then the denominator would go to 0
#help-23
tawny summit
This makes more sense thank you
Sorry I have more questions
Why don't you take the integral of this
misty bay
you're asked for a tangent line
you want to know the slope of it and the intercept
that only depends on the derivative
so why integrate
safe radishBOT
@tawny summit Has your question been resolved?
tawny summit
and what is this
how do they get to 0 shouldnt it be 1 because at a high value of x it would subtract so little from 1 that it would just be 1 and would effectively turn into e^1
1;'
safe radishBOT
@tawny summit Has your question been resolved?
tawny summit
not really
wicked axle
Hello. Given the following:
w(x, y, z) = xye^(2x-4z)
- Find
dw(how to find derivative without respecting some variable?) - Find
dw@ (x, y, z, w) = (16, -6, 8, -96) - Approximate
w(16.4, -6.5, 7.2)
safe radishBOT
Hello. Given the following:
```
w(x, y, z) = xye^(2x-4z)
```
- Find `dw` **(how ...
wicked axle
Would love if someone can help me solve this. I missed the class where this was taught and I have an exam 6 days later... would love any assistance on this ^^
safe radishBOT
@wicked axle Has your question been resolved?
wicked axle
<@&286206848099549185> Anyone?
wicked axle
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mint veldt
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mint veldt
Where can I go from here
tame raft
it does
tame raft
now you can cancel with the bottom h
mint veldt
wintry condor
Ig you subb in h=0
wintry condor
Good
But ur original function (7/t^2) was in terms of t, so ur derivative also needs to be in terms of t
dusty obsidian
safe radishBOT
hardy lion
why is 2 neither?
hardy lion
dusty obsidian
Sure, I am aware of the rules, but what I would like to know, is what f: {1, 2, 3, 4} -> {1, 2, 3, 4, 5} means, and how to apply to it to 2. f(x) = x + 1
What exactly does it mean?
does it mean that we get a new co-domain and domain
this what I understand from the problem now
wild cape
the definition of injective basically says different inputs have different outputs. surjective is f hits each element of B
dusty obsidian
the definition of injective basically says different inputs have different outpu...
so would they all be injective?
dusty obsidian
this is what I interpreted from the problem
dusty obsidian
this is the original problem.
wild cape
rather than ask me to confirm, check each function against what i said
dusty obsidian
okay
I am correct!!!
@wild cape @hardy lion thank you. I got the problem correct
They are all injective ONLY
.close
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wintry arch
hihi, i need help as to how to find the exerior angles of a trapezoid
wintry arch
i think its a right trapezoid im not rlly sure bcs i had to make my own for a math project
devout shale
Could you send a picture?
wintry arch
This is the trapezoid
Oh yea I’m doing that rn
It’s like 4 trapezoids put together to make a big polygon
I have the interior angles
My friend just told me I only have to find the sum of the exterior angles
devout shale
Two angles that lie on the same line must sum to 180 degrees
If you have the interior angles
wintry arch
Apparently all polygons have a sum of 360 degrees? For ext angles
devout shale
that statement should help you find the exterior angles
wintry arch
Two angles that lie on the same line must sum to 180 degrees
👍
But since my shape isn’t regular it wouldn’t be calculated that way right
supple shore
Even it's not regular you can calculate it with the same method
supple shore
👍
wintry arch
I think?
I’m not rlly sure
I mean I’m tryi bg to use a compass but I never really learned how to use one
supple shore
I would say more like 60 degrees
Your polygone is an hexagon right
Or an octogone
wintry arch
I have no idea
My friend is trying to teach me how to use a compas over text
And if I’m reading this correctly it’s 30-60
So it’s 30 degrees ??
supple shore
An hexagon has 6 summit and an octogon has 8 summit, if it's an octogon you are right
wintry arch
HELP ME
my friend is trying but IM STRUGGLING
Idk how to use a protractor 😭😭
.close
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keen birch
help
split ether
Why do you think so?
unkempt plume
The coefficient of x^2 is negative and the answer is C or D
pseudo scroll
im very certain its D
And did you use the vertex to narrow it does from C and D?
keen birch
Why do you think so?
nah i was thinking that it was D as when you add a negative number it must shift to the left right?
keen birch
And did you use the vertex to narrow it does from C and D?
no i havent
pseudo scroll
How did you determine its D
split ether
nah i was thinking that it was D as when you add a negative number it must shift...
