I would then
#help-13
mental quail
Pi-theta found in calc
theta of what?
mental quail
so that gives the result of 1.5217 radian
sly abyss
How did u get that
mental quail
pi subtract 1.8942
sly abyss
I get 1.2473
mental quail
idk how that happened. 1.2473 is what i got now
sly abyss
And that’s acute
sly abyss
Is cosine is positive
It’s just arccos
If cosine is negative
It’s arccos
Pi-theta
mental quail
I get 1.2473
this was also the answer from taking the second choice but i dont get why
cos(theta) = (0.3178) and solving for theta
cedar kilnBOT
@mental quail Has your question been resolved?
mental quail
its posted above and im asking about finding the acute angle of tan / cos / sin
and why the example takes the magnitude
of that number
mental quail
it is here
i want to know if i always just take the absolute value or magnitude for each sin cos tan type of questions that are like = -number
mental quail
im confused
mental quail
draw a schematic
could you just start back at this point and say in a complete sentence what you want me to do to understand how calculating the acute angle needs the magnitude or not for cos/tan/sin ?
sweet crest
draw a graph
a vertical line
a horizontal line
arrow heads at the end
label them y and x
mental quail
cedar kilnBOT
@mental quail Has your question been resolved?
whole vortex
cot A + cotB + cotC = √3 and A + B + C = π, Solve for cotB + cotC.
cedar kilnBOT
cot A + cotB + cotC = √3 and A + B + C = π, Solve for cotB + cotC.
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@whole vortex Has your question been resolved?
whole vortex
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
1
cedar kilnBOT
@whole vortex Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
nova echo
cedar kilnBOT
livid hound
suvat equations
cedar kilnBOT
@nova echo Has your question been resolved?
vapid edge
nova echo
thanks
fringe mauve
how do i find $\integral \frac{1}{1 + \sin{x}} dx$
cedar kilnBOT
how do i find $\integral \frac{1}{1 + \sin{x}} dx$
wraith daggerBOT
Big Chicken
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
proven thistle
What have you tried?@fringe mauve
fringe mauve
using u sub
i turend 1
into the identity
sin ^2 x + cos ^2 x
but that didnt raelly get me anywhere
idk what to sub u as
proven thistle
Have you tried eliminating the denominator
fringe mauve
dont know how to
proven thistle
?
fringe mauve
that still has a denomiator
fringe mauve
oh cos ^2 x
proven thistle
Yessir
proven thistle
Once the denominator is a monomial what should you do?
fringe mauve
split tehf raction
proven thistle
Yessir
proven thistle
Just use trigonometric identities
proven thistle
You should be getting sec²x-secxtanx
And yes, you can use u sub
But refrain using it since it takes a bit of timw
And don't depend on a single technique
fringe mauve
You should be getting sec²x-secxtanx
isnt it harder to integrate this
proven thistle
No?
fringe mauve
oh yeah
proven thistle
fringe mauve
that is faster
proven thistle
You could skip half these steps with practice
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
how do i solve this
cedar kilnBOT
how do i solve this
opal basin
Have you heard of the power of a point theorem?
cedar kilnBOT
@crimson sedge Has your question been resolved?
stone coral
cedar kilnBOT
tropic oxide
you are supposed to just magically guess what the n'th term is, i guess?
right now it is not immediately clear what they meant it to be.
livid hound
n(n+1)/2^(n-1)
probably
cedar kilnBOT
@stone coral Has your question been resolved?
mystic wren
What’s wrong with this?
cedar kilnBOT
What’s wrong with this?
crimson sedge
First issue: notational problem with writing $\ds \pdnv 2[f]x = \pdv[f]x \pdv[f]x$. You should instead write: [
\pdnv 2[f]x = \m{\pdv x}{\pdv[f]x}
]
Second issue: you didn't take the first partial derivative with respect to $x$ correctly so it seems [
\pdv[f]x \c r{\ne} \f y{2x(x^2 + y^2)}
]
wraith daggerBOT
sharp cape
How to go about solving this?
cedar kilnBOT
How to go about solving this?
crimson sedge
the writing is a bit unclear, can u write what's written after the two sets
A = {1, 2, 3, 4}, B = {1, 3, 5}. R: A->B. What more is given?
?
sharp cape
(a, b) <the trident like sign> R <=> a<b
sharp cape
so we need to find R and inverse of R?
yes we need to find R of R inverse
sharp cape
Yes.
crimson sedge
every first element of R should belong to A and second to B. Further, first element should be less than the second
Is it done?
sharp cape
Yah
crimson sedge
now that u have R. Just flip each elements. What I mean is that say u have (1, 3) in R. Make it (3, 1)
and do it for every element in R
sharp cape
Till this, it's done.
