then it would be
#help-13
jade stag
crimson sedge
thats a different problem??
jade stag
1+(x^2 )^3
crimson sedge
what
jade stag
left side is accurate, right side isnt
crimson sedge
dude ignore the left side
jade stag
ok
crimson sedge
huh
jade stag
-1(x-1)
wraith daggerBOT
hibyehibye
crimson sedge
$(a+b)+c = a+(b+c)$
wraith daggerBOT
hibyehibye
jade stag
if it was 1-1x instead of x-1 then ud distribute the 1?
jade stag
**hibyehibye**
i get it now, but what does parenthesis represent then
crimson sedge
if it was 1-1x instead of x-1 then ud distribute the 1?
no (1-x)-1 = -x
halcyon marlin
so (x+1)*5 means you add x+1 first then multiply becuase parenthesis is the 1st order of operation
jade stag
if it was 1-1x instead of x-1 then ud distribute the 1?
1-1(1-x) -> 1-1+x = 2+x
halcyon marlin
x+1*5 means you multiply first then add x becuase multiplication is the 3rd order and adding is the 5th
crimson sedge
1-1(1-x) -> 1-1+x = 2+x
oh thats correct
wait it isnt
1-1 is 0
but like the idea to distribute the negative sign is correct
jade stag
so (x+1)*5 means you add x+1 first then multiply becuase parenthesis is the 1st ...
u cant x+1 though, so u distribute the 5 to x+1
i understand pemdas
halcyon marlin
yes so you can resolve the parenthesis
jade stag
but some things are strange
jade stag
like -5(x+5)(x+5)
crimson sedge
$-(a+b) = -1 \cdot (a+b)$
jade stag
u do x+5 * x+5 first
wraith daggerBOT
hibyehibye
halcyon marlin
u do x+5 * x+5 first
because multiplication is commutative yes
also its (x+5)(x+5) not x+5*x+5
crimson sedge
right? or can u do -5(x+5) first
order doesnt matter
jade stag
u get same answer in the end tho right
jade stag
also its (x+5)(x+5) not x+5*x+5
im aware
halcyon marlin
so why is it weird?
jade stag
the order
halcyon marlin
well yea multiplication is commutative
jade stag
cause hibyehibye
says u dont
says
it doesnt matter
in that situation
-5(x+5)(x+5)
jade stag
order doesnt matter
^
i understand what ur saying
but trying to figure out
why both of you are saying different things
crimson sedge
we arent
halcyon marlin
we are saying the same thing lmao
crimson sedge
commutative means a * b = b * a
halcyon marlin
no
jade stag
-5(x+5)(x+5)
apply pemdas or not
halcyon marlin
ofc u do
jade stag
ok
crimson sedge
yes always but multiplication is commutative
halcyon marlin
yes you are doing parenthesis first which is why you have to distribute it
jade stag
-5 is outside parenthesis tho
its multiplication
pe(M)das
while others are (P)emdas
or are both
multiplcation
so its same sht
halcyon marlin
you are adhering to the rule that parenthesis is first by distributing -5 instead of only dojng -5*x
how is this not clear
jade stag
boop
crimson sedge
$(-5)(x+5) = -5x -25$
wraith daggerBOT
hibyehibye
jade stag
didnt know the -5 had an invisible parenthesis
halcyon marlin
everything technically can
you just put it around negative terms often to make things more intuitive
like 5+(-2) or 5*(-2) instead of 5+-2 and $5\times-2$
wraith daggerBOT
Køter
jade stag
(x-1)-1 t first glance man
looks a lot like -1(x-1)
i wish they did this
(x-1) + -1
well either way this is very awkward
halcyon marlin
ive never heard of this before
jade stag
so rule of thumb
if its on the right side of parenthesis
dont distrubute
dont multiply
halcyon marlin
is that what you got out of this
jade stag
si
halcyon marlin
the rule thumb is
if youre subtracting
dont multiply
becuase subtracting is not the same as multiplying
halcyon marlin
wdym see it that way
how have you ever seen 5-3 for example
have you ever turned that into $-3\times 5$
wraith daggerBOT
Køter
jade stag
-1(x-1) your multiply a minus number
halcyon marlin
or been confused as to what 5-3 means?
halcyon marlin
im not asking you to caluclate it lmao
im saying have you ever been confused as to what 5-3 means
and confused it for $-3\times 5$
wraith daggerBOT
Køter
jade stag
i know how to multiply and subtract
just at first glance
to the untrained eye
it looks like -1(x+1)
thats all
dont over think it
jade stag
ty for the help
ill be careful on this
the order
will mean + or -
or multiply
bsaed on its location
t
y
jade stag
i got it man
halcyon marlin
no you clearly dont if you still think it has anything to do with order
or location
jade stag
u can rewrite it
jade stag
from (x-1)-1 to -1+(x-1)
i understand
its like a psychology thing
"are you left brained or right brained" and u watch a cinderella spin
left or right
depending on which side of ur brain u use the most
.close
smoky stump
why does the cardinality of Real is the same as the cardinality of positive reals
smoky stump
whereas the cardinality of R is not the same as the cardinality of integars
terse silo
The cardinality of a set refers to the size of the set, which is given by the number of elements in the set. Two sets have the same cardinality if there exists a bijection (a one-to-one and onto mapping) between them.