Think about where the axis of symmetry should be
unkempt plume
The axis of symmetry of the function is x = b/2
Because b > 0
Answer is C
Chinese junior high school math problems
pseudo scroll
I think it should be C lol
unkempt plume
CCC
pseudo scroll
Because the x coordinate of the vertex is $\frac{-b}{2a}$
flat frigateBOT
NEONPerseus
keen birch
ok so i derived it and got 0<-b/2
pseudo scroll
And it says b is positive, so -b is negative; a is -1, which results in a positive quantity
Since -b/2a > 0, the vertex lies the the left of the y axis
keen birch
And it says b is positive, so -b is negative; a is -1, which results in a positi...
sorry im having trouble trying to understand it says b is positive, so -b is negative
pseudo scroll
Yeah
And a is negative as well?
-1
So -b/2a is positive
Because negative by negative
keen birch
And it says b is positive, so -b is negative; a is -1, which results in a positi...
what does the a symbolise again?
flat frigateBOT
NEONPerseus
keen birch
$ax^2 + bx + c = 0$
ahhh got it
keen birch
ehlp
dull sequoia
that's very vague
it doesn't even have a y axis
for all we know that's just a terrible drawn straight line
keen birch
bruh ok, the y intercept is 1
dull sequoia
ok, where is the y intercept of 1
keen birch
above it ?
dull sequoia
what's the x value
bro i dont even know where 1 is
how can i know where the y intercept is
random star
that could be the gaussian function with a lot of fantasy 
dull sequoia
can you post the original question instead
dull sequoia
why is this so different to the question
dull sequoia
.
keen birch
just lost with how im supposed to get h(x) for this one
thin bridge
you're not supposed to explicitly find the function
do not attempt to find equations for f(x) and g(x) either
consider how you'd usually find locations of stationary points
keen birch
what do you mean then how else are you supposed to draw the graph?
keen birch
consider how you'd usually find locations of stationary points
when the gradient of the tangent is 0 right?
thin bridge
what do you mean then how else are you supposed to draw the graph?
who said anything about drawing a graph
did the question ask you to draw a graph?
keen birch
> what do you mean then how else are you supposed to draw the graph?
who said an...
no but it asks you to find stationary points
which may be easier when you draw a graph
thin bridge
not here it isn't
keen birch
welp...
thin bridge
when the gradient of the tangent is 0 right?
try setting up an equation to find that
keen birch
for g(x) and f(x)?
thin bridge
no
for h(x)
because you're being asked for the number of stationary points for h(x)
keen birch
but how am i meant to find h(x) in the first place😭
keen birch
these are two different graph
thin bridge
h(x) = f(g(x))
that's all you really care about h(x)
keen birch
wait do u have an image in your head of how its supposed to look like?
thin bridge
the graph no
dull sequoia
wait do u have an image in your head of how its supposed to look like?
what do we want to know about h(x)
thin bridge
lets say for a random function p(x)
keen birch
ok
thin bridge
what would be the steps that you'd take to determine
when the gradient of the tangent is 0 right?
keen birch
what do we want to know about h(x)
its stationary points?
dull sequoia
just follow what ramonov is saying
keen birch
what would be the steps that you'd take to determine
> when the gradient of the ...
by finding the derivative of the function.
thin bridge
yes
and do the exact same thing here
you're interested in the stationary points of h(x)
so apply the exact same principle
differentiate
dull sequoia
h(x) = f(g(x))
that's all you really care about h(x)
using this as your guide
keen birch
i dont think you understand my problem here, you cant just differentiate two graphs to make one.
and then differentiate it
dull sequoia
if h(x) = f(g(x)), what is h'(x)
keen birch
f'(g(x))
keen birch
chain rule
random star
what's the derivative of f(g(x))
thin bridge
exactly as the chain rule states
keen birch
f'(g(x)) * g'(x) ?
