Available help channel!
#help-10
obtuse pebbleBOT
Available help channel!
shadow jewel
How would I set up 19
obtuse pebbleBOT
How would I set up 19
latent walrus
take the length of the cutout squares sides to be x
then what are the other lengths
distant seal
obtuse pebbleBOT
distant seal
confused on my mistake
i assume it has something to do with the ^2
but not sure if that messed up my whole calculation or there's a solution
obtuse pebbleBOT
@distant seal Has your question been resolved?
tough reef
u=(lnx)^2
\ln^2{(x)} \cdot -\frac{1}{x} - \int( -\frac{1}{x} \cdot 2\ln{(x)} \cdot \frac{1}{x})dx
warm shaleBOT
mari
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
distant seal
?
tough reef
You let u = lnx
distant seal
i did that no?
tough reef
**mari**
Compile Error! Click the <:errors:504266556054962196> reaction for more...
You did not do this
tough reef
i did that no?
You aren’t meant to let u = lnx
tough reef
I already set up the integral for you
distant seal
yea
tough reef
2lnx is from the derivative of (lnx)^2
tough reef
Yes
tough reef
**mari**
Compile Error! Click the <:errors:504266556054962196> reaction for more...
This
tough reef
You have to partially integrate again
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
plucky trail
How do I know if a number is divisible by 4?
obtuse pebbleBOT
How do I know if a number is divisible by 4?
plucky trail
234,562
234,564
234,566
I thought I looked at the last two digits
added them
then saw if they were divisible by 4
high lily
you don't add the digits
plucky trail
do I multiply them?
high lily
no
plucky trail
234,562
234,564
234,566
so for these I have 62, 64 and 66
high lily
yes
obtuse pebbleBOT
timid silo
how about...
y as t?
and x as t^(2/3)
also this parameterization will give an equation:
(t, 3/2)
which is a constnat lien
warm shaleBOT
a
worn yoke
in the original equation y can be negative but in this parameterization it can't
warm shaleBOT
icannotdoanymorecauchy
timid silo
u should consider their domain too
it should be t
but the same constriction goes for y
steady plinth
HI! Can anyone help check my solution? I'm solving differential equations and the answer I get is so similar to the answer my professor says but it's a tad bit off. Can anyone tell me where I went wrong?
obtuse pebbleBOT
HI! Can anyone help check my solution? I'm solving differential equations and th...
steady plinth
First image is my solution, second image is the said final answer
The answer I get is the same except for the exp(4x√3), which my professor said it's supposed to be exp(4√3x)
Maybe I missed something or did the algebra wrong somewhere...?
Edit: figured it out
obtuse pebbleBOT
@steady plinth Has your question been resolved?
steady plinth
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dry horizon
how do I do this? It doesn't seem there's enough information given?
obtuse pebbleBOT
how do I do this? It doesn't seem there's enough information given?
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
2
unreal musk
Where did you get stuck? Do you at least have a picture of how it would look like?
dry horizon
its a..rectangle topped by a semicircle
norman window as it's called
I'm having trouble setting up an equation
there's no relationship it seems I can create
unreal musk
Did you label any of the lengths in it?
dry horizon
the radius as r and the base of the rectangle as 2r
unreal musk
And the rectangle's height? Shall we call that h?
dry horizon
yep
unreal musk
Cool, then, in terms of h and r, can you find an expression that represents the perimeter of the window?
warm shaleBOT
albert einstein
unreal musk
Cool, yep, you've done well 
Now, can you find an expression for the area of the window in terms of r and h?
dry horizon
$A = \frac{{\pi}r^2}{2}+2rh$
unreal musk
Wait, pi * r^2/2, remember it's a semicircle
dry horizon
ah yeah
warm shaleBOT
albert einstein
unreal musk
**albert einstein**
Anyways, we could rearrange this here to make h the subject, which would make our life much easier, you can do that right? 
dry horizon
$h = \frac{p-{\pi}r-2r}{2}$
warm shaleBOT
albert einstein
unreal musk
**albert einstein**
Cool, that allows us to then put that in here, which hopefully should make life easier(?)
dry horizon
wait does introducing p not affect anything?
unreal musk
Not really, p is a constant in the context of this question (and the answer we find probably will depend on p, which is fine!)
dry horizon
Not really, p is a constant in the context of this question (and the answer we f...
how is p a constant if it's based off of r and h
unreal musk
p is fixed at the start of the question
You could e.g. have p = 69 given to you at the very start of the question, and everything you find will be based around that
Throughout p will not change, only r and h can change
dry horizon
Throughout p will not change, only r and h can change
thanks, that makes sense
does the problem want r defined in terms of p?
unreal musk
It does
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
tawdry vortex
so
What i was thing is doing
10.81= x/0.310
and to find x which is the mass
i would multiply right?
