oh, do you mean for vector B?
#help-27
wooden wraith
restive river
oh, do you mean for vector B?
Yes
wooden wraith
yeah you'll have to use trig to find the x and y components for that one
x = r cos theta
y = r sin theta
where r is the length of the vector
and theta is the angle in standard position
wooden wraith
(or you can just draw a triangle)
restive river
(or you can just draw a triangle)
Ok so what do I do with this info
I was looking for my calc mb
wooden wraith
ok so now you've got
restive river
Ye
wooden wraith
A = (0,5)
can you also write B and C in component form?
like that
you already found the components
do you get what I mean?
like
B = (6.3, -2.9)
wooden wraith
so add the x components
and add the y components
well, subtract the components for C
wooden wraith
B = (6.3, -2.9)
can you write all three vectors in this form
and then do A + B - C
devout snowBOT
@restive river Has your question been resolved?
restive river
and then do A + B - C
Oh I figured it out isn’t it this
Kinda weird they are the same tho imo
Is square root 8.4 the angle?
But how’d I get the displacement?
wooden wraith
It's A + B - C though
so your 2.1's should be the opposite
because you're subtracting C
x = 6.3 + 0 + 2.1
y = -2.9 + 5 - 2.1
restive river
Yes
woven radishBOT
Result:
8.4
,calc -2.9 + 5 - 2.1
woven radishBOT
Result:
0
wooden wraith
For your x and y
restive river
Ok
wooden wraith
The resultant is (8.4, 0)
wooden wraith
no problem 👍
restive river
.close
proud perch
$$3^x = 1 (mod 100)$$
devout snowBOT
$$3^x = 1 (mod 100)$$
woven radishBOT
Mr. Gamer
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@proud perch Has your question been resolved?
proud perch
@low holly elaborate?
totient method gives me 40
i would like to justify 20 without brute force
low holly
you want the smallest answer?
proud perch
yes
that would make computation of the power tower much cleaner
i need the last two digits of 3^3^3^3...
low holly
hmm
that's the Carmichael function but I don't know how to compute it in general
apparently there's a formula you can use to calculate it: https://brilliant.org/wiki/carmichaels-lambda-function/
proud perch
alright i got it
phi(100) = 100 - 50 - 20 + 10
= 40
check each divisor of 40
1 2 4 5 8 10 20 40
3^1 = 3
3^2 = 9
3^4 = 81
3^5 = 43
3^10 = 43x43 = 49
3^20 = 49x49 = 1
then:
3^3 = 27
3^27 = 3^7 = 43*9 = 87
3^87 = 3^7 = 43*9 = 87
then 3^3^3^3^... = 87 mod 100
proud perch
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long elbow
can someone tell me why is it dne? is it because the denominator cant be 0?
long elbow
please ping me if youre here
supple knot
can someone tell me why is it dne? is it because the denominator cant be 0?
the limit as x goes to zero of f'(x) doesn't exist. plot it and see
long elbow
the limit as x goes to zero of f'(x) doesn't exist. plot it and see
is that whats called a point of inflexion?
supple knot
no that's something else
long elbow
no that's something else
then one of these?
long elbow
then one of these?
technically this is also going from concave up to concave down
long elbow
the bottom one
then why isnt it a point of inflection?
supple knot
then why isnt it a point of inflection?
Where did you demonstrate the function changes concavity?
long elbow
technically this is also going from concave up to concave down
here
supple knot
then one of these?
This is for different functions
supple knot
can someone tell me why is it dne? is it because the denominator cant be 0?
Than your problem
supple knot
Where did you demonstrate the function changes concavity?
For the original problem
long elbow
sorry i dont quite understand
but anyway i cant use a graphing tool for my exam, how would i know if the derivative of a function will be dne in future?
long elbow
Practice more limit problems
practice getting the derivative from the limit method?
like the h one
devout snowBOT
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unkempt quiver
Why is cosx/x undefined?
devout snowBOT
Why is cosx/x undefined?
tranquil bloom
the limit?
unkempt quiver
I meant why is the limit as x approaches 0 of cosx/x undefined but the limit as x approaches 0 of sinx/x 1?
tranquil bloom
since the limit from the left and right aren't equal
for cosx/x as x->0
therefore doesn't exist
unkempt quiver
Yep
tranquil bloom
for the limit for sinx/x, both the left side and right side are equal and limit exists
unkempt quiver
since the limit from the left and right aren't equal
What about coskx/hx
Is that also always undefined
For the limit as x approaches 0?
