@ebon heath Has your question been resolved?
#help-0
lone heartBOT
carmine leaf
Jesus went to the bank to exchange his money for coins. He had bills of $5, $2, $1, and $0.50. In total, Jesus had 795 coins. When counting them, he noticed that the number of $5 coins was one-third of the number of $2 coins, half of the $1 coins, and double the number of $0.50 coins. How many $2 coins did Jesus receive from the bank?
carmine leaf
pls help
lost osprey
are you stuck with the start or are you maybe struggling in the middle steps of algebra
glacial raptor
@carmine leaf ??
carmine leaf
are you stuck with the start or are you maybe struggling in the middle steps of ...
im stuck in every way that its possible to think right now
I did that
lost osprey
i see
ok rather than defining 5 = x, 2 = y, etc
try doing, let x equal the number of $2 coins
because thats what we're solving for
in fact
we dont need any other variables
can you see why?
lost osprey
i didnt look at the right mb
ill db check
to see if problem wrong
oo ok
so
for example
when it says the # of $5 coins is 1/3
the number of $2 coins
it would be 3x instead of x/3
i believe
mm but doing that still gives a decimal
this is a pretty simple problem so im more inclined to believe the question is wrong, but i could always be wrong
lone heartBOT
@carmine leaf Has your question been resolved?
carmine leaf
this is a pretty simple problem so im more inclined to believe the question is w...
yeah it must be wrong
i mean i tried to solve it in different ways and still got decimals
lost osprey
yeah
you could ping a helper once to see if they could figure something
or just close
ur choice
carmine leaf
<@&286206848099549185>
small ice
yes
simple wigeon
i mean i tried to solve it in different ways and still got decimals
what's the og equation
carmine leaf
x+y+z+w=795
simple wigeon
okay
simple wigeon
are the starred functions the given?
lost osprey
are the starred functions the given?
this is original question:
"Jesus went to the bank to exchange his money for coins. He had bills of $5, $2, $1, and $0.50. In total, Jesus had 795 coins. When counting them, he noticed that the number of $5 coins was one-third of the number of $2 coins, half of the $1 coins, and double the number of $0.50 coins. How many $2 coins did Jesus receive from the bank?"
lost osprey
what are starred functions
the ones you put a Asterix next to
carmine leaf
this is original question:
"Jesus went to the bank to exchange his money for coi...
oh yes thats the problem
carmine leaf
the ones you put a Asterix next to
OH
simple wigeon
oh okay then
small ice
this is original question:
"Jesus went to the bank to exchange his money for coi...
for our salvific ransom.
simple wigeon
so you designated each bill to a variable
at that point, you want to create a series of equations you know to be true
small ice
this is original question:
"Jesus went to the bank to exchange his money for coi...
But i don't blive in god or jesus
lost osprey
But i don't blive in god or jesus
i didnt write the problem
small ice
k
winter night
Could someone help me with an specific factorisation problem?
small ice
yes
simple wigeon
<@&286206848099549185>
hopefully this makes sense
lost osprey
hopefully this makes sense
1590 / 13 gives the 122.3 decimal
simple wigeon
yes ik i just rounded
lost osprey
o
carmine leaf
hopefully this makes sense
Yeah it must be that
That was the second answer i got when i solved it again
Thank you guys. Tomorrow im gonna show that to my miss and tell her that the problem is bad
simple wigeon
yea but make sure u finish it and find the # of $2 coins
the one you found is the # of $5
carmine leaf
the one you found is the # of $5
Its in the first *
I already multiplied 122.30 x 3
@simple wigeon can you help me if i get another tricky question? I dont usually ask for help so i wont annoy you
simple wigeon
<@793257560127569941> can you help me if i get another tricky question? I dont u...
yes ofc!!! u can add me on here idm at all
lone heartBOT
@carmine leaf Has your question been resolved?
lavish dock
hey
tribal field
hey
tribal field
!da2a
lone heartBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
tribal field
Just send your question
tribal field
Do you mean the sum of all natural numbers to n?
tribal field
There's actually a story about Gauss about that
Either way consider this, if we have the sum till 7
1+2+3+4+5+6+7
We can rearrange it as (1+7)+(2+6)+(3+5)+4
And the sums inside parentheses are all 8
hot hatch
It's just arithmetic progresion
lavish dock
There's actually a story about Gauss about that
Either way consider this, if we...
okay
hot hatch
Do you need Gauss law for that?
hot hatch
sum of: 1+2+3+4+5+n
It's n(n+1)/2
tribal field
Do you need Gauss law for that?