10.81 times 0.310
Huh
But i get the wrong answer 😭
answer is 3.31g but i get 3.3511g
unreal musk
,calc 10.81 * 0.31
warm shaleBOT
Result:
3.3511
modern cosmos
tawdry vortex
and i knew the ones with 10^-25 would be wrong
unreal musk
Strange 
probably they wrote the options wrong
safe haven
or just round 10.81 down to 10
warm shaleBOT
Result:
0.028677150786309
lol
viral blade
,calc .331 * 6.022*10^23
warm shaleBOT
Result:
1.993282e+23
cunning otter
"Two points A and B are at the same distance from a point C = (1, -1). If the x-coordinate of A is 1 and the x-coordinate of B is 5, what are the y-coordinates of A and B?"
I did pythagoras to get the distances between A and C, and B and C, I equaled them but I got stuck there, can someone help me?
obtuse pebbleBOT
"Two points A and B are at the same distance from a point C = (1, -1). If the x-...
light flume
"Two points A and B are at the same distance from a point C = (1, -1). If the x-...
can you show your working out so far
cunning otter
can you show your working out so far
normal cairn
well as a first suggestion, id recommend removing the square roots at this point with a +/-. it seems tempting to just remove the square and the root but by keeping the root on the right hand side youre just making it harder on yourself
afterwards it seems icky but i think the only real way to go about it is to solve for one of the variables using the quadratic formula
cunning otter
afterwards it seems icky but i think the only real way to go about it is to solv...
I see, so you don't see a simpler way to do it? It's a high school assignment, I'm surprised there's no straightforward formula to solve it
I will try that, ty
normal cairn
frankly im confused as to why there arent just infinite solutions...are you sure there isnt anything else the question asked?
cunning otter
Yep, look, this is the original, I translated it directly from Spanish (there is no more information outside of this)
cunning otter
frankly im confused as to why there arent just infinite solutions...are you sure...
I'm also surprised, I am about to use a trivial answer like A = (1, 3) and B = (5, - 1) and explain it, I don't know if it is feasible to talk about the infinite solutions
normal cairn
yeah i went on desmos and worked up that same trivial answer as well and it looks a lil like this, but i dont see why i couldnt just move one of the points along the same line its defined by the x-coord, create a circle with that distance of AC or BC as the radius, and just assume that the other point (either A if we chose BC or B if we choose AC) is just the point where the circle is on said x value
i worded it funny but do u get what i mean
obtuse pebbleBOT
@cunning otter Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
dim burrow
is it possible without lhopital
obtuse pebbleBOT
is it possible without lhopital
marble sphinx
Take the log of that quantity
nova vale
let k = this question
dim burrow
yeah i know how log works lol
nova vale
why aren't you applying l hospital tho
nova vale
ah
dim burrow
real
marble sphinx
you get $\frac{1}{x}(f(x+1)-f(x))$
warm shaleBOT
bourbactif
marble sphinx
You don't kneed l'Hopital
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
grand marten
Hello
restive gorge
I like how bit by bit the dx and integral sign vanished
restive gorge
How did you get from 1-cot²(x) to csc²(x)?
restive gorge
How is this answering, I don't see it
restive gorge
1-cot²(x) = 2-csc²(x)
grand marten
1/cosec²x is sin²x
grand marten
1-cot²x= cosec²x
I used this formula
slate hamlet
That's not a formula
slate hamlet
Cosec^2 x = 1 + cot^2 x
.
grand marten
Ok
I will start from scratch
I was trying to short the answer but I end up getting blunder
@slate hamlet
I am going right?@slate hamlet
slate hamlet
<@456117510429868062>
You forgot to write a plus in the beginning but you are doing it correctly
obtuse pebbleBOT
@grand marten Has your question been resolved?
obtuse pebbleBOT
grand marten
Yes
obtuse pebbleBOT
Available help channel!
royal edge
Where did I make a mistake and why?
obtuse pebbleBOT
Where did I make a mistake and why?
royal edge
Can’t I take out the negative to apply it after ? Like -a+b=-(a+b)
warm shaleBOT
Result:
-2
tardy epoch
,calc -(5+3)
warm shaleBOT
Result:
-8
Hmm okay thanks, I can follow the rule but I don’t know why it’s like that.
