There is no mistake in there.
#help-13
frosty ocean
waxen crater
where did this come from?
waxen crater
oh so I missed the equal sign
frosty ocean
Yeah
waxen crater
how bout 6/-3=-2 where did that come from
frosty ocean
Same
half forge
i thnk the last two calculations came from factoring out the -3 from the -9x+6 in the second line
frosty ocean
You have +6 in the last term and you're factoring out a -3
cedar kilnBOT
@waxen crater Has your question been resolved?
crimson sedge
Can someone tell me what they get here for a)?
cedar kilnBOT
Can someone tell me what they get here for a)?
scarlet garnet
Can someone tell me what they get here for a)?
max amplitude of 2
period of 2/3 pi
,w graph 2sin(3x)
wraith daggerBOT
scarlet garnet
,w convert 2/3 pi to radians
wraith daggerBOT
crimson sedge
max amplitude of 2
period of 2/3 pi
Amplitude is measured in what
crimson sedge
Oh i see
wraith daggerBOT
crimson sedge
Man i was thinking there was two measurements for amplitude but it made no sense lmao
Thanks i got it
.close
cedar kilnBOT
scarlet garnet
Man i was thinking there was two measurements for amplitude but it made no sense...
I guess you could say its from -2 to 2
gloomy berry
You know angle ACE
Angle sum property of a triangle
You get ACE = 70°
Then the reflex angle of ACE must be 360-ACE
solar cypress
145
gloomy berry
Then you can use the angle sum property of quadrilaterals for ADEC
cedar kilnBOT
@crimson sedge Has your question been resolved?
bitter finch
Since the exact places where the points are isn’t specified, consider what happens if F coincided with B
yea that’s what i mean by coincide
that they overlap
no
oh the parallelograms wont overlap fully
there’ll still be DEA
and FGC
try drawing a diagram
did u make a diagram?
show me ur diagram
it should look something like this
66 is right
mossy gull
How do I factorize this expression?
cedar kilnBOT
How do I factorize this expression?
mossy gull
1)There isn't a common factor for all.
2)If I try to factor by a number a number will be left bcs they arent in even number
mossy gull
Ok wait
Oh
(4b-1)^2
@tropic oxide what next?
I have 4 terms but 2 are into the ()
So I can't factor out
blazing zephyr
you can factor the -8bc+2c
mossy gull
By 2c?
blazing zephyr
yep
mossy gull
Maybe - 2c
blazing zephyr
oh yeah sorry
mossy gull
Ok done
Another one it's a bit tricky for me
@blazing zephyr i factor by a
And I got
$a[(a-2y)^2-2ay+4y^2]$
wraith daggerBOT
Sarkes_the_jack
blazing zephyr
uh
blazing zephyr
i havent tried this but maybe expabding the square might help
wraith daggerBOT
Sarkes_the_jack
mossy gull
What can I do
blazing zephyr
wait did i mess up
mossy gull
?
blazing zephyr
oh nvm
mossy gull
Uhm so
blazing zephyr
how did you get 8y²
blazing zephyr
how about that other -2ay in the equation
mossy gull
Wdym
blazing zephyr
so
mossy gull
$(A-2y)^2=a^2+4y^2-2ay$
blazing zephyr
you got -4ay from the (a-2y)² right
wraith daggerBOT
Sarkes_the_jack
mossy gull
Like this
blazing zephyr
$(a-b)^2=a^2+b^2-2ab$
wraith daggerBOT
Skill_Issue
mossy gull
$4ay^2:a =4y^2$
wraith daggerBOT
Sarkes_the_jack
blazing zephyr
if you plug that in you get a²+(2y)²-2a(2y)
blazing zephyr
dont understand where?
mossy gull
$a[(a-2y)^2-2ay+4y^2]$
wraith daggerBOT
Sarkes_the_jack
mossy gull
What have I to do
blazing zephyr
**Sarkes\_the\_jack**
expand the square, you just accidentally made a mistake here
mossy gull
$a(a^2+8y^2-4ay)$
wraith daggerBOT
Sarkes_the_jack
mossy gull
Isn't it?