I somehow think you've overestimated the age of the questioner by a lot
hot hatch
$\frac{n(n+1)}2$
ocean sealBOT
Monarch of Eternal Night
winter light
sum of: 1+2+3+4+5+n
n + 15
tribal field
It's n(n+1)/2
But yeah, that
I was going to explain how one might derive it
But if you just want an answer, take that
hot hatch
I somehow think you've overestimated the age of the questioner by a lot
In my case, Gauss law was taught later than AP
tribal field
n + 15
We've already established they're actually asking for the sum of natural numbers up to and including n
tribal field
In my case, Gauss law was taught later than AP
I got taught this in Algebra 2 at the latest
winter light
We've already established they're actually asking for the sum of natural numbers...
Ah alright. It was just to let him understand that notation is important
But then I didn't see your messages sorry
hot hatch
For me, they just used it as alternate method to solve some binomials
tribal field
I learned it in middle school 🤷
lavish dock
gauss law is taught in grade 6 i think
i'am from viet nam
hot hatch
Country barriers
tribal field
I learned it in middle school 🤷
Although that was more of a fun story time thing about Gauss
hot hatch
For me, they just used it as alternate method to solve some binomials
In grade 12/high school
lavish dock
grade 7
zinc haven
@lavish dock send the original question
hot hatch
Or just memorize it?
zinc haven
in screenshot
hot hatch
<@1230079439250128967> send the original question
Sum of n natural numbers
lavish dock
Well, do you want him to explain the method?
yes i do
hot hatch
@tribal field
tribal field
Ok, so it's a bit easier to derive for even numbers, so I'll do that first
zinc haven
There's actually a story about Gauss about that
Either way consider this, if we...
vietnamese students are also taught about it iirc
though not under the name "gauss law"
tribal field
Fairly sure it wasn't Gauss's anyways
lavish dock
vietnamese students are also taught about it iirc
are you vietnamese
zinc haven
yes
tribal field
Ok, so it's a bit easier to derive for even numbers, so I'll do that first
Consider
With any even number, we can pair up the first and last numbers, the second and second to last numbers, and so on so forth
zinc haven
but i prefer to speak english because there are also other people here who want to help
tribal field
E.g. 1+2+3+4+5+6+7+8
=1+8+2+7+3+6+4+5
lavish dock
but i prefer to speak english because there are also other people here who want ...
oke bro
tribal field
Each of those pairs add to 8+1=9
lavish dock
Each of those pairs add to 8+1=9
uk
tribal field
This can be proven when we realize the sum of the xth number and xth from last number would be x +(n-x+1)
Which is always equal to n+1
And since we are adding n numbers, there are n/2 pairs
tribal field
And since we are adding n numbers, there are n/2 pairs
(remember, for now, we assume n is even)
lavish dock
ok
tribal field
So the sum of the whole thing would be (n+1)n/2
Since we have n/2 pairs of (n+1)
That's how you do it for even numbers, for odd numbers it's a bit different
Since you can't pair up every number
Rather you would have (n-1)/2 pairs
And then have an extra number remaining
This extra number will always be (n+1)/2
E.g
1+2+3+4+5=1+5+2+4+3
So the total sum would be of (n-1)/2 pairs of (n+1) and a single (n+1)/2
So (n+1)(n-1)/2+(n+1)/2
=(n+1)/2(n-1+1)
=n(n+1)/2
Voila
lavish dock
ok
tribal field
It's true for both even and odd numbers, so it's always true
lavish dock
ok i understand
tribal field
Alternatively, you could do an induction proof, but that might be a bit too far in your future
lavish dock
Alternatively, you could do an induction proof, but that might be a bit too far ...
=))))
lavish dock
=)))
tribal field
So 2 x your sum would be the area of the rectangle
lavish dock
So 2 x your sum would be the area of the rectangle
Are you a professor or a student?
lavish dock
okay thank you
lone heartBOT
@lavish dock Has your question been resolved?
cunning trout
how did they get from that to that line?
lone heartBOT
how did they get from that to that line?
gray isle
integrate each term
basic power chain rule was applied for the second and third
if you can't see it, do the sub u = cos(x) for each one
stark scaffold
Y'all question
2 log 5 +log 4 - log 2
lone heartBOT
Y'all question
2 log 5 +log 4 - log 2
winter light
What?
lone heartBOT
@stark scaffold Has your question been resolved?
alpine sable
Im able to solve any kinematics problem (excluding circular motion chapter)
elder forge
Something harder
tf u mean harder?
u can do irodov?
