do you even know what a reciprocal is
#help-26
sturdy oracle
woven kettle
yes
sturdy oracle
I mean you can legit simplify 20/20
woven kettle
yes so its -1
sturdy oracle
Yeah and then the reciprocal of -1 is?
woven kettle
so would the negative reciprocal be 1?
sturdy oracle
Yeah
topaz sinewBOT
um so x=-3 is correct but the second value of x is 13
rotund spoke
while mines is 15
idk what iβm doing wrong
ππhelp pls
if i do the removing fraction thingy then i get 13 but not 3
ππ
toxic grove
how did you get -20/4 = -3?
toxic grove
so you had x = -20/4
rotund spoke
u have to take - and +
rotund spoke
so you had x = -20/4
yes
toxic grove
can you divide that once more for me
toxic grove
it's -5
rotund spoke
supposed
toxic grove
im just saying both your answers are wrong. let's look at the previous steps then
something must've gone awry there
frozen goblet
Youre probably confused about the absolute value so why not substitute y for it
Then solve for y and then x
toxic grove
$\frac{3}{2} |x-5| - 8 = 12 - |x-5| \implies \frac{5}{2} |x-5| =20$
thorny flameBOT
nebula40
toxic grove
if you substitute y = |x-5| like he said this is easier to see
rotund spoke
how did they even do that
rotund spoke
if you substitute y = |x-5| like he said this is easier to see
um ok
but that will only give me one value
i need two values of x
rotund spoke
at what step do i take - and +
topaz sinewBOT
topaz sinewBOT
Available help channel!
lilac furnace
topaz sinewBOT
lilac furnace
Can someone help me to simplify that please
frozen goblet
Factor out m+1
frozen goblet
$this equals (m+1)*(4m/2)$
thorny flameBOT
L12sg
lilac furnace
Alright thx
lilac furnace
$this equals (m+1)*(4m/2)$
I donβt know how to manage the rest after I take it out
I think im dumb
I mean for each terms
sweet shard
I mean for each terms
You can simplify 4/2
sweet shard
How
frozen goblet
How did you get an equal sign when it was about simplifying
frozen goblet
No it shpuld be 4
lilac furnace
Itβs too much
sweet shard
How did the 4 turn into a 2
sweet shard
You can simplify 4/2
Can you simplify this?
lilac furnace
2
sweet shard
Use that here
topaz sinewBOT
@lilac furnace Has your question been resolved?
sweet shard
@lilac furnace did you simplify this correctly yet
topaz sinewBOT
@lilac furnace Has your question been resolved?
topaz sinewBOT
neon iron
.close
topaz sinewBOT
Available help channel!
soft lily
topaz sinewBOT
soft lily
is there a faster way to do this problem than calculating the individual probabilities of each of the 12 outcomes and then deriving the mean from them?
because...
that's a lot of calculating
topaz sinewBOT
@soft lily Has your question been resolved?
soft lily
<@&286206848099549185>
soft lily
<@&286206848099549185>
Please, I can't figure this out
the hypergeometric distribution didn't simplify anything
Please someone?
<@&286206848099549185>
anyone?
<@&286206848099549185>
help please
pleeeeeeeeeeaaaaaaaaaaasssssseeeeeeeeeeeeeee
fuck you guys
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
solemn jay
The leading term of the polynomial function p is a_nx^n, where a_n is a real number and n is a positive integer. The factors of p include (x-3), (x-i) ,(x-(2+i)). What is the least possible value of n?
topaz sinewBOT
The leading term of the polynomial function p is a_nx^n, where a_n is a real num...
iron harness
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
opal vault
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
nice sync
iron harness
probably 1
Try constructing a ccandidate function that has these factors.
iron harness
Not a specific term, I just invite you to try something that will probably make you see the solution.
What function could you imagine to have the 3 factors?
