What you wrote is not equal to my 3rd line
#help-33
cloud topaz
silk plover
Hmm
cloud topaz
silk plover
Is it just because DeMorgan's law only works with single complement terms?
cloud topaz
Well, it's iterative.
So you can use it for infinite compliment terms, but you have to flip the sign every time.
silk plover
Okay so with !!(DB) you started with the most internal complement and broke it up, but left the top one alone
cloud topaz
(DB)cc = (Dc + Bc)c
Yeah
You can then break up the next one, but you have to flip the sign again
So you get:
silk plover
Okay okay and if we did it again it would just undo what we did.
silk plover
Okay. This helps.
cloud topaz
I hate writing double compliments. There's not any practical reason to write them. If you see two compliments over the same term, just cancel them and skip the confusing stuff in the middle lol
E.g.
(DB)cc = DB
Similarly,
Dcc = D
Etc.
silk plover
Yeah I know I can just use double complement law for sure. But I was worried that if I don't thoroughly understand things I'll be mega confused later
cloud topaz
That's fair.
silk plover
I always ask why instead of just accepting things for what they are lol
Thank you. I appreciate the time that you spent here with me.
cloud topaz
No problem. I needed an excuse to avoid my own homework haha
silk plover
What are you working on?
cloud topaz
Current problem:
marsh citrusBOT
marsh citrusBOT
Available help channel!
pallid agate
marsh citrusBOT
Available help channel!
wet peak
How do I factor x^3+5x^2-x-5
marsh citrusBOT
How do I factor x^3+5x^2-x-5
late geode
try approaching it with grouping
still creek
try grouping it and see if something interesting happens
(hint: something interesting should happen)
marsh citrusBOT
@wet peak Has your question been resolved?
late geode
$$x^3+5x^2-x-5 = \blue{(x^3+5x^2)} + \orange{(-x-5)}$$
can you factor the blue and the orange individually
elfin berryBOT
ℝamonov
marsh citrusBOT
marsh citrusBOT
Available help channel!
winter parcel
Find the largest volume of a cube with the maximum surface area among the cubes
that can be enclosed in a sphere. ( r = 1)
marsh citrusBOT
Find the largest volume of a cube with the maximum surface area among the cubes
...
hidden plaza
This just over complicates things
winter parcel
then how do i ?
hidden plaza
You know the diagonal of the cube must be 2
winter parcel
sure
hidden plaza
Use Pythagorean theorem
noble nebula
hello i new
dawn lagoon
wait me
hidden plaza
Use Pythagorean theorem
Let’s say side length of the cube = a
dawn lagoon
hidden plaza
?
winter parcel
hey
dawn lagoon
a.b.c>0
hidden plaza
No
hidden plaza
Yes
winter parcel
aha..
i forgot the z
then x^2+y^2+z^2 = 4 right?
f(x,y,z)= 2xy+2yz+2xz subject to: x^2+y^2+z^2 = 4
is this a right way ?
winter parcel
i thought r=1, dianoal is 2
winter parcel
yeah
hidden plaza
Equation of a sphere
hidden plaza
Anyway back to our problem
winter parcel
okay
hidden plaza
$a^2 + a^2 + a^2 = 4$
elfin berryBOT
Pure
winter parcel
what about a rectangular?
hidden plaza
Probably tbh I’m not really sure
hidden plaza
I’ve got to go very soon
winter parcel
not xyz?
hidden plaza
2x 2y 2z multiplied together
random pier
What happens when an exponent is a fraction with a numerator greater than one? Like 4^(3/2)
marsh citrusBOT
What happens when an exponent is a fraction with a numerator greater than one? L...
crimson frost
random pier
Oh ok thanks that makes sense
Do I need to type some command to close this problem now?
crimson frost
.close
random pier
.close
white willow
If a drink containing 40% alcohol is mixed with an equally large drink containing 30% alcohol, what would be the alcohol-percentage in the mixture?
marsh citrusBOT
If a drink containing 40% alcohol is mixed with an equally large drink containin...
tight furnace
we might want a variable for the size of the drink here
marsh citrusBOT
@white willow Has your question been resolved?
white willow
we might want a variable for the size of the drink here
700ml
both of them are 700ml
ive been struggling with combining percentages
white willow
First one is 40%, so 40% of 700ml
tight furnace
well I suppose there's a shortcut as well
white willow
Second one is 30%, so 30% of 700ml
tight furnace
since it's the same amount each time you average the percentages
The danger is there's some scenarios where this doesn't work
white willow
like, alcohol posioning?
tight furnace
like, alcohol posioning?