In the case of the real numbers (R) and positive real numbers (R+), we can define a bijection between them. Specifically, we can define the function f(x) = e^x, which maps each real number x to its positive exponential e^x. This function is one-to-one (since e^x is always positive) and onto (since every positive real number y has a corresponding value x such that y=e^x).
On the other hand, there does not exist a bijection between the set of integers (Z) and the set of real numbers (R). This can be shown using Cantor's diagonal argument, which demonstrates that there is no way to list all of the real numbers in a countable sequence. Therefore, the cardinality of R is greater than the cardinality of Z.
In summary, the cardinality of R+ is the same as the cardinality of R because there exists a bijection between them, while the cardinality of R is not the same as the cardinality of Z because there is no bijection between them.
cedar kilnBOT
@smoky stump Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
how can I do this
cedar kilnBOT
how can I do this
buoyant latch
Which one
south tundra
Could you translate?
crimson sedge
Could you translate?
wait a minute
idk if it will be 100% like in my language, but we'll see
buoyant latch
I’m going to guess it’s asking what m value gives you 1 single real root
For the first question
south tundra
Close enough
south tundra
Okay, so first you need to consider the case when that quadratic has a single root
buoyant latch
@crimson sedge what do you know about the nature of roots of a quadratic from its coefficients?
buoyant latch
If I give you y = ax² + bx + c
crimson sedge
cause math is universal
buoyant latch
What can you tell me about the roots
crimson sedge
there is 2
crimson sedge
2 roots
buoyant latch
Are you sure there are 2 roots
buoyant latch
How many roots does y = x² + 1 have
crimson sedge
cause the - or + of the delta
crimson sedge
How many roots does y = x² + 1 have
idk lol
buoyant latch
y = 1x² + 0x + 1
crimson sedge
1
buoyant latch
There is 1 root?
crimson sedge
idk, it is?
crimson sedge
Well I’m asking you
why
crimson sedge
What does a root mean
the possible results?
buoyant latch
the possible results?
No
crimson sedge
so what is it
buoyant latch
Given f(x) = ax² + bx + c, if f(x₀)=0, then x₀ is a root of f(x)
So
If I give you y = ax² + bx + c
What can you tell me about the roots
crimson sedge
its not function?
crimson sedge
If I give you y = ax² + bx + c
What can you tell me about the roots
one root?
buoyant latch
Why are you guessing
crimson sedge
Why do you say 1 root
"y"
buoyant latch
How many roots does y = ax² + bx + c have?
buoyant latch
How do you know it’s 1
sour basalt
Lmaooo
crimson sedge
You alredy asked it lmaoooo
buoyant latch
There is at least 2
This is wrong.
sour basalt
Unless it is x^2
crimson sedge
There is at least 2
I thought it was
sour basalt
This is wrong.
Bro had to stop me before I could finish
buoyant latch
Unless it is x^2
This is also wrong/incomplete
crimson sedge
there is only one root if delta = 0
buoyant latch
there is only one root if delta = 0
Yes
sour basalt
This is also wrong/incomplete
Please elaborate
crimson sedge
so why youre saying that
buoyant latch
This is the relationship between the coefficients of the quadratic and the number of roots
sour basalt
This is the relationship between the coefficients of the quadratic and the numbe...
Tell us
buoyant latch
<@456226577798135808> what do you know about the nature of roots of a quadratic ...
That’s my first question
sour basalt
You tell us
crimson sedge
<@456226577798135808> what do you know about the nature of roots of a quadratic ...
idk
crimson sedge
You tell us
vouch
buoyant latch
Please elaborate
y = x² is not the only way to have only 1 root, and is still wrong when combined with your above statement
crimson sedge
I don't know how much I know about this
sour basalt
y = x² is not the only way to have only 1 root, and is still wrong when combined...
Yes but explain please
I want to know why
crimson sedge
sour basalt
Lol
crimson sedge
use this and solve ur questions
buoyant latch
I want to know why
y=(x+1)² also only has 1 root
crimson sedge
you guys are being rude to the person helping you for free lol
sour basalt
y=(x+1)² also only has 1 root
So functions compose at x^2?
buoyant latch
Hence y = x² is not only not the only quadratic with 1 solution, but also does not make the statement “there is at least 2” correct
“There is at least 2” means there are 2 or more solutions to a quadratic
That is incorrect
sour basalt
y=(x+1)² also only has 1 root
The inner function is composed at x^2
buoyant latch
There is at most 2 unique solutions to a quadratic
crimson sedge
@buoyant latch and that question?
buoyant latch
Well, what does the question say?
crimson sedge
buoyant latch
The channel name has the OP’s name
sour basalt
The channel name has the OP’s name
Lol
buoyant latch
So how many roots does 2x² - (m-1)x + 2 = 0 have?
cedar kilnBOT
@crimson sedge Has your question been resolved?
oblique vault
I'm not sure how to get from the 1st inequality to the 2nd inequality. Do I put a power of -1 on all sides of the equation, or am I not supposed to do that?
dire geode
I'm not sure how to get from the 1st inequality to the 2nd inequality. Do I put ...
yes taking the reciprocal of all terms is correct
cedar kilnBOT
@oblique vault Has your question been resolved?
distant cedar
What have you tried?
amber lagoon
For two distinct roots b^2-4ac = 0
cedar kilnBOT
For two distinct roots b^2-4ac = 0
amber lagoon
.reopen
cedar kilnBOT
Available help channel!
elfin plaza
Mr moss brought 80 shares of X corporation at 28 3/4 and sold the shares a year later at 31 1/2. Her profit, before paying the commission was?
