lol
#help-36
urban sky
urban sky
ok do you understand what the symbols mean ?
frosty swift
yes, sigma
i know it means i need to calculate the sum
the 24 is the last number i think
r is first number i think
and 9-4r is formula i think
urban sky
you have to put values of r from 1 to 24 in the formula and calculate the sum
urban sky
so put r=1 then r=2 then r =3 and calculate the sum
urban sky
wtf does r=1 mean?
it means r starts from 1 and goes till 24
frosty swift
(9-4r)
(9-4 (24))
(9-96)
u24=87
urban sky
yes
urban sky
but you do realise that the series is an arithmetic progression right?
frosty swift
how would I know that
urban sky
write the first few terms
urban sky
for r=1 r= 2 r=3 etc
urban sky
(9-4r)
(9-4 (24))
(9-96)
u24=87
u24 = -87 btw
frosty swift
wowowow
urban sky
-4
urban sky
5-87*
urban sky
s24 = 24/2 (5-87)
in this
frosty swift
I hate maths with a passion
urban sky
lmao calm down you just gotta be careful
frosty swift
s24 = -984
frosty swift
lmao calm down you just gotta be careful
yessir i make tons of errors
frosty swift
that's what I said
urban sky
lol
frosty swift
so its sum from 61 to 158 minus 63,66,69...
mm yes
urban sky
and 63, 66,69....153,156 find this sum and subtract
frosty swift
how am I wrong
urban sky
what does un-u1 give you?
urban sky
put 158 in formula of un and find n
frosty swift
good sir I didn't understand
urban sky
you know d?
frosty swift
is it not just 158 - 61 + 1
frosty swift
you know d?
one
urban sky
yes
urban sky
yes
urban sky
yes
urban sky
why do you keep doing un - u1 +1
frosty swift
i mean it gives the right answer tho no?
urban sky
no
urban sky
why do you keep doing un - u1 +1
oh yea i see this works for d=1
frosty swift
156 = 63 + (n-1)3
156 = 63 + 3n - 3
156 - 63 - 3 = 3n
90 = 3n
n = 30
mm mm mm
wait now do i use geometric sum or arithmetic sum
urban sky
156 = 63 + (n-1)3
156 = 63 + 3n - 3
156 - 63 - 3 = 3n
90 = 3n
n = 30
156-63+3=3n
frosty swift
156-63+3=3n
okay yes 32
urban sky
3n=96
frosty swift
n = 32
urban sky
arithmetic series is when you keep adding the same thing
and geometric is when you keep multiplying the same thing
urban sky
so whats the sum
urban sky
why 72?????/
urban sky
63 + 156?
urban sky
uh what was the sum for 61 to 158
frosty swift
10293
urban sky
ok
frosty swift
soooo yes?
urban sky
yes
urban sky
slight correction
urban sky
not 6789 terms
frosty swift
ENGLISH
urban sky
like 6789 is the answer of the sum you were supposed to calculate
its not number of terms
small crag
final saddleBOT
small crag
The expressions in this triangle below represent the measures of the interior angles. Based on the information provided, what type of triangle is shown in the diagram?
i. Equilateral ii. Isoceles iii. Acute iv. Acute v. Scalene
If your on pc and its hard to read:
Top angle = 10x + 70
Bottom left angle + 6x
Bottom right angle + 4x + 10
I don't really have any work to show because I have no idea what to do
final saddleBOT
@small crag Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
plush stag
final saddleBOT
plush stag
I'm not sure how to go about solving this problem
I've looked at examples, and what I don't understand is where these numbers are coming from
main steppe
I'm not sure how to go about solving this problem
pi/4 and pi/3 are unit circle values, do you know how to find the tan and csc of them?
plush stag
I know how to find those things from a triangle, but not here
This is what other problems have asked, which I had no trouble with
main steppe
This is what other problems have asked, which I had no trouble with
That same chart applies to this problem, although this is a very strange way to teach it (to me)
An explanation of the unit circle is here: https://tutorial.math.lamar.edu/extras/algebratrigreview/TrigFunctions.aspx although if you have to do it the way it was taught I'm not sure
It's basically a bunch of pre-computed triangles for you to use
plush stag
Ohh. That chart was for filling out one of the previous problems. We've gone over the unit circle, but I think I'm having trouble with applying sin, cos, tan, etc to it
main steppe
Ah I see, those values will always hold for those angles. Basically, if you have sin of an angle, you take the y-value of the point. cos of an angle is the x, and tan is y/x. Then you flip them for sec, csc, and cot
main steppe
So this is how I'd work it out?