:O
lucid hinge
moni has obesity, so he runs quite slow
white willow
lol
but i was thinking
if we take the pure alcohol of both drinks
and add them together
then take 700*2
and divide the amount of alcohol by that?
lucid hinge
since it's the same amount each time you average the percentages
u just average 30 and 40
lucid hinge
69110 and then close
marsh citrusBOT
@white willow Has your question been resolved?
elder gust
At a traffic light, a two-digit display shows the number of seconds before the light turns green. The digits on the display are are shown in Figure 1. Part of the display is obscured by a vehicle (see Figure 2). On the visible part of the screen, the light was the same a second ago. How many different two-digit numbers the display can show now?
marsh citrusBOT
At a traffic light, a two-digit display shows the number of seconds before the l...
elder gust
trying to visualize how many types of number there could be
considering that the visible portion of the traffic light was the same a second ago
there is 3 or 2 solution less
wait
because this shows the seconds
the second digit cannot change
which makes it into this
what makes it into 3
sleek lake
it's just 2?
elder gust
why do you think its 2?
sleek lake
digit 2 is fixed and digit 1 is two or three
elder gust
or 7
sleek lake
right my bad
elder gust
thanks for the question tho
i go close this
thanks for joining me btw
cya
.close
little schooner
There is a team that has 10 members and they clean up weekly, cleaning can be done in 2 hours 48 mins when all 10 members are cleaning how long it takes when 3 members taking free time (not cleaning)?`
marsh citrusBOT
There is a team that has 10 members and they clean up weekly, cleaning can be d...
little schooner
ambulance driving at 80 km/h and arrived at the hospital in 30 mins , if ambulance was driving 100 kmh how quickly he would be arrived to hospital? (only in minute answers)
sorry for my english
there are the questions im stuck
<@&286206848099549185>
marsh citrusBOT
@little schooner Has your question been resolved?
little schooner
no
marsh citrusBOT
@little schooner Has your question been resolved?
daring dune
lost apex
(-4,4) means x=-4 and y=4. Does that make the given equation true?
marsh citrusBOT
marsh citrusBOT
Available help channel!
junior compass
marsh citrusBOT
dry prawn
What's giving you issue?
dry prawn
a looks fine
b has argument x, not 6
Actually b is slightly off further, it looks like you constructed f ° g instead of g ° f
Double actually, why are you asking for help on an exam?
junior compass
this is a redo exam and the teacher said i could use any means neccesary
as long as i go along and learn it
dry prawn
Fair enough
junior compass
so would i subtract 12-5 then multiply 1/36 by that?
or multiple 1/36 by 12 then subtract 5
PEMDAS applies here, right?
dry prawn
g(x) is 2x - 5, and you need to multiply f and g
So which of those do you think is more appropriate?
junior compass
well, on the first question, follow pemdas...
so id multiply 1/36 by 12
to get 1/3
dry prawn
Your pemdas changes if you introduce parentheses
(1/36)(12-5)
What would you do now?
junior compass
then multiply whatevers in the parentheses
but i keep the parentheses when i multiply 6 and 2?
dry prawn
Yes
junior compass
so then the -5 would still be out of it
dry prawn
So you clearly understand f*g(6) = f(6)*g(6), which is good
junior compass
right
dry prawn
However, I think you need to pay a little more attention to the following algebra
1/36 * 12 doesn't work, because 12 isn't g(6)
If you compute f(6) and g(6) separately, what are they?
dry prawn
So their product must be 7/36
dry prawn
Perhaps seeing f*g as (f)(g) would help
So you naturally include the parentheses needed
dry prawn
Because (1/36)*12-5 and (1/36)*(12-5) are not equivalent
dry prawn
No
dry prawn
That I agree with
junior compass
ok, so whats the first step
dry prawn
Well what's 2 * (1/x^2)
junior compass
2/x^2?
dry prawn
Yep
junior compass
so 2/x^2 - 5 is the answer?
thats as simple as it gets, right
cant really evaluate if the variable isnt a number...
dry prawn
Unless your teacher wants you to remove the x^2 from the denominator
junior compass
ooh right
dry prawn
But otherwise yeah it's complete
junior compass
likek sovlve for x
junior compass
right, ok
dry prawn
But you could rewrite 2/x^2 to not be a fraction
Whether or not it's required is up in the air, but it's an option
junior compass
.close
hollow crater
Could anyone explain to me why ln(1+x^2)=2ln(x) +ln(1+1/x^2) please , I feel dumb not understanding this
marsh citrusBOT
Could anyone explain to me why ln(1+x^2)=2ln(x) +ln(1+1/x^2) please , I feel dum...