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
mellow imp
I need help with Arithmetic Sequence
lone heartBOT
I need help with Arithmetic Sequence
mellow imp
in this part where it says "pomnozimo sa -2" means multiply by -2, why do they do that
and how did they get from this,
to this:
elder forge
in this part where it says "pomnozimo sa -2" means multiply by -2, why do they d...
to eliminate
it is called solving equations by elimination method
mellow imp
and how did they get from this,
and how did they get 3d = -3 out of this:
elder forge
yes but why -2
to eliminate a1
elder forge
and how did they get 3d = -3 out of this:
add both
mellow imp
so now they can cross out both -2ai?
elder forge
to eliminate a1
we need the coefficients of a1 in 2 equation to be +a and -a so when we add, it will get canceled
elder forge
so now they can cross out both -2ai?
yes
mellow imp
and that leaves us with -6d and + 9d
elder forge
yes
elder forge
yes
mellow imp
lemme find it
elder forge
ok
mellow imp
oh im cooked i don't even know what this problem is about
okay well at least i know this i hope i can get a D or something
tysm @elder forge ill open a new thread if i find the issue
wait actually
one more question
see this long ass problem
you explained me everything good just this last part is kinda weird
how did he get an + 3 = 1
at the end
mellow imp
not mine
it says
an + 3 = 1
at the end
which doesn't make sense
how he get 3
or 1
or the equation
elder forge
can u show the question?
elder forge
ok wht do i find
elder forge
using some formula we got
yea in tht, they solved for d and a1
not an
it is a1 + 3 =1
elder forge
put d=3 in either one of these two
mellow imp
ooh
elder forge
yes so now im asking u to find a1
elder forge
dude look
mellow imp
alright
elder forge
for u to know
the ap
u need two things
those are first term and common difference
ie a1 and d
mellow imp
yes
elder forge
u found out that d=3
so now using tht, u need to find a1
by putting d=3 in any one of those equations
then u can find an
from there
mellow imp
in which equations though that's what im asking about
elder forge
any one of these
mellow imp
i understand t hat but the issue is how did he get a1 + 3d = 10
d doesn't exist there how can i put it in there
elder forge
d doesn't exist there how can i put it in there
fine consider first equation
mellow imp
okay that's
elder forge
2a3 - a4 + 3a2 = 4
mellow imp
and a2?
elder forge
a1+d?
mellow imp
2 * (a1+2d) - (a1+3d) + 3 * (a1+d) = 4
mellow imp
yes
mellow imp
2a1 + 6 - a1 - 9 + 3a1 + 3 = 4
mellow imp
2*3?
elder forge
3*2*2```2d*2
mellow imp
oh yeah
mellow imp
2a1 + 12 - a1 - 9 + 3a1 + 9 = 4
elder forge
yes
elder forge
yes
mellow imp
4a1+12=4?
elder forge
yes
mellow imp
4a1 = -8
elder forge
yes
mellow imp
a1 = -8/4 = -2
elder forge
-2
mellow imp
a1 = -2?
elder forge
yes
elder forge
idk lol
mellow imp
lmao alrighr
elder forge
mhm
elder forge
np
mellow imp
now we got like extra class for learning b4 our test
b4 so ill ask some of questions t here
i hope i can get a D at least
tysm one more time
/close
elder forge
no problem!
elder forge
its .close
mellow imp
.close
elder forge
lol
lone heartBOT
lone heartBOT
Available help channel!
blissful isle
lone heartBOT
gray isle
!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1.I don’t know where to begin
gray isle
start with drawing a diagmra
blissful isle
blissful isle
start with drawing a diagmra
Like this??
main junco
Connect it so it's a rectangle
blissful isle
Yes
gray isle
connect those edges at the top so that it reaches the river
main junco
don't put an extra line along the river
Oh oops I didn't read that part mb
gray isle
gray isle
then introduce varialbes for the length and width
gray isle
yes
blissful isle
How and I find the area
gray isle
then apply formula for area
and do a sub to express that in terms of a single variable
main junco
How and I find the area
Have u learned AM-GM inequality
blissful isle
But I know that x*y=330
gray isle
xy isn't 330
blissful isle
How can I find the maximum area
lone heartBOT
@blissful isle Has your question been resolved?
final olive
Hello
final olive
The question indicates there are 3 lengths that need to be covered for fencing. 2 sides perpendicular to the river and 1 side parallel to the river
Let's call the 2 lines perpendicular to the river length a and the line parallel to the line length b
blissful isle
Ok
blissful isle
Yes
final olive
You can swap the equation and turn it into b = 330 - 2a
blissful isle
Yes
final olive
The area of the field inscribed by the fence is a * b, which you can substitute the equation b = 330 - 2a
Area = a * (330 - 2a)
blissful isle
What
final olive
The height of the rectangle is b and the width of the rectangle is a
Area = height * width = a * b
proud roost
How can I help you
blissful isle
So u mean 330-2a=b
final olive
So u mean 330-2a=b
Yes
final olive
And then you get an expression that expresses the area
Find its maximum through completing squares or whatever method you wish
That's basically it I think
blissful isle
330a-2a^2=area??
final olive
Yes
alpine sable
tf u mean harder?
u can do irodov?