Perfect!
plush stag
What about ones where there is a number in front, like this?
main steppe
You would do just cos(pi/4) and then multiply the result by 3, and the same process for the sin
main steppe
And how does an exponent on sin, cos, tan, etc work?
kinda the same way, you do cos(45 degrees) then square it, you can treat it like (cos(45 degrees))^2
swift vessel
does anyone know how to get the p0 = 12 at the very end?
final saddleBOT
does anyone know how to get the p0 = 12 at the very end?
static fractal
plugging 20 into f(p) (or g(p)) it looks like
swift vessel
lmao i tried that but i got a different answer, prob did smth wrong
thanks though
.close
final saddleBOT
final saddleBOT
Available help channel!
sudden musk
do u guys have idea why there is the need for i+1-i/i(i+1) if we could already essentially have 1/i(i+1) as thr tule for this sigma notation
final saddleBOT
do u guys have idea why there is the need for i+1-i/i(i+1) if we could already e...
sudden musk
as the rule*
yes but how or why was telescopic sum implemented to that series i cant comprehend it fully
sorry'j
:((
lime shard
Jesus loves yall
lol
use mathway it helps a lot, idk if u have been on that website
lime shard
what is 1+1
Just as 1+1 is 2, so is the fact that Jesus is the I AM, “I am the way and the truth and the life. No one comes to the Father except through me” (John 14:6)., Before they died
Confucius said,
“I am not the WAY.”
Buddha said,
“Seek for TRUTH.”
Mohammed said,
“I don’t know the purpose of LIFE.”
JESUS Christ said,
“I AM the WAY”
“I AM the TRUTH”
“I AM the LIFE”
"I AM the bread of LIFE"
final saddleBOT
Available help channel!
sudden musk
shouldnt it be just 2 (20)(21)/2?
final saddleBOT
shouldnt it be just 2 (20)(21)/2?
tired walrus
shouldnt it be just 2 (20)(21)/2?
this looks like a typo on the book's part, but can you take a photo of the entire page just in case?
soft zealotBOT
final saddleBOT
@sudden musk Has your question been resolved?
vital crag
,rotate
soft zealotBOT
sonic crystal
Find the volume of solid generated by the region under the curve y = tanx for 0 to pi/4, rotated about the x-axis.
final saddleBOT
Find the volume of solid generated by the region under the curve y = tanx for 0 ...
sonic crystal
so im not sure how to integrate tan
final tangle
usub
sonic crystal
let u equal what? x?
sonic crystal
so u = ?
final tangle
it would help to first express tan(x) as sin(x)/cos(x)
there aren't that many options to consider
try and see what happens
tired walrus
actually you dont even need u-sub
just write $\tan^2(x)$ as $\frac{1}{\cos^2(x)} - 1$
soft zealotBOT
Ann
tired walrus
note you will be integrating tan^2(x) not tan(x).
sonic crystal
but wouldn't that affect the volume
tired walrus
wdym?
sonic crystal
like that would change the whole answer
tired walrus
how
final tangle
sry, missed the original question
sonic crystal
because ur taking tan squared
tired walrus
tan^2(x) is equal to 1/cos^2(x) - 1
tired walrus
because ur taking tan squared
remember the disk method formula tho?
tan is supposed to be squared
sonic crystal
oh yeah
lol
$\pi\int_{0}^{\frac{\pi}{4}}\tan^{2}xdx=\pi\int_{0}^{\frac{\pi}{4}}\frac{1}{\cos^{2}x}dx$
soft zealotBOT
water beam
sonic crystal
okay yeah thats easier now
soft zealotBOT
Ann
soft zealotBOT
Ann
sonic crystal
$\tan^2(x) = \sec^2(x) - 1$ might look more familiar to you
so i have thiis
$\pi\int_{0}^{\frac{\pi}{4}}\left(\frac{1}{u^{2}}-1\right)\cdot\frac{du}{-\sin x}$
soft zealotBOT
water beam
sonic crystal
but im not exactly sure what to do next
perhaps change the -1 into u^2/u^2?