late geode
2ln|x| though
fallen galleon
$2ln(x) + ln(1+\frac{1}{x^2})$=$lnx^2 + ln(1+\frac{1}{x^2})$=ln(x^2(1+\frac{1}{x^2}))$
elfin berryBOT
Springsskateboard
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
fallen galleon
2ln|x| though
oh yeyeye^^
marsh citrusBOT
@hollow crater Has your question been resolved?
smoky marsh
i feel like im forgetting something but is there a law where it goes something along like 1/x=1/y then x=y
marsh citrusBOT
i feel like im forgetting something but is there a law where it goes something a...
smoky marsh
if they have the same numerator can you do something like that
worn nimbus
yes
smoky marsh
do you know the know the name of the law? i'd like to look more into it
pulsar flume
It’s commonly referred to as “cross-multiplying”
late geode
cross multiplication
late geode
justified algebraically by multiplying both sides by the product of the denominators (or to be more efficient use the lcd)
smoky marsh
me too man me too
worn nimbus
its part of the process
smoky marsh
part of why i love it so much as well
worn nimbus
hahah yeah weirdly yes
glossy adder
How to solve this problem on paper?
All I have been told leading up to this problem is this
"If one task can be accomplished in x different ways and, following this task, a second task can be accomplished in y different ways, then the first task followed by the second task can be accomplished in x * y different ways. (This counting principle can be extended to any finite number of tasks.)"
An even number is one whose last digit is a multiple of 2
I have 6 numbers to choose from, for the hundredth place.
I have 5 numbers to choose from, for the 10th place.
The choice for the last digit depends how we chose the first two
Case 1: First two digits are odd
6 x 5 x 3 = 90
Case 2: First two digits are even
6 x 5 x 1(?) = 30 (I have my doubts...but if both are even then we are only left with a single even number innit?)
Case 3: One of the first two digits even only
6 x 5 x 2 = 60
Wrote a python program and the answer is indeed 60, via bruteforce
lst = list(filter(lambda x: x % 2 != 1, range(100, 666)))
# print(len(lst))
count = 0
for i in lst:
if set(['0', '7', '8', '9']).isdisjoint(set(list(str(i)))):
if len(list(dict.fromkeys(str(i)))) == 3:
count += 1
print(count)
I was hoping to gain some insight but..., the program just counted the numbers via brute force.
Also is it coincidence that the arithmetic average of 30, 60, 90 equals 60?
smoky siren
A number is even is it ends in a multiple of 2 so that is 3 choose 1. Then you choose 2 numbers for the other digits, which is 5 choose 2, and 2 ways to order those 2 aforementioned digits.
marsh citrusBOT
Available help channel!
glossy adder
.reopen
glossy adder
A number is even is it ends in a multiple of 2 so that is 3 choose 1. Then you c...
I am sorry, what does choose mean?
marsh citrusBOT
I am sorry, what does choose mean?
cloud iron
3 choose 1 is the number of ways to pick one element from a set of three
smoky siren
The last digit has to be 2 4 or 6. That is 3 choose 1. There are 2 more digits to select among a remaining pool of 5. That is 5 choose 2. Those 2 digits can have any order. (3 choose 1) x (5 choose 2) (2 choose 1) = 3 x 10 x 2 = 60
For example, select the 6 to be the last digit (3 choose 1)
You can now choose between 1 2 3 4 5. Lets choose 2 and 3 (5 choose 2). So now there is either 236 or 326 (2 choose 1).
marsh citrusBOT
dusk coral
oh right
wraith cobalt
no its not
dusk coral
wraith cobalt
it is not that, the inequalities are not a<b and b>a, they are a<b and b<a in this case
its about the logical definition of if then
stoic saddle
"If [false statement] then [WHATEVER]" is always true
wraith cobalt
^
stoic saddle
or if you speak latin, ex falso sequitur quodlibet
remote salmon
ah
nova totem
or if you speak latin, `ex falso sequitur quodlibet`
Using this
I'm gonna destroy arguments with that
nova totem
But also
It's true because if 2 > 3 is false then 3 > 2 is true
Something like that
remote salmon
oh i completely misread it yeah
wraith cobalt
can f and g have the same limit at a?
