Oh its that simple
#help-42
pulsar granite
beta = pi/2 - alpha so yes
shell rune
Yea thanks
I knew this was easy i just though the solution used identity i didnt know
Well thanks to you 2
.close
tepid flame
f(x) = (1+2x)^(1/x)
why extended function value at x = 0 is 7.4
tepid flame
you're a god to me <3
u
but how
lemme type the entire question out rq
jesus christ its a 100+ word paragraph
Graph the function f to see whether it appears to have a continuous extension to x=0
if the function does not appears to have a continuous extension, can it be extended to be continuous at x=0 from the right or from the left? If so, what do you think the extended function's value(s) should be?
i give up
.close
shell rune
f(x) = (1+2x)^(1/x)
why extended function value at x = 0 is 7.4
Thats e^2
calm coralBOT
calm coralBOT
Available help channel!
zenith jasper
Number 24
prisma mango
Apply exponent rules and simplify that
prisma mango
Apply exponent rules and simplify that
zenith jasper
Ok
humble cairn
Isn't number 24 quotient rule tho?
humble cairn
Oh okok
prisma mango
The way the OP is doing is another
prisma mango
As what?
zenith jasper
Wait wdym?
prisma mango
Is that the derivative or when you simplified using exponent rules?
zenith jasper
1/x
prisma mango
What about $\frac{x^{1/2}}{x^2}$?
potent lotusBOT
dldh06
zenith jasper
1/x^3/2
prisma mango
So you can take the derivative of each term now, right?
zenith jasper
Yes let me do that on my paper
Can I bring the bottom number to the numerator which gives an negative exponent?
prisma mango
What number in the numerator?
prisma mango
If it gives a negative exponent, the second term is wrong
zenith jasper
Oh okay
I got my answer
I checked the back of the book and it so correct
Thank you
.close
eager mist
two cars are travelling at 100km per hour. a safe braking distance is to stay 2 seconds behind the car in front of you. if two cars are 40 metres apart, do they have a safe braking distance between them?
calm coralBOT
two cars are travelling at 100km per hour. a safe braking distance is to stay 2 ...
@eager mist Has your question been resolved?
eager mist
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haughty fjord
calm coralBOT
topaz geode
he dont know the answer
topaz geode
explain reasoning with arrow markings on the diagram
i think he dont know how to tell where the limit is
from what i see in my dm
dull wagon
why do you think i'm requesting him to do this
to see what he does know/what he's capable of
topaz geode
he told me i dont know how to reply to you thats why i said that...
dull wagon
why don't they tell that to me themselves here
calm coralBOT
@haughty fjord Has your question been resolved?
neat heath
how does the combination formula always return an integer?
calm coralBOT
how does the combination formula always return an integer?
neat heath
n!/(n-k)!*k!
amber bolt
e.g. 7 choose 3
7*6*5/(3*2)
one of the numbers on the left has to be divisible by 3 because there are 3 of them
neat heath
uh-huh
amber bolt
it's not the full explanation but that's the best i can give
amber bolt
yeah
dreamy void
calm coralBOT
dreamy void
Sorry im still lost
dreamy void
I dont think thats what im supposed to do for this is it?
winter hazel
um theres no poles or weird behavior
ancient thistle
what is definition referring to
humble cairn
Doesn't x→2 mean "as x approaches 2"?
dreamy void
Idk thats all it says 😭
dreamy void
Doesn't x→2 mean "as x approaches 2"?
Yes
ancient thistle
what are you required to show
because if it's just evaluate the answer
then you sub it in
dreamy void
So the problem is just done
ancient thistle
i mean
when people say definition
they usually mean epsilon delta
but unless you know that
you would just sub it in
winter hazel
omg i forgot that hahaha
dreamy void
How would i solve through epsilon delta?
ancient thistle
do you know epsilon delta
dreamy void
Kinda
winter hazel
ε,δ
dreamy void
He's def taught it but i missed out on a few lectures
ancient thistle
well
winter hazel
yep yep
ancient thistle
substitution would be insufficient to show that the limit is indeed 1
because continuity is not yet assumed
humble cairn
What does "use definition" even mean? Are you supposed to explain it?
winter hazel
prob ε,δ
ancient thistle
"use the epsilon-delta definition of the limit to show that it is 1"
dreamy void
Ill watch a vid on epsilon and delta to catch up
winter hazel
yep yepp atb
dreamy void
If possible could you help explain this one thing really quick
ancient thistle
|x - 2|<δ
winter hazel
how to choose δ?
