I need help checking my soln
#help-10
gaunt tiger
...
n(n+1)/2 being even implies n = 4k , 4k-1...
n=4k implies the sum of red(or greens) has to be 4k^2 + k which has an odd factor so never a power of two... Similarly n = 4k-1 implies the sum is 4k^2 - k which also is not a power of two.
Now use the fact that any number not equal to a power of two can be written as the sum of consecutive numbers.
So, the sum of the reds = the sum of greens
kind hawk
what do consecutive numbers have to do with this
what if these sums include the same numbers?
obtuse pebbleBOT
@gaunt tiger Has your question been resolved?
gaunt tiger
what if these sums include the same numbers?
So that we can be sure that we are not colouring the same number twice
kind hawk
well yes that is the potential problem
gaunt tiger
I mean to say...
kind hawk
which you didnt argue about at all that it won't happen
gaunt tiger
18 = x + (x+1) + (x+2) + (x+3) green
What ever x is
And the rest of the numbers are coloured red
...
kind hawk
examples dont show anything
gaunt tiger
No
The total sum ( green + red) is 2z and if one say green, is z then the red sum automatically becomes z as well
What ever the terms that add up in the red maybe
They are not in green because they are coloured red
...
kind hawk
ok now we are getting somewhere
gaunt tiger
ok now we are getting somewhere
The consecutive part only matters to ensure that the terms of the sum are distinct
Also I need to show that the terms are less than 4k or 4k-1
tepid mountain
I think we can say that
Because the number of elements in the list is even
It means that the number of elements devisable by two
As it is devisable by 2 it can be distributed equally between 2 colors
So if it is distributed equally between the 2 colors the number of green elements should be equal to the number of red elements
kind hawk
the sum 3+5 is even but you cannot colour it in that way
kind hawk
How can I improve my proof
previously it wasn't for example clear that you wanted to write z as a sum of consecutive numbers
you just wrote that numbers can be written that way but not to which number you want to apply it to
obtuse pebbleBOT
@gaunt tiger Has your question been resolved?
gaunt tiger
you just wrote that numbers can be written that way but not to which number you ...
So is this a valid proof?
kind hawk
well you wrote down the correct steps but now you have to put them together properly
gaunt tiger
🤔
Ok
Let me write it up again
The sum of the numbers of the set {1, 2, 3,... n} is S = n(n+1)/2.
S = 2z implies n = 4k or 4k-1
n = 4k implies green or red sum(z)= 4k^2 + k and n = 4k-1 implies the green or red sum (z) = 4k^2 - k
In both cases z is not a power of two as it contains an odd factor.
Now use the fact that any number not equal to a power of two can be written as the sum of consecutive numbers.
So... z can be written as the sum of consecutive numbers that are distinct.
We colour these consecutive numbers Green and the rest are coloured Red. Q.E.D
By construction these numbers have sum equal
delicate edge
Hello, I have a simple question can I write interval as: K = (−17,+∞)∩Z?
versed stratus
Is there any context to this question?
sage geode
The notation is valid, yeah, assuming you are trying to express the set of all integers greater than -17 here
delicate edge
Is there any context to this question?
Of course
versed stratus
Yeah, bits it's redundant though, the first part already conveys that
delicate edge
Hello, I have a simple question can I write interval as: K = (−17,+∞)∩Z?
So i justed wanted to know if this notation is correct.
versed stratus
Yeah, seems right
obtuse pebbleBOT
obtuse pebbleBOT
@neon citrus Has your question been resolved?
limber token
obtuse pebbleBOT
@neon citrus Has your question been resolved?
obtuse pebbleBOT
@neon citrus Has your question been resolved?
royal onyx
Im confused how to get B
obtuse pebbleBOT
Im confused how to get B
royal onyx
and it doesnt give me a formula either
and usually to find the middle point i would use the m formula or add or subtract it
but i cant here because it doesnt seem right since im given 2/5
timid silo
Im confused how to get B
What is AC
timid silo
What is A
royal onyx
-20
timid silo
What is C
royal onyx
-5
timid silo
What is AC
royal onyx
-25….
warm shaleBOT
royal onyx
6
timid silo
what is AC
timid silo
Oh wait nevermind sorry
I have led you astray
Actually AC is not A * C
It's a line segement. They just didn't notate it
royal onyx
😭
timid silo
It's one dimensional
you only have x
You can still use the distance formula
just ignore the part with the y
royal onyx
15?
timid silo
Correct
royal onyx
timid silo
The question says the distance between A and C is 2/5 of the distance between A and C
royal onyx
wjats 2/5
grizzled shore
The question says the distance between A and C is 2/5 of the distance between A ...
