Channel closed
Closed by @violet cloud
Use .reopen if this was a mistake.
#help-17
wise shell
Hey guys, can someone explain why -log(x) is the same as log(1/x). I don't understand the Theory behind this.
vocal sleetBOT
Hey guys, can someone explain why -log(x) is the same as log(1/x). I don't under...
wise shell
so in this case it is log(x)^-1 is log(1/x). I just don't understand why the - sign is removed...
wise shell
But why does the - before the log(H3O+) dissapear?
outer warren
they used a roundabout way of doing this using the quotient rule
wise shell
i just don't understand how they go from -log(H30+) to log(1) - log(H3O+) to log(1/H3O+)
outer warren
$\textbf{method 1:}$ \
applying power law: \
$-\log(k) = \log(k^{-1})$ \
applying exponent law: \
$=\log\br{\frac1k}$ \
\
$\textbf{method 2: (their work)}$ \
using $\log(1) = 0$ \
$-\log(k) = \log(1) - \log(k)$ \
applying quotient law \
$=\log\br{\frac1k}$
twin meteorBOT
ℝamonov
remote lake
Can someone help me solve this question using a diagram ?
vocal sleetBOT
Can someone help me solve this question using a diagram ?
lyric fossil
have you tried to draw a diagram?
remote lake
I have
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
lyric fossil
do you understand what choice A is saying?
remote lake
Yes
lyric fossil
is it true?
remote lake
no
lyric fossil
then do we know A to be true?
remote lake
no it is false
lyric fossil
so then A is not one of the correct choices
remote lake
yes
remote lake
the answer is E but how
lyric fossil
all what
remote lake
yes
lyric fossil
are some of those red?
thin root
-epsilon + 3 < 6/x < epsilon + 3
If I reciprocal this do I flip the inequality signs?
thin root
I am trying to prove a limit btw using epsilon delta for practice
honest ridge
oh, so i guess i can't help
thin root
why
honest ridge
but btw is x just any rational number or a positive integer?
because if x is a fraction, tre reciprocal would get proportionally bigger as the value of x approaches 0
waxen harness
-epsilon + 3 < 6/x < epsilon + 3
If I reciprocal this do I flip the inequality ...
when you have a<b and you take the reciprocal the sign ONLY changes if both are positive or both are negative
easy example is -1<1
you wont flip the sign if u take recip
waxen harness
-epsilon + 3 < 6/x < epsilon + 3
If I reciprocal this do I flip the inequality ...
considering your ε will be small 3-ε is positive so u can take recip and change the signs
but note it s not true for every ε anymore
thin root
damn
vocal sleetBOT
@thin root Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
lethal plank
prove that A is irrational
vocal sleetBOT
prove that A is irrational
lethal plank
i've simplified until 15^n * 8
and factorized as 3^n * 5^n * 2^3
stuck now
@river minnow
you basically have to prove that it isn't a perfect square
river minnow
I mean you are basically done
Even if n is even, then A is 3^(n/2) * 5^(n/2) * 2 * sqrt(2)
And sqrt(2) is irrational
Btw the expression under the root not being a perfect square does not imply the root is irrational
E.g. the square root of 4/9 is 2/3
But the thing is that for odd n you would need to prove that sqrt(30) is irrational 
Got any tools that could speed up the rigorous process of that? Like having proven that square root of an integer that is not a perfect square is always irrational
vocal sleetBOT
@lethal plank Has your question been resolved?
vocal sleetBOT
@lethal plank Has your question been resolved?
lethal plank
.close
vast sparrow
Hey I was wondering if somebody could help me through this weird shell method question?.. I've finally got a grasp for it, but this one is def unique
vocal sleetBOT
Hey I was wondering if somebody could help me through this weird shell method qu...