Now how do i get "R of R inverse"?
sharp cape
No...
crimson sedge
there's no such thing as R of R inverse
the relation is defined on two sets. So u need two sets
R alone is not enough to build any relation
sharp cape
U know, like g(f(x)), gof.
crimson sedge
yeah, and in that too g accepts only one value
that's why we pass f(x) which returns one value for each x
even here, g can't be of the form g(x, y)
sharp cape
hmm...
crimson sedge
since g accepts 2 values now and f returns only one, we can't find g(f(x))
unless f is a multivalued function
but that's another case
confirm the question with someone. I am sure something is wrong
sharp cape
okey.
crimson sedge
is it a homework question?
I looked online somewhere, and someone used this notion of R o R-1 as to refer to inverse of inverse
and if that's the case, just reverse the R inverse again, u will get back R
do u know what the correct answer to this is?
sharp cape
How to go about solving this?
It's "c" as written in the corner.
sharp cape
is it a homework question?
It's like a question from my maths teachers notes that he told everyone to solve.
So, homework in a sense.
sharp cape
and if that's the case, just reverse the R inverse again, u will get back R
But then there should be 12 elements in the answer. And there aren't in any.
cedar kilnBOT
@sharp cape Has your question been resolved?
sharp cape
the logic I came up with is, R maps A to B
and R inverse maps B to A
so R of R inverse should map A to A.
But i still don't know if it's correct or I could get the answer this way.
cedar kilnBOT
@sharp cape Has your question been resolved?
cedar kilnBOT
sharp cape
.reopen
cedar kilnBOT
✅
cedar kilnBOT
@sharp cape Has your question been resolved?
sharp cape
<@&286206848099549185> any help possible?
cedar kilnBOT
@sharp cape Has your question been resolved?
cedar kilnBOT
@sharp cape Has your question been resolved?
cedar kilnBOT
@sharp cape Has your question been resolved?
modest shadow
how do i do this from the beginning 😭 i am so lost
cedar kilnBOT
how do i do this from the beginning 😭 i am so lost
silver oxide
sub in the values for r and v0
cedar kilnBOT
@modest shadow Has your question been resolved?
modest shadow
ic thanks
modest shadow
how do i do this from the beginning 😭 i am so lost
wait holdup how do i solve this without a calculator
cedar kilnBOT
wait holdup how do i solve this without a calculator
modest shadow
can you do arcsin without a calculator
silver oxide
lemme check
modest shadow
0.655
modest shadow
uh
teacher said no calculator
he said u could do it without
and we had to beg him for one
blissful bolt
some teachers say no calculator but will accept an answer of sin^-1(0.655)
silver oxide
thats not gonna work here
answers to 1 d.p.
and it would have to be sin^-1(300/{121^2/32})
blissful bolt
give me one second then to look at the numbers
modest shadow
oh
modest shadow
some teachers say no calculator but will accept an answer of sin^-1(0.655)
but its an online test
and im pretty sure it wouldbt take that
silver oxide
it wouldnt work like that
modest shadow
wdym
silver oxide
there is no way he would be expecting exact form on an online test like that,
it asks for 1 decimal place
silver oxide
wdym
modest shadow
and it would have to be sin^-1(300/{121^2/32})
like this
silver oxide
ur final answers would be $\theta= \frac{sin^-1(\frac{300}{\frac{121^2}{32})}{2} and \frac{180-sin^-1(\frac{300}{\frac{121^2}{32}})}{2}$
well i messed that up
but its too much effort anyways
wraith daggerBOT
Galaxy
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
marble ermine
hello, how do i find the lim of $\frac{x^2+y^2}{\sqrt{x^4 + y^4}}$ when (x,y)->(0,0)?
wraith daggerBOT
lilisworld
cedar kilnBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
upper abyss
Have you tried a few lines that pass through (0,0)?
If it doesn't exist, you can get that really quickly this way
marble ermine
Have you tried a few lines that pass through (0,0)?
like (x, x) and (x, 0)?
i don't understand what you mean by lines
but f(x,x) is different from f(x, 0) when x->0
upper abyss
Approach with y = x, and y = 0 sure
Yep! You get two different limits, and so the limit doesn't exist
marble ermine
@upper abyss ok but can you tell me what is the point of the upper bound, if i find |f(x, y)| is bounded by two functions that approaches 0 when (x, y)->(0,0) then what does that mean?
if i find: 0<= |f(x,y)| <= g(x,y) and g(x,y) approaches 0 when (x,y) approaches (0,0) then what does that mean?
upper abyss
Not too sure
marble ermine
mmhh ok thanks
marble ermine
Not too sure
for ex. here
if we want to show that f is continuous at (0,0), do we find the limit of f(x,y) when (x,y)->(0,0) and check if it is 0?