I know, I'm asking you based on the information in the premises, can f and g have the same limit at a
(the answer is yes)
If f and g were continuous, the result would hold, but allowing for discontinuities allows us to come up with this counterexample where f and g both limit to 0 at 0, but f<g over R
dusk coral
"If [false statement] then [WHATEVER]" is always true
is this a completely consistent rule or are there exceptions
wraith cobalt
Well there's nothing saying whether f or g can be discontinuous so there's nothing wrong with choosing discontinuous functions as counterexamples to the statement.
wraith cobalt
is this a completely consistent rule or are there exceptions
In logic, (If A then B) is defined to be false when A is true and B is false, and True for any other truth values of A and B.
so yes, it is completely consistent
stoic saddle
is this a completely consistent rule or are there exceptions
there are no exceptions
harsh nova
marsh citrusBOT
dusk coral
there are no exceptions
So whats the actual logic behind it, if a false statement is true we have no way of disproving another statement?
I dont want to waste your time(and distract the channel from Rayaans question, any reading about this you'd recommend or the actual concept name?
stoic saddle
vacuous truth is what it's called
harsh nova
.close
marsh citrusBOT
dusk coral
vacuous truth is what it's called
thanks, also did some reading into the princple of explosion
marsh citrusBOT
Available help channel!
thin bison
Hi
hushed egret
A => B means "If A then B"
A <=> B means (A => B) and (B => A)
so "If A then B, and if B then A"
so "A if and only if B"
hushed egret
logical equivalence
abstract forge
what the fuck is this
marsh citrusBOT
what the fuck is this
abstract forge
some ppl say its not a parabola and why does it go in a straight line
how the hell does y go -10, -9, -8 ,-7, -6, -5, -4
desert dirge
can barely see it
stoic saddle
some people say the graph of f(x) = (x+1)^2 - 8 is not a parabola?
is that what you are saying?
desert dirge
yeah, it is one
abstract forge
yes
stoic saddle
who is saying that?
abstract forge
I was trying 2 get help from other ppl but they say its not a parabola
stoic saddle
they're lying to you lmao
abstract forge
ok
stoic saddle
a parabola this graph very much is
abstract forge
but then when u plug in the other numbers its a straight line
stoic saddle
also do not omit the parentheses when writing down a point via its coords.
also show exactly what you are plugging in and what results you are getting. where is your table of values?
mystic minnow
I will bet money you're missing parenthesis
stoic saddle
ok then show your table of values.
stoic saddle
ok let's go through those one by one
abstract forge
ok
stoic saddle
how did you get -10 for f(-3)?
mystic minnow
yup. This is the graph of (x+1)-8 or x + 1^2 -8. you're either missing the square or parenthesis.
abstract forge
how did you get -10 for f(-3)?
-3 +1 -8
desert dirge
no
stoic saddle
no, it would not!
desert dirge
yes
native anchor
marsh citrusBOT
lost apex
I think the right way to think about this kind of question is, "What is the probability that the first letter is a B." Then, "Assuming we got a B for the first letter, what's the probability that the second letter is E" etc
native anchor
so like NCR(10,1) *NCR(9,1) etc?
lost apex
like 1/10 * 1/10 * ...
native anchor
Yep okay, so that is the right for question c just need to divide it by NCR(10, 4)
native anchor
Because it is a probability so you would have to divide by the total number of possible outcomes
like how many combinations
lost apex
ok, it's fine to do it that way- then the number of correct out comes is 1 * 1 * 1 * 2
and the number of total outcomes is 10^4
ncr doesn't get you what you want in this case
native anchor
Oh okay, but what about D though, since there isnt any replacement?
lost apex
how many outcomes are there for the first draw?
think about it logically over memorizing a formula
native anchor
10 outcomes because it have 10 letters right?
lost apex
right! but how many outcomes are there for the second draw?
native anchor
9
lost apex
ok, i think you understand
native anchor
so I do that 4 times because it is 4 letters I need right?
lost apex
yeah -on the third draw there will be 8 outcomes
native anchor
So how would i write that as a probability then if I know how many outcomes there are?
lost apex
how many correct outcomes are there?
native anchor
1098*7= 5040
native anchor
wait I mis wrote my last question it is 1098*7=5040
lost apex
yeah
lost apex
oh, i was about to say something wrong
actually zero
right?