B*
timid silo
$$ \overline{AB} = \frac{2}{5} \overline{AC}$$
warm shaleBOT
timid silo
You know what $\overline{AC}$ is
warm shaleBOT
warm shaleBOT
royal onyx
i@ mot good with fractions
warm shaleBOT
royal onyx
UHHHHHHHH
warm shaleBOT
royal onyx
IS B 15
royal onyx
well
technically…
ACTUALLY
leg m do the amth
so
wait
how do i find b
@timid silo
OHH
wait why isnt it 15
20-15 is 5
woven silo
its negatives melly
timid silo
what
timid silo
no
woven silo
I DIDNT MEAN THE ANSWER
timid silo
wait -15
You will have to relearn fractions 
because
if you don't know what $\frac{2}{5}$ is you won't be able to solve this
warm shaleBOT
woven silo
she doesn’t know multiplication
woven silo
12*13
royal onyx
ummm
royal onyx
royal onyx
yes..
timid silo
so that means the $\frac{2}{5}$ would be smaller than 1 right?
warm shaleBOT
timid silo
umm
woven silo
i promise u she’s not in 3rd grade or something
timid silo
but 2 is bigger than 1
do you know what $\frac{5}{5}$ is?
warm shaleBOT
timid silo
so
royal onyx
:01:
timid silo
why would it become 40 if you subtract from from it
royal onyx
but ifs division
timid silo
$$\frac{5}{5} - \frac{3}{5} = \frac{2}{5}$$
warm shaleBOT
timid silo
if $$\frac{5}{5} = 1$$ and $$\frac{2}{5}$$ is less than $\frac{5}{5}$ how does $$\frac{2}{5} = 40$$
warm shaleBOT
timid silo
no
plain crater
becuase 2 divided by 5 is 40
how do you get a bigger number from that
woven silo
becuase 2 divided by 5 is 40
how
woven silo
MELA
scarlet gale
% means you divide by 100.
timid silo
MY FRIEND SIAD ITS 40%
what is 40% of 1
woven silo
WHATS 40% IN DECIMALS
royal onyx
WHATS 40% IN DECIMALS
0.4
woven silo
FINALLY
scarlet gale
It means per cent or per 100.
plain crater
MY FRIEND SIAD ITS 40%
.4 = 40% of 1
royal onyx
WJERE ARE THESE PEOPLE COMING FROM
royal onyx
It means per cent or per 100.
so tje answe is 100
timid silo
.4 = 40% of 1
40% of 100 is 40 not .4 😭
woven silo
WJERE ARE THESE PEOPLE COMING FROM
it’s bc ur so stupid
plain crater
40% of 100 is 40 not .4 😭
whoopsie
royal onyx
it’s bc ur so stupid
IM@NOT
plain crater
meant 1
woven silo
idk how u have the confidence to ask problems anymore
timid silo
I JUST GOT INTO GEOMETRY
Get out
scarlet gale
it’s bc ur so stupid
<@&268886789983436800>
timid silo
@scarlet gale stop being weird
woven silo
STOPP
timid silo
They're not
timid silo
no
timid silo
You will need to relarn how fractions work. do you want me to find you a book to read so you can do that?
or like, you know what khan academy is right?
royal onyx
😨
woven silo
omg khan academy…..
timid silo
yeah, but aleks is teaching you geometry?
royal onyx
yea!
radiant osprey
What is occurring here
timid silo
You don't know how to do fractions
timid silo
What is occurring here
@scarlet gale being weird
royal onyx
What is occurring here
this guy wants to reteach me fractions cuz idk how to do them and im in geometry
:01:
Oh
Yea
timid silo
They came because of the ping
woven silo
sushi is my friend
woven silo
yes
royal onyx
she calls me dumb all tje time!
radiant osprey
Yes this channel is a mess
royal onyx
im not dumb though
radiant osprey
What is the question here
woven silo
here
radiant osprey
I see
royal onyx
I KNOW A LOT
I DID THE DISTANCE FORMULA
AND GOT -15
:01:
wjy is that emoji gone
radiant osprey
Do you know how to calculate 2/5 ths of a number
royal onyx
radiant osprey
So to work out half of a number, let's say 8, we divide into two equal pieces
Yes exactly
So to find half of 8 we divide it by two
8 divided by 2 is 4
So half of 8 is four
Agreed?
