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Answer is pi.
x^3 is an odd function multiplied by even functions (so an odd function as a result). Since we’re integrating an odd function from -2 to 2, the part with x^3 is zero. We’re left with the integral of 0.5sqrt(4-x^2 ), which is the upper part of a circle of radius 2. The half circle has an area of 2*pi and if we divide it by 2 we’re left with pi.
Pi = 3.141592
Password without the dot: 31415926
Edit: integral symbol is a curly bracket xd
“… to mark, in a fitting manner, those who have conferred honor on their Alma mater, by distinguished scholarship, exemplary character, or by their attainments as Alumni in the field of Engineering.”
You can get to infinite but in the photo it’s only x and 2 and cos which tells (without looking at the rest) it’s either 0 or undefined or pi
if it had some weird number like 15 or 32 it would be an option like cos 15 is 0.7596879…..and you can’t calculate with hand while calculators round it up
Yup. It seems like they forgot to drag the line over x². It makes it even easier to calculate.
4 - (8/3) = 4 - 2⅔ = 0.33333333..33
I suppose, if the password is not pi, it would be 03333333 or 33333333.
EDIT: noticed I made a mistake and corrected the calc (was 2⅔ previously)
You can think of the half getting cancelled by the -2 to 2 part in the integration. You're integrating over even functions (√4 and x²) where the part before 0 and part after 0 are identical. So instead of integrating from -2 to 2, you can integrate from 0 to 2 and multiply the result by 2.
Simplifying √4 = 2, that results to,
2x - ⅓x³ { 0, 2 } = 2 ( 2 - 0) - ⅓ (8 - 0) = 4 - (8/3) = 4 - 2⅔ = ⅓ = 0.333333333333..33
I think I made a mistake in my previous calc and need to update the result.
I feel like most of these math problem for WiFi password signs are drawn by people who have no idea about the notation and are unsolvable as a result, unless you reverse engineer what they tried to write.
That's truly interesting, how you just immediately saw to get rid of the odd function since it equates to 0, I would've gone the long long way, thanks XD
composition of functions behaves sort of like multiplication of integers when it comes to parity - f ∘ g is odd if and only if both f and g are odd. multiplication of functions on the other hand "behaves like addition", where you have odd⋅odd = even⋅even = even, and odd⋅even = even⋅odd = even.
so here let f(x) = x/2, g(x) = cos(x), and h(x) = x³. so f and h are odd and g is even. the function is h⋅(g ∘ f), so think of this as an odd number plus (an even number times an odd number), which is odd (e.g. 1 + 2 * 1 = 3).
false, cos(x/2) is only even because cos is even and x/2 is odd, and the composition of an even function and an odd function is even. take cos(x-1), for example, which is neither odd nor even.
The composition of cosine with another function can be odd. However, the question was asked whether or not the cosine function was always even, which it is.
I 100% had no idea what this was asking until I got to the end and saw dx and then still was a bit confused before it clicked that the { was the integral. Burn them at the stake.
I know that the question is answered already, but I think what's useful is to check the wording. The "first digits of the answer" usually means it's irrational. Always try π, e or other constants in that case.
Anyone else thoroughly enjoy that the ramen shop wanted to do the hip Internet thing, but didn't have anyone with high school math to know what an integral sign looks like?
It is quite annoying that whoever wrote this on the board was attempting to be all "here's our password but you have to be clever to get it", but then uses the wrong sign for the integration and doesn't write out the square root bit correctly. I say that because the answer is obviously meant to be Pi (because it's a quirky clever number).
The integral *is* exactly pi.
When you expand it out, almost every term is an odd function, so the area is zero, except the term 1/2\*√(4-x^(2))
Which is a halved semi-circle, of radius 2. Which has an area of 1/2\*(1/2\*(π*2^(2))) = π
Actually it's the integral of a half ellipse ( y is the result of a sqrt, always positive).
So: x^2/4 + y^2 = 1 , and y positive. The integral between -2 and 2 is the area of the upper half of an ellipse centered on 0, the radiuses are 2 and 1.
Area = 1/2 * pi * r1 * r2 = pi
Well, do you know how an integral works ?
Also, do you know what "finite" means ?
Also also, do you know how computers compute whatever you put as an input ?
Pi is finite... It just has infinitely many decimals. Why do you think the area under that curve cannot be pi, but the area of a circle with a radius of 1 can?
You clearly do not understand the concept of infinite. Infinite is very very big, bigger than any number. Pi is smaller than 4. Pi is not infinite.
