winter ivy
Thanks for your effort
#help-0
pliant wedge
lone heartBOT
odd depot
,rccw
ocean sealBOT
pliant wedge
I need help with b) and c) (fundemental theorem of calculus)
with a) its just by definition, with b) i did a substitution t = u^2
But im not sure i understand how the interval of integration is affected by this substitution
pliant wedge
I also have to calculate the derivatives of both
not sure if b) is correct thats what im asking
and for c) i don't know
last tendon
For b) you should consider the function $H(x) = \int_0^{x} f(t) dt$ and notice that $H(x^2) = G(x)$.
ocean sealBOT
Hexicle
pliant wedge
Okay, how does that help me?
last tendon
This lets you calculate H'(x) directly using the fundamental theorem of calculus
and consequently you know how to calculate H'(x^2) = G'(x)
pliant wedge
So, H'(x) = f(x) and then H'(x^2) = f(x^2) = G'(x) ?
last tendon
No. You need to use the chain rule
last tendon
I don't even know what C is asking. That's not even a complete sentence.
pliant wedge
oh right, its asking what is the minimum and maximum amount of solutions the equation F(x) = G(x) can have?
i was thinking that G'(x) > F'(x) so its increasing a lot faster but for x in (0,1) its not true and a lot can happen on that interval
last tendon
Is that actually what it's asking? I'm just a little surprised
last tendon
Well you should differentiate both sides of F(x) = G(x) consider different cases of f(t).
I just haven't seen this asked before, it's not a bad exercise, but it's new to me
pliant wedge
i still dont understand
f(t^2)(1-2t) = 0
f is never 0 since f() is always positive so the only solution is t = 1/2
is this right?
@last tendon sry for ping but u are the only one helping me rn
last tendon
I don't know what R - (0, inf) means
Is that a function with a domain where it is the reals without the interval (0, inf) or is that a function from the reals to the interval (0, inf)
pliant wedge
I don't know what R - (0, inf) means
R -> (0, inf)
sorry it should have been an arrow there
last tendon
That seems fine then
pliant wedge
I checked the solution and it says "The equation can have one or two solutions"
last tendon
There is probably a subtlety I am overlooking with the x^2 term adding a second solution but I would need a pencil and paper and I have neither right now.
I don't see it at a glance and f(x^2) (1-2x) = 0 looks right to me doing it in my head
pliant wedge
i mean i can see the problem being that we derived and we lost some solutions, but f is always positive so f(x^2) (1-2x) = 0 this will always just be x = 1/2
last tendon
I guess F'(x) = G'(x) tells you that 1/2 must be a solution, but you are asking for solutions to F(x) = G(x) and both are even functions
frosty gull
please explain how to find the factor of root twelve in the below image
frosty gull
vale wigeon
sqrt(12) = sqrt(3*4) = sqrt(3) * sqrt(4)
vague coral
$\sqrt{12} = \sqrt{4\times 3}$
ocean sealBOT
Herels
trim tendon
cartesian products
lone heartBOT
cartesian products
trim tendon
is 5. just a convention?>
trim tendon
wouldn't it be (something from A, nothing)
(nothing, something from A)
why is that equal to "nothing"
or empty set
heady pollen
the x is the cartesian product
so if we have sets A and B with a in A
then we will for example have the elements (a,b1), (a,b2), ..., (a,bn)
and this for all a in A
but since in this case A has no elements at all, we just get "nothing"
lone heartBOT
@trim tendon Has your question been resolved?
high gate
perimeter of this rectangle, isnt the answer 2 root 2 + 2 root 5?
magic arch
perimeter of this rectangle, isnt the answer 2 root 2 + 2 root 5?
it is
magic arch
what does it say?
alpine sable
textbook answer is wrong
high gate
ok thanks
noble trail
Is there even a contradiction here? I can't seem to explain which one is.
modern sedge
Yeah, there is a contradiction. Try making truth tables
alpine sable
hi! why is the friction force multiplied by x? I know that Ffr = µ*Fn
lone heartBOT
hi! why is the friction force multiplied by x? I know that Ffr = µ*Fn
@alpine sable Has your question been resolved?
alpine sable
pls help me
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
alpine sable
At what age do you study this?
first year of uni, bio engineering
regal flicker
first year of uni, bio engineering
Looks interesting
hardy tangle
which of the x is bothering you ?
ahh i see
do you know the expression of work done
in terms of change in the total kinetic energy of the system since we are talking about inelastic collision that is why we are accounting for the work done by the frictional force on the system
thus influencing the change in the kinetic energy of the system
$W=\int F \cdot dx$
ocean sealBOT
[ɸ]=1.618033988749....
hardy tangle
@alpine sable
alpine sable
ohhh so F here is our normal force?
alpine sable
oh right
hardy tangle
cause the work done is by the frictional force
alpine sable
wait so why do i have equate the kinetic energy to the potential + work done?
unkempt sundial
collision is not elastic so kinetic energy is conserved
alpine sable
waitttttt so is potential energy + work done equal to the KE?
unkempt sundial
yah sure
alpine sable
no my brain hurts
so initial KE = final KE
so i get why we have the potential energy
but the work is still confusing
hardy tangle
but the work is still confusing
any change in the kinetic energy can be accounted by the work done on the system by any external force such as frictional forcce in this case
alpine sable
aaaaaahhhhh i think i understand so work done is the kinetic energy of the final system
thank you guys for your help!!!
unkempt sundial
thank you guys for your help!!!