thin bridge
f(g(x))
is a generic function composition
there's a rule (specifically the chain rule) explicitly stating the derivative for that
keen birch
wait
keen birch
f'(g(x)) * g'(x) ?
this is correct
keen birch
> f(g(x))
is a generic function composition
there's a rule (specifically the ch...
if I'm not wrong obviously
well anyway how would you find f'(x)
random star
can u make a guess of what happens when u differentiate g(x)
keen birch
well obviously, its going to be 2ax - b
thin bridge
well anyway how would you find f'(x)
you're not supposed to
random star
well obviously, its going to be 2ax - b
what happens when u different a polynomial p(x) = ax^n + bx^(n-1) + cx^(n-2)...
thin bridge
f'(g(x)) * g'(x)
consider when that will be 0 by looking at the graph
keen birch
> f'(g(x)) * g'(x)
consider when that will be 0 by looking at the graph
when they intercept pherhaps?
keen birch
> f'(g(x)) * g'(x)
consider when that will be 0 by looking at the graph
your words are very vague i dont understand how im supposed to make an equation 0 when i dont even have one
keen birch
like am i supposed to have an equation or not?
thin bridge
so far this is pretty much applying what you said earlier
setting the derivative of h(x):
which is f'(g(x)) * g'(x)
equal to 0, is the equation that you set up to find the location of stationary points
i assumed that you already had that
keen birch
bro there are no values i can use
how am i supposed to make one out of no where
and claim it is a location of the SP?
thin bridge
lets step back for a sec, and confirm whether you understood everything up until now
f'(g(x)) * g'(x) = 0
do you agree that taking the derivative of h(x) and setting that to 0, gives you that equation?
keen birch
yes i understand that, but it doesnt make sense
keen birch
no i dont understand then
thin bridge
its the exact same principle if you didn't have a composition function
if you had a function p(x)
then to find the location of stationary points,
you'd differentiate that and set it to 0 right?
i.e. make the equation
p'(x) = 0
keen birch
yes
thin bridge
(note that you implied that this is what you'd do)
now, instead of p, your function here is h
and to find the location of stationary points you'd set up the equation
h'(x) = 0
does that make sense
keen birch
imma just jump all the way to the end, do you have a numerical value as your equation?
keen birch
like a polynomial or something?
thin bridge
any function
keen birch
alright
thin bridge
just like p(x), h(x) is just another function of x
keen birch
thats true
thin bridge
the name of the function doesn't matter
f, p , q, r, s, t, 🍌 whatever
to find the location of stationary points
you make the equation
f'(x) = 0
p'(x) = 0
q'(x) = 0
r'(x) = 0
🍌'(x) = 0
t'(x) = 0
keen birch
yes i know that
thin bridge
and in the case of your question
h'(x) = 0
keen birch
i agree
thin bridge
and as established earlier
since h(x) = f(g(x))
h'(x) = f'(g(x)) * g'(x)
by chain rule
keen birch
yes ok
thin bridge
giving you the equation
f'(g(x)) * g'(x) = 0
keen birch
ok yes
thin bridge
does everything make sense up to this point
thin bridge
now consider the zero product property
ab = 0 iff
a=0, or b = 0
and apply that here
keen birch
yes and the other will be g'(x)
thin bridge
starting with the simpler case
can you identify from the graph where
g'(x) will be 0?
thin bridge
can you tell me the value of x where that occurs
keen birch
x=3?
keen birch
x ≈ 1 ?
thin bridge
f'(something close to 1) is 0, yes
and then consider from the graph how many solutions there are to
g(x) = 1
(or something very close to 1)
you don't need to find the exact value, just identify the number of solutions
keen birch
what now though ?
thin bridge
wdym
keen birch
how do i find the no. of solutions?
thin bridge
by looking at the graph
keen birch
like there is only 2 then right?
thin bridge
yes
keen birch
x=3 and x=1
thin bridge
no
keen birch
so the answer is 2?
thin bridge
no
keen birch
there are 2 SP?
thin bridge
no
thin bridge
consider drawing the line y=1
keen birch
ok
thin bridge
can you identify how many times that intersects the graph of y=g(x)
keen birch
once
thin bridge
can you show what you drew?