royal edge
Most of those yes, including 9
tardy epoch
what happens if a=-1
royal edge
This was my thinking
tardy epoch
yes and that's wrong
royal edge
what happens if a=-1
-a
tardy epoch
Can’t I take out the negative to apply it after ? Like -a+b=-(a+b)
if you can't understand this, then your work is irrelevant
use 9. to factor out -1
royal edge
Idk, it’s a* b* c, here it’s -1* 438* 719+ 438* 719
I’m assuming we can’t distribute without dealing with the * -1, so -1 * 438* 719 + -1 * 438* 719 ?
tardy epoch
I’m assuming we can’t distribute without dealing with the * -1, so -1 * 438* 719...
then you'd be wrong
royal edge
Is this algebraic logic wrong ?
obtuse pebbleBOT
@royal edge Has your question been resolved?
royal edge
I’m sorry but I’m struggling to understand how you got to the last step
tardy epoch
you're just getting confused because of all the numbers
just do it with simpler numbers or better yet variables
say instead you have -2 * 3 + 2 * 3
how do you factor out a -1 from the sum?
tardy epoch
using this
obtuse pebbleBOT
royal edge
.reopen
obtuse pebbleBOT
✅
royal edge
how do you factor out a -1 from the sum?
Don’t know how to do it with the distributive property here. -1 is only being multiplied to the first 2 * 3 here.
tardy epoch
Don’t know how to do it with the distributive property here. -1 is only being mu...
but you WANT to factor out -1
you keep trying to get to this
royal edge
-1 can’t get factored from a non negative expression I think
obtuse pebbleBOT
@royal edge Has your question been resolved?
royal edge
so (-2 * 3) + (2 * 3) = -1 * (2 * 3) + (2 * 3) = -1(2 * 3) + (-1(-1(2 * 3))) = -2 (3 + (-1) * 3). I get that the negative 1 gets multiplied to the second 3,
but I don't understand how (-1(-1(2 * 3))) = (-2 * -3) = which i am assuming is the intermediary step in the last part, im just guessing
tardy epoch
but I don't understand how (-1(-1(2 * 3))) = (-2 * -3) = which i am assuming is ...
(-1) * (-1) = 1
royal edge
multiplication doesnt distribute over multiplication does it?
and, i guess i dont understand how -1(2 * 3) and -1(-1(2 * 3) gets factored, because you have an extra -1 in the second term - IDK how that gets shuffled around to get multiplied to the second 3.
obtuse pebbleBOT
@royal edge Has your question been resolved?
obtuse pebbleBOT
@royal edge Has your question been resolved?
tardy epoch
and, i guess i dont understand how -1(2 * 3) and -1(-1(2 * 3) gets factored, bec...
-a + b = (-1) * a + (-1)(-1)b = (-1) * (a + (-1) * b) = -(a-b)
you should do nothing else in your problem until you understand that ^
royal edge
-a + b = (-1) * a + (-1)(-1)b = (-1) * (a + (-1) * b) = -(a-b)
i understand that there is a (-1) left over from the second term, which you throw in front of the second 3, but i dont understand why its placed there specifically instead of in front of the equation like (-1)(-1)(a+b) or after like (-1)(a+b)(-1) from the expression (-1)(a + b) + (-1)(-1)(a + b). if you could somehow show that (-1)(-1)(a + b) = (-a + -b), then it would make much more sense in my head so i can factor that with (-a + b) into -(a+-b)
tardy epoch
you could somehow show that (-1)(-1)(a + b) = (-a + -b),
this is incorrect
tardy epoch
have you seen these before
read 5.
royal edge
> you could somehow show that (-1)(-1)(a + b) = (-a + -b),
this is incorrect
how would you carry that expression out?
tardy epoch
you need to stop making up your own rules and follow ones from the axioms above
tardy epoch
have you seen these before
.
every step you make should follow from 1 of the 9 axioms
royal edge
I’ll take your word for it, but I just don’t have anything in my head that makes it make sense. Feels like I’m arbitrarily throwing in the -1 in there just because.
tardy epoch
,calc (-1) (2)(3) + (-1) (-1) (2)(3)
warm shaleBOT
Result:
0
good job
royal edge
Thanks. Can you give me some practice problems ? Doing a double negation to factor out a negative just feels like black magic to me.
tardy epoch
royal edge
hmm okay well thanks, ill just move on from this and hope i never have to do it again
lucid totem
hey guys i have a stats question could anyone explain what to do here? im completely lost
obtuse pebbleBOT
hey guys i have a stats question could anyone explain what to do here? im comple...
tardy epoch
Do you know what uniform distribution is
tardy epoch
could you explain please
Just read the continuous one
So this is what uniform distribution is
lucid totem
I’m so confused 😵💫😵💫
tardy epoch
I’m so confused 😵💫😵💫
Ok
obtuse pebbleBOT
@lucid totem Has your question been resolved?
lucid totem
<@&286206848099549185>
tardy epoch
<@&286206848099549185>
What is your question
tardy epoch
So this is what uniform distribution is
About this
lucid totem
how does that help explain my question?
tardy epoch
hey guys i have a stats question could anyone explain what to do here? im comple...