@vast sparrow Has your question been resolved?
vocal sleetBOT
Available help channel!
naive elbow
what happens to rotational motion if the radius is 0
vocal sleetBOT
what happens to rotational motion if the radius is 0
radiant plinth
if radius is 0, the object is essentially a point mass, and there's nothing you can physically rotate around, so no rotation can occur in those circumstances
but all real life objects have a finite size and cannot be reduced to what mathematics consider a point
naive elbow
alr
i have another quesiton
compare the Fn between something that has 0 raidus and some thing that has a raidus R
radius*
i would o
do
Fn-Fg=mv^2/r right
but Fn=Fg so its
0=mv^2/r
i cant compare the Fn then because its 0
idk what to do
radiant plinth
what is Fn?
radiant plinth
mv^2 / r is an expression for centripetal force, I'm not sure how you're using it here
naive elbow
wym
the original question is.
a plane has radius R spins with an angular velocity omega(w) about an axis through the North Pole.
what is the ratio of normal force experienced by a person at the equator to that experienced by a person at the north pole? Assume a constant gravitaional field(g) and tha both people are stationary relative to theplanet and are at sea levle. Express your answer in terms of R,w,andg
i drew a diagram
but idk how to set the equations
radiant plinth
okay...how does zero radius have anything to do with this?
radiant plinth
what makes you use r = 0?
naive elbow
because at equator there is no radius
radiant plinth
what happens to rotational motion if the radius is 0
just noticed this sounds like an xy problem
radiant plinth
a plane has radius R spins with an angular velocity omega(w) about an axis throu...
an axis through the north pole...and equator is at a very certain radius around that axis (aka around the earth)
to me, this sounds like you have to determine angular velocity of the Earth (rotation, not revolution, in other words, the spinning of earth around its own axis, not around the sun) from the given data about that plane, and then calculate the ratio of normal forces
omega = R/T, where T = 1 day
correct me if I'm wrong please
radiant plinth
this is a mathematics server and I'm not pro in physics, but centripetal / centrifugal forces do relate to normal force, if you can imagine a bowl full of water, normal force on the edges when bowl is stationary is smaller than if the bowl is spinning in a circle (where water presses the inside of the bowl) so normal force increases by 3rd newton law
naive elbow
ok thank you
radiant plinth
sorry for not being able to help you much, but what I think is that since the earth is rotating, it's assumed that the person at the north pole doesn't feel any centrifugal force therefore the normal force for a person on the equator is smaller than on the north pole
and for the airplane... (probably, don't take my word for it) it's centrifugal force equals it's gravity force , mg = mv^2/R, so you can get v
however it isn't mentioned if the airplane itself is moving, or it's just floating but affected by earth's gravitational field
I agree it's a bit confusing
radiant plinth
a plane has radius R spins with an angular velocity omega(w) about an axis throu...
you mention planes here
do you refer to mathematical plane as a a flat surface?
radiant plinth
why would it have radius zero then in the first place 😛
it's better to just send a photo or a screenshot of that problem because people very often mess things up when copying
naive elbow
radiant plinth
,rotate
twin meteorBOT
radiant plinth
and okay then it's much easier, since
v = 2 pi R / T
w = 2 pi / T
you get that v = w * r
use that v in the equation for that force
twin meteorBOT
7o1
radiant plinth
on the north pole normal force is equal the gravity
radiant plinth
while on the equator, there is centrifugal force that is from the planet's center to the space
(it's the same as centripetal but the vector direction is reverse)
naive elbow
ye
radiant plinth
and okay then it's much easier, since
v = 2 pi R / T
w = 2 pi / T
you get that ...
from these equations you get the relation of v, w and R
(because the problem asks you to express with w and not v)
radiant plinth
naive elbow
yea
radiant plinth
**7o1**
$\frac{F_{N_{equator}}}{F_{N_{north pole}}} = \frac{\cancel{m} g - \cancel{m} \frac{v^2}{R}}{\cancel{m} g}$
radiant plinth
but
you have to use
w
instead of v
in that fraction
i'll leave that to you
also you're welcome
twin meteorBOT
7o1
radiant plinth
.close if you don't need anything else
radiant plinth
for the bottom part is it from
again, there is no centripetal centrifugal force on the north pole so no need to use mv^2/r
it's just Fn = Fg
radiant plinth
also the fraction can be simplified to $1 - \frac{v^2}{Rg}$
twin meteorBOT
7o1
radiant plinth
v = R * w
sudden hill
help
ornate ember
what do all of the probabilities have to add up to?
sudden hill
1
sudden hill
welp
vocal sleetBOT
@sudden hill Has your question been resolved?
empty linden
so, where do i start?
vocal sleetBOT
so, where do i start?
empty linden
i only know how to solve for the 3 main trig ratios, but i havent solved the other 3 before
empty linden
what can i do?
eager swan
cos(x + 45) = 1
empty linden
45 is an angle right?
