yes
#help-28
round turret
the radius is reflected along the x axis
oh shit i see ur right
what do you mean by this
im having trouble conceptualizing that
celest tapir
what do you mean by this
if you plot from 0 to π, you already have the circle
π to 2π traces over the same circle again
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honest quest
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honest quest
Partial fractions problem, I figure how find B but with A I need set up equal to polynomial to figure it’s coefficient but idk how to
I grouped it
raw quartz
$\frac{3}{2}\frac{3-x}{x+1} - 3\frac{3-x}{2x-1}$
honest quest
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Shoshir
raw quartz
but look like maybe not
For a 2nd degree rational polynomial $P\left(x\right)$, $\frac{N\left(x\right)}{P\left(x\right)}$ $A \cdot P_1\left(x\right) + B\cdot P_2\left(x\right) = N\left(x\right)$ where $P_1 \times P_2 = P\left(x\right)$, $A = \frac{N\left(x\right)}{P_1\left(P_2^{-1}\left(0\right)\right)}, \quad B = \frac{N\left(x\right)}{P_2\left(P_1^{-1}\left(0\right)\right)}$ so $\frac{A}{P_1\left(x\right)} + \frac{B}{P_2\left(x\right)} = \frac{N\left(x\right)}{P\left(x\right)}$
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Shoshir
honest quest
im sorry i sorta dont understand this 😦
i figured it out tho!
i grouped it wrong, so i redid it
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restive whale
suck my d
brittle cliff
how do i solve part d?
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how do i solve part d?
gritty rose
use the error or remainder formula for taylor series
brittle cliff
i know the error bound formula but dont know use it
gritty rose
i know the error bound formula but dont know use it
brittle cliff
https://math.colorado.edu/math2300/resources/instructorresources/spring2018/will...
i checked your pdf but still dont know how to do it
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brittle cliff
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manic ocean
Why can we not find C for this power series representation?
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Why can we not find C for this power series representation?
atomic hare
Why can we not find C for this power series representation?
maybe cuz theres no initial condition
manic ocean
that's not the issue
in previous examples we could set x = 0 and solve for C for the power series
in this one we cannot
atomic hare
show the previous examples
manic ocean
??? there's no bounds on the integral
atomic hare
uh yeah but the thing you are evaluating with a power series isnt
so we have the initial condition
c is 0
manic ocean
so the fact that im trying to evaluate a power series representation of a function vs an integral of a function determines whether or not I ave an initial condition?
because 1/(1+0) = 1
atomic hare
so the fact that im trying to evaluate a power series representation of a functi...
yes because the integral is indefinite and will have a +c when you evaluate it whereas the standalone function doesn't have a +c to solve for
manic ocean
so I have to solve for C because the initial function doesn't have a C (it has to match), wheresas with the indefinite integral, I can't solve for C because it's an integral
atomic hare
so I have to solve for C because the initial function doesn't have a C (it has t...
you cant solve for c because it doesnt ask you to find the particular solution and doesnt give you the initial condition
an intial condition would be like f(1) = 3 so now you have a point to anchor the integral to
manic ocean
right, I get that. I just guess the fact that we had to solve for C for when the initial function is not an integral is throwing me off for when the initial function is an integral
atomic hare
right, I get that. I just guess the fact that we *had* to solve for C for when t...
i think your teacher or whoever is just doing it for completeness since you expressed the function as an integral of a power series
manic ocean
@atomic hare I appreciate your help ^-^
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crystal cloud
Hello! I’m struggling with understand where my error of understanding is in this problem. I have my notes included in the following two images and the question is the first image.
I will be sitting in the chat ready to quickly reply as to not waste your time!
tepid walrus
Hello! I’m struggling with understand where my error of understanding is in this...
Nope. Your arithmetic's correct, but you didn't assign 25° to the correct angle. What is the definition of an angle of depression?
crystal cloud
Nope. Your arithmetic's correct, but you didn't assign 25° to the correct angle....
I thought a depression means to go downwards innit?
tepid walrus
I thought a depression means to go downwards innit?
Indeed. In your diagram, we'll say that the top of the lighthouse is located at the highest vertex of the triangle. If there's an individual looking down towards the ship, then we'd get the angle of depression (ϴ), as ϴ is the angle formed from the horizontal line of sight and the diagonal distance from the ship to this person.
crystal cloud
Okay Im with you so far 
tepid walrus
Therefore, it doesn't make much sense that you've assigned ϴ to the angle which is not between the line of sight and this distance. For starters, you've 'ought to draw this line of sight, as it is independent from the triangle itself.
In total, you should have 4 lines for your diagram, so you are already quite close.
crystal cloud
In total, you should have 4 lines for your diagram, so you are already quite clo...
So we have the triangle
sides abc
a = 179
This 4th line is the 25deg depression Im assuming?
If Im understand you correctly Im actually no longer understanding anymore.
tepid walrus
So we have the triangle
sides abc
a = 179
This 4th line is the 25deg depressi...
That's alright. This is, of course, a problem which can be completed with ease through visuals. I would recommend drawing it out instead of describing it.
"a" by itself cannot be 179-ft. It is simply a point on the triangle (but you can ignore this last part if these specifics are too confusing!).
crystal cloud
That's alright. This is, of course, a problem which can be completed with ease t...
"From the top of a 175ft light house" would insinuate that a would be 175 no? Especially if we are looking at a ship from the top of it ?
Edit: Im still not understanding how angle assignment is incorrect
tepid walrus
Close, but not quite. It implies that the distance between a and another vertex in the triangle is 179-ft. A single point cannot have a distance. I'll provide you with an example to help.
crystal cloud
Close, but not quite. It implies that the distance between a and *another vertex...
Thank you for the wisdom!
tepid walrus
Here's a problem, admittedly, very similar to the one which you're grappling with. Does it make sense if I tell you that the height of the building is AB = 50, and not A = 50?
tepid walrus
Awesome. And you see that horizontal line extending from the man's head? We call that the horizontal line of sight. When a person looks down to observe something (i.e., point c in the photo), we form an angle from this straight line, and we call it the angle of depression.
tepid walrus
Distance of the two points doesnt = length of side
No, it does. A single point doesn't equal the length of the side. We need two points to calculate a distance. Think of the Distance Formula.
crystal cloud
No, it does. A single point doesn't equal the length of the side. We need two po...
d= square root of (x2-x1)^2 + (y2-y1)^2?
Im sorta sad that individually everythign is making sense but something just just not connecting
Even the image makes sense
Am I interpreting correctly?
tepid walrus
d= square root of (x2-x1)^2 + (y2-y1)^2?
