Ya
#help-10
edgy needle
rich plume
SSA is not a valid criteria
edgy needle
SSA is the same as SAS
rich plume
No
edgy needle
Wut
edgy needle
Thats confusing
edgy needle
Oh
rich plume
not any other one
edgy needle
So how do i do it
rich plume
use AAS
edgy needle
Idk how to find another angle
edgy needle
How do u prove that theyre isosceles
rich plume
How do u prove that theyre isosceles
since radii
edgy needle
Wait can i do this wait let me do it
rich plume
oa, ob, oc are radii
edgy needle
oa, ob, oc are radii
Hello
rich plume
how do you prove AD is perpendicular to BC
obtuse pebbleBOT
@edgy needle Has your question been resolved?
edgy needle
That would not work always
Does it work in this instance?
edgy needle
Or can i do this
Am i right by saying AO = BO = CO (radii)?
sage dagger
I dont understand how they got this answer
obtuse pebbleBOT
I dont understand how they got this answer
sage dagger
a^2/b^2 has powers right so it wouldnt be a constant?
drifting void
yes they did the power rule twice, recgonized that the last term a^2/b^2 is constant so it vanishes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
plain grove
im kinda confused on how id find the laplace transform of X^(1/2) if X is
plain grove
i keep getting a huge integral that just looks wrong
do i first sub in Y = X^(1/2) into the pdf
obtuse pebbleBOT
@plain grove Has your question been resolved?
obtuse pebbleBOT
@plain grove Has your question been resolved?
obtuse pebbleBOT
@plain grove Has your question been resolved?
next basalt
can someone show me how they simplified this?
obtuse pebbleBOT
can someone show me how they simplified this?
next basalt
ik the lcd is 11+h,11 but how did they simplify it?
alpine raven
$\frac{10}{11+h} - \frac{10}{11} = \frac{110}{11(11+h)} - \frac{10(11+h)}{11(11+h)}$
warm shaleBOT
Herels
worn yoke
$\frac{10(11)-10(11+h)}{11(11+h)}$
warm shaleBOT
cloud
heavy umbra
Can someone give me a hint on how to solve this? I actually dont know where to start
An equilateral triangle becomes an isosceles triangle by extending two sides by 6cm each. The isosceles triangle has a perimeter of 24cm. Calculate the side length of the equilateral triangle
obtuse pebbleBOT
Can someone give me a hint on how to solve this? I actually dont know where to s...
fierce lagoon
Let each side of the equilateral triangle be x
Then you can build an equation using the perimeter of the isosceles triangle
heavy umbra
Then you can build an equation using the perimeter of the isosceles triangle
The perimeter of the isosceles triangle would be 2* (x+6) + b, where b is the base, correct?
That was the equation I had built before aswell, but how do I continue from there? Since I have 2 unknowns
heavy umbra
Ohhhh I was dumb, I kept the angles the same and therefore had a new base. But I can change them to keep the base at x right? @fierce lagoon
heavy umbra
I had the image in my mind of just extending 2 of the sides of the equilateral triangle. If I had done that, the base would have gotten larger. Do you know what I mean? Thats where my mistake was @fierce lagoon
fierce lagoon
Yeah
obtuse pebbleBOT
@heavy umbra Has your question been resolved?
crude cape
Hi, I was having doubts about the riemann hypothesis and wanted to ask if anyone knows how to solve it.
\zeta(s) = \sum_{n=1}^{infty} \frac{1}{n^s}
or maybe there are missing axioms to prove it.
obtuse pebbleBOT
Hi, I was having doubts about the riemann hypothesis and wanted to ask if anyone...
kind hawk
I have discovered a truly marvelous proof of this, which this discord chat is too narrow to contain
obtuse pebbleBOT
@crude cape Has your question been resolved?
teal turret
I have discovered a truly marvelous proof of this, which this discord chat is to...
Dm me so I can check (just to make sure ur right)
crude cape
I have discovered a truly marvelous proof of this, which this discord chat is to...
JAJAJA
crude cape
is that not the millenium prize ?
Yea
crude cape
I have discovered a truly marvelous proof of this, which this discord chat is to...
Rather, they were asking whether you think that because of Gödel's incompleteness theorem, the Riemann hypothesis would be impossible to solve.
That is, instead of solving it, it can be shown that it cannot be solved, just like the problem of the sizes of infinities.
obtuse pebbleBOT
@crude cape Has your question been resolved?
exotic creek
how ould you integrate $\frac{1}{y(y-1)}$?
obtuse pebbleBOT
how ould you integrate $\frac{1}{y(y-1)}$?
exotic creek
sorry i wrote it wrong
warm shaleBOT
yomiko
grand sky
np
exotic creek
.close
wooden blade
Given any function f : R → (0, +∞) we define a new function ∆f : R → R
per:
∆f(x) = f(x + 1) − f(x).
Define ∆2f(x) := ∆(∆f)(x) and, given any n ∈ N, define ∆nf(x) = ∆(∆n−1f(x)).
- Prove that ∆(f + g)(x) = ∆f(x) + ∆g(x).
- Prove that ∆(f · g)(x) = f(x + 1)∆g(x) + g(x)∆f(x).
- Prove that ∆(f/g)(x) = (g(x) · ∆f(x) − f(x)∆g(x))/(g(x)g(x + 1)).