there's only one b
but if we were trying to spell bear, it would be two
native anchor
Yeah that is what I was confused about at first but I thought that there had to be a solution that i was not seeing
lost apex
because you can use the black r or the white r
yeah, i think you were right
but now you know how to do this if it asks about something that's actually possible haha
native anchor
So wait, sorry to ask again but how do I do C exactly?
lost apex
ok, so how many outcomes spell bear?
native anchor
all g so that is how I get the full probability right?
lost apex
yeah that would be the denominator
native anchor
ah okay so then how would I find the ones that spell BARB?
lost apex
well without replacement there are zero outcomes
if it were with replacement there would be 3 for the same reason
marsh citrusBOT
lost apex
you too!
marsh citrusBOT
Available help channel!
halcyon rune
(solve the question using the formula below) I seriously cant figure out how to do this as my answer always either goes above or way too low
marsh citrusBOT
(solve the question using the formula below) I seriously cant figure out how to ...
stoic saddle
ah yes, the classic "use this formula, except we deliberately give you the wrong formula for your problem!"
halcyon rune
ah yes, the classic "use this formula, except we deliberately give you the wrong...
i was thinking the same thing lmao
i wanna message my teacher to see if it was just a mistake but she doesnt even read my messages 💀😭
still creek
ah yes, the classic "use this formula, except we deliberately give you the wrong...
so classic
stoic saddle
okay we can assume it's talking about geometric progressions and (a_n) is such a progression
even tho that's kind of a big ask
without any more context, that is
but then like. the formula you've shown gives the SUM of the first n terms of the progression
halcyon rune
i mean, yeah considering her who doesnt explain things any further, that might just be the case
stoic saddle
and you are asked only for one term
halcyon rune
and you are asked only for one term
yeah that problem exists...
stoic saddle
so... bit of a wtf moment there
halcyon rune
well i can just skip this one since i've solved other problems similar to this that i managed to solve but just this one...
stoic saddle
well like
a_6 = a_1 * r^5
but this does not make use of the formula and so might be rejected on those grounds alone
rain leaf
what is S_n? is it the sum a_1 + ... + a_n?
halcyon rune
sn = the number that came out using the formula
rain leaf
so you do know this number?
rain leaf
aren't you asked to figure a_6?
halcyon rune
yeah
the thing is, i got an answer but its way too far from the answer i got just by computing 4 x 3 again and again
the answer that came out using the formula needs to be the same as the one i just computed by doing 4 x 3
rain leaf
i kinda don't understand, they want you to figure out S_6 and a_6 at the same time using this single equation?
halcyon rune
i mean, if the formula wasnt necessary and i can just compute it however i want then yeah
but sadly the formula provided needs to be used in that way
halcyon rune
(solve the question using the formula below) I seriously cant figure out how to ...
<@&286206848099549185> is this just wrong or im dumb?
lost apex
You're asking if the formula provided is appropriate for the question asked, yes?
the formula you were given is for the sum
marsh citrusBOT
@halcyon rune Has your question been resolved?
cyan crypt
In your own words please define to me the meaning of Interpolation Search Algorithm (Position Probing)
marsh citrusBOT
In your own words please define to me the meaning of Interpolation Search Algori...
@cyan crypt Has your question been resolved?
gloomy dome
[Statistics newbie]
I don't understand this concept.
Wasn't "sum of squares" the sum of the residuals (i.e. the distances of each data point from the line) squared?
Shouldn't the result be a positive value above 0?
marsh citrusBOT
[Statistics newbie]
I don't understand this concept.
Wasn't "sum of squares" the...
rose torrent
(solve the question using the formula below) I seriously cant figure out how to ...
Is this even a question 😒
Even a kid can solve this
gloomy dome
What about my question?
gloomy dome
Also in math terms, when they say that an equation Q1 performs worse than a Q2 equation, does it mean that Q1's result r1 is smaller that Q2's result r2?
gloomy dome
So Q1 is less accurate than Q2 in my example?
rose torrent
So Q1 is less accurate than Q2 in my example?
In what context you said q1 is worse ?
And by result do you mean value of each equation when put with a specific value in both of them
For example when we put x=3 in 3x²+4 we get 3*3²+4= 27+4=31
gloomy dome
Uhm, let me get the notes
Here, he says that if we would to consider in an analytic context that mouse size is influenced by all of those parameters, they would get reduced to 0.
So this equation wouldn't perform worse than the one on the bottom
rose torrent
Here, he says that if we would to consider in an analytic context that mouse siz...