Your question specifies uniform distribution
tardy epoch
could you explain please
And you didn't know what it was
lucid totem
.close
muted linden
Me need help
obtuse pebbleBOT
Me need help
muted linden
tardy epoch
f/g means f divided by g
When you divide by a fraction, you multiply by the reciprocal
viral blade
I can't believe you can read that
wary badger
zoom in
viral blade
ah
static dove
We have the same laptop lol
wary badger
We have the same laptop lol
We have the same laptop lol
static dove
Also the answer is x/x+1 when x is not equal to -1
obtuse pebbleBOT
@muted linden Has your question been resolved?
sour marsh
can someone explain question 5? im not quite sure how the teacher simplified
frozen sedge
can someone explain question 5? im not quite sure how the teacher simplified
Like how your teacher answered it?
deft magnet
t = 0, -1/3 makes denominator 0 so the fraction becomes undefined
sour marsh
5 comes from t-5?
sour marsh
she crossed it out when simplifying
deft magnet
ah ye
sour marsh
but on the second step how can 4t simplify 2t(squared)
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
haughty creek
I need real constants a,b,c,d such that the following holds:
$(ad - bc)^2 \le \frac{1-(ac+bd)}{2} $and $0<\frac{1-(ac+bd)}{2}<1/4$
Shit mb
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
no man
tardy epoch
,rotate
warm shaleBOT
obtuse pebbleBOT
@stable shore Has your question been resolved?
slate agate
obtuse pebbleBOT
slate agate
is there a good way to further simplify this or is my thinking correct that this is just going to be a giant fucking mess
ember frost
i mean you could try evaluating the derivative
not guaranteeing it will come out better tho
slate agate
thats what im doing right now
i just cant see if theres anything immediately useful for simplifying
full scarab
Hi, I'm trying to solve a difficult derivative question. I looked up ways to find the integral of sqrt(tan(x)) dx, and found [this](https://socratic.org/questions/how-do-you-integrate-sqrttanx) on Socractic. So I'm trying to take the derivative of that to get sqrt(tan(x)). The problem is the algebra is tricky, and I'm not sure what to do next. Is there something to factor? A way to change tangent into secant or vice versa with tan^2x + 1 = sec^2x. Maybe a clever factoring of something like tan^2x + 2tanx + 1 = (tanx + 1)^2.
obtuse pebbleBOT
Hi, I'm trying to solve a difficult derivative question. I looked up ways to fin...
full scarab
wary badger
you’re asking how to take the derivative of the anti derivative of sqrt(tanx)
full scarab
Yes, but without using the fact that the derivative of the antiderivative is the function itself
The point is to just solve a really difficult derivative question and use algebra skills
wary badger
,w integrate sqrt(tan(x))
warm shaleBOT
full scarab
There's at least 6 different solutions I've seen to integral sqrt(tanx) dx
wary badger
this is the one where you do u^2 and u^4
patent osprey
this should be straightforward chain rule no?
do you recall the derivative of arctan(x)
tan(x)
wary badger
,w differentiate (1/sqrt(2)) arctan((tanx - 1)/sqrt(2tanx)) + 1/(2sqrt2) ln|(tanx - sqrt(2tanx) + 1)/(tanx + sqrt(2tanx) + 1)|
patent osprey
and ln(x)?
warm shaleBOT
patent osprey
what is bro cooking 💀
full scarab
what is this
What do you mean?
orchid wind
serene fossil
lol did wolfram forget Pythagorean theorem?
patent osprey
tik tok math 😭
orchid wind
I saw this problem on tiktok like two days ago
wary badger
https://www.tiktok.com/t/ZTFBo88jn/
goat
wary badger
lol did wolfram forget Pythagorean theorem?
maybe
patent osprey
brain rot math on tik tok 😭
patent osprey
What do you mean?