dreamy void
Alright ive gotten a few problems such as this and in each one the suppose is |x-2| is that coincidence or is it like that for every problem
ancient thistle
that's because x->2
ancient thistle
|x - 2| means the distance of x from 2
winter hazel
for a generic x->c ud use |x-c|<δ
ancient thistle
so |x - 2|<δ puts you in the vicinity of 2
dreamy void
Ok tytyty
winter hazel
dreamy void
.close
toxic dew
Hi
toxic dew
y'(x) - 3*y(x) = 2 How do I start with this, Im confused about the y(x) in the middle
What do I do with it
ancient thistle
you can write it as y' = 3y + 2
toxic dew
And what happened with the y(x)?
ancient thistle
well the (x) is just to say that its a function of x
not really anything thats
significant
its just notation
toxic dew
Okey so later on I have another one that has two of those: 2y'(x) + 6y(x) - 2/e^2x = 0
I just rewrite it as 2y' + 6y - 2.....
?
potent lotusBOT
dusk spear
Hi could someone help me understand some linear algebra concepts?
dusk spear
dusk spear
for part c, it says that if (v1,v2,v3) are L.Depedent, then (v1, v2, v3, v4) are also linear dependent. Why is this true?
clever ruin
So if vectors are linearly "DEPENDENT" then you can make one of the vectors using a linear combination of the others
so $v_1=\lambda v_2 + \mu v_3$ where $\mu$ and $\lambda$ are some numbers you can find
potent lotusBOT
Max..
dusk spear
i see, I was at the assumption that you were putting a random vector as v4, thus creating a linearly independent system.
clever ruin
Now if this is true for just 3 vectors, then clearly it must be true for 4 vectors? $v_1=\lambda v_2 +\mu v_3 + \delta v_4$
potent lotusBOT
Max..
clever ruin
what would be $\delta$ ?
potent lotusBOT
Max..
clever ruin
i see, I was at the assumption that you were putting a random vector as v4, thus...
yeah so v1, v2,v3 are linearly dependent so the set is linearly dependent HOWEVER v4 might be linearly INDEPENDENT from the others still but that doesnt really matter
the set would still be considered linearly dependent
dusk spear
i see, for example if v1 and v2 were linearly dependent, then it wouldn't matter if v3 was seperately independent from the system of equations, is this the corrrect assumption to make?
dusk spear
Now if this is true for just 3 vectors, then clearly it must be true for 4 vecto...
Also I'm not familiar with this set of notations. I'm sorry
clever ruin
A set of n vectors is linearly independent if for each $v_i$ we can't do the following $x_i=\lambda_1 v_1 +\lambda_2 v_2....\lambda_{i-1} v_{i-1}+\lambda_{i+1}v_{i+1}....+\lambda_n v_n$ where each $\lambda_i$ is just some number that can be found
potent lotusBOT
Max..
clever ruin
i see, for example if v1 and v2 were linearly dependent, then it wouldn't matter...
yes
clever ruin
Also I'm not familiar with this set of notations. I'm sorry
the greek letters are just some number, as it could be anything ive used these greek letters to say it could be anything not one set number
clever ruin
**Max..**
clearly if delta is 0 then we've found a linear combination by our assumption
dusk spear
i see, I was a little taken aback, because I realized now that my textbook uses alpha1,2,3 instead of the rest of the greek letters
clever ruin
yeah which is fine and if anything better lmao as it expands to n
dusk spear
that's neat
clever ruin
but yeah does that make sense?
clever ruin
sure
clever ruin
just copying so I dont have to scroll
dusk spear
e) v1, v2, v3, in the set of R^3 be L.D. Then they cannot span R^3, because they cannot generate the given vectors necessary
clever ruin
and might as well part e) since they are related
First of all a key fact if you have n linearly INDEPEDENT vectors then they span $\mathbb{R}^n$ and are what is called the "minimal spanning set"
potent lotusBOT
Max..
clever ruin
e) v1, v2, v3, in the set of R^3 be L.D. Then they cannot span R^3, because they...
yeah so they cant span
dusk spear
First of all a key fact if you have n linearly INDEPEDENT vectors then they span...
the definition for a minimal spanning set, is when the set has no redundacies right?
dusk spear
as in dim(of the set of vectors?)
clever ruin
"If it's able to span $\mathbb{R}^3$ then we are able to form a basis of 3 vectors. But this is not possible... why?"
potent lotusBOT
Max..
dusk spear
err... I could prove it in terms of computing a determinant, but conceptually I don't know?
wait nvm
that's for proving linear dependency
if it's linearly dependent then you cannot form a basis of 3 vectors
but that's not a direct cause? ( I don't know how to word it)
clever ruin
So as they are linearly dependent, then you can write one of the vectors in terms of a linear combination of the other 2.