Because both these equations are exactly the same
It's simple
You can write 3y³+5y as 3y³+ 0y²+ 5y +0
gloomy dome
Yeah but what if one of those parameter was instead multiplied by 1?
Why would you say that the above one performs worse than the bottom one?
rose torrent
Yeah but what if one of those parameter was instead multiplied by 1?
Why would y...
If those parameters really have got something to do with mouse weight, multiplying by a coefficient would give you a more accurate answer .
If those parameters are of no use , multiplying by a coeff gives you a less accurate aka a worser result
rose torrent
Yes but one thing , you have to use the proper coefficient not any arbitrary number
gloomy dome
?
I'll learn what you mean along the way I guess, right now though I'm attending class, sorry to cut our conversation short, if I didn't the bot probably would have eheh
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
gaunt pine
the top one
marsh citrusBOT
the top one
gaunt pine
.close
fallow compass
what is this method of rationalising trigs called?
marsh citrusBOT
what is this method of rationalising trigs called?
ruby mulch
I don't recall having a name for that technique. Just "multiplying both sides of the fraction with a constant", "expanding the expression", and "Pythagoras theorem"
fallow compass
so rationalising trigs is a thing?
hadnt seen anything like this except in case of irrational number
upper briar
i think its quite specific to this Q
glacial hedge
I wouldn't give any generality to this method. Most trig stuff is just about rewriting and since it's an exercise there's got to be a way that works
fallow compass
right
ruby mulch
It's a thing for basically every rationals ever
teal isle
how would i start this? i think i can make a exact value traingle using x/2
teal isle
flat geyser
I need help to solve this
If polynomial p(x)= x^3+x^4+x^5+…+x^2021 divided by (x-1)^3 leaves ax^2+bx+c then find the value of 4a+2b+c
marsh citrusBOT
I need help to solve this
If polynomial `p(x)= x^3+x^4+x^5+…+x^2021` divided by ...
@flat geyser Has your question been resolved?
signal bronze
Find the volume of a quadrangular prism whose base is a triangle with base 4.2 cm and height 3.8 cm and the height of the prism is 10 cm V = ??
elfin berryBOT
stoic saddle
@still temple do you know your way around special points on the graph of a function? i.e. ones at which the first or the second derivative is 0
yes, dy/dx = 0 gives you stationary points and d^2y/dx^2 = 0 gives you points of inflection
blink blink
sorry that was a little too word-salady for me and i got thrown off track lmao
still temple
One message removed from a suspended account.
marsh citrusBOT
One message removed from a suspended account.
wooden oriole
expand it
still temple
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One message removed from a suspended account.
wooden oriole
expand $(\vec{x}-\vec{y}) \cdot (\vec{x}-\vec{y})$
still temple
One message removed from a suspended account.
elfin berryBOT
秋水
wooden oriole
$\vec{x}$ and $\vec{y}$ are orthogonal, so $\vec{x}\cdot \vec{y}=0$
elfin berryBOT
秋水
still temple
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wooden oriole
so you get the answer
still temple
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hushed egret
pythagrawr
still temple
so you get the answer
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wooden oriole
The two vectors inside are perpendicular to n.
still temple
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still temple
The two vectors inside are perpendicular to n.
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still temple
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still temple
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still temple
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marsh citrusBOT
@still temple Has your question been resolved?
still temple
`1*(-2)+2*a-3*b=0`
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wooden oriole
Just a suitable set of solutions is okay, you can let a = 1.
wooden oriole
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the other is 1*c+2*0-3*1=0, you can get c straightly
still temple
Just a suitable set of solutions is okay, you can let a = 1.
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still temple
the other is `1*c+2*0-3*1=0`, you can get c straightly
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wooden oriole
The way span is written is not unique
still temple
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wooden oriole
As long as the two vectors inside are linearly independent.
still temple
Just a suitable set of solutions is okay, you can let a = 1.
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wooden oriole
when a=1, the two vectors are linearly independent, you can check, so you can let a=1
still temple
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marsh citrusBOT
still temple
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marsh citrusBOT
✅
wooden oriole
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vector a and b are linearly independent if a≠mb （m≠0）
so it's easy to see
still temple
vector a and b are linearly independent if a≠mb （m≠0）
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wooden oriole
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that's from the definition
still temple
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wooden oriole
the plane equation is
$\vec{n} \cdot (\vec{x}-\vec{p})=0$
elfin berryBOT
秋水
wooden oriole
just calculate it
still temple
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wooden oriole
$\vec{x} = (x,y,z)$
elfin berryBOT
秋水
still temple
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still temple
$\vec{x} = (x,y,z)$
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wooden oriole
what do you mean?