.close
crimson sedge
cedar kilnBOT
crimson sedge
how to do 4b
I got an answer, but it was wrong
also, i dont understand why they changed the starting point to n=4
tardy hull
What answer did you get
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
tardy hull
Oh whoops
viscid crater
what is -2y=-14
grizzled igloo
7
viscid crater
oki thx
tardy hull
<@296036238719451136> i got (-1)^n+1 (x^n+3/n)
By this you mean $\sum_{n=1}^\infty (-1)^{n+1} \frac{x^{n+3}}{n}$, right
wraith daggerBOT
aldo booze
tardy hull
Okay, these are the same thing
Notice how the first term of your answer is $x^4$, and same with theirs
wraith daggerBOT
aldo booze
tardy hull
Substitute $k = n + 3$ everywhere you have $n$
wraith daggerBOT
aldo booze
tardy hull
So, for example, the sum will now go from $k = 4$ (corresponding to $n = 1$) to infinity
wraith daggerBOT
aldo booze
tardy hull
I don't really know why they did it like that
But it's equivalent to what you wrote
I guess they just wanted the power of $x$ to be $n$
wraith daggerBOT
aldo booze
ancient vector
how to convert r=1/5-5sintheta to rectangular form
cedar kilnBOT
how to convert r=1/5-5sintheta to rectangular form
blissful bolt
Multiply both sides by r and it will become more apparent. Then apply the conversion formulas for polar to rectangular
ancient vector
could i send u some of the work i did to verify if im doing it right or wrong?
I used desmos to check if the equations match up but the graphs don't seem right.
cedar kilnBOT
@ancient vector Has your question been resolved?
fallen moat
checking
and also, you can write your final equation in the form of y=something if you like it
fallen moat
ancient vector
i tried a different way and got it to match on desmos but im not 100% sure if its correct
fallen moat
that'll do too
fallen moat
and also, you can write your final equation in the form of y=something if you li...
I'm just used to that form lol
ancient vector
Ok so for this type of problem it's also different ways to get to the answer then. I suppose.
fallen moat
true
fallen moat
y=5/2x²-1/10
fallen moat
Can I see how you do it if u got time?
oh, i just got it in mind, by reading your workings of course
ancient vector
ok
i understand both forms mean the same thing but how did u get from x = something to y = something
curious
fallen moat
oh, i see what you mean
ancient vector
yea yea im trying to see the work and process of what can be done
fallen moat
it's just that i would find the simplest form of varible
e.g.
you got
25x²-10y=1
then I'll think that
hmmm x² is a bit difficult
but y, ah that's nice
lemme use y as subject
ancient vector
so meaning u isolated the y to one side and did the rest of the math massaging?
fallen moat
yep
ancient vector
ok ok. yea sometimes in math class its hard to always catch what the teacher is doing as in the work or how he is thinking so i try my best to visualize what the steps are
fallen moat
ok ok. yea sometimes in math class its hard to always catch what the teacher is ...
that's a very good practice
fallen moat
yep
ancient vector
Thanks for the help!
fallen moat
Cheers!
ancient vector
.close
tawdry sonnet
Anyone?
tawdry sonnet
<@&286206848099549185>
vagrant pewter
These kinds of questions aren’t particularly tough but very tedious
You’re gonna have to use quotient rule
Then use chain rule and product rule
I would recommend starting by simply writing the radicals in power form so you can apply the power rule easier
So instead of $\sqrt{x+3}$ you write $(x+3)^{1/2}$
wraith daggerBOT
llspacebarll
vagrant pewter
And do that to the cube root too
ruby lion
for what real values of p do the equations px^3+x+2=0 and x^3+px+2=0 have exactly one common root
ruby lion
i dont have a good method to solve this
ebon pulsar
if p = 1 u agree that we get the same equations?
ebon pulsar
u should make a system of equations and use the fact that they share a common root.
ruby lion
set the eq = to each other and compare coefficients??
ebon pulsar
Let r be the common root for the 2 equations then find which values of r make it
ebon pulsar
set the eq = to each other and compare coefficients??
ye
cedar kilnBOT
@ruby lion Has your question been resolved?
ruby lion
Let r be the common root for the 2 equations then find which values of r make it
aight thanks
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
mystic wren
what did i mess up on? :0
cedar kilnBOT
what did i mess up on? :0
hollow trail
the x-component of your surface normal doesn't seem to be right
mystic wren
ohhh thanks
uneven crest
can someone exlapin how my teacher did this im lost in the algebra
uneven crest
do i multiply top and bot by two or nah
bold hinge
1 - 1/sqrt(10) =
uneven crest
ion know gang
bold hinge
Now multiply the top and bottom of this fraction by sqrt(10)
uneven crest
(10-sqrt(10)/20
bold hinge
(10-sqrt(10))/10
uneven crest
wait what
uneven crest
how did they get the 20 up top guess i dont know that rule
uneven crest
yea
uneven crest
huh
bold hinge
Wait actually that's right
But you're missing one more step
sqrt(a)sqrt(b) = sqrt(ab)
bold hinge
Yes!!!