blazing zephyr
check the ay part again
mossy gull
Uhm
blazing zephyr
ok ok
blazing zephyr
ok
mossy gull
$a(a^2+8y^2-6ay)$
wraith daggerBOT
Sarkes_the_jack
mossy gull
im going to go to sleep bye
Wait a sec
blazing zephyr
yeah
mossy gull
Now what I have to do
blazing zephyr
idk XD
wraith daggerBOT
Sarkes_the_jack
lucid iris
F(x)= (x+4)^2 (x-3) take derivative
cedar kilnBOT
F(x)= (x+4)^2 (x-3) take derivative
lucid iris
I don’t understand how
crimson delta
product+chain rule
lucid iris
Mmmm
crimson delta
do you know how to take the derivative of (x+4)^2
lucid iris
Mm 2x+8
clear berry
Do you know the chain rule?
cedar kilnBOT
cedar kilnBOT
Available help channel!
proper fjord
how do i go about solving this?
cedar kilnBOT
how do i go about solving this?
atomic vapor
I would break each vector down to sin and cos
atomic vapor
after summing them up you will get the overall effect of the 3 vectors
proper fjord
after summing them up you will get the overall effect of the 3 vectors
i sum up the x and y components separately?
atomic vapor
I think so
proper fjord
also if i already have the magnitude of the 3, i thought i would just have to do basic addition and subtraction
winged bay
proper fjord
this would be the resultant vector approximately i think
if you add all of em tip to tail
atomic vapor
looks right
proper fjord
i still dont really know how i would find that remaining distance back to the origin
it's probably not a nice number
atomic vapor
Pythagorean theorem would work
I hope
if you know his effect on x and y you could use it to find the vector
cedar kilnBOT
Available help channel!
ember warren
Heya! Im trying to factorize this equation using the quadratic formula, but I dont understand quite how they arrive at this answer. The fractions are honestly messing me up
ember warren
Most videos tell me to solve it by turning the fractions into non-fractions, but my lecturer told me to keep them as fractions. Suffice it to say, he himself struggled to explain this solution to me as well, since in most worlds, I see this as an outcome, so where am I going wrong?
Even if you do tell me that the power of 2 belongs to 1/6 and not the x, that still confuses me as to how 1*1 becomes 25 all of a sudden merged with a +4/6
sharp lotus
first off, why are you putting x's under the square root sign
when you use the quadratic formula, a, b, c just refer to the coefficients in the polynomial
so a = 1, b = 1/6, c = -1/6 there should be no mention of x's in there
sharp lotus
Most videos tell me to solve it by turning the fractions into non-fractions, but...
so this would be:
$\frac{-1/6 \pm\sqrt{(1/6)^2-4(1)(-1/6)}}{2*1}$
except my latex is rusty :p
wraith daggerBOT
Sooshon
sharp lotus
something like that if i havent made any more typos
ember warren
Hmmm, yes this is sorta what it turned into
But im doing something wrong at this point
Since 1/6^2 becomes 1/36 and -4*1/6 becomes 4/6
But clearly the solution doesnt agree with me here
sharp lotus
which solution are you even talking about
you sent two things and one of them seems like complete nonsense
(the second one)
ember warren
The very first image
sharp lotus
right so 4/6 becomes 24 / 36, add that to 1/36 = 25/36
ember warren
wait hold on, how does 4/6 become 24/36?