So if we were to form a basis with these vectors the maximum dimension would be 2
potentially they could be multiples of each other and then it has dimension 1
dusk spear
and thus they cannot span in R^3
dusk spear
ok, and then part f) using the logic for part e) having 3 vectors but in the set of R^2, means the maximum dimensions could be 2. It doesn't necessarily mean that it CANNOT span in R^2, is this correct?
clever ruin
ok, and then part f) using the logic for part e) having 3 vectors but in the set...
yes!
clever ruin
potentially it could span but also they might all be multiples of each other so in that case it wouldnt
clever ruin
That was very helpful thank you so much!
np!
dusk spear
potentially it could span but also they might all be multiples of each other so ...
but in this case the problem states it as a definitive
so it would be false
and thank you again
.close
tiny mortar
calm coralBOT
tiny mortar
No clue where to start, can someone tell me where to begin ;-;
Nvm i got
It
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broken crow
<@&286206848099549185>
calm coralBOT
@broken crow Has your question been resolved?
tribal ember
@broken crow still need help?
So we want to find the largest $\sigma$ such that
$$P\qty(\mu - 1.75 \leq X \leq \mu + 1.75) \geq 0.95$$
potent lotusBOT
nvx
tribal ember
X is a normal random variable here, so we probably want to normalize it to X ~ N(0, 1)
First normalize X, simplify the expression, then write the P(...) using the CDF of the standard normal distribution to get an inequality you can work with
cumulative distribution function, its called $\Phi$ for the normal distribution
potent lotusBOT
nvx
tribal ember
For example, if $X \sim N(0,1)$
$$\Phi(10) = P(X \leq 10)$$
potent lotusBOT
nvx
broken crow
omg, i don't follow
tribal ember
did you learn about the normal distribution? did you use other notation?
calm coralBOT
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Available help channel!
spice kayak
Help with 3 (B is wrong forgot to erase it)
calm coralBOT
Help with 3 (B is wrong forgot to erase it)
half arrow
Well first, find the equation of the line, then plug in the possible x's and see which one makes the corresponding y
The equation is y = -5x+5
So put in -45, 9, and -10 as x, and see what the y becomes
Then see what makes sense
spice kayak
.close
calm coralBOT
calm coralBOT
Available help channel!
fiery talon
What methods do I need to use to integrate the rational function (x^3 + 2 x + 2)/(x^4 + 7 x + 3)
frank gull
hmm I'm not sure that can be done without numerical methods. You could get an approximation with Simpsons' rule I guess
but you would need to be careful where the denominator = 0
also what's your bounds of integration?
if you don't have any and you're looking for a generic integral I'm not sure one can be found with traditional methods
fiery talon
Yea, I'm trying to find the generic integral. Bummer
frank gull
yeah I'm not sure. At least I couldn't after playing around with it for a second
I mean just LOOK at that thing lmao
fiery talon
Yea, I don't even know where to begin to compute the anti-derivative. I guess my only chance is to use table integration
frank gull
it looks like according to Wolfram Alpha one does exists but it requires the use of imaginary numbers
fiery talon
Yea, I have no idea how wolfram is able to find that integral
frank gull
people much smarter than any of us here lmao
fiery talon
Haha, yea. They don't even give me an option to see a step-by-step solution 😦
I'll close this out. Thanks for giving it a shot
.close
calm coralBOT
frank gull
yep np
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Available help channel!
wintry glacier
how do i minimize a function with 2 unknowns?
calm coralBOT
how do i minimize a function with 2 unknowns?
wintry glacier
like suppose i have a function in terms of theta, n and c
and im supposed to find c such that the expression is as low as possible
how would i go about that?
solar spruce
do you know how to minimize a function of 1 unknown?
wintry glacier
yes
solar spruce
is your function in terms of theta, n and c differentiable with respect to c?
wintry glacier
yes
solar spruce
then take the derivative of your function with repsect to c, $f_c$ and find when $f_c(\theta, n, c)=0$
potent lotusBOT
maximo
solar spruce
yeah
wintry glacier
or increasing whoops
solar spruce
can you give us the function you want to minimize?
solar spruce
can you send a screenshot or pic
wintry glacier
yeah sure but ill have to grab my phone
solar spruce
ur fine then
wintry glacier
okay actually my phone is still locked for 4 minutes so ill just work on it till then
sorry about that
actually theres not much point in writing out the variance since its not in terms of c but i did it anyways
thats why its such a mess
are you still here @solar spruce ?