uneven crest
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
slow bobcat
my trig final in two days, im panicking badly cuz theres more lecture to watch in hours then time left until final, and im clueless
slow bobcat
are those difficult, realistically in two days could i learn how to those
<@&286206848099549185> (sorryy)
cedar kilnBOT
@slow bobcat Has your question been resolved?
river topaz
cedar kilnBOT
river topaz
does resultant force increase or decrease?
the mark scheme says it decreases but why?
its decellerating
if its decellerating acceleration is in negatives
F=MA
spice kraken
,rotate
wraith daggerBOT
river topaz
force is not getting smaler its just going in the opposite direction
spice kraken
it's both going in the opposite direction and getting smaller
cedar kilnBOT
cedar kilnBOT
Available help channel!
cobalt sentinel
Hi to everyone. I have a problem with integrals. I need to calculate the percentage difference between the integral in the interval 15/20 and the integral in the interval 20/40. Can anyone help me? I didn't study them at school yet but I found them in a biology homework assignment.
cobalt sentinel
I'm Italian, if there is something unclear in my English please tell me
not considered the one written in pencil
cedar kilnBOT
@cobalt sentinel Has your question been resolved?
cobalt sentinel
<@&286206848099549185>
cedar kilnBOT
@cobalt sentinel Has your question been resolved?
cobalt sentinel
<@&286206848099549185>
cedar kilnBOT
@cobalt sentinel Has your question been resolved?
tulip silo
Is it acceleration / velocity = time or velocity / acceleration = time
tulip silo
Or same thing
gritty galleon
Is it acceleration / velocity = time or velocity / acceleration = time
neither
alpine rune
latter dimensionally, try matching your dimensions next time
gritty galleon
latter dimensionally, try matching your dimensions next time
(its v-u not v)
alpine rune
(its v-u not v)
I meant it to be dimensionally, which is why I edited it ^
gritty galleon
I meant it to be dimensionally, which is why I edited it ^
ah sorry i did not notice
alpine rune
change in velocity
gritty galleon
well
gritty galleon
change in velocity
exactly
alpine nova
Positive integral solutions of
x^3 = y^2 + 27
cedar kilnBOT
Positive integral solutions of
x^3 = y^2 + 27
alpine nova
with steps plz
alpine rune
what did you try
cedar kilnBOT
@alpine nova Has your question been resolved?
alpine nova
how can you factor x^3 - 3^3?
Already tried that
livid hound
show what you've done
alpine nova
I hv triend using congruencies but could not solve it completely
I was geting the only inter solution (3,0)
But the qn demanded for positive integers, so I was not sure about my method
@livid hound
livid hound
you might need to wait for someone more qualified, problem was more complicated than it looked
cedar kilnBOT
@alpine nova Has your question been resolved?
alpine nova
you might need to wait for someone more qualified, problem was more complicated ...
Yess
slim jasper
The help channels are mostly for problems that can be solved with high school or early undergraduate methods. you may have better luck finding someone with the right knowledge in one of the advanced channels -- depending on where you encountered the problem, that might be #advanced-number-theory or perhaps #algebraic-geometry. If you met the problem in a class context, be sure to mention which class.
cedar kilnBOT
@alpine nova Has your question been resolved?
alpine nova
<@&286206848099549185>
alpine nova
The help channels are mostly for problems that can be solved with high school or...
This is a question of pre college non routine
severe sun
crimson sedge
how can you factor x^3 - 3^3?
wouldn't it be (x-3)(x^2 + 3x + 9)
cedar kilnBOT
@alpine nova Has your question been resolved?
silent finch
This has an elementary solution
No need for advanced stuff, just some Euclidean algorithm spam and substitution
First, try to get x is a multiple of 3 and y is a multiple of 9
silent finch
wouldn't it be (x-3)(x^2 + 3x + 9)
You can get it by considering the gcd of these factors
arctic cosmos
cedar kilnBOT
arctic cosmos
tbh
im completely lost
and am really failing to understand all this planes stuff
subtle harbor
parallel to plane means it has the same normal vector as the plane its parallel too, you can use the line to find a point on the plane
then use this formula
i.e. use the line to find x0,y0,z0, (fix a t value, say 0), then use the formula for a plane to find a,b,c (set parallel plane equation =0, find the corresponding a,b,c)
arctic cosmos
so would the normal vector be <2, 1, 1> for the plane?