If we could then further see that it is the smallest one and the leading coefficient is psotivie, we would be done! π
solemn jay
If we could then further see that it is the smallest one and the leading coeffic...
p(x) = x^3 - 6x^2 + 13x - 6 - 6ix + 3i
this is what I got for that
opal vault
oh my you didn't need to expand
solemn jay
oh
iron harness
Anyway
solemn jay
p(x) = (x - 3)(x - i)(x - (2 - i))
iron harness
is the leading coefficient positive?
solemn jay
yeah?
iron harness
So what would be the n here?
solemn jay
a positive integer?
iron harness
The leading term of the polynomial function p is a_nx^n, where a_n is a real num...
^
Here you were asked about an n.
iron harness
p(x) = (x - 3)(x - i)(x - (2 - i))
For this we know exactly.
iron harness
p(x) = x^3 - 6x^2 + 13x - 6 - 6ix + 3i
or this 
solemn jay
So what would be the n here?
1?
iron harness
π¦
iron harness
The leading term of the polynomial function p is a_nx^n, where a_n is a real num...
a_n*x^n was supposed to be the leading term.
iron harness
p(x) = x^3 - 6x^2 + 13x - 6 - 6ix + 3i
What is the leading term here?
solemn jay
What is the leading term here?
x^3
iron harness
it#s not just any real number though
solemn jay
3?
iron harness
it is OUR leading coefficient
solemn jay
cause the degree is 3?
iron harness
They wrote it a bit confusingly I admit, but n is just the degree.
solemn jay
ok ty but how to go ahead?
iron harness
p(x) = (x - 3)(x - i)(x - (2 - i))
Which is also why you do not need oto multiply out.
solemn jay
Which is also why you do not need oto multiply out.
Ohhhhh now I see
iron harness
The degree is just 3 because 3 linear factors.
solemn jay
is that why I was getting confused?
solemn jay
3 is the smallest?
iron harness
Do you think we can find a polynomial with less degree?
iron harness
cause degree of function is 3
Perhaps we just found a bad function that is more convoluted than we needed.
iron harness
You chould have suggested p(x) = (x-1)(x-3)(x-i)(x - 2 + i) first.
Then we would have concluded n=4.
it surely also has a positive leading coefficient and the 3 factors!
iron harness
well we don't know yet whether maybe there is one with 2
Okay I will help out.
There isn't.
I think one short way to argue is because your function needs to have 3 zeros
at 3, i and 2-i
3 zeros means at leastr degree 3.
solemn jay
well we don't know yet whether maybe there is one with 2
bro u made me think my whole life again
just to tell me its not possible
π
iron harness
just to tell me its not possible
!nosols
topaz sinewBOT
just to tell me its not possible
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
iron harness
you are welcome.
iron harness
When this comes in exam, I will remember cause of u man
yay
solemn jay
!close
iron harness
.close
solemn jay
.close
topaz sinewBOT
iron harness
solemn jay
its been a while :)
topaz sinewBOT
Available help channel!
solemn jay
Im back for more π ,
topaz sinewBOT
Im back for more π ,
opal vault
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
2
A) Q(-5) = 0: This statement cannot be determined from the given information. The fact that Q(5) = 0 does not guarantee that Q(-5) = 0.
B) Q has two complex roots: This statement cannot be determined from the given information. We only know that Q(5) = 0, but this does not provide information about the nature of the roots of the polynomial.
I know its NOT A or B
its C or D
excuse me anyone?
opal vault
its C or D
Yep, that's a good conclusion
solemn jay
wow that message lagged
solemn jay
Yep, that's a good conclusion
ty but how do u determine C or D
I was thinking about writing this as my explanation
'but am not sure
Q(x) can be expressed as P(x)/(x-5) where P(x) is a degree of 4: This statement cannot be determined from the given information. While we know that (x - 5) is a factor of Q(x), it does not necessarily mean that Q(x) can be expressed in the form P(x)/(x-5), where P(x) is a degree 4 polynomial.
north canyon
Do all degree 4 polynomials have 5 as a root?
solemn jay
no the info aint given
north canyon
Or wait it is can nvm
opal vault
Do all degree 4 polynomials have 5 as a root?
this has nothing to do with what we're doing
So first of
north canyon
Yea didn't see it says can be expressed
opal vault
Can you do the division of Q(x) by (x-5)?
opal vault
Do we agree that we can write Q(x) = (x-5)P(x) + R(x)?