solar spruce
yes
the same still applies
if you just need to minimize wrt to one variable, you should be able to compute the derivative with respect to c and find it's 0
wintry glacier
alright
alright so it was an absolute mess and i couldnt get the right answer lol
but one more question
i dont know theta
im supposed to estimate theta
so wouldnt it be weird to have optimal c in terms of theta?
is there any way to avoid that?
i was hoping theta would magically melt away but
calm coralBOT
@wintry glacier Has your question been resolved?
calm coralBOT
@wintry glacier Has your question been resolved?
wintry glacier
No
calm coralBOT
@wintry glacier Has your question been resolved?
calm coralBOT
@wintry glacier Has your question been resolved?
calm coralBOT
@wintry glacier Has your question been resolved?
calm coralBOT
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Available help channel!
pastel lava
I was wondering how they got an answer of 0.36 here for the probability? What I did was do P(weekend) * P(not brushing your teeth) = 2/7 * 0.35 = 0.1001
pastel lava
I tried to do some googling to see where I went wrong, and I could see maybe if the answer was exactly doubled for Saturday and Sunday, but I don't see how they got 0.36 instead
<@&286206848099549185>
inner zealot
P(A|B)
pastel lava
I just tried doing that, I want P(weekend | forgot to brush) = P(forgot to brush | weekend) * p(weekend) / P(not brushing)
but how do I get P(not brushing)?
real sentinel
it would be P(weekend and forgot to brush |forgot to brush)
because otherwise you include the probability it's a weekend and he did brush
inner zealot
It helps to draw a picture.
pastel lava
but just to do some scratch work
P(Weekend and Forgot to Brush | Forgot to Brush)
= P( Weekend and Forgot to Brush AND Forgot to Brush ) * P(Weekend and Forgot to Brush)
/
P(Forgot to Brush)
But, how do the first probability?
inner zealot
real sentinel
$\frac{P(W' \cap B')}{P(B')}$
potent lotusBOT
I can't believe you've done this
pastel lava
I don't think that can be right, because if I'm given they didn't brush, why would I need to include that in the conditional probability?
Is that P(not Weekend and not Brushing) / P(not brushing)
real sentinel
not weekday* but yes
pastel lava
P(weekend and not brushing) / P(not brushing)
real sentinel
yes
pastel lava
okay
but then, another question, if I may
how do I get the probability of not brushing overall, if it's different for weekday and weekend?
is it like 0.25 * 5 + 0.35 * 2
all divided by 7?
real sentinel
yeah pretty much
real sentinel
did you get P(didn't brush) as 0.2785
pastel lava
Yes
real sentinel
what about for P(weekend and didn't brush)
pastel lava
that would be 2/7 * 0.2785 no?
pastel lava
oh
i think
i get what you mean
it's like weekend -> saturday and sunday and then each of those has their own brush or not brush
real sentinel
yeah
pastel lava
but the probabilities to brush and not brush aren't equal, so i'm not sure how I would find the summation of the two probabilities
it can't be as simple as 0.35 * 2 all divided by 4 can it?
real sentinel
it's 0.35 * 2/7 for P(weekend and didn't brush)
because P(Weekend and didn't brush) = P(weekend) * P(didn't brush on a weekend)
so that would be 2/7 * 0.35 if that makes sense
a tree diagram visualises it very well
it's just i don't have one sadly
pastel lava
okay, I think I understand
another question, if I may
P(Weekend and Forgot to Brush | Forgot to Brush)
that was the original thing you said right
real sentinel
yeah
real sentinel
Well P(A given B) is P (A and B)/P(B)
pastel lava
ohh
i thought it was P(A and B) * P(A) / P(B)
oh wait
im confusing conditional probability
and bayes theorem
i think
im sorry
real sentinel
don't worry sometimes it's hard to remember all the formulae
i still struggle with it
real sentinel
np
pastel lava
.close
calm coralBOT
calm coralBOT
Available help channel!
misty pine
hi i tried to watch a lot of videos about fundamentals of logic but i cannot still get it from how to read the symbols to actual answering if true or false huhu help i'm dying
leaden thunder
do you have specific questions about specific videos
misty pine
i dont know how to read "`p^q=(p)^q"
leaden thunder
i dont know how to read "`p^q=(p)^q"
what timestamp in the video has this
"`p^q=(p)^q"
calm coralBOT
@misty pine Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
earnest minnow
i need help with math
calm coralBOT
i need help with math
warm wren
my brother in christ don't we all
earnest minnow
what is the square root of 100
warm wren
,ask what is the square root of 100
potent lotusBOT
warm wren
who knows
earnest minnow
,ask what is the cubed root of 100
modest viper
we love wolfy
calm coralBOT
Available help channel!