sharp lotus
multiply numerator and denominator by 6 to get common denominator (36), just basic fraction addition
$\frac{4}{6}\times\frac{6}{6} = \frac{24}{36}$
wraith daggerBOT
Sooshon
sharp lotus
i'm not jesus christ but youre welcome
livid horizon
i need help with an integral
cedar kilnBOT
i need help with an integral
livid horizon
$\int_0^{\pi}\sin(x)\sin(\alpha x)\dd{x}$
wraith daggerBOT
RickyDicky
livid horizon
i did some work but idk why im not getting the right result
$\int_0^{\pi}\frac12\left(\cos(x-\alpha x) - \cos(x+\alpha x)\dd{x}\right)$
radiant fjord
what's your work so far
wraith daggerBOT
RickyDicky
livid horizon
$\frac12\left(\frac{\sin(x-\alpha x)}{1 - \alpha} - \frac{\sin(x+\alpha x)}{1 + \alpha}\right)^{\pi}_0$
wraith daggerBOT
RickyDicky
livid horizon
when we substitute pi in
first one sin(x- alpha x) becomes sin(pi * alpha)
and second one sin(x + alpha x) becomes -sin(pi * alpha)
(Im actually not sure why that is but i figured that out, some explanation would be helpful)
$\frac12\left(\frac{(1+\alpha)\sin(\pi\alpha) + (1-\alpha)\sin(\pi\pi)}{1-\alpha^2}\right)$
wraith daggerBOT
RickyDicky
livid horizon
,w integral from 0 to pi sin(x)*sin(nx)dx
wraith daggerBOT
livid horizon
look at what wolfram gets
even the denominator is different
there's no 1/2 in wolfram's answer
clear berry
**RickyDicky**
yeah cause here you'd get 2sin(pi * alpha) in the numerator
That 2 cancels the 1/2
livid horizon
and in the denominator
clear berry
what's the issue with the denominator
clear berry
yeah and it also has a minus sign infront
livid horizon
ah
can u explain to me that thing earlier
about how sin(x-alpha x) becomes sin(pi * alpha)
clear berry
x = pi right? so, sin(x - alpha x) becomes sin(pi - alpha pi)
livid horizon
**RickyDicky**
I think i also got this part wrong here when i substituted pi
$\frac12\left(\frac{(1+\alpha)\sin(\pi\alpha) - (1-\alpha)\sin(\pi\alpha)}{1-\alpha^2}\right)$
clear berry
$\sin(\pi - \alpha \pi) = \sin \pi \cos \alpha \pi - \cos \pi \sin \alpha \pi = \sin \alpha \pi$
wraith daggerBOT
numbpy
clear berry
$\frac12\left(\frac{(1+\alpha)\sin(\pi\alpha) - (1-\alpha)\sin(\pi\alpha)}{1-\al...
How did you get a minus sign everywhere?
clear berry
Remember it in this way, pi - theta would lie in the 2nd quadrant, sin is positive there
wraith daggerBOT
RickyDicky
clear berry
yeah, correct
livid horizon
$\frac12\left(\frac{(1+\alpha)\sin(\pi\alpha) + (-1+\alpha)\sin(\pi\alpha)}{1-\alpha^2}\right)$
wraith daggerBOT
RickyDicky
livid horizon
then we get this
clear berry
Now just simplify
livid horizon
$\frac{\sin(\pi\alpha)(\alpha^2-1)}{1-\alpha^2}$
wraith daggerBOT
RickyDicky
livid horizon
somehow i end up with that
clear berry
**RickyDicky**
This should be + (1 - alpha) sin(pi alpha)
livid horizon
$(1+\alpha)\sin(\pi\alpha) + (-1+\alpha)\sin(\pi\alpha) = 2\sin(\pi\alpha)(\alpha^2 - 1)$
wraith daggerBOT
RickyDicky
clear berry
cause $\sin(\pi + \alpha \pi) = -\sin(\alpha \pi)$
clear berry
yep
livid horizon
ok well then
wraith daggerBOT
numbpy
livid horizon
the numerator would be
$\sin(\pi \alpha)(1+\alpha) + \sin(\pi\alpha)(1-\alpha) = 2\sin(\pi\alpha)(1-\alpha^2)$
wraith daggerBOT
RickyDicky
clear berry
nah dude
you're thinking too much
$\sin(\pi \alpha)(1+\alpha) + \sin(\pi\alpha)(1-\alpha) = \ \sin(\pi \alpha) + \alpha \sin(\pi \alpha) + \sin(\pi \alpha) - \alpha \sin(\pi \alpha)$
wraith daggerBOT
numbpy
fast sundial
I don’t understand derivatives
cedar kilnBOT
I don’t understand derivatives
muted bear
One is integration
fast sundial
How do you know when to use what
So say 16x^2
16 • line thingy x^2dx
16 • x^3/3 = 4x+c
but why not 16 • 2x
radiant fjord
integration symbol
fast sundial
only 13 
muted bear
Yeah when you have $\int$, you integrate
wraith daggerBOT
GarlicBredFries
fast sundial
oh
radiant fjord
$\frac{d}{dx} , x^2 = 2x ; \int{x^2}dx = \frac{x^3}{3} +c$
wraith daggerBOT
baro | awake
radiant fjord
no worries
fast sundial
.close
glacial brook
I need help with this
cedar kilnBOT
I need help with this
glacial brook
can I just use limit property and equate this to 0?