keen birch
no matter where
my bad 2
i did x=1
so there will be 2 intersects
or 0
or 1 actually
thin bridge
so it is 0, 1 or 2
keen birch
yes
thin bridge
that wasn't intended to be a yes/no question
keen birch
2
thin bridge
ok good,
and to be rigorous, are the x-coords of those locations within the specified interval
i.e. are the x-coords of those intersection points between 1 and 5 (inclusive)
keen birch
the x coords will be at x= 3/2 and 9/2
thin bridge
decent assumption
but the scale isn't precise enough to conclude those exact values
all you really care about is if they're between 1 and 5 inclusive
which they are
keen birch
yes they are
thin bridge
now putting all that together,
how many stationary points will there be?
keen birch
2
thin bridge
how are you getting 2
keen birch
so there are 3 stationary points
thin bridge
yes
blazing rune
safe radishBOT
blazing rune
I got the first one but having trouble with second one
Here what i did for second .
Okay no worries , i got it where i made mistake
.close
harsh canopy
how he did that
safe radishBOT
how he did that
split ether
The method is called partial fraction decomposition
slow fern
Oh, it's given there as well
flat frigateBOT
A Lonely Bean
harsh canopy
oh i guess i get it thx
split ether
Which involves multiplying both sides by (v - 1)(v + 1) and setting the coefficients of each of the terms from RHS and LHS equal
harsh canopy
y y thx
lean otter
**A Lonely Bean**
just as a sidenote, try to make all your variables in mathmode even during paragraphs
like it is best to write $A$ and $B$ rather than just A and B
flat frigateBOT
split ether
Yeah, I was thinking about that rn
lean otter
just to remove ambiguity
split ether
Just wasn't sure if [] and $$ work together
harsh canopy
.close
safe radishBOT
lean otter
Just wasn't sure if [] and $$ work together
no they dont
but like
aaaaaaaaaaaa
[
xd
]
aaa $b$ aaaa $c$
flat frigateBOT
split ether
Ye I got it
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Available help channel!
regal swallow
how to graph 3sin2(x -pi/2) + 7
safe radishBOT
how to graph 3sin2(x -pi/2) + 7
regal swallow
faint seal
because of the periodicity of the sine function
faint seal
sin(2x-pi) just becomes -sin(2x)
it would be negative mb
regal swallow
because of the periodicity of the sine function
im sorry, what is periodicity?
faint seal
,w graph sin(x)
flat frigateBOT
regal swallow
2pi?
flat frigateBOT
faint seal
what would be the period in this case
regal swallow
pi?
flat frigateBOT
faint seal
it just flips
the graph is just a flipped version of sin(2x)
because of the similarity
,w graph sin(2x), sin(2x-pi)
flat frigateBOT
regal swallow
oh ok
faint seal
you could also use the angle sum/difference identity to prove this rigorously if you have learnt them
earnest wagon
The interesting thing to note here is that to get graph of sin(2x) or sin(kx) if k>0 just divide x axis by 2 or k
safe radishBOT
@regal swallow Has your question been resolved?
harsh canopy
safe radishBOT
harsh canopy
what happend here
slate drift
well its like I = x - I
I is here ur original ques
and x is eusinu - eucosu
so I = x/2
i know this is shit but it was best i could do to explain
slate drift
it is thats why he did it
split ether
but why he did that isnt this like infinity integrate
If you do IBP again, you get I = x - (x - I)
Which is I = I
So
And you will just keep alternating between I = x - I and I = I
harsh canopy
why I = x - (x - I)
why not I = x - (x + I)
IT LIKE l = x + l not l = x - l so it become l = x/2
THERE is + not -
@split ether
split ether
Look at the sign in front of ( )
lean otter
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@lean otter Has your question been resolved?
lean otter
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white swallow
Factorisation
pseudo scroll
By factoring 1/2 out and bringing xy into the parenthesis
white swallow
c there is just an arbitrary constant, 2c is just another constant
But imo they should clarify that it’s another constant
lean otter
Okay so it should be 2c
white swallow
It should be 2c_1=c_2
safe radishBOT
lean otter
.reopen
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✅
lean otter
It should be 2c_1=c_2
When you factor out -i/2 why is it still plus c?