Im sorta sad that individually everyth...
Not to worry. As long as you find an interpretation that clicks for you, specifically, every single definition will begin to make sense.
And yes, that is the Distance Formula. I was simply pointing it out because you can't calculate a distance if you only have (x_1, y_1). Does that make sense?
tepid walrus
Am I interpreting correctly?
Absolutely! You've got it!
Take note about something interesting about the base of the triangle and this horizontal line of sight: they are both parallel to one another. Do you know what that must mean for one of the angles in your triangle?
crystal cloud
So then I’m assuming these labels would be fine too?
crystal cloud
Take note about something interesting about the base of the triangle and this ho...
OH MAN…
tepid walrus
So then I’m assuming these labels would be fine too?
Sure. You can write it like that.
crystal cloud
The light has been lit in my brain from the light house problem
LOL
So the angle of depression made a 90 degree angle
No
My eyes see it but my mind is organizing it still
tepid walrus
We're close...remember, only perpendicular lines create 90 degree angles. When a transversal crosses through two, parallel lines so that we have interior angles formed on alternating sides, what can we say about those two angles?
crystal cloud
Since we have an angle depresison of 25 degees and that is where the boat is located we are trying to figure out how far the boat is from teh base of the lighthouse
Which allows us to draw a line from the boat to the base
The 25 depression comes from the point that is at the top of the light house which is 175ft high
This depression can only exist from the horizontal line of vison since the boat [obviously] isnt in front of us but its our reference point [ a straight line]
We sorta just made a rectangle
Which gives us a 90 degree angle which means that we should be doing trig from the 90 degree angle we made right?
Can we attribute the height of this "vision triangle" to 175ft high?
tepid walrus
Since we have an angle depresison of 25 degees and that is where the boat is loc...
Yep, we did. But we're focusing on this triangle which is a part of this rectangle, because that'll give us the distance between the boat and the lighthouse.
tepid walrus
Which gives us a 90 degree angle which means that we should be doing trig from t...
Yes, usage of Trig Ratios. But you cannot use SOHCAHTOA on a 90 degree angle; you have to use it with one of the other, two angles.
tepid walrus
Updated professional drawing for confirmation of understanding
Much obliged. And the given illustration is very much correct—you can absolutely use that second triangle formed on the right-hand side, but if you'd like to take the conventional (and faster) approach, I would recommend proving that one of the angles in the triangle on the left-hand side is equal to the angle of depression.
crystal cloud
the angles of a triangle add up to 180 innit?
tepid walrus
Yes.
carmine plinth
hi
tepid walrus
No worries. Are you familiar with theorems involving parallel lines?
carmine plinth
just a question
crystal cloud
No worries. Are you familiar with theorems involving parallel lines?
Lets just say I dont and run me through it, Im taking notes as we are speaking.
carmine plinth
isint it 179 feet?
crystal cloud
isint it 179 feet?
It is, but I dont care to correct it more concerned about understanding hte concept at this point
crystal cloud
Now I am here 😭
crystal cloud
thats all if yall need help just ping
Thank you!
carmine plinth
just another suggestion why dont u name the corners of the triangles
its good practice and makes it ease to understnad
tepid walrus
Lets just say I dont and run me through it, Im taking notes as we are speaking.
Sure thing. Here are four categories of angles which are formed when a transversal crossed through parallel lines. Focus on the angles D, F, G, and J, as those angles utilize the same rule which you need for this problem.
tepid walrus
its good practice and makes it ease to understnad
The convention is to label vertices as one-letter variables, but I'm not too picky with notation for beginners. He's got the idea down, and he's simply referring to the sides of the triangle as you would in the Pythagorean Theorem.
crystal cloud
OH
tepid walrus
Check this out. This is the alternate interior angles theorem. Did it click for you?
crystal cloud
Now I understand what oyu meant when you said I attributed theta from the wrong angle
The angle was supposed to come from the direction of the ship innit?
But I had to use those rules to do so?
carmine plinth
The convention is to label vertices as one-letter variables, but I'm not too pic...
👍
tepid walrus
But I had to use those rules to do so?
Yes!
Using the theorems of parallel lines allows you the reach the conclusion of which angle is equal to the angle of depression! It's quite fascinating, like detective work.
vivid marsh
@crystal cloud ,what website are you using for this type of questions
carmine plinth
btw polinski he can just use the 65 right why r u teaching him this
tepid walrus
btw polinski he can just use the 65 right why r u teaching him this
Of course he can. But he wouldn't have been able to deduce that the angle was 65 if he didn't already know that the angle in the bottom right corner was 25.
crystal cloud
<@845007820898566145> ,what website are you using for this type of questions
This is a failed assesment that I had from my asyncronus class.
I get to have two tries so im trying to understand what I got wrong to get a better grade for the next run.
I got a 70% last time I passed but I need As so going to try again after I understand what i got wrong here.
vivid marsh
This is a failed assesment that I had from my asyncronus class.
I get to have t...
Okay
All the best
tepid walrus
not really 25+x=90 and x=65 right?
Yes, it does. But we can prove that the triangles are similar through parallel lines.
crystal cloud
Am I understand worse or better friends?
tepid walrus
The triangles are obviously similar, but it is not wise to assume anything in mathematics. Teaching how to prove similarity (or in this case, congruency) in triangles is vital and not something to gloss over.
tepid walrus
Am I understand worse or better friends?
Yep, you've got it. But remember, it's 179, not 175.
crystal cloud
TRUE LOL
carmine plinth
lmao
crystal cloud
Clearly I have computational power
Just the understanding of the concepts kill me
But I can understand Torque vectoring and statics conceptually completely fine
tepid walrus
Cool! I'm in Engineering too. Don't worry, if you can understand the higher-level mathematics, it should only be simple review for you going backwards.
crystal cloud
Am I cooked?
carmine plinth
which year are yall in?
crystal cloud
which year are yall in?
My first ever semester Im a HS dropout
carmine plinth
whats hs?
carmine plinth
Am I cooked?
179/0.4663076587 💀
tepid walrus
Am I cooked?
Right, you've got it. Isolate b now.
crystal cloud
Shh Im writing fast bruv
Wait guys... I feel a bit stupid...
I have some huge gaps in my brain
Im just realizing this
HOW tf do I isolate that
tepid walrus
HOW tf do I isolate that
Take the multiplicative inverse of "0.466307..." on both sides.
crystal cloud
With the help of amazing friends I have learned new things.
If I’m finding the distance of the SHIP to the base of the triangle I need the angle that comes from the ship to even attempt to find the measurement I’m looking for.