royal onyx
YA CUZ 4+4 IS 8
radiant osprey
Exactly
Now then
The question is asking about 2/5
This is two fifths
Let's think about just a single fifth for the time being
Given that halving a number is the same as dividing by two
Have a guess how we might calculate a fifth
radiant osprey
Yes that's half of 5
But instead of half
How about a fifth
Say, of 10
How might we calculate a fifth of 10
royal onyx
OKAY
radiant osprey
So
royal onyx
YA
radiant osprey
To work out a half of a number we divide by two
To work out a fifth we divide by five
Now the question says that the length of AB is two fifths of the length of AC
You already worked out that the length of AC is 15
So the first thing we need to do is work out is what a fifth of 15 is
radiant osprey
That's a half of 15 but you have the right idea
royal onyx
😭
royal onyx
15/5
royal onyx
3
radiant osprey
Yes!
OK finally
We don't just want a fifth of AC
We want two fifths of AC
If one fifth of AC is 3
Then what is two fifths of AC?
royal onyx
6
radiant osprey
There you go
royal onyx
royal onyx
YES
radiant osprey
We have just worked out 2/5s of AC
The final step is to add this distance on
A is at -20 and B is 6 units away
So, where is the point B?
royal onyx
-14
royal onyx
U HAVE AN ANSWER KEY?????
ITS AT TJE BOTTOM
radiant osprey
Yep
royal onyx
WE JUST NEED TO SHOW OUR WORK
woven silo
ohh
radiant osprey
So that's how fractions work
radiant osprey
If you have 2/5 you divide by 5 and multiply by 2
If you have 38/235 or something you divide by 235 and multiply by 38
Easy as that
woven silo
i still hate fractions
i bet u don’t like multiplication too…
woven silo
yeah i’m pretty sure
verbal niche
This is for a game that I’m playing
obtuse pebbleBOT
This is for a game that I’m playing
verbal niche
I’m trying to rule out that the loot boxes aren’t rigged
I rolled 7000 times, the thing I’m trying to get is 1/4000
I did the math like this :(3999/4000)^70000
Which is the chance that I don’t get it in 7000 rolls
I kind of just want confirmation for this
gilded needle
that's correct (typo, should have been 7000 instead of 70000 but otherwise fine)
verbal niche
Interesting
And then there’s like the 2nd rarest item
I got 13 of them in 5000 rolls, the chances of getting those are 1/200 how would I calculate that?
I know you have to use nCr but I honestly just forget what you would do
verbal niche
It’s been 2 months since my exam lol
wooden cipher
so it would be like this: $\newline \binom{#rolls}{#wins} (probability of winning)^{#wins}(probability of losing)^{#losses}$
warm shaleBOT
GarlicB
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
gilded needle
without explicitly computing the probability of exactly 13 successes in 5000 attempts, you can check whether it seems reasonable with a much easier calculation, just find the expected number of successes in 5000 attempts.. That will simply be 5000/200 = 25
wooden cipher
hopefully that makes sense, its kinda a paint o fix the errors
gilded needle
and you can also compute the variance of the number of successes
and see if you lie within say one standard deviation of the mean
wooden cipher
yeah you should expect 25 wins, so the probabilities for both seem to be skewed
verbal niche
I mean with one look I thought it was weird
But the devs of the game just said “no small sample size”
wooden cipher
you do have to be careful about looking at the probability of winning 13 times because that is one result in 5000 different results, the probability will be low
gilded needle
variance is (N)(p)(1-p), which in this case would be (5000)(1/200)(199/200) = 24.8, which gives a standard deviation of about 5
so anything from 20 to 30 would be well within the expected range
verbal niche
13 is extremely low then lol
wooden cipher
yeah
gilded needle
and say, most outcomes should be within 15 to 35 if we approximate the distribution as normal
wooden cipher
what i meant to say was looking at the probability winning exactly 13 in isolation
but yeah, in comparison to other probabilities, it is still very low
verbal niche
Oh how do you check for all cases of 13?
gilded needle
yea, might be more meaningful to ask, what is the probability that it would have been 13 or lower
verbal niche
I have stats again in uni so
gilded needle
and that probability's gonna be quite low, like less than 2.5% again assuming the normal approximation (which is probably fine since you have 5000 trials)
verbal niche
**GarlicB**
Compile Error! Click the <:errors:504266556054962196> reaction for m...