you are not cooking tbh
orchid wind
10 hours a day minimum
patent osprey
this is derivative is rather straightforward
can you compute the derivative of the inside expression
chef @full scarab
patent osprey
Yeah, it's [ sec^2x (tanx+1) ]/(sqrt(2tanx))
huh
I got something like
2tan(x)
on the denominator
wary badger
quotient rule
full scarab
on the denominator
Yes I did this too
patent osprey
Yes I did this too
but like that's not it
you also get a \sqrt{2tan(x)} term
in the denominator
full scarab
patent osprey
$\frac{\sec :^2\left(x\right)\sqrt{2\tan :\left(x\right)}-\frac{\sec :^2\left(x\right)}{\sqrt{2}\sqrt{\tan :\left(x\right)}}\left(\tan :\left(x\right)-1\right)}{\left(\sqrt{2\tan :\left(x\right)}\right)^2}$
warm shaleBOT
Kafer
patent osprey
yes?
full scarab
This is the same as my answer above
patent osprey
This is the same as my answer above
chef what was ur simplified answer
full scarab
I'm going to do the whole arctan((tanx-1)/sqrt(2tanx)) first, then simplify
patent osprey
I'm going to do the whole arctan((tanx-1)/sqrt(2tanx)) first, then simplify
I would simplify intermediate here
it's going to make ur life easier
full scarab
Ok I'll try that then
patent osprey
Ok I'll try that then
want a early birthday present?
full scarab
want a early birthday present?
Sure
patent osprey
$\frac{\sec ^2\left(x\right)\tan \left(x\right)+\sec ^2\left(x\right)}{2\sqrt{2}\tan \left(x\right)\sqrt{\tan \left(x\right)}}$
warm shaleBOT
Kafer
patent osprey
that's ur simplified answer
full scarab
**Kafer**
Also, this is the same answer as the one I got
I think I got that part down, I really would like help with simplifying this algebraically
patent osprey
CHEF what's going on
full scarab
There's also a chance I did a mistake with the other term of the derivative, so I will check that
full scarab
why is that not here?
What do you mean?
patent osprey
What do you mean?
do you mind if we work this step by step
your work is very confusing
I would recommend you working in a more organized fashion in general
to avoid mistakes
in the future too
full scarab
I think I might ask someone else. I appreciate your help though, thanks
obtuse pebbleBOT
@full scarab Has your question been resolved?
obtuse pebbleBOT
@full scarab Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
Can anyone help me with qn.no 4?
junior granite
Can anyone help me with qn.no 4?
what do you want to do with it?
junior granite
are you supposed to just use Row/Column operation to prove it?
or you could use some another way?
surreal forge
any method that is not “manually compute the determinant”
is the intended approach to such problem
fickle wren
I can say , column 1 implies column 1 - column 2
Or such things
I can take commons
junior granite
I can say , column 1 implies column 1 - column 2
your way is alright
fickle wren
How do I do it?
junior granite
I can say , column 1 implies column 1 - column 2
just how you stated here
after that you can do C2 -> C2-C3 and so on
surreal forge
nw
fickle wren
junior granite
,rccw
warm shaleBOT
junior granite
instead of C1 -> C1 + C2
better use C1 -> C1 - C2
by doing that you'll be able to get that x-z factor easily
oh wait
what
junior granite
,rccw
warm shaleBOT
junior granite
it is supposed to be -z+x
junior granite
bruh
that's z^2 not 2z
Z^2s will be cancelled
and that negative sign will be compensated by that x-z
as on the right hand side it is z-x
fickle wren
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
heady turtle
I have problem dealing with this
obtuse pebbleBOT
I have problem dealing with this
tepid mountain
I have problem dealing with this
Best hand writing ever
heady turtle
Thx haha
tepid mountain
So what's is the problem you are having
heady turtle
Idk how to solve this limit
tepid mountain
So you solved the integrations inside it?
heady turtle
Yea but it's not the right track ig
It's complicated
And I used machine or I can't solve its antider
I want to know how to solve this limit by hand
tepid mountain
But you need to solve the integrations, specifically the first one because x can't be less than -1 in it
heady turtle
Then how? Without machine
tepid mountain
The integration itself
We can start with the left integration
We use a trig substitution for it
We can say
t = sin(theta)
dt = cos(theta) d(theta)
I noticed something
Do you want to solve for f(x)
Or for the limit as x goes to - infinity of f(x)
heady turtle
specifically the first one because x can't be less than -1 in it
Why?
heady turtle
I noticed something
Do you want to solve for f(x)
Or for the limit as x goes to ...