Then everything else is simply understand angle relationships
tepid walrus
If I’m finding the distance of the SHIP to the base of the triangle I need the a...
Hm, not necessarily. But we don't have to get precise at the beginning. Just keep in mind that you need either angle inside the triangle which is not the 90 degree angle, and another (or two!) side lengths in-order to calculate similar prompts.
crystal cloud
Hm, not necessarily. But we don't have to get precise at the beginning. Just kee...
Main issue is that i conflated the 25 depreciation for an angle that is literally 25 degrees in the original triangle I made.
When the depreciation actually comes from a horizontal vision line since we "have to look down"
tepid walrus
Main issue is that i conflated the 25 depreciation for an angle that is literall...
Yep, yep. You got that part down. And you're right in the case of angle relations, nicely done!
crystal cloud
Thanks guys! everyone getting FQs now shoutouts to my engineering majors
Imma start helping people in here w problems too so I can start getting more reps
Because MAN its needed.
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timid flint
Can someone explain how lagrangrs therum is usdd
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Can someone explain how lagrangrs therum is usdd
onyx stream
lagrange's theorem tells you x^(mp^n) = e
so x^sm raised to the power of p^n is e, which means x^sm is in H
similarly, x^tp^n is in K
hallow oxide
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eager jackal
@hallow oxide is there anything you've tried? what do you need help with specifically?
hallow oxide
<@469336769935179787> is there anything you've tried? what do you need help wit...
Question 12
hallow oxide
<@469336769935179787> is there anything you've tried? what do you need help wit...
ive tried everything
not able to find out the answer
eager jackal
Question 12
I figured, but is there any step/sub problem you're stuck with or you can't do anything out of the three problems
(a,b,c)
hallow oxide
I figured, but is there any step/sub problem you're stuck with or you can't do a...
i cant do any of them including a,b,c i dont know wherd to start or anything im clue,ess
eager jackal
ah
alright, so beginning with the first one
since the we're working with a box, the faces of the box are rectangles right?
and we know the length of the diagonal of the bottom face, and one of it's sides
so we can figure out the other side by using the pythagorean theorem since if we divide a rectangle using it's diagonal, we get two right angled triangles
Now using this you can figure out the "length of the other edge"
and we know that length is also it's height
hallow oxide
yes
eager jackal
then you can just solve for volume using length into base into height resulting in the volume
after getting this, you can differentiate wrt x and solve for max volume
hope that's clear
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stuck fiber
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stuck fiber
Thought I knew how to do this and I got some nice numbers but apparently its wrong 😔
A is obviously (0, 3)
The vertex is -(-4)/(2)(1) which is x = 2
subbing in x = 2 into the parabola gives -1
So T is (2, -1)
onyx glen
so far so good
stuck fiber
Then we can see that the x value of T is in between A and B so B must have an x value of 4
So B is (4, 3)
So A is (0, 3), B is (4, 3) and T is (2, -1)
void nova
All good yeah
stuck fiber
I then want to calculate the slope of the blue line, because it would give us the inverse slope of the red line
(-1-3)/(2-0) = slope m
so the slope is -2
Which gives us the slope of the red line 1/2
void nova
I believe you're overcomplicating it
stuck fiber
Ok but 1 moment I will just finish showing what I did
void nova
Just recall the general equation of a circumference, i.e. x²+y²+ax+by+c=0
void nova
Ok but 1 moment I will just finish showing what I did
Yeah sure
stuck fiber
Then to get the equation of the red line we sub in the point B (4, 3)
3 = (4)(1/2) + c
c = 1
So the equation of the red line is y = x/2 + 1
Then we do the same for the other side, but we already know the slope of the red line is -1/2
So subbing in A (0, 3) into the equation of the line we get 3 = (0)(-1/2) + c
giving us the equation y = -x/2 + 3
Then we take the 2 equations of the 2 lines we got, y = -x/2 + 3 and y = x/2 + 1 and set them equal
-x/2 + 3 = x/2 + 1
so x = 2
Then subbing x = 2 into y = x/2 + 1 gives us 2 again
So our midpoint should be (2, 2)
Then for the radius its just the distance formula from A (0,3)
sqrt((2 - 3)^2 + (2 - 0)^2)
sqrt(1 + 4)
= sqrt(5)
So our final equation should be
(x - 2)^2 + (y - 2)^2 = 5
But they wanted something else...
Which step went wrong?
void nova
I'm not sure which method it is the one you used, honestly
stuck fiber
Just found the intersection of the 2 red lines in the 2 images
That should be our midpoint right?
void nova
Yes, but I don't think it's guaranteed to be the center of the circle
stuck fiber
Just recall the general equation of a circumference, i.e. x²+y²+ax+by+c=0
Ok maybe we forget my way, can you explain this lol it seems way easier 😄
void nova
If it was the center of the circle, it's distance between A and T would be the same, which in this case doesn't look like, right?
stuck fiber
It was very rough, but yeah I guess youre right
void nova
Ok maybe we forget my way, can you explain this lol it seems way easier 😄
I've got a lesson in few mins sorry
stuck fiber
Just recall the general equation of a circumference, i.e. x²+y²+ax+by+c=0
Do you know the name of the method so I can maybe watch a video on it?
void nova
Just recall the general equation of a circumference, i.e. x²+y²+ax+by+c=0
I suggest you do this, btw
And you'll get a system of 3 equations in 3 unknowns (the parameters a, b, c)
void nova
Do you know the name of the method so I can maybe watch a video on it?
It doesn't have a name, just make each of the three points satisfy the equation of the circumference
stuck fiber
I suggest you do this, btw
And you'll get a system of 3 equations in 3 unknowns ...
I can do it but I care more about understanding what I do then getting the answer hehe
stuck fiber
It doesn't have a name, just make each of the three points satisfy the equation ...
But like what can I search in youtube to find a video on it
.close
honest roost
Hi guys im having trouble with some trigonometric expressions. I tried asking chatgpt and deepseek but they use rsin and similar which i havent done. Ill send pics of what i have done and what example i have to do. As you can see i was trying to find a common denominator to have below the line but im not sure how to proceed or if thats even the correct way
waxen cliff
Im sorry for putting this in a already occupied chat didnt see it
it's okay it happens
covert heath
what do you have to do
sturdy valve
what is the question g
honest roost
Oof sorry
1/sin10°-sqrt(3)/cos10°=4
Also i cannot just use numerical forms of sine and cosine
sturdy valve
1/sin10°-sqrt(3)/cos10°=4
first take LCM
then i think you'll have to multiply and divide by root (a^2+b^2)
i hope u know this?