glad silo
calm coralBOT
glad silo
this is false, but why?
winter hazel
that
null set is not in the set of {0}
for it to be contained it has to have like
{0, {}}
or
{{}}
night torrent
{}
alpine stone
If it was true you'd be able to see the empty set in {0}, but do you?
glad silo
If it was true you'd be able to see the empty set in {0}, but do you?
from that statement, it's obvious that there is no empty set in {0}. What confused me was this one theorem I read that every set includes an empty set and itself
alpine stone
You mean empty set is a subset to every set*?
glad silo
yes
carmine sorrel
from that statement, it's obvious that there is no empty set in {0}. What confus...
the empty set is a subset of every set. It is not an element of every set
glad silo
oh
alpine stone
Well that's different
glad silo
element , I see
alpine stone
Being a subset to a set and being an element of a set are different things
calm coralBOT
winter hazel
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Available help channel!
lyric heath
I need to find the indefinite integral of csch(12x+12)coth(12x+12), Ive done a u-sub so it is csch(u)coth(u), and obviously at the end I'll be putting the u back in, from there I tried -csch(12x+12)+c, as the derivative of csch(x) is -csch(x)coth(x), so I assumed integrating csch(u)coth(u) would just move the negative but it's wrong
dense cargo
- 5 times the complement of an angle is equal to twice the supplement of the angle. Find the angle, its complement, and its supplement.
- Find the measure of an angle in which 6 times thee angle decreased by twice its complement is equal to the angle's supplement.
calm coralBOT
@lyric heath Has your question been resolved?
lyric heath
Ok I figured it out, I forgot to apply the du, which after u-sub would be du/12
Thanks for trying jowo lol
.close
jade spire
if we have (sqrta)^2 does it equal a but if we're in set of real numbers a has to be >=0 and if we're in set of complex numbers a can be any number?
languid sphinx
if we have (sqrta)^2 does it equal a but if we're in set of real numbers a has t...
a has to be bigger than 0 if you're working with the real numbers since you can't take the sqrt of a negative number. Complex numbers were created to solve that issue, and you can take the sqrt of a negative number if you're working with them. You're going to get the same result as if a was positive, but your answer is going to be multiplied by i, which is a "constant" which is equal to √(-1), also known as the imaginary unit
jade spire
a has to be bigger than 0 if you're working with the real numbers since you can'...
so if we're in real numbers a>=0 and if we're in complex a e C
languid sphinx
Yes, with reals you need to make sure numbers under even roots (sqrt, 4th root, 6th root etc) are positive or 0, with complex numbers you can have anything under them
jade spire
just making sure, had this in test yesterday and right before the test my teacher said something weird, she wrote on the board that
(sqrta)^2=|a| and that (sqrta)^2=sqrt(a^2) and didnt mention what a has to be, had me confused bc i was sure that it was the other thing i think she just messed up
jade spire
Yes, with reals you need to make sure numbers under even roots (sqrt, 4th root, ...
thank you
.close
calm coralBOT
calm coralBOT
Available help channel!
swift magnet
Can anyone help me?
calm coralBOT
Can anyone help me?
swift magnet
<@&286206848099549185>
carmine sorrel
if it's a perfect square then each of it's prime factors would be raised to an even power
calm coralBOT
@swift magnet Has your question been resolved?
swift magnet
if it's a perfect square then each of it's prime factors would be raised to an e...
im still kinda confused how am i suppose to solve this again?
carmine sorrel
look at the prime factorization
What do you need to multiply each factor by to get those powers to be even.
multiply your answers together and that's the number.
swift magnet
look at the prime factorization
What do you need to multiply each factor by to g...
could u explain a bit more simple
carmine sorrel
50 = 2 * 5^2
if I multiply by 2, I get 2^2 * 5^2
since each factor is raised to an even power, I know 2^2 * 5^2 is a perfect square.