Latter, the limit
tepid mountain
Because of the square root
Oh wait
Yeah I see it
But still we need to get the integration done
Because the area under the square root from -infinity to 1 is infinity
heady turtle
,w integrate sqrt(1+x^2)
warm shaleBOT
heady turtle
We can say
t = sin(theta)
dt = cos(theta) d(theta)
int cos^2t dt
tepid mountain
That would not have worked
I should have used tan not sin
heady turtle
That would not have worked
I should have used tan not sin
int sec^2t tant dt
tepid mountain
Yeah
sec^2 can be equal to (1+tan^2)
Or wait
That's just
The result is just sec^2(theta)/2
Derivative of tan is sec^2 by the way
So we should have integrated sec^3
heady turtle
Yea as I said, this is too complicated😭
tepid mountain
$$t = \tan(y), dt = sec^2(y) dy$$
$$\int_{\arctan(x)}^{\frac{\pi}{4}} sec^3(y) dy$$
heady turtle
Yea
warm shaleBOT
Sherif Player
warm shaleBOT
Sherif Player
tepid mountain
$$\int_{\arctan(x)}^{\frac{\pi}{4}} sec(y) + tan^2(y)sec(y) dy$$
warm shaleBOT
Sherif Player
tepid mountain
And now it is a little bit easy
$$[\ln(\abs{\sec(y)+\tan(y)}) + \frac{\sec^2(y)}{2}]$$
warm shaleBOT
Sherif Player
tepid mountain
Now substitute
junior granite
how's that {sec^2y}/2?
junior granite
**Sherif Player**
I think it is better to just write sec^3 as sec^2 and sec
then IBP, that'll be simpler imo
tepid mountain
,wolf \int tan^2(x)sec(x)
warm shaleBOT
junior granite
I think it is better to just write sec^3 as sec^2 and sec
then IBP, that'll be s...
.
it is not that much
heady turtle
I think it is better to just write sec^3 as sec^2 and sec
then IBP, that'll be s...
I get [ \frac{1}{2} \sec(x) \tan(x) + \frac{1}{2} \ln | \sec(x) + \tan(x) | + C ]
warm shaleBOT
kae
tepid mountain
tepid mountain
Yeah
heady turtle
Then what's the next
tepid mountain
Substitution
heady turtle
,w plot secx, tanx
warm shaleBOT
tepid mountain
Tan(π/4) = 1
And sec(π/4) = √2
Tan(arctan(x)) = x
sec(arctan(x)) = √(x^2+1)
So
$$\frac{\sqrt{2}}{2} + \frac{\ln(1+\sqrt{2})}{2} - \frac{x\sqrt{x^2+1}}{2} - \frac{\ln(x+\sqrt{x^2+1})}{2}$$
warm shaleBOT
Sherif Player
heady turtle
This is insane
tepid mountain
$$\frac12 (\sqrt{2} + \ln(1+\sqrt{2})) - \frac12 ( x\sqrt{x^2 + 1} + \sinh^{-1}(x))$$
warm shaleBOT
Sherif Player
tepid mountain
Here is seems that the right part of this goes to something as x goes to - infinity
Let's get into the second integration shall we 
heady turtle
,w plot x sqrt(x^2+2), sinhx
warm shaleBOT
warm shaleBOT
Sherif Player
warm shaleBOT
Sherif Player
heady turtle
,w plot (1+x^2)^(3/2)
warm shaleBOT
heady turtle
Oof
tepid mountain
$$\frac12 (\sqrt{2} + \ln(1+\sqrt{2})) - \frac12 ( x\sqrt{x^2 + 1} + \sinh^{-1}(x)) +\frac23(1+x^2)^{\frac32} - \frac23(2)^{\frac32}$$
warm shaleBOT
Sherif Player
junior granite
ngl it doesn't seems to have a nice answer
heady turtle
I guess that this isn't the right track but seems like this is the only way we can think of
junior granite
timid silo
cant we take 2/3 common ?
tepid mountain
Hmm this seems to be going to infinity
heady turtle
Which infty
junior granite
Which infty
what does the original problem supposed to be?
heady turtle
what does the original problem supposed to be?
Find the limit as I said
So which infty
tepid mountain
$$\frac23(1+x^2)^{\frac32} - \frac12 ( x\sqrt{x^2 + 1} + \sinh^{-1}(x)) $$
warm shaleBOT
Sherif Player
tepid mountain
Because the second part is approaching - infinity as x goes to -infinity
It will go to positive infinity because of the negative multiplied by it
Also the first one goes to positive infinity as x goes to negative infinity so the whole thing goes to positive infinity
,wolf graph \frac23(1+x^2)^{\frac32} - \frac12 ( x\sqrt{x^2 + 1} + arcsinh(x))
warm shaleBOT
tepid mountain
Ok
heady turtle
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
gloomy vector
A,B,C,D is on a circle where AB=8, BC=10, BD=x and is the angle divisior of ABC which is 60, find x
obtuse pebbleBOT
A,B,C,D is on a circle where AB=8, BC=10, BD=x and is the angle divisior of ABC ...