You're welcome anytime, but would probably get better help in a physics server, can be found in #old-network
oh you already asked there 💀
slim juniper
yoyo
slim juniper
A rectangular strip has length A and width B. When folding the strip, the overlap of its ends formed a square of side B and the result of the fold was a pentagon without any hole in the center, as indicated in the figures. What is the a/b ratio?
copper delta
do u understand now?
lone heartBOT
@slim juniper Has your question been resolved?
alpine sable
is this correct?
lone heartBOT
is this correct?
lone heartBOT
lone heartBOT
Available help channel!
slim gazelle
5 and 6
slim gazelle
<@&286206848099549185>
alpine sable
What
exotic belfry
echo socket
What is your question?
modern sinew
<@&286206848099549185>
tawny condor
Read #❓how-to-get-help
This channel is taken, and you're not supposed to ping helpers straight away
modern sinew
oh because I saw this person ping so i thought i could
lone heartBOT
@slim gazelle Has your question been resolved?
lone heartBOT
@slim gazelle Has your question been resolved?
uncut epoch
lone heartBOT
uncut epoch
So I’m not sure what to do with this step
vale wigeon
do you want to find f'(a) for arbitrary a or do you want to find f'(0) specifically
either way you would plug shit into the limit defn regardless. there's no choice to be made yet
lone heartBOT
@uncut epoch Has your question been resolved?
cloud mulch
This is probably a mistake i have made due to not paying attention, but I got 2 out of this, while the answer cannot be 2. Here is my work (only took me 20 goddamn minutes to put togheter digitally like this 😕 )
placid zinc
Line 3:
a √3 should actually be 3
Your method works, but it might be easier to start by rationaling the denominator on the first fraction instead, especially since you end up rationalizing in the end
lone heartBOT
@cloud mulch Has your question been resolved?
spiral dirge
y = secx - tanx/sec x + tan x , what is dy/dx
lone heartBOT
y = secx - tanx/sec x + tan x , what is dy/dx
spiral dirge
what?
raven rover
You should know to put parentheses man
spiral dirge
ok (sec x - tan x)/ (sec x + tan x)
raven rover
!status
lone heartBOT
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
between 2 and 3
raven rover
spiral dirge
ah
so first,
i simplified y,
rationalise with (sec x - tan x) on numerator and denominator,
you get y = (secx - tan x)^2
turned it into
1 + 2 tan sq x -2 tanx/cos x( as sec x isnt easily differentiable)
upon differentiation,
you get 0 + 4secxtanx -2cos^2/cos^3
and the answer is far off
which is 2 sec x(2tan x - 1)
raven rover
so first,
i simplified y,
rationalise with (sec x - tan x) on numerator and den...
Simplify your answer
spiral dirge
i turn 1 into sec^2 - tan ^2?
that seems like unsimplifying..
<@&286206848099549185> , could you please explain how (2tan - 1) turns into (sec - tan )^2
tacit arch
<@&286206848099549185> , could you please explain how (2tan - 1) turns into (sec...
Have you learned trig identities
spiral dirge
yes
tacit arch
i turn 1 into sec^2 - tan ^2?
Find the one that has both sec and tan
spiral dirge
sedc^2- tan ^2 = 1?
tacit arch
so first,
i simplified y,
rationalise with (sec x - tan x) on numerator and den...
Did you use that at this step?
When you say "simplified y"
spiral dirge
i did..
spiral dirge
which is 2 sec x(2tan x - 1)
..
ocean sealBOT
tacit arch
so first,
i simplified y,
rationalise with (sec x - tan x) on numerator and den...
Does your expansion of (sec(x) - tan(x))^2 match
tacit arch
this is the answet
What is? You're referring to your work and the solution both as "the answer"
spiral dirge
You said that was the answer
thats the answer in the textbook
spiral dirge
i got 2sec(2tan - 1)
this is what i got
tacit arch
Write your answer in terms of sec and tan
And where did you do this
spiral dirge
And where did you do this
i barely used anything but sec and tan lol
spiral dirge
i got 2sec(2tan - 1)
plus this is in terms of sec and tan only
tacit arch
What is? You're referring to your work and the solution both as "the answer"
You're still doing this
spiral dirge
(sec x - tan x)/ (sec x + tan x)
i simplified y,
rationalise with (sec x - tan x) on numerator and denominator,
you get y = (secx - tan x)^2
turned it into
1 + 2 tan sq x -2 tanx/cos x( as sec x isnt easily differentiable)
upon differentiation,
you get 0 + 4secxtanx -2cos^2/cos^3
and the answer is far off
which is 2 sec x(2tan x - 1)
lone heartBOT
@spiral dirge Has your question been resolved?
tacit arch
(sec x - tan x)/ (sec x + tan x)
i simplified y,
rationalise with (sec x - tan x...