Wait why doesn’t this cover all cases?
verbal niche
and that probability's gonna be quite low, like less than 2.5% again assuming th...
Ty
wooden cipher
Wait why doesn’t this cover all cases?
this looks specifically at 13 wins
verbal niche
Oh I see
wooden cipher
or whatever number of wins
but you dont really know what it means without knowing the other probabilities
verbal niche
So I would need to make a normal graph to make a better understanding?
wooden cipher
something like that
verbal niche
Well not normal, it would be skewed
gilded needle
with 5000 trials, it's reasonably close to normal
either way the probability that you would have had 13 or fewer successes in 5000 attempts is on the order of 1%
0.637% if computed exactly, 1.056% if computed using the normal approx
(assuming this applet's calculation is accurate)
i got 0.637% using matlab and the binomial distribution, but it complained about large binomial coefficients
wooden cipher
yeah thats definitely not normal
wooden cipher
I did the math like this :(3999/4000)^70000
i did check this, its around 17%
gilded needle
close enough for asking this sort of question ("how likely is it that i only got 13 successes")
if you don't need high accuracy that is
wooden cipher
so its definitely a possible and repeatable scenario within a reasonable amount of time
gilded needle
it can't be ruled out that you were just unlucky... try repeating the test for another 5000 to 7000 attempts, if you can use a bot and not do it manually
obtuse pebbleBOT
@verbal niche Has your question been resolved?
verbal niche
I’ll do a few thousand more
But I can’t not do it manually, I do have an auto clicker, still takes hours
verbal niche
it can't be ruled out that you were just unlucky... try repeating the test for a...
At what point do you rule it out?
My stats teacher would have definitely been suspicious if this was a question lol
That’s a question for ethics though I guess
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
runic void
obtuse pebbleBOT
runic void
is it asking, if G contains 4 elements does x^4=e works for all elements?
royal basin
yes that is what it is saying...
runic void
I'm not sure where to start
my gut says, since the set is finite, and groups are closed, for each element in G, there is some n such that a^n=e
royal basin
your job is to tick the statement if it is true and not tick it if if it false
royal basin
my gut says, since the set is finite, and groups are closed, for each element in...
that is true yes but you kinda have it the wrong way around
atomic bobcat
can you point me to right direction a bit
can you find a example of group with 4 elements
royal basin
i can't think of what to say that wouldn't just give it away like || for any finite group G, x^|G| = e for every x in G||
atomic bobcat
as a theorem
yeah
royal basin
Lagrange's thm
or rather it's a couple steps removed from that
- the thm itself: the order of any subgroup divides the order of its parent group
- the order of an element equals the order of the subgroup generated by it
- x^n = e is equivalent to ord(x) divides n
burnt otter
I did part a but i'm stuck on part b
obtuse pebbleBOT
I did part a but i'm stuck on part b
frank monolith
just take cos^-1 on both sides for the equation cos2theta = 7/25
burnt otter
I'm sorry i don't quite understand
plucky rivet
just take cos^-1 on both sides for the equation cos2theta = 7/25
Do this then you already know what $ \theta$ is equal to,sub that in place of $\theta$
warm shaleBOT
Cyrenux
burnt otter
hmmm
plucky rivet
Reminder that $$ \arccos = \cos ^{-1 }$$ is inverse of $$\cos $$
warm shaleBOT
Cyrenux
plucky rivet
And for inverse functions we have $$ f^{-1}(f(x)) = x = f(f^{-1} (x))$$
warm shaleBOT
Cyrenux
plucky rivet
@burnt otter
plucky rivet
just take cos^-1 on both sides for the equation cos2theta = 7/25
So use it
plucky rivet
You know what theta is equal to
Look what its equal to
And sub that in place of theta
And boom
plucky rivet
so both sides would equal 2theta
Inverse trigonometric functions give angles yes
trim portal
What exactly is the inductive hypothesis in this case? I dont get that part of the proof
obtuse pebbleBOT
What exactly is the inductive hypothesis in this case? I dont get that part of t...
trim portal
the system is natural deduction btw, the rule of inference is modus ponens
ping me if you answer please
obtuse pebbleBOT
@trim portal Has your question been resolved?
trim portal
.close
calm shadow
Hey can I please get help on this question? I have put my working and the question as well
obtuse pebbleBOT
Hey can I please get help on this question? I have put my working and the questi...