So the smallest number I should multiply 50 by to get a perfect square is 2.
swift magnet
50 = 2 * 5^2
if I multiply by 2, I get 2^2 * 5^2
since each factor is raised to ...
so what can i exactly do for 2^3 x 3 x 5^2
carmine sorrel
factors are not raised to an even power?
swift magnet
factors are not raised to an even power?
so i raise them to 2^4 x 3^2 x 5^2
carmine sorrel
yes.
what do you need to multiply by to get from this 2^3 x 3 x 5^2 to this 2^4 x 3^2 x 5^2
swift magnet
6
carmine sorrel
yep
swift magnet
for b its raising the powers to a 3 right
so 27000
@carmine sorrel I have another question do you mind helping me?
carmine sorrel
if 6 is a factor, then so are 2 and 3.
to be a factor of 2 the number must be even (i.e. the last digit is even)
if it's a factor of 3 then the sum of the digits is also a multiple of 3.
so you need to find all the values were 5+diamond+3+2 is a multiple of 3.
swift magnet
okay
calm coralBOT
@red gale Has your question been resolved?
calm coralBOT
@red gale Has your question been resolved?
calm coralBOT
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last lark
- If class is canceled, l go to the beach with my friends I didn't go to the beach with my friends yesterday: so class wasn't canceled
Is it deductive? Or inductive reasoning
alpine stone
If a => b, then not b => not a
whole panther
I understand the first step of the solution. How do we get from sinθ/(sinθ/cosθ) = cos θ?
winter loom
$\frac{a}{\frac{b}{c}} = \frac{ac}{b}$
potent lotusBOT
What the hell am I doing here?
mellow crater
I understand the first step of the solution. How do we get from sinθ/(sinθ/cosθ)...
dividing by a fraction = multiplying by reciprocal
whole panther
sinθ * cosθ/sinθ, sin cancels out, leaving me with cosθ?
winter loom
yeah
whole panther
I can do this with real numbers (ie. polynomicals etc) but when it comes to trig my brain just forgets everything.
(guess I should be VERY careful with using the word real numbers in this discord)
winter loom
whole panther
I went through the trig section on khan as a refresher but it didn't really touch on this. If I have cos θ here at θ> pi should I be finding it on the unit circle?
half jolt
Well you can just plug in x = pi
Since cosine is a continuous function
But for practice, doing it on the unit circle isn't a bad idea
calm coralBOT
whole panther
.reopen
calm coralBOT
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whole panther
actually @half jolt if I can't plug in x (no calculator), is the unit circle the only way?
half jolt
actually <@282398643519225857> if I can't plug in x (no calculator), is the uni...
Though that's only for multiples of pi/2.
For other values you'll find it is too hard.
You can also memorize sine and cosine of pi/6, pi/4 and pi/3. Then use the unit circle to find sine/cosine of multiples of these values.
whole panther
Up to this point we're only dealing with 1-1 for sin (for example). There's no calculators allowed on anything
whole panther
I mean to say from -1 to 1 on the x axis, if that makes sense
Not feeling too hot today but I have a unit test at the end of the day.
I haven't done math since high school pre-cal 9 years ago, so trying to get my ducks in a row has been difficult.
remote mural
the lesson of this question is function transformations right?
magic viper
remote mural
i have the answers, it looks weird asf
idh transformation for my test tmr, i just like to make 100% sure that this is trans
.close
bleak plume
calm coralBOT
alpine stone
I'd try dropping a height from B onto AC
bleak plume
then?
calm coralBOT
@bleak plume Has your question been resolved?
alpine stone
Let's say BD is the height
Notice that the angle DBC = 2a
Hmm this doesn't really help though
night torrent
looks some sine law thingy
not sure tho
you might try
yep
sine law it is
uhh @bleak plume do you know sine law?
oh no they’ve went afk
not again
umbral tangle
looks some sine law thingy
Yeah, sine law is probably best for this problem
night torrent
$\frac {\sin \theta} 6 = \frac {\sin a} 2$
potent lotusBOT
umbral tangle
Sina/2 = sin(pi/2+a)/6
night torrent
Yeah, sine law is probably best for this problem
no, it is tailored problem for sine law
umbral tangle
Pretty much
night torrent
$\frac {\cos a} 6 = \frac {\sin a} 2$
potent lotusBOT
night torrent
so tan a = 1/3
bleak plume
uhh <@768500169419259944> do you know sine law?
yes
calm coralBOT
night torrent
,w sin(pi/2 +a) = cos a
potent lotusBOT
night torrent
ayyy
umbral tangle
Nice
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bleak plume
isnt it 2/sina = 6/sin theta
calm coralBOT
isnt it 2/sina = 6/sin theta
umbral tangle
I really need to review my trig identities lmao
night torrent
$\frac 6{\sin \theta} = \frac 2{\sin a}$
potent lotusBOT
night torrent
$\frac 6{\cos a} = \frac 2{\sin a}$
potent lotusBOT
bleak plume
oh yes but how did we find tana 1/3?