What do P(x) and R(x) verify?
that's euclidian division btw
solemn jay
Do we agree that we can write Q(x) = (x-5)P(x) + R(x)?
no cause I have no idea what this is
opal vault
ok
solemn jay
Im sorry but we werent taught that :(
opal vault
Do you at least know the polynomial division theorem?
solemn jay
yes
opal vault
Can you cite me the theorem?
solemn jay
Can you cite me the theorem?
word for word?
If the polynomial P(x) is divided by x β c, then the remainder is the value P(c)
here u go ig
??
nvm I got it
.close
long stirrup
neon iron
Given a 7 digit number, where the first digit is from 2-9 inclusive, and the two digits immediately after cannot be 1 consecutively, find the number of possibilities
neon iron
So one of the right ways to do this is total possibilities - possibilities of digits 2 and 3 being 1
I tried doing it like 8 * 10 * 9 * (10 * 10 * 10 * 10) where 10 * 9 was the possible combinations for the second and third digits, but this is wrong and I'm not sure why
elfin sparrow
I tried doing it like 8 * 10 * 9 * (10 * 10 * 10 * 10) where 10 * 9 was the poss...
if the second and third digits can each not be one, then aren't there 9 possibilities for each of those two digits?
not 10 and then 9
neon iron
if the second and third digits can each not be one, then aren't there 9 possibil...
woops messed up the question, edited now
elfin sparrow
oh, either one of them can be 1, but they can't both be 1?
neon iron
yeah
elfin sparrow
well then you still don't have 10 choices and then 9. That's sort of assuming that the first can be 1 but the second can't
neon iron
I thought it wouldn't matter since 9 * 10 would be the first not 1 and the second being 1
elfin sparrow
well, you'd want to count those possibilities separately, but it's kinda tricky since the two cases overlap a lot
they overlap wherever neither digit is 1
I think maybe it's eaiser to think of these two digits together, as a single event
neon iron
ic
elfin sparrow
do you know what I mean? like just consider those two digits for a moment. How many possibilities are there if you're just choosing two digits?
neon iron
yeah it makes sense by doing it through complement
I guess I was wondering how it would be done if it wasn't through complement
elfin sparrow
You could do 10*9 to count the possibilities like you did originally
but you also have to consider 9*10 separately, since this is the case that allows the third digit to be 1, rather than the second
so 10*9 + 9*10
and then subtract all the cases we double counted, which are the cases where neither digit is 1
which is 9*9
neon iron
I was thinking about that, but I thought it would be much larger than the total possibilites should be
elfin sparrow
if you subtract the overlapping 9*9, the result should be the same
elfin sparrow
sure thing π
combinatorics is tricky, it's super easy to lose track of what you have/haven't counted or what you've counted more than once
elfin sparrow
that's why I like to try to think of other ways to structure it
like those two digits being anything from 00-99, except for 11
is much easier to see that way that there are 99 possibilities
in my opinion anyway
topaz sinewBOT
elfin sparrow
you too π
topaz sinewBOT
Available help channel!
atomic blade
I know this is easy, but I need help lol
topaz sinewBOT
I know this is easy, but I need help lol
atomic blade
The def of a laplace transform is this. But the graph shows the wavefrom from a to b. So do I change the bound of 0<t<infinity to a<t<b?
neon venture
$f(t) = \begin{cases} c & t \in [a,b] \ 0 & t \notin [a,b] \end{cases}$
thorny flameBOT
Herels
neon venture
The def of a laplace transform is this. But the graph shows the wavefrom from a ...
the bound will obviously change
since f(t) only has a value between a and b
you know what that means
topaz sinewBOT
topaz sinewBOT
Available help channel!
hot belfry
topaz sinewBOT
hot belfry
??
final mural
do you nkow the definition of a function being even or odd?
hot belfry
do you nkow the definition of a function being even or odd?