sharp lotus
did you try l'hopitals?
glacial brook
I dont know how to do that
jade sonnet
You don’t need to I don’t think so, you can split the fraction
sharp lotus
you didn't learn that yet, sure? because these kinds of problems usually are built for that and it makes it trivial but yeah there are other ways
jade sonnet
Do you know what the small angle approximation is?
steady fossil
you can also try to apply lim sin x/x = 1
dire geode
you can also try to apply lim sin x/x = 1
Use this after multiplying the top and bottom by 1+cos(2x)
soft owl
OR use this :
Cos(2x)= 1 - 2Sin²(x)
steady fossil
ye so you have 2sin²x/2x
soft owl
ye so you have 2sin²x/2x
multiply by x/x and isolate sin(x)²/x²
steady fossil
it screams for hopital ngl but he isnt allowed to use it
steady fossil
so whenever you have 0/0 or some other undefined forms cant remember em you are allowed to take the derivative from your top of your fraction and your bottom
sharp lotus
l'hopitals is basically: if the limit of the numerator and denominator individually is each 0 (this is one case at least, there are others with infinity), the limit of the whole thing is equal to the limit of the derivative of the top / derivative of the bottom
$\lim\frac{f}{g} = \lim\frac{ f'}{g'}$
something along those lines
glacial brook
I'll watch the vid... im super new to this topic
sharp lotus
man im bad at latex 😄
wraith daggerBOT
Sooshon
sharp lotus
if it's 0 / 0
wraith daggerBOT
Mehdi_Moulati
$\lim_{x \to a}\frac{f(x)}{g(x)} = \frac{\lim_{x \to a} f'(x)}{\lim_{x \to a} g'(x)}$
sharp lotus
$\lim_{x\to 0}\frac{1-cos(2x)}{2x} = \lim_{x\to 0}\frac{2sin2x}{1}$
as x - > 0 yeah mehdi is writing it much nicer, i forgot how to even do the limits on it
so as you can see that second one is a lot easier to do, you can immediately see what the answer is
@soft owl how do you get the color in your latex code anyhow?
wraith daggerBOT
Sooshon
$\lim_{x\to 0}\frac{1-cos(2x)}{2x} = \lim_{x\to 0}\frac{2sin2x}{1}$
soft owl
<@942843959783333890> how do you get the color in your latex code anyhow?
like how to change text color ?
sharp lotus
yeah
and well also this shows some kind of clearer coloring for the code itself
not sure how you got the bot to also show the code
oh i just answered my own question 😬
soft owl
```tex
write your code here
Sooshon
soft owl
add tex near the first 3 backquote
glacial brook
guys, after getting the derivatives of deno and numerator, I got 2sin(2x)/2
what do I do next?
soft owl
guys, after getting the derivatives of deno and numerator, I got 2sin(2x)/2
calculate the limit
glacial brook
so I just substitute?
sharp lotus
the limit on the right
yeah it's a continuous function so basically it's the same as the value i.e. plugging it in
cedar kilnBOT
@glacial brook Has your question been resolved?
hasty narwhal
In the figure, there are 2 triangles.
calculate the length of the segment DE if AC = 4,5 AB = 7,8 and BE = 3,5
cedar kilnBOT
In the figure, there are 2 triangles.
calculate the length of the segment DE if...