is that allowed
I let u be cosx btw
worthy shale
substitution was not necessary
sonic crystal
huh
tired walrus
you need to recognize 1/cos^2(x) as the derivative of tan(x)
$\int \frac{1}{\cos^2(x)} \dd{x} = \tan(x) + C$
soft zealotBOT
Ann
sonic crystal
oh
tired walrus
and don't forget to integrate the -1 into -x obviously as well
sonic crystal
lol
ok
i see
Now for the region bounded by $y=\sqrt{x}$ and $y=\frac{x}{2}$ rotated about the x axis the integral would be $\pi\int_{0}^{4}\left(\sqrt{x}-\frac{x}{2}\right)dx$ ?
soft zealotBOT
water beam
soft zealotBOT
water beam
sonic crystal
i feel like its just random when you do the minus functions part but like right here It seems to have made sense to subtract upper - lower function
worthy shale
is it region or volume
sonic crystal
im finding the volume
also new quesitpon
for the region bounded by $y=\sqrt{x}$ and $y=\frac{x}{2}$ rotated about the y axis
soft zealotBOT
water beam
sonic crystal
should i first get these in terms of x
worthy shale
if you're finding the volume between two functions, that's the same as the volume from one minus the volume from the other
yes
worthy shale
if you're finding the volume between two functions, that's the same as the volum...
which is not what you did
tired walrus
$\pi\int_{0}^{4}\left(\sqrt{x}-\frac{x}{2}\right)^{2}dx$
this integral is a pseudopolynomial
you don't need any trickery for it
tired walrus
ok in fairness "pseudopolynomial" is a term i made up
but anyway like
you know how to integrate polynomials you don't need any special trickery right?
you can just apply the power rule
sonic crystal
uh huh
tired walrus
yes i never said you didn't
what im saying is that the "just apply the power rule" thing is still true even if you don't require the exponents on x to be positive integers, but allow them to be whatever
as long as they're still exponents on just x and not on something funkier
so the stuff under your integral is $\paren{x^{1/2} - \frac12 x}^2 = x - x^{3/2} + \frac{1}{4}x^2$
soft zealotBOT
Ann
thin kernel
How do you plug this equation into the calculator do solve for x I have no clue
thin kernel
final saddleBOT
@thin kernel Has your question been resolved?
thin kernel
<@&286206848099549185>
remote sorrel
since it is mc i think you just put in the value to x to find the answer
thin kernel
since it is mc i think you just put in the value to x to find the answer
It's asking for the x value at y=2 I think
remote sorrel
ummm... in my way i think i will just put the a value(0.512) b value (1.849) ... to the f'(x) then find out which close to the 2
floral talon
So for 2605, I figured out how to do the the first one, but I still don’t get how to solve all the other parts? Is there a certain method I should be thinking about?
final saddleBOT
So for 2605, I figured out how to do the the first one, but I still don’t get ho...
ivory ingot
Yes
Well, in fact, you can even compute each of cos and sin, but that night not be advisable.
floral talon
What should I be doing then?
amber moss
use the fact that sin^2x + cos^2x = 1
floral talon
How does that apply to 2605 b?
amber moss
well
ivory ingot
$\sin^2 \alpha + \cos^2 \alpha = 1$
soft zealotBOT
Absta
ivory ingot
So there's a trick to compute a - b from a + b knowing ab.
(a - b)^2 = (a + b)^2 - 4ab.
ivory ingot
..Difference of squares..?
floral talon
(a-b)^2= (a-b)(a+b)
ivory ingot
You are likely thinking of a^2 - b^2 = (a + b) (a - b)
ivory ingot
No, use (a - b)^2 = (a + b)^2 - 4 ab
tranquil pine
you know the first part so you can just put that value there
sharp tundra
hi
soft zealotBOT
Umbe
sharp tundra
yes or no?