gloomy vector
stat 1
fallow cove
so x is the diameter of the circle?
gloomy vector
no
balmy oyster
it could be but theres no way of knowing or proving it, so you cant rely on that being true
gloomy vector
maybe i shouldve drawn it better
rose scroll
if it was diameter, both chord lengths would be equal
junior granite
A,B,C,D is on a circle where AB=8, BC=10, BD=x and is the angle divisior of ABC ...
have you found the value of AC?
junior granite
yeah
try to make use of the intersecting chords theorem
join AC which splits BD
gloomy vector
try to make use of the intersecting chords theorem
how?
junior granite
I mean like that
better use x-c instead of d
so a+b = sqrt{84}
ab=c(x-c)
you can find the values of a and b in terms of c (by using law of cosines in smaller triangles)
and then try to isolate the x from everything else
obtuse pebbleBOT
Available help channel!
daring vessel
obtuse pebbleBOT
daring vessel
help please
hidden compass
!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
At least I hope you have studied the basic theory on second degree equations...
daring vessel
I found the discriminint
hidden compass
I found the discriminint
So you actually knew where to begin, awesome
hidden compass
I found the discriminint
What value did you get?
hidden compass
(-2)^2 - 4(1)(3)
Why 3?
daring vessel
I meant -15
hidden compass
Ah alright, yep
daring vessel
yas
daring vessel
Δ
hidden compass
So that I can use your same notation
daring vessel
hidden compass
Since $\Delta = 64$, how many roots do you have?
warm shaleBOT
Alberto Z.
hidden compass
Didn't you do this: $\Delta = {(-2)}^2 - 4\cdot1\cdot{(-15)}$ ?
warm shaleBOT
Alberto Z.
daring vessel
Yes I got it
hidden compass
Perfect
hidden compass
**Alberto Z.**
Which is this
hidden compass
Note that you aren't asked the numerical values of the roots, but instead you're only asked how many roots that eqn has
hidden compass
hidden compass
Your teacher should have taught you something along the lines of this
hidden compass
This is another exercise 🤔
hidden compass
Exactly this, yeah
daring vessel
Exactly this, yeah
is it correct?/
hidden compass
is it correct?/
What?
hidden compass
Ahn I didn't see that message sorry
No, it's not true in general and also it doesn't answer to question (b)
hidden compass
Because they are not necessary rational
daring vessel
impossible
hidden compass
You only ahve to read exactly what it's written here
hidden compass
impossible
Bruh can you read or not??
daring vessel
sorry
hidden compass
Yeah it's correct, but I think they wanted "2 distinct real roots" as the answer to question (b)
But in this case they are rational, as well
It depends on what the book/teacher wants
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
eternal dust
in water, the pressure rises evenly the deeper you go down. the pressure at the surface is 1 atmosphere (atm). the pressure in 15 meters is 2.5 atm
a) describe the relationship between the pressure and the water depth as a regulation and graph
b) calculate from the regulation how big the pressure is at a depth of 7 ms
c) calculate from the prescription how deep you are down if the pressure is 4.5 atm
obtuse pebbleBOT
in water, the pressure rises evenly the deeper you go down. the pressure at the ...
obtuse pebbleBOT
@eternal dust Has your question been resolved?
eternal dust
<@&286206848099549185>
timid silo
@eternal dust does evenly mean its like f(x)=a*x+b ?
obtuse pebbleBOT
@eternal dust Has your question been resolved?
gusty berry
obtuse pebbleBOT
timid silo
R choose N
gusty berry
wdym
timid silo
wait im helping someone else ill brb
wanton pond
wdym
it means to choose r number of things out of n number of things
its also known as combination
gusty berry
it means to choose r number of things out of n number of things
im not quite sure what does that mean
wanton pond
do u know permutation?
warm shaleBOT
R4F43L1006
wanton pond
@gusty berry
gusty berry
do u know permutation?
yea
wanton pond
so combination is like permutation but seeing
(1,2,3)
(2,1,3)
(1,3,2)
(2,3,1)
(3,1,2)
(3,2,1)
as the same thing
gusty berry
yea but
gusty berry
how does that relate to this
warm shaleBOT
R4F43L1006
wanton pond
and in $(x+1)^n=(x+1)(x+1)\cdots(x+1)$, when you expand it, let's say ur solving for the coefficient of the $x^r$ term, it's like you are choosing $r$ number of $x$s out of $n$ of them to multiply then adding them
warm shaleBOT
R4F43L1006
wanton pond
that is, there are $\binom{n}{r}$ number of $x^r$s
warm shaleBOT
R4F43L1006
wanton pond
and i just saw that in ur example the n and r are switched
lone echo
**R4F43L1006**
(n-r), not (n-1)
obtuse pebbleBOT
@gusty berry Has your question been resolved?