$\vec{n}=(1,2,1)$,$\vec{p}=(1,0,1)$
$\vec{x}-\vec{p} = (x-1,0,z-1)$
elfin berryBOT
秋水
wooden oriole
$\vec{n} \cdot (\vec{x}-\vec{p})=(1,2,1) \cdot (x-1,0,z-1)=x-1+(z-1)=0$
still temple
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marsh citrusBOT
Available help channel!
bright hedge
I need help to solve an exercise about functions and function limits.
marsh peak
First of all you can simplify (x^3 - 2x^2 + x - 2)/(x - 2)
bright hedge
okk
so one moment I write down
ok this is the simplification
Now I can delete x-2
upper briar
define x=2 separately
marsh peak
If it was zero, it wouldn't be as simple as to just cancel out
upper briar
exactly what is being done in f lol
bright hedge
ok, this is clear, so remains
x^2 + 1
upper briar
ye find the turing pts of it
marsh peak
So the range of outputs on [-1, 3] is the same as the range of outs puts of x^2 + 1 on [-1, 2)U(2, 3] united with {a}
upper briar
wait im drunk LOL
bright hedge
So the range of outputs on [-1, 3] is the same as the range of outs puts of x^2 ...
so I have to write
[-1, 2) U (2, 3] U a
marsh peak
No
bright hedge
oh sorry I didn't understand this passage
marsh peak
(range of x^2 + 1 for x in [-1, 2)U(2, 3]) U {a}
bright hedge
aaah okkk
marsh peak
That's not it but okay forget it
Just find the range of x^2 + 1 on [-1, 2)U(2, 3] first
upper briar
i like to draw it
bright hedge
That's not it but okay forget it
I know the scription is uncorrect
bright hedge
Just find the range of x^2 + 1 on [-1, 2)U(2, 3] first
okk I try
upper briar
,w graph y=x^2+1
elfin berryBOT
upper briar
omg bad scale
marsh peak
Post your question in an available help channel
wise dove
ohh okay okay
upper briar
wise dove
sorry but it's my turn. Wait a minute please
AH sorry i just joined i didnt know
upper briar
bright hedge
In x = 2 the function doesn't exist
bright hedge
AH sorry i just joined i didnt know
no problem :D
upper briar
👽
wise dove
<#488120190538743810>
ty!!
upper briar
thus that circle
bright hedge
So I have to find the range separately?
1 ≤ x^2 + 1 < 2
and
2 < x^2 + 1 ≤ 3
upper briar
well
upper briar
i kinda alr gave it to u
bright hedge
and what 'bout "a"? How can I insert this parameter in a range?
bright hedge
yes this is clear but how?
Sorry if I seem stupid, but I really am ahaha.
So these are the ranges:
1 ≤ x ≤ 2 and
2 < x ≤ 3
upper briar
those r the domain
idk
trivially just put f(x) as x->2
would always work as polynomials are cont
bright hedge
lim f(x)
x->2
Theorically I understand, but I can't solve it algebrically
MAYBE I DID IT
So
if I put:
bright hedge
would always work as polynomials are cont
do u think that this M.O. might be correct?
marsh citrusBOT
@bright hedge Has your question been resolved?
still temple
still temple
marsh citrusBOT
still temple
Can anybody help me with d, Im not sure what the question meant
hidden hollow
Question . Im trying to convert -225 into radians. I got -5pi/4 . I know that its going to be -225 * pi/180. I broke down 225(45 x 5) and 180 (45 x4), after canceling everything I ended up with -5pi/4. I looked up the answer and its -37pi/30......where did I go wrong? @marsh citrus <@&286206848099549185>
marsh citrusBOT
@still temple Has your question been resolved?
unique mural
$(1 + i)^{12}$
marsh citrusBOT
$(1 + i)^{12}$
elfin berryBOT
ahmed349
unique mural
Is binomial theorem the only way to do this
smoky siren
You would usually write 1+i in polar coordinates instead
unique mural
Polar coordinates?
trim quest
Like $re^{i\theta}$ form
elfin berryBOT
tatpoj
unique mural
Ah not familiar with that unfortunately
trim quest
You can imagine a complex number as a point on the complex plane, sort of like a vector.