floral talon
I don’t know man
sharp tundra
im saying this
floral talon
I think so
soft zealotBOT
Umbe
sharp tundra
let me check rq
sharp tundra
$√x(25) = \frac{10^3x}{200}$
soft zealotBOT
Umbe
floral talon
Let’s see
sharp tundra
I believe its true
floral talon
Yes
floral talon
True
floral talon
Wait your right
sharp tundra
so we'll get x5
sharp tundra
$x\left(5\right)=\sum_{n=4}^{14}n+\frac{26x}{5}$
soft zealotBOT
Umbe
sharp tundra
uhm
sharp tundra
k
so the sigma will get 99
so n=99
99+ 26x/5
x(5) = 99+5.2x
which is false
am I correct
sharp tundra
k
and this is the last problem I have,
$x\left(3\right)+\ x\left(7\right)=\log_{4}\left(64\right)x+\log_{7}\left(823,543\right)x$
soft zealotBOT
Umbe
floral talon
X =0
floral talon
No the second one
sharp tundra
k
floral talon
The top one looks right to me
sharp tundra
The top one looks right to me
so the sigma one is false
floral talon
Right
floral talon
What kind of math are you doing💀
sharp tundra
What kind of math are you doing💀
oh
floral talon
You went from 2rd grade up to 10th real fast
floral talon
Mhm
sharp tundra
$f\left(x\right)=\int_{5x}^{7x}n+\frac{d}{dx}$
soft zealotBOT
Umbe
floral talon
Alright buddy
sharp tundra
Let me check the equation
its fine
floral talon
No I got it
sharp tundra
it's not even in my homework lol
it's just what are we going to learn
after what I'm doing
floral talon
What are you doing now💀
floral talon
Your ducked💀
sharp tundra
Your ducked💀
fr
floral talon
Like when you started off with algebra
I was like
This kid is 7 years old
Then you jumped to intergrals💀
sharp tundra
idk why it's like that
basically our teacher said most of our questions are true and false for this area of math
floral talon
You got a wack teacher 🥶
sharp tundra
You got a wack teacher 🥶
eh
and he's also teaching us complex math like this
$\left(\sum_{n=5}^{24}n+\sin^{-1}\left(0.74\right)\cdot x^{\sqrt{187}}\right)\log_{6}\left(216\right)$
soft zealotBOT
Umbe
sharp tundra
Like Algebra 2 LOLL
sharp tundra
That is NOT algebra 2
at this point idk my teacher is teaching me loll
but my classmates think that's what were actually learning
floral talon
I don’t think so💀
floral talon
Calc if your are solving integrals
sharp tundra
he said were learning integrals sooner in the year of algebra 2
for pre-cal
anyway
thanks for your help
.close
eternal wharf
How to solve this one?
final saddleBOT
How to solve this one?
blazing orbit
Fermat's Little Theorem?
Just suggesting, I haven't actually tried I'm sorry if it's not right
final saddleBOT
@eternal wharf Has your question been resolved?
cosmic warren
I think I got a sln?
wait hold on
ok yeah and it does sort of involve fermat's little theorem, I might be able to cut a few steps by actually using fermat's directly but w/e
So fermat's theorem basically says $a^{p- 1} \equiv 1 \mod p$
soft zealotBOT
992qqoloy
cosmic warren
The ez way to prove that is using group theory
the harder way to prove that I dunno tbh 
but yeah if you're curious: $Z/pZ$ has $(p - 1)$ elements, by a slightly indirect application of Lagrange's thereom every element in the group has order divisible by the order of the group, i. e. divisible by $p - 1$, so $a^{p-1}$ equiv to identity
soft zealotBOT
992qqoloy
cosmic warren
Well the multiplicative group of Z/pz
If u don't know group theory trust me this is like first few weeks basics it's not actually that bad 
but w/e that's just a tangent
scarlet sequoia
$\bZ / pq\bZ \approx \bZ / p\bZ\times \bZ / q\bZ$.