In a test whenever they ask that would I always just write undefined??
Idk when it's undefined and when it's not
unkempt quiver
would still be undefined.
Yep
Oh
Is there a rule for it
Cause ik lim x-->0 of sinkx/hx = k/h always
And same for tan
brazen star
not that i know off, haven't touched limit in years.
unkempt quiver
Why is it different mathematically for cos
unkempt quiver
not that i know off, haven't touched limit in years.
Oh ok
Well what about algebra
Why does that diverge
While cos and sin have a constant value at that point
Are you rusty at the algebra as well?
brazen star
huh?
oh wait ik
so the difference is that
cos(-x) = cos x
where as
sin(-x) and tan(-x)
becomes
-sin(x) and -tan(x)
so when you take the limit x->0^- cos x / x , the value will become lower and lower because cos x will be positive whereas x will be negative.
and when you take the limit x-> 0^+ cos x / x, the value will become greater and greater because cos x will be positive and x will be positive
so one diverges to negative infinity while the other diverges to positive infinity
idk how to word it better, that's just how i understand it
maybe wait for someone more experienced than me.
devout snowBOT
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livid geyser
Why is it different mathematically for cos
cosx/x isn't an indeterminate Form, since cos(0) = 1,so the limit would be of the term 1/0. But even if you allow for infinity to not be the same as undefined, it won't exist since the right handed limit would be positive infinity and the left handed limit will be negative infinity
Whereas sinx/x for one is 0/0 so it could possibly have a limit
And you can prove it's 1 with squeeze theorem
dusk pewter
How would I go about doing this?
devout snowBOT
How would I go about doing this?
cunning needle
Does this mean that The cost of the dress is reduced by 14?
willow helm
I think so, yeah
cunning needle
If it is, then 14 is 25% of the original price. Then you find what is 75% and 100% , for sale price and original price of dress respectively
Let x be the original price $14=\frac{25}{100} \cdot x$ afterwards. Solve for x
woven radishBOT
Chat Bot
dusk pewter
Does this mean that The cost of the dress is reduced by 14?
I think it means the price of the dress after the decrease of 25% is £14
cunning needle
If that is the case, it means that 14 is 75% of the original cost
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wooden axle
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wooden axle
In this question can we consider
Lembda-5<0
When a>0 D<0 this is valid too
Why are we not using this?
devout snowBOT
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fossil lagoon
hi
fossil lagoon
I got a question
to do with ODE's
Ordinary Differential Equations, can anybody help me?
brave vapor
Post the question
fossil lagoon
I got the method over here, but I don't fully understand it
yeah, I read through it multiple times
I don't fully understand what my first step will be
help?
devout snowBOT
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fossil lagoon
h
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ancient ravine
you can ping the helpers
ebon crown
The side AB of the rectangle ABCD lies on the straight line with direction angle a = 45° and A(4; 1), C(3; 6). Write the equations of the lines on which the sides of the rectangle AB, BC, CD, DA lie. Draw these lines.
I managed to do AB and CD ( y=x-3 ; y=x+3 ), but how to make BC or DA work is beyond me.
Would be nice if someone could explain to me how to do it.
devout snowBOT
The side AB of the rectangle ABCD lies on the straight line with direction angle...
ebon crown
ebon crown
rn it's more like parallelogram, than it is rectangle.
keen anchor
perpendicular lines have negative reciprocal slope
ebon crown
I still don't quite get it.
<@&286206848099549185>
help pls...?
Sorry for ping, now i get it.
.close
steel thunder
im trying to prove what real values α and β must have so that the limit there is equal to 0
devout snowBOT
im trying to prove what **real** values α and β must have so that the limit ther...
steel thunder
but i got stuck here
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steel thunder
<@&286206848099549185> ?
