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Coolguy52 11 months ago

Geometry questions are difficult to pose in this format, so unfortunately for you I can’t easily provide one. I am generally quite good at most branches of mathematics at high school level, although I will say that geometric questions can sometimes trip me up if I didn’t spot the method correctly. I found high school algebra and calculus to be a bit more procedural and therefore easier to find the solution. I think finding anti-derivatives (integrating a function) is the one example where this is a bit less procedural but I don’t often struggle here either, unless the function is very weird.

PuzzleFan 11 months ago

I'm not really that good at advanced math class. I was good at geometry, but calculus and algebra 2, no.

suhangha 11 months ago

Exactly Correct, cool guy, This means that the number of messages was 6859.

Coolguy52 11 months ago

I'm not sure if I understand your question correctly, but:

SPOILER

x=19, n=3? 19^3=6859 and that's fairly close to the number of messages, so the cube root of the number of messages would be a little bit above 19.

suhangha 11 months ago

solution is a pair of answer
Both values were sine & cosine (one-twelfth & five-twelfth pi)

guess a natural number 'x' that it's nth-root of number that is close to the current topic count, and also together that 'n' at the "'n'th-root" ; where both x and n is less than 20

Coolguy52 11 months ago

I'm glad you noticed the trigonometric link, that was actually my inspiration for these equations. I wanted to make x and y being exact values for sine and cosine of pi/12, so the equations are a unit circle (Pythagorean identity) and related to the double angle formula as you noticed. My method for solving algebraically was slightly different, but yours reduces the complexity a lot sooner than mine, and at a point you need to realise that sqrt(2+sqrt(3))=(sqrt(2)+sqrt(6))/2, which is not immediately obvious. I will post that method if anyone wants as an edit to this message.

nelson90 11 months ago

There are at least 2 ways of solving this set of equations.

first solution:

SPOILER

x^2+y^2=1
4xy=1 ==> 2xy=0.5
Using remarkable identities, we obtain
(x+y)^2=x^2+y^2+2xy=1.5 and (x-y)^2=x^2+y^2-2xy=0.5
Taking the square roots:
x+y=sqrt(1.5)
x-y=sqrt(0.5)
The solutions of this linear system are:
x=(sqrt(1.5)+sqrt(0.5))/2
y=(sqrt(1.5)-sqrt(0.5))/2

second solution:

SPOILER

The second expression is the equation of a circle of center (0,0) and radius 1. We can then define an angle 'a' such that x=cos(a) and y=sin(a).
We substitute in the first equation: 4cos(a)sin(a)=1
Using the relationship sin(2a)=2sin(a)cos(a), we get: 2sin(2a)=1
sin(2a)=0.5 ==> 2a=pi/6 ==> a=pi/12
The solutions are:
x=cos(pi/12)
y=sin(pi/12)

Due to the symmetry of the equations in x and y, there is another solution obtained by swapping the values of x and y.

Coolguy52 11 months ago

36=2^2*3^2 (not prime), 361=19^2 (not prime).

Try to solve for x and y, where x and y are positive:

4xy=1, x^2+y^2=1

chris3000 11 months ago

It's been so nice being at home and not having to be woken up every 3-4 hours in the ER. You can't get any rest there.

suhangha 1 year ago

try to prove whether 36 is prime or not. must be easy for you ||||| try 361 too

chris3000 1 year ago

Hello, what's up? Did everyone have a good Mother's day holiday? Never forget your mom on that special day. I earned a valuable lesson about my selfishness.

john96 1 year ago

Mine are Snoopy, Woodstock, Linus and Patty.

chris3000 1 year ago

What are your favorite characters in "The Peanuts?"
Mine is Charlie Brown, Patty, Lucy and Snoopy

Coolguy52 1 year ago

Ok. Hint for second method below:

SPOILER

a+b+ab=35 => ab+a+b+1=35+1=36 => (a+1)(b+1)=36. a and b have to be positive whole numbers, so you need two numbers x and y so that x*y=36, x and y distinct and neither can be 1. There are multiple options.

Solving these kinds of equations is not always easy because it's not necessarily got one answer that you can just find with normal algebra. It's also kind of hard to give proper hints without displaying most of the methods.

chris3000 1 year ago

I'll figure that problem out later, or if you want to give us another hint. Maybe someone other than me can solve that one.

Coolguy52 1 year ago

There are two ways to find the three answers where both a and b are positive whole numbers and a>b.

SPOILER

One way is to exhaust the options for b and find a corresponding answer for a. A hint with this method is that if you plug (5,5) into the expression a+b+ab you get 35. However this isn’t a solution to my question as a is not strictly bigger than b. However, this does mean that b<5, as if b>5, a>5 which means the expression is bigger than 35, and using (5,5) gives 35 as shown before.

Another is to rearrange the equation into a form where you can factorise it. If you want help with this second way feel free to ask.

chris3000 1 year ago

The solution to your equation John is 13. Now let's solve CG's equation, can we have a hint please in a spoiler?

Coolguy52 1 year ago

3x+(-8+8)=31+8
3x=39
3x/3=39/3
x=13.

If a+b+ab=35, solve for a and b as whole numbers and a>b>0.

john96 1 year ago

Solve for x.

3x-8=31

chris3000 1 year ago

Harry Potter is one of my favorite book series. What are your favorite books to read? And by what author? I also like the movies about Harry Potter and his friends at Hogwarts