What is 2sec(x) (2tan(x) -1? The answer or your work?
tacit arch
Write your answer in terms of sec and tan
You said you did this but I don't see it
spiral dirge
What is 2sec(x) (2tan(x) -1? The answer or your work?
that is my work
tacit arch
this is the answet
What does this mean then
tacit arch
i didnt get the answer
Show the answer
spiral dirge
it is what i got
it isnt the actual answer
the answer to the problem was 2sec(sec - tan)^2
lone heartBOT
@spiral dirge Has your question been resolved?
spiral dirge
<@&286206848099549185>
its been almost 2 hours.
ah screw it i ll just go to bed.. its 3 am
lone heartBOT
@spiral dirge Has your question been resolved?
true acorn
is anybody able to help me with this question?
lone heartBOT
is anybody able to help me with this question?
willow patio
Hmmm, well when you are finding volume you need three dimensions (length, width and height). Correct @true acorn ?
And problem a) wants possible dimensions.
What three things multiply to be $4x^3 - 21x^2+29x-6$
ocean sealBOT
jpsz
willow patio
Yes!
true acorn
but idk how
willow patio
Ah, well, do you remember the (x-k) rule?
royal socket
RRT 
true acorn
no clue
i remember doing something like this
i have it infront of me, but i just cant remember i cant connect the dots
willow patio
when you have a factor (x-k) you can plug in k to the equation (for x) and find the whole equation to equal 0
trail remnant
oh, you could test values of x and see if any equal 0. but i cant think of a way to work this out without a calculator
willow patio
So, can you think of a number that you would plug in for x to get $4x^3 - 21x^2+29x-6 = 0$
ocean sealBOT
jpsz
trail remnant
then if you find V(x) = 0 for an x then its a factor, making polynomial division
true acorn
do i need to do long division tp find a factor
wait i could just plug into desmos right
willow patio
Yup, so can you divide x-2 out of the polynomial?
trail remnant
ah, now you can use x = 2, so you want to do (x-2)/(4x^3-21x^2+29x-6)
foggy current
According to a theorem (I forgot it's name), if a is is a root of a polynomial, then the polynomial is divisible by x-a
trail remnant
then from the x^2 polynomial uses quadratic formula
true acorn
oh shit i think im remembering now
trail remnant
According to a theorem (I forgot it's name), if a is is a root of a polynomial, ...
factor theorem :)
torn elk
According to a theorem (I forgot it's name), if a is is a root of a polynomial, ...
rational root theorem?
true acorn
factor therem?
foggy current
rational root theorem?
I don't think we need the name for this
torn elk
the name is useful to find information when needed anyways
willow patio
Ok, ok people. Give @true acorn a chance to solve this.
Maclain, can you divide 4x^3-21x^2+29x-6 by x-2?
true acorn
yeah im doing synthetic division rn
willow patio
Cool!
proven leaf
According to a theorem (I forgot it's name), if a is is a root of a polynomial, ...
Remainder Theorem? :))
foggy current
Oh yeah
willow patio
Awesome that's the answer to a!
Now, looking at b what are the restrictions that keep the volume from being negative
willow patio
when does it stop being negative?
royal socket
bc x=1 = 0
that is some truth
willow patio
hm, really? when you plug in 1 you get 0?
foggy current
the volume will be negative if an odd number of factors are negative
true acorn
yeah when i plug x=1 i get 0
willow patio
(1-2)(1-3)(4(1)-1) = (-1)(-2)(3) = 6?
foggy current
are you able to write out the conditions for V to be negative according to the hint above?
true acorn
(1-2)(1-3)(4(1)-1) = (-1)(-2)(3) = 6?
oh shoot my bad
should i just keep doing trial and error
willow patio
well, 2 gives you a zero right?
so that is gonna be one of your boundary points.
What other points give 0?
true acorn
x-3 and 4x-1
willow patio
So what values of x?
willow patio
Yup, so what ranges are viable and which aren't?
willow patio
well we know that 1 is positive right (6)
willow patio
YEA!
true acorn
i think i remember now
WOOOOOOO
holy
thanks for refreshing my memory
that helped so much
holy lets go
youre the best fr
willow patio
Np, glad I could help!
tidal bane
So im guessing this is not possible XD
lone heartBOT
So im guessing this is not possible XD
naive valley
So im guessing this is not possible XD
this is all valid if 2x+1 > 0
but you also need to consider the case 2x+1 < 0
willow patio
but since he just defined it as x>2, I think he is good, no?
naive valley
well that work implies that if 2x+1 > 0, then x > 2
it doesn't mean that x > 2 in the other case
the first line doesn't imply -x + 2 < 0 if the denominator is negative
willow patio
Sure, but if 2x+1 <0 you still perform the same operation and get the same answer, right?
willow patio
ah, gotcha. Ya, you are right
tidal bane
wait I dont get it ,what do you mean
2x + 1 < 0
then
-x +2 >0
willow patio
because that implies that 2x+1 is negative so when you multiply it the < becomes >
tidal bane
I still dont get is
2x + 1 < 0 okay this means 2x+1 is negative so what is the problem
naive valley
I still dont get is
2x + 1 < 0 okay this means 2x+1 is negative so what i...
to see the problem, can you explain what you did in order to go from line 1 to line 2?
tidal bane
I multiplied bot h sides with 2x+1
naive valley
yes
and what happens if you multiply both sides of an inequality by a negative number?
tidal bane
the sighn changes ?