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raven swift
help?
restive river
I need help solving systems of equations
devout snowBOT
I need help solving systems of equations
woven radishBOT
Miguel
woven radishBOT
Miguel
restive river
From the second equation, and you substitute that in the first one
$26k = -6 \mod 40$
woven radishBOT
Miguel
restive river
As $\gcd(26, 40) = 2$ and $2|-6$, there is a solution
woven radishBOT
Miguel
restive river
Doing Bézout you get $26*(-3)+ 402 = 2$ which means $26(-3)*(-3) = -6 \mod 40$
woven radishBOT
Miguel
restive river
So $k = 9 \mod 40 \Rightarrow k = 9 + 40n$
woven radishBOT
Miguel
restive river
**Miguel**
Now we put that back into here
$x = 22+26(9+40n) \Rightarrow x = 256 + 1040n$
woven radishBOT
Miguel
restive river
So I understand this all
What I don't understand
Is that now the teacher said, "if you want to write x as an equivalence of a mod what you do is take the $\text{lcm}(26, 40) = 520$
woven radishBOT
Miguel
restive river
And you do $x \equiv 256 \mod 520$
woven radishBOT
Miguel
restive river
My question being, why would you take the least common multiple? She said something that you lose solutions or whatever, I just don't see it
devout snowBOT
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dapper tiger
from here, it already makes more sense to split
44 = 2² * 11
26 = 2*13
since x = 22 mod 26, x = 9 mod 13
since x = 16 mod 44, x = 5 mod 11
and your solution should be unique mod 4*11*13
which is why a least common multiple "pop out"
you have to "split" the information about x
and then by the chinese remainder theorem, if your system doesn't have a contradiction, you'll have unique solution mod lcm
but then because you have 2 as common factor (in 26 and 44)
you may have a problem about the contradiction part (in fact, it's corrected once you notice x = 0 mod 4, and this third equation allows a solution once you convince yourself of the equivalence, x = 0 mod 2 is just redundant)
devout snowBOT
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restive river
and your solution should be unique mod 4*11\*13
That kinda makes sense
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sand summit
I need help with a proof… I don’t know where to begin
devout snowBOT
I need help with a proof… I don’t know where to begin
sand summit
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@sand summit Has your question been resolved?
craggy granite
PLS
craggy granite
WHEN U REFLECT AN EQUATION
like if u have y=(x+1)+5
and u reflect it in the x axis
would it be y=-(x+1)+5 or y=-(x+1)-5
if it reflected in x u multiply the outer by (-1) but do u multiply ur k value by (-1) too
?
pls help me
im dying
@lusty sapphire
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heady eagle
if it reflected in x u multiply the outer by (-1) but do u multiply ur k value b...
do u still need help?
whenever you reflect a function along the x axis you negate the y value and whenever you reflect the function across the y axis u negate the x value
so when we want to reflect a function across the x axis our new function would be
$-y = (x-1)^3+2$
woven radishBOT
0_0
heady eagle
$\therefore y = -(x-1)^3 - 2$
woven radishBOT
0_0
hexed ocean
can someone explain how this was achieved?
devout snowBOT
can someone explain how this was achieved?
pseudo basin
show your table?
north nimbus
For #72 can anyoen explain to me what to do if theres an e in the exponent when finding the derivatives? Im in AP Calc AB, and Im confused as to why t^-e is multiplied by (1-e).
devout snowBOT
For #72 can anyoen explain to me what to do if theres an e in the exponent when ...
north nimbus
help?
rapid merlin
You gave us 11 questions in the picture and I can't find t^-3 in any of them
You can take the derivative of them by taking the ln of both sides
Then taking the implicit differentiation to get y' of it
And any y you get in the result just substitute it by the first equation you had before even taking the ln of both sides
And you will get the answer without any confusion
devout snowBOT
@north nimbus Has your question been resolved?
north nimbus
You gave us 11 questions in the picture and I can't find t^-3 in any of them
#72 and also mb i meant t^-e
if the formula that i learned was d/dx a^u = a^u * lna * du/dx
in the context of #72
ik a&u is just t^(1-e)
and ln of t is t^-1
which makes the original t^-e
what is the derivative du/dx of (1-e?
north nimbus
?
devout snowBOT
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zealous cosmos
Is
finite briar
Yes
finite briar
Its .close
zealous cosmos
.close
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zealous cosmos
thank you lol
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zealous cosmos
What am I doing to get a different answer then this site?
devout snowBOT
What am I doing to get a different answer then this site?
zealous cosmos
the web site gets 4/25, while I am getting 2/5
I assume I messed up
<@&286206848099549185>
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zealous cosmos
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dawn chasm
hmm?