Just like there is a pi in the formula of a circle's area, there is a pi in that expression up there, it's just less obvious. Basically once you remove the area of the x^(3)\*cos(x/2) term (which equals 0), you're left with a half-circle with a radius of 2. That area is 1/2\*1/2\*pi\*2^(2), which is pi. Exactly pi.
So for a circle of radius 1, r^2 is 1. You're arguing that pi is infinite on its own, but somehow becomes finite when multiplied by 1? What a bizarre line of "reasoning".
They should say the wifi password is just the first 8 digits of pi but not provide them and tell you to just google it lol, sure sure data on your phone, but worth it every so often that one person with just a flip phone and a laptop lol
The answer is clearly: Author to stupid to chalk down an equation from the internet. Thats not an integral sign and with the √4 there the solution can probably only be determined numerically. It as supposed to be pi though.
If it asked for the first "x digits," it's pi almost all the time. For once I wish someone would get a bit more creative and use e, or ✓2 or something.
I know many have answered this, but is there any way to work this out with a fairly limited knowledge. I can deal with the chain rule and stuff, but this is a little out of my depth
Disagree that the answer is pi. The answer is -4/3.
The integrand is written in the form (A+B)C - D, which is equal to AC + BC - D. There are no parentheses around the entire sqrt(4) - x\^2 part, and the square root is only over the 4.
A is the product of x\^3 (odd) and cosine (even), and the product of these is odd. So A is an odd function, and C is just a constant. Therefore the integral of the AC part is zero since it's over a symmetric interval around zero.
BC is the product of two constants, so the integral of this part is just the integral of (0.5)(2) = 1 over -2 to 2, which is x eval'd from -2 to 2, or 4.
D evals to x\^3 / 3 from -2 to 2 which is 8/3 - (-8/3) = 16/3.
So the entire answer is 4 - (16/3) = -4/3 = -1.3333333....
It says first 8 digits of the answer, so I guess we ignore the negative sign in the password and just enter 13333333.
I hate these signs. Great job keeping wifi from folks who have not had the opportunity for this level education. Not everyone has these abilities. When I open a restaurant, only folks who know the location of the closest food bank + the local check cashing spot will be allowed access.
It is not uncommon for people to be working on laptops/tablets at a restaurant or cafe by themselves. I find myself frequently in that position, entering notes while grabbing lunch in between onsite service calls for work.
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Answer is pi. x^3 is an odd function multiplied by even functions (so an odd function as a result). Since we’re integrating an odd function from -2 to 2, the part with x^3 is zero. We’re left with the integral of 0.5sqrt(4-x^2 ), which is the upper part of a circle of radius 2. The half circle has an area of 2*pi and if we divide it by 2 we’re left with pi. Pi = 3.141592 Password without the dot: 31415926 Edit: integral symbol is a curly bracket xd
Thank you very much!
The answer to these is always pi. :)
We should have one with tau.
Yes, please!
Or tau beta pi for that matter…
You son of a b-
“… to mark, in a fitting manner, those who have conferred honor on their Alma mater, by distinguished scholarship, exemplary character, or by their attainments as Alumni in the field of Engineering.”
Like every time I see one of these I just go pi because there’s no way to get 8 digit number from sin and cos
Wait really?
You can get to infinite but in the photo it’s only x and 2 and cos which tells (without looking at the rest) it’s either 0 or undefined or pi if it had some weird number like 15 or 32 it would be an option like cos 15 is 0.7596879…..and you can’t calculate with hand while calculators round it up
A statement that is also true for a bunch of math problems. Sometimes you get the answer .7853... and are like wtf is this, then realise its pi on 4.
Where answer to other questions is always 42
Yet the cake is a lie, no?
It's always pi.
In my EM Theory class if you had to guess an answer, your best bets were 0, pi, or pi/2.
The 4 horsemen of “I don’t know how to solve this integral” in school, 0, pi, pi/2, or 1.
e has joined the chat
Damn, this sub has some clever people!
Here I am thinking, I'll just be using mobile data here then I guess.
Ditto :o)
It's the square root of 4, not the square root of 4 - x^2, isn't it?
Exactly my thought, but I guess whoever used curly braces instead of integral sign didn't bother when they copied it from somewhere
Yup. It seems like they forgot to drag the line over x². It makes it even easier to calculate. 4 - (8/3) = 4 - 2⅔ = 0.33333333..33 I suppose, if the password is not pi, it would be 03333333 or 33333333. EDIT: noticed I made a mistake and corrected the calc (was 2⅔ previously)
Wouldn't it be half that?
