question 10
#help-0
alpine sable
tulip oak
After graphing it in desmos, i can see that is 0 yes
But how do you find that alebgraically?
tulip oak
Yea it says evaluate using squeeze theorem
alpine sable
maybe u could squeeze it with x^2-9 and -(x^2-9)
cuz like the equation is kinda like the piecewise of -(x^2-9) for x < 3 and x^2-9 for x > 3 or smth
tulip oak
I don't understand, how'd u come up with a piece wise function?
alpine sable
well u said the right side is a step function and thats correct
another way u can write a step function
is as a piecewise
like (x - 3) / |x - 3| is -1 for x < 3 and 1 for x > 3 right?
alpine sable
well since the other part of the expression doesnt change so abrupty (not piecewise) we could multiply the -1 and the 1 to get the piecewise of the entire thing
right cuz x^2 - 9 is just a parabola
alpine sable
oops what
tulip oak
And multiplying it by the other one since they should be equal
lone heartBOT
alpine sable
And multiplying it by the other one since they should be equal
yeah
tulip oak
Hm
I understand what you've done
But where are you going with that?
How do you "trap" the function to apply squeeze theorem
alpine sable
well since its a piecewise of two functions
u can squeeze it with those functions
x^2-9 and -(x^2-9)
both of which are 0 as x approaches 3
alpine sable
yeah
tulip oak
As x-->3
tulip oak
Na it helped
alpine sable
lmao sorry i was pretty bad at limits when i studied this so
not the best at explaining
tulip oak
Thank you
tulip oak
Ty
lone heartBOT
Available help channel!
broken compass
I have no idea if this is right or wrong but it seems very very wrong can someone please help?
lone heartBOT
@broken compass Has your question been resolved?
broken compass
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lone heartBOT
@broken compass Has your question been resolved?
azure shuttle
Which line if the x + y >3 constraint?
azure shuttle
I have no idea if this is right or wrong but it seems very very wrong can someon...
Made any progress?
@broken compassI get the line for 20y + 8x <= 100. That seems good. Which side of this line are we looking?
left isle
not sure the objective function should be an inequality. the one you gave would only be true if you had 1 veteran and 1 high schooler, any more than 1 of each would make your statement untrue. i think it may be better to write it as a function, like f(x,y)=200y+50x, where f(x,y) is your number of items shelved.
also where did you get the y>=x+3
azure shuttle
@left isleMaybe if they come back, we should start at the beginning and get the constraint lines correct first?
If they come back.
scenic wing
How did he ignore all of the n's
lone heartBOT
How did he ignore all of the n's
ocean sealBOT
putridplanet
ocean sealBOT
Mental Wolf
leaden sigil
$\frac{27(2n^2+3n+1)}{6n^2}$
ocean sealBOT
Mental Wolf
lapis ingot
pretty much when it goes to infinity only the highest degree has weight in the limit
scenic wing
yeah watching pjmt vid and just got it
ocean sealBOT
Asagao 朝顔
lone heartBOT
@scenic wing Has your question been resolved?
gaunt hare
HELP
me
ebon sparrow
gaunt hare
WHAt is 2+2
ebon sparrow
<@&268886789983436800>
gaunt hare
OH HELL NAH
night geyser
.close
elfin coyote
lone heartBOT
elfin coyote
I know how we found the denominator in this one but how do we know what the numerator is and how does that relate to the oblique asymtope
tribal haven
sick, never had an image act like a moire flashbang before
also you find the asymptote by doing polynomial long division
elfin coyote
also you find the asymptote by doing polynomial long division
yea but like how do you get to x+1 x-1 in the numerator
tribal haven
yea but like how do you get to x+1 x-1 in the numerator
you’re straight up given x intercepts
plug them in and check that (x+1)(x-1)/(x+2) =1/2 and you’re immediately done
(if not then you multiply by a constant)
lone heartBOT
@elfin coyote Has your question been resolved?
dapper forge
lone heartBOT
dapper forge
is the first step
intergrate the function 0-5?