zealous cosmos
I am sure its something stupid, I just cant figure it out
zealous cosmos
sorry, I actually think its getting 4/5, while I am getting 2/5
dawn chasm
neither do i haha
winter patrol
you messed up your power of 2 for the (n+1)th term
zealous cosmos
ok, but then why would it not get canceled out with the other 2^2n
winter patrol
$2^{2(n+1)} = 2^{2n + 2}$
woven radishBOT
ℝam()n()v
zealous cosmos
OOOOOOOOOOOOOOOOoooooooooooooooooooooooooooooooooooooooooooooo
winter patrol
2^(2n) is still cancelled, you just lost a factor of 2 because you had
2n + 1 instead of 2n + 2
zealous cosmos
wai
I think I see it now
thank you so much
been banging my head about if for an hour
thank you @winter patrol
.close
devout snowBOT
hard ermine
.
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marble quail
(ABCDEF)_16
a) write it in binary and and then base 8
b) write it in base 9
marble quail
I managed to solve a)
by writing ABCDEF as binary, (1010,1011,1100,1101,1110,1111)_10
and then made it (101, 010,111,100,110,111,101,111)_8
but why is base 8 only three numbers?
of the binary
and how do i solve b) with base 9
sand dove
8 = 2³, so one digit base 8 corresponds to 3 digits base 2
sand dove
and then made it (101, 010,111,100,110,111,101,111)_8
Now you have to convert each digit to what it is in base 8
101_2 = ...
sand dove
More exactly : you exactly need 3 bits
sand dove
so we need 4 bits?
Here's the part where it fails
brazen needle
so base 16 is actually 4 bits
sand dove
Base 9 is not in bits, so the "4th" bit will have remainders
brazen needle
no
sand dove
Nope
sand dove
by writing ABCDEF as binary, (1010,1011,1100,1101,1110,1111)_10
So, take the binary representation
brazen needle
well in binary represenation sure cause both will require 4 bits
think of it this way
2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16.....
16 32 64 128...
marble quail
That's a little confusing
brazen needle
base 9 and base 10 (decimal) both require at least 4 bits to represent
marble quail
I understand now that base 8 uses 3 bits since 0-7 only needs 3
but 9 is a little weird
marble quail
base 9 and base 10 (decimal) both require at least 4 bits to represent
Yeah
brazen needle
base 4-8 can be represented using 3 bits, base 9-16 can be represented using 4 bits etc..
marble quail
Ok
sand dove
In any case, the "bit" approach doesn't work for base 9 because it is not a power of 2
sand dove
So what you need to do :
- find the quotient and remainder of your number divided by 9
- repeat the process, with the new number being the quotient
Until the quotient is 0
marble quail
What is quotient?
marble quail
So i take my binary number or with base 8?
sand dove
What is quotient?
Example : 10/8, the quotient is 1, the remainder is 2
marble quail
I have to mention
this is supposed to be solved without a calculator
As i wont get one on the exam
brazen needle
yup thats fine
sand dove
Yes it can be solved without calculator
sand dove
No, this is an example
marble quail
Oh
marble quail
So 2?
sand dove
The remainder is 2
brazen needle
basically you do long division of 52746757/8
sand dove
And quotient is 1
sand dove
Oh nono
Oh wait sorry
I forgot you can do it the other way around
So
5/9 isn't useful, because the quotient is 0
marble quail
y
marble quail
ooh so we take
sand dove
So, 52 base 8 is...
sand dove
Basically, starting with a quotient of 0 is like adding a 0 in front of the number
marble quail
48 + 4
sand dove
Like 100 is the same number as 0100
marble quail
52 / 10
marble quail
Yeah i'm so fucking lost lmao
marble quail
Hold on i'm trying to get back on track
We have (52746757)_8
Yes?
And we want to make it into base 9
sand dove
Yes
marble quail
Do i need to make it base 10 first? before making it base 9?
or can i go directly too 9
marble quail
marble quail
ok
sand dove
Yeah we need to start from the remainder
So converting from base 16 to base 10 should be easy
But the number is really big
marble quail
But the number is really big
This is the solution provided on the exam
but i have no fkn idea what he does
sand dove
Ah i see what he's doing
So using base 8, we're going to compute the remainder of our number when divided by 9
But since 8 and -1 have the same remainder mod 9
We can replace all instances of 8 by -1 to compute the remainder
marble quail
sand dove
This helps us tremendously because now we don’t have to compute 8^k, we only have to compute (-1)^k, which is either 1 or -1
marble quail
i'm sooooooooo lost
how does this work
How is 10 * 16^5 = 1*4?