white swallow
Oop mb
I mean -2c_1=c_2 there
But really the c there can be any constants
So whatever operations you are doing
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smoky gull
Hi, this is not a homework or anything, I'm just confused. I think I need help with this picture. There is a table with 7 rows and 7 columns. The first row/column starts with the number 4 and makes the arithmetic progression with the difference of 3. The second row/column is the arithmetic progression with the difference of 5, the third row/column is the AP with the difference of 7 and so on. The table can be, theoretically, infinite. Also, each cell happens to be equal to (R)+(C)+(2RC), where R is the number of the column and R is the number of the row, where the cell is. Can anybody explain how does it happen? Why is every cell equal to (R)+(C)+(2RC)? How to prove that every cell is in this form?
safe radishBOT
Hi, this is not a homework or anything, I'm just confused. I think I need help w...
smoky gull
This is basically the sieve of Sundaram but I can't seem to find the proof anywhere.
proven current
for the first row
(R)=1
so indeed every cell is 1+(C)+2(C)=1+3(C)
for the second one 2+(C)+4(C)=2+5(C)
which is clear since it's an ap with the difference of 5 starting with 7
you can proove the whole thing by induction
safe radishBOT
@smoky gull Has your question been resolved?
jade magnet
(R+1)+(C)+(2C(R+1))=(R+C+2CR)+2C+1
smoky gull
sorry for responding so late, I had to leave for a bit
Oh, sure! I see it now! Oh, thanks to both of you :) ❤️
.close
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steady vault
How do I find the value of slope , y intercept, r squared if I have these values
safe radishBOT
How do I find the value of slope , y intercept, r squared if I have these values
@steady vault Has your question been resolved?
safe radishBOT
@steady vault Has your question been resolved?
safe radishBOT
@steady vault Has your question been resolved?
oak wraith
How do I find the value of slope , y intercept, r squared if I have these values
use a calculator to do the regression for you
steady vault
hmm?
oak wraith
Aren't you essentially asking for the line of best fit?
steady vault
i dont know what use a calculator to do the regression for you means
steady vault
Okay, how have you been getting ur r^2 previously?
This is the first time I need to answer a question like this
and I got no guidance
oak wraith
U need a calculator for it
It possible to do it by hand but it's just not reasonable and probably out of the scope of whatever ur learnign
ur best option is to do what's called a linear regression on that data
search for "linear regression calculator" and u will find many
steady vault
i cant use SI?
oak wraith
ur typing it in with a lot of weird formatting man
ur mixing E and x10^
try just using E notation
steady vault
ok this gave me alot of information that I dont even understand
theres a whole page of info
are these slope and y incercept?
oak wraith
yeah it is
just round it to like 3 decimal points so ur y-int is 0
and the slope is 22040.982
steady vault
what about the r2?
safe radishBOT
@steady vault Has your question been resolved?
rotund wolf
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@rotund wolf Has your question been resolved?
rotund wolf
<@&286206848099549185>
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@rotund wolf Has your question been resolved?
woven swan
isn’t ur answer# $x=4z(1-4y^2)$?
flat frigateBOT
Intrer
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
woven swan
divide by 4 on both sides
woven swan
look at the answer choices
rotund wolf
Yeah it’s the closest to my answer
But it’s not exactly the answer that I got
Why is there that discrepancy
woven swan
u can divide the equation by 4 on both sides and it gives u answer choice a
dividing by 4 on both sides doesn’t change anything
are u asking how come the answer choices are like that in the first place?
rotund wolf
**Intrer**
Compile Error! Click the <:errors:504266556054962196> reaction for mo...
Why is it 4 times then if you are dividing
woven swan
$x=4z(1-4y^2) \iff \frac{x}{4}=z(1-4y^2)$
flat frigateBOT
Intrer
woven swan
Why is it 4 times then if you are dividing
i mean you can divide it by 4 on both sides
and doing that doesn’t change the equation
hasty dove
safe radishBOT
hasty dove
Can you show me what you did to get this answer?