1 + x² = y
2xdx = dy
60xdx = 30dy
i did like that much
jagged cobalt
intergrate the function 0-5?
yup, id agree, though the substitution isnt necessary
im not sure what you did there actually
dapper forge
in which step
jagged cobalt
nvm, i see
but it doesnt really work i dont think
dx=dy/2x
but then you just have a 1/2x in your integral, and replacing it with a function of y gets messy
id just integrate it wrt x, its a simple one to do
jagged cobalt
ah i see, but even then, still just do wrt x
it would be 60 * int (x+x^3) dx not bad
i wouldnt do a sub unless its really necessary
jagged cobalt
no worries
dapper forge
give me 120 seconds
jagged cobalt
very specific
jagged cobalt
,w integrate (60(1+x^2)) between 0 and 5
ocean sealBOT
jagged cobalt
nice
ocean sealBOT
dapper forge
woah
thats cool
so
how would i write the answer to the problem
@jagged cobalt would i write "the min monthly charge that should be added to cover a 5-year lease would be $2800"?
jagged cobalt
$2800 is the cost of the whole 5 years, not a monthly charge
you have to split that 2800 across 60 months
dapper forge
oh righttt
Minimum monthly charge for a 5-year lease = 2800/60 dollars per month.
?
dapper forge
lone heartBOT
dapper forge
okiee
ocean sealBOT
jagged cobalt
Between 2000 and 2015, 18765 billion cubic feet of natural gas was consumed
is about as compact as it could be
dapper forge
m(x) is minimum at x=-3, so are we supposed to integrate s(x) from -3 to 0?
jagged cobalt
x cant be negative
what you want to do is find when m(x)=s(x), this will be your upper integral limit
then integrate s(x)-m(x)
jagged cobalt
,w solve (x^2+6x=360-2x^2)
ocean sealBOT
jagged cobalt
not quite no, youre integrating s(x)-m(x) from 0 to 10
since thats the net savings (rate)
dapper forge
,w solve (x^2+6x=360-2x^2)
whats this
jagged cobalt
thats just solving s(x)=m(x)
dapper forge
i got 2300
jagged cobalt
,w integrate (360-2x^2-x^2-6x) from 0 to 10
ocean sealBOT
jagged cobalt
nice
dapper forge
yayyy
jagged cobalt
rereading the question, the answer is just the 10 lol
but youve provided how much the net savings actually are, so bonus marks
dapper forge
but youve provided how much the net savings actually are, so bonus marks
to bad i dont actually get bonus marks
doing the same thing here, finding the value of q where both are equal?
@jagged cobalt
broken compass
also where did you get the y>=x+3
I got that bc it says that there needs to be 3 employees total working at a time
dapper forge
azoooooooooooooooooooooooo
:((
i dont gets it
q = 52.7 for supply = demand?
<@&286206848099549185>
helppppppppppppppppppp
<@&286206848099549185>
severe cloak
hi
severe cloak
what help tell
severe cloak
(Q) is the symbol that is used to represent rational numbers. Rational numbers are sometimes called fractions. They are numbers that can be written as the quotient of two integers. They have decimal representations that either terminate or do not terminate but contain a repeating block of digits.
dapper forge
(Q) is the symbol that is used to represent rational numbers. Rational numbers a...
this q is different
lone heartBOT
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shut lintel
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alpine sable
what have you tried and where are you facing difficulties
shut lintel
tbh i don’t know where to start
shut lintel
is it the coefiencts ?
alpine sable
yeah
shut lintel
okay i’m just confused on how to get the w,x and z
alpine sable
\[
\begin{alignedat}{7}
2x && {}-{} && 4y && {}+{} && 2z && {}={} && 2 \\
-4x && && && {}-{} && 2z && {}={} && -2 \\
x && {}-{} && y && {}+{} && z && {}={} && 3
\end{alignedat}
\longrightarrow
\left[\begin{array}{@{}rrr|r@{}}
2 & -4 & 2 & 2 \\
-4 & 0 & -2 & -2 \\
1 & -1 & 1 & 3
\end{array}\right]
\]
alpine sable
as an example
shut lintel
yes yes yes ok
alpine sable
okay i’m just confused on how to get the w,x and z
it's fine can you please just set up your matrix first and we can start working on that
alpine sable
your matrix should end up looking like this:
ocean sealBOT
shut lintel
yes!