Irodov kinematics is a piece of cake
(sorry for interrupting, continue)
final olive
How can I do that
Have you learned the completing of squares
final olive
330a - 2a^2 = area, not 0
Essentially you want to transform the expression -2a^2 + 330a into an expression in the form of a(x + b)^2 + c
blissful isle
330a=2a^2+area
final olive
330a=2a^2+area
Correct, but that doesn't get you much closer towards the answer
The questions is asking the maximum value of the area
Which means the maximum value of -2a^2 + 330a
blissful isle
Essentially you want to transform the expression -2a^2 + 330a into an expression...
I dont understand how can I apply -2a^2+330a into a(x+b)^2+c formula
final olive
I dont understand how can I apply -2a^2+330a into a(x+b)^2+c formula
Have you learned the method of completing squares
blissful isle
Is this related to parabola
final olive
You could use a parabola to solve it
blissful isle
Ok yes I learned it but😭😭😭 uhhh idk how to solve it in general
final olive
If you find the vertex of the parabola, the y-coordinate is the maximum value of the expression
final olive
Ok yes I learned it but😭😭😭 uhhh idk how to solve it in general
It's alright, I'll show you a systematically method to solve it
The expression is -2a^2 + 330a
The first thing you do, is take away whatever constant is in front of x^2
That means factoring the -2 out
-2a^2 + 330a = -2(a^2 - 165a)
final olive
The target of this transformation is to make it into the format of a(x + b) + c, now you have to use the formula (a - b)^2 = a^2 - 2ab + b^2.
The expression -2(a^2 - 165a) is missing a constant after it in order to make it into the format of (a + b)^2.
This step can be a bit complicated at first. -2(a^2 - 165a + (165/2)^2 - (165/x)^2.
(a^2 - 165a) is missing (165/2)^2 to create a complete square (165/2 is evaluated by dividing 165 by 2, as stated in the formula, this is the 2ab part, so to get b^2, simply divide the coefficient of a by 2 and then square it)
But when you add (165/2)^2, you need to minus it again in order to balance the equation.
Now you can complete the square.
-2(a^2 - 165a + (165/x)^2 ) + (-2)(-(165/2)^2) = -2(a - 165/2)^2 + 165^2/2
final olive
165a^2=330a
Not really
final olive
The target of this transformation is to make it into the format of a(x + b) + c,...
Since a real number squared is always non-negative, (a - 165/2)^2 is always non-negative, and when multiplied by -2 it is either 0 or less than 0
blissful isle
I’m gonna cry
final olive
This means the maximum value of the expression is 165^2/2 (as to attain a maximum value from the expression, you must have (a - 165/2)^2 0, or else the expression can be larger
blissful isle
I don’t understand
final olive
Its a pretty hard concept
I suggest you watch videos on youtube to understand the concept, its hard to explain in messages and I really aren't the best at explaining concepts
This is one I found
There are other videos explaining it as well
blissful isle
Thank you so much for everything i’ll watch it😭
final olive
Np, good luck!
blissful isle
Np, good luck!
Can we be friends tho🙏🏻
final olive
Sure
blissful isle
Omg yes I love smart friends I need smart friends
tardy stag
flip both sides
or just cross multiply
if $\f\rsq\gsq = \f\bsq\psq$, then $\f\gsq\rsq = \f\psq\bsq$
ocean sealBOT
hayley
ocean sealBOT
hayley
tardy stag
so $5\cdot XY = 25\cdot 9.5$
ocean sealBOT
hayley
final olive
Isn't that 2.5
tardy stag
oh yeah it is
final olive
At least proportion wise it should be
sour dome
Ok thank you
full hedge
i am working on a game, and im trying to simulate some physics, imagine you have a wheel, and there's 2 weights attached. I think that the forces on the wheel would even out so that the wheel rotates until the weights are parralel. But when i check this formular i could find, the 2 weights cancel eachother out.
What am i missing? (game gif is a previous version, the behavior looks correct but i wasn't using a physically accurate formular so it broke when there was only one weight, or more than 2)
clear relic
maybe in this case it would be better using the formula torque = force x perpendicular distance? instead of doing the cross product
full hedge
perpendicular distance from what?
also the formular was suggested by someone else in here yesterday, so im not very good at different terms haha
tardy stag
there's no reason a wheel would do that
clear relic
perpendicular distance from what?
perpendicular distance from axis of rotation(centre of wheel), in this case it would be equal to radius of the wheel
full hedge
there's no reason a wheel would do that
it wouldn't rotate to even out?
tardy stag
i don't see why it would
clear relic
i don't see why it would
if the wheel is free to rotate it would
full hedge
well if you replace the wheel with a seesaw, it definetely would right?
clear relic
i don't see why it would
thats how a beam balance works
full hedge
perpendicular distance from axis of rotation(centre of wheel), in this case it w...