naive valley
the direction of the inequality changes
the < becomes >
so your second line would be wrong if the denominator was negative
tidal bane
interesting I never saw this interaction
naive valley
easiest to see with some specific numbers
of course 1 > 0 is true
what happens if you multiply both sides by -1
if you didn't change the inequality direction you would get -1 > 0, which is obviously false
naive valley
so usually in situations like this where you have a fraction in an inequality and you want to multiply both sides by the denominator, you consider two cases
tidal bane
naive valley
yep, that's the correct work in the case where 2x+1 < 0
so now you have to interpret your results in the two cases
tidal bane
so I cant just say x < 2 I have to do both
-x + 2 < 0
2x + 1< 0
naive valley
so I cant just say x < 2 I have to do both
-x + 2 < 0
2x + 1< 0
right, check out the graph of the function
there are two regions where it's negative
x > 2
and x < something (not 2)
you have to work out the latter
tidal bane
okay I got it now I just dont see how there are 2 instance where its negative isnt only one line in negative ?
naive valley
okay I got it now I just dont see how there are 2 instance where its negative is...
well everything over on the left is negative
and then everything to the right of x=2 is negative
but you can see for example that at x=1 it's positive
so there's some interval in the middle where it's positive
tidal bane
and then everything to the right of x=2 is negative
thanks I got it now !! will have to do few more but I got the idea 👍
swift sequoia
Hi, can somebody help me out with this?
lone heartBOT
Hi, can somebody help me out with this?
proven rune
so wtf
just subsitute x = -4y-r/3
in 2nd equation
ull get a quadratic
in terms of y
use D=0 for tangency
random gorge
what is the discriminant?
no need to that
you can find the circle center and then using that radius is perpendicular to tangent line in the tangent point
proven rune
you can find the circle center and then using that radius is perpendicular to t...
yea u can also do this
swift sequoia
you can find the circle center and then using that radius is perpendicular to t...
well, the centre is (-5, -13) and radius = 10
then what?
random gorge
well, the centre is (-5, -13) and radius = 10
then calculate the distance of center from the given line
do you know the formula ?
swift sequoia
the perpendicular distance?
random gorge
yep
swift sequoia
from where to where?
random gorge
from the center to your line
swift sequoia
but I need to make that line tanget to the circle by changing the parameter r on the line equation
I can only move the line
random gorge
use the formula with r
and then because it should be size of radius
you can solve for r
swift sequoia
do you mean this?
random gorge
I struggled a lot with that one
your welcome
swift sequoia
your welcome
can you help me with another one?
random gorge
can you help me with another one?
if i know the solution why not
swift sequoia
I need to find the circle that passes through these points
swift sequoia
if i know the solution why not
thx ly
random gorge
I need to find the circle that passes through these points
ok
so you know that the perpendicular bisector of the chords of circle pass throug its center
random gorge
do you know what is a perpendicular bisector ?
swift sequoia
not really
random gorge
ok
pale coral
@swift sequoia
Do you know the general equation of a circle?
pale coral
Yes.
First, create 3 equations and form a triple simultaneous equation.
For the first equation, substitute in the first point into x and y.
Repeat with the next two points with the next two equations.
Now, use algebra and/or simultaneous equations to solve for h, k, and r.
random gorge
For the first equation, substitute in the first point into *x* and *y*.
Repeat ...
yeah this is a good solution too
pale coral
Substitute your h, k, and r values into the formula to find your general equation.
swift sequoia
First, create 3 equations and form a triple simultaneous equation.
(0-h)^2+(0-k)^2=r^2
(0-h)^2+(5-k)^2=r^2
(5/2-h)^2+(5-k)^2=r^2
like this?
pale coral
(0-h)^2+(0-k)^2=r^2
(0-h)^2+(5-k)^2=r^2
(5/2-h)^2+(5-k)^2=r^2
like this?
Yes.
Now solve for the three unknowns.
swift sequoia
ok, then solve for the rest
pale coral
Once you have all three, substitute them back into (x-h)^2+(y-k)^2=r^2 to find the equation.
swift sequoia
Now solve for the three unknowns.
yes, thank you
swift sequoia
Once you have all three, substitute them back into (x-h)^2+(y-k)^2=r^2 to find t...
thank you so much
pale coral
thank you so much
No problem. Is your question resolved?
swift sequoia
I think it is
pale coral
Glad to be of help.
swift sequoia
.close
dusk moat
eager walrus
I need help with this problem
lone heartBOT
I need help with this problem
placid zinc
Can you solve that for k?
random gorge
it has to be possible i copied it exactly from a test
maybe you can multiple x^5 in two sides and write it (3x)^5 = e ^kx
then get a ln from both sides and then solve it
i dont know if this works
or not
placid zinc
I know that's the info you have.
Do you know the steps needed to solve that for k?
eager walrus
I can
placid zinc
k = ln(243x⁵) / x
eager walrus
right, but i don't know what to do with that
placid zinc
I thought that would be more illuminating, haha
We can do this:
k = 5ln(3x)/x
k = 5ln(3)/x + 5ln(x)/x
random gorge
We can do this:
k = 5ln(3x)/x
k = 5ln(3)/x + 5ln(x)/x
cant we just sketch its graph ?
and see what is the range of our function
placid zinc
Yeah. Basically that. But I assume we can't just use tech
placid zinc
When x = 1, k = 0
When x approaches inf, k approaches 0,
So there's a maximum somewhere
random gorge
When x = 1, k = 0
When x approaches inf, k approaches 0,
So there's a maximum s...
yeah
random gorge
i mean we can aproximate the graph
how to aproximate the graph is out of my knowledge but if you can the problem is solved
sharp island
can help me with pie
lone heartBOT
can help me with pie
wary stream
can help me with pie
What about $\pi$?
ocean sealBOT
dldh06
sharp island
circumference
wary stream
What about it?