- Find a function h(x) that satisfies:
∆h(x) = h(x).
obtuse pebbleBOT
Given any function f : R → (0, +∞) we define a new function ∆f : R → R
per:
∆f(x...
kind hawk
!status
obtuse pebbleBOT
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
1
kind hawk
the first three are just plugging in
wooden blade
what?
kind hawk
plug ∆f(x) = f(x + 1) − f(x) in and simplify
fair notch
what is the difference between gaussian elimination and row reduction in matrices?
obtuse pebbleBOT
what is the difference between gaussian elimination and row reduction in matrice...
nocturne minnow
Gaussian elimination is a method to reduce matrices
fair notch
could you show an exmaple of how they are different?
kind hawk
I don't think anyone makes a proper distinction between the two
unless you are trying to be overly formal
steep fractal
Refer to the graph of 𝑦 = cos 𝑥 to find all the values of 𝑥 that satisfy the
equation cos 𝑥 = √3/2
steep fractal
referring to the unit circle, I came up with this answer: x=pi/6 + 2pi(n) and x=11pi/6 + 2pi(n)
just wondering if someone can confirm what I did was correct.
crystal solstice
It's correct 
steep fractal
awww ye, thanks random discord guy
brave oxide
Can someone help me find my mistake here please?
obtuse pebbleBOT
Can someone help me find my mistake here please?
brave oxide
Answer should be 1/2
I know I shouldn’t have decomposed the bracket but nevertheless it should work right?
brave bramble
Can't break the denominator like that
brave oxide
Whatttt
But it’s just 1 in the numerator
1/(a+b) not equal to a^-1+b^-1?
Hm he
Ye
I guess
Thx
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
agile zealot
Hi guys, I'm stuck with a linear algebra problem.
obtuse pebbleBOT
Hi guys, I'm stuck with a linear algebra problem.
agile zealot
It says as follows: demonstrate that if A is a matrix of mxn, then tr(At.A)=tr(A.At)= s, s being the summatory of the squares of the elements of A
I have been able to demonstrate that tr(At.A)=tr(a.At), but I haven't found a way to demonstrate that those things are equal to s.
English is not my first language so please let me know if anything about my question is unclear
I got this problem from the third edition of introduction to Lineal Algebra by howard Anton, it's the 23 problem of the 1.4 section
obtuse pebbleBOT
@agile zealot Has your question been resolved?
obtuse pebbleBOT
@agile zealot Has your question been resolved?
obtuse pebbleBOT
@agile zealot Has your question been resolved?
tardy epoch
I have been able to demonstrate that tr(At.A)=tr(a.At), but I haven't found a w...
You just do the matrix multiplication
tough bolt
Original problem: suppose that $0\leq f(t)\leq Me^{at}$ and $0\leq f'(t)\leq Ke^{at}$ for $t\geq0$, where $M$, $K$ and $a$ are constants and $f'$ is continuous. If $F(s)=\int_0^\infty{f(t)e^{-st}: dt}$ and $G(s)=\int_0^\infty{f'(t)e^{-st}: dt}$, show that $$G(s)=sF(s)-f(0)$$ for $s>a$.
First of all, I used integration by parts with $u=e^{-st}$ and $dv=f'(t): dt$ on $G(s)$, which ended up with $$sF(s)-f(0)+\lim_{x\to\infty}{e^{-sx}f(x)}.$$.So I only need to show the limit on the right is 0, but I'm stuck.
obtuse pebbleBOT
Original problem: suppose that $0\leq f(t)\leq Me^{at}$ and $0\leq f'(t)\leq Ke^...
warm shaleBOT
Math Is Fun
latent fjord
$\lim_{x\to\infty}{e^{-sx}f(x)$ so you need to prove this part only ?
warm shaleBOT
[ɸ]=1.618033988749....
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
obtuse pebbleBOT
@tough bolt Has your question been resolved?
tough bolt
yes
obtuse pebbleBOT
@tough bolt Has your question been resolved?
tough bolt
<@&286206848099549185>
latent fjord
we know that f(x) is constraint in the finite value whereas the exponential function in the denominator reaches infinity , therefore it will reach zero
$\frac{f(x)}{e^{sx}}$
warm shaleBOT
[ɸ]=1.618033988749....
latent fjord
@tough bolt
obtuse pebbleBOT
@tough bolt Has your question been resolved?
rocky nymph
Hello everyone,
May I please ask on how to integrate -log(x)
knotty gulch
rocky nymph
<#488120190538743810>
Thanks
sleek mural
obtuse pebbleBOT
sleek mural
Could someone plz solve #2 and lmk what they get?
This is my process + answer (circled)
obtuse pebbleBOT
@sleek mural Has your question been resolved?
rich plume
It’s pi*r*l+pi*r^2
that is TSA
not CSA
the circle part of cone is covered by the cylinder so it won't count even when considering TSA
sleek mural
that is TSA
Idk what that means
sleek mural
the circle part of cone is covered by the cylinder so it won't count even when c...
Yeah, that’s why I subtracted by pir^2
It’s the same thing
Could u just lmk what u get?
rich plume
The formula for this would be pi*r*l+2*pi*r*h+2*pi*r
CSA of cone + CSA of cylinder +area of bottom circle
My bad your answer is correct
@sleek mural
sleek mural
My bad your answer is correct
Got it, nw, ty
obtuse pebbleBOT
@sleek mural Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
how do I do this
dusk pasture
plug into a formula
timid silo
what formula
dusk pasture
your teacher didn’t give you it?
timid silo
naw he didnt
timid silo
you don't need a formula
you can come up with the solution just by looking at the shape
is 18 a
dusk pasture
nope
obtuse pebbleBOT
@timid silo Has your question been resolved?
hard citrus
How does the cotangent part becomes the -cos(a)/sin(a)?
obtuse pebbleBOT
How does the cotangent part becomes the -cos(a)/sin(a)?
native inlet
How does the cotangent part becomes the -cos(a)/sin(a)?