stiff locust
wanton pond
what is the length of OB
stiff locust
dk wasnt given
plucky rivet
Then pythagoreas (or gogou) theorem
obtuse pebbleBOT
Available help channel!
candid ridge
Guys how do you do this
obtuse pebbleBOT
Guys how do you do this
candid ridge
fathom light
First rectangle has one side as (x-2)?
fathom light
Well form 2 equation of area of rectangle
Then replace either H by 1+h or h by H-1 from the given equation
candid ridge
cuz it’s area
fathom light
What is area of rectangle?
candid ridge
ohh wait
fathom light
Bruhhhh
Why so complex
@candid ridge what will be formula of area of 2nd rectangle?
candid ridge
h*y=20
candid ridge
H-h=1
fathom light
H-h=1
Can we write H = 1+h from this ?
Now what is the formula of area of the 1st rectangle?
Well it's ok
Let my method be
candid ridge
(y-2)*H
fathom light
I think you have already found out
What will be value of h
I think the factorization is wrong
wet dove
how do I find angle POQ?
languid ridge
how do I find angle POQ?
Is this the ques?
wet dove
yes
languid ridge
Can you click a pic from top?
timid silo
how do I find angle POQ?
the question isn't visible
in figure 10,POQ is a sector with centre O and radius 26 cm. SRT.....
that's the only visible data of given ques
S is midpoint of OP then SP =1/2 OP
SP=26/2
we will get sp
For st, use s=r*theta. We have theta as 90°; hence theta=π/2 in radian now substitute it above you will get s(arc length).
obtuse pebbleBOT
@wet dove Has your question been resolved?
foggy merlin
i need help with part B not sure what to do
obtuse pebbleBOT
i need help with part B not sure what to do
warm shaleBOT
knief
foggy merlin
so fg + faY = fn?
wary badger
yes
foggy merlin
then with the fn should i find the coefficient of friction?
wary badger
so fg + faY = fn?
this is all you need
wary badger
"calculate the value of the normal force acting on the object"
wary badger
👍🏻
foggy merlin
wary badger
what’s FR
wary badger
ahh ok
so the 12kg object is moving from the right to left
shouldn’t the reaction force be going the other way for the 4kg object
foggy merlin
no theyre moving together left
warm shaleBOT
knief
wary badger
which reads as "the force object 1 exerts on object 2" and vice versa
foggy merlin
sure
wary badger
your fbd misses that
foggy merlin
kinda confusing but ill use urs
wary badger
do you see why that’s important?
foggy merlin
wary badger
because if we consider the net force on each individual block
let’s call block 1 the 12 kg block
and block 2 the 4 kg block
F_12 is a force pointing to the left on block 2
foggy merlin
ye i got it
wary badger
ok in yours it’s pointing to the right for the smaller block though
you have the reversed direction
the force from block 1 on block 2 should be to the left
and the force from block 2 on block 1 should be to the right
foggy merlin
and the force from block 2 on block 1 should be to the right
it is
wary badger
but since it’s on block 1 that means the vector tail starts on block 1
the force is on block 1
foggy merlin
like this?
wary badger
close
now reverse the direction of F21
the 12kg block pushes the 4kg block to the left
foggy merlin
this?
wary badger
nope like this <—
foggy merlin
why is f21 not acting on object 1
wary badger
you’re right we did define it to be from object 2 on object 1
but we could just as easily redefine the notation to be on object 2 from object 1
it doesn’t really matter
just have to be consistent
foggy merlin
but we could just as easily redefine the notation to be on object 2 from object ...
but its not on object 2 to 1
its object 1 resisting object 2
or putting a force on object 2
foggy merlin
yes so the question is asking what force does object 2 exert on object 1
so thats f21 and the arrow is from object 2 exerted onto 1
wary badger
i need help with part B not sure what to do
it says "what force does the 4kg object exert on the 12kg object when the two are moving together"
which is equivalent to F_21 but you have your arrows on the wrong boxes
wary badger
but we could just as easily redefine the notation to be on object 2 from object ...
ok maybe it’s better to define it as this
since you already have the arrows where they are
so in your diagram we are looking for F_12
force on 1 by 2
wary badger
so thats f21 and the arrow is from object 2 exerted onto 1
if it’s exerted on object 1 then the tail of the arrow starts on object 1
because the force is applied to that object
@foggy merlin
foggy merlin
i dont get anything anymore
wary badger
💀