@hasty narwhal Has your question been resolved?
hasty narwhal
.reopen
cedar kilnBOT
✅
cedar kilnBOT
@hasty narwhal Has your question been resolved?
cedar kilnBOT
@hasty narwhal Has your question been resolved?
hasty narwhal
.close
obtuse quartz
cedar kilnBOT
obtuse quartz
how is this a negative?
number?
like the answer
4 -
should be a postive
positive
bc equal amount of -
wraith daggerBOT
kappa
runic adder
how is this a negative?
therre isn't parenthesis so -4^4 = - (4x4x4x4)
runic adder
parenthesis = ()
runic adder
(-4)^2 = (-4)x(-4) =16
obtuse quartz
then it would be a pos
runic adder
- 4^2 = - 4x4 = -16
runic adder
you're welcome!
cedar kilnBOT
@obtuse quartz Has your question been resolved?
mossy gull
Prove that, if in a triangle an exterior angle is congruent to the adjacent interior angle, then the other interior angles are acute. How can I prove this
mossy gull
So I know that I have 2 angles of 90°
silent finch
The exterior angle is the sum of the other 2 angles
silent finch
Let’s call our angles a,b, and c. Let the exterior angle be a+b, so that the adjacent angle is c, or 180-a-b. Then we 180-a+b=a+b. Simplifying, we get a+b=90
Ok one sec
silent finch
silent finch
I don’t understand French
silent finch
de meme
silent finch
Why is this not okay? Just set c and a+b equal and show that a+b=90, thus a and b are acute
mossy gull
silent finch
This is different
mossy gull
Why is this not okay? Just set c and a+b equal and show that a+b=90, thus a and ...
It's Euclidean Geometry
silent finch
Yea, I’m proving it using Euclidean geometry, not noneuclidean
silent finch
Ask what
silent finch
Just leave it here, let someone else try because I don’t understand
silent finch
I don't have to use calculus
Obv lol
mossy gull
Maybe I have to let you see an example
nimble veldt
just make a sketch, name the exterior angle like you want, and name the adjecent interior angle like you want. and then show me your sketch. i will try it.
mossy gull
Ok
nimble veldt
and of course name all angles in the triangle like you want.
nimble veldt
ok, we know the sum of the angles in a triangle is 180. can we use this?
mossy gull
I don't think
I think I have to create another triangle
Equal to another
And prove that the two ugual angles are 90° and then I have to say that the others angles are less then 90°
So basically I can only say
From the start
That omega and delta are 90°
Because they are ugual and their sum make 180° by costruction
So I can write
nimble veldt
if we cant use, that the sum of angles in a triangle is 180, then i have to pass. sorry.
nimble veldt
hmm, the sum of the angles = 180 is IMHO a main criteria of euclidian geometry. if this doesnt hold we are non euclidian.
nimble veldt
then you are ready.
mossy gull
Btw seems to easy
nimble veldt
alpha + beta = 90, alpha > 0, beta > 0.
nimble veldt
Btw seems to easy
the whole example seems to be one of the easier ones.
mossy gull
So let's try this
Prove that in a triangle ABC each of the two angles formed by the bisector AS with the side BC is greater than half the angle A.
@nimble veldt
Did you understood the request?
I used Google translate so I don't know
If it's clear
nimble veldt
what is S?
mossy gull
It's like the point that the bisector have in, common with bc
nimble veldt
just a moment
mossy gull
Okok
nimble veldt
nimble veldt
you mean S = D, and whe should prove the both angles at D are greater then half of A:
nimble veldt
ok
nimble veldt
ADB + ADC = 180
mossy gull
Ok
nimble veldt
Assume ADB = ADC -> both are 90 degrees.
mossy gull
Oh k
I see where do you point
I send one page of my book
So you can try to understand what we learned
To apply
nimble veldt
in this case we are ready, sinc CAB < 180, therefore is the half < 90.
nimble veldt
ok, i see what you learned. just give me a little time.
try to draw a line trough A which is parallel to BC
mossy gull
??
nimble veldt
the two new angles at A are the same as thoose two at D, an its obvious that the half at A is smaller
mossy gull
Uhm
Can you try to demonstrate
Like in the book
Just a try
Then I will adjust by myself
nimble veldt
and this works with both sides/angles at S,
nimble veldt
it means this two lines are parallel
nimble veldt
nothing else. we are ready. the black angles are "the half of A", the two red angles are the same. and the red angle is greater then the black one.
mossy gull
.
Here says for example
EDb =Adc because opposite at the top
They are ugual for the 1st criteria of congruence.,...