I’m not sure what I’m supposed to do
blazing roost
what is 8 squared
urban ibex
Can you show me what you did to get this answer?
Just take square root of the values
hasty dove
Just take square root of the values
I got this long decimal
blazing roost
I got this long decimal
what is 8 squared
urban ibex
I got this long decimal
Take square root of values individually
hasty dove
urban ibex
Sqrt of 64 and sqrt of 121
urban ibex
Easy peasy
hasty dove
I appreciate the guidance my friends
blazing roost
I appreciate the guidance my friends
lol
blazing roost
ok
lean otter
Let $\AA$ be the set of all disjoint unions from $\set{(a,b], (a, \infty), \emptyset : -\infty \le a < b < \infty}$ Prove that $\AA$ is an algebra.
safe radishBOT
Let $\AA$ be the set of all disjoint unions from $\set{(a,b], (a, \infty), \empt...
lean otter
can someone tell me what in the hell is an 'algebra'
misty bay
basically a sigma algebra but weaker conditions
flat frigateBOT
misty bay
I don't actually remember exactly LMFAO
lean otter
LOL
light shoal
it's like a sigma algebra except not necessarily closed under countable operations, just finite
misty bay
but there's something to do with pi-systems and lambda systems and dynkin whatever
light shoal
- it must contain the empty set and the "universe" set
- it must be closed under complements
- it must be closed under finite unions
misty bay
there it is
left willow
any hints
misty bay
I think it's basically given to you
left willow
I think it's basically given to you
haven't been able to find those sets
safe radishBOT
@left willow Has your question been resolved?
left willow
<@&286206848099549185>
safe radishBOT
@left willow Has your question been resolved?
peak estuary
try doing it explicitly for eg n=4
safe radishBOT
@left willow Has your question been resolved?
left willow
try doing it explicitly for eg n=4
i don't get it for n=2 either
could u explain, just for n=2
im just able to draw arrows similar to shroder berstein's proof
peak estuary
$|A_1\cap A_2| = |A_1|+|A_2| - |A_1\cup A_2|$
flat frigateBOT
Denascite
left willow
$|A_1\cap A_2| = |A_1|+|A_2| - |A_1\cup A_2|$
not what i thought of
so for n=4 do i just keep brute forcingly expand?
peak estuary
n=4 is still small enough to not be completely bullshit. and sometimes doing smaller examples can help understanding the big picture
do n=3 first if you dont wanna do n=4 I guess
left willow
**Denascite**
if all i have do is expand using this for n=3 i can do it
but not sure if thats how they directed
@peak estuary
orange makes it worse
left willow
safe radishBOT
@left willow Has your question been resolved?
safe radishBOT
@left willow Has your question been resolved?
manic heart
I need help with doing this as I don't know how to start
safe radishBOT
I need help with doing this as I don't know how to start
manic heart
what happened
thin bridge
you essentially told me to bugger off
manic heart
I didn't say that
thin bridge
by closing the previous channel where I was assisting you
thin bridge
and said that you're going to find someone else
manic heart
but that's not being rude
I went to find someone else
who can make me understand the work
so I can become successful
thin bridge
have you ever used a ruler before?
thin bridge
the principle is exactly the same
thin bridge
did you do the one with $1\frac34"$ yourself?
flat frigateBOT
ℝamonov
thin bridge
I did this before but
I've done a improper fraction
give me a representation of the length shown in the first ruler
in any form you want, mixed fraction, improper, fraction, decimal,
i don't care
thin bridge
no
thin bridge
huh?
manic heart
um
manic heart
the first one
junior smelt
and if u count to 2 its 4
Why are you counting to 2?
thin bridge
what exactly are you looking at
manic heart
ITS 3/12
thin bridge
no
manic heart
ugh
ok so
let me explain
the dark blue is where you have to count till
and the light blue goes to where you stop so it's 3
and then you count all the way to the end
which is 12
thin bridge
you aren't being asked for the ratio of the length to the ruler
manic heart
oh
thin bridge
the length of this isn't 5
manic heart
what is it asking
thin bridge
thin bridge
what would be the distance between consecutive notches,
marked in red
manic heart
wdym
thin bridge
if the red line has length 1,
and that notch marks middle between 0 and 1,
how long is that blue line
thin bridge
yes
and that's essentially what i was asking you in the previous question
the length marked in red will be 0.5
manic heart
1.5
thin bridge
and there's a fraction on the right equivalent to that
manic heart
but how will we get the mixed fraction
manic heart
how do u do that
thin bridge
how old are you?