alpine sable
okay so row reduction has like 3 things you can do
what you can do is apply the replacement part first
you want to get echelon form to begin with for your matirx
do you know what echelon form is
shut lintel
is that all zeros at the bottom ?
alpine sable
not sure what you mean by "bottom" but this is the principle of it:
so you want to make a zero appear under what we call the "pivots"
do you know what a pivot is?
shut lintel
no
alpine sable
"A pivot position in a matrix is the location of a leading entry in the row-echelon form of a matrix. A pivot column is a column that contains a pivot"
you use this pivot to do all your calculations
shut lintel
ok ok
shut lintel
okay okay
alpine sable
now
I'll try to guide you
[ \left[\begin{array}{@{}rrrr|r@{}}
\c g 1 & 1 & -1 & -9 &-2 \
\c r 2 & 3 & 2 & 16 & 11 \
2 & 1 & 2 & 4 & 5
\end{array}\right]
]
ocean sealBOT
alpine sable
the green 1 is your pivot
shut lintel
yes yes
alpine sable
you will use that to eliminate the 2 in the red
shut lintel
ok
alpine sable
okay now an algebra question for you
shut lintel
shit
alpine sable
what do you multiply 1 with so that when added with 2 it gives you 0?
equivalently,
1x + 2 = 0
find x
shut lintel
all of the numbers ?
alpine sable
yes
alpine sable
it's equivalent to doing
-2(x+y-z-9w) = -2(-2)
this is just a 1 degree equation remember
so the algebra is all the same
shut lintel
ok
alpine sable
so multiply and distribute as you would otherwise
alpine sable
yes great
shut lintel
ok ok
alpine sable
we care about the coefficients since this is a matrix
so
-2 -2 2 18 -4
now
add this row
with the second row
what do you have
alpine sable
I think your last one is wrong
shut lintel
-4 + 11?
alpine sable
-2x - 2y + 2z + 18w = -4
ah yes it's here. it should be 4 not -4
alpine sable
0 1 4 34 15
this seems fine
so niw
[ \left[\begin{array}{@{}rrrr|r@{}}
\c g 1 & 1 & -1 & -9 &-2 \
0 & 1 & 4 & 34 & 15 \
2 & 1 & 2 & 4 & 5
\end{array}\right]
]
ocean sealBOT
alpine sable
you eliminated your first position
shut lintel
we leave the last row alone?
alpine sable
continue repeating this process
no
it's time to eliminate the 2 in the bottom left
shut lintel
ok
alpine sable
I have to go now sorry
alpine sable
by the way this is called a wide matrix. You will realise this system of equations has a property that always holds
shut lintel
okay
alpine sable
I want you to figure it out yourself
and yes continue
your pivots are always among the diagonal
so eliminate everything else other than your pivots on the column
meager summit
help
hushed locust
i would change them to a common base, yes
hushed locust
use the change of base formula to change the base of one to match the other
static needle
you could also just evaluate the expression no?
meager summit
use the change of base formula to change the base of one to match the other
thanks
that's what i did
static needle
$$ 2(\frac{1}{2} + 2)$$
meager summit
i forgot that change of base formula lets you change the base to anything you want
ocean sealBOT
Bananas in the sky
meager summit
i thought it had to be just normal base 10
meager summit
you dont even need to change bases
well for mental math
i had to change the base to 3
since log base 3 of 3 is 1
static needle
no but you can look and evaluate those logs
meager summit
and log base 3 of 9 is 2
static needle
you dont need a calculator
meager summit
no but you can look and evaluate those logs
wdym
static needle
$$log_9 3 = \frac{1}{2}$$
ocean sealBOT
Bananas in the sky
ocean sealBOT
Bananas in the sky
meager summit
yeah
ocean sealBOT
Bananas in the sky
ocean sealBOT
ScriptedEli
meager summit
i just did this
static needle
yea that works, its just a step longer
lone heartBOT
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Available help channel!