yes
i want to know how to move further with the problem onto solving it
final mural
what did you try so far?
hot belfry
what did you try so far?
the problem is i dont know how to solve it
opal vault
so, the function will be even or odd depending on your expression of f(-x)
hot belfry
yes i know
opal vault
so start by computing f(-x)
hot belfry
substituting x as -x?
opal vault
yes, in this expression
hot belfry
i got it as f(-x)=a^-x-a^x-sinx
hot belfry
i got it as f(-x)=a^-x-a^x-sinx
after this what do i do
opal vault
and is this possibly f(x)? -f(x)?
do you recognize f(x) or -f(x) in that expression of f(-x) you wrote?
hot belfry
do you recognize f(x) or -f(x) in that expression of f(-x) you wrote?
i do not understand
opal vault
i got it as f(-x)=a^-x-a^x-sinx
is f(-x) = f(x)? Is f(-x) = -f(x)?
hot belfry
is f(-x) = f(x)? Is f(-x) = -f(x)?
ye how do i solve it till here
i got till only this
f(-x)=a^-x-a^x-sinx
after substituting
@opal vault
opal vault
yes it is
rapid mantle
when do you apply continuity correction for normal distribution?
rapid mantle
I'm really confused since everything seems to contradict
topaz sinewBOT
@rapid mantle Has your question been resolved?
sweet shard
Normal distributions are already continuous
topaz sinewBOT
@rapid mantle Has your question been resolved?
rapid mantle
Normal distributions are already continuous
oh i meant like
when you approximate binomial to normal
sweet shard
...
What exactly are you talking about then
What statements are contradictory to you?
noble basin
topaz sinewBOT
noble basin
I need to know in this how you get the 25sec^2+25
I have no clue how you get the 25 in this problem
distant nymph
They have done it wrongly in the picture. Part on the right side. Maybe, that's what is tripping you up.
It should be:
$$=25\tan^2{t} + 25$$
$$=25(\tan^2{t} + 1)$$
$$ = 25\sec^2{t}$$
thorny flameBOT
Enemagneto
noble basin
okay but how do you get the 25
Thats the only thing I just am not sure on the algabra of where the 25 came from
thorny flameBOT
Enemagneto
distant nymph
See the $+25$ there?
thorny flameBOT
Enemagneto
distant nymph
You substituted, $x = \frac{5}{7}\tan{t}$
thorny flameBOT
Enemagneto
gritty cedar
topaz sinewBOT
lyric gazelle
Hi, how do I simplify this expression?
topaz sinewBOT
Hi, how do I simplify this expression?
timber current
combine the fractions inside the big square root
then split the square root on the top and bottom
so you can remove the sqrt2 on the bottom
lyric gazelle
so you can remove the sqrt2 on the bottom
alr, how would i simplify the nominator
when i insert it into wolframalpha it gave me the answer 5, so im kinda confused π
timber current
multiply by sqrt2/sqrt2
lyric gazelle
ok wait
timber current
or
wait
i didnt realize you meant it like that
you dont need to multiply
just add the left and right
idk, how you got five though
it should be irrational
wait
is that a plus or minus
lyric gazelle
plus
lyric gazelle
yeah XD
timber current
do you know imaginary numbers
lyric gazelle
idk why my teacher gave me that and told me to simplify π
lyric gazelle
do you know imaginary numbers
i mean yeah? i dont know how to use it though
like in calculus prob
timber current
bruh
make sure you got the problem right
because the one you gave is simple precalc
lyric gazelle
i can give you the full problem
lyric gazelle
because the one you gave is simple precalc
no im just saying
you tend to use imaginary numbers more in calc right
timber current
yeah
its first introduced in precalc
and then calc 3 i think
or end of calc2
i forgot
lyric gazelle
ok ill deem it as no real answer for now, thanks
timber current
yeah
lyric gazelle
.close
topaz sinewBOT
timber current
or just write out the imaginary
lyric gazelle
alr
topaz sinewBOT
Available help channel!