night torrent
so tan a = 1/3
half jolt
@night torrent What's up with the alignment there
night torrent
<@915145402859278366> What's up with the alignment there
texit hates bg color changes
night torrent
it crops whenever it likes
i had a fix
but
it breaks
in
tikz
so
i had to pass that
anyways
half jolt
Alright lol
potent lotusBOT
calm coralBOT
night torrent
np
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alpine crown
I need help solving
calm coralBOT
I need help solving
alpine crown
66x + 44 = 0 in mod 154
so far I have found the GDC(66, 154)= 22
but since the gcd is not 1, there is no invers
But I don't really know why but there was this method I learned that says if the GCD(66, 154)| 44 then you can divide the entire thing with 22
which will leave me with
3x≅-2 (mod 154)
no I mean 3x≅-2 (mod 7)
but then I will have 20+ solutions and I don't know if that is correct
finite scroll
well if you think about it there are infinitely many multiples of 154 so there are infinitely many solutions
alpine crown
yeah I know but the question tells me to find all the x's in mod 154
and there are I think 22 solutions under 154
and above 0
alpine crown
But do you think I did correct so far?
finite scroll
think so
calm coralBOT
@alpine crown Has your question been resolved?
remote mural
just wait long enough
oblique current
you realise if you keep spamming and closing and opening your channel your question moves off the screen and people are unlikely to scroll up and see what you asked
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tepid crypt
if it's
a+c < 0
then is it also
a<c
?
calm coralBOT
if it's
```a+c < 0```
then is it also
```a<c```
?
oblique current
Try (-1)+(-2)
tepid crypt
yes, i know, but my teacher made like that... i think he was wrong
oblique current
Well then you know for yourself that it's not true
tepid crypt
im trying to formulate the real problem now...
In the first case, K-L-M all negative. And what can it be their negative-positive value in the second case?
Here are the cases
calm coralBOT
@tepid crypt Has your question been resolved?
worldly dew
if im trying to prove that limit laws won’t hold if a limit doesn’t exist do I go any further than this? ie what could I write to replace the ‘??’ this is early university calc
worldly dew
idk the question kinda sounds stupid but I don’t know what to write other than ‘??’
calm coralBOT
@worldly dew Has your question been resolved?
haughty fjord
calm coralBOT
vernal plaza
haughty fjord
K
hasty fiber
calm coralBOT
@haughty fjord Has your question been resolved?
blissful ridge
I'm a little stuck and don't know what to do. Can someone guide me?
warm warren
What does domain mean?
calm coralBOT
warm warren
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steady palm
I am factoring but there are only two things? What do I do in this case?
vagrant valve
imagine it as k^2 +0k-25
winter hazel
$(a-b)(a+b) = a^2-b^2$
potent lotusBOT
dull wagon
the factorisation in q13 is incorrect
steady palm
oh what did I do
vagrant valve
on 17, you can move y to the right
and then divide both sides by y
and then you get 64x^2=1
and then you can subtract the 1 and get $64x^2-1=0$, and you can solve that
potent lotusBOT
InfinityMango
calm coralBOT
@steady palm Has your question been resolved?
steady palm
<@&286206848099549185>
steady palm
What did I do wrong on q13
steady palm
<@&286206848099549185>
steady palm
What did I do wrong
umbral tangle
that's not how you factor by grouping
steady palm
can you explain in words?
umbral tangle
can you explain in words?
basically, we just factor out 4w in the first (16w+4w), and 1 out of (4w+1), and then we just get 4w(4w+1) + 1(4w+1)
then, we just group it to get (4w+1)(4w+1)
wintry shard
calm coralBOT
wintry shard
hey guys im trying to learn how to do this in ahead of time
so whats the steps for sovlving x ?
calm coralBOT
@wintry shard Has your question been resolved?
calm coralBOT
@wintry shard Has your question been resolved?
wintry shard
.close
remote mural
if f(x) = f(x-1) + 1001
.
how can I solve f(9999)
calm coralBOT
if f(x) = f(x-1) + 1001
.
how can I solve f(9999)
glass aurora
what is f(0)
remote mural
no clue
glass aurora
f(1) = (0) + 1001
glass aurora
Okay that's it
warm wren
then nvm
glass aurora
😎
remote mural
ok one sec let me send the full question
glass aurora
what is f(2) in terms of f(1)
warm wren
oh god that looks like logarithmic cauchy equation
remote mural
it has nothing to do with logarithms as far as I know its just a function question
remote mural
oh
remote mural
ok then lol
warm wren
log cauchy is f(xy)=f(x)+f(y)
remote mural
so what do I do here
warm wren
and i proved with the m and n thing is f(x) = f(x-1) + 1001
if you have this
then I recommend trying some values
until you find a pattern
then proving that pattern
remote mural
how can i try some patterns
f(x) and f(x-1)
i cant just plug in random numbers for x
warm wren
what is f(1)?