<@&286206848099549185>
marble quail
Make me understand
worthy geyser
ok 1 sec
marble quail
(ABCDEF)_16 to base 9
worthy geyser
i only understand greek terms so 1 sec
trying my best here
ok im already confused
lemme open microsoft paint
i feel like theres something missing
idk
devout snowBOT
@marble quail Has your question been resolved?
marble quail
this is supposed to be solved without calculator.
worthy geyser
i mean i tried with microsoft paint
what i got is like (10) (4^2)^5 + (11) (4^2)^4
idk
this is what i somehow got
then its like
idk its a bit weird
marble quail
<@&286206848099549185>
How do i go from a base to another base? For example. (2983)_10 to base 7 without using a calculator
real pewter
<@&286206848099549185>
How do i go from a base to another base? For example. (2...
oh part of its cut off
it just
b c c
devout snowBOT
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winter sphinx
supple knot
are we supposed to know what F(x) is
winter sphinx
are we supposed to know what F(x) is
I think it’s force and v(x) might be potential
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lethal osprey
devout snowBOT
lethal osprey
does anyone know how i can write this parabola to hit 6?
pastel pasture
you just want a parabola with repeated roots at x = 4 and a y intercept of 6?
lethal osprey
yeah
pastel pasture
(3/8)*(x - 4)^2
lethal osprey
(3/8)*(x - 4)^2
how did you know to put 3/8?
pastel pasture
because we want the value to be 6 at x = 0
pastel pasture
$f(x) = a(x - 4)^2$
woven radishBOT
jan Nejon
pastel pasture
Correct?
We want f(0) = 6
Oh wait do you wanna know why we chose to multiply the thing with a instead of add it or something else?
lethal osprey
Yea :D
pastel pasture
Ah I see
its because if you add or subtract then it alters the roots of the equation
$f(x) = (x - 4)^2 + a$ this no longer has 4 as a root
woven radishBOT
jan Nejon
pastel pasture
But choosing the multiply $a$ like this works $f(x) = a(x - 4)^2$
woven radishBOT
jan Nejon
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iron siren
I need help w/ my double integral!
devout snowBOT
I need help w/ my double integral!
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onyx grove
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onyx grove
What prevents the answer from being b
given this solution
at pi, pi and pi, -pi and -pi, pi and -pi, -pi there are solutions in both b and c
so the solution doesn't seem to decide betwee nthe 2
close
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restive river
Can someone help me with this this is what i have so far
devout snowBOT
Can someone help me with this this is what i have so far
@restive river Has your question been resolved?
restive river
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safe tulip
can you take a dot product of vector fields, and if so, is the result also a vector field?
devout snowBOT
can you take a dot product of vector fields, and if so, is the result also a vec...
mystic scarab
The dot product between two vectors returns a scalar
safe tulip
The dot product between two vectors returns a scalar
thanks
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mild basin
devout snowBOT
mild basin
why am i not allowed to do the second method?
winter patrol
because those powers only apply to the x and y
wheat pebble
winter patrol
$\log(ab^c) \redneq c \log(ab)$
woven radishBOT
ℝam()n()v
winter patrol
basic intro in #resources
if you understand function notation should be relatively easy to get started
also depending on what you're told about x and y,
ln|x|, ln|y| should have been used
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mild basin
OK ty
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lusty swift
Referring to this screenshot:
When this says "sinθ > 0, which means θ must be in Quadrant I or II", that's because sinθ is the y coordinate of a point, and that point (in this case 3/5) is positive, right?
The part here that says "θ must also be in the range of the inverse sine function. This range is [-π/2, π/2]. So θ must be in quadrant I."
My brain isn't following this conclusion, and I could use some help understanding how those two things are connects.
We know that the point is at (x, 3/5). We know that the point lies above the x axis. We know that the point can't be outside of the range of y = arcsinx. How do all of those pieces fit together to say that θ is in quadrant I and not in quadrant II?
lusty swift
trail eagle
arcsin(x) is injective. sin(x) is not. A bit like how x = sqrt(4) can be seen as a solution to x^2 = 4, you have to be careful of your range when "cancelling" out stuff.