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honest roost
Uh i kind of did it but im not sure its the right way.
honest roost
first take LCM
cursive trout
<@957552694451666995> r u learning matrices
i did it
i nearly completed the entire syllabus of maths
honest roost
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torn jolt
i nearly completed the entire syllabus of maths
? 💀
did u complete circles,quadratic equation n stat?
torn jolt
nice to meet ya broo
ye bro same
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cursive torrent
I need help, ill claim this channel so I can write out my question without the channel dissapearing again
cursive trout
did u complete circles,quadratic equation n stat?
stat not done, others done
cursive trout
I need help, ill claim this channel so I can write out my question without the c...
stat, probaility and trigonometry left, lol i love maths
cursive torrent
I need help with this game dev math, I am using image projection to map my pixel art onto objects which will later be used for shading and simple lighting. now i want to render the scene pixel perfect so i have my reference reoslution and all thats left to do is snap the camera movment to a set increment. Example for the x axis since that was easy as the x axis doesnt get stretched while projecting. i know that the x axis contains 32pixels/m so i know i need to move the camera in game in 1/32m increments. My question is how i would go about calculating the increment for the Z axis since thos pixels are distorted by the ortographic projection
cursive trout
I need help with this game dev math, I am using image projection to map my pixel...
game dev, aah yeah
cursive trout
I need help with this game dev math, I am using image projection to map my pixel...
okay, can you tell in simple words, what u tryna achieve?
cursive torrent
Im trying to get the pixelated textures on the objects to perfectly allign with the low resolution camera
cursive torrent
okay, can you tell in simple words, what u tryna achieve?
or even simpler, pixel perfect rendering
cursive trout
so, the probelm on Z axis
because their screen-space or whateevr it is called, it gets compressed
in orthographic projection
is that
cursive trout
objects far away appear smaller
torn jolt
No nerd, fully extrovert
still
cursive trout
i've completed dark souls 1,2,3
black myth wukong
the last of us
1
All The GTAs
Play minecraft with friends daily
torn jolt
U completed half of concise 😭
cursive trout
Manhunt 1,2
torn jolt
damn
cursive trout
U completed half of concise 😭
doesn't matter, not done any other subject
well, its better to DM
torn jolt
I only completed 2
cursive trout
I only completed 2
yep, its the average speed
torn jolt
matrices n banking
torn jolt
well, its better to DM
sure
cursive trout
matrices n banking
nice
@cursive torrent okay i was just distracted
so the basic solution u can do is
find scale factor for the Z axis
scale factor is how much the pixels will be compressed due to this distance
General formula - (u may know it)
1/(Z of object - Z of camera)
then, find the pixel increment
cursive torrent
i have never heard of that formula
cursive torrent
well it might work but i don't understand what it does
cursive trout
If you know that the camera moves in 1/32 meter increments on the X-axis
the same kind of idea can apply to the Z-axis, but we have to adjust for the scale factor due to the projection
cursive torrent
the same kind of idea can apply to the Z-axis, but we have to adjust for the sca...
yes but no matter what i tried i couldnt calculate the correct increment
could the issue be that the pixels along the y axis are less stretched than those on the z axis ?
cursive trout
could the issue be that the pixels along the y axis are less stretched than thos...
okay thats an issue
i guess this happens because Y-axis projection is typically not influenced by the camera's Z position in terms of scaling
Z-axis projection does influence how pixels are mapped onto the object’s surface
To fix this
uhh
You can keep Y-axis resolution consistent
cursive torrent
To fix this
project from a 45° angle ?
cursive torrent
or do pixel perfect calculation for Z-axis
but i dont know how TT
cursive trout
project from a 45° angle ?
yes absolutely
you can fix the pixel stretching by using a perspective projection instead of an orthographic projection
but listen up,
perspective projection
cursive torrent
you can fix the pixel stretching by using a perspective projection instead of an...
I dont think so, that would just stretch it even more and way worse
cursive trout
causes distortion of textures
cursive torrent
._.
cursive trout
okay so
lets do it step by step thenn
firstly check that the camera moves in fixed increments on z axis
use the formula
1/z of object - z of camera for the scale factor
cursive torrent
1/z of object - z of camera for the scale factor
what exactly do you mean with z ?
cursive torrent
you mean z coordinate ?
cursive trout
you mean z coordinate ?
yes
cursive torrent
and what do you mean with scale factor ?
cursive trout
in this context
The scale factor describes how much the pixel resolution of the object will change due to its distance from the camera
cursive torrent
its orthographic man, the distance doesn't matter at all
cursive trout
okay, i really need to understand from core
cursive torrent
whats important is the increment of the cameras coordinates so the camera alligns with the objects textures
cursive trout
orthographic projection means no depth scaling
The camera should move along the Z-axis in increments of 1/32 meters
to maintain pixel perfect rendering
you need to snap the camera's Z - position to a grid that corresponds to the pixel resolution of your texture
cursive torrent
eg the 1px is 1m then youd use an increment of 1 aka the camera can only use whole numbers as its position that way you will never have the pixel art missaligned what would result in weird anti aliasing or stretching of certain pixels
cursive torrent
The camera should move along the Z-axis in increments of 1/32 meters
that is only for the x axis, as i said earlier. but for the z axis im not sure how to calculate the value
cursive torrent
nah im closing this stupid help thing, instead of working on the problem im just wasting my time hearing other people repeat my problem and trying to explain my problem
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tacit fossil
can anyone proove me why the definite integral always gives the area under the curve between two points a and b
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tight mortar
original message is in different channel now
narrow ermine
can anyone proove me why the definite integral always gives the area under the c...
You'll need another channel, but really the integral is sort of defined such that it computes the area under a curve.
delicate heron
can I repost my question?
tight mortar
ya
narrow ermine
You need another channel too, you were the original claimant and you deleted your post.
narrow ermine
It's already closed. It'll disappear on its own, as per the automated message above.
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lean sky
Can someone help me understand trigonometry? Like it's a little biased and i cant figure out how do i make this ab = bc = ac thingies when i have other triangles. And finding like their distance between each angle.
covert heath
it's a little what
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faint drift
One more thing. I am having trouble with another problem in regards to orthogonal trajectories. How do I separate k out of this one?
y = x / 1 + kx
celest tapir
is it y = x/(1 + kx)?
you could just multiply through I guess
y + kyx = x
y' + k(y + xy') = 1
k = (1 - y')/(y + xy')
and sub that back in
faint drift
Got it. I felt really dumb not knowing how to get k out of that problem @_@
Thank you once again.