Do you have a question/problem to ask?
No one can read your mind, if you just state "can someone help me with pie".
sharp island
no just like main things
sharp island
only circumference
wary stream
You're not understanding, what about circumference?
sharp island
yea
wary stream
What about it
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-area-circumference/v/circles-radius-diameter-and-circumference
Btw google stuff if you don't know what it means, like this
sharp island
ty
lone heartBOT
Available help channel!
noble frost
is using geometry the only way to find the number of possible tangents on a function from a certain point
noble frost
when the function is a transcendental one
acoustic beacon
is using geometry the only way to find the number of possible tangents on a func...
We can use differentiation . . . ? I don't think I get the question.
placid zinc
What is a transcendental function?
acoustic beacon
is using geometry the only way to find the number of possible tangents on a func...
I mean, if the function is differentiable the number of possible tangents from a certain point are basically infinite.
noble frost
thats not true
acoustic beacon
thats not true
See.
noble frost
but you cant
acoustic beacon
You can use smaller and smaller increments and get a new tangent every time.
acoustic beacon
I said if the function was differentiable.
placid zinc
Is that not 200 different tangents all taken from different points?
acoustic beacon
It's possible.
noble frost
no
what about a cubic
thats a differentiable function
but the number of possible tangents is limited
acoustic beacon
acoustic beacon
You said from a certain point.
noble frost
??
acoustic beacon
function from a certain point
noble frost
yeah like (1,2)
u have a set of points
ur misunderstanding
the question
im asking rn
placid zinc
This question has gone a weird direction. What did you want to know? Other methods from geometry?
placid zinc
Oh I see
noble frost
and if the function is a polynomial i can prove it algebraically
acoustic beacon
Oh I got it.
placid zinc
The number of tangents that pass through a certain point
acoustic beacon
Yeah.
noble frost
so this isnt my question
acoustic beacon
Yeah I get that now.
acoustic beacon
so this isnt my question
Sorry had to got for a bit. But basically you find the equation for the tangent line of the function and then plug in the x and y values of the specific point and solve for the remaining variable.
Ping if you didn't understand.
lone heartBOT
@noble frost Has your question been resolved?
noble frost
Sorry had to got for a bit. But basically you find the equation for the tangent ...
that works if you have a calculator
noble frost
look at log(x)
you cant solve the eq without a calculator
ill just ask in other sites
.close
lapis gyro
Person's base swimming speed is 5 mph
person can swim 4 miles up stream in the same amount of time that he can swim 16 miles down stream.
The homework assignment wants you to use direct and inverse variation
I can solve the problem using a system of equations but I have no idea how to solve the problem using k=xy and y=k/x
lapis gyro
So far I got
4=(5-c)t
16=(5+c)t
for the person swimming up and down stream respectively
so what is the rate of water?
Also I am trying to set each side equal to t and solve for c that way but it doesnt seem to be working
wait i am a moron
i still need help
but i just figured out what i was doing wrong with the t part
.close
hidden pier
how do you find the anti-derivative of sqrt(2/x)
lone heartBOT
how do you find the anti-derivative of sqrt(2/x)
vale wigeon
how do you find the antiderivative of x^p?
ocean sealBOT
🙛𝕍ѳrtєx🙙
ocean sealBOT
🙛𝕍ѳrtєx🙙
hidden pier
but multiplied by sqrt2
lapis gyro
but multiplied by sqrt2
i am just an idiot...college math has rotted my brain so i cant do basic algebra anymore
hidden pier
i am just an idiot...college math has rotted my brain so i cant do basic algebra...
nah you're good
ok so this is the same as $\sqrt2\cdot x^{-1/2}$
lapis gyro
nah you're good
when you do trig and stats all day long and you just use a calculator for all of it the simple stuff slips by
ocean sealBOT
🙛𝕍ѳrtєx🙙
vale wigeon
yes it is
lapis gyro
thank you for your help i am good
hidden pier
got it ty Ann!
hidden pier
when you do trig and stats all day long and you just use a calculator for all of...
yeah fair, makes sense
.close
final totem
What's the thing with these again? You just write them in the form that makes them equal?
final totem
Like 16^x = 2^4x or something?
vale wigeon
yes like that
heady void
why
surreal meadow
why what
surreal meadow
these are isosceles triangles
heady void
I don;t get it
surreal meadow
would you know what the angle BCD is?
what can you say about the line segments BC and CD?
surreal meadow
and BC and CD are parallel
perpendicular
but yes to the others
seeing as those are right triangles and isosceles, you can deduce the triangles are 45 45 90 triangles
you should be able to figure out the side lengths from this alone
junior crystal
I have no clue
lone heartBOT
I have no clue
vapid shuttle
What does it mean for a function to be odd?