lone heartBOT
ocean sealBOT
ocean sealBOT
filipth3narcissist
lone heartBOT
@proven osprey Has your question been resolved?
proven osprey
no
sharp thorn
lol
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@proven osprey Has your question been resolved?
unborn birch
lone heartBOT
unborn birch
I've used double angle formula for both denominator and numerator and im at 1+2sinacosa/1+2cos^2a however I'm unsure what to do
cinder sundial
Are you trying to prove the equality
unborn birch
yes
hasty creek
$\frac{1+2\sin\left(a\right)\cos\left(a\right)}{2\cos^{2}\left(a\right)}\to\frac{\sin^{2}\left(a\right)+2\sin\left(a\right)\cos\left(a\right)+\cos^{2}\left(a\right)}{2\cos^{2}\left(a\right)}$
ocean sealBOT
Combustion
unborn birch
$\frac{1+2\sin\left(a\right)\cos\left(a\right)}{2\cos^{2}\left(a\right)}\to\frac...
then i can just do perfect square
hasty creek
yep
unborn birch
thank you bro
hasty creek
cinder sundial
I was thinking if it can be solved through geometry standpoint
As for the left side of the equation can be considered as a slope of a particular line
unborn birch
As for the left side of the equation can be considered as a slope of a particula...
bro ngl that is way beyond what i knnonw
lmao
unborn birch
<:catthumbsup:614540188747563008>
wait im confused what to do next
hasty creek
$\frac{\left(\sin\left(a\right)+\cos\left(a\right)\right)^{2}}{2\cos^{2}\left(a\right)}\to\frac{\left(\frac{\sin\left(a\right)+\cos\left(a\right)}{\cos\left(a\right)}\right)^{2}}{2}$
ocean sealBOT
Combustion
unborn birch
ok just divide by cos squared and then 1 + tan a squared on 2
OH THANK YOU
💀 i would not have seen that
hasty creek
do enough problems and these will be really really easy
unborn birch
can you give me some material on this please
unborn birch
<:catthumbsup:614540188747563008> do enough problems and these will be really re...
what year r u
hasty creek
university
hasty creek
can you give me some material on this please
i don't really have any
hasty creek
r u studying maths
nah
devout cypress
does this fall into case 2 or 3? do i take into account sin is raised to 1 by default or naw
hasty creek
does this fall into case 2 or 3? do i take into account sin is raised to 1 by de...
case 2 is when there's only cos OR sin, not and
devout cypress
case 2 is when there's only cos OR sin, not and
mhm but sin is raised to 1 which is an odd exponent no? so does it fall under case 2
hasty creek
small rock
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small rock
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small rock
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@small rock Has your question been resolved?
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@small rock Has your question been resolved?
small rock
sorry. if this feels spammy, but I just want some guidance. i am super stuck. I know the brach is supposed to die and I have most of the work. I think I am missing something stupid.<@&286206848099549185>
copper rock
You may be better off asking in #discrete-math
lone heartBOT
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Available help channel!
alpine sable
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alpine sable
I dont understand why if the bottom is even why theres 2 answers
junior vigil
because you have one associated with 3x+3=27, and one with 3x+3=-27
alpine sable
but why does it turn into + and -
like why does the bottom of fraction being even make it + and - answer
same with this one
junior vigil
well they say, why, += because 4 is even.
well, for example, if we have x^2=4
2 is a solution
2^2=4
but -2 is also a solution
(-2)^2=(-2)(-2)=4
alpine sable
so if in the problem theres an even power
itll always have 2 answers?
when solving for x
junior vigil
well, not necessarily
(x-2)^2=0 has only 1 solution, but in general, if you have to take an even root of both sides, you will have a plus minus
this one only has one solution because plus minus 0 is still 0
alpine sable
but if it wasnt 0 it would have 2 solutions?