thin bridge
its something you should know how to do already
thin bridge
you can go an inefficient route and multiply by 10/10 to get 5/10
and would you be able to simplify that fraction?
manic heart
how did u get the 10/10
thin bridge
10/10 is 1,
you can multiply by 1 to get something equivalent
manic heart
ohh
thin bridge
using 10/10 gets rid of decimals
thin bridge
you can, to be the most efficient you can use 2/2
thin bridge
what do you have after simplifying 5/10 and or multiplying 0.5 by 2/2
thin bridge
no
thin bridge
1.5 = 1 + 0.5 = 1 + 1/2
thin bridge
represented as a mixed fraction will be $1\frac12$ and that option is available in the right column
flat frigateBOT
ℝamonov
manic heart
ohhh
thin bridge
hence you should write $1\frac12"$ in that first empty box
flat frigateBOT
ℝamonov
thin bridge
depends if you actually meant $2\frac14$ or literally $2 - 1- 4$
flat frigateBOT
ℝamonov
thin bridge
then yes
deft palm
safe radishBOT
deft palm
can someone please draw a diagram and explain it please
i would really appreciate if you can draw a diagram and show ur working/explanation
slate drift
bearing means
deft palm
<@&286206848099549185>
slate drift
!status
safe radishBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
deft palm
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
i just need a diagram with someone explaining it
worthy hemlock
We're not here to do the work for you
deft palm
im confused on how to do it
thin bridge
can you start by drawing a compass axis centred at B
deft palm
okay
thin bridge
(similar to how there's an axis centred at A)
thin bridge
on this diagram, can you mark (with an arc) which angle they want you to find
do not make any attempt to calculate the numerical measure of the angle at this stage, only indicate what you think you need to find
thin bridge
yes
thin bridge
yes
safe radishBOT
safe radishBOT
Available help channel!
coral lark
how do you differentiate this
pseudo scroll
You can take the natural log on both sides and differentiate it that way or use the chain rule
brave wolf
how do you differentiate this
Chain rule is probably easier
coral lark
could you show a step by step please. I cant seem to get it right
safe radishBOT
@coral lark Has your question been resolved?
brave wolf
could you show a step by step please. I cant seem to get it right
Show your work
fickle abyss
is the minimum not when (os (feta - 77.320) = -1 ?
safe radishBOT
is the minimum not when (os (feta - 77.320) = -1 ?
faint seal
the cos(x) term is in the denominator
meaning it must be as large as possible for the overall value to be the minimum
gusty glacier
Question: Determine the general solution to the differential equation.
gusty glacier
Part of the answer they gave: provided that x 6= 0. (If x = 0 there is only y = 1, which is, so to speak, unsolved.) This is a linear
differential equation, with integrating factor eln |x| = |x|, since ln |x| is a primitive function to
1/x. Multiplication by the integrating factor gives...
What is happening here?:
Like where did e^ln|x| come from?
and the derivative of |x|y
?
They mention that e^ln|x| is the integrated factor
whatever that is
flat frigateBOT
NEONPerseus
pseudo scroll
Whenever you have a DE in this form, I forgor what it's called, you can solve them by multiplying throughout by the integrating factor (I.F.) since it becomes a perfect derivative of a product
gusty glacier
Whenever you have a DE in this form, I forgor what it's called, you can solve th...
hmm ok, but where did they get |x|*y on the Left side? and why is it the derivative of that?
pseudo scroll
**NEONPerseus**
They divided by x that way they get it in this form
P(x) = 1/x and the integrating factor became e^ln |x| = |x|
And they multiplied both sides of the equation with it
gusty glacier
And they multiplied both sides of the equation with it
So just so that i understand:
They mulitply the equation below with |x|(I.F).
so they get:
?