Can you give me an example of an odd function?
junior crystal
f(x) = x
vapid shuttle
Why is that an odd function?
junior crystal
it holds for any x value
vapid shuttle
What holds?
alpine sable
What is the definition of an odd function, to you?
junior crystal
the equation, in the domain of f it will hold for x and -x
vapid shuttle
That is not what it means to be an odd function, I don't know what you mean by "it holds"
junior crystal
thats what my notes say, im not really sure ig
vapid shuttle
I think you are forgetting a key piece
median oar
What do you think your notes mean?
vapid shuttle
an odd function, has the property f(-x)=-f(x)
Can you tell me what this means?
your function, y=x, was an odd function, because it has that property
But what does that property really mean
in simple terms
vapid shuttle
Basically, the function is unchanged if you rotate it 180 degrees about the origin. Whatever value y is to the right of the y-axis, it is the negative version of that the same distance away to the left of the y-axis
,w plot y=x
ocean sealBOT
vapid shuttle
for example
f(1)=1
so f(-1)=-1
you can think of taking the function on the right hand side of the y-axis, and just flipping it about the y, and then the x- axis's and that will be what you get on the left hand side of the y-axis
so another example
,w plot y=x^3
ocean sealBOT
vapid shuttle
can you see what it means to be odd?
junior crystal
yes, its symmetric around the origin
so rotating it 180 degrees maps the graph back onto itself
vapid shuttle
so looking back here
what do you know about the value of the integral of f(x) from say -2 to 0
ocean sealBOT
vapid shuttle
is the area on the left the same as the area on the right? (over symmetric bounds)
or is it the negative version of the area on the right?
junior crystal
shouldnt it be negative since its below
median oar
Remember that $\int_a^bf(x)dx=\int_a^cf(x)dx+\int_c^bf(x)dx \forall c\in [a, b]$
vapid shuttle
yes, it should
ocean sealBOT
Frosst
vapid shuttle
shouldnt it be negative since its below
so, the value of $\int_{-2}^{0} f(x) dx = ?$
ocean sealBOT
AustinU
junior crystal
-5
vapid shuttle
and the value of $\int_{0}^{2} f(x) dx = we know is?$
ocean sealBOT
AustinU
junior crystal
5
vapid shuttle
you didn't finish answering my second question about the last question
vapid shuttle
**AustinU**
?
junior crystal
it is the same isnt it
junior crystal
its just being done seperately in the first one
junior crystal
theyre symmetric around y axis
junior crystal
yes
junior crystal
for this one, since the integral from 0 to 10 = 4
from -10 to 0 it would also be 4 right?
vapid shuttle
yes
junior crystal
then adding the sum of that would be 8
vapid shuttle
yes
junior crystal
okay thank you, ima do some more practice on them
vapid shuttle
The two things that you just realized here is
the integral from -a to a of an odd function is zero
and the integral from -a to a of an even function is 2 * the integral from 0 to a
these are nice properties to know
good work!
lone heartBOT
vapid shuttle
thank you, you should get a raise
perhaps an 100% raise. 0+100% (0) = 0 
lone heartBOT
Available help channel!
unique peak
not really a math question, but it has statistics in mind so i guess it fits to ask
unique peak
so im writing the conclusions for our research paper
and i wanted to follow it up with a mention of the results
which of the two tables do i talk about?
lone heartBOT
@unique peak Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
obsidian marten
hi, sorry for the noob question but where is the modus button on the sharp calculator? i need to calculate stuff like 23%7 etc, but the 2nd function % gives me ERROR 1
obsidian marten
but when i type 27 then press 2ndF % it gives me ERROR 1
surreal meadow
oh i see
obsidian marten
is there a function for that or do i need to do it manually? e.g. 23-(3*7)
surreal meadow
i’m not sure, i don’t know this calculator
but something with small numbers like these should be relatively easy to do manually
obsidian marten
true was looking for a lil speed boost hehe
thanks for ur time and help ❤️
.close
grizzled zephyr
i have a question
lone heartBOT
i have a question
grizzled zephyr
do you have a written problem statement?
its on by book but it looks exactly like this
the answer is 60 anyways
but i was wondering why
doesnt central angle = 1/2 arc
vale wigeon
no, the central angle equals the arc itself,
but also with this diagram it is impossible to tell that angle P is central
lone heartBOT
@grizzled zephyr Has your question been resolved?
grizzled zephyr
.close
lone heartBOT
lone heartBOT
Available help channel!
young ore
lone heartBOT
young ore
im stuck here. No idea how to start
stable pecan
Are you familiar with derivatives and integrals?
stable pecan
I see
I will suggest to review how position, displacement, velocity and acceleration are related using derivatives and integrals
As this will be required information to proceed studying further Kinematics
barren shuttle
For now note that velocity is the derivative of position and acceleration is the derivative of velocity
young ore
I will have a look into that but i was hoping for someone to help me solve the question as I need them for tomorrow
stable pecan
It's difficult to understand the solutions with clarity if you aren't familiar with these concepts. However, to proceed here, you should find the integral of v to get position s
young ore
i've worked it out just to confirm from you guys if its right
s = 3t^3 - 6t^2 + 5t - 7
this was my answer
stable pecan
This is correct. Good job!
young ore
thank you very much
its really not that hard once I understood the basics
but thanks again for the advice 🙂
.close
lone heartBOT
lone heartBOT
Available help channel!