It has a magnitude r and a direction theta
Then re^(i*theta) is equal to that complex number
1+i is like the vector [1,1]
Do you know what its magnitude and direction are?
from the origin
trim quest
r is the magnitude, e is euler's number
unique mural
I haven't learnt about Euler's yet
trim quest
Oh, okay. Then you'll probably learn what I'm talking about soon
unique mural
Alright, I will stick to binomial for now, thanks, I will keep the above formula in mind
edgy flint
ax^2+bx+ma+nb=0 where n^2+m<0, a,b,m,n real numbers, a not equal 0, find what kind of solutions does this equation have
marsh citrusBOT
ax^2+bx+ma+nb=0 where n^2+m<0, a,b,m,n real numbers, a not equal 0, find what ki...
tardy monolith
look at the discriminant
edgy flint
b^2-4(a^2)m-4abn
marsh citrusBOT
@edgy flint Has your question been resolved?
edgy flint
<@&286206848099549185>
marsh citrusBOT
@edgy flint Has your question been resolved?
bleak reef
marsh citrusBOT
still temple
plz help
sharp lichen
ax^2+bx+ma+nb=0 where n^2+m<0, a,b,m,n real numbers, a not equal 0, find what ki...
still need help?
bleak reef
GET OUT MY CHANNEL 😈
bleak reef
wtf is this
hidden plaza
Makes no sense or at least I don’t know how to interpret that. Seems just like an abuse of notation.
But if you really had to do it, you could argue dx is just an infinitesimally small amount
bleak reef
Makes no sense or at least I don’t know how to interpret that. Seems just like a...
ye that's what I thought
elfin berryBOT
Pure
bleak reef
ya alright, ty pure, I guess it was just a silly question. somebody asked me it 🤷♂️
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
tardy canyon
I kinda forgot where else to go from here, do I bring down the 3 when I solve the denominator?
marsh citrusBOT
I kinda forgot where else to go from here, do I bring down the 3 when I solve th...
tardy canyon
I think i see now, is the answer then (3a-1)(a+4) which makes the zeros 4 and 1/3
-4
lean flame
You got it bro
tardy canyon
my homework question says that it is incorrect however
Oh wait
I’m slow nvm
.close
marsh citrusBOT
daring wadi
still temple
but in the answer it says $(x-4)^n$ instead of $(\frac{x-4}{4})^n$
elfin berryBOT
umadbruh
still temple
and also how do they know it's $2^{1-2n}$?
elfin berryBOT
umadbruh
marsh citrusBOT
@still temple Has your question been resolved?
still temple
<@&286206848099549185>
long fjord
Can someone help with 53c I have done a and b but don’t understand c
marsh citrusBOT
Can someone help with 53c I have done a and b but don’t understand c
@long fjord Has your question been resolved?
long fjord
<@&286206848099549185>
marsh citrusBOT
@long fjord Has your question been resolved?
long fjord
.close
vernal coral
marsh citrusBOT
vernal coral
im so confuse on this logic diagram
obsidian bone
Some@people
vernal coral
dude u just went on an alt
chrome silo
@vernal coral Just make a truth table with the inputs and outputs and go through the diagram
vernal coral
<@589305100036734977> Just make a truth table with the inputs and outputs and go...
im confuse on this
chrome silo
what are you confused by?
vernal coral
how to get c amd d values
chrome silo
then get out a paper
and go through a possible input
if you write it down its not too difficult
vernal coral
yeah i have the a nd b set up
chrome silo
ok then lets go through a case
lets have a = 0 and b = 0
what are the outputs of these three gates then?
vernal coral
the first one would be 1
chrome silo
which one is the first one?
vernal coral
the other two would be 0
chrome silo
the middle?
vernal coral
yes
chrome silo
the middle gate would recieve two 0 inputs
and since its a nand gate, it would output 1
vernal coral
agree
vernal coral
the top would be a 0 beccause there is a 1 going thorug itfrom a\
chrome silo
what are the two inputs for the top gate?
vernal coral
input is 1 and a 0
vernal coral
oh so it would be 1
chrome silo
yes
vernal coral
i got confuse with and
vernal coral
yes
vernal coral
oh so c woul;d be 0 then?
vernal coral
it would be 0 because 1 is going throug a not gate
chrome silo
Yes
vernal coral
ahhh i see thanks so much ,am
chrome silo
np
vernal coral
.close
livid maple
marsh citrusBOT
stoic saddle
@livid maple have you made progress thus far?
marsh citrusBOT
@livid maple Has your question been resolved?