empty linden
so would '1' be the 1 period of the unit circle? which is 2pi or 360 degrees
eager swan
you can write cos (x + 45) = cos (0)
so x + 45 = 0
only in the first quadrant this is valid
empty linden
but what happened to the 1
eager swan
cos 0 = 1
for other quadrants you have to take n pi values
wait lemme double check if its n pi
empty linden
ill go check my unit circle
empty linden
so is '1' half the unit circle?
eager swan
so for every 2n pi angles, cos values repear
empty linden
on the first quadrant, cos = 0
eager swan
yes
empty linden
sorry, i meant 3pi/2
empty linden
ohh because sec is reciprocating it?
eager swan
see where x = 1 in the whole circle
only at 0
and 360
which is 2 pi radians
so cos 2n pi = 1
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
need help simplifying don't know where to start: (((x ∧ y) ∨ z) ∧ (¬x)) ∨ (¬z)
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
.close
obtuse minnow
can someone check this
vocal sleetBOT
can someone check this
obtuse minnow
what theorem would i use for this
i assumed it was SAS bc the two angles where B is are intersecting
so they could be equal
and then two sides are given for both
mild flower
so they could be equal
could be, or are?
obtuse minnow
could be
spiral turtle
are.
obtuse minnow
it's not shown but because they are intersecting im assuming they are
spiral turtle
It's a theorem
spiral turtle
You have two sides and an angle between the two sides, implying...
obtuse minnow
SAS?
spiral turtle
Correct
obtuse minnow
so would this one be ASA?
bc they both share a side and there are two angles?
or would this be AAS?
those two theorems confuse me
spiral turtle
It's ASA, the theorems are named descriptively of the situations they apply to.
So ASA is Angle-Side-Angle or one side between two angles.
vocal sleetBOT
obtuse minnow
.reopen
vocal sleetBOT
✅
obtuse minnow
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
astral pebble
vocal sleetBOT
astral pebble
I understand the basic concept of a sign chart but idk how to identify those values on it
Ik a local max is going from + to- and a min is - to +
astral pebble
And does it help you?
I just dont understand how to use the second deriv chart
wet tendon
Ok so the second derivative shows concavness (if that's how you say it in English)
astral pebble
would you say -4 is a min bc it switches from - to +
wet tendon
No
Ok let's do a little lesson
You have function f
To find its extrema
You want to solve f'(x)=0
wet tendon
You want to solve f'(x)=0
The roots of this equation CAN be points of an extrema
To know for sure
You find f''(x)
astral pebble
ohhhhhhhhh wait so -4 is an inflection point right?
wet tendon
Indeed
astral pebble
hmm
is -3 a min
bc it goes negative to positive 2 times
it goes - + +
or wait
-1
not -3
astral pebble
huh
wet tendon
Change in sign in f'(x) but no change in sign in f''(x) --> Extrema
Change in sign in f'(x) and a change in sign in f''(x) --> Inflection
A change in sign in f''(x) --> Inflection
astral pebble
so there are 3 inflection points right? -4, -1, 3
wet tendon
so there are 3 inflection points right? -4, -1, 3
-3 is also an Inflection
astral pebble
Change in sign in f'(x) but no change in sign in f''(x) --> Extrema
Change in si...
by that definition is there no extrema?
wet tendon
by that definition is there no extrema?
Why? 4 is an extrema
astral pebble
bc there are no points where you have a sign change in f'(x) but not f''(x)?
wet tendon
0 is an extrema
wet tendon
bc there are no points where you have a sign change in f'(x) but not f''(x)?
Are you sure?
-2 is extrema
wet tendon
3 extrema, 4 inflection
wet tendon
Indeed
wet tendon
bc you switch from + to -
Yes
wet tendon
So...
a) -2, 4
b) 0
c) -4, -3, -1, 3
astral pebble
wait
wet tendon
Look again
wet tendon
Not that 3 is extrema and 4 is inflection
The opposite is right
astral pebble
so does this seem good?
(a) Answer: -2, 4
Reason: If the sign changes from "+" to "-", it indicates a local maximum at that point.
(b) Answer: 0
Reason: If the sign changes from "-" to "+", it indicates a local minimum at that point.