subtle harbor
so would the normal vector be <2, 1, 1> for the plane?
no...be careful
set the parallel plane equation=0
arctic cosmos
2x +y -z +1 = 0
arctic cosmos
<2, 1, -1> then
subtle harbor
mhm
arctic cosmos
ah i see
subtle harbor
then you use the line to find x0,y0,z0 (you can just use t=0)
subtle harbor
x0,y0,z0 is a point
you can define any plane in R^3 with a point, and a direction vector (perpendicular to the plane)
arctic cosmos
ok wait so if i just get my bearing a lil bit
the line is a point (3, 5, 1) and a direction vector <1, 1, 3>
and the plane is a normal vector <2, 1, -1> (idek what this is, is this the same as the direction vector?) and also a point
?
cedar kilnBOT
@arctic cosmos Has your question been resolved?
subtle harbor
then use this formula
fix, a point, and a direction from that point. That defines a plane, with the plane being the set of all vectors perpendicular from that vector, and eminating from that point. see this ^
with the link below
arctic cosmos
wait a min
so plane is kinda like grass?
idk how to explain my brain rn
or like plane is like the ground
and the set of all vectors is like the grass coming off it
i thought it was more like the plane was like a plane and all the vectors went along it
subtle harbor
i thought it was more like the plane was like a plane and all the vectors went a...
think of one blade of grass, and all the vectors sprawling away from that one blade of grass
arctic cosmos
then use this formula
this doesnt seem right
or was i supposed to use (3,5,1)
oh wait it worked when i used (3, 5, 1)
arctic cosmos
think of one blade of grass, and all the vectors sprawling away from that one bl...
i dont really get this tbh
oh wait
i kinda get it
subtle harbor
with the set of all the vectors perpendicular from N
eminating from a point x0,y0,z0 hence (x-x0, y-y0, z-z0)
subtle harbor
or was i supposed to use (3,5,1)
3,5,1 is when t=0 yes
arctic cosmos
yeah my final answer was 2x+y-z-10=0
arctic cosmos
wait so all a plane needs is x0,y0,z0 and a normal vector right?
so the plane itself
subtle harbor
wait so all a plane needs is x0,y0,z0 and a normal vector right?
yes
arctic cosmos
is basically just a line
i think im confusing myself
wait, all you need to define a plane is the point and vector
but the plane itself
is the set of all the other vectors coming perpendicular from it?
subtle harbor
yeah, the set of all (x-x0,y-y0,z-z0) perpendicular to N, which is precisely when dot product is 0
arctic cosmos
would that not be an infinitely big set
subtle harbor
and the plane is infinitely big sheet :)
subtle harbor
it's like z=0 is a plane (the xy plane)
arctic cosmos
is it useful for anything
subtle harbor
is it useful for anything
wydm
arctic cosmos
or like, why would you want it to be in that form
what can you use it for
<2, 1, -1> is the normal vector
but what does the -10 represent
subtle harbor
it's just a form a plane can be in
line how lines can be in many different forms, sometimes people want them in particular forms to make looking at things easier.
i.e. point slope form for a line (in R^2)
arctic cosmos
fair enough
well thanks for your patience lmao
this is a result of schools skipping teaching vectors cos of covid
and it carries on a bunch of clueless people into uni
uhh, how do i close this again
ah
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
opaque acorn
this is a polar equation for a conic. how would you find the vertexes / y-intercepts? i would think to make theta equal zero, but cos 0 = 1, and that would be dividing by zero, so itd be undefined... but when you graph the equation, the vertex is at (-1.5, 0). am i missing something?
hollow trail
because the x-axis is also at θ = π
opaque acorn
i dont really understand what you mean at all. θ = π fits the solution but i dont really get how youd get there at all
hollow trail
if you're looking for x-intercepts, you need to find where it crosses the x-axis. the angle corresponding to the positive x-axis (y = 0, x ≥ 0) is θ = 0, and the angle corresponding to the negative x-axis (y = 0, x ≤ 0) is θ = π
you can think of the angles in polar in terms of the unit circle
opaque acorn
you can think of the angles in polar in terms of the unit circle
OHHHHHHH this makes a lot more sense
so last question: when checking for intercepts, should i check both positive and negative? or do you only check one based on the circumstances
hollow trail
you should check both. but how many angles that is depends on the period of your function (some functions may not connect back to themselves until angle θ = 4π, in which case you'd need to check 0, π, 2π, 3π, and so on)
hushed mason
help
dire geode
hushed mason
ye
so 2 - i is a root aswell
but then what do i do
<@&286206848099549185>
???