muted crow
topaz sinewBOT
muted crow
What limit rule is this
sturdy oracle
Limits are what a function will approach towards at a certain x value. For a continuous function like 3x-7, it'll just be what the function is evaluated at that value
That should be a logical connection
slate pebble
π€
craggy haven
i think you need $\lim_{x\to a} x = a$ first
thorny flameBOT
hayley!
craggy haven
then you can use these 
muted crow
what
craggy haven
wdym what
muted crow
do I really have to have limx=a
craggy haven
like
if you want to use those limit laws to find the limit you asked about
then yes
i think
if you just want to use the fact that for a continuous function, you can just substitute the value in, then you can just do that instead
muted crow
.close
stark rivet
topaz sinewBOT
stark rivet
need help with 51
This is what iβve got so far I donβt know where to go from here
or if I messed up somewhere
waxen yarrow
no thats correct
stark rivet
Alright
stark rivet
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
tacit glacier
Hey could somebody help me with 2) a)? I believe the function is d(p) = sqrt( (p^2) + (3^2))
topaz sinewBOT
Hey could somebody help me with 2) a)? I believe the function is d(p) = sqrt( (p...
tacit glacier
I believe this finds the distance between the tree and the bird but Iβm not sure if Iβm right
neon iron
tacit glacier
Lol
topaz sinewBOT
@tacit glacier Has your question been resolved?
tacit glacier
.close
gritty cedar
topaz sinewBOT
gritty cedar
what is the first step supposed to be
proven tundra
what is the first step supposed to be
gritty cedar
I saw this video before coming here but the question is so different from them
somebody pls hellppppp
.close
graceful leaf
topaz sinewBOT
drifting swift
your handwriting has room for improvement. it's hard to see what you tried to do...
did you multiply both sides by (x^2 - 1)?
drifting swift
...
right
so you did multiply both sides by (x^2 - 1).
then $\frac{x^2-1}{x+1}$ should have simplified to $x-1$, not to $x+1$ as you wrote.
thorny flameBOT
Ann
drifting swift
you would have had: $$x - 1 + 2x + 2 = 3x^2 - 3$$
thorny flameBOT
Ann
graceful leaf
Oh
restive willow
Dude i sent you a video for this type of problem you're still stuck?!?!
Its been 2 hours
Oh my
graceful leaf
?
at least im trying
eventually i will get it
idc how long
so something like that?
drifting swift
,rcw
thorny flameBOT
drifting swift
why did the right-hand side become 3(x^2 - x) all of a sudden
it wasn't supposed to be that
drifting swift
,rccw
thorny flameBOT
drifting swift
3(x^2 - 1) is not 3x^2 - 1.
toxic grove
I could swear i've seen the exact same question recently
craggy haven
pull everything to one side and then factor
toxic grove
do you know how to solve quadratics?
toxic grove
so suppose it was something like 3x^2 + x + 1 =0, you know how to solve it right?
graceful leaf
quadratic formjula?
toxic grove
yes
toxic grove
so let's make this equation look like a "normal" scenario
let's subtract 1 from both sides of the equation
graceful leaf
Ok
toxic grove
what do we have now?
graceful leaf
3x=3x^2-4
toxic grove
then we subtract 3x from both sides
does this look like something you can solve now?
toxic grove
3x^2-3x-4 = 0
toxic grove
imo it's not good practice to forget a side of the equation, even if it happens to be zero
but anyways you can go ahead with using the quadratic formula now
graceful leaf
Ok
yes i will keep practice
I have question
can i do complete square for this one or not allow
eh tht will make it harder nvm
toxic grove
it's probably faster to use the formula
toxic grove
you've made a mistake in the b^2 - 4ac part
toxic grove
you should be able to simplify it a bit then
topaz sinewBOT
@graceful leaf Has your question been resolved?
upper prawn
Hello, i have this question. is there a quick way to find the answer without having to solve for the roots for each equation?
topaz sinewBOT
Hello, i have this question. is there a quick way to find the answer without hav...