soft zealotBOT
rafilou2003
scarlet sequoia
and then $p^{q-1} = (0,1)$ and $q^{p-1} = (1,0)$
soft zealotBOT
rafilou2003
scarlet sequoia
so $p^{q-1} + q^{p-1} = (1,1)$
soft zealotBOT
rafilou2003
scarlet sequoia
which is the element 1 in $\bZ / pq\bZ$
soft zealotBOT
rafilou2003
final saddleBOT
cosmic warren
well only problem is I think arjuun is doing jeet so high schooler so idk why I even went on the tangent 
scarlet sequoia
.reopen
final saddleBOT
✅
scarlet sequoia
the other way to do it, much simpler to grasp :
$p^{q-1} + q^{p-1} \equiv 1$ mod $q$ and $p^{q-1} + q^{p-1} \equiv 1$ mod $p$ by Fermat's
cosmic warren
but idk what the jeet expects you to know either
soft zealotBOT
rafilou2003
scarlet sequoia
so $p^{q-1} + q^{p-1} \equiv 1$ mod $pq$ because $p$ and $q$ are coprime
soft zealotBOT
rafilou2003
final saddleBOT
@eternal wharf Has your question been resolved?
final saddleBOT
soft zealotBOT
gkeocog
hollow plover
whoops sorry
eternal wharf
well only problem is I think arjuun is doing jeet so high schooler so idk why I ...
Nope. I have read group theory too but not in deep. I am graduated poorly but reading jee material and csir net material to crack teaching exam
This is not in jee syllabus
tame karma
is my solution to teh following integral incorrect
i cant find any mistakes but it doesnt match with wolframalpha
final saddleBOT
is my solution to teh following integral incorrect
i cant find any mistakes but ...
tame karma
$ \int \frac1{x^2-1} \dd{x}$
tired walrus
$\int \frac{1}{x^2 - 1} \dd{x}$
soft zealotBOT
Ann
tired walrus
show your answer & show wolfie's
tame karma
Let $x = \sec\theta$, then $\dd{x} = \tan\theta\sec\theta \dd{\theta}$
$\= \int \frac{\tan\theta\sec\theta \dd{\theta}}{\tan^2\theta}$ as $tan^2\theta = \sec^2\theta -1$
soft zealotBOT
CoolShot
tame karma
$= \int \csc\theta \dd{\theta} = -\log(\csc\theta + \cot\theta)$
soft zealotBOT
CoolShot
eternal wharf
Coool coool
tame karma
putting $\theta = \arcsec x$ this becomes $-\log\left(\frac{x + 1}{\sqrt{1 - \frac{1}{x^2}} x}\right)$
soft zealotBOT
CoolShot
tame karma
however just putting the integral into wolfram gives
$\frac12(\log(1 - x) - \log(1 + x))$
soft zealotBOT
CoolShot
eternal wharf
**CoolShot**
I guess denominator mistake
tame karma
I guess denominator mistake
ok yes idk why wolfram gave this as an "alternate form" but its just
$-\log\left(\frac{x+1}{\sqrt{1 - \frac{1}{x^2}}}\right)$
soft zealotBOT
CoolShot
tame karma
but this is $\frac12(\log(x-1) - \log(x + 1)) - \log x$ which still isnt equal to the other quantity
soft zealotBOT
CoolShot
tame karma
somehow (x-1)<->(1-x) and theres an extra -log x
final saddleBOT
@tame karma Has your question been resolved?
scarlet sequoia
**CoolShot**
this is wrong
scarlet sequoia
**CoolShot**
this is correct
scarlet sequoia
**CoolShot**
keep the x in the square root, write it as $-\log\Big(\frac{x+1}{\sqrt{x^2-1}}\Big)$
soft zealotBOT
rafilou2003
scarlet sequoia
then this is $-\log(x+1) + \frac{1}{2}\log((x-1)(x+1))$, which is $\frac{1}{2}(\log(x-1)-\log(x+1))$
soft zealotBOT
rafilou2003
past mesa
final saddleBOT
past mesa
Is tension labelled correctly here?
As in going in the right direction
Feels iffy but also should be right
worn wharf
Could someone help me find part d to this question?
final saddleBOT
Could someone help me find part d to this question?
worn wharf
This is my work so far, I don’t know where to go from this tho
I did convert x^2+y^2 into r^2 already.
worn wharf
sorry forgot the trigger warning
final saddleBOT
@worn wharf Has your question been resolved?
halcyon oyster
the question is the limit in the top left corner
i wanted to know whether or not it was correct for the second line where i expanded the x^2y^2 to (x^2+y^2) (x^2+y^2)
i already went through and solved that the limit is equal to 0 but need to prove it with the delta/epsilon proof
solemn umbra
yeah: x^2y^2 <= (x^2 + y^2)y^2 <= (x^2 + y^2)(x^2 + y^2). the first is true because x^2 > 0 and the second is true because y^2 > 0 (and everything involved is nonnegative)
halcyon oyster
so using that was correct in the answer being cubed root epsilon?