(c) Answer: -4, -3, -1, 3
Reason: Look for intervals where the signs of the second derivative change. If the sign changes from "-" to "+", or from "+" to "-", it indicates an inflection point at that point.
wet tendon
I would add in the extrema explanations "and there is no change in sign in the second derivative"
Because by "If the sign changes from "-" to "+", it indicates a local minimum at that point", -4 is a minima, which is not true
astral pebble
@wet tendon I have one more question I am confused on as it feels like a trick question
f'(x) = -8/x^3
Setting f'(x) = 0 gives:
-8/x^3 = 0
8/x^3 = 0
x = 0
Obviously 0 cant be a critical point because the domain is x>0
what do I do here?
anyone that can help?
lunar hearth
<@532903217248600074> I have one more question I am confused on as it feels like...
Redo the derivative
Not quite true
astral pebble
Possible derivation:
d/dx(4/x^2)
Factor out constants:
= 4 (d/dx(1/x^2))
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = -2.
d/dx(1/x^2) = d/dx(x^(-2)) = -2 x^(-3):
= 4 -2/x^3
Simplify the expression:
Answer: |
| = -8/x^3
@lunar hearth
Idk what more to do
even wolfram alpha says no roots exist
wet tendon
<@532903217248600074> I have one more question I am confused on as it feels like...
Oh hello there
Well can you find the derivative of f(x)?
astral pebble
Oh hello there
huh?
wet tendon
Well can you find the derivative of f(x)?
?
wet tendon
Well, how are you gonna find the critical points of f(x) without finding its derivative?
astral pebble
Well, how are you gonna find the critical points of f(x) without finding its der...
I did
astral pebble
Possible derivation:
d/dx(4/x^2)
Factor out constants:
= 4 (d/dx(1/x^2))
Use ...
here
astral pebble
f'(x) = -8/x^3
Setting f'(x) = 0 gives:
-8/x^3 = 0
8/x^3 = 0
x = 0
here
wet tendon
f'(x) = -8/x^3
Setting f'(x) = 0 gives:
-8/x^3 = 0
8/x^3 = 0
x = 0
You forgot something really small
You found the derivative of 4/x^2
But f(x) is (4/x^2)+x
astral pebble
omfg
wet tendon
Yea it's really pissing off when you miss stupid little details
The wording is very interesting
It says "points" like there are more than 1, but there is only one
astral pebble
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
silk ibex
vocal sleetBOT
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
@silk ibex Has your question been resolved?
vocal sleetBOT
@silk ibex Has your question been resolved?
vast jewel
bruv its easy
u see
similar
no
dw
wait what
why doe they delete msgs with restarted in it
dang
silk ibex
idk
vast jewel
it gets auto delted
alr anyways
on to question
okay
so
u know differnce between similar and congruent right?
silk ibex
yes
vast jewel
u can tell circles are similar or no?
vast jewel
okay so if we go according to definition
yes ik
they asked a fking paragraph
ur teachers the resterted one here
silk ibex
yea
vast jewel
so
now
if we go accorsing to definiton of similar cicrles
or similar figures
then similar figures are the figures which have the same / similar shape
silk ibex
yes
vast jewel
btu not necesarrily similar siize
here
we can see
both the figures have the same shape
i.e a circle
and all circles are similar
they are similar because
nah
here
u go
ezz
vast jewel
dw
no wait
u might not understand that
just write how the ratio between the circumference and radius
is constant for all circles
thus all the cricles are simila
vocal sleetBOT
@silk ibex Has your question been resolved?
vast shale
it says here, that there are similar formulas that can be obtained. If I for example want to create a formula for the left endpoint, how would that look?
vocal sleetBOT
it says here, that there are similar formulas that can be obtained. If I for exa...
vast shale
[a, b] is the interval
n is the number of sub-intervals in the interval
would that just be switching the sign of a?
like turning it from +a to -a
vocal sleetBOT
@vast shale Has your question been resolved?
boreal path
vocal sleetBOT
boreal path
idk how to start this
vocal sleetBOT
@boreal path Has your question been resolved?
boreal path
<@&286206848099549185>
glossy maple
(a) is just asking you, how many sets of 3 points can you select from the 5 points
order of the points doesn't matter
@boreal path
boreal path
(a) is just asking you, how many sets of 3 points can you select from the 5 poin...