$\cot\theta=\frac{1}{\tan\theta}=\frac{1}{\frac{\sin\theta}{\cos\theta}}=$\fbox{$\frac{\cos\theta}{\sin\theta}$}
warm shaleBOT
XxMrFancyu2xX
hard citrus
what exactly are you trying to do? what does the h mean?
we are just trying to simplify it to the bottom
timid silo
1+cot^2 = cosec^2
timid silo
**XxMrFancyu2xX**
you can prove that by writing out cot like this ^
timid silo
put the 1 on a common denominator with cos^2/sin^2
hard citrus
so sin^2/sin^2
hard citrus
so 1 - cot
timid silo
$1+\cot^2\theta=1+\frac{\cos^2\theta}{\sin^2\theta}=\frac{\sin^2\theta+\cos^2\theta}{\sin^2\theta}=\mathrm{cosec}^2\theta$
warm shaleBOT
Toby
timid silo
you are missing squares
hard citrus
yeah
timid silo
wait so 1 + cot^2 = cosecant^2
yes
hard citrus
so how does it become -cos(a)/sin(a)
fringe minnow
obtuse pebbleBOT
candid yarrow
!status
obtuse pebbleBOT
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
@fringe minnow Has your question been resolved?
Available help channel!
sleek surge
How do I find the CV of this
sleek surge
Help
rich plume
what do you mean by CV?
rich plume
oh derivative of this?
sleek surge
oh derivative of this?
rich plume
Ramonov's here and he'll prolly explain it better
sleek surge
Oh okay
high lily
determine locations where:
- the derivative is 0
- the derivative is undefined but the original function is defined
sleek surge
determine locations where:
- the derivative is 0
- the derivative is undefined b...
Yeah it’s undefined
so how do I find the min and max and stuff
high lily
for the location where
the derivative is 0
you can attempt to use the second derivative
for
the derivative is undefined but the original function is defined
consider the slopes before and after that location
sleek surge
for the location where
> the derivative is 0
you can attempt to use the second d...
I meant it’s not required for me to do that
high lily
then use the first derivative around the location where
the derivative is 0
as well
that seems what they want you to do from that table with f'
high lily
determine locations where:
- the derivative is 0
- the derivative is undefined b...
what were you three x values from this
were there examples on how they wanted you to put in the table
sleek surge
what were you three x values from this
I’m confused
If it’s undefined how else am I supposed to the critiCal points
high lily
use the original function
the derivative is undefined but the original function is defined
is indicative of stuff like corners or cusps
for what values of x are f'(x) undefined
sleek surge
But to find Critical points you must use the first derivative right?
high lily
yes...
which you have...
missing - sign in the second line btw
not sure what's with the 0 at the end
you have
$$f'(x) =\frac{4x}{3(x^2-4)^{\frac13}}$$
warm shaleBOT
ℝamonov
high lily
when is that undefined
obtuse pebbleBOT
@sleek surge Has your question been resolved?
odd mountain
obtuse pebbleBOT
odd mountain
Hey! Aftersolving the solution i got x belongs to {2, 4} which means its only 2 real solutions but the correct answer is 3
tame narwhal
does the exponent ever equal 0?
trim portal
does the exponent ever equal 0?
||yeah, there are 2 more solutions, which means that correct ans is either incorrect, or x belongs to {2, 4} is incorrect||
tame narwhal
||yeah, there are 2 more solutions, which means that correct ans is either incor...
yea I noticed that
trim portal
Hey! Aftersolving the solution i got x belongs to {2, 4} which means its only 2 ...
2 is wrong solution
trim portal
why 4?
brisk matrix
the exponent has 2 solutions no?
trim portal
oh abs
brisk matrix
trim portal
~~2 is wrong solution~~
Sorry, it's correct. I forgot about the absolute value. So by solving for exponent = 0, you will get one more solution, since the other solution will result in 0^0 which is undefined
odd mountain
ohh wait i was away, could anyone just explain it again sorry 😬
odd mountain
~~2 is wrong solution~~
is it?
tame narwhal
you also want to see where the exponent equals 0
since x^0 = 1 for any x (as long as x isn't 0 as well)
odd mountain
ok so, its either that log |x-3| = 0 or the quadratic is 0 right?
and then take the union of both solutions
tame narwhal
yea I think that's a fine approach
obtuse pebbleBOT
agile halo
Can someone send a solution of this. I am getting stuck on the last step.
fierce lagoon
Just plug in each of the solutions to see if they're true
I wouldn't bother with the algebra of finding the point(s) that work
Just check to see if each point works
agile halo
ohhh I was trying to solve it first. so i just need to plugin the points in any one of the equation?
and thta's it?
fierce lagoon
Well yeah. They gave you a list of possible solutions
agile halo
ok perfect got it
fierce lagoon
Just determine which ones are actual solutions. The easiest way to do that is to check each one
agile halo
thanks
rancid leaf
why the solution is 0? I don't understand it :c
obtuse pebbleBOT
why the solution is 0? I don't understand it :c
fierce lagoon
Translate it
tame narwhal
f is a continuous function such that f(x, y, z) = -f(x, y, -z). find the value of the triple integral if D = that set
fierce lagoon
Well idk if "odd" is the correct term for multivariable functions
But that's kinda what's happening
spice citrus
z-odd?