calm shadow
I first write it in polar form and then divide the cis theta whole raising the absolute value to the power of 20
steel parcel
I first write it in polar form and then divide the cis theta whole raising the ...
ok think of 1+i as z, a complex number
using the roots of unity, what can you say about z^20?
this should give you an idea of how to solve this
oh wait de moivres theorem
you should convert 1+i into the form of rcis(theta)
same with 1-i
steel parcel
ok let’s say you get like root2cis45
you can then do (root2)^20cis(20*45)
but note that 1-i yields -45
calm shadow
Yes then I got 1024 cis 20root2
steel parcel
i think you messed something up
calm shadow
but note that 1-i yields -45
I think this is where I went wrong, since I'm using degrees I did 360-45 giving 315 instead of -45
steel parcel
root(2)^20 = 2^10 (DONT EXPAND THIS YET)
2^10cis(900) + 2^10cis(-900)
try and simplify that
calm shadow
Wait where did 900 come ftom
steel parcel
no
calm shadow
Since cis= cos + isin
calm shadow
So 20(cos45+sin45) no?
steel parcel
So 20(cos45+sin45) no?
you are saying the magnitude (r) is 20
calm shadow
Oh so I only multiply the theta and not the whole trig function
steel parcel
yep
uneven night
Determine a system of equations (five equations) from which the node potentials V1, V2, V3, V4, and V5 can be solved. The equations must be written in the form of a1iv1 + a2iv2 + a3iv3 +a4iv4+a5iv5 = bi where i is the number of a certain equation in the system, and the coefficients a1i, a2i a3i, a4i,a5i and b, must not contain the node potentials but instead the potentials va, vb and vc
obtuse pebbleBOT
Determine a system of equations (five equations) from which the node potentials ...
royal basin
kirchoff's laws?
uneven night
kirchoff's laws?
I did like this but I’m little uncertain about it, I tried with kcl on each node. But the problem that I have here in dependent current source which makes it hard
@royal basin
compact shadow
Shouldn’t there be two laws? One for node one for circuits
I see you used one. Or these two are equivalent you only need one?
uneven night
I see you used one. Or these two are equivalent you only need one?
I don’t understand
But anyway
This is similar question but I don’t understand the solution, may someone help me understand the solution?
compact shadow
This is what I said for the second law
Might be equivalent, this one is more convenient I think. Since you have 4 circuits, but 6 nodes. Using the second law is more convenient
uneven night
Might be equivalent, this one is more convenient I think. Since you have 4 circu...
You mean 5 nodes
uneven night
But do you understand the solution?
They used KCL
But I don’t know how they did for example on node 1
.close
obtuse pebbleBOT
compact shadow
Sorry no idea. Seems to be called node potential method, which is a physics thing I don’t know anything about
obtuse pebbleBOT
Available help channel!
rugged canyon
hi can i get some help really quick
obtuse pebbleBOT
hi can i get some help really quick
high lily
its neither
high lily
show your work
rugged canyon
okay hold on
rugged canyon
show your work
high lily
show your work for the deriviative of
x^3 - 2x
because you're pretty much asserting that its 3x, (or 3x^2),
both of which are wrong
how exactly are you getting those?
obtuse pebbleBOT
@rugged canyon Has your question been resolved?
compact shadow
(f/g)’=f’(1/g)+f(1/g)’=f’(1/g)-f(g’/g^2)=(gf’-g’f)/g^2
high lily
well there the derivative of 5x-2 is actually 5
and the derivative of x^2+1 is actually 2x
you have been introduced to stuff like power rule right?
and linearity of the derivative operator
ignoring the rest of the question can you apply those to
$$\dv{x}(x^3 - 2x)$$
warm shaleBOT
ℝam()n()v
frank monolith
no
high lily
are you implying that whatever appears after the first term is irrelvant?
i.e. implying that
$$\dv{x}(f(x) + g(x)) \wthonk f'(x)$$
warm shaleBOT
ℝam()n()v
high lily
that if i instead asked for
$$\dv{x}(1 \red{+ x^3 + x^{123} - 7x})$$
you'd say 0?
warm shaleBOT
ℝam()n()v
obtuse pebbleBOT
@rugged canyon Has your question been resolved?