How do I solve this? I tried to use 31 1/2 - 28 3/4 but it didnt work
tropic oxide
feels like there might be something missing from the problem statement...
what kind of currency unit is quoted in fractions like this?
@elfin plaza just to make sure, do you have a picture or screenshot of the problem?
elfin plaza
ill take a picture
sorry my phone is very laggy for some reason
its the 4th question
elfin plaza
feels like there might be something missing from the problem statement...
thats what i thought, but thats all I have from the question
tropic oxide
,rcw
wraith daggerBOT
tropic oxide
huh
then what do those numbers mean lmao
price per share maybe...? but what's with the fractions and the lack of a dollar sign
elfin plaza
This chapter is about interest, kind of but I dont see any in this question
tropic oxide
buy at $28.75/share, sell at $31.50/share
wraith daggerBOT
Ann
tropic oxide
and you've got 80 shares
elfin plaza
(31.5-28.75)*5?
tropic oxide
why times 5...?
tropic oxide
why times 8...?
tropic oxide
yes that's more like it
ocean halo
hey
stray otter
Straight to the question pls
ocean halo
so how did we come up with this? the answer is a + b. i got -a -b
ocean halo
Straight to the question pls
sorry ahaha
ocean halo
so how did we come up with this? the answer is a + b. i got -a -b
this is IGCSE math (Gr 9/10)
ocean halo
yup
ocean halo
I suck at it lol
ahaha it's fine
stray otter
sry
ocean halo
so how did we come up with this? the answer is a + b. i got -a -b
any1?
tropic oxide
how did you get -a-b?
ocean halo
how did you get -a-b?
i just went in the backward direction
since they want it in terms of a and b, i went from V->U->T->S->R->Q->P->W
tropic oxide
.... ????
you did all that work...? so expressing vectors UT, TS, SR and so on in terms of a and b?
ocean halo
you did all that work...? so expressing vectors UT, TS, SR and so on in terms of...
wait one second
tropic oxide
sounds like you did about seven times more work than necessary imo
ocean halo
~~sounds like you did about seven times more work than necessary imo~~
can u explain how i'm i supposed to do it in the right way?
i didn't take it in school since my teacher is absent and i'm struggling to study it myself
tropic oxide
you've got yourself a square grid for a reason
vector VW is clearly (4,0) while a and b are (2,2) and (2,-2) resp
static schooner
Hi, could someone guide me through this question. Its fairly new to me.
terse fiber
cedar kilnBOT
wild spear
i need help on this one, i know to find the minimum area that A' = 0, but i dont know the equation needed
red pumice
often times you need to derive formulas yourself
cedar kilnBOT
cedar kilnBOT
Available help channel!
halcyon oyster
Can somebody check if my work is correct?
cedar kilnBOT
Can somebody check if my work is correct?
halcyon oyster
Can somebody check if my work is correct?
I have to apply stokes theorem
<@&286206848099549185>
thanks!
actually in the example i got the equation for the surface as 4y^2+z^2=4; which means its a circle in the yz plane ig? and i substituted y=2sin(theta) and z=2cos(theta) because in other examples my teacher had done that but i dont actually know why the substitution happens and if it is right, ig its related to parametric equations and i missed all those classes so i am not sure
'-'
hmm i don't think i can tell enough
no its fine
cedar kilnBOT
@halcyon oyster Has your question been resolved?
eager remnant
cedar kilnBOT
livid hound
use y=x^3
and exponent laws
tame wraith
crimson sedge
why cross the Y's at the end?
cedar kilnBOT
why cross the Y's at the end?
tropic oxide
poor way of writing the operation of adding those two equations together, after which the +2y and -2y will cancel to zero
crimson sedge
following #help-16 message
is this fine now?
livid hound
very dodgy notation
crimson sedge
how so
livid hound
f(0) itself is undefined,
when attempting to evaluate the limit, that 0/0 would be an indeterminate form
lim shouldn't be there after plugging in the specified value
you shouldn't be taking the limit of a void
and limit as x→a isn't necessarily the same as f(a)
cedar kilnBOT
cedar kilnBOT
Available help channel!
regal steeple
The diagonals of a parallelogram ABCD intersect at O. A line through O intersects AB at X and DC at Y. Prove that OX = OY
regal steeple
My status is that I have a question about someone else's worked solution
Consider ΔAXO and ΔCYO.