5c3 ?
glossy maple
yes
now (b)
in order to form a triangle, you need 3 vertices (points)
but you will notice that not all sets 3 points can create a triangle
so its not just the number of ways to choose 3 points
boreal path
that’s what i was struggling with
glossy maple
so what do the points have to satisfy in order for you to be able to form a triangle with them?
hint: is has to do with collinearity
if you choose 3 collinear points, can they make up a triangle? @boreal path
boreal path
no
i wrote that down
but i didn’t know how to go from there
to be honest i forgot about this question
glossy maple
so if the 3 points are not collinear
can they make up a triangle
@flat whale ? 
is that a warning triangle or a 
type of thing
making me nervous here
flat whale
is that a warning triangle or a <:this:489575168314966026> type of thing
No warning. Just a triangle
glossy maple
ok
vocal sleetBOT
@boreal path Has your question been resolved?
glossy maple
ok so find the number of ways to choose 3 points, such that they are NOT collinear
that will give you the number of triangles
glossy maple
"one collinear"?
do u know what collinear means
you can only talk about "collinear" when its at least 3 points
that means they lie on the same line
all 3 of them
boreal path
why not two
glossy maple
two points always lie on the line connecting them
glossy maple
you just need the number of sets of 3 points, such that they are NOT collinear
no
you already calculated the number of sets where they ARE collinear
its just 5C3
because any other 3 points will NOT be collinear
glossy maple
the only sets of 3 points that are collinear are those that come ONLY from the 5 mentioned points
if you take any point thats not in those 5 points, you already know it will NOT be collinear with any other 2 points
boreal path
yes
boreal path
well@five points are not collinear
and i guess maybe you can say two of the 5 points they mentioned count as well ??
7c3?
glossy maple
no
boreal path
is it just also 5c3
glossy maple
the 5 red points are collinear
any other 3 points, that aren't all red, are NOT collinear
boreal path
so i can make a triangle with two red and one black
glossy maple
ok
thats not all though
there's a much easier way to solve this using the result from part (a)
boreal path
10c3-5c3
south mango
i have to write a two column to prove something. Attached is the image of the question. I have figured out how AD and BC are congruent but dont understand how to make AB and Dc congruent and by what postulates and theorems, pelase help
vocal sleetBOT
i have to write a two column to prove something. Attached is the image of the qu...
south mango
please help anyone
rugged orchid
What’s an isosceles trapezoid
rugged orchid
I’m asking you
rugged orchid
Yes
south mango
basically a trapezoid where the base angles are congruent or equal
they are parallel i believe not the same size
and the legs are congruent i believe
rugged orchid
Ok now given the information that AE = AD
rugged orchid
and the legs are congruent i believe
And from this we have AE = BC
rugged orchid
What could you conclude about the angles of triangle AED and the angles of ABCD
south mango
??
angle EDA is congruent to angle DCB i suppose?
angle EAD is equal to angle ABC maybe?
thats what i can conclude
rugged orchid
EAD and ABC aren’t equal
south mango
EAD and ABC aren’t equal
oh ok
rugged orchid
Parallelograms just need parallel lines
Or same angles
The length just pops out I think you don’t need to mention it here
Just show that the opposite angles are the same is sufficient to call ABCD a parallelogram
rugged orchid
(Since 1 set is already parallel)
Well
That’s why we want to consider the triangle
rugged orchid
What could you conclude about the angles of triangle AED and the angles of ABCD
.
Let’s start with triangle AED
What do you notice about it?
south mango
it has three sides.....
ad and ae are congruent
points e and d are also congruient
rugged orchid
it has three sides.....
That makes it a triangle
rugged orchid
ad and ae are congruent
What kind of triangle does this make it?
south mango
isoceles triangle
rugged orchid
points e and d are also congruient
Points can’t be congruent
If they were congruent they would be the same point
south mango
ye sry mb
rugged orchid
isoceles triangle
What do we know about isosceles triangles?
What’s special about them besides 2 equal side lengths
south mango
the angles opposite to the two sides are equal/
rugged orchid
And what else do we know about AED
south mango
is congruent to ADC
south mango
corresponding agles?
rugged orchid
They are absolutely not congruent
south mango
ok then waht can we notice?
rugged orchid
Well
What is a isosceles trapezoid
What was the thing I picked out from the list of properties you wrote
south mango
oh its congruent to BCE?
rugged orchid
Then by the properties of isosceles trapezoids, ADE = AEC (E and C lie on the same line)
Then what do we know about angle DAB
We need to show DAB = BCD
Because that restricts the shape to be a parallelogram
south mango
~~Then by the properties of isosceles trapezoids, ADE = AEC (E and C lie on the ...