<@&286206848099549185>
cedar kilnBOT
@hushed mason Has your question been resolved?
cedar kilnBOT
@hushed mason Has your question been resolved?
crimson sedge
Hey
void dock
What is frequency distribution table
cedar kilnBOT
What is frequency distribution table
limber marsh
a frequency distribution tells you the number of things a category
void dock
Can you tell me how to represent it
limber marsh
so a frequency distribution table would list out the possible categories on the left and the number on the right
yeah
void dock
I am getting confused when there are decimal values
limber marsh
can you give me an example?
limber marsh
,rotate
wraith daggerBOT
limber marsh
okay, so we'll go through the steps to make such a table
void dock
Ok then ??
limber marsh
the first thing is to list the possible classes on the left
void dock
Sure thing
limber marsh
so what are our classes?
limber marsh
98.1 to 98.6 89 to 89.2
for #3, the classes are going to go by twos, so we have 84-86, 86-88, 88-90, 90-92, and so on, we don't have any decimals on the left
we are not using the data yet
in 3a it is telling us which categories/classes to use (so those go on the left)
void dock
Oooh , now I understand
limber marsh
great!
void dock
Thank you you are the best👍☺️
limber marsh
are you good with the rest?
void dock
Thanks for the help bye
fickle kelp
Please please please for the love of all things holy help me understand truth tables
upper abyss
Have an example you're struggling with?
fickle kelp
I literally dont understand a thing
upper abyss
Missing the question up top
fickle kelp
Ah mb, it says “Determine if the following arguments are valid or not by completing truth tables for each”
upper abyss
And the red is your work?
fickle kelp
Yeah
Im literally not understanding a thing
Tried going through the modules again but its just so confusing
upper abyss
I'd just make a table-column for each line
"If it rains, then the ground will be wet"
Is P → Q
Know what the table for P → Q is?
gusty forum
they have an attempt on the right
but you only have 2 variables in P and Q, so you only need 2^2=4 rows in the truth table
upper abyss
Oh I see. You're trying to let P → Q be a third variable, but it actually depends on P and Q
fickle kelp
upper abyss
Third column should be
T
F
T
T
fickle kelp
But P is false on the 3rd and 4th row so wouldnt it be false?
upper abyss
No
fickle kelp
Im so confused
upper abyss
There's no logic to it. This table is just how we define P → Q
This is something you memorize, not necessarily understand
fickle kelp
So theres no logic behind logic is what you’re saying
upper abyss
I'm saying there's nothing to be confused about here. You memorized the table wrong, but we can fix that
fickle kelp
But then how do I determine if the statement is valid or not?
upper abyss
- We know the ground was wet, so include at any row where Q is T.
- We know that P → Q, so include any row where that's T.
Is P always T in those rows?
fickle kelp
No
upper abyss
I see a way where Q and P → Q are true, but P is still false. So, there's a logical error in the question
fickle kelp
So basically if the 3rd column has a false in it then its false?
upper abyss
What's false?
fickle kelp
I mean then its a logical error
upper abyss
- We know the ground was wet, so include at any row where Q is T.
- We know that P → Q, so include any row where that's T.
Is P always T in those rows?
fickle kelp
No
upper abyss
Or in other words, there's a row where each of the premises are T, but the conclusion is F. That can't happen if the argument is correct
Where the premises are columns 2 and 3, and the conclusion is column 1
fickle kelp
Interesting
OHHH I THINK I GET IT
So for the 2nd one, the table would look like this?
.close
cedar kilnBOT
steep summit
So for the 2nd one, the table would look like this?
nah, it'd be T, T, F, T
try writing down the values of $\sim p$ and $\sim q$ to compare it to the truth table for $p \to q$
wraith daggerBOT
marieme
cedar kilnBOT
Available help channel!
gilded remnant
how come k=-1,0,1,2
cedar kilnBOT
how come k=-1,0,1,2
gilded remnant
could it be k=0,1,2,3 instead?
cedar kilnBOT
@gilded remnant Has your question been resolved?
gilded remnant
<@&286206848099549185>
gilded remnant
<@&286206848099549185>
upbeat knoll
could it be k=0,1,2,3 instead?
yes it could be any of k = a, a+1, a+2, a+3
as cis(x) is periodic every 2π
but they chose a = -1 because it keeps the output z = cis(x) values inside the principle angle range which is θ ∈ [-π/2, π/2]
gilded remnant
whats the principle angle range
upbeat knoll
whats the principle angle range
i think its called the principle argument for the given complex number
its just that by convention we take the argument, the angle, of the complex number to be in the range
as cis(x) = cis(x+2π)
unique isle
unique isle
<@&286206848099549185>
crimson sedge
Hey
plucky merlin
First solve for Y, or get as close as you can
crimson sedge
It should be union
Solve once by taking value inside modulus as positive
Make the case on number line
2nd time take value inside as negative
You will get y€(-inf,-14) union (0,inf)
@unique isle
Do you have a problem solving the inequality?