sacred root
**ℝam()n()v**
You can set up a emoji, damn
steel urchin
obtuse pebbleBOT
steel urchin
doing number 24, and ive gotten 4^1/4 e^((ipi + 2kpi) / 4)
glossy basalt
nice
worthy cargo
nice
obtuse pebbleBOT
steel urchin
.reopen
obtuse pebbleBOT
✅
steel urchin
.close
obtuse pebbleBOT
steel urchin
.reopen
obtuse pebbleBOT
✅
steel urchin
yea, just be careful with the k's you choose
okay can you explain to me why the solution for this one to be right is pi - tan^1(0)
and just not tan^1(0)
glossy basalt
like you have to choose k=0,1,2,3
steel urchin
im pretty confused about this point
steel urchin
yes
glossy basalt
okay can you explain to me why the solution for this one to be right is pi - tan...
it's simply because it's on the negative real axis
steel urchin
because i thought it could also be 4^1/4 e^0i/4
glossy basalt
and it's 180°
so, pi
for complex planes, we can't just consider its slope
but we also have to consider where it is
e.g. which Quadrant or where on the axes
steel urchin
so whenever you have something on the negative real axis with no imaginary part its going to be pi?
as the angle?
glossy basalt
so whenever you have something on the negative real axis with no imaginary part ...
yes
or pi +2kpi
steel urchin
okay okay strange
glossy basalt
fun
steel urchin
but if i did 2pi would this be e^0i/4??
glossy basalt
gtg, good luck!
obtuse pebbleBOT
steel urchin
me too f1 qually starting 😛
obtuse pebbleBOT
Available help channel!
tiny saddle
obtuse pebbleBOT
tiny saddle
what does constant proportionality mean?
polar fossil
it means how much does one thing go up when the other thing goes up
in this case it literally is y/x as it says
harsh remnant
tiny saddle
it means how much does one thing go up when the other thing goes up
like gradient?
polar fossil
yeah
royal basin
and you don't need to know
f(x) = (x-1)(x-2) Q(x) + (Ax + B)
where Q is the quotient, a polynomial you can stay blissfully ignorant about
no, you are not assuming deg(f) = 2
nor 3, nor anything else
(divisor * Quotient) + (remainder * divisor)
no
it's f(x) = divisor * quotient + remainder
just the remainder
not the remainder times the divisor
i didn't and i never said it was.
that's the remainder
and its degree is 1 less than that of the divisor, (x-1)(x-2)
compact shadow
By CRT, k[x]/(x-1)(x-2) is isomorphic to k[x]/(x-1) product k[x]/(x-2), you need to find the inverse image of (3,14)
royal basin
By CRT, k[x]/(x-1)(x-2) is isomorphic to k[x]/(x-1) product k[x]/(x-2), you need...
are you actually fucking serious about this CotM
i know you have a fetish for overcomplication but COME ON
assuming your arithmetic is correct, it looks reasonable.
compact shadow
The inverse image of (1,0) (0,1) respectively are 2-x and x-1
obtuse pebbleBOT
compact shadow
I thought since it contains concept like remainder it must be from an algebra course sorry…
royal basin
I thought since it contains concept like remainder it must be from an algebra co...
polynomial long division is learned a bit before that.
obtuse pebbleBOT
Available help channel!
vivid arrow
so x^2 = -1 has no real roots
obtuse pebbleBOT
so x^2 = -1 has no real roots
vivid arrow
but if i square both sides, i get x^4 = 1
where there are real roots
doesn't this mean x^2 = -1 has real roots asw
royal basin
no
squaring both sides of an equation can (and in this case does) introduce extraneous solutions
vivid arrow
so it's not exactly the same as multiplying both sides by the same number
royal basin
indeed it is not
timid silo
so x^2 = -1 has no real roots
It does
haughty coyote
so it's not exactly the same as multiplying both sides by the same number
it's applying the function f(x) = x² to both sides
vivid arrow
indeed it is not
cool thnx
compact shadow
x^4-1=(x^2-1)(x^2+1) your x^4-1=0 has two real roots, x^2-1=0 has two real roots , minus, your x^2+1=0 still has zero real roots
haughty coyote
since it's not injective, it can introduce extraneous solutions
vivid arrow
x^4-1=(x^2-1)(x^2+1) your x^4-1=0 has two real roots, x^2-1=0 has two real roots...
thanks
timid silo
what
NVM answer will be variable
I mean an unsolved term
...
