explain to me the last 2 steps here . I am done with the derivation but i am bad in factorisation and simplification.
devout snowBOT
Can someone explain to me the last 2 steps here . I am done with the derivation ...
@dull cairn Has your question been resolved?
Available help channel!
lament schooner
devout snowBOT
lament schooner
what is this.
faint gorge
what is this.
It's a system of linear equations
,, \left [ \begin{array}{ccc|c} 1 & 2 & -3 & 4 \ 3 & -1 & 5 & 2 \ 4 & 1 & a^2-14 & a+2 \end{array} \right ]
woven radishBOT
bacc
lament schooner
okay after that what should i do for the a
faint gorge
So to make 0's
sand dove
okay after that what should i do for the a
the "a" will only show up on the last row
faint gorge
okay after that what should i do for the a
After you did that you would compare these two components
but only after you reduced
not right now
You basically need three row operations
lament schooner
After you did that you would compare these two **components**
like a^2 = a
how can i just remove the a
is what im stuck at
faint gorge
like a^2 = a
Can you first show your system overall
,, \left [ \begin{array}{ccc|c} 1 & 2 & -3 & 4 \ 0 & -7 & 14 & -10 \ 0 & 0 & a^2-16 & a-4 \end{array} \right ]
woven radishBOT
bacc
faint gorge
This is what you should end up with
Notice you can write a²-16 = (a-4)(a+4)
And now you consider some cases
If both components are 0 then that means infinite solutions
Otherwise you can can divide by a²-16 and observe for which values of a you get one solution
and in order to have no solutions there must be such a so that a²-16 = 0 and a-4 is not 0
devout snowBOT
@lament schooner Has your question been resolved?
restive river
sorry i was feeding my cat
lament schooner
Otherwise you can can divide by a²-16 and observe for which values of a you get ...
wait divice what by a^2-16
faint gorge
wait divice what by a^2-16
You didive by a^2-16
woven radishBOT
bacc
faint gorge
You should see now that you have z = 1/(a+4)
lament schooner
You should see now that you have z = 1/(a+4)
ahhhhhhhhh thats what you meant
okay yes
z = 1/(a+4) where can i proceed with this O_O
i mena i feel like its infinite solution but
faint gorge
z = 1/(a+4) where can i proceed with this O_O
ok
So if a is not 4 or -4 then you get one solution
because we just divided by (a-4)(a+4)
that should make sense
lament schooner
yes