drifting swift
do you know in general how to reconstruct an equation from its roots
upper prawn
No
drifting swift
... do you know anything about factorization, maybe?
upper prawn
Yeah sort of im not very good at it though
drifting swift
well let's forget this complex numbers stuff for a moment and i'll give you a simpler problem that you could solve.
give me a quadratic equation with roots x=2 and x=3.
upper prawn
ok one sec
drifting swift
in factored form.
craggy haven
yes but i think you typo'd
drifting swift
^
craggy haven
if you wanted a quadratic with roots at $\blue{1 + 2i}$ and $\purple{-3 + i}$ then it would just be $$(x - \blue{(1 + 2i)})(x - \purple{(-3 + i)}) = 0$$
thorny flameBOT
hayley!
craggy haven
yeah
craggy haven
yeah just distribute the - sign
when you're multiplying these you kind of have to pretend that i is a variable
and then deal with i^2 = -1 later
upper prawn
so it become (x+3 and then how do i do (x-+i)
drifting swift
no
upper prawn
is that just x-i
drifting swift
(z - (-3+i))(z - (-3-i)) is what you should've had
which simplifies into (z + 3 - i)(z + 3 + i)
upper prawn
oh ok i get that now. the i always messes with me
drifting swift
the i is just a letter
upper prawn
alright so after expanding i got z^2 +6z +10
drifting swift
sounds about right.
lucid junco
Verify $\frac{1-\sec\theta}{1+\sec\theta}=\frac{\cos\theta-1}{\cos\theta+1}$
How should I start this?
thorny flameBOT
water beam
drifting swift
could start from the left-hand side and write sec(ΞΈ) as 1/cos(ΞΈ)
then simplify that nested fraction
lucid junco
wait how do I simplify this lol
$\frac{\left(1-\frac{1}{\cos\theta}\right)}{1+\frac{1}{\cos\theta}}=\frac{\left(1-\frac{1}{\cos\theta}\right)}{1}\cdot\frac{\cos\theta}{1}??$
thorny flameBOT
water beam
lucid junco
oh wait no
i got this
trust
$\frac{\left(1-\frac{1}{\cos\theta}\right)}{1+\frac{1}{\cos\theta}}=\frac{\left(1-\frac{1}{\cos\theta}\right)}{\frac{\left(\cos\theta+1\right)}{\cos\theta}}=\left(1-\frac{1}{\cos\theta}\right)\cdot\frac{\cos\theta}{\cos\theta+1}$
thorny flameBOT
water beam
lucid junco
how legal is this on a scale of 1-10
$\frac{\left(\cos\theta-1\right)}{\cos\theta}\cdot\frac{\cos\theta}{\left(\cos\theta+1\right)}$
thorny flameBOT
water beam
lucid junco
$\frac{\left(\cos\theta-1\right)}{\cos\theta}\cdot\frac{\cos\theta}{\left(\cos\theta+1\right)}=\frac{\cos\theta\left(\cos\theta-1\right)}{\cos\theta\left(\cos+1\right)}$
thorny flameBOT
water beam
lucid junco
then simplify that nested fraction
is this good?
i hope its legal
that was a lot of labour
drifting swift
how legal is this on a scale of 1-10
legality is a much coarser scale than 1-10.
also 1-10 scales suck anyway, the correct scale is 0-10.
drifting swift
anyway this is legal but too roundabout for my taste.
no you are not wrong, you're just detouring.
lucid junco
ok cool
nice nice nice
I assume i should expand now
$\frac{\left(\cos^{2}\theta-\cos\theta\right)}{\cos^{2}\theta+\cos\theta}$
thorny flameBOT
water beam
drifting swift
oh my god
drifting swift
hold on a minute
lucid junco
what
drifting swift
i need to make a comparison
drifting swift
Blindly applying cross multiplication \ (as well as ignoring factorization): \
\begin{align*} \frac{x}{123456789} &= \frac{987654321}{123456789}\
123456789x &= 121932631112635269 \
x &= \frac{121932631112635269}{123456789} \ &= 987654321 \end{align*}
thorny flameBOT
Ann
drifting swift
credit to @restive inlet
lucid junco
what the hell is that
drifting swift
this is an exaggerated example of how to make your life difficult
lucid junco
$\frac{\left(\cos^{2}\theta-\cos\theta\right)}{\cos^{2}\theta+\cos\theta}=\frac{\cos\theta\left(1-\cos\theta\right)}{\cos\theta\left(1+\cos\theta\right)}$
wooooohoooooooooooooooo
thorny flameBOT
water beam
drifting swift
ok yeah sure you did.