solemn umbra
yeah if you pick \delta such that \delta^3 < \epsilon, then whenever 0 < ||(x,y)|| = (x^2 + y^2)^{1/2} < \delta, you get the rest
, hopefully we didn't both make a mistake
ok tysm!
final saddleBOT
final saddleBOT
Available help channel!
empty plaza
can some1 explain me how to do it? Like whats Ao An and Bn here?
final saddleBOT
can some1 explain me how to do it? Like whats Ao An and Bn here?
empty plaza
vital crag
can some1 explain me how to do it? Like whats Ao An and Bn here?
Did you try plugging s into the definition of the coefficients?
Also is there any other information on s(x)
empty plaza
I actually dont even know how to start since the format is so different
thats all of what was given in the problem
scarlet sequoia
what's the red crossed out part?
empty plaza
scarlet sequoia
Ah there we go
empty plaza
I though were two separate
scarlet sequoia
nope, they go along together
vital crag
...
vital crag
Why did you cross it out here
empty plaza
Why did you cross it out here
I though they were two distinct problems
empty plaza
but anyway, how do I move on from there?
ebon smelt
sometimes reading comprehension is a bit harder than the math itself
ebon smelt
but anyway, how do I move on from there?
move on to what?
empty plaza
well I think I didnt include the second part of s(x)
empty plaza
so is this the end of the exercise?
ebon smelt
yep
final saddleBOT
vital crag
.reopen
final saddleBOT
✅
ebon smelt
(i didnt check if its correct)
vital crag
Did you just use a calculator to do the integral for Bn or just omitted your work?
empty plaza
Did you just use a calculator to do the integral for Bn or just omitted your wor...
calculator
final saddleBOT
final saddleBOT
Available help channel!
tranquil pine
final saddleBOT
tranquil pine
shouldn't it be 30+x(0.03) for the second piecewise eqn?
since it's per additional minute and not just a flat charge??
and how would you save $6 by breaking the threshold of 200 mins 😂
sweet summit
not quite. I see why you would say that but basically the problem is that the function needs to be continuous at the point x = 200.
Logically, you are correct that we start charging 0.03 cents per min after 200 minutes, but we need to consider that we're not starting from the origin, but rather at x = 200.
So if we can take two known points say x = 201 and x = 202and fine a linear line for that. At x = 201, we get the charge will be 30 + 0.03 = 30.03. Similarly, at x = 202, we get 30 + 2(0.03) = 30.06. So our coordinate points are (201, 30.03) and (202, 30.06) respectively.
then we can use the point slope formula like so:
y - 30.03 = (30.06 - 30.03)/(202 - 201)(x - 201)
y - 30.03 = .03(x - 201)
y - 30.03 = 0.03x - 6.03
y = 0.03x + 30.03 - 6.03
y = 0.03x + 24
so that's the equation that represents the charge after 200 minutes
I took some more verbose steps here, but I wanted you to see why
sweet summit
Solve this
#❓how-to-get-help , channel is occupied
sweet summit
and how would you save $6 by breaking the threshold of 200 mins 😂
And you're not saving $6 here. Plug in x = 200 and you'll get 24 + 0.03(200) = 24 + 6 = 30 🙂
sweet summit
The only thing here is that your 2nd equation should be 24 + 0.03x, not 24 + 0.03
tranquil pine
The only thing here is that your 2nd equation should be `24 + 0.03x`, not `24 + ...
yeah the per minute thing threw me off
seems like a complex procedure
sweet summit
seems like a complex procedure
nah not really. It's just having to consider the fact that we're not starting at 0 minutes for the 2nd equation
here's a visual between the two:
See how there's a jump?
tranquil pine
yeah I see
so we're making a formula so that we start at the original $30 charge when x=200
yeah now I see how my first eqn was wrong
we would be paying the 200 minutes + $30 as soon as the 200 minutes is over
sweet summit
yep exactly
I feel you though, intuitively it seems like it should be 30 + 0.03x, lmao
tranquil pine
yeah, that'd be the equation if x=additional minutes
but a formula like that wouldn't make sense if you're looking at it graphically
Ok, I understand it now. Thanks : )
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trim lance
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trim lance
can some one help me out with this
should i u sub 3t
or
apply an identity
im stuck
random forge
can some one help me out with this
should i u sub 3t
or\
apply an identity
im st...