How?
rugged orchid
AEC = BCE
rugged orchid
That’s because AED is isosceles
Now we say AED = AEC
Because D and C lie on the same line
south mango
what theorem or postulate is that?
next sleet
i have to write a two column to prove something. Attached is the image of the qu...
||by definition every isosceles trapezoid has one pair of parallel sides. In this case that pair is AB and CD, and since you know AD and BC are parallel you're done.||
Oh you only said you know AD and BC are congruent not parallel
south mango
ye
next sleet
i have to write a two column to prove something. Attached is the image of the qu...
use angles
next sleet
what is the relation between angles AEC and BCE? How about angles AED and ADE
rugged orchid
I have no idea what people call these stuff
rugged orchid
I would just say they lie on the same point but maybe someone knows
south mango
it doesnt make sense either way that AED and AEC
rugged orchid
What do you mean it doesn’t make sense
south mango
like how can they remotely even be equal
it doesnt make sense there lengths would be compeltely different
south mango
OH SHIT YEA
oof mb for bad language
i wasnt looking at that that was oof i get it now
ADE = AED
AED = AEC
now what?
rugged orchid
Then what do we know about angle DAB
Here
rancid linden
AB//CE
rancid linden
angle EDA is congruent to angle DCB i suppose?
with this we have AD//BC
south mango
thats already true
i need a way to prove AB is congruent to DC
or the opposite angles are congruent
south mango
ye
vocal sleetBOT
@south mango Has your question been resolved?
rugged orchid
is it equal to ADE or soemthing?
Yes but why
rugged orchid
Yeah
So the opposite angles are the same
And you have a pair of parallel lines
So it’s a parallelogram
south mango
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
hi
vast shale
i think i read the info right
i need help with a trig problem. im not sure what to do to solve it
basically, i have all sides and idk how to get angle A and B
with trig btw^
trig func
outer warren
use the appropriate inverse trig function
flat whale
okay im still confused rip 😭
Do you know what inverse trig functions are
vast shale
okay
but since i have no angles how am i supposed to apply that
if i just do arcsin(6/11) then i get a number below 0
i mean less than 1
patent nymph
are you in radians mode?
vast shale
no im in degree. i also tried radian mode and it still didnt work
patent nymph
,w arcsin(6/11) in degrees
twin meteorBOT
patent nymph
,w arcsin(6/11)
twin meteorBOT
lament linden
You dont need an angle to evaluate another angle, you are already given length of all sides of the triangle
outer warren
no im in degree. i also tried radian mode and it still didnt work
can you show what you're putting into your calc
vast shale
can you show what you're putting into your calc
lemme try putting my calc in degree again first
lament linden
You can use law of cosines as well
This is what typically one would do if it wasnt a right triangle
vast shale
ok so now its working 💀 idk why it didnt in the first place but for angle A i got 33.05 deg
lament linden
This is what typically one would do if it wasnt a right triangle
(Must be given all side lengths though)
vast shale
ok so now its working 💀 idk why it didnt in the first place but for angle A i g...
is 33.05 correct ?
outer warren
sounds about right
vast shale
ill check it rn
outer warren
,W arcsin(6/11)*180/pi
lament linden
Its close to 45° so i'd say so
twin meteorBOT
outer warren
round properly though
flat whale
,calc asin(6/11) * 180 / pi
twin meteorBOT
Result:
33.055731150854
.close
coarse gust
How do I reconcile this into one expression? The correct answer is x>1 only
coarse gust
This is a pretty simple doubt tbh
thorn crater
x>1>-3 maybe
coarse gust
This is a pretty simple doubt tbh
But I don't get it
karmic imp
,rotate
twin meteorBOT
thorn crater
But the answer is x>1
but you wanted to combine to two inequalities right?
coarse gust
Yes but in a way that it gives x>1 somehow
thorn crater
just put x>1 or x>1>-3 i guess
coarse gust
just put x>1 or x>1>-3 i guess
But that according to basically all math calculators is untrue.