AO = OC [Diagonals bisect each other]
∠AOX = ∠COY [Vertically opposite angles]
∠AXO = ∠CYO
[Alternate angles]
∴ΔAXO ≅ΔCYO.
[AAS congruency]]
Can I also say that Angle OAX = Angle OCY as the opposite angles of parallelogram are always equal?
leaden ledge
Yes theyre also alternate angles as AB and DC are parallel
regal steeple
Yes theyre also alternate angles as AB and DC are parallel
So i can say that Angle OAX = Angle OCY as AB || DC and AC is the transversal
leaden ledge
👍
regal steeple
.close
nova hedge
I need help on this Quadratic Equation.
cedar kilnBOT
I need help on this Quadratic Equation.
nova hedge
The first step is getting the vertex but I am confused on how to do it.
Then I find 2 coordinates
I would appreciate any help
fickle trellis
Do you know the vertex form of a parabola?
nova hedge
y = a(x-h)^2 +k
fickle trellis
Yes
So, here you could do some comparing.
And find the vertex (h,k)
You could write the equation as.
livid hound
h isn't 2
leaden ledge
-2 is the only root, hence it will cut the x axis only on -2, which will be the vertex, and if you put x = 0 we get y = -32 as intercept I suppose thats enough?
fickle trellis
Isn't 2.
nova hedge
-2 is the only root, hence it will cut the x axis only on -2, which will be the ...
How did you get y = -32
fickle trellis
If you put x=0 ...
tight siren
ye
leaden ledge
How did you get y = -32
Putting x as 0 in the original equation
As we need to find the point where it cuts the y axis
cedar kilnBOT
cedar kilnBOT
Available help channel!
storm dock
Hello, can anyone help me with equations?
cedar kilnBOT
Hello, can anyone help me with equations?
storm dock
I don't understand well equations
And I'm from grade 8
Ummm, can uuhh someone give me equation problemes?
Ok no one will help me, Bye.
.close
idle storm
Hi, im confused about a solution for this question, so I found the intercepts and stuff, but in the solution, they do integral minus the line - (the quadratic) shoulnt it be the opposite
edgy hornet
the parabola is above the line therefore its minus
idle storm
yh but shouldnt it be the parabola minus the line?
south tundra
Generally you would need to write it as |f(y) - g(y)| where x = f(y) and x = g(y) are the graphs inbetween which is your area that you are trying to solve for
But, in this case, we have f(y) > g(y) on the interval
orchid stratus
can someone help me
cedar kilnBOT
can someone help me
orchid stratus
Im a bit confuse
gilded sierra
Im a bit confuse
just use formula for area of triangle (½ x base x height)
orchid stratus
like this?
@gilded sierra
I used the formula already
but still can’t get the answer
is there anything wrong with my calculation?
gray blade
gilded sierra
like this?
i think it's right
gray blade
there may be something wrong with the choices
orchid stratus
I see…
gilded sierra
or the answer is typo
orchid stratus
yeah
gilded sierra
u did it well
cedar kilnBOT
@orchid stratus Has your question been resolved?
plush shore
cedar kilnBOT
plush shore
I need help with this problem, linear algebra, involving linear transformations
What I thought is,
being that g o f(v) = 0
that means that f(v) must belong to the nucleus of g.
And being that f(v) must belong to the image of f, and the image of f is equal to H, then f(v) must be contained within the nucleus of g and H at the same time.
cedar kilnBOT
@plush shore Has your question been resolved?
plush shore
Alternatively, I would also appreciate if anyone helped me define the equation of the linear transformation
cedar kilnBOT
@plush shore Has your question been resolved?
small cloak
does infinity means discontinous or continous
cedar kilnBOT
does infinity means discontinous or continous
tropic oxide
"infinity", "discontinuous" and "continuous" are three words with distinct meanings.
dull oxide
Discontinuos and continuous are related in that discontinuous means "not continuous"
Infinity just means "not finite"
tropic oxide
so they are not related
"distinct" does not mean "not related".
lusty grotto
When a function approaches infinity somewhere, we say it is discontinuous there
small cloak
When a function approaches infinity somewhere, we say it is discontinuous there
oh
so a infinite function
is discontinous
dull oxide
Not quite
I'm not even sure "infinite function" is a proper term. Any thoughts on that, @tropic oxide?
tropic oxide
yeah, it's bullshit.
what is an "infinite function"?
also @small cloak i've noticed you misspell this consistently, so: continuous. like in the word "continue".
heady spindle
I don't how to star doing this exercise, I think that is a differential equation of separable variables, but the q(x) :(((( maybe I have to do the both cases? when 0<=x<1 and x>=1 or only the case 0<=x<1?
cedar kilnBOT
I don't how to star doing this exercise, I think that is a differential equation...
@heady spindle Has your question been resolved?
short blade
heady spindle
okay okay
cedar kilnBOT
cedar kilnBOT
Available help channel!
celest merlin
How can I show that for this function:
[
f(x,y)=\frac{xy}{x+y}
]
we have that (f(x+\Delta x, y-\Delta y)>f(x,y)) when (y>x>\Delta y>Delta x>0)? Basically, how do I show this function increases if I increase (x) a little and decrease (y) a little when (y>x).
cedar kilnBOT
How can I show that for this function:
\[
f(x,y)=\frac{xy}{x+y}
\]
we have that ...