fierce lagoon
If (x, y, z) is in D, then (x, y, -z) is also in D
Up here
Note that D is a cylinder
rancid leaf
right
then it will be a circle on the plain xy, and a circle is not a odd function :c
fierce lagoon
Well think about it
If (x,y,z) is in D then (x, y, -z) is also in D
That's what it implies
Now because, in terms of X and Y, because a cross section is just a circle centered at the origin
The x and y values don't matter
But the z and -z, they will cancel each other out
rancid leaf
why the x and y terms don't matter?
kind hawk
write it as an iterated integral. int_circle int_z f(x,y,z) dz dcircle
fierce lagoon
Because it's a circle. There are an equal number of positive x-value coordinates as there are negative; likewise there are en equal number of positive y-value coordinates as there are negative.
x + -x = 0
y + -y = 0
That's what the x^2 + y^2 < 1 implies
rancid leaf
Because it's a circle. There are an equal number of positive x-value coordinate...
Eeeh and why if are the same equal number of positive and negative, they don't cancel outf?
rancid leaf
I'm lost :c
fierce lagoon
Because it's a circle. There are an equal number of positive x-value coordinate...
Think about this
obtuse pebbleBOT
@rancid leaf Has your question been resolved?
whole drift
I am attempting to prove this formula to be a tautology using logical equivalences: [ (p-->q)^(r-->s) ] -->[ (pVr)-->(qVs) ]
obtuse pebbleBOT
I am attempting to prove this formula to be a tautology using logical equivalenc...
whole drift
So far I have gotten this in steps for my proof:
[ (p-->q)^(r-->s) ] -->[ (pVr)-->(qVs) ]
x = (p-->q)^(r-->s)
y = (pVr)-->(qVs)
x -> y
~x V y. Conditional rule. Substitute back in
~ ((p-->q)^(r-->s)) V (pVr)-->(qVs)). De Morgan's Law
((p ^ ~q) V (r ^ ~s)) V (pVr)-->(qVs))
z = (r ^ ~s) Substitution
(p ^ ~q) ^ z V (pVr)-->(qVs) Distribution
I am wondering if I am on the right track at all and if my steps make sense. If I am not where did I go wrong in my steps
tame narwhal
your line after DeMorgan's Law is not correct. it should be a logical OR on the left hand side
also how do you conclude that r = (r ^ ~s)?
whole drift
also how do you conclude that r = (r ^ ~s)?
Should i use a different variable name. I was trying to substiute the value so I can preform distributive law
tame narwhal
yes because then the "r" on the left is different from the "r" on the right
in the following line
whole drift
I see what you mean the two values are different in the formula so it would be confusing and not right
are the steps I took correct?
Should i attempt to simplify the right hand side or something else like the whole formula again
tame narwhal
they look valid, at least. are you sure it's a tautology?
whole drift
Yeah the original function is a tautology just not sure if my simplified function is logically equivalent
tame narwhal
are you allowed to use a truth table
whole drift
i have to verify in two ways, truth table and logical equivalnces
I did the truth table and it was a tautology
obtuse pebbleBOT
@whole drift Has your question been resolved?
tame narwhal
OK I think I have a way to do this one
starting with the left, you have $[(p \rightarrow q) \land (r \rightarrow s)] \iff [(\neg p \lor q) \land (\neg r \lor s)]$
warm shaleBOT
cwatson
tame narwhal
and then I think, by "addition" the latter is equivalent to $[(\neg p \lor q \lor s) \land (\neg r \lor q \lor s)]$. see if you can figure out how to get the RHS from there
warm shaleBOT
cwatson
tame narwhal
but i'm not 100% sure if the last step would be valid
obtuse pebbleBOT
@whole drift Has your question been resolved?
golden spear
The question is for which set of values for p the sequence is increasing
golden spear
Can you give more context?
alpine raven
a sequence (a_n) is increasing if a_{n+1} - a_n > 0, thats it
the work remaining is just algebra
languid pelican
its increasing if a_{n+1} - a_n > 0
Does this work EVERYTIME?
Irrespective of whether you use p or g or t or whatever or how complex it is
Asking for my own self use
alpine raven
Does this work EVERYTIME?
I've never said it does. The question is asking for which values of p the sequence a_n is increasing. So I will just come back to the definition. If the definition doesn't work I'll think of something else.
languid pelican
I've never said it does. The question is asking for which values of p the sequen...
The definition is
languid pelican
its increasing if a_{n+1} - a_n > 0
This?
languid pelican
I'm not trying to disprove you.
I'm learning myself
When will this definition fail?
alpine raven
what do you mean by failing
languid pelican
I mean you said it'll increase if {the stuff} > 0
When will it still be increasing but {the stuff} != 0
golden spear
ok so how do I solve this?
languid pelican
I'll go sleep.
Thanks for the question
Will brainstorm someday later
golden spear
@alpine raven
obtuse pebbleBOT
@golden spear Has your question been resolved?
golden spear
I suppose this is the correct solution
Another one: what is the biggest value of the function in this range?
alpine raven
I suppose this is the correct solution
yes gg
fossil mountain
How can I find the global min and max of a function of two variables in a certain region?
obtuse pebbleBOT
How can I find the global min and max of a function of two variables in a certai...
royal basin
do you know any multivariable calculus
obtuse pebbleBOT
@fossil mountain Has your question been resolved?
obtuse pebbleBOT
fossil mountain
do you know any multivariable calculus
Yes.