Here, you have t = arcsin(3/5). This means that t is a solution to sin(t) = 3/5.
In particular, in must be in quadrants I or II since it represents a positive y coordinate.
However, the way the arcsin function is defined is with a range of -pi/2 to pi/2, so it cannot have been in quadrant II since that would make t > pi/2
devout snowBOT
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lusty swift
However, the way the arcsin function is defined is with a range of -pi/2 to pi/2...
This is good information, and I appreciate it! I'm just trying to really understand this.
lusty swift
However, the way the arcsin function is defined is with a range of -pi/2 to pi/2...
Actually, I think this is a lost cause. I'm going to go read more of my textbook + watch more videos. I'm clearly missing some huge piece of the puzzle here.
trail eagle
Maybe if we keep the sqrt analogy. If you know x = sqrt(4), then it is pretty clear (since sqrt is the inverse of squaring) that x^2 = 4. So we can just think about what a solution to x^2 = 4 might be. However, if we look at it that way, you might notice that this has two solutions, one positive and one negative. Now, the sqrt function has range that is >= 0, so we can't have had the negative answer to begin with since x = sqrt(4) is in the range of sqrt.
At the end of the day, writing it as sin(t) = 3/5 introduces a new solution because there are two such angles (one in quadrant I and the other in II), so then thinking about the range of arcsin gives you a hint as to which one it originally was BEFORE you wrote it another way
lusty swift
Hey, I really appreciate the help. You're very kind. I'm going to close this chat and keep trying to grok all of this. My brain just isn't making the connections that it should be making.
Thanks again!
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rancid dune
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dapper tiger
always use what you know, if what you've learnt until now is about quadratics, try to get some
for example by summing the two eq, you get y²+2y = 82-19 = 63
so y²+2y-63 = 0
dapper tiger
I think it's (x+9)(x-7)
placid rover
y
rancid dune
oh oops
dapper tiger
so y = -9 or y = 7
dapper tiger
-x²+2(-9) = -19
-x²-18 = -19
-x² = -1
so x² = 1
and x = 1 or x = -1
so when y = -9, you have two solutions, x = 1 and x = -1
then you have the y = 7 case
dapper tiger
there are two eq, you should check in the other eq too
so that you don't find a fake sol
x²+7² = 82
-x²+2*7 = -19 are your two eq
so x² = 82 - 49 = 33
and x² = 14+19 = 33, no contradiction
and in this case either x = sqrt(33), or x = -sqrt(33)
rancid dune
why is it positive or negative?
dapper tiger
x² = a (a > 0) always has two solutions, x = sqrt(a) and x = -sqrt(a)
rancid dune
i see
so a problem i dont understand
the answer set they say is right
is (1, -9)
which is 1 of the four we came up with
dapper tiger
,w x²+y² = 82, -x²+2y = -19
woven radishBOT
dapper tiger
the 4 sol we found
rancid dune
or actually idk
thats just in there not neccessarily correct
anyways ty for ur help
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grizzled fractal
grave vortex
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jade oak
take derivative with respect to x twice
grave vortex
okay! will try that out
jade oak
keep in mind d/dx(y)=y'
grave vortex
but y has 2 solutions
So that's where it gets tricky
Well they both do
So once I solve for one of them, I have two numbers to work with
I think the answer is probably either C or D
Am I on the right track?
jade oak
Does not look like it
grave vortex
I'm leaning towards A now
jade oak
That is what I got
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barren garden
hello I have a question about computing the determinant using the multiplication of the main diagonal when your matrix is in upper triangular form
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hello I have a question about computing the determinant using the multiplication...
barren garden
how do you know wether or not to divide your answers or not
for an example if I have a row [ 0 12 10 6 ]
how do I know if I divide it by 2 and then multiply the numbers on the main diagonal to get the determinant
or just multiply them without dividing
trail eagle
If your matrix is upper triangular, isn't the determinant always the product of the diagonal entries?
barren garden
If your matrix is upper triangular, isn't the determinant always the product of ...
yeah but my question is won't it change if I multiply and divide rows?
like if I change [ 0 12 10 6 ] to [ 0 6 5 3 ] (by dividing the whole row by 2)
when I multiply the numbers on the main diagonal, im now going to be multiplying by 6 instead of 12
trail eagle
Yes it would. Just like any determinant if you multiply a row by a scalar k, then the determinant is also multiplied by k.
barren garden
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trail eagle
Is what you're trying to prove true to begin with?