craggy token
Determine all natural numbers n such that it is possible to cover an n x n board with T tetrominos and odd number of O tetrominos with no overlaps.
craggy token
How would I solve this one?
upbeat hornet
What have you tried?
craggy token
I've tried to find the configurations, but the one I ended up with use even numbers of O tetrominos
I'm still trying to find the configurations
lone heartBOT
@craggy token Has your question been resolved?
upbeat hornet
I've tried to find the configurations, but the one I ended up with use even numb...
what size board did you do them on?
upbeat hornet
I've tried to find the configurations, but the one I ended up with use even numb...
try a 6 by 6 board
craggy token
Ah, alright.
upbeat hornet
Determine all natural numbers n such that it is possible to cover an n x n board...
is there any restriction on T tetrominoes?
craggy token
No, there aren't
I've found a configuration using a 6 x 6 board
Using 5 O tetrominoes
upbeat hornet
Using 5 O tetrominoes
can you extend this to bigger boards?
upbeat hornet
It also works with 10 x 10
Any more? You should start to see a pattern
upbeat hornet
I've found a configuration using a 6 x 6 board
(generalizing this configuration)
craggy token
6 x 6, 10 x 10, 14 x 14
I'm guessing it works when n = 4k + 2 for natural numbers k
(just a guess)
upbeat hornet
I'm guessing it works when n = 4k + 2 for natural numbers k
If you found the configurations for those, you can form a proof
upbeat hornet
I'm guessing it works when n = 4k + 2 for natural numbers k
what about k = 0?
upbeat hornet
I'm kind of confused, sorry.
Could you put your configurations here?
craggy token
Sorry if it’s kind of messy
upbeat hornet
Sorry if it’s kind of messy
just needs to be clear enough to understand
craggy token
Sorry if it’s kind of messy
If I extend this board to 10 x 10, i can replace any 4 x 4 square I see with those 4 T tetrominoes
upbeat hornet
Yes, but are there any gaps?
upbeat hornet
yes
craggy token
no there aren't
upbeat hornet
no there aren't
then can you draw the configuration for a 10x10 board?
craggy token
Alright, hold on.
upbeat hornet
because this is to confirm a describable pattern
craggy token
My thought is that, for an (4k + 2) x (4k + 2) board, I can replace any 4 x 4 i see with those 4 tetrominoes, and it'll leave an (4k + 2) x (4k + 2) L-shape that I can fill with odd number of O tetrominoes
upbeat hornet
No, there aren't
just realized, if there’s no restriction, then can there be 0 T tetrominoes?
craggy token
Yes
upbeat hornet
then it’s much easier to prove that n = 4k + 2 can be filled
craggy token
for n = 4k + 2 the board will have an area of (4k + 2)^2 = 16k^2 + 16k + 4 = 4(4k^2 + 4k + 1) which is divisible by 4 (the area of an O tetromino), so we would need 4k^2 + 4k + 1 number of O tetrominoes, which is clearly odd
Is that what you mean?
assuming there are no T tetrominoes
upbeat hornet
for n = 4k + 2 the board will have an area of (4k + 2)^2 = 16k^2 + 16k + 4 = 4(4...
the idea is right
but being pedantic, I will point out that the area being divisible by 4 doesn’t necessarily imply that it can be filled by O tetrominoes
for example, 1 x 4 rectangle
upbeat hornet
for n = 4k + 2 the board will have an area of (4k + 2)^2 = 16k^2 + 16k + 4 = 4(4...
other than that, this is correct
craggy token
how about odd n and n = 4k?
upbeat hornet
have you tried proving/disproving fillableness for n = 1 and n = 3 and n = 4? small cases are easier
craggy token
yeah
upbeat hornet
can you extend those proofs to bigger numbers?
craggy token
n = 1 clearly can't, because we have a 3 x 1 and 2 x 2 tetrominoes
n = 3 also can't because a 3 x 1 tetromino and 2 x 2 tetrominio will leave no room for other tetrominoes, and will leave gaps.
n = 4 also can't because we would require even number of O tetrominoes (even 0, if we are using 4 T tetrominoes)
craggy token
can you extend those proofs to bigger numbers?
how can I do it?
upbeat hornet
or you can prove the simpler/weaker case of having no T tetrominoes
upbeat hornet
what have you got?
craggy token
I'm using the idea of the areas again.
for odd n, i can prove simply for n = 1 and n = 3 that it does not work. For odd n >= 5, I can say that n = 2k + 1 will have an area of 4k^2 + 4k + 1. I can try to cover it with O tetrominoes and T tetrominoes, but it will always leave gaps that can't be filled (for example, an L shape with dimension 1 x (2k + 1)).
for n = 4k, i can say that it will be filled with T tetrominoes and no O tetromino at all, or even number of O tetrominoes, which defies the question's requirement.
is it good enough?
i'm not sure for odd n >=5 though
upbeat hornet
I'm using the idea of the areas again.
for odd n, i can prove simply for n = 1 a...
just realized, for odd n, you don’t even have to consider gaps: just use divisibility by the areas of tetrominoes
upbeat hornet
I'm using the idea of the areas again.
for odd n, i can prove simply for n = 1 a...
for n = 4k, there is one last hole to fill in the proof(actual, not pedantic): how do you know the T tetrominoes can’t make any other square than 4 x 4?