could you explain how i would calculate perpendicular distance?
clear relic
could you explain how i would calculate perpendicular distance?
it is equal to the radius of the wheel
tardy stag
clear relic
but i dont think my formula would work with your simulation
full hedge
it is equal to the radius of the wheel
in that case both wheels would get equal force in either direction and so there would be no rotation
tardy stag
in your drawing, there is the same amt of potential energy in both states
clear relic
https://physics.stackexchange.com/questions/13474/why-does-the-weighing-balance-...
thats what we're saying?
full hedge
https://physics.stackexchange.com/questions/13474/why-does-the-weighing-balance-...
so it's about the center of mass?
tardy stag
thats what we're saying?
the key is the needle / weight underneath the balance
full hedge
okay, so if i potentially used the same formular, but the 2 weights where like offset down a little bit, then they would behave like i was expecting?
tardy stag
yes, if they were not exactly opposite each other then the system would evolve towards the lowest energy state
clear relic
in your drawing, there is the same amt of potential energy in both states
the weight at a higher position would have more PE
tardy stag
the weight at a higher position would have more PE
as one rises the other sinks by the same amt
clear relic
as one rises the other sinks by the same amt
yes, and when they are left free in that position, the system would self correct to equilibrium
full hedge
the formular i showed i plugged in, and yes regardless of the rotation they both exert equal force so it stands still
but i guess it makes sense, if it looked like this instead
then they would equal out?
tardy stag
but i guess it makes sense, if it looked like this instead
then they would equa...
if those are attached at one point like earrings then it's the same
clear relic
but i guess it makes sense, if it looked like this instead
then they would equa...
if the wheel was set like this, it would rotate till theyre both at the same level
full hedge
if those are attached at one point like earrings then it's the same
the same as in it would still stay still at every position?
tardy stag
yea
clear relic
the same as in it would still stay still at every position?
it would only if there was no gravity
tardy stag
because again it's symmetric
full hedge
but the radius from center of wheel to the weights center of mass would be different tho right?
so there would be a little difference
clear relic
but the radius from center of wheel to the weights center of mass would be diffe...
radius to any point on the circumference is the same
full hedge
tardy stag
if they're attached at one point like earrings i don't see how it's any different than the first case
full hedge
see the x's left one is outside of the wheel, right is inside
so their center of mass would change depending on the wheels rotation
this atleast sounds correct to me. It also sounds like the forumar i was using was perfectly correct, i just didn't realize the center of mass on the weights worked like that
tardy stag
this is effectively the same as a weight on a string right?
anyway the PE is still the same at every angle
full hedge
what's the difference between a wheel and a seesaw then in this case?
tardy stag
well one's round...
full hedge
lol yeah, but isn't the formular for torque the same?
tardy stag
the torque isn't being applied at the center of mass
again think about a weight on a string
the torque is being applied where it connects to the wheel
full hedge
if i had this, would it still stays perfectly still?
clear relic
if i had this, would it still stays perfectly still?
no
assuming the weights are equal
tardy stag
if i had this, would it still stays perfectly still?
in a perfect world if it's balancing on a pin yes
clear relic
in a perfect world if it's balancing on a pin yes
what?
in the presence of gravity it would move and balance at the horizontal
full hedge
if you hold a pen in your hand, between your fingers, kinda like this picture, what happens when you tilt it?
gravity is prsent if i wasn't clear yeah
clear relic
if you hold a pen in your hand, between your fingers, kinda like this picture, w...
with a pen, there arent individual weights involved, so then it would depend on the centre of mass
but in this case, the weights cancel out so it is still the same as if it was a pen
full hedge
with a pen, there arent individual weights involved, so then it would depend on ...
well say you hold it at it's center of mass
clear relic
well say you hold it at it's center of mass
it would balance then
i think you might need to implement a system of centre of mass in your simulation to make it compatible with one or more weights
tardy stag
with a pen, there arent individual weights involved, so then it would depend on ...
why would it be any different with discrete weights vs continuous weights lol
full hedge
so it would rotate till it's plane with the ground right?
tardy stag
anyway in the real world you can never get it exactly at the center of mass
i saw a really good diagram explaining the seesaw issue but i can't find it now
clear relic
anyway in the real world you can never get it *exactly* at the center of mass
thats negligible difference
full hedge
i saw a really good diagram explaining the seesaw issue but i can't find it now
i would like to see it, maybe it'd help me
full hedge
if i had this, would it still stays perfectly still?
like intuitively, i feel this would rotate till the seesaw is plane with the ground right? So why is that
tardy stag
one very crappy drawing later
the pivot point changes
so more of the beam weight is on the right now
full hedge
sure that makes sense, but if the pivot point is in the center of the beam
like attached by a socket or something
tardy stag
if (this is impossible) the pivot is precisely in the center, and attached in such a way that it can rotate freely but not slide
then every state will be equally energetic
full hedge
i dont think that makes sense
full hedge
if i had this, would it still stays perfectly still?