That's for the reaction
royal basin
those are both bad ways to describe the imaginary unit i.
timid silo
Ik
royal basin
i isn't a "variable" or an "unsolved term".
it is i.
and it is also not a real number.
timid silo
No
royal basin
ok bye ¯_(ツ)_/¯
compact shadow
Nothing sus as long as one is discussing math
haughty coyote
terrible behavior regarding complex numbers and discussing math
sends people to his DMs rather than staying here
compact shadow
I see
obtuse pebbleBOT
@vivid arrow Has your question been resolved?
slim cypress
It's a simple question but what is a "unit" on a coordinate grid?
obtuse pebbleBOT
It's a simple question but what is a "unit" on a coordinate grid?
timid silo
unit length means 1
slim cypress
so like is the red dot a unit?
high lily
no
high lily
that would be a lattice point
slim cypress
you're not referring to unit vectors right?
no
high lily
do you have the specific context where this wording is coming up?
slim cypress
yea like i have to plot some points that indicate it's some sort of city building on a coordinate grid and its mimicking a "layout" of a city and the instructions say "Each unit on the grid 1 block"
and im just trying to know what a unit on the grid is
timid silo
1 unit probably refers to the footprint of a sector of a building
high lily
length of 1
timid silo
a sector
hexed gull
@slim cypress is it resolved? 🐣
slim cypress
im still confused on what a unit is
obtuse pebbleBOT
@slim cypress Has your question been resolved?
polar fossil
a unit is a distance, it's the distance between two parallel blue lines
obtuse pebbleBOT
@slim cypress Has your question been resolved?
slim cypress
so this is a unit? or the whole square
tardy epoch
so this is a unit? or the whole square
unit length and unit square are two different things
tardy epoch
It's a simple question but what is a "unit" on a coordinate grid?
So it depends on context where you read "unit" from
slim cypress
yea like i have to plot some points that indicate it's some sort of city buildin...
@tardy epoch
tardy epoch
Yea it's length
slim cypress
so this is a unit? or the whole square
so is this unit length or na
polar fossil
yes those are both unit length
fringe sparrow
could anyone help me figure this out?
obtuse pebbleBOT
could anyone help me figure this out?
mighty jacinth
the first interval just excludes integer multiples of pi, csc is continuous everywhere except integer multiples of pi, so the first one is continuous on its interval
e^3x is continuous for all positive x, so in this context it's continuous over the interval
the last one is not continuous over its domain
fringe sparrow
whats the difference between it being continuous over its domain vs continuous over its interval? @mighty jacinth
mighty jacinth
well, there's only really a specific interval if they provide one, otherwise, the instructions imply that the interval is the domain
for example, it said tan(x) on the interval [0, 2pi]
but if it had just said tan(x) the implied interval would be the domain of tan(x)
i just changed the wording to be consistent with the assignment
mighty jacinth
oh wait
i just realized the box on the left says over the domain
no u got all 3 of those right
or maybe move the one on the top to continuous over the interval
instead of domain
that seems most plausable
fringe sparrow
would any of them be “not continuous over its domain”?
i feel like i’m missing one but all of them seem correct to me
mighty jacinth
wait yes
the one on the bottom of continuous over the domain isnt
its not continuous on pi/2
sorry
fringe sparrow
Okay thank you so much!
mighty jacinth
no problem
wild forge
How do i
wild forge
Like cancel this out
Tried this but it doesnt seem to be going anywhere
This is the actual problem
gilded needle
your denominator is wrong, both terms should have a factor of (4 + x sqrt(x)), but the second one only has (4 + sqrt(x))
gilded needle
instead of multiplying and dividing by 4 + sqrt(x), which as you observed isn't really helping, try instead factoring the denominator
gilded needle
no, in the original problem
gilded needle
yes and then...
cinder lintel
instead of multiplying and dividing by 4 + sqrt(x), which as you observed isn't ...
It does help tho
The questions done
gilded needle
The questions done
how so?
gilded needle
the num and denom still go to 0 when you plug in x=16
cinder lintel
No?
gilded needle
1/x 4+rootx
yes, with the approach i suggested, but not with the original approach
gilded needle
Do i rwtionalize it as normal?
no, factor the (16 - x) in the denominator (observe that x = (sqrt(x))^2 since you're only concerned with positive x)
cinder lintel
16-x cancels
From multiplying dividing.4 +root x only
Multiply divide by 4+root x and youll get the answer
cinder lintel
Dont multiply
Keep as brackets
16-x/(16x-x²)(4+rootx)
You have this
If you take out x from 16-x²
Numerator will cancel put
wild forge
Ohh
Got it
Thanks bro!