@nimble veldt
Understood?
nimble veldt
- EF is parallel BC
- FAS = ASB
- FAS > SAC
- EAS = ASC
- EAS > BAS
nimble veldt
if a line intersects two parallel lines then the angles are the same.
mossy gull
Oh k
Didn't know
Ok I figure out
How I factor this?
@nimble veldt
It's one of the last factor I have to do
I have to divide by 2?
Or like 2atcx
But I don't get ot
nimble veldt
i would try first to expand this and then have a look whats left.
nimble veldt
you will get $4a^2t^2+4c^2x^2+4c^2t^2+4a^2x^2$
wraith daggerBOT
ThM
nimble veldt
then group by t^2 and x^2
nimble veldt
$4(at+cx)^2=4(a^2t^2+2atcw+c²x²)$ ok?
wraith daggerBOT
ThM
nimble veldt
you missed 4 in the first line
nimble veldt
yes, but do it with the 4 and then add.
nimble veldt
you will lose the actx term, which is very helpful
mossy gull
It's like u
There are a lot of squares
But I think I can factor out
It's better
Two by two?
Or all with 4?
nimble veldt
just group. the two with t^2 and the two with x^2
mossy gull
Ok I think
nimble veldt
yes, i would take the 4 out, but yes.
nimble veldt
what does the book say?
wraith daggerBOT
mossy gull
,rotate
wraith daggerBOT
mossy gull
,rotate
wraith daggerBOT
mossy gull
I though it was ax^2+bx+c at the start
nimble veldt
there is, after you group.
nimble veldt
$b^2+3b-4+bx+4x=b^2+3b-4+(b+4)x=(b+4)(b-1)+x(b+4)$
wraith daggerBOT
ThM
nimble veldt
there is one step left -> (b+4)
nimble veldt
$b^2+3b-4+bx+4x=b^2+3b-4+(b+4)x=(b+4)(b-1)+x(b+4)=(b+4)(b-1+x)$
mossy gull
No I don't think
wraith daggerBOT
ThM
mossy gull
How did you think of that
.
Like at the start you thought already I had to factor by x
Why
nimble veldt
its just expirience. a long expirience.
nimble veldt
just to explain.
nimble veldt
there are two terms with x. two out of 5 terms. -> group them
mossy gull
Like you look and says:oh I have to do this ahah
nimble veldt
there is a b^2, so there is maybe someting like (b-a)(b-c)
mossy gull
Like I understand how to do
mossy gull
there is a b^2, so there is maybe someting like (b-a)(b-c)
Oh
I will do the most difficult expression by myself so
Of the book
I want to see if I'm ready for the tomorrow test
So I let you see that
nimble veldt
I want to see if I'm ready for the tomorrow test
good luck, but you did so much the last days, i have no doubt that you will be sucesslful.
nimble veldt
sound ok
nimble veldt
take out 2^3 instead of 2.
mossy gull
You mean factor out by 2^3?
nimble veldt
yes
mossy gull
But I have 2^2n+1
How
Maybe I don't have to factor it
But only the second and third term
nimble veldt
doesnt matter $ 2^{2n+1}=2^32^{2n-2}$
wraith daggerBOT
Sarkes_the_jack
nimble veldt
yes.
mossy gull
Ok let's try
nimble veldt
but if n>0 it is not negative.
wraith daggerBOT
Sarkes_the_jack
mossy gull
Is it fine?
nimble veldt
yes. see you the next step?
wraith daggerBOT
Sarkes_the_jack
mossy gull
Can it be?
nimble veldt
yes. (2^3 missing, but yes)
nimble veldt
oh no, -1
nimble veldt
$2^3(2^{n-1}-1)^2$
wraith daggerBOT
ThM
wraith daggerBOT
Sarkes_the_jack
nimble veldt
its is just the same.
nimble veldt
$2(2^n-2)^2=2(2(2^{n-1}-1))^2$
wraith daggerBOT
ThM
wraith daggerBOT
Sarkes_the_jack
nimble veldt
just look at $(2^n-2)^2$
wraith daggerBOT
ThM
mossy gull
Ok
nimble veldt
$(2^n-2)^2=(2\cdot (2^{n-1}-1))^2$
wraith daggerBOT
ThM
nimble veldt
$2^2(2^{n-1}-1)^2$
wraith daggerBOT
ThM
nimble veldt
yes
nimble veldt
if you have any questions just DM me.
mossy gull
I didn't understood nothing before help XD
mossy gull
if you have any questions just DM me.