lucid junco
can you show me the other way
craggy haven
just multiply the first fraction by cos/cos lol
drifting swift
^
$\frac{1 - \frac{1}{c}}{1 + \frac{1}{c}} =\frac{(1 - \frac{1}{c}) \cdot c}{(1 + \frac{1}{c}) \cdot c} = \frac{c - 1}{c + 1}$
thorny flameBOT
Ann
drifting swift
abbreviating cos(ΞΈ) as c for my own convenience.
craggy haven
yay i love shortcuts
topaz sinewBOT
@lucid junco Has your question been resolved?
lucid junco
$\frac{1 - \frac{1}{c}}{1 + \frac{1}{c}} =\frac{(1 - \frac{1}{c}) \cdot c}{(1 + ...
hmmmmmm
how would i know to do that tho 
drifting swift
nested fractions
lucid junco
what is a nested fraction
drifting swift
fraction within a fraction
drifting swift
??
craggy haven
bc we've got cosines all over the place
drifting swift
^
also like
generally
for a nested fraction, a good move is to multiply the outer top and bottom by the LCM of the inner denominators
drifting swift
it isn't if you practice simplifying nested fractions a bunch.
if you're ok waiting like an hour or so, i can cook up a worksheet for you to practice on.
but if you don't want that, tell me as such. so that i don't waste effort making it.
lucid junco
thats thoughtful of you but i probably wont be able to work on it right now because my exam is tomorrow and im just catching up on everything rn
lucid junco
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
atomic ermine
"In a bank card code there are four digits. You have forgotten your code, but you know that one of the digits is 3, and no digit can be the same. What's the maximum amount of necessary attempts you need to crack the code?"
topaz sinewBOT
"In a bank card code there are four digits. You have forgotten your code, but yo...
atomic ermine
I think it is 9 times 8 times 7 for the remaining digits, and then multiply that by 4! (24) for the correct order
but book says it is 2016, or 9 times 8 times 7 times 4
why?
rough plover
instead of multiplying by 24 think about deciding the place of the 3 first, then choosing the other digits
atomic ermine
instead of multiplying by 24 think about deciding the place of the 3 first, then...
but even if you have the correct place for the three and you know the other digits, you don't have the code because you need the correct order for the remaining digits as well?
rough plover
but even if you have the correct place for the three and you know the other digi...
9 times 8 times 7 already decides the order
you would only need to multiply for order if you had done something like 9c3 to choose the digits, but here youve already assigned digits to these spaces
If that makes sense
atomic ermine
ok i get it
10 times 9 times 8 times 7 is the number for possible codes, and when we know one, it becomes 9 times 8 times 7
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
rain stratus
hello i have a question abt this question im working on
topaz sinewBOT
hello i have a question abt this question im working on
stuck forum
rain stratus
so the result I got is
$3042.37
but
my question is
would it be the increase of debt or total amount
I think its total amount
but I could be wrong
its probably the increase
stuck forum
Ok
Does that formula remind you of anything?