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celest fulcrum
This is from homomorphisms and im a little confused. To clarify, the $\Phi^{-1}$ is not a reverse map as homomorphisms do not need to be bijective right
glossy valveBOT
BOSS
celest fulcrum
as in, there is no bijective map from $H_2$ to the preimmage of $H_2$
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BOSS
timber knoll
Yeah, $\phi^{-1}(H_2) = {g \in G_1 : \phi(g) \in H_2}$
glossy valveBOT
ucheo
celest fulcrum
Ok, bet. So there is not nessisarely a bijective map from $H_2 \rightarrow \Phi^{-1} (H_2)$
glossy valveBOT
BOSS
timber knoll
No. If there were, then $\phi$ would be injective in $H_2$.
tribal epoch
wha
glossy valveBOT
ucheo
torn jolt
can someone show me the steps of doing this
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can someone show me the steps of doing this
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keen phoenix
hi
multivariable calculus question on inverse function theorem
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Charky
keen phoenix
and to do that we find if the partial derivatives are continouos at 0, 0
which i did limit of partial derivatives to 0, 0 = partial derivative at 0, 0
but my problem is
the inverse function theprem requires C1 around 0, 0
which means it has to have cont partial derivatives everywhere around 0, 0
am i doing that even tho i am only looking at cont partial derivatives of 0, 0?
also forgot to mention i found the determinant of jacobian not equal to 0 but i am confused about the C1 part mostly
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keen phoenix
<@&286206848099549185>
onyx stream
which means it has to have cont partial derivatives everywhere around 0, 0
my understanding is yes, you need to impose this
however note that it only really matters on the line x=0
since it is obviously continuously differentiable off of the line
keen phoenix
so i would show that the 2partial derivatives for only F_1 not all 4 at (0, y) are continouos? aka limit to (0, y) = partial derivative at this point (0, y)? and then it will be sufficient
onyx stream
yes, but i am now realizing this should look basically the same as the statement for continuity at (0,0)
so really there is not much to show
onyx stream
well (0,0) is already of the form (0,y)
onyx stream
so you can just generalize your argument
keen phoenix
right
onyx stream
since y=0 is not special like x=0 is
onyx stream
np
keen phoenix
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keen phoenix
new problem i guess
what does local inverse mean exactly
i understand local inverse is different to global inverse, cuz local inverse everywhere does not mean global inverse
but what does the inverse function theorem tell us
consider $f(x) = x^3$
glossy valveBOT
Charky
keen phoenix
the derivative is 3x^2, which is 0 at x = 0
but then inverse function theorem says no local inverse
but there is a global inverse cube root x
wide sundial
there are open sets U containing a and V containing f(a) and a function g:V -> U such that...
keen phoenix
ye but why is it different to global inverse
wide sundial
look at x^2
keen phoenix
the derivative is 3x^2, which is 0 at x = 0
like why is there no local inverse here
wide sundial
it doesn't have a global inverse
wide sundial
but around every point you can find a local inverse (except at the vertex)
keen phoenix
but then x^3 does not have a local inverse at x = 0
keen phoenix
but around every point you can find a local inverse (except at the vertex)
why not vertex tho
wouldnt either inverse defintion like sqrt(x) be ok there
wide sundial
because no matter how small you pick your neighbourhood around x = 0
you always go up on both sides
aka not surjective
wide sundial
aka not bijective
wide sundial
aka the jacobian is not invertible
onyx stream
but then inverse function theorem says no local inverse
as far as i can tell, the inverse function theorem never states the converse
wide sundial
what about x^3
this is not invertible for the other reason
its jacobian doesn't exist at x = 0
keen phoenix
its jacobian doesn't exist at x = 0
but why
wide sundial
for x^2 the jacobian is 0 aka singular aka not invertible
wide sundial
well it's not differentiable at x^3
wide sundial
oh wait
keen phoenix
yet no local inverse at x =0
onyx stream
yet no local inverse at x =0
it does have a local inverse
keen phoenix
doesnt make sense
wide sundial
i got confused
keen phoenix
it does have a local inverse
so the inverse function theorem is not exhaustive
onyx stream
yeah
keen phoenix
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wide sundial
it does have a local inverse
this is correct
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mint jackal
Hi I'm in step (d) any idea? Brain hurt. Thank you 🙂
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Hi I'm in step (d) any idea? Brain hurt. Thank you 🙂
mint jackal
hi?
I am stuck on (d). brain hurt. Thank ou 🙂
Suppose $d_n$ is the number of $n$-digit numbers that don't contain the digit ' 3 ' twice in a row.\\
(a) Compute $d_1, d_2$, and $d_3$ by explicitly counting the sequences described (you don't have to list them, but you should have a counting argument).
\\\\
(b) Use a counting argument to show that $d_n=9\left(d_{n-1}+d_{n-2}\right)$ when $n \geq 3$.
\\\\
(c) Use the recurrence from (b) to find values for $d_4, d_5$, and $d_6$.
\\\\
(d) Use the initial conditions and recurrence you found in (a) and (b) to find the generating function \\$D(x)=\sum_{n=0}^{\infty} d_n x^n$ as a rational function in $x$.
\\\\
(f) What is your closed formula for $d_n$ ? Compare the values given by your formula to the ones found earlier.
\\\\
HINT: you during the partial fraction step, you will need to use partial fraction long divison.
\\\\
For reference:\\
$d_0 = 1, d_1 = 9, d_2 = 89, d_3 = 882, d_4 = 8739, \\d_5 = 857,952$
languid junco
Hi I'm in step (d) any idea? Brain hurt. Thank you 🙂
$d_n - 9d_{n-1} - 9d_{n-2} = 0$, so suppose $d_n = k^n$ for some real number $k$. then you end up with the quadratic
$k^2 - 9k - 9 = 0$
solve for $k$, and then $d_n$ is a linear combination of the two solutions you get, i.e.