You could do it in one step, but you can do u sub with u = 3t, then do another usub (with a different letter obviously) of s = sec(u)
trim lance
You could do it in one step, but you can do u sub with u = 3t, then do another u...
how in one step
random forge
u = sec(3t) looks like itd work
just more likely to make an error with less steps i suppose
trim lance
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soft zealotBOT
trim lance
do you know the $\sin\alpha\cos\beta$ identity?
not really
random forge
$\sin\alpha\cos\beta = \frac12(\sin(\alpha-\beta) + \sin(\alpha+\beta))$
trim lance
if its an identity ill just look it up
soft zealotBOT
trim lance
ah
random forge
i assume you can solve from here?
lament carbon
wait @random forge is this possible if we do integration by parts
random forge
wait <@153882568322711553> is this possible if we do integration by parts
probably not? or at least not trivially
random forge
sin and cos both cycle, and the fact that they dont have matching interiors means we can never combine them
im pretty sure you have to use this trig identity at some point
you are welcome to try, but even if it works its surely the harder solution
lament carbon
ah okay
trim lance
you are welcome to try, but even if it works its surely the harder solution
😵
lmao ur gonna end up with 3 lines solution
@random forge
,rotate
soft zealotBOT
random forge
with what am i going to sub it with
this is NOT the same problem!
you now have two terms added together
instead of multiplied
trim lance
wait what
random forge
and as we know $\int a+b = \int a + \int b$
soft zealotBOT
random forge
well the next step of your work is integrating, and both of those integrals are simple u sub
since you have two terms added together, you get 2 different integrals, of which you know how to solve both
trim lance
well the next step of your work is integrating, and both of those integrals are ...
which u sub tho
random forge
please split it into 2 integrals
blazing lion
Can someone help me with a Venn diagram?
final saddleBOT
Can someone help me with a Venn diagram?
queen mica
!status
final saddleBOT
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
Considering what is colored in the previous images, nothing is colored here?
blazing lion
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
2
queen mica
hmm?
blazing lion
I must color each part of the expression, what I don't understand is that at the end of coloring what is the "intersection", I think that nothing should be colored?
Where am I going wrong?
queen mica
according to your previous images,
the parts where
k,c,n exist
h,l, exist
are colored
blazing lion
Can you explain me why? that is why i dont get it
queen mica
when there's A = {1,2,3,4}, B = {3,4,5,6} then what's A∩B?
blazing lion
1,2?
blazing lion
Oh
queen mica
can you do that now?
blazing lion
Yes
queen mica
queen mica
so maybe
velvet mist
fossil shuttle
how would I do this
final saddleBOT
how would I do this
unborn basalt
how would I do this
Which?
fossil shuttle
first one
unborn basalt
first one
U can just sub the points in
Then use inequalities when u get the LHS answer (Left-Hand Side)
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@fossil shuttle Has your question been resolved?
fossil shuttle
U can just sub the points in
how tho
I don't know if it's inside, outside or on the circle
unborn basalt
Issokay, I know hahaha
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slender mesa
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slender mesa
any sources that will help me find answers for these
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@slender mesa Has your question been resolved?
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@slender mesa Has your question been resolved?
honest charm
hi
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fiery prism
can someone help me
final saddleBOT
can someone help me
sand portal
Show us your work
fiery prism
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@fiery prism Has your question been resolved?
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@fiery prism Has your question been resolved?
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warm python
$if z^5-z^4-1$=0, find the number of roots with modulus 1
final saddleBOT
$if z^5-z^4-1$=0, find the number of roots with modulus 1
soft zealotBOT
physicsrocks
warm python
where z is a complex number
I was thinking of using $z=rcos(x)+isin(x)$ but I was hopping to avoid both trig and the binomial therom(Which I would have to use if I use $z=x+iy$. Is there any other way to solve this?