maybe it would for this
but imagine this then
full hedge
no it's only attached in the center of the beam
tardy stag
no i mean the weights are
intuitively you'd expect that to tip over
not restore itself
full hedge
that's a form of restoration isn't it
tardy stag
i guess sure
but if it tips all the way over upside down, then the center of mass will be lowered
full hedge
i am coding the "earing" example now
tardy stag
thanos's sausages are fat
full hedge
clear relic
lol
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full hedge
idk man has it?
ill close just after i finish up
this is current code. So i tried offseting the center of mass down on the weights, but that ended up making so the weights rotated to be vertical to eachother, not horizontal? (is that correct, should they do that)
here instead i've offset so the center of the wheel is offset slightly downwards, i guess like the pivot on a seesaw being slightly offset? and that yields the result i'd expect
could it be that gravity inherently offsets the wheels center?
im not fully satisfied with this because i dont quite understand it
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lunar glade
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lunar glade
can anyone give me an idea where to start?
lethal belfry
find the derivative of the inverse of a function in terms of the function itself
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verbal breach
Hey. can you help me
Everybody knows one solution of this : lg(1)=ln(1) , x=2
but there's another root how can i find it?
rancid jay
lnx = 2.303logx
verbal breach
lnx = 2.303logx
?
verbal breach
lnx = 2.303logx
i dont think this is true you can do that
ln(x^2-4x+5)/ln(10)=ln(x^2-6x+9)
ln(x^2-4x+5)=2.303* ln((x-3)^2)
but actually when i'm in exam i can't calculate that with my brain ln(10)=2.303...
verbal breach
but actually when i'm in exam i can't calculate that with my brain ln(10)=2.303....
or even i calculate how can i find the solution
@rancid jay
rancid jay
but actually when i'm in exam i can't calculate that with my brain ln(10)=2.303....
its just good to remeber lnx = 2.303logx
rancid jay
im not so sure abt that
i shall think abt it
or im pretty sure another helper will come along
verbal breach
okay
runic glacier
but actually when i'm in exam i can't calculate that with my brain ln(10)=2.303....
apply base e to cancel the logarithms
verbal breach
apply base e to cancel the logarithms
i applied
but i couldnt cancel
ln(x^2-4x+5)=ln(10)* ln((x-3)^2)
runic glacier
but i couldnt cancel
Yeah mb, forgot you can't split the product
verbal breach
Yeah mb, forgot you can't split the product
Yeah
runic glacier
I don't think there is a way of solving this without a calculator
presumably the other root is not a nice number
verbal breach
presumably the other root is not a nice number
yeah its like 4.56.....
runic glacier
You wouldn't be asked to find the other root if its a non calc exam
verbal breach
You wouldn't be asked to find the other root if its a non calc exam
actually book asked for solution (not one) but the book's answer is only 2 so book's answer was false because there isn't one root
runic glacier
That doesn't make the book's answer false. x=2 is still a solution, you just weren't expected to find the other
verbal breach
That doesn't make the book's answer false. x=2 is still a solution, you just wer...
yeah but i think book have to be asked for natural solution and then it would be true
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verbal breach
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real oasis
How did we go from that to that?? Please explain... Someone.
ocean hawk
what to what?
real oasis
Can you explain why the rate of commission is
[(100 × 750) / 15000 ]
Why did we multiply 750 with 100?
ocean hawk
to make it a percent
real oasis
And we divided it by 15000 for??
||(i know this is stupid, i think I need to improve my basics, but rn, i need to know where I'm going wrong and why..) ||
ocean hawk
And we divided it by 15000 for??
to get the rate of commission
real oasis
Can you explain with an example
(If possible)
Assuming X is the rate of commission, i have found the my answer..
.close
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still vortex
yo is anyone good at probability and stuff like that?
lone heartBOT
yo is anyone good at probability and stuff like that?
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
solar pebble
yo is anyone good at probability and stuff like that?
^
gentle ivy
ask your question dont ask for a specific person to be in chat
spiral lily
yeah i'm so good at probability and stuff like that
gentle ivy
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for every...
people may answer it if you actually put it here, ur chance is smaller to get an answer if you ask for someone to help without the question
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heady trellis
i dont know if this server is the right place but i basically need to make a regular expression out of this.
what i have figured out so far is that it accepts every string made out of 0,1 BUT the ones which have 11 as suffix. i dont know where to start from here.
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trim cedar
Hi there. Really struggling with understanding this problem.
I'm not really sure if I am doing it right. I am being told to use the sum/difference formula, but I have never used it in this kind of scenario.