Or opening the modulus?
cedar kilnBOT
@unique isle Has your question been resolved?
minor depot
help please
cedar kilnBOT
help please
minor depot
I beg
bold frost
Can someone help me complete this
cedar kilnBOT
Can someone help me complete this
bold frost
I can translate it
Identify the characteristics of a function. Use the drawing of the function f to answer the questions
Determine f(3)
Determine f (-3)
Obtain all the x for f(x) = 0
Obtain all the x for f(x) = 2
Determine the x intercept(s)
Determine the y intercept(s)
Determine the domain of f
Determine the range of f
cedar kilnBOT
@bold frost Has your question been resolved?
bold frost
<@&286206848099549185>
verbal gust
Identify the characteristics of a function. Use the drawing of the function f to...
Linear equation
I'd suggest learning from YouTube using your own language since it'd be much easier but if you want to I can walk you through it with English
bold frost
I can understand it in English dw
bold frost
Yes
bold frost
Determine f(3)
Determine f (-3)
Obtain all the x for f(x) = 0
Obtain all the x f...
I have to fill all of this
bold frost
A bit..
crimson sedge
Hmm I see
Graph is a plot between variables which helps determine the relation between them
bold frost
Okayyy
crimson sedge
Any idea about what the x axis and y axis are?
bold frost
Yes
crimson sedge
And coordinates?
bold frost
Yes
crimson sedge
So basically f(3) is the y coordinate at which x=3
First you go ti x=3 on x axis
To*
And then move upwards towards the y axis
bold frost
Okayy I get it
crimson sedge
Sure?
My bad you dont only move upwards
Here you will need to move downwards
As the graph is below x axis for x=3
bold frost
Question, functions are basically on the x asis and inverse functions are on y asis right?
crimson sedge
Nope
The value of function of x is plotted on y axis
Y=f(x)
What grade are you in?
bold frost
11 precalc but we are very behind
crimson sedge
Inveree functions is a different thing
Inverse*
This is the first time doing graphs?
crimson sedge
Okay
So if there is a function y=2x
So if we move to x=2 how much do we move in y?
bold frost
4
crimson sedge
Yes
So you have to check the value of y fir x=3
Thats it
F(3) is value of y when x=3
F(-3) is value of y when x=-3
bold frost
Ohhh that’s makes much more sense😭
crimson sedge
And so on
bold frost
Okayy
crimson sedge
Tell me the value of f(3) in your question
bold frost
-3
bold frost
2
bold frost
I translated it wrong
bold frost
Obtain all of the x’s when f(x) = 0
crimson sedge
Sure?
bold frost
yes
crimson sedge
What does it mean by all the x?
Do you have any idea?
I can make an equation in x and y for this graph but there will be only 1 value of x for f(x)=0
bold frost
From what my friend explained you have to go by the graph and the answer is( 0.5, 0)
crimson sedge
Okay lets see
bold frost
But i have no idea otherwise
bold frost
find all x for which f(x) = 0
bold frost
Oh my god? I
crimson sedge
Sorry?
bold frost
No no I understand
crimson sedge
For f(x)=2 , put y=2 in the equation and you will get value of x
bold frost
3
crimson sedge
Basically this is equation of straight line
bold frost
Im doing this from my head so if it isnt the answer sorry
crimson sedge
X=-3 for the 4th question
crimson sedge
Do you know what intercepts are?
bold frost
Yes
bold frost
Yes
crimson sedge
Okay go ahead
bold frost
Int y (0 , -0.5)
int x: (-0.5, 0)
bold frost
Sadly no i wasnt taught how yo
Like how to get the equation for a graph
Like I said we are very behind im sorry
crimson sedge
Ohh here we learn in it grade 9,10 so I assumed you know how to
No worries
It will be better if you learn it from your teacher
bold frost
Okay
bold frost
Domain (-3,3)
Range: (-3, 2)
From what I understood in a video
But my teacher hasn’t given this to us so I could be very very wrong
crimson sedge
Yep that is correct but I do have a confusion
bold frost
Yes?
crimson sedge
The domain and range you mentioned is for the specific plot given
bold frost
Yes
crimson sedge
But for the function this wont be true
As the function is not confined to a particular part of the plot
But I think you are doing it the correct way
bold frost
I hope
crimson sedge
I in grade 12 so still learning
bold frost
Since from what I also understand it could be the x coordinates
crimson sedge
Pardon me for any of my mistakes
crimson sedge
Since from what I also understand it could be the x coordinates
Domain is the values of x one can put in a function
bold frost
Its okay we are learning stuff from 9 and 10 in 11th so youre betyer off than me
bold frost
Domain is the values of x one can put in a function
Exactly that I just can’t phrase myself right my bad
crimson sedge
Range is the output or the value of y we obtain on putting values x in the domain
crimson sedge
Exactly that I just can’t phrase myself right my bad
No worries no need to feel bad
bold frost
Range is the output or the value of y we obtain on putting values x in the domai...