I don't think it is
Apart from some parentheses you could've used in the line all in red, therest seems like fine deduction, but what you proved is that x is in (S\T)U(S\V), not (S\T)n(S\V)
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sleek estuary
Given a venn diagram like this for example, how am I supposed to know the set operation performed? They showed set theory for like 5 mins and didn't really showed us how to do problems like this. Can anyone explain to me how?
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Given a venn diagram like this for example, how am I supposed to know the set op...
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still rune
At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 22 knots and ship B is sailing north at 17 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) Would anyone be able to help me with this? This is what I did so far but the answer was wrong.
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At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west ...
still rune
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urban crystal
Can someone work this out and tell me what answer they got
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Can someone work this out and tell me what answer they got
viscid cedar
What’s the whole question?
urban crystal
just to find what it is in the form a + ib
robust dust
try converting 10+4i into euler or exponential form
you can then multiply the sqrt into the exponent and convert back
urban crystal
i've already done the working i just need someone to check my answer
robust dust
,w sqrt(10+4i)
woven radishBOT
urban crystal
ill send my working out
viscid cedar
Only when it’s x^2=10+4i, then it’s plus minus
urban crystal
sorry i realised it shouldn't be 12 it should be 4, so 2/x
oh nvm im correct
no i mean my answer is now correct
thanks for the calulator!
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cerulean crater
9 3 5
3 1 1 ] ```
This matrix when converted to row echelon form has a rank of 2 (counting the pivot elements or non zero rows), but if observe the independent columns of the original matrix then only the last col is independent so why is the rank not 1?only the last col is independent
what do you mean by this?
it sounds like you misunderstand the concept of linear independence
also for my own sake: $\bmqty{0 & 0 & -3 \ 9 & 3 & 5 \ 3 & 1 & 1}$
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Ann
cerulean crater
1st col is 3 times the 2nd col right. So I am ignoring those two
pseudo basin
you can't ignore BOTH of them
you can ignore one of them but not both!
you can't express the vector $\bmqty{0 \ 30 \ 10}$ using the 3rd col only.
woven radishBOT
Ann
cerulean crater
okay so I thought if a col can be derived from other col then it is not independent.
pseudo basin
okay so I thought if a col can be derived from other col then it is not independ...
again you misuse the word "independent"...
linear independence isn't a property of individual vectors, but of SETS of vectors.
i think it would be better to say that if a column can be expressed in terms of other columns in the set, then it is REDUNDANT
and here either the first column or the second column can be viewed as redundant, but you can't make them BOTH redundant!
otherwise you are a double-eyepatched pirate.
cerulean crater
oh i see
makes sense only one is redundant
so in the original matrix there are 2 LI columns
Thanks
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midnight bear
I think im just being dumb at this point, but my instructor's solutions simply cite a theorem that every cyclic group of infinite order is isomorphic to Z. but is Z_n infinite? I know it is cyclic, but doesnt it have order n?
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I think im just being dumb at this point, but my instructor's solutions simply c...
stone stump
if Z_n stands for modulo n, yeah thats wrong
midnight bear
it does
thank you for confirming
oh fuck I just realized i copied the problem down wrong though
its nZ not Z_n
so i am wrong
midnight bear
okay thanks for reaffirming that i am at least not crazy about Z_n lol
appreciate it
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west tinsel
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west tinsel
I need to use this to get the full solution to the homogenous linear system
weak cove
!original
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Please show the original problem, exactly as it was stated to you. A picture or screenshot is best.
If the original problem is not in English, then post it anyway! The additional context might still help helpers help you. Do your best to translate.
west tinsel
We previously found out that the rank of this matrix is 3 and that its RREF is: ...
Use the RREF to describe the complete solution to the homogenous linear system with coefficient matrix A
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west tinsel
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lucid rock
Exercise 2
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Exercise 2
lucid rock
It says get K for verifying p(x) is a density function
My problem is this
It says x=1,2,3... That means all Integer numbers
From 1 to infinite
Adding all would be an integral
And would be this
But
🤔 and solution says solution for k is 3
Not 5,55 (4Ln4)
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spring sundial
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spring sundial
what does it mean that n is exponential in the number of bits?
stone stump
well with k bits you can write numbers up to 2^k
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sleek estuary
What's wrong with what I did to solve the 2nd question?