alpine sable
like this has 2 solutions but didnt take square root of it
junior vigil
you did take an even root. 1/4
you can think of 3/4 as cubing(^3), then taking a 1/4 root
alpine sable
i see ok i think i get it just wish there was an easy way to tell if it had 2 answers or not
.close
sweet yarrow
lone heartBOT
sweet yarrow
If i've got sucha function
and i need to give a set in which this function is continius and what type of discontiniutity it is
if it is
does that mean, that i just say that the denominator != 0
haughty acorn
does that mean, that i just say that the denominator != 0
yes cuz u cant divide by 0
sweet yarrow
and say that function is continius in domain R \ {-2, 1}
haughty acorn
aha
sweet yarrow
and count left-hand, right-hand limits, to state the type of DC?
for both points
and it is continius, since its a quotient of a polynomial and an id(x) + constant?
elementary functions?
haughty acorn
and count left-hand, right-hand limits, to state the type of DC?
you mean like the bottom part subbed by lim x-->3- and limx-->3+?
haughty acorn
u do that when
haughty acorn
x+2 if x<0
3x+4 if x >=0
sweet yarrow
and lets say, lim x->3- f(x) = -inf
did not count it
oh
ah yes
here we got just empty points?
in this domain
no
it could be hyperbolic
In desmos, i can see that for x = -2,
x is a cluster point, but its not in the domain
that means its a removable type of discontinuity?
haughty acorn
-2 and 1 aint from domain
haughty acorn
i just dont remember how to calc the type of disc
sweet yarrow
just not in the domain
sweet yarrow
not yet shown in my calculus class
in a few lectures, yes
but not yet
hence cant use it
anyone else?
Cause I assume thats the way im supposed to do it:
Calculate the domain, we get that R \ {-2, 1}.
Then get the limits f(x) when x->-2, and x->1
we do it for 2+, 2-, 1+, 1-
And I get that
lim x->2- f(x) = lim x->2+ f(x)```
That should mean that -2 is a cluster point of the domain but is not in the domain, so the DC is removableand doing that for 1+, 1-, we get -inf and +inf
So its an infinite jump at point 1
sweet yarrow
i guess i answered it myself 
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tough dawn
I’m working on conic sections and I need to find the center, vertices and foci
tough dawn
I know how to do that by only when I have something that looks like this equation
Oh guess I should also specify that this is an ellipse
alpine sable
[
a = \f1{\f1a}
]
ocean sealBOT
alpine sable
so you still have what's in your equation
tough dawn
So is a =81?
alpine sable
yeah
tough dawn
Ok so it’s just
tough dawn
But I thought you said a = 81
alpine sable
you misinterpreted what I wrote
alpine sable
don't forget parentheses
tough dawn
Ok
tough dawn
Ok
alpine sable
Ok so it’s just
also you exponentiated the 81 and 49 out of nowhere
you are meant to rewrite them as 9^2 and 7^2 to represent what you are trying to say here
tough dawn
81 = 1/(1/81)
This still means a is 81 so why isn’t a = 81 in my problem?
alpine sable
you are looking for a^2 in the denominator
you only have the numbers as integer coefficients
you can make the 81 be in the denominator to satisfy x^2/a^2 by saying 1/(1/81)
thus a^2 = 1/81
and a = 1/9
tough dawn
Oh ok
Gotcha
So with questions like these I basically have to find the square root of the number and replace a and b with the square root?