I know I'm supposed to do partial derivatives.
late flare
why am wrong
obtuse pebbleBOT
@late flare Has your question been resolved?
tardy epoch
That's not the correct corresponding angle to 38
timid silo
please help with fifth
obtuse pebbleBOT
please help with fifth
azure anchor
!status
obtuse pebbleBOT
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
i don't know where to begin
knotty gulch
send full q
timid silo
That is all I have
knotty gulch
after the =?
azure anchor
none of these are special angles. you just do this by calculator usually.
30 is the only one
knotty gulch
i think it would be useful to get them all in a sin
tardy epoch
,calc cos(30 deg) * sin(40 deg) * cos(70 deg) * sin(80 deg)
warm shaleBOT
Result:
0.1875
knotty gulch
that’s nice
azure anchor
wow rational
knotty gulch
find why
tardy epoch
,tex .prod2sum
warm shaleBOT
riemann
tardy epoch
maybe use the middle equation twice. or the first and last equation.
warm shaleBOT
riemann
timid silo
cos30sin40cos70sin80=sin60sin40sin20sin80
,calc sin (60 deg) * sin (40 deg) * sin (20 deg) * sin (80 deg)
warm shaleBOT
Result:
0.1875
cos30sin40cos70sin80=cos30cos50cos70cos10
,calc cos (30 deg) * cos (50 deg) * cos (70 deg) * cos (10 deg)
warm shaleBOT
Result:
0.1875
.close
sacred crown
I've forgotten how to deal with exponents when rearranging, please walk me through how to solve for r
EDIT:
While we're at it, please show me how to solve for t as well
obtuse pebbleBOT
I've forgotten how to deal with exponents when rearranging, please walk me throu...
azure anchor
is r a variable or a constant
tropic lantern
I've forgotten how to deal with exponents when rearranging, please walk me throu...
you could try distributing
azure anchor
well, to start, exponentiation is an operation. all operations have an opposite counterpart. in this case, the opposite operation of exponentiation is a logarithm
the exponent function has two components, a base, and the power.
in this case the base is (1 + r)
sacred crown
Yup I'm with you
azure anchor
A/P = (1 + r)^t right
to get t we need to log both sides. since using (1 + r) as a base of our logarithm is, well, not really practical. we are going to use something better as a base, usually e.
logarithms with base e are natural logarithms
this also opens up a whole slew of ways to manipulate our expressions
look up natural log laws when you get a chance
sacred crown
Yeah 100% was goiing to ask
azure anchor
to take natural log of both sides will look something like this, including an application of change of base formula
$\ln\left(\frac{A}{P}\right)=\frac{\ln t}{\ln\left(1+r\right)}$
warm shaleBOT
b0ngl0rd
azure anchor
then you can use some standard algebra to get this
$\ln\left(\frac{A}{P}\right)\ln\left(1+r\right)=\ln t$
warm shaleBOT
b0ngl0rd
azure anchor
then to undo logarithms you raise an expression as a power of the base
natural log base is e
oops
dawn trout
If a velocity as expressed in polar is R,θ: (a + bt, k + st), how do I get the position equation (In polar, without converting to cartesian)?
t is time, the others are constants.
Simply integrating like in cartesian doesn't seem to be enough- Or rather, the integration method seems to be different and I can't find how to do it.
obtuse pebbleBOT
If a velocity as expressed in polar is R,θ: (a + bt, k + st), how do I get the p...
@dawn trout Has your question been resolved?
tardy epoch
I imagine integration would be even worse
calculations in this thread the second to last OP asked the question #help-36 message
dawn trout
I imagine integration would be even worse
Oof. Are you suggesting I should give up on it?
haughty coyote
Unless you're really motivated, yes
Convert to cartesian, integrate, convert to polar
If you're a computer it's not a problem anyways
dawn trout
Unless you're really motivated, yes
I'm surprised it's so complicated. the polar vector equation is so straightforward
haughty coyote
It's a coordinate system, it doesn't behave as well as one that is derived from a basis of a vector space, such as cartesian coordinates
There's basically no reason to expect it to be nice
dawn trout
It's a coordinate system, it doesn't behave as well as one that is derived from ...
I guess that's true..
dawn trout
calculations in this thread the second to last OP asked the question https://dis...
Just to clarify, do you actually know how to do it? I'm assuming not?
dawn trout
There's basically no reason to expect it to be nice
Thankies for the guidance, in any case ^^ I'll give it one last try on my own and then move on
silver plover
can we use greens thm for part a?
obtuse pebbleBOT
@silver plover Has your question been resolved?
cerulean bay
How would I solve this
obtuse pebbleBOT
How would I solve this
fleet cloud
I'm sure there's probably an easier way than what I'm about to give but you could set y = 0 for each and then use the quadratic formula and see which equation gives you the same values you have on the graph.
Whichever one spits out positive 4 and positive 9 will be the correct one. Are you familiar with the quadratic formula?
cerulean bay
Yeah I was going to to do this but I was wondering if there was a easier way then trying that with each equation. But thank you!
fleet cloud
np
obtuse pebbleBOT
@cerulean bay Has your question been resolved?
obtuse pebbleBOT
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timid silo
obtuse pebbleBOT
timid silo
For systems of inequalities, do we simply just treat the inequalities as equal signs and solve as if they are equations.
languid pelican
For systems of inequalities, do we simply just treat the inequalities as equal s...