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Hi there. Really struggling with understanding this problem.
I'm not really sur...
@trim cedar Has your question been resolved?
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@trim cedar Has your question been resolved?
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@trim cedar Has your question been resolved?
trim cedar
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tight nest
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tight nest
oh damnn
glacial patrol
Also I said triangle CED
tight nest
i should redit it carefuly
glacial patrol
Yeeeee 
glacial patrol
np
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crimson quail
f(x)= 5/(2x+1) for x is a real number, x >= 2
b) Find the Domain of f^-1 (range of f(x))
f^-1(x) = (5-x)/2x
buoyant saddle
well it’s for x>2
so what is the function at 2
and what is the function at infinity
@crimson quail
crimson quail
function at 2 is
f(2) = 5/2(2)+1
f(2) = 1
function at infinity is no idea
buoyant saddle
well what does the denominator go to
buoyant saddle
which is infinity
buoyant saddle
2(infinity) + 1
you shouldn’t use it like this^
you should just know that as n->inf, 2n+1 ->inf
and 5 stays constant
what’s happens when the numerator stays the same and the denominator gets really big
what happens to the quotient
like what would the number start to look like
crimson quail
it decreases
buoyant saddle
to what
crimson quail
0
ocean sealBOT
buoyant saddle
what do you mean
it’s f(x)
not x
because the maximum is at f(2) which 1
then it decreases to zero at infinity
crimson quail
for the domain its x is it not
buoyant saddle
its not =<1
crimson quail
oh wait i miswrote it
buoyant saddle
for the domain its x is it not
yes but it said >=2
crimson quail
the end part is supposed to be domain of f-1(x)
buoyant saddle
which is the range of f
buoyant saddle
mhm
that would be the range of f^-1 btw
by definition the range and domain of inverse functions are reversed
meaning
the domain of f is the range of f^-1
and the range of f is the domain of f^-1
crimson quail
yeah and i found the range of f for domain of f^-1
but i dont get why its less than 1 or equal to becuase the x isnt negative im not sure how to graph this other than going like x: -1, 0, 1 and finding the y values for that
buoyant saddle
but i dont get why its less than 1 or equal to becuase the x isnt negative im no...
because that’s the range
are you confused why the range of f is (0,1]
crimson quail
i mean i didnt fully understand it i kind of just plugged the 2 into the equation and got the 1 as the y value for the range
and then x (symbol) 1
im not sure on why taht symbol is less than 1
and normally i would graph it but thats when i have the vertex from a completed square form or smth bc the equation is 5/(2x+1) and it doesnt give any simple ways to plot it
buoyant saddle
well 5/(2x+1) is like an inverse function it’s just like 1/x
it isn’t a quadratic
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@crimson quail Has your question been resolved?
crimson quail
No
thank you for the help man but i js cant seem to understand it today
im tired so ill revisit this tmrw i guess but thanks anyways
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strange fractal
Hii
paper mango
expand as you attempted :)
strange fractal
How would i expand it
Is it a dot a + a dot b + a dot b + b dot b + a dot b
And then the signs
paper mango
(a+b) * (b-a) = a * (b-a) + b * (b-a) = a * b - a * a + b * b - b * a
just distributive law twice yes
and note that a * a = |a|²
and b * b = |b|²
so you get = a * b - |a|² + |b|² - b * a
= |b|² - |a|²
@strange fractal mostly clear or stuck on a step? :)
strange fractal
and note that a * a = |a|²
Hmm how come?
I thought sometimes it equaled 1
When does it equal one?
paper mango
When does it equal one?
do you mean a * a generally?
it equals 1 if a is normalized
meaning if a has length 1
makes sense, since if a is normalized, then |a| = 1, meaning |a|² = 1, meaning |a|² = a * a = 1
it's crucial to have a clear interpretation of the operations, the dot product * is always equal to the length of one vector times the projected length of the other vector
so if those are a & b (with arbitrary lengths)
then this would be the vector a projected onto b
and the dot product a * b = |ap| * |b|
which means if you take two perpendicular vectors
then the projected ap will just lie in the origin
so the length of ap is 0
meaning a * b = |ap| * |b| = 0
which is true for any two perpendicular vectors
now what happens if we take the dot product of a vector a with itself?
well a projected onto itself is just a again, so ap = a
meaning a * a = |ap| * |a| = |a| * |a| = |a|²
strange fractal
Oh
paper mango
thereby, if the length of a is 1
strange fractal
Hey ive done this before
paper mango
then a * a = 1
strange fractal
This is scalar projection
paper mango
This is scalar projection
exactly!
it works in any dimension btw, but I don't want to twist your head :P
so from the above you can take away the three main messages:
a * a = |a|²
a * b = 0 if a and b are perpendicular
a * b = |ap| * |b| in general. Where ap is vector a projected onto b
strange fractal
makes sense, since if a is normalized, then |a| = 1, meaning |a|² = 1, meaning |...