Ok
By nothing I mean: what I have to use and when
Bye bye
cedar kilnBOT
mossy gull
Thx again
cedar kilnBOT
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lucid yoke
I am trying to solve this question for an assignment of mine.
It's mostly a coding problem but I am not understanding how to translate from the problem description to actual code. I am willing to learn any free package in C++/python/julia to get this done
lucid yoke
I just need help understanding how to go from the equation to actual code
cedar kilnBOT
@lucid yoke Has your question been resolved?
cedar kilnBOT
@lucid yoke Has your question been resolved?
lucid yoke
No bot, if people are not replying then it has not been solved
cedar kilnBOT
@lucid yoke Has your question been resolved?
cedar kilnBOT
@lucid yoke Has your question been resolved?
lucid yoke
Not bot, it has not
gilded elm
Not bot, it has not
question might be more appropriate for #computing-software
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cedar kilnBOT
cedar kilnBOT
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celest pecan
cedar kilnBOT
celest pecan
This is homework from my class and I have completely forgotton how to do these questions
tropic oxide
,rcw
wraith daggerBOT
cedar kilnBOT
@celest pecan Has your question been resolved?
cedar kilnBOT
@celest pecan Has your question been resolved?
lethal jackal
This is homework from my class and I have completely forgotton how to do these q...
then you should review the material given. question (a) is a purely conceptual question (okay, there's some very light geometry there) question (b) is just a torque balance, and question (c) is another conceptual one
celest pecan
part a and c are easy I just forgotten how to do the method for part b). There is not any resources my teacher has given that I can find I was just looking for an outline of some of the steps
I can try to find my own resources though so dw about it
celest pecan
.close
cedar kilnBOT
cedar kilnBOT
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abstract lily
cedar kilnBOT
acoustic shore
they factorized the numerator and denominator so that the factor which was causing the expression to become 0/0 can get eliminated
and the limit can be evaluated without 0's getting in the way
the rest is that simple algebra
abstract lily
can you explain to me how they factored?
i really dont get it
like how did the 2x^2 become 2x in the next step and what happened to -27
limpid agate
(2x² - 15x - 27) = (2x + 3)(x - 9)
cedar kilnBOT
@abstract lily Has your question been resolved?
grim lantern
for questions like this do i use pi on the calculator or 180
buoyant latch
I believe they likely result in exact values
And if not you write it in exact form
Unless the question says something like solve xxxxxx (Round to 2 decimal places)
grim lantern
I believe they likely result in exact values
when i used pi i got some long decimal but when i used 180 i got 3/4
buoyant latch
when i used pi i got some long decimal but when i used 180 i got 3/4
That’s your calculator not being in radians mode
random forge
For calculating the weight of this boulder do you use sin or cos?
random forge
It's sin right because sin is the longest line / shortest line in the triangle?
cedar kilnBOT
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random forge
@uncut veldt
I've figured out that i's actually cos. So is it 600 * 1.8 = boulder * 0.2 * cos 30 ?
cinder shard
Cos makes sense. Otherwise an angle of zero degrees would give “zero” force
However, you need to also account for angle with the 600N
random forge
I see. Is that cos60 then on the 600N side?
Otherwise they'd just cancel each other out right
<@&286206848099549185>
cinder shard
No also 30
They do cancel out
Because both are the same angle from horizontal
If the bar wasnt straight then you would need to account
random forge
so it's just 600 * 1.8 = boulder * 0,2 then?
cinder shard
Yeah
hot ether
Can someone help with me with Division
cedar kilnBOT
Can someone help with me with Division
deep pendant
sharp lotus
this channel is being used by someone else already, go to #❓how-to-get-help
sharp lotus
Can someone help with me with Division
cedar kilnBOT
@hot ether Has your question been resolved?
hot ether
No
cedar kilnBOT
@hot ether Has your question been resolved?