$d_n = ak_1^n + bk_2^n$
solve for $a$ and $b$ using your initial conditions, then use geometric series to solve for $D(x)$
glossy valveBOT
doaby
mint jackal
my brain, sorry actually i pasted it not there. theres an (e) part thats the one I need help with! sorry!
for (D) i got
$D(x) = \dfrac{-x^2 + 1}{1-9x-9x^2}$ <- I checke it with wolfram and it looks good
now, (e) says the following:
(e) Use partial fractions to take D(x) apart into simpler pieces, and find a series representation of D(x).
glossy valveBOT
bnn
languid junco
take out a -9 from the denominator, so you'll have
$\frac{x^2-1}{9(x^2+x-1/9)}$.
then solve for the roots of $x^2+x-1/9 = 0$ and rewrite it as $(x-r)(x-s)$, where $r, s$ are your roots. then you can do partial fractions. that's not the way they suggest but it's probably easier...
glossy valveBOT
doaby
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little plover
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little plover
i might need help with the last two
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little plover
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torn jolt
Differentiation
what did i do wrong help
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# Differentiation
what did i do wrong help
torn jolt
final answer
slate violet
# Differentiation
what did i do wrong help
$uv'$ should just be $3x^2 \cdot \frac{2x}{\sqrt{2x^2 + 3}}$
glossy valveBOT
south
torn jolt
wait
slate violet
yeah you didn't divide everything by sqrt(2x^2 + 3)^2 = (2x^2 + 3)
torn jolt
can u show me where it is i cant tell
slate violet
can u show me where it is i cant tell
where what is?
torn jolt
also where's your denominator???
that was my denominator
slate violet
yeah then you need brackets around the entire thing
torn jolt
ohh
slate violet
okay let me fix it on your diagram
torn jolt
otherwise it would only
fathom saddle
Denominator should be squared
torn jolt
multiply with one term
fathom saddle
That's the only mistake
slate violet
fathom saddle
Not using brackets is a poor choice, but you didn't let it affect your answer
torn jolt
it should look like this right
torn jolt
no square root because it cancels out
slate violet
no square root because it cancels out
correct
torn jolt
damn calculus
slate violet
Not using brackets is a poor choice, but you didn't let it affect your answer
but it does make it really hard to read
like if you've been accidentally marked wrong, this is probably why
fathom saddle
Yes I would personally mark against that
slate violet
yeah so if you divide by sqrt(2x^2 + 3) and not (2x^2 + 3)
you end up needing to divide by an extra sqrt(2x^2 + 3)
fathom saddle
Still, well done, this is a complicated derivative
slate violet
the denominator would be $(2x^2 + 3)^1 \cdot (2x^2 + 3)^{1/2}$ and hence
glossy valveBOT
south
slate violet
that's how you can fix your work
$\frac{y'}{y} = \frac{2}{x} - \frac{1}{2} \frac{4x}{2x^2 + 3}$ go brrr
glossy valveBOT
south
slate violet
logarithmic differentiation
slate violet
make it in exponent form
yes
slate violet
no worries!
tight mortar
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analog raptor
limit of a sum = integral?
onyx glen
$a_n = \sum_{k=0}^{n-1} \frac{1}{\sqrt{n^2-k^2}}$
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Ann
tight mortar
we take $\lim_{n\rightarrow\infty}$
glossy valveBOT
blahaquil
tight mortar
i got up to there but i dont know how to proceed
is there some trigonometric substitution?
gritty flax
Smells riemann sum
Factor by n² inside the sqrt
Take it out
And then you will have the 1/n waited
Now idenitfy the a,b of the riemann sum
onyx glen
is there some trigonometric substitution?
did you turn it into an integral
tight mortar
limit of a sum = integral?
wait on further thought i don't think i really understand this
like just as a riemann sum?
tight mortar
ohk
analog raptor
$\int_{a}^{b} f(x) \mathrm{d}x = \lim_{n \to \infty} \sum_{i=0}^{n} f(x_{i}) \delta x$
glossy valveBOT
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tight mortar
hmm
analog raptor
factor out a 1/n from the inside of the sum
that way you can get delta x
and identify x_k
onyx glen
<@&268886789983436800> scam
tight mortar
so like \begin{align*}
a_n &= \sum_{k=0}^{n-1} \frac{1}{\sqrt{n^2-k^2}}\
&=\sum_{k=0}^{n-1}\overbrace{\frac{1}{\sqrt{1-\left(\frac{k}{n}\right)^2}}}^{f(x_i)}\frac{1}{n}\
\end{align*}
tight mortar
i canNOT do latex
glossy valveBOT
blahaquil
analog raptor
yes
tight mortar
man i really need to review my foundations
analog raptor
,tex $\text{so, } x_{k} = a + i \Delta x
\Delta x = \frac{b-a}{n}
\text{ from here you can try and guess values of a and b, and then simplify}
$
glossy valveBOT
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(You may edit your message to recompile.)
analog raptor
what did i type incorrectly
tight mortar
something with the $$
analog raptor
oh well
tight mortar
$\sum_{k=0}^{n-1}\overbrace{\frac{1}{\sqrt{1-\left(\frac{k}{n}\right)^2}}}^{f(x_i)}\frac{1}{n}=\sum_{k=0}^{n-1}\frac{1}{\sqrt{1-x_k^2}}\Delta x\text{ where $a$ and $b$ are probably let's say like 0 and 1? we know }b=a+1\text{ i guess?}$
glossy valveBOT
blahaquil
tight mortar
im definitely getting something wrong here i think
analog raptor
yeah, so
x_k = k/n
not squared
we know that delta x = 1/n, and so this looks like the form k delta x
only thing missing is a lower bound a
however, this looks like 0 + k delta x, so you can set a = 0
pretty standard from there
tight mortar
so its $\int_0^1 \frac{1}{\sqrt{1-x^2}} dx$? and then just trig sub blah blah blah?
glossy valveBOT
blahaquil
analog raptor
yep
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stuck loom
Consider a > b.
By Euclid's lemma of division, a = bx + r for some integers x and r where 0 <= r < b.
Divide the L.H.S and the R.H.S by b, and we get:
(a/b) = x + r/b
Lemma (Forget the variables mentioned here, they are just for the sake of this lemma): If (b,c) = d, then (ac+b, c) = d
That is, if we have a + b/c where b/c is reducible by d, combing the terms to form a single fraction (ac + b)/c, we have that (ac + b)/c reducible by d.
Proof: Let (b,c) = d.
K = a + b/c = a + dk/dl where b = dk and c = dl. So (l,k) = 1
K = a + dk/dl = (adl + dk)/(dl)
We need to prove that (adl + dk, dl) = d
K = (adl + dk)/(dl) = ((adl + dk)/d)/(dl/d) = (al + k)/l
We basically need to prove that (al + k, l) = 1
Let (al + k, l) = d_0
d_0 divides l and (al + k). So d_0 divides k.
So d_0 is a common factor of k and l. The only common factor of k and l is 1. So d_0 = 1
Since d_0 = (al + k, l) = 1, (al + k)/l is irreducible.
(al+k)d/l(d) is reducible by only d, because after reducing it by d, we can't reduce it further. So (ald + dk)/(dl) is reducible only by d.