Ohh makes snese
paper mango
So normalised vector is a unit vecotr?
if that's the terminology you've been introduced to you yes
paper mango
so from the above you can take away the three main messages:
`a * a = |a|²`
`a *...
oh but the one very crucial thing to keep in mind is that the direction of ap is taken into consideration
so if ap goes in the opposite direction of b, then the dot product will be negative:
a * b = -|ap| * |b| for that case
which means if you take the dot product of a with any other vector b
if b points in the same direction, the dot product will be positive
if b points in the opposite direction, the dot product will be negative
if b is perpendicular to a, the dot product will be 0
wheat isle
bummmmmmmmmmmm chicken
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strange fractal
so from the above you can take away the three main messages:
`a * a = |a|²`
`a *...
Ahh ok thank u
I actuakly understand where it comes from now
paper mango
I actuakly understand where it comes from now
neat 🐛
hybrid ravine
hello for part c i'm getting confused on what i'm meant to sub t into to get the tangent (i got t=0 and 2)
elder forge
wht did u do?
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alpine sable
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alpine sable
what do I need to put in the 2 boxes bottom left?
and how can I find it
with the formula
coral flower
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alpine sable
Ktu vector calculus important questions booklet
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Ktu vector calculus important questions booklet
elder forge
lol
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livid sage
insane
prime glacier
dawg
alpine sable
xD
small lance
https://www.google.com/
It was considerate of you
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copper flicker
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copper flicker
I don't quite understand how to write them as the same?
The previous task asked us to show that the upper one is integral by using derivation for x/(1-x)
elder forge
I don't quite understand how to write them as the same?
for upper one, add and substract 1
copper flicker
Why does adding and subtracting 1 do anything?
elder forge
yea
see
x-1+1/1-x
write it as
x-1/1-x + 1/1-x
x-1/1-x is -1
which is a constant again
so left is 1/1-x
@copper flicker
copper flicker
which is a constant again
okay so since it is a constant again, you could express it as the C_2?
im absolutely cooked for the exam
elder forge
np
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proper gazelle
i dont know how to ask my question properly, but i have to determine the price for 1 sandwich and 1 bottle of water using equations
so 3 Sandwiches and 1 bottle of water cost 3,00€
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warped gulch
pls help im so confused
lone heartBOT
pls help im so confused
warped gulch
so we're finding taylor polynomials
and in this example my prof was able to use the well known series to find the taylor polynomials
but when i tried to do it w this example it didnt give the same output as using this equation
why does it work for one but not the other
wait it totally does
nvm
i got it
so when unsure abt whether or not I can turn it into a series using the well known series I should use the formula provided?
subtle light
most of the time it should match up with a known series, but when you can’t like with tan(x), just use the taylor series formula
warped gulch
but when i tried to do it w this example it didnt give the same output as using ...
is this the taylor series formula or r u talking abt something else
subtle light
yes
tight nest
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hoary nimbus
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hoary nimbus
How do i do (iii)?
My working for (i) and (ii)
I got (iii) till here but i don’t know how to proceed
I think i have to somehow incorporate the result of a<-3 into the last line i wrote but I don’t exactly know how that works
hoary nimbus
I got (iii) till here but i don’t know how to proceed
I realise now i forgot to change signs for 3c and 3ab, it should be 3ab and -3c
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past owl
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past owl
on the left is what i thought n* would be and on the right is the real solution
i don't know why
these are mathematical sequences
n represents the amount of terms
nvm i think i get it
!close
.close
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gritty gazelle
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tacit iron
Can someone help me on part b?
lone heartBOT
Can someone help me on part b?
tacit iron
Don't get how to do it
modern sedge
Don't get how to do it
what's g(x) equal to?
g(x) = ?
it doesnt need to be a number, it can be an expression btw
containing the variable x
tacit iron
Idk it doesn't say what g is equal to
But how do I do the question? Is there a formula or something?
modern sedge
tacit iron
Yeah other than that
spiral lily
But how do I do the question? Is there a formula or something?
no
modern sedge
g: x -> 4x - 5 has a meaning
g(x) = 4x - 5
it's different notation for the same thing
tacit iron
Ok I get that so what do I do next?
modern sedge
so if you're finding t(g(x)), you're just finding t(4x-5)
tacit iron
Oh
tacit iron
Yeah
modern sedge
do you know how to find t(4x-5)?
tacit iron
I thought I knew but I don't remember
I'm going over algebra again to revise
modern sedge
ill just change the variable for y for a moment to make it less confusing
tacit iron
Yeah
modern sedge
t(y) = y^2 - 5y + 1
tacit iron
What does the thing between the x and two mean? Was that the y?