alpine sable
lone heartBOT
alpine sable
I'm doing lagrange multipliers constrained optimization for x^2+y^2 for fand x^4+y^4=1 for g
I don't understand how to get the points 1,0 and 0,1
and then negatives of those
if x has to equal +-y
thanks
like here would i have to solve for lambda or can i set the two lambdas equal to eachother
<@&286206848099549185>
finite sphinx
I have a question in topology which might be pretty trivial
How does collection of some subsets of X which obey the rules of topology help in giving a notion of closeness
For example, X = {a,b,c,d}
Suppose taking
Suppose I 'm constructing topology and suppose I want to add subsets {a,b} , {c,d},
I would easily be able to do it
t1 = {phi, X, {a,b}, {c,d}}
whereas when I want to construct a topology {a,b} and {b,c}, I am required to add additional sets from rules of topology for it to be a topology , ( My best guess would be the two sets I want to add can also describe closeness of two more subsets as well ? )
t2 = {phi, X, {a,b}, {b,c}, {a,b,c}, {b}}
I fail to see how t2 tells anything about closeness of any points , I fail to see how this notion of closeness which topology claims to solve : /
I've tried looking up what the topological space and open sets are useful on stackoverflow and reddit, they always use analogies and metaphors to describe topology and I don't see how these analogy translate to point set topology
I've never seen a concrete example , Maybe clarifying one would help
steep rover
I have a question in topology which might be pretty trivial
How does collectio...
post this in another channel pls
steep rover
I'm doing lagrange multipliers constrained optimization for x^2+y^2 for fand x^4...
im taking this class rn too but i wanna try this
lemme get to where u r
i got different equations
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slate vortex
Could someone help with #14? I'm not exactly sure how to work this out.
slate vortex
I parameterized the sides in the xy & xz planes as lines, but I don't think that's the correct approach.
actually I just thought of something
.close
fossil raptor
Does this math add up? Currently, outside diameter the lid is 33.20 mm. Becuase of this, if the lid is not a snap fit for you, you can adjust the scale. Adjusting the .3% adujusts the outside diameter by about .1 mm (.0996 to be exact). This is all assuming my math is correct lol. With this in mind I would reccomend adjusting the scale of the lid by .3% at a time depending if it is to large or to small.
Creating a github readme for something I am working on and this is for one of the stl parts
this is the part by the way, just a small ring:
fossil raptor
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exotic gate
for finding the total distance, how do i approach this part of the question?
exotic gate
<@&286206848099549185>
azure shuttle
Can you explain how the green and white boxes are read?
Or. alternatively, explain what youi want help with?
exotic gate
the green means i got them correct and the white are the ones im still working on
im curious on how to find the total distance
part of the question
exotic gate
s(t) is speed i believe
and the derivative of that is velocity (answered in question A)
exotic gate
yea i tried v(t) as well for this question, im starting to think its just an error on the applications part
azure shuttle
s is often used for position ot distance
exotic gate
ah i see, thank you for your help
azure shuttle
So any idea what the curve of position looks like?
I guess total distance is the positive distance plus the negative distance
But, you must work out where it stops at t=8
exotic gate
gotcha, thank you
exotic gate
thank you
azure shuttle
Enjoy
exotic gate
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harsh halo
Need help solving 3
lone heartBOT
Need help solving 3
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@harsh halo Has your question been resolved?
unkempt compass
how would i go about trying to solve this? im running into lots of problems
harsh halo
.reopen
unkempt compass
occupied
harsh halo
Oof
unkempt compass
<@&286206848099549185>
lone heartBOT
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@unkempt compass Has your question been resolved?
molten pivot
last walrus
still havent found a way to solve this yet 😦
Are you still working on this question? Happy to help
unkempt compass
Are you still working on this question? Happy to help
yeah
i still havent found a way to solve it, its too diffcult for me alone to do
last walrus
What do you know about exponential or logarithmic equations? Like do you know how to solve them?
unkempt compass
i suppose i know how to solve them
i know the exponential and logarithmic laws and how to manipulate them
for the most part
last walrus
Thats great!
OK we want to start with part (a). Can you make a quadratic that has x=1 and x=2 as solutions
unkempt compass
i know...the basic forms in the functions like y = a (function) (k(x-d)+c
(x-1)(x-2)=y
last walrus
Good, let's take y=0, so that (x-1)(x-2)=0
unkempt compass
ok, i understand that part
last walrus
Now let's take the exponential of both sides.
do you know about e (natural exponential?)
or should we use a base that's not e?
unkempt compass
i know of the ln function and that base e is some number
last walrus
ok cool
unkempt compass
and ln_e (e) = 1
last walrus
so if we take e of both sides, we would get $e^{(x-1)(x-2)} = e^{0}$
ocean sealBOT
unkempt compass
alright, im still following
last walrus
Do you know what is e^0 ?