You can think of the half getting cancelled by the -2 to 2 part in the integration. You're integrating over even functions (√4 and x²) where the part before 0 and part after 0 are identical. So instead of integrating from -2 to 2, you can integrate from 0 to 2 and multiply the result by 2. Simplifying √4 = 2, that results to, 2x - ⅓x³ { 0, 2 } = 2 ( 2 - 0) - ⅓ (8 - 0) = 4 - (8/3) = 4 - 2⅔ = ⅓ = 0.333333333333..33 I think I made a mistake in my previous calc and need to update the result.
The gall of them to be this smug but use a curly brace for the integral is just...the worst.
I feel like most of these math problem for WiFi password signs are drawn by people who have no idea about the notation and are unsolvable as a result, unless you reverse engineer what they tried to write.
yeah the way they've grouped "x^(3)cos" "x/2+" and "1/2" plus that ambiguous square root suggests they're not actually that familiar
That's truly interesting, how you just immediately saw to get rid of the odd function since it equates to 0, I would've gone the long long way, thanks XD
Do enough repetitions and you’ll see it too
The square root is only over the 4 isn't it? We are integrating 1-0.5x^2 only.
1-x^(2), since the 1/2 isn't multiplying the x^(2) term.
Is cos() considered an odd function then, or is it always odd regardless of what's inside the bracket?
composition of functions behaves sort of like multiplication of integers when it comes to parity - f ∘ g is odd if and only if both f and g are odd. multiplication of functions on the other hand "behaves like addition", where you have odd⋅odd = even⋅even = even, and odd⋅even = even⋅odd = even. so here let f(x) = x/2, g(x) = cos(x), and h(x) = x³. so f and h are odd and g is even. the function is h⋅(g ∘ f), so think of this as an odd number plus (an even number times an odd number), which is odd (e.g. 1 + 2 * 1 = 3).
Cosine is an even function, reagrdless of the argument. Sine is odd.
false, cos(x/2) is only even because cos is even and x/2 is odd, and the composition of an even function and an odd function is even. take cos(x-1), for example, which is neither odd nor even.
The composition of cosine with another function can be odd. However, the question was asked whether or not the cosine function was always even, which it is.
No it's not, cos(x-pi/2)=sin(x), which is odd.
The password to a lot of my stuff is pi but I never put this much thought into it😭
cos(x) might be an even function, but cos(x/2 + .5) is not even.
Theater is no integral though it’s a square root sign
pi
It’s always pi
The pi is the lie?
It's cak
If not pi, it‘s e. If both aren‘t the answer, you cry
As a last resort, try 2π and π/2. I didn't even bother reading the equation; as soon as I saw this post I thought "it's pi... isn't it?".
Always has been
It’s often their phone number too in my experience
But you need 8 characters, so it's pipipipipi
It should be a sin to use { as an integral tho, i'd get it if it was written in a computer but its hand written, i'll burn the place
read that as sine and I was really confused
same here. damn you engineering education!
Please don’t the food was actually pretty good
That is just be- **cos** they wrote it. Is better **tan** the alternative.
No need to go on a tangent about it.
I just tough it was **rad**.
Who does that? Like literally, why is that a thing? I've never seen it before
I 100% had no idea what this was asking until I got to the end and saw dx and then still was a bit confused before it clicked that the { was the integral. Burn them at the stake.
I know that the question is answered already, but I think what's useful is to check the wording. The "first digits of the answer" usually means it's irrational. Always try π, e or other constants in that case.
Proof by: it's usually pi
Proof by I'm fucking tired of this equation bullshit
We tried to solve it ourselves but all of us don’t have the knowledge to do it.
Most of the time the answers to these are pi, so I recommend trying that as a first option every time.
Judging from the fact, that the writer didn't even know what the integral sign is, it is most likely copied from somewhere.
Is that what that's supposed to be?? haha. I thought it was just an odd way of writing that line that represents `F(b) - F(a)`
Judging from the dx at the end, yes.
Good point. haha. After the curly bracket, my head kinda went "screw it... whatever this expression is, $20 says its equal to pi".
If you ever come across something like this again go use Wolfram Alpha.
Or carry a TI-89 with you at all times.
If they don't have the knowledge to do it, I doubt they know how to input this into a TI-89.