@celest merlin Has your question been resolved?
marsh pond
Do computers miscalculate storage due to log2?
cedar kilnBOT
Do computers miscalculate storage due to log2?
marsh pond
for example you can purchase a new computer with 1GB of storage, but when you look at the specs it's not exactly 1GB
log2(1000) equals approximately 10, but not quite
should be log2(1024) = 10 to be exact
celest merlin
They just don't use SI units, your operating system counts 1kB = 1024 bytes while the storage manufacturer sells it as 1kB = 1000 bytes
There is a unit meant to deal with this confusion, it's called KiB (kibibyte) and mebibyte and so on
marsh pond
They just don't use SI units, your operating system counts 1kB = 1024 bytes whil...
Why does the industry allow manufacturers to do this?
marsh pond
https://en.wikipedia.org/wiki/Byte#Multiple-byte_units
Thanks! I never heard of these before
celest merlin
I'm no authority on this topic but I would assume because the average consumer can "think" in powers of ten better than powers of two, and it's "close" enough
marsh pond
interesting..
I suppose it's kinda similar to we can quickly measure our bandwidth, when the ISP says "50Mbps"
We can divide that number by 10 to get an approximation in MB, (5MB/second), while it's not perfect, it's close enough
marsh pond
I'm no authority on this topic but I would assume because the average consumer c...
From what I recall, in Computer Science log2 is how bytes would work, multiplying by 2 for each of the 8 bits. From what I gather, each bit can be represented in log2:
Bit 1: 1
Bit 2: 2
Bit 3: 4
Bit 4: 8
Bit 5: 16
Bit 6: 32
Bit 7: 64
Bit 8: 128
So the outputs would be 0-255 depending on which of the 8 bits are being turned on and off. 0 is a strange one to me, as normal math logs cannot have 0 as an output.
celest merlin
From what I recall, in Computer Science log2 is how bytes would work, multiplyin...
(\log_{a}(1)=0) for any base (a>1) so it can have zero as output
idk why the bot is dead
marsh pond
oops I meant input
celest merlin
Not sure why that thing say you can't plug in numbers not equal to 1
marsh pond
ya that's from Quora lol
celest merlin
Are you confused about the 0-255 range of an 8 bit number?
marsh pond
I think so
I do understand if you turn off all bits in a byte, you get 0
so it's like turning off all inputs
but how would this be written mathematically as log2 to get 0 for the output?
modern compass
what do you mean log2 tells you the bit string?
marsh pond
.reopen
cedar kilnBOT
✅
marsh pond
what do you mean log2 tells you the bit string?
Bit 1: 1
Bit 2: 2
Bit 3: 4
Bit 4: 8
Bit 5: 16
Bit 6: 32
Bit 7: 64
Bit 8: 128
every bit in a byte is calculated using base2
marsh pond
except for 2^0 .. I thought anything >0 with ^0 is 1?
marsh pond
how do you use log2 and 10101010 to get 128?
that's just counting the bits that are turned on (as "1")
so maybe this is just base 2?
log2 and base2 are different I suppose.. it kinda acts like a small logarithm, except for the 0 value
modern compass
???
counting bits turned on in this case is 4, if you mean converting to base 10, it's 170
obsidian coral
log2 tells you the bit string
That's a poor way to say it. Using log would tell you what position you're in, not the value, I believe
marsh pond
???
counting bits turned on in this case is 4, if you mean converting to base 1...
Are you familiar with binary?
you count each bit that is activated
modern compass
yes
obsidian coral
Like $log_2(128)$ only says the exponent is 7
marsh pond
from right to left
so in this case only bits 2, 4, 6 and 8 are activated
2+8+32+128 = 170
obsidian coral
Zybikron is familiar with binary, your phrasing is just poor and terrible and, I believe, not correct
marsh pond
Oh.. which part?
obsidian coral
Well first, how would you use log2 to determine that 1010 1010 in base 2 is 170 in base 10?
marsh pond
marsh pond
Well first, how would you use log2 to determine that 1010 1010 in base 2 is 170 ...
Hmmm good point.. so some conversion is going on?
To change it from log2 for binary to log10 that we can read?
When we say 01010101 is 170, it's calculated using binary logarithm, and then expressed as a base10 number?
obsidian coral
You don't need logs to do that
modern compass
this is just a standard logarithm base 2. It doesn't necessarily relate directly to binary numbers. There's some things going on in the middle there
obsidian coral
That's the process that most people do, that isn't log related
modern compass
yes
marsh pond
Ah, I see now. 1 and 0 are the base
and anything with base of 0 is gonna be 0
brilliant
modern compass
0 and 1 are not the bases here
marsh pond
they aren't?
modern compass
they're the digits
modern compass
yes
marsh pond
but 1 and 0 allow for the base to be activated (like a light switch, on or off)
when Gottfried Wilhelm Leibniz from 1600s invented binary was he thinking about computers at the time?
or was it intended for other purposes at the time
modern compass
11011011 are the digits of a binary number. They represent the place value, and yes that is the exponent on the base that is 'activated'
it's exactly the same for decimal numbers.