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What's wrong with what I did to solve the 2nd question?
sleek estuary
$P(I \cap T^{C}) + P(I^{C} \cap T)$
pseudo basin
well the \cup definitely doesnt belong where you put it
sleek estuary
Why
pseudo basin
(number) ∪ (number) doesnt make any sense
sleek estuary
hmm ok
woven radishBOT
LeGM
sleek estuary
why is this wrong?
pseudo basin
why are you certain that this is where you fucked up?
this part of your work isn't wrong.
pseudo basin
and who told you I and T were independent?
sleek estuary
ohhh yeah
pseudo basin
in fact they're known NOT to be --- if they were, the percentage that gets both services would not have been 50% but 0.6 * 0.8 = 48%
sleek estuary
i shouldve drawn venn diagram
inland tiger
so if the turning point form of a parabola is y=a(x-h)^2+k, does the sideways form of x=y^2 have turning point form of x=a(y-k)^2+h????
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so if the turning point form of a parabola is y=a(x-h)^2+k, does the sideways fo...
tardy gulch
I need help understanding the extended euclidean algorithm. I don't understand how they came up with line one and why it works, and why do we require (a, b) = 1?
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I need help understanding the extended euclidean algorithm. I don't understand h...
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tardy gulch
<@&286206848099549185> Could someone please help
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tardy gulch
.reopen
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✅
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balmy mason
can someone help me with this
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can someone help me with this
vocal crown
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jaunty gazelle
Could someone help me
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Could someone help me
jaunty gazelle
oh
sand dove
By definition, gcd(a,b) is the minimum of all non-negative divisors of both a and b
jaunty gazelle
Can I show you part 2 of my proof?
jaunty gazelle
By definition, gcd(a,b) is the minimum of all non-negative divisors of both a an...
ok
sand dove
Can I show you part 2 of my proof?
yes sure
jaunty gazelle
technically correct
Okay, thanks!
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dapper raptor
What do I do here?
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dapper raptor
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restive river
I dont understand, is mod the same thing as modulus or is it a different operation
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I dont understand, is mod the same thing as modulus or is it a different operati...
restive river
like if the number i want to test is 5
i do 2^(5-1)
so 16
and i do 1 mod 5
which is 1
so 5 is composite?
dense jay
if its 1 then n is prime
restive river
1 mod any number greater than 1 is 1
dense jay
try 6, 2^6=32, 32 mod 6 = 2 so 6 is composite
thats not what it says
let me rewrite it:
if a^(n-1) mod n = 1 then n is prime, if not then n is composite
thats what its saying
[is a^(n-1) =1 mod n?] is the condition, which returns yes or no
'is' is the keyword
we write mod n after the equation if thats whats confusing you
its not say 1%n
restive river
so the slide is saying is a^(n-1) = 1 when mod n
restive river
why do people write it like this bruh
dense jay
you doing abstract?
restive river
discrete mathematics 2
dense jay
aha nice
restive river
alright ty ty
quaint citrus
The last time I used congruent, it was in 8th grade geometry, and it was with a equals sign with a squiggly line
restive river
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torpid storm
hey, I have a question
the problem says that theres a plane (pi) that contains three points a=(4,6,9) b=(4,12,16) and c=(-2,9,10), and we know that the vector n thats given by n=(-30,beta,gamma) its a normal vector to pi, and I have to calculate gamma
what i've done so far is get the equation of pi, which to my understanding is pi: -15x-42y+36z=12
but I don't know how to get the normal vector
wicked turtle
can you find two linearly independent vectors parallel to the plane?
coral field
hey, I have a question
the problem says that theres a plane (pi) that contains ...
youre almost there
given a plane ax + by + cz + d = 0, its normal vector is parallel to <a, b, c>
if you know how to treat parallel vectors, then, you are done
torpid storm
I don't think I know how to do that
the only thing that comes to mind it's to do a dot product of the normal vector and the point a
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stark shale
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river gorge
do a substitution and let x = asinh(u)
pseudo basin
can we see parts a-c
stark shale
what i was did was trying to get
so i divided numerator and denominator by a
and i got
1/a / sqrt(1 + x^2/a^2)```you mean sqrt(1 + x^2/a^2)