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physicsrocks
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@warm python Has your question been resolved?
warm python
.close
tranquil pine
So
soft zealotBOT
lyric stirrup
x is an element of the real numbers
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rare marlin
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rare marlin
Would i need to plot points to show this geometrically?
rare marlin
but they are askign you to explain it only
it says geometrically however doesn't it?
Doesn't that mean use a graph?
sand portal
Let's set y=c(x), so you get all the points of coordinates (x,y) such that y=c(x)
So ... (x,c(x))
You've shown (I hope) that c(-x)=c(x)
So that means
(x,c(x)) is on the representative curve of c, as well as (-x,c(-x))
Ow, but you know c(-x)=c(x)
So (-x,c(-x)) = (-x,c(x))
So (x,c(x)), as well as (-x,c(x)) are on the curve of c
So that means
If you take a point (x,y) on the curve
You will get (-x,y) on the curve as well
Now with that explanation, you can proceed to explain what it means geometrically
sand portal
You will get (-x,y) on the curve as well
You can try out with few points which follows that property for a simpler function which has the property f(x)=f(-x)
Like the function f(x)=x²
You can find by yourself what this means
By plotting
Multiple points on the curve, so multiple points of coordinates (x,x²)
With x positive
So you then look at the point (-x,x²)
And observe where this second point is
Compared to the first
Then, if you so this for multiple points, what will happen to your curve overall ?
👍
rare marlin
So its essentially because of the fact that its a parabola a reflection along the y axis wouldnt change anything?
sand portal
Yeah, the parabola has this property
But that doesn't mean the curve of c is a parabola
You really have to pinpoint that geometrical reflection property
rare marlin
Id have to plot it to find out if the curve c had the property?
sand portal
You know it has the same property than a better known function
Why not use that better known function to remind yourself of what this means ?
rare marlin
better known function?
sand portal
I think it helps a lot to come back to simpler examples !
Well like the function I just told you about
The square function
rare marlin
yeah
sand portal
(-x)²=x²
rare marlin
So if i've proved that on the given function i can assume that the function is a parabola?
sand portal
I will repeat myself
For example
The parabola is only a simple example
You have other functions which follow that property and are not parabolas
Look at the cosine function for an other example
rare marlin
oh yea
sand portal
That doesn't mean c is a cosine function as well as a parabola (it would be almost impossible actually for it to be both at the same time...)
So you take an x
Which ever you want
You look at what the point (x,f(x)) is, for a function f such that f(-x)=f(x)
It will indeed show you that reflection
Well you mentioned that reflection
So I guess you don't need to
But you basically pinpointed the geometrical thing happening
That means the graph of c has that geometrical property
Because c(-x)=c(x) for any x
rare marlin
okay so i have the reflection property but i still don't really understand, is that the answer?
sand portal
Well it's a geometrical thing you have to explain
And I think what I described makes the deal
Or what you said too
rare marlin
So like i explain the fact that for any value of x, -x would result in the same y value hence the function is the same when it is reflected?
sand portal
Okay for the first part, nailed it, glad my explanation make sense
Now though
"hence the function is the same when it is reflected?"
I'd say
"Hence, the curve of c defined at (-inf,0] is a reflection of the curve of c defined at [0,+inf) along the y axis" for example
Here, that's better
But you absolutely get the idea though, it's all about formulating it
rare marlin
Hmm if the original function covers (-inf, 0] already wouldn't the reflection c(-x) result in the exact same curve?
sand portal
When you say "the same curve", that's what's really blurry
If I literally copy paste the curve on [0,+inf) to (-inf,0], you're just not going to get back the whole curve
Because when you do a reflection, you don't copy the function
sand portal
When you say "the same curve", that's what's really blurry
So I'm asking you to be more accurate in your saying
rare marlin
Oh ok so is it a different curve that looks identical to the original curve?
sand portal
It's not identical though
It's a reflection
A reflection doesn't create an identical curve
rare marlin
A curve that looks identical?
sand portal
But you see how loose you are being in your words ?
rare marlin
yeah
sand portal
"c has a reflexion axis of equation x=0"
Boom
That's the most concise way I've got
Does it seem better to you ?
rare marlin
Yeah i understand. So when they say explain geometrically for questions we target a property of the function correct?