101 base 2 is 2^2 + 2^0
101 base 10 is 10^2 + 10^0
marsh pond
I get how this would be 100 100 base 10 is 10^2
marsh pond
101 base 2 is 2^2 + 2^0
101 base 10 is 10^2 + 10^0
but I don't get how this would also be 100 100 base 2 is 2^2
if 2^0 and 10^0 each account for 1
obsidian coral
Because from right to left, starting with 0, the digit position is the exponent, no matter the base
So 100 base 2, the 3rd position from right, is position 2, hence exponent of 2
marsh pond
but isn't 2^2 = 4? even if it's base 2?
modern compass
that's why the base is important.
4 is the base 10 representation of 2^2
the binary (base 2) representation is 100
obsidian coral
4 in base ten is represented as 4 x 10^0
marsh pond
4 in base ten is represented as 4 x 10^0
Oh I see
it's like multiplying by 1
100 base 2, would be 100 * 2^0?
modern compass
in base 2, there are no digits other than 1 and 0
because if you go to 2, then that's 2 * 2^n = 2^(n+)
so you'd go to the next digit.
obsidian coral
100 base 2, would be 100 * 2^0?
No
modern compass
in other bases, you get digits besides 1 and 0
marsh pond
"digit", is this from math or CS?
I don't normally hear this word in math classes, just making sure
nvm, just forgot
each is their own digit
1 million is a 7 digit number
obsidian coral
100 base 2, would be 100 * 2^0?
Each digit is the coefficient for that position
100 in base 2, is represented as 1 x 2^2 + 0 x 2^1 + 0 x 2^0 = 4 in base 10
100 in base 3 is is represented as 1 x 3^2 + 0 x 3^1 + 0 x 3^0 = 9 in base 10
marsh pond
Each digit is the coefficient for that position
100 in base 2, is represented as...
but if this is true.. then what is this?
base 2 or base 10?
obsidian coral
The binary value of 170
marsh pond
so it's base 2
obsidian coral
Yes
marsh pond
but here you said 100 is 100 in base 2, is represented as 1 x 2^2 + 0 x 2^1 + 0 x 2^0
obsidian coral
Don't see what you're confused about
It's literally the same
What I typed and what is shown in that image is the same
marsh pond
1100100 is 100 in binary
obsidian coral
No it's not
What are you trying to say?
1100100 in binary is 100 in base 10
1100100, I'm pretty sure you are trying to say that's a binary number, is not the same as 100
marsh pond
https://cdn.discordapp.com/attachments/903430334681608232/1079174355768066078/1PaXUsW94HYWK12ycliXJbQ.png so this is not base 2, this is base 10?
marsh pond
base 2 and binary are not the same thing?
obsidian coral
They are the same
marsh pond
that's why I am confused.
01100100 is 100 in binary
marsh pond
binary
marsh pond
https://cdn.discordapp.com/attachments/903430334681608232/1079174355768066078/1P...
I'm writing it like this
10101010 is 170 in binary, and 01100100 is 100 in binary
obsidian coral
That's the process that most people do, that isn't log related
You need to follow this process
When you convert binary to decimal
marsh pond
obsidian coral
You should watch that
marsh pond
OK
obsidian coral
"Binary equivalent of 100" means 100 in base 10, represented in binary is 1100100
01100100 is 100 in binary
This is a very bad way to say it
If you were saying that, 01100100 is 100 in binary, most people are going to understand that as 01100100 = 100 in base 2
Not 01100100 base 2 = 100 base 10
marsh pond
https://www.youtube.com/watch?v=VLflTjd3lWA&ab_channel=TheOrganicChemistryTutor
I already knew all of this
except for the decimals in binary, that's new for me
but I get the impression he is saying the same thing I have been saying
10101010 is equivalent to 170 if you count in binary
obsidian coral
https://cdn.discordapp.com/attachments/903430334681608232/1079174355768066078/1P...
If you knew that then what is confusing you with
100 in base 2, is represented as 1 x 2^2 + 0 x 2^1 + 0 x 2^0
Or this image?
obsidian coral
"Binary equivalent of 100" means 100 in base 10, represented in binary is 110010...
Also read this chunk of text
marsh pond
If you knew that then what is confusing you with
> 100 in base 2, is represente...
Yes, 100 in base 2 is equivalent to 4 in base 10
base 2 can only have 1's or 0's
I was reading it as "the number 100, in base 10" written as base 2
I get what you are saying now
obsidian coral
People default to base 10 when given single numbers, like 234, 100, 101, etc. But when you start giving more numbers and bases, that's when you need to be more specific with each number.