pseudo scroll
Yeah and when they did the left perfectly became a derivative of |x|y
But if you ask me this was unnecessary and an eagle eye would be enough to get to this point
boreal cypress
how do you graph x^3 +5(x)^2 -7x+1 without calculator
safe radishBOT
how do you graph x^3 +5(x)^2 -7x+1 without calculator
boreal cypress
also if set to 0, x(x^2 +5x-7) = -1. why cant u get rid of -1? by dividing by -1 to each side then multiplying it by 0 to other side? can -1 not be touched? so its x(x^2 +5x-7) +1 ?
split ether
Dividing by -1 yields -x(x^2 + 5x - 7) = 1
And you can't multiply both sides of the equation by 0
thin bridge
well you "can", you'd just get 0 = 0
something pretty much meaningless to you when the goal is to graph a function
ideally you'd try and factorise the whole polynomial,
not just parts of it
boreal cypress
multiplying by 0 to both sides is allowed? lol
thin bridge
well yeh, you're applying the same algebraic operation to both sides of the equation
thin bridge
wdym
thin bridge
you "can multiply both sides of the equation by 0
you'd just get 0 = 0
something pretty much meaningless to you when the goal is to graph a function
so there's no point in doing it
boreal cypress
oh
0(x^2..........)=0
0=0
well i just wanted
to get rid of -1
on the right
thats all
so just +1
then
thin bridge
well subtracting 1 from both sides at the start works against you
you just ended up getting back to what you just started with
realising it didn't help
thin bridge
you mean +1
boreal cypress
ye
thin bridge
x(x^2 +5x-7) +1
isn't an explicit product so that doesn't help
so you can't really apply zero product property here
boreal cypress
explicit product?
boreal cypress
(P*q) +1
thin bridge
x(x^2 +5x-7) is a product of two expressions
x(x^2 +5x-7) + 1 is not
because when finding roots/key components you want something in the form
pq = 0
so that you can actually apply the zero product property to identify roots/x-intercepts
thin bridge
so that you can actually apply the zero product property to identify roots/x-intercepts
who's history
using a simpler example like
x^2 + 3x + 2
factoring x out of the first two terms to get
x(x+3) + 2
doesn't really help that much does it?
boreal cypress
why is pq not like +c
just a joke, of why a+b, doesnt like +c
when set to 0
but i get it now
thin bridge
you shouldn't be joking
boreal cypress
its the only way
thin bridge
spend less time on thinking of jokes and more effort concentrating
thin bridge
on what people are telling you
so as mentioned at the very start
ideally you'd try and factorise the whole polynomial,
not just parts of it
in which case you can approach it with stuff like
rational root theorem
in combination with polynomial/synthetic division
boreal cypress
using a simpler example like
x^2 + 3x + 2
factoring x out of the first two terms...
no it doesnt but can u still graph that? at the bottom?
cause the calculator seems like like the bottom too
thin bridge
there's "can" and then there's what would you rather have / which gives you more info
boreal cypress
in which case you can approach it with stuff like
rational root theorem
in combi...
what are the two rows at the bottom?
you mean quadratic formula?
boreal cypress
idk those
thin bridge
look them up
boreal cypress
i remember rational root
btw no i cant i gotta do 10 problems so i can sleep
x^3+5x^2-7x+1 , rational root is sqrt1? or just 1?
boreal cypress
in which case you can approach it with stuff like
rational root theorem
in combi...
i understand both now
rational "root" theorem
idk
if c was -49
then root would be 7 and -7
but in this case
its 1
idk how
but it is
thin bridge
do you know what a "root" means in the context of polynomials
boreal cypress
root is -6 and 1
i wanna know how
lol
root in conext of poly
is the last number
in the poly
constant
1
but tbh thought it was suppose to be = 0
boreal cypress
root is -6 and 1
halp 
root = where y =0, all x = zeros
x intercepts
bro professor gonna make us take next calc exam without calculator
im so screwed
😄
thin bridge
where's -6 coming from
thin bridge
still dunno how you're getting -6 from that
thin bridge
,w x^3+5x^2-7x+1 when x=-6
flat frigateBOT