No
They're special
languid pelican
I don't have expertise in this area
But y=7x is a straight line graph
So here, y can be ON the line (w.r.t a given x co-ordinate)
Or below it
Same for the 2nd equation
You draw a rough graph i guess, then try to see what the values of y can be for both lines
And find the max
Try it
I'm sure you'll come across 2 lines which will intersect.
The intersecting point should be the max possible
brisk arrow
obtuse pebbleBOT
brisk arrow
Why the smaller triangle’s area isn’t (1/3)A
native inlet
The ratio of areas is a squared factor to the side lengths
so if you 1/3 the side lengths
you (1/3)^2 the area
brisk arrow
How to explain the phenomenon, I mean it does looks like it is 1/3 A
Meanwhile we know it’s not
With the perspective of geometry
native inlet
and what about a sqaure with side length 2S?
native inlet
double the side length
quadruple the area! 
as for your example $\frac{\sqrt{3}}{4}\cdot\left(\frac{1}{3}\right)^2=\frac{\sqrt{3}}{36}$
warm shaleBOT
XxMrFancyu2xX
native inlet
🎉
brisk arrow
I feel like the whole world has changed, the way I look into things are different now
Thank you so much
native inlet
Thank you so much
yw man! have a great day!
brisk arrow
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maiden owl
Help on solving this without a caluclator? There's some piece of info or tool i must be skipping cause you can't just solve it following our little guide here...
obtuse pebbleBOT
Help on solving this without a caluclator? There's some piece of info or tool i ...
maiden owl
😦
forest sinew
are you sure you copied the problem correctly?
obtuse pebbleBOT
@maiden owl Has your question been resolved?
high lily
are you sure this is a non-calculator question
maiden owl
Hmmmm.... if there doesnt seem to be a way around it
Then it must be a calculator problem after all
Sadge
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obtuse pebbleBOT
obtuse pebbleBOT
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fresh shale
4sin^3 (x) - 3sin (x) + 4sin^2 (x) = 3
need to find the General Solution in Radians
obtuse pebbleBOT
4sin^3 (x) - 3sin (x) + 4sin^2 (x) = 3
need to find the General Solution in Ra...
fresh shale
i tried factoring using synthetic division and substituting sin(x) = A but it did not work. not sure how to proceed
pine sail
Factor sin(x) from first two terms.
And write the other two terms just like that.
Of course, everything needs to be in the same side.
fresh shale
sin(x)( 4sin^2 (x) + 4sin(x) ) - 3 sin(x) - 3 = 0
got it down to (sinx+1)(4sin^2(x) - 3) = 0
how do i find the general solution for 4sin^2 (x) - 3??
?
obtuse pebbleBOT
@fresh shale Has your question been resolved?
fresh shale
<@&286206848099549185>
fresh shale
how do i find the general solution for 4sin^2 (x) - 3??
^
obtuse pebbleBOT
@fresh shale Has your question been resolved?
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timid silo
why when i add a number to tanx^2 it becomes like a sinusoidal function?
dark vector
why when i add a number to tanx^2 it becomes like a sinusoidal function?
$(\tan^{2}(x) + 1)^{-1} = \left(\frac{\sin^{2}(x) + \cos^{2}(x)}{\cos^{2}(x)}\right)^{-1} = \left(\frac{1}{\cos^{2}(x)}\right)^{-1} = \cos^{2}(x)$
warm shaleBOT
OutOfNosh
timid silo
yeah i see i tried writing that this way but i did a mistake and there were like 10 sines
thanks
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obtuse pebbleBOT
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fleet hull
pls help me im going to rip my hair out
obtuse pebbleBOT
pls help me im going to rip my hair out
ashen zenith
Hello guys I want to learn Limits and Functions, if anyone has lectures in google drive or any tutor whose lectures are available in YouTube then kindly guide me! I'll be thankful to him!
Start from basic.
karmic field
I would split it up into a few faces: the top down view, the side x 2, the bottom or base, the front and the back
The base is 8.9 by 4.6 meters. The front face is 1 m by 4.6 m. The top is 8.8 meters by 4.6 meters. Do you know how you would calculate the side area?
karmic field
this is supposed to be the answer btq
Yes so what you want to do is fine the areas of each of the faces, add them together then multiply them by the cost of the tiles so 85
Okay so you need to split the side face into two areas
An area of a square which is 1m by 8.9m Then a triangle which is 1m by 8.9m.
You can then add the area of the square and triangle together
fleet hull
huh???
fleet hull
is it okay if you draw it out? im a visual learner and i need to see a drawing to understand lol
knotty gulch
how do you know which angles are right angles
karmic field
I can draw it out don’t worry
fleet hull
thank you smm
karmic field
Here are the faces of the areas you are trying to calculate
In order to calculate the areas you are multiplying lengths that make it up, so for the top left it is 4.6 x 1, for the top right it is 8.8 x 4.6
fleet hull
why is it one tho???
karmic field
Because in the diagram you showed me, the side length was 1 meter
fleet hull
oh
karmic field
So to find the area of the side face, how would you approach it knowing it needs to be split into a rectangle and a triangle and then the areas added together
karmic field
You can use Pythagoras here yes!