Like 01100100 is 100 in binary, you declared 01100100 as base 2 already, then your next part was 100 in binary and like mentioned, you did not declare what base it was, because 01100100 was in base 2, people would assume 100 was base 2 as well since that was the mentioned base
Clarity is needed when using bases
marsh pond
so when you go up in bases, you are just adding an extra number
base 3 uses 0,1,2
base 4 uses 0,1,2,3
base 5 uses 0,1,2,3,4
are there any useful reasons to use base 1, or base 3 to base 9? or would base 2 and base 10 be pretty much the only ones to think about
obsidian coral
You can also remember what digits are used just by knowing this, base n, the digits goes from 0 < n
obsidian coral
are there any useful reasons to use base 1, or base 3 to base 9? or would base ...
Base 8 and 16 are commonly used
Base 1 is probably the most useless one
marsh pond
except for base 1, that uses 1 as the only digit? https://en.wikipedia.org/wiki/Unary_numeral_system
marsh pond
Base 8 and 16 are commonly used
in Computer Science?
obsidian coral
Yes
marsh pond
that's when we start adding letters, past 10, right?
obsidian coral
Yes
obsidian coral
in Computer Science?
Base 8 is used in unix commands, for read, write, execute permissions for user, group, and other
obsidian coral
777 in unix command for permissions, as mention is 111 111 111, where you are giving read, write, execute (shorthand is rwx) to user (first group of numbers), rwx for group (second grouping), and rwx for others (last group)
700 is giving rwx for users, and no permissions to group and others
marsh pond
ah OK so 777 is max privilege, I knew about this somehow but didn't know the reason for this number
Are you a Linux user?
obsidian coral
Nope
marsh pond
I tried a few times but couldn't stick with it
macOS is fine for me, but it's Unix based, and Linux is like a fork of Unix back in the day
I think something else came before Unix made by AT&T but can't remember the name, it wasn't open source
and Microsoft released a Unix based OS but went their own way soon afterwards
this stuff from 1970s is so old now, kinda obsolete and useless, but we wouldn't be here today without it
marsh pond
ah OK
would there be any reason to go one more?
base 32?
I see this for minifying images on the web
Not sure how it works exactly, I guess it stores a photo inside of code
It sounds like base 128 is not used
obsidian coral
Base 8 and 16 are really useful in condensing base 2 numbers
1238335 in base 10 is 100101110010100111111 in base 2 but no one want to write out that many 1s and 0s, so base 8 and 16 could be used where 1238335 in base 10 is 4562477 in base 8 and 12E53F base 16
obsidian coral
That's one of the reasons
lethal jackal
base 64
marsh pond
that makes sense, if you are working with millions of lines of computation at any given second
lethal jackal
base 256 too
marsh pond
base 256 is used?
lethal jackal
that makes sense, if you are working with millions of lines of computation at an...
no
obsidian coral
16 is a power of two, specifically 24. That means that a single digit of hexadecimal exactly maps to a 4 digit binary number, and that two hexadecimal digits can represent a single byte.
The problem with binary is that while it's convenient for computers, it's way to long for people to figure out what you mean if you write it down. Hexadecimal numbers are easier to remember and easier to recognize if you see them on a page than a long string of binary.
lethal jackal
base 256 is used?
yes in cryptography, where sometimes byte sequences are interpreted as base-256 numbers and plugged into polynomials or whatever
lethal jackal
no
see, that's why memorizing names and stuff is not useful
you say nonsensical stuff
obsidian coral
An interesting factoid, you can use prefixes for bases, like 0b is to denote binary, 0 is octal, and 0x is hexadecimal so 2542 a base 10 number, you can say 0b100111101110 to denote binary, 04756 for octal, and 0x9EE for hex
cedar kilnBOT
@marsh pond Has your question been resolved?
cedar kilnBOT
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Available help channel!
olive flint
cedar kilnBOT
olive flint
I don't understand how i am supposed to find this expression
stray epoch
ivory moss
can someone help me understand this?
cedar kilnBOT
can someone help me understand this?
ivory moss
the derivative of a^x is a^xlna
I get why the coefficient is 6 and not 2 (because I needed to use chain rule on 3y)
long arrow
treat x as constant
ivory moss
but why is it lnx and not ln 2x
right, I get that, I just don't understand what happened to the 2 inside the LN
isn't 2x the constant in this case?
long arrow
let's start from taking out 2 as constant
then we have x^(3y)
it's like derivative of a^x which is a^x * ln(a)
(+ chain rule as you mentioned)
ivory moss
ah ok, I didn't realize you could do that with the 2.. so basically saying [d/dx]2x^3y = 2[d/dx]x^3y
or d/dy in this case
long arrow
yep
hazy zealot
Could someone please explain to me how to do this? I got the square root of 32 + the square root of 24 over 2 but that is wrong. Teacher has not explained his answers at all
cedar kilnBOT
Could someone please explain to me how to do this? I got the square root of 32 +...
Show your work, and if possible, explain where you are stuck.
viral cloak
What have you tried? What steps did you take?
viral cloak
What have you tried so far?
hazy zealot
I tried multiplying 2 square root 2 by square root of 16 and square root of 12 and for the denominator i got 16-12 then divided the numerator and denominator by 2
viral cloak
You need to multiply the top and bottom by the conjugate.