Only x>1 is the real answer
thorn crater
Only x>1 is the real answer
x>1 is the simplest answer
coarse gust
x>1 is the simplest answer
No it is the only answer
thorn crater
on the first part instead of removing x from both sides you should add 3 to each side so you will get x<x+4. you multiply by 2 to make 2x<2x+4 and add them toghether and get 2x+4>2x>2. divide by 2 and you get the final answer of x+4>x>1
sorry for the wall of text
coarse gust
Yes but that still doesn't conclude x>1 as the only answer
thorn crater
it does?
coarse gust
How?
thorn crater
x+4>x could easily be written as just x
coarse gust
x+4>x could easily be written as just x
It still ends with True. How can it be written as x
mild spear
as the inequality say x+1 > |x-3| , this condition is statisfied for the region x>1
thorn crater
Yes but methodically
you already solved the problem dude the answer is x>1
mild spear
Look at inequality, it is asking what will be value of x for which the inequality is TRUE
coarse gust
What about the true part? Doesn't that imply that all values of x will be true?
mild spear
no, The inequality will be TRUE for x>1 and wil be False for other values of x
thorn crater
So what does True say?
it means that -3 is less than 1
mild spear
can you elaborate your question
coarse gust
it means that -3 is less than 1
It doesn't imply on x then?
coarse gust
it means that -3 is less than 1
This means that all real x satisfies
So how do we reconcile that?
vocal sleetBOT
@coarse gust Has your question been resolved?
median harbor
Let f(x)=x^4+x^3-3x^2+x+2. Show that the polynomial (f(x))^n has at least 1 negative coefficient for all n.
vocal sleetBOT
Let f(x)=x^4+x^3-3x^2+x+2. Show that the polynomial (f(x))^n has at least 1 nega...
median harbor
my only ideas are
: a graph of a func with only pos coeffs is strcitly inc on the pos side
pale widget
I've only thought about this for all of 5 seconds, but the first thing I would try is probably to separate out the -3x^2 and the rest of the polynomial then apply the binomial theorem and see what happens.
wide rapids
Oh
half imp
i think that leads to lots of interference
mild flower
my only ideas are
: a graph of a func with only pos coeffs is strcitly inc on th...
x^n > 0 if x > 0 
i like this idea
half imp
my only ideas are
: a graph of a func with only pos coeffs is strcitly inc on th...
this is a great idea
are graphing calculators allowed, this seems like a competition question
wide rapids
Moni let me take over, thanks…
half imp
ok go ahead, what's your idea
wide rapids
2 sec
half imp
show that positive coefficients add up to more than f(1)^n?
median harbor
are graphing calculators allowed, this seems like a competition question
not provided
my friend just sent me that
half imp
i think if 0<x<1 then -3x^2+x+2 > 0 (as x^2 < x < 1)
half imp
3x^2 = x^2 + x^2 + x^2 < x + 1 + 1
boreal star
my only ideas are
: a graph of a func with only pos coeffs is strcitly inc on th...
Okay, if this statement is correct, then I got the solution
median harbor
i think if 0<x<1 then -3x^2+x+2 > 0 (as x^2 < x < 1)
no i get this im asking how does it contribute
median harbor
Okay, if this statement is correct, then I got the solution
send it out
well
hint me through the way if you insist
median harbor
Okay, if this statement is correct, then I got the solution
and it has to be correct because like
theres nothing to be negative about
half imp
oh, strictly increasing, not strictly positive
median harbor
literally everything is adding on nothings taking away
urban edge
f(x)=(x^4-3x^2+2)+(x^3+x)
=(x^2-2)(x^2-1)+(x+1)(x^2-x+1)
I mustve done something wrong, this implies x=-1 is a root but its not
half imp
product rule works out so that showing the derivative of f(x) is negative at any point x>0 works?
urban edge
Oh im stupid
mild flower
i've been trying to find the roots of f' with no success
half imp
4x^3 + 3x^2 - 6x + 1
urban edge
f(x)=(x^2-2)(x^2-1)+(x)(x^2+1)
Hmmm
half imp
x=1/2 works
mild flower
yeah it would help if i had written down 4x^3 instead of x^3
median harbor
guys the question asking to prove that there must be a negative coefficient, not a negative value
median harbor
right
median harbor
now plug in 1/2 for x
but this should work because
if we find a neg value
then there has to be a neg coeff
median harbor
hm
half imp
my only ideas are
: a graph of a func with only pos coeffs is strcitly inc on th...