So first find the area of the rectangle which is 1 meter by 8.8 meters as in the diagram we saw that the side left length was 1m and the across length was 8.8 meters
Would would be the area of this rectangle?
karmic field
It’s all good don’t worry
So I drew a green line across the shape
We want to calculate the area of the face that is facing us
And that is above that green line
So can see that is it 1 meter tall
And 8.8 meters length
So yes we multiply 1 x 8.8
karmic field
Yeah my earlier explanations were too complicated
Okay so now we know the area of the rectangle
All we now need to do is find the area of the triangle below
fleet hull
ok
karmic field
You suggested Pythagoras
How would you apply Pythagoras to this shape?
To help find the area
fleet hull
l^2 = a^2 + b^2
= 8.9^2 + 1^2
= 80.21
square root 80.21
= 8.95600........
karmic field
Close
fleet hull
huh
karmic field
But we already have l and we are trying to find either a or b
So we need to rearrange the equation to be b^2 = l^2 - a^2
Here is my working
This is because Pythagoras is trying to find the longest length of a right angled triangle
Because we already have the longest length
We have to re arrange the equation to make it so we can find the length we don’t have
In this case I said it was b
fleet hull
i did it and got 8.843641....
karmic field
That is correct! I just chose to leave it in the square root form so I don’t have to write out all the decimals
fleet hull
so whats the answer
karmic field
Okay so now we have the base length and the height of the triangle, we need to now find the area of this triangle
karmic field
So we multiply together our a and b and then multiply it by 1/2
So we get
Well now we need to add the area of the rectangle above so 4.42 + 8.8
So that’s how we get 13.2 as seen as part of the answer
karmic field
Okay well for the final answer all you need to do is add up all the areas
So
(4.6 x 1) + (8.9 x 4.6) + ( 2 x 4.6) + 13.2 + 13.2
We add the 13.2 which is the area of our triangle twice because it is on two sides
NOTE: we did not include the top area because a swimming pool is open on the top and so we are not trying to tile the roof and make it into a box
After adding it up, multiply it through by 85 and you will get your answer
We multiply it as it is the cost of each m^2 of time
fleet hull
(4.6 x 1) + (8.9 x 4.6) + ( 2 x 4.6) + 13.2 + 13.2
which is 2 x 4.6
karmic field
Ah fair enough lol
fleet hull
THANK U SO MUCH FOR UR HELPPP 💗
karmic field
All good
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
trail musk
first find the eigenvalues
set det(lambda*I - A) = 0
then that should give you an polynomial of degree n in lambda
@tawdry vale
tawdry vale
yah i found that for Q7
and i assume i somehow figured out how to do Q7
but not for Q14
yet
trail musk
so x = [x1, x2]
this doesn't make sense
the dimensions of the matrices are not compatible
tawdry vale
well university shits doesnt make sense anyway
trail musk
no your prof is actually wrong on this
tawdry vale
trail musk
you can't multiply those two matrices
tawdry vale
wait but x is 2x1
so
i suppose can?
or am i just too tired to notice what's wrong
trail musk
unless x is a scalar...
tawdry vale
random sun
but i dont know how to convert to real from
Apply when x(0)
An error in latex or coding is quite common actually. Its so funny
tawdry vale
i am able to reach here
but idk how to conevrt to the similar sin cos stuff form from chegg
New progress
But something went wrong
With reference to this
math is not mathing
<@&286206848099549185> please help
it might sound ridiculous but this thing is deadline in 20mins
smoky plume
are you kidding
tawdry vale
no
but this is only worth 0.16 mark of my grading, so whatever i guess
so basically all i want is to learn how to solve it
cus exam is on monday
smoky plume
ok
tawdry vale
i hope it's not this 0.16 mark that would cause me a grade
smoky plume
tell me the question
tawdry vale
tawdry vale
please help
Q14
tawdry vale
my current progress
smoky plume
what does it say
tawdry vale
the trajectory is correct so just ignore it
smoky plume
ok
tawdry vale
umm
smoky plume
what
tawdry vale
first find eigenvalues and eignevectors
then use it to make a general form of solution
turn it into real form
and solve with the x(0)=[-2;2]
smoky plume
you are a good solver than me
smoky plume
haha
tawdry vale
backup required
smoky plume
why
tawdry vale
nah just kidding
smoky plume
how old are you
smoky plume
i'm 200
timid silo
idik if im missing something in this problem but i have to prove that $\frac{\cos^{4}x+\sin^{4}x}{1-2\sin^{2}x\cos^{2}x} = 1$ so i started by expanding the numerator and i got $\frac{\cos^{2}x\sin^{2}x}{1-2\sin^{2}x\cos^{2}x}$ and the $\sin^{2}x\cos^{2}x$ cancells out right? so im left with $\frac{1}{1-2}$ idk am i missing something here?
obtuse pebbleBOT
idik if im missing something in this problem but i have to prove that $\frac{\co...
warm shaleBOT
MrTrim
gleaming ridge
Use the fact that a^2 + b^2 = (a + b)^2 - 2ab
Choose a & b nicely and you'd be done in 2 steps
@timid silo
timid silo
lol i tried looking up a formula for that
it said not expandeble
good to know
why it doesnt work out that way doe? i checked on the wolfram and the expanding of the numerator is correct
pure sun
Also 0 way something like x^2 * y^2 is equal to x^4 + y^4
old isle
how r u cancelling out the sin^2cos^2 
timid silo
ye it doesnt seem kinda right i didnt know what else to do
old isle
theres a monus sign in the denominator
old isle
Use the fact that a^2 + b^2 = (a + b)^2 - 2ab
just do this
timid silo
ye i already did
timid silo
but idk there must be some other way i wasn't thaught this formula in school
timid silo
whatd u use as a and whatd u use as b
sin^2(x) and cos^2(x)
but now that im thinking this formula is just deduced from another one so why my book said it didn't exist weird
old isle
(a + b)^2 - 2ab
a^2 + 2ab + b^2 - 2ab
a^2 + b^2
old isle
sin^2(x) and cos^2(x)
???