unkempt compass
=1
last walrus
yep yep
now we just need to get the -12 in there
so let's multiply both side by -12
unkempt compass
-12e^(x-1)(x-2) = -12
unkempt compass
e is not considered a variable?
last walrus
no it is a number somewhere between 2 and 3, so x is the only variable in this equation
unkempt compass
but otherwise it does seem to be a solution although i was coming at the problem thinking we needed two graphs that intersect at x=1 and x=2
last walrus
-12e^(x-1)(x-2) = -12
In this equation we actually need both the LHS and RHS to be equal to -12 when x=1 and x=2 (this is what we mean by a solution)
in green is the exponential function and in purple is the function y=-12
unkempt compass
ahhhh
that makes a lot of sense
just throwing this out there but, would e^(x-1)(x-2)(x-12)=1 be another solution?
last walrus
I think that should work too
In this case 1, 2, and 12 are solutions to the equation, but I think this is OK
unkempt compass
one thing that got me confused was that...these graphs dont exactly look like exponential functions in the sense that they aren't shaped like a hockey stick
last walrus
Very true. When you have a quadratic power (or in your last example a cubic power) things can look very different!
e^{ax+b} will always look like a hockey stick 🙂
unkempt compass
I think that should work too
the log version of this would be a bit more difficult because we cant have a log of (x-1) ?
im just plugging into a calculator right now
last walrus
Yeah i had to be sneaky to use logs lol
unkempt compass
and quickly just by extension to satisfy the last part of the question..we have infinite amount of solutions because we could just add extra factors to the exponential equation? that is e^(x-1)(x-2)(x-12)(x-14)(x-15)=1 ect ect ect
unkempt compass
Yeah i had to be sneaky to use logs lol
was there a log solution? im curious about that part
last walrus
and quickly just by extension to satisfy the last part of the question..we have ...
yes there are infinite solutions to this question
for the log part I did something weird like this $-12\log_{2}(2^{(x-1)(x-2)}) = 0$
ocean sealBOT
last walrus
So the log_{2} and power of 2 "cancel" and youre left with -12(x-1)(x-2)
unkempt compass
this whole question is just about trying to find ways to sneak in an exponent or logarithm and not actually have graphs that look like logs or exponential graphs 😵💫
unkempt compass
my interpretation of it was to find log(x)=log(x) and have points of contact like in this image
and that seemed very difficult to solve for
unkempt compass
its a bit of a weird question
im not sure if seeing that changes your view on how this problem should be solved?
last walrus
I don't disagree with you, I think it just makes the overall question very hard!
unkempt compass
.close
lavish pier
is this to answer to question c correct or incorrect ?
lone heartBOT
is this to answer to question c correct or incorrect ?
lavish pier
there’s nothing wrong with the 2 being inside the second bracket right
lone heartBOT
sharp thorn
how the fuck did you get to knowmy name
sharp thorn
thanks sanjith 🤙
OI
lavish pier
what do you mean your name
lean prairie
how the fuck did you get to knowmy name
look at your profile 🫣
lone heartBOT
Available help channel!
fringe pine
Do you guys help with physics?
lone heartBOT
Do you guys help with physics?
ionic jewel
physics questions usually get help if its easily reducable to math or is kinematic stuff
theres a physics server linked somewhere
limpid turret
Do you guys help with physics?
sick crest
lone heartBOT
sick crest
could sm1 explain
this plz
like how must the rref of R be 1 1/2
should it not be 1 2
cerulean thistle
lone heartBOT
cerulean thistle
Yo
cerulean thistle
Bot is down pretty sure
weak plinth
1 sec
weak plinth
cerulean thistle
Okay
weak plinth
then obviously we can focus on the right now
cerulean thistle
Okay
weak plinth
do you know how we can simplify it
cerulean thistle
Cancel out the x?
weak plinth
no dawg think about exponent rules
cerulean thistle
we combine like terms?