Do you know what that would be?
viral cloak
So, you must multiply top and bottom by the conjugate.
hazy zealot
that's what I did but it's wrong
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
viral cloak
Then from there you must simplify. What did you get? I'll work it out quickly to check your work.
obsidian coral
that's what I did but it's wrong
Show your work
hazy zealot
alright hold on then
viral cloak
alright hold on then
Sure thing.
hazy zealot
hazy zealot
I'm not really too sure since the teacher didn't explain it
he linked us a video of some random youtuber and that was it
viral cloak
So, to simplify square roots, the way I like to do it is - break it down to primes.
hazy zealot
the guy didn't go over this in the video
viral cloak
So, for sqrt 32, break it down to primes. What do I multiply by what to = 32? 16 * 2.
hazy zealot
ok
viral cloak
16 = 2 * 2 * 2 * 2, so times the other 2 gives us 5 two's, right?
hazy zealot
yeah
viral cloak
2 * 2 * 2 * 2* 2 = 32. Do you agree? And 2 is a prime number - so I've broken it down to its primes.
Now, it's a square root, so I can pull PAIRS out of the square root. I have 2 pairs of 2's...then one 2 left over.
Do you see that?
(2 * 2) (2 * 2) * 2
The 2 pairs are in parentheses.
hazy zealot
ok
viral cloak
So, they can come out of the square root.
viral cloak
Which means I have pulled out 2 pairs of 2. So, out comes 2 and 2; 2 * 2 = 4. Then you'll still have the loner 2 still in the square root. So it becomes 4sqrt2
hazy zealot
12 and 2
viral cloak
These are some examples to reference.
So, what would sqrt 24 become?
Break it down to its primes and pull out the pairs - what does it simplify to?
hazy zealot
hold on I'm looking at something real quick
viral cloak
np
viral cloak
Good job!
viral cloak
So, you've simplified the 2 roots now so you've got 4sqrt2 + 2sqrt6 / 2 - just simplify now
Np
hazy zealot
yeah it's now 2 square root of 2 and square root of 6
i just have one more question tho
Can you simplify if there's a number behind the square root?
for example 6 square root of 24
viral cloak
6 * sqrt24?
hazy zealot
yeah multiplied by
viral cloak
? by what
olive cairn
Let me try. You can just simplify sqrt 24 and it will be simplified to 2sqrt 6 and so you will have like 6sqrt24 simplified to 6 * (2 sqrt 6) = 12 sqrt 6
viral cloak
i mean something like this
No, you can still simplify.
hazy zealot
ok thanks
viral cloak
Whatever you are able to "pull out" of the square root will get multiplied to the 2 outside already.
viral cloak
Let me try. You can just simplify sqrt 24 and it will be simplified to 2sqrt 6 a...
2sqrt24 is not equal to 12 sqrt 6
olive cairn
for example 6 square root of 24
I was referring to this.
viral cloak
I was referring to this.
Oh, then yes. XD
cedar kilnBOT
@hazy zealot Has your question been resolved?
cedar kilnBOT
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Available help channel!
tough linden
how to prove that the binary representation of a number n will have floor(lg(n)) + 1 bits?
tough linden
I need a mathematical proof
undone basin
how to prove that the binary representation of a number n will have floor(lg(n))...
try using induction
show that the number 1 has floor(lg(1)) + 1 bits, 2 has floor(lg(2)) + 1 bits, 3 has floor(lg(3)) + 1 bits, 4 has floor(lg(4)) + 1 bits, then assume that because of this pattern, the kth number has floor(lg(k)) + 1 bits. To complete the proof, show that the number n = k+1 has floor(lg(k+1)) + 1 bits
cedar kilnBOT
@tough linden Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
ember lichen
cedar kilnBOT
ember lichen
i just can't figure out how to get the rest...?
errant vector
f(a)?
errant vector
the point the tangent touches
ember lichen
oh
errant vector
😭 its way too late at night for this
ember lichen
bro doesn'yt get it
errant vector
idk if i even remember corrwcrtly at this point
errant vector
i am not
ember lichen
at least 2
errant vector
i just got told sqrt4 = 2 =/= -2
ember lichen
since this is a circle
errant vector
atleast 2 what
errant vector
no we dont gotta solve for a
unless i read the problem wrong
yeah a is just there
ember lichen
ohh i see
errant vector
idek what the question is asking
ember lichen
OH LMAOOO
ember lichen
cuz don't we need it to solve for slope of tangent?
errant vector
it just wants the equation for a
its 1
"parallel to the straight line defined by x-y=2"
im tripping
ember lichen
no way
errant vector
im doing something stupid i just cant see it
errant vector
lol
so ig solve dy/dx = 1
right
thats how we get a
OHHH
OHH IM ACTUALLY
since we know the tangent is 1, now we gotta find where the slope of the actual function is 1
lmfao 😭
wraith daggerBOT
dannylewastaken
errant vector
2x - x y' + y + 6y y' = 0
ill just go w urs
so then
$$\frac{y - 2x}{6y - x} = 0$$
wraith daggerBOT
amukh1
errant vector
oh wait
ember lichen
alr
errant vector
so implicit differentiation
2x - x y' - y + 6y y' = 0
are you following this bit so far
ember lichen
yep