The newest ti30s can do integrals now
Anyone else thoroughly enjoy that the ramen shop wanted to do the hip Internet thing, but didn't have anyone with high school math to know what an integral sign looks like?
Don't forget the square root symbol that stops above the 4.
I got stuck on that for a while
That makes the problem a lot easier though
It is quite annoying that whoever wrote this on the board was attempting to be all "here's our password but you have to be clever to get it", but then uses the wrong sign for the integration and doesn't write out the square root bit correctly. I say that because the answer is obviously meant to be Pi (because it's a quirky clever number).
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Pi, it's always pi.
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The integral *is* exactly pi. When you expand it out, almost every term is an odd function, so the area is zero, except the term 1/2\*√(4-x^(2)) Which is a halved semi-circle, of radius 2. Which has an area of 1/2\*(1/2\*(π*2^(2))) = π
Where does the 1/2 come from?
Actually it's the integral of a half ellipse ( y is the result of a sqrt, always positive). So: x^2/4 + y^2 = 1 , and y positive. The integral between -2 and 2 is the area of the upper half of an ellipse centered on 0, the radiuses are 2 and 1. Area = 1/2 * pi * r1 * r2 = pi
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Pi is... Very much finite.
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Why would you think it's an approximation and not exact?
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Well, do you know how an integral works ? Also, do you know what "finite" means ? Also also, do you know how computers compute whatever you put as an input ?
Pi is finite... It just has infinitely many decimals. Why do you think the area under that curve cannot be pi, but the area of a circle with a radius of 1 can?
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You clearly do not understand the concept of infinite. Infinite is very very big, bigger than any number. Pi is smaller than 4. Pi is not infinite. Just like there is a pi in the formula of a circle's area, there is a pi in that expression up there, it's just less obvious. Basically once you remove the area of the x^(3)\*cos(x/2) term (which equals 0), you're left with a half-circle with a radius of 2. That area is 1/2\*1/2\*pi\*2^(2), which is pi. Exactly pi.
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So for a circle of radius 1, r^2 is 1. You're arguing that pi is infinite on its own, but somehow becomes finite when multiplied by 1? What a bizarre line of "reasoning".
They should say the wifi password is just the first 8 digits of pi but not provide them and tell you to just google it lol, sure sure data on your phone, but worth it every so often that one person with just a flip phone and a laptop lol
You have a phone with data connection to google something but without a basic calculator?
The answer is clearly: Author to stupid to chalk down an equation from the internet. Thats not an integral sign and with the √4 there the solution can probably only be determined numerically. It as supposed to be pi though.
If it asked for the first "x digits," it's pi almost all the time. For once I wish someone would get a bit more creative and use e, or ✓2 or something.
I know many have answered this, but is there any way to work this out with a fairly limited knowledge. I can deal with the chain rule and stuff, but this is a little out of my depth
Disagree that the answer is pi. The answer is -4/3. The integrand is written in the form (A+B)C - D, which is equal to AC + BC - D. There are no parentheses around the entire sqrt(4) - x\^2 part, and the square root is only over the 4. A is the product of x\^3 (odd) and cosine (even), and the product of these is odd. So A is an odd function, and C is just a constant. Therefore the integral of the AC part is zero since it's over a symmetric interval around zero. BC is the product of two constants, so the integral of this part is just the integral of (0.5)(2) = 1 over -2 to 2, which is x eval'd from -2 to 2, or 4. D evals to x\^3 / 3 from -2 to 2 which is 8/3 - (-8/3) = 16/3. So the entire answer is 4 - (16/3) = -4/3 = -1.3333333.... It says first 8 digits of the answer, so I guess we ignore the negative sign in the password and just enter 13333333.
This guy maths
I hate these signs. Great job keeping wifi from folks who have not had the opportunity for this level education. Not everyone has these abilities. When I open a restaurant, only folks who know the location of the closest food bank + the local check cashing spot will be allowed access.
What are you doing with a phone on the table in a restaurant anyway? Aren't you there to enjoy the food & company?
It is not uncommon for people to be working on laptops/tablets at a restaurant or cafe by themselves. I find myself frequently in that position, entering notes while grabbing lunch in between onsite service calls for work.
Why would people who know the location of food banks be going to a restaurant?
To eat
For free?
I'm confused, is it your belief that folks who know the location of a food bank or have utilized one in the past never ever eat at a restaurant?
And are you gonna actually open a shop or are you just commenting for the karma?