I see
I think that’s it thankfully 😭
bold frost
Thank you sm 🤍
bold frost
.close
celest otter
Can someone explain how to do 4a and #5?
cedar kilnBOT
Can someone explain how to do 4a and #5?
@celest otter Has your question been resolved?
full trail
cedar kilnBOT
full trail
what is the explanation for Gaussian Elimination+Partial Pivoting being O(n^2) for sparse matrices
i'm trying to understand if it's really true or just a typo
cedar kilnBOT
@full trail Has your question been resolved?
full trail
<@&286206848099549185>
cedar kilnBOT
@full trail Has your question been resolved?
cedar kilnBOT
@full trail Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
small radish
What is the answer to number 5?
cedar kilnBOT
What is the answer to number 5?
@small radish Has your question been resolved?
Available help channel!
coral swallow
$\int_{}^{}\frac{cos^4(x)}{sin^8(x)}$
cedar kilnBOT
$\int_{}^{}\frac{cos^4(x)}{sin^8(x)}$
wraith daggerBOT
Bobba
coral swallow
How do you calculate this integral? I was taught when there are two even exponents you should look for a cotangent or tangent substitution, but when I try to get a cotangent you get left with 1 over sin^4(x) which can't be used for a cotangent substitution
(sorry I forgot the dx at the end 😅 )
cedar kilnBOT
@coral swallow Has your question been resolved?
cedar kilnBOT
@coral swallow Has your question been resolved?
elder swallow
you know that $\int_{}^{}\frac{cos^4(x)}{sin^8(x)} dx = \int_{}^{}\frac{1}{sin^8(x)} dx * \int_{}^{}cos^4(x) dx$
wraith daggerBOT
this_is_a_trap
elder swallow
And you know that $cos^4(x) = cos(x^4)$
wraith daggerBOT
this_is_a_trap
wraith daggerBOT
this_is_a_trap
coral swallow
Both things you said are not true... you can't split an integral of a product into two serparate integrals
you can only do that with + or -
And cos^4(x) is not equal to cos(x^4) but it is equal to (cos(x))^4
but I don't see how that helps in this case
coral swallow
**this\_is\_a\_trap**
So yea this is what I was trying to achieve so that I could substitute the cot(x) for t, however dt would then be equal to 1/sin²(x) which you can't work away since you have soo many sines
cedar kilnBOT
@coral swallow Has your question been resolved?
verbal gust
So yea this is what I was trying to achieve so that I could substitute the cot(x...
Cot(x)²+1 = CSC(x)²
Does that ring a bell
coral swallow
With that in mind I got integral of (1+1/sin²x)²*1/sin^4(x)
Or is that not what you're getting at
verbal gust
So yea this is what I was trying to achieve so that I could substitute the cot(x...
So in this part you already get t² * 1/sin(x)² right?
That is because the derivative of cot² is CSC²
coral swallow
So you substitute cot² for t right?
verbal gust
And you cancel it out with the 1/sin(x)² because you turn it into CSC(x)²
verbal gust
So you substitute cot² for t right?
Yes
You can use the same method to get
t² * CSC(x)²
coral swallow
That is because the derivative of cot² is CSC²
Isn't the derivative of just cot equal to csc²?
verbal gust
Isn't the derivative of just cot equal to csc²?
Wait yeah mb
So yeah you're left with t⁴ * CSC(x)² since it was 1/sin(x)⁴
And you can turn the 1/sin(x)⁴ into CSC(x)⁴
Is that understandable or
coral swallow
Hold on
verbal gust
So yea this is what I was trying to achieve so that I could substitute the cot(x...
Your first process was already correct
This one
Instead of staying with 1/sin(x)² you can turn it into CSC(x)² instead
coral swallow
But then you get the integral of t^4*csc^4(x) times csc²(x)
So aren't you mixing t and x here
coral swallow
can you just work with sin please because I never work with csc and it's really confusing 😂
verbal gust
Can't work it out with sin
coral swallow
but csc is just 1/sin isn't it
verbal gust
but csc is just 1/sin isn't it
Yeah but it'll be long
coral swallow
But then you get the integral of t^4*csc^4(x) times csc²(x)
I was wrong here, but you still get something with t and x mixed. If I work it out and substitute cot for t then I get:
t^4 * csc²(x) dt
Two of the csc(x) get "turned into" dt and the other two idk
verbal gust
Cot(x)²+1 = CSC(x)²