timid silo
and
old isle
show ur work i think you did something wrong
timid silo
wait
old isle
if you did it that way it should be done in literally 2 steps
timid silo
$\frac{(\cos^{2}x+\sin^{2}x)^{2} - 2\sin^{2}x\cos^{2}x}{1-2\sin^{2}x\cos^{2}x}$ so the $1 -2\sin^{2}x\cos^{2}x}$ cancells out and im left with $\frac{1}{1}$ so it's 1
old isle
you cant just cancel out the last part thats not how fractions work but yes the entire thing cancels out
timid silo
oh yeah the entire thing cancells out mb
warm shaleBOT
MrTrim
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
old isle
yeah
timid silo
i wonder if there is another way to do this doe
gleaming ridge
You can also write 1 as (sin^2(x) + cos^2(x))^2
The 1 in the denominator I mean
But this is probably more complicated to think
timid silo
Use the fact that a^2 + b^2 = (a + b)^2 - 2ab
it still would require this or no?
gleaming ridge
Yes, in-directly
timid silo
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obtuse pebbleBOT
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vivid creek
For question 6
obtuse pebbleBOT
For question 6
vivid creek
Why is it when I used the formula ar^n-1 I get it wrong?
But ar^n is right
When that ain’t the formula
timid silo
@vivid creek just find 15% of 20000 and take it as d but take -ve value as deppreciation occurs ( d is common diffrerence)
timid silo
-ve as if value comes 100 then take d as -100
as its depriciating case
@vivid creek
vivid creek
So -0.85?
vivid creek
?
willow lynx
<@1086523102038597662> bro let him solve by himself
alright
vivid creek
So the formula ar^n-1 is wrong?
willow lynx
Price after depreciation = Initial price × (1 - depreciation rate)^number of years
timid silo
idk about formula which you said they taught us (n/2 )*(2a+(n-1)d ) as sum of n terms
vivid creek
Yea I know that formula as well
timid silo
$(n/2 )*(2a+(n-1)d$
warm shaleBOT
Vansh Bagga
vivid creek
So I used this formula to find the answer?
timid silo
yes
timid silo
Price after depreciation = Initial price × (1 - depreciation rate)^number of yea...
or u can use this method also
its just basics
obtuse pebbleBOT
obtuse pebbleBOT
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median dome
hi, I was observing some trigonometric graphs and I noticed that $y=|\sin(x)|+|\cos(x)|$ and $y=1+(\sqrt{2}-1)|\sin(2x)|$ have the same graphs. can anyone think of a way to prove this?
obtuse pebbleBOT
hi, I was observing some trigonometric graphs and I noticed that $y=|\sin(x)|+|\...
warm shaleBOT
kheerii
median dome
probably the easiest way would be to check it quadrant by quadrant
but i want to know how i can somehow derive this
crystal solstice
Unfort7nately, this is not true. The graphs are really similar, but if you zoom in you can see they are different functions
You can get an expression in terms of |sin(2x)| by squaring y, simplifying and then taking the root
obtuse pebbleBOT
@median dome Has your question been resolved?
brave oxide
A never ending loop of integration by parts. What am I missing ?
obtuse pebbleBOT
A never ending loop of integration by parts. What am I missing ?
viral blade
sometimes if you use integration by parts to write an integral in terms of itself
you can replace it with a variable and solve for the variable
obtuse pebbleBOT
@brave oxide Has your question been resolved?
vagrant dawn
Can someone help me with this limit?
obtuse pebbleBOT
Can someone help me with this limit?
vagrant dawn
I'm not sure what to do from here
I know I could just use lhopitalls rule but this is a question given before it's taught in the book so there's a way to do it without that probably
trim portal
I'd suggest rewritting 5^x as e^ln(5) and 2^x as e^ln(2)
warm shaleBOT
MathIsAlwaysRight
vagrant dawn
Like this?
trim portal
yeah, now try to factor out e^xln(2) from the numerator
trim portal
**MathIsAlwaysRight**
it will be somewhat messy, but you will be able to get form of that limit soon
vagrant dawn
**MathIsAlwaysRight**
OK I managed to solve it! Thanks! I just have one more question, how do we know that limit equals 1?
trim portal
I'm not exactly sure bout that, but I guess it could be proved by substituting limit definition of e
yes, it can
and it's really simple
so $e=\lim_{x \to \infty} \left(1+\frac{1}{n}\right)^{n} = \lim_{h \to 0} \left(1+h\right)^{\frac{1}{h}}$
warm shaleBOT
MathIsAlwaysRight
trim portal
**MathIsAlwaysRight**
substituting that as e should help
oh and h would be just x
since they approach same value
vagrant dawn
hmm I'm kinda struggling to fit it into that form
I'm trying to somehow put t as a power of e^(1/t)-1
trim portal
$\frac{\left(\left(1+x\right)^{\frac{1}{x}}\right)^{x}-1}{x}$
warm shaleBOT
MathIsAlwaysRight
trim portal
**MathIsAlwaysRight**
this is what I got when I directly substituted this
vagrant dawn
ooooh I didn't release you could so it like that
I understand now 
Thanks!
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versed pecan
i'm doing b)
obtuse pebbleBOT
i'm doing b)