Same in the answer key
So its better to not
Multiply immediately
.close
turbid charm
in this , am i supposed to take it as x would b the intersection
of the given interval and |x+3|-1/|x|-2 >= 0 right ?
obtuse pebbleBOT
in this , am i supposed to take it as x would b the intersection
of the given in...
vale solar
how to distribute signs in algebra
royal basin
how to distribute signs in algebra
please open your own channel (read #❓how-to-get-help) or ideally go to #prealg-and-algebra
royal basin
in this , am i supposed to take it as x would b the intersection
of the given in...
missing parentheses but yes
cloud igloo
obtuse pebbleBOT
obtuse pebbleBOT
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
1
cloud igloo
this some kind of troll?
No
cloud igloo
also multiple counts of badtex.
Huh?
royal basin
$tanh$ instead of $\tanh$, $cosh$ instead of $\cosh$, $log$ instead of $\log$
warm shaleBOT
Ann
royal basin
anyway this looks mighty ugly but at the same time
tanh and cosh can be rewritten in terms of exponentials
cloud igloo
I see
royal basin
so this might help somewhat
cloud igloo
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
slow fulcrum
obtuse pebbleBOT
compact shadow
These three roots, call them u,v,w
a=-(u+v+w)
b=(uv+vw+wu)
c=-(uvw)
Direct calculation then, assuming u+w=2v
(Replacing v with (u+w)/2)
obtuse pebbleBOT
@slow fulcrum Has your question been resolved?
slow fulcrum
Direct calculation then, assuming u+w=2v
how do we know if u+w = 2v?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
velvet plover
hi i need help with a question math 180 calc
obtuse pebbleBOT
hi i need help with a question math 180 calc
velvet plover
do i just plot in the x to the formula provided for point Q?
if i do that, these are the answers i get
but im not too sure if thats correct
obtuse pebbleBOT
@velvet plover Has your question been resolved?
fresh trail
but im not too sure if thats correct
Your numbers look reasonable, if you were plugging in the given x-values to the formula they give for m then you were doing it right. For the first one you would've done (sqrt(11.5-3)-3) / (11.5-12) and so on like that.
velvet plover
Your numbers look reasonable, if you were plugging in the given x-values to the ...
would this be the answer?
these are my answers, but im not too sure if they are going to be negative,
fresh trail
would this be the answer?
I think your square root goes too far and 12 isn't included int he fraction
I get 0.16905 for the first one
fresh trail
I think what you posted is [ (sqrt(11.5-3)-3)/11.5 ] - 12 rather than (sqrt(11.5-3)-3)/(11.5 - 12)
fresh trail
Almost! They all need parentheses for the numerator and the ones after the first one shouldn't have the square root go as far (to match the first one). The results should all be close together but slightly different
velvet plover
Almost! They all need parentheses for the numerator and the ones after the first...
i feel like im doing something wrong tbh
fresh trail
Now it's doing multiplication on top, it should be like (sqrt(11.5-3) - 3), so the first parenthesis should be at the very start and the last one for the numerator after the last 3
(sorry that it's so weird to get right)
velvet plover
all good
fresh trail
Ok so close, just get rid of the parentheses around the last (-3)
fresh trail
Ok great!
fresh trail
I think that's everything, it's a lot of words just saying to plug numbers into a formula it seems
velvet plover
ok got it so the answer for x=11.5, m_sec = .16905?
median coral
What is the domain of f+g? Select the correct choice below, if necessary, fill in the answer box.
(I completed the first part but struggling on the second.)
velvet plover
What is the domain of f+g? Select the correct choice below, if necessary, fill i...
wrong channel
gray turtle
What is the domain of f+g? Select the correct choice below, if necessary, fill i...
read #❓how-to-get-help
fresh trail
ok got it so the answer for x=11.5, m_sec = .16905?
Yep, that's what I get, and the other questions should be really similar decimals but slightly different
median coral
my fault
fresh trail
Yep! Those are all good. I think the point of the problem is to notice that the answers are slowly approaching 0.16667 or thereabout
velvet plover
Yep! Those are all good. I think the point of the problem is to notice that the ...
ok great! so for my part b its asking to estimate the slope of the tangent to curve at P
would it just be .16667?
or do i need to use the m_tan formula?
fresh trail
would it just be .16667?
Yeah it should be, the values for the previous question with x=12.something should also go to 0.16667
I wasn't taught it this way with m_tan and m_sec, but since it says to use the results of part a, i think you wouldn't have to use a second formula