So (ald+ dk, dl) = d
Putting c = dl and b = dk, we get:
(ac + b, c) = d
So we have proven that if (b,c) = d, then (ac + b, c) = d
Exeunt.
Coming back to our original equation, we had:
a/b = x + r/b
Consider x + r/b.
Let (b, r) = d
By our lemma (bx + r, b) = d
Since a = bx + r, we have (a, b) = d = (b, r)
If a > b, then we can write a = bx + r
We have proved that (a, b) = (b, r).
Q. Is this a correct proof of Euclid's division algorithm?
onyx glen
Exeunt.
who are the people exiting?
other than that, yes, it looks sound.
wordy, but there are no "jumps out at me"-level errors.
@stuck loom
rain merlin
looks correct
stuck loom
Thanks y'all.
stuck loom
> _Exeunt._
who are the people exiting?
It's obvious.
I should keep a Mathematics diary for all of this s*it.
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@cold nebula Has your question been resolved?
woeful thunder
log(50) = log(5)+log(10)
base 10
now try to write log(5) in terms of a again
yeah thats it
yeah ig
better to make a new one
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shrewd mango
help with 2d vector 2d transformation and boolean algebra
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help with 2d vector 2d transformation and boolean algebra
covert heath
thats the least specific thing ever
celest tapir
this isn't a search engine
covert heath
or gpt
shrewd mango
well i was hoping someone could explain these in detail so i could ask more follow up question. but obv thats doesnt seem like something you do
queen pond
still not clear on what you want explained, ur original message is very unspecific
shrewd mango
sorry, its currently within computer archetecture, learning about things above. within the 2d transformation i need to Produce an Excel spreadsheet demonstrating the implementation of 2D transformations (translation, rotation, reflection in axes, scaling and shear) applied to a 2D vehicle of your choice. however im not looking for an answer, im more looking for someone to help explain how to achieve the answer
queen pond
google it.
shrewd mango
i already have, but i find easier to do it through virbal communication where i can ask plenty of specific follow up questions. its how i work.
i mean if u cant i get it.
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silver ruin
if a point divides a line segment in a negative ratio why does it mean that it divides the line that ratio externally?
covert heath
what?
alpine pecan
yeah, it means that tht point lies on tht extension of the line formed by the other two pts
silver ruin
yeah, it means that tht point lies on tht extension of the line formed by the ot...
why
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crude kayak
if a point divides a line segment in a negative ratio why does it mean that it d...
you can understand this using "linearity of area of triangles"
as described in the answer for my math.SE question
https://math.stackexchange.com/q/4437117
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undone wave
Hello
undone wave
Is there a way to make an unknown irrational number a rational one via some operation? For example by multiplication, exponentiation or something else?
hot herald
without changing the value of the irrational number, no
undone wave
Of course it should change, it can be any other value, as long as it is smaller
minor crater
Is there a way to make an unknown irrational number a rational one via some oper...
let b be that number, b/b is rational 
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
hot herald
multiply by 0
undone wave
Ok, my bad for not restricting the condition initially as best as I could
The new number should be between 0 and the irrational number
minor crater
Of course it should change, it can be any other value, as long as it is smaller
you want a rational approximation?
cuz "make a number rational" is super vague tbh
hot herald
what's the original task that requires you to do such a thing
lean cloak
simply use the axiom of choice and decide what you want it to be
undone wave
I am trying to prove that right limit of f(x) does not exist around 0
and f(x) is 1 if x is irrational, and 0 if x is rational
hot herald
what's f(x) here
minor crater
and f(x) is 1 if x is irrational, and 0 if x is rational
now we are talking
are you doing an epsilon-delta proof?
lean cloak
Hint: in any neighbourhood, there are infinitely many irrationals
minor crater
(and rationals)
lean cloak
I figured that one didn't need to be explicitly said but yes that too
undone wave
Well I handled the case when epsilon is rational
as I multiply it by sqrt(2)/2 to make it irrational
but if epsilon is irrational, I am not sure how to proceed
spark wren
the limit does not exist i guess
minor crater
the limit does not exist i guess
that's what he is trying to prove
lean cloak
You don't need to try different cases of epsilon
Remember the defintion: for ALL epsilon greater than 0, there exists a delta....
If you can prove that there is just one epislon that does not have a corresponding delta, you have proven the limit does not exist
spark wren
that's what he is trying to prove
sooo just use a case of Epsilon that delta does not exist
lean cloak
So if you've already handled the case where epsilon is rational, you're done
spark wren
you can do the inverse
minor crater
Well I handled the case when epsilon is rational
can you show your work so far?
spark wren
if for all Epsilon there exists delta
the reverse if for one Epsilon then all delta does not work
so delta is the rational
we need to make Epsilon a function of delta
lean cloak
I don't fully understand what you're saying, but it's definitely not correct in this case
You don't need to make epsilon anything, that is the point. Epsilon can be arbitrary and you just have to show there is no such delta that satisfies the definition
spark wren
You don't need to make epsilon anything, that is the point. Epsilon can be arbit...
thats what I meant
it's 1 at rational and 0 if irrational
or reversed
so what is our value
perhaps 0
undone wave
can you show your work so far?
I have that if epsilon is rational, then I get 2 numbers, f(epsilon/2) = 0, f(epsilon * sqrt(2) / 2) = 1. Then there is no epsilon-band that satisfies both values. And I decided to prove that case where epsilono is not rational
spark wren
I have that if epsilon is rational, then I get 2 numbers, f(epsilon/2) = 0, f(...
why would that matter isnt an inequality
lean cloak
Try letting $\epsilon = x$, where $x$ is a small number that's easy to work with, like 1/4, and see where you go from there
glossy valveBOT
Oliver
lean cloak
By the definition, your next line should then be $|f(x)-L| < 1/4$. Then try bounding L according to the conditions of the indicator function
glossy valveBOT
Oliver
lean cloak
You should get something like for rational values of $x$, $L$ has to be in interval $(a,b)$ and for irratioanl values of $x$, $L$ has to be in the interval $(c,d)$ where $(a,b) \cup (c,d) = \varnothing$
glossy valveBOT
Oliver
lean cloak
In other words, you should get two boundaries that have no overlap. Thus $L$ cannot exist
glossy valveBOT
Oliver
spark wren
use a real numbers
what value of x are we approaching
I say zero lol
cause its easy
undone wave
Honestly I am not sure how a proper proof would look like from these answers
lean cloak
The limit is 0 from the right, but you shouldn't be doing questions for people anyway
spark wren
I have a picture of what I mean lol
steel solar
the reverse if for one Epsilon then all delta does not work
⚠️ (Converses of statements like these are very “volatile”, I would not recommend saying this.)
lean cloak
Honestly I am not sure how a proper proof would look like from these answers
So first pick some small real value of $\epsilon$ obviously greater than 0.