weak plinth
IDK what that means
cerulean thistle
how did u get that
cerulean thistle
i think she might provide that
weak plinth
you should make it second nature
cerulean thistle
what does that mean
weak plinth
it should be really easy
to the extent you dont need her to provide it
its just intuitive
so do the rest of the worksheet
weak plinth
use the product rule
weak plinth
cerulean thistle
where did the 7 come from
weak plinth
-1 + -4/3 = -7/3
weak plinth
yeah
cerulean thistle
how do i add that
weak plinth
how do i add that
you wanna make the denominators equal
cerulean thistle
so 1+2=3
weak plinth
no
cerulean thistle
so
cerulean thistle
cross multiply?
weak plinth
the key is to realise 2 = 2/1
weak plinth
yeah
now youve done everything you can right now
so look back to the exponent rules
cerulean thistle
ok
weak plinth
and see if theres something else you can apply
cerulean thistle
how
There the same
so do they stay the same? i know the bottom number stays the same
weak plinth
cerulean thistle
o
weak plinth
weak plinth
i used the negative exponent rule
cerulean thistle
the red is her answer
cerulean thistle
ok
weak plinth
do you see why her answer works?
cerulean thistle
ok
weak plinth
weak plinth
night quest
lone heartBOT
split mantle
Do you find a pattern?
night quest
I don't 
split mantle
Let's say, the big one is the sum of the small ones.
Try finding a pattern based on that.
In other words, see the arrows as vectors.
lone heartBOT
@night quest Has your question been resolved?
night quest
thank you Good !
crimson crag
yo
lone heartBOT
@crimson crag Has your question been resolved?
alpine sable
i need to solve this equation
how will you without further info
lone heartBOT
@crimson crag Has your question been resolved?
final nimbus
there is 5 blue marble 3 red marbles and 2 white marbles
one marble get picked and does not get replaced
then another gets picked
what is the probabilty of the marble being the same colour
final nimbus
This question is on probability
lone heartBOT
@final nimbus Has your question been resolved?
alpine sable
there is 5 blue marble 3 red marbles and 2 white marbles
one marble get picked a...
@final nimbus still need help
hollow sorrel
friend of mine needs help with this equation
lone heartBOT
friend of mine needs help with this equation
hollow sorrel
<@&286206848099549185>
feral hawk
hollow sorrel
learning
hollow sorrel
ahh k
lone heartBOT
@hollow sorrel Has your question been resolved?
full dome
lone heartBOT
lone heartBOT
Available help channel!
weak parcel
.
fallow wadi
For which a,b,c,d is 4^a + 5^b + 6^c = 7^d
lone heartBOT
For which a,b,c,d is 4^a + 5^b + 6^c = 7^d
thorny mountain
can someone help me with this please
fallow wadi
For which a,b,c,d is 4^a + 5^b + 6^c = 7^d
abcd are from Natural numbers including 0
thorny mountain
huh?
thorny mountain
oh mb idk how to use this server properly lol
lone heartBOT
@fallow wadi Has your question been resolved?
young parrot
could someone help me understand this proof?https://www.quora.com/Can-you-use-induction-to-prove-that-the-sum-of-any-two-consecutive-Fibonacci-numbers-is-always-another-Fibonacci-number#:~:text=Yes%2C we can use mathematical,F(n%2B2).
lone heartBOT
could someone help me understand this proof?https://www.quora.com/Can-you-use-in...
tardy stag
wait wtf
F(k+1) + F(k+2) = F(k+3) follows from the definition of Fibonacci numbers; you don't even need an inductive step at all, and it's unclear why the author is (mis)using it
young parrot
right?
tardy stag
honestly I suspect this was ai generated and not reviewed
young parrot
i also suspecct that
tardy stag
i hate the modern Internet
young parrot
but it has 230 positive ratings
just botting?
but yeah i have a final in an hour and fibonacci and induction are the concepts
so i thought id check out inductive proofs of various properties of fibs
tardy stag
no it has 230 views
tardy stag
this is sickeningly gpt