The one the problem asks you to calculate
rain stratus
is it the formula for derivatives?
stuck forum
Let's do even more basic than that
Like algebra class
Does that formula remind you of anything
rain stratus
nah
rain stratus
ohh
rain stratus
is it the formula for calculating the slope
rain stratus
i see i see
stuck forum
So "rise" is the change in the debt value
and the "run" is the number of years it took for that change to happen
rain stratus
yea
stuck forum
So that means you have 3042.37 increase in debt from year 9 to year 10
rain stratus
so I guessed it right
stuck forum
Yes
rain stratus
but now I see why its that
stuck forum
I was just trying to explain
stuck forum
I think its total amount
Just making sure because you said this π
stuck forum
in this case it's the average increase in debt
rain stratus
how could the total amount be less than what it was at first
after certain years passed
stuck forum
Yes. That's an excellent way of double checking your answer
stuck forum
Sure, let me know if you need help
rain stratus
doesn't the limit mean when x approaches the point on the graph?
or just x approaching whatever value you put there
stuck forum
Right. But is there a condition on "how" it must approach it? What I want to know is when does a limit exist
rain stratus
tbh i dont even remember
I havent done math in years
ah
is it when they approach at the same values from both sides?
stuck forum
is it when they approach at the same values from both sides?
DING DING DING
stuck forum
So does that happen here?
stuck forum
No. For the limit to exist, the left- and right-hand limits at a point must be equal
clearly they approach different values here
one is negative, the other is positive
Btw i'm not saying no to your answer, I'm agreeing that the answer is no
rain stratus
ahh
thats true
one is positive and the other negative
so if thats ever the case does that always mean the limit doesnt exist?
stuck forum
At x = 0, yes
rain stratus
I see
stuck forum
everywhere else it does
rain stratus
wym?
rain stratus
OHh
ok
me understands
ok how about
this question
maybe its too small to see
gimme a sec
stuck forum
sure
stuck forum
Alright, let's start by graphing -4x^2
stuck forum
Oh I thought you were doing it by hand
rain stratus
I aint that advanced yet
stuck forum
No it's fine. I'm sure you can do it
stuck forum
yes
rain stratus
2?
rain stratus
4
stuck forum
That's right
rain stratus
i mean y = -16
rain stratus
ok
stuck forum
what's the easiest one you can think of
rain stratus
1?
rain stratus
-4
rain stratus
i'td be 0
rain stratus
-4 still?
stuck forum
Yep. And you'll see the same patter with -2
So now you have 5 points
can you make a plot now?
rain stratus
hmmm can I ?
stuck forum
Yes, you can
it's not gonna bite π
If you want more points to work with, I suggest looking at x = 1/2 and -1/2
stuck forum
Haha I'm sure you'll manage.
rain stratus
I cant draw so im gonna try using a website to plot this graph
my graphing calculator is dead too
sigh
stuck forum
Well, do you know what a parabola looks like?
stuck forum
wait what website are we talking about
stuck forum
do you just want to see what it looks like or are you planning on printing it?
rain stratus
i just wanted to see
stuck forum
stuck forum
never used desmos
rain stratus
i graphed the question
rain stratus
how does one do that
stuck forum
Do you know derivatives?
stuck forum
Right! In other words, it gives you the slope of the tangent line at that point
So the problem has two parts
we want to find the slope of the tangent line
rain stratus
the slope?
stuck forum
and we want to know what the equation for it is
stuck forum
lol at the last one
stuck forum
But seriously though we need to calculate the slope
rain stratus
ok
stuck forum
so what's the derivative of y = -4x^2
rain stratus
isnt the slope y1 - x1 / x - y ?
rain stratus
ok
stuck forum
because, by definition, a tangent line only touches the graph at one point
so you can't have a "rise" or "run"
That's where the notion of a limit comes in
rain stratus
ahh
stuck forum
You say that second point approaches the first one
So that they're on top of each other
That's the derivative
stuck forum
Yes tha'ts right
so now we're interested in the slope at x = -2
so what's that then
rain stratus
the slope?
stuck forum
Okay, that's fine
So you have a function
and you want to know the slope of the tangent line at a certain point of the graph
rain stratus
Do u use y2 -y1/x2-x1?
stuck forum
You can't do that for a tangent line it only touches the graph at one point
stuck forum
Your suggestion about using the slope formula isn't wrong
However, it will only give you a secant line
For it to be a tangent line, you want to take the limit as one point approaches the other
Kinda like that
rain stratus
What
stuck forum
The red one is the tangent