Now notice you have $|f(x)-L| < \epsilon$.
Next observe that $x \in \mathbb{Q} \rightarrow f(x) = 1$ and thus you have $|1-L| < \epsilon$.
Similarly for $x \not\in \mathbb{Q} \rightarrow f(x)=0$ and thus you have $|0-L| < \epsilon$.
Finally prove that these cannot both be true
Idk what the compile error is that looks perfect to me 🤷♂️
steel solar
“Epislon”
lean cloak
OHHH
glossy valveBOT
Oliver
steel solar
So it reads it correctly by default
lean cloak
well now i feel like an fool 😔
steel solar
There are...worse errors.
spark wren
⚠️ (Converses of statements like these are very “volatile”, I would not recommen...
so that's not a converse statement
undone wave
**Oliver**
I can follow your logic and proved L can't exist for |1 - L| < e and |0 - L| < e
So thank you very much for your help
but I think now I am curious if there is a way to generate a random rational number between 0 and some random irrational number?
undone wave
Is that the same thing Oliver mentioned earlier? Using the axiom of choice over the set of real numbers between 0 and n (n being that irrational number)?
spark wren
yeah
are you playing with that axiom
you don't have to
the axiom of choice is from what I understand is if you pick a whole bunch of sets one element from them you have a new set
that you can make a unique set from choices
but we just have two subsets of the real numbers irrational and rational
and if x is part of one set or the other set and if they can't fit that's a problem
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gaunt falcon
Suppose that the acceleration of a particle is a function of x, given by the following expression:
$a = 2s^{-2}x$
Knowing that its speed is 0 when x = 1m, find the speed of the particle when x = 3m
glossy valveBOT
ransik (gmdn)
gaunt falcon
(s is just the unit for seconds)
so we know:
$v = \frac{dx}{dt}$ and $a=\frac{dv}{dt}$
glossy valveBOT
ransik (gmdn)
glossy valveBOT
ransik (gmdn)
gaunt falcon
$a=\frac{dv}{dt} \frac{dx}{dx}$
glossy valveBOT
ransik (gmdn)
gaunt falcon
$a=v \frac{dv}{dx}$
glossy valveBOT
ransik (gmdn)
torn jolt
Suppose that the acceleration of a particle is a function of x, given by the fol...
in terms of s?
torn jolt
Oh
torn jolt
wheres the m then
gaunt falcon
m will come from us solving for x through integration
gaunt falcon
that's a's unit
severe igloo
**ransik (gmdn)**
if you integrate the accleration twice you'll get the displacement. You also integrate once and you get velocity
gaunt falcon
severe igloo
Looks good
full forumBOT
full forumBOT
Available help channel!
waxen canyon
i only understand what orthonormal basis is, i have no idea what the soltuion is
umbral dome
which part is confusing you?
waxen canyon
which part is confusing you?
what w is and the solution for b)
waxen canyon
what exactly does b) prove
umbral dome
although the method is specific to that particular basis (since it was computed directly)
that formula applies to all orthonormal bases
basically it means that you can write r as having components in the u, v, and w directions (the same way we normally write it as having components in the x, y, and z directions)
and that those components are just the dot product with that particular basis vector
waxen canyon
and that those components are just the dot product with that particular basis ve...
dot product of r?
umbral dome
dot product of r and each basis vector, yes
waxen canyon
dot product of r and each basis vector, yes
r = r dot a basis vector? what does this represent
umbral dome
,align \vb r &= x \vb i + y \vb j + z \vb k \
&= (\vb r \cdot \vb i)\vb i + (\vb r \cdot \vb j)\vb j + (\vb r \cdot \vb k)\vb k \
&= (\vb r \cdot \vb u)\vb u + (\vb r \cdot \vb v)\vb v + (\vb r \cdot \vb w)\vb w
glossy valveBOT
cloud
umbral dome
so we can break up r into components, either traditionally in the x, y, and z-directions, or into the new directions represented by u, v, w
rapid rain
r = r dot a basis vector? what does this represent
r = (its component along direction u) * u + (its component along direction v) *v + (its component along direction w) * w
waxen canyon
so we can break up r into components, either traditionally in the x, y, and z-di...
so like 3 new axis?
clever iris
Plsss help idk what mistake I made
full forumBOT
Plsss help idk what mistake I made
spiral spindle
didnt they just not change the bounds properely
glacial pasture
still wrong to write it that way but you do undo it, ill keep looking
spiral spindle
all the way at the top
all they did was swap them
i could be wrong tho
havent done this in like 6 months
glacial pasture
i think its fine purely because the limits arent functions of variables
glacial pasture
,w integrate cos(2x+y), x from 0 to pi/4, y from pi/4 to pi/2
glossy valveBOT
glacial pasture
cos(pi)=-1
cos(3pi/4)=-root2/2
so its 1/2[1+root2/2]
spiral spindle
didnt change your limits when you did a substitution
isnt this correct? shouldnt the bounds for the first integral be y to pi/2 + y
glacial pasture
think its a small sign issue
glacial pasture
isnt this correct? shouldnt the bounds for the first integral be y to pi/2 + y
they wrote it dodgily, but in the first case they undid the sub before evaluating, in the second they change the limits at the last step
spiral spindle
ah gotcha
glacial pasture
so dodgy writing yes, result no
glacial pasture
cos(pi)=-1
cos(3pi/4)=-root2/2
so its 1/2[1+root2/2]
i think this is it though
theres a lot of minuses flying around in the last evaluation
but its -(-root2/2) so + rather than their -root2/2
glacial pasture
which matches with this at least
wait
or not
one mo
oops
no its --- so yeah -root2/2
there is actually no problem
spiral spindle
glacial pasture
tis all fine, besides the writing of it making me violently ill
clever iris
wait so what did i do wrong?
clever iris
np
spiral spindle
they integrated this wrong
the top one
it should come out to -cos(pi/2 +y) + cos(y)
im like 95% sure atleast
glacial pasture
this should be positive
glacial pasture
this should be positive
then we get -root2/4+1/2-root2/4=1/2-root2/2
glacial pasture
they integrated this wrong
1/2 [-cos(pi/2+y)+cos(y)]
clever iris
Thx alot i got it correct
glacial pasture
they do get to that
glacial pasture
Thx alot i got it correct
np
but please write your maths properly it makes me cry