crimson sedge
it is the absolute value function
the absolute value converts the negative to positive
so $|-4| = 4$
wraith daggerBOT
Lixera
crimson sedge
i would assume so, because if they did not, then the equality wouldn't be correct
the | | are the usual notation for absolute value
type .close haha
cedar kilnBOT
crimson sedge
in general, you can represent the absolute value function as
[|x| = \begin{cases} \hphantom{-}x, &\quad x \geq 0 \ -x, &\quad x < 0 \end{cases} ]as a fyi
wraith daggerBOT
Lixera
crimson sedge
it makes sense because what it means is basically like
if you have a positive number then it stays positive
if you have a negative number then the thing becomes -(-4) for example which is just 4
so again, positive
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slim dome
One number is six less than three times another number. If the sum of the numbers is 38, find the numbers.
Enter the two numbers separated by a comma, with the smaller number first.
slim dome
not sure how to do this
red pumice
algebra
red pumice
a is 6 less than three times b
red pumice
when the number is 38?
a + b is 38
slim dome
gotcha gotcha
I forgot were just writing it
Okay I got that from there on do we sub one of the letters for 38?
slim dome
so in our final equation we would have 38-3b= 6?
slim dome
hmm
slim dome
what happened to the b on the left side
red pumice
we added b to both sides
red pumice
no it doesnt become squared
tawny monolith
Hello, how do I draw a graph given information about the limit? Specifically, if I know there's a vertical asymptote at a certain x value, but the limit from the right is a finite value?
tawny monolith
For example, if f(x) has a va at 9, but lim->9+ is finite
modern compass
then the graph would go to the finite number on the right. And go up/down to positive/negative infinity on the left.
untold onyx
untold onyx
do i just combine these matrices and row reduce?
modern compass
yes
untold onyx
.close
crimson sedge
cedar kilnBOT
gleaming cloud
f isn't even defined at 0 but ok
feral juniper
f isn't even defined at 0 but ok
that doesnt matter tho
gleaming cloud
If it's not defined there, it doesn't make sense to ask if it's continous there
feral juniper
I think the question should be is f at 0 continues with x -> 0
gleaming cloud
Should be if f can be made continous for an appropriate choice of f(0)
i.e. if the left and right limits are the same
And finite
crimson sedge
yeah anyways, we need OP to engage here. Clearly the function is not defined at x = 0, thus it is discontinuous there. You have to show what type of discontinuity there is at x = 0 by checking the limit of the function as it approaches 0, as giannis has stated @crimson sedge
crimson sedge
yeah anyways, we need OP to engage here. Clearly the function is not defined at ...
What does x =/= 0 at x = 0 mean? I'm confused to that part.
crimson sedge
What does x =/= 0 at x = 0 mean? I'm confused to that part.
test the function's continuity at x = 0 and everywhere else basically
cedar kilnBOT
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blazing bison
how can i prove that $\frac{x \ln x}{x^2-1} < \frac{1}{2}$ if $x>0, x\neq 1$ ?
wraith daggerBOT
пчел
crimson sedge
find the max of the lhs using calculus
south tundra
And also don't forget to show that the lhs doesn't approach infinity anywhere
cedar kilnBOT
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terse grail
hello
terse grail
how did they got the second line?
i know that
P--->Q == notP V Q
so if they used this, it needs to be
notA(x) V B(x)
stable osprey
right
but top line has notB(x)
so if that individually is true, the entire conditional is true
cursive drift
The mistake of missing a negation sign is one that you’ll never stop making as a mathematician
stable osprey
OR not A(x) like they have for vacuous truth
terse grail
The mistake of missing a negation sign is one that you’ll never stop making as a...
so the 2nd line isn't true?
terse grail
but
stable osprey
chicken butt
stable osprey
yea
you can also think of ur actual conditional in terms of p/q
where Q is (not B(x))
if Q, the conditional is true
visual berry
if gcd(a,b)=1 then -1^(a/b) is imaginary
cedar kilnBOT
if gcd(a,b)=1 then -1^(a/b) is imaginary
gritty viper
a=1, b=1
gritty viper
b isn't 1 anyways
silent finch
Since a and b are coprime, they don’t share any factors, thus a/b is not an integer
visual berry
damn