craggy token
what do you mean? like can't it make a square with other dimension?
upbeat hornet
what do you mean? like can't it make a square with other dimension?
like what if it can make 6 x 6 square? then your claim wouldn’t be valid for 4n
lone heartBOT
@craggy token Has your question been resolved?
upbeat hornet
how would i tackle that problem..
you could consider different arrangements of T tetrominoes
radiant dirge
$x^2 - x \equiv 31 (mod 3025)$\
here's what ive done:
- used chinese remainder theorem to split into 2 equations
$$x^2 - x \equiv 31 (mod 121)$$
$$x^2 - x \equiv 31 (mod 25)$$
both of the equations can be transformed into this
$$(x-6)(x+5) \equiv 1 (mod 121)$$
$$(x-3)(x+2) \equiv 0 (mod 25)$$
ocean sealBOT
ta
vale wigeon
first one looks useless
radiant dirge
I can see that 6 + 5 = 11 and 3 + 2 = 5 but idk whats next
vale wigeon
\pmod{3025} btw
anyway i think you may be best off completing the square here
so like
x^2 - x = x^2 + 120x = (x+60)^2 - 60^2
mod 121
,calc (31+60^2) mod 121
ocean sealBOT
Result:
1
so (x+60)^2 ≡ 1 (mod 121)
and then
x^2 - x = x^2 + 24x = (x+12)^2 - 12^2
,calc (31 + 12^2) mod 25
ocean sealBOT
Result:
0
so you have (x+12)^2 ≡ 0 (mod 25)
radiant dirge
wait can you explain what are you doing
radiant dirge
x^2 - x = x^2 + 120x = (x+60)^2 - 60^2
i understand this
vale wigeon
completing the square
radiant dirge
,calc (31+60^2) mod 121
idk what this is for
vale wigeon
your mod 121 equation rewrites as $(x+60)^2 - 60^2 \equiv 31 \pmod{121}$
ocean sealBOT
Ann (glomed)
radiant dirge
oh that makes sense now
radiant dirge
,calc (31 + 12^2) mod 25
here you do the same trick but shouldnt it be 1
vale wigeon
whats "it"
radiant dirge
31
like (1 + 12^2) mod 25
nvm
so now we have $$(x+60)^2\equiv 1 \pmod{121}$$ $$(x+12)^2\equiv 0 \pmod{25}$$
ocean sealBOT
ta
radiant dirge
x + 12 should be dividable by 5 and x + 60 by 11?
from this i got x = k28 k=1,2,...
and its wrong lol
upbeat hornet
$x^2 - x \equiv 31 (mod 3025)$\\
here's what ive done:
1) used chinese remainder...
I remember helping someone with this exact question, what we did was to reduce down to mod 5 and mod 11, try out all possible x, then go back up to mod 25 and mod 121, and then combine back to mod 3025
radiant dirge
how would you reduce to mod 5 and mod 11
radiant dirge
oh
radiant dirge
thats what i got
upbeat hornet
so have you solved it for mod 25 and 121 yet
radiant dirge
im trying to solve for 121
upbeat hornet
what did you get for mod 11
radiant dirge
i currently have (x+59)(x+61) congruent 0 mod 121
radiant dirge
**ta**
cause i used this equation
so this means either x+59 or x+61 divides 121 so x = 60 or x = 62?
upbeat hornet
I think so
upbeat hornet
want: x^2 - x congruent to 9 mod 11
0(10) = 0, 1(0) = 0, 2(1) = 2, 3(2) = 6, 4(3) = 1, 5(4) = 9, 6(5) = 8, 7(6) = 9, 8(7) = 1, 9(8) = 6, 10(9) = 2,
so x congruent to 5 or 7 mod 11
which agrees with x = 60 mod 121 or x = 62 mod 121
upbeat hornet
62*4 = 3 mod 5
then what is it mod 3025
radiant dirge
i completely dont understand what you did there xd
upbeat hornet
i completely dont understand what you did there xd
reduced mod 11, then tried all x(x-1) for integers mod 11
inelegant but simple and the first thing I thought of
upbeat hornet
i completely dont understand what you did there xd
but your method looks much better
radiant dirge
why only try integers <= 11?
upbeat hornet
why only try integers <= 11?
because reduced mod 11
radiant dirge
that i get
but what if there is integer > 11 that satisfied x^2 - x congruent to 9 mod 11
oh nvm
you can write x as (11k + r)
so now I have
x ≡ 3 mod 5
x ≡ 60 or 62 mod 121
it seems x can only be equal to 60 or 62
bruh why is this so difficult
nvm
121*(3+10k) + 60 or 121*(10k+1) + 62 would satisfy both equations right
<@&268886789983436800> pls
night geyser
Sigh
radiant dirge
thank you!
ok so i finally conclude that there are 6 solutions <= 3025 which look like this: 121*(3+10k) + 60, 121*(10k+1) + 62 and k=0,1,2
thanks everyone who helped
.close
rustic lily
If the braking force is constant does that mean acceleration is constant?
wind cloak
Yes
wind cloak
Because F = ma
Mass is a constant
And if Force is constant
That means acceleration is constant
limpid turret
If the braking force is constant does that mean acceleration is constant?
What is breaking force?
ocean hawk
"braking", probably
alpine sable
hi