remote mural
2
warm wren
what is f(2)
remote mural
i dont know
and i dont know how to find that
if i can find f(2) then I could just go straight to f(9999)
remote mural
you cant plg in x=2 for f(x-1)
warm wren
why can't you?
remote mural
i dont know but it is not how i it works in other questions i did
warm wren
you can't
just be patient
we'll get there soon
now f(3)
I won't go all the way
I just want you to find a pattern
warm wren
what do you mean by "normally"
remote mural
f(x-1)
warm wren
what about it
remote mural
idk
lol
im just confused now
i get what your saying
it makes sense
functions is just very confusing
for me
what no
@silent elm
warm wren
probably typed it in the wrong channel
remote mural
i have not learned summation notation is that an issue here?
in presenting proper work i mean
in finding the answer not but work maybe
@warm wren
i found the pattern
f(x) = 1001(x-1)+2
warm wren
🥳
remote mural
sorry for doubting your solution i am not used to working with functions, but I need to get used to it because its what im using in calculus
.close
formal tartan
potent lotusBOT
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noble cedar
calm coralBOT
noble cedar
I believe I did vertex correctly to find maximum height (x) but I’m not sure how to find maximum distance?
Maximum distance in total, not at peak height but how far the projectile actually travels in total
trim galleon
maximum distance as in range along x axis of projectile?
or the parabolic path of projectile
noble cedar
Above ground so it would be when the projectile touches the x axis as it lands
It appears to be a downward parabola so I think this formula should work?
trim galleon
u need to integrate the equation of trajectory of projectile bounded from 0 to range
noble cedar
Would I just multiply distance at peak (31250) by 2?
Since this is the axis of symmetry for parabola
trim galleon
wait i still dont get it
noble cedar
How far the projectile travels
trim galleon
the point where the projectile touches the x axis right
trim galleon
range = u²sin2θ/g
trim galleon
Indeed that is
noble cedar
range = u²sin2θ/g
I need to review my trig identities
trim galleon
are u given the angle and speed of projection
trim galleon
multiplying max height with 2 should work
if it's a perfect parabola
as in the angle of projection needs to be like 45° iirc
noble cedar
Lol this is all the data I have so it appears to be a half circle I am drawing
Max height and max distance are the same
trim galleon
oh?
noble cedar
Because of axis of symmetry
I can determine max height of vertex will have equal horizontal distance to the left and to the right of the vertex
Hence the symmetry of parabola
trim galleon
yeah that is a half circle
calm coralBOT
sick plover
Yes
No
Brackets mean you include the endpoints
But -∞ and ∞ aren't numbers that can be included
Or use parenthesis instead of brackets
rich trout
Um so heres the thing.
In the last step I have 0.054 = the square root of 696340/r
How do I single out the variable at this point? Couldnt really find an online video to help me here and would appreciate step by step instructions.
rich trout
I got r by using an online calculator but I realized its better to actually learn the method to solve it
sick plover
Is r in the square root
sick plover
How can you get rid of a square root?
rich trout
Squaring it right?
sick plover
And what do you get after doing that?
rich trout
696390/r = 0.029 since you have to square that.
Then you do cross multiplication to get 696390 =0.029r
Then divide again.
Oh. Man I really made that more of a problem then it actually was.
rich trout
And what do you get after doing that?
Thanks for helping a dummy like me I didnt think you could square again lol
At least I think after thats how you do it?
Correct me if im wrong
sick plover
Yes
faint plover
I need help with the following: (x+4)^2 + 3(x+4)(x-1)
calm coralBOT
I need help with the following: (x+4)^2 + 3(x+4)(x-1)
faint plover
its factorization and whatnot
so uh
yeah
if anyone can help I'd be more than grateful
faint plover
I need help with the following: (x+4)^2 + 3(x+4)(x-1)
im confused on how to solve it basically
<@&286206848099549185>
please 
calm coralBOT
@faint plover Has your question been resolved?
calm coralBOT
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remote mural
calm coralBOT
https://prnt.sc/mT0JSWBcvwFO
calm coralBOT
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buoyant mauve
hey
jade bobcat
Can someone help me with scalar product of two signals?
calm coralBOT
Can someone help me with scalar product of two signals?
@jade bobcat Has your question been resolved?
calm coralBOT