so i was using this, you said strictly inc
not just strictly positive
so we show (f(x)^n)' < 0 at some point, x>0
glossy maple
i graphed and I think its not
mild flower
if there are only positive coefficients on any f(x)^n then it's strictly increasing on positive values
which means that f(x) is increasing for all positive values (all exponents are monotonic)
which means that f ' (x) > 0
so if we show that f ' (x) < 0 at some point then
half imp
Parabola shaped but with two bowls?
boreal star
Okay, if you have all positive coefficients, then the derivative will also have all positive coefficients, which means it will be strictly increasing for x>0
half imp
let her think lol
glossy maple
why are you assuming its for all n?
half imp
!nosols
vocal sleetBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
mild flower
oh i thought we already were at that point? i saw people talking about derivatives
median harbor
didnt expect we had to use calculus
glossy maple
idk i also recently joined, but aren't you supposed to assume its false for SOME n
if you want to prove by contradiction
glossy maple
I didn't say choose, but saying that it's not all positive coefficients for ALL n doesn't imply anything
glossy maple
if there are only positive coefficients on any f(x)^n then it's strictly increas...
this I mean
half imp
That's not what we're doing
mild flower
i'd have said all if i meant all
boreal star
if you want to prove by contradiction
You can try to apply contradiction inductively. Suppose it isn't true for n=2, then contradiction. Then n=3, then contradiction. This isn't the way its generally done, but in this case you'll see why it will hold for general n. In short, it's heuristic, and also handwavy
glossy maple
ok 🗿
half imp
not even induction really
boreal star
Hand wavy
half imp
just a proof by contradiction that it doesn't work for n, where we assume n is some arbitrary natural
or you mean like
eh nvm idk
boreal star
I meant get your hands dirty with n=2, n=3 and you'll see why it holds for all n. Yeah, this is stupid. The idea works directly for any n. Really bad choice of words from me
glossy maple
we get n*f(x)^(n-1)f'(x)
isnt that a good solution
half imp
yes it works
glossy maple
showing that the derivative is negative between 0 < x < 1
moni how did u even think of that lol
limber wedge
Can someone help with this question
Let z = ax+by+c contain the line x = 1+5t, y=1+4t, z=1+t and is perpendicular to the plane x+2y-z + 1 = 0. Write the value of b
half imp
finding which "direction" the plane is pointed in is always helpful for problems like these
so, can you find 2 vectors which are "contained" in the plane
limber wedge
I have three equations that i arrived at
One was
1=a+b+c since the plane contains the point (1,1,1)
The other was 1-5a-4b=0
half imp
The other was 1-5a-4b=0
did you get this by plugging in another point?
limber wedge
And the last one was (-a, - b, 1)*(1, 2, - 1)
half imp
oh i see
limber wedge
did you get this by plugging in another point?
No, since the plane contains the given line, the direction ratios multiplied by the plane direction ratios resulted in zero
half imp
i think you may be missing the c component though
limber wedge
I got three equations, three variables. I don't think i may be missing the c component
Am i missing something?
vocal sleetBOT
@limber wedge Has your question been resolved?
limber wedge
the direction ratios are 5 to 4 to 1?
Of the line? Yes
half imp
and taking the dot product with <a,b,c> is supposed to yield 0?
limber wedge
Yes
half imp
Your equation does not represent that
limber wedge
Oh
Isn't the direction ratios of the plane (-a, - b, 1). Taking the dot product with (5, 4, 1) gives the equation - 5a-4b+1=0?
half imp
Maybe I don't know what it meant by "direction ratio of the plane" but that doesn't seem right
And I don't know what the vector (-a, -b, 1) has to do with the plane
It doesn't point in a direction of the plane and it doesn't point normal to the plane either
vocal sleetBOT
vocal sleetBOT
Available help channel!
vocal sleetBOT
opal obsidian
What’s the formula for covariance?
astral pilot
opal obsidian
I’m sorry, i can’t go through each calculation
If you know excel, you can find it easily
or check if there is a covariance calculator online
twin meteorBOT
vocal sleetBOT
@peak yacht Has your question been resolved?
pale widget
Most applications like excel implement two versions of variance/covariance depending on if you need a finite population correction factor or not. You can't just blindly throw equations into a program without reading it's documentation.
vocal sleetBOT
vocal sleetBOT
Available help channel!
deep cliff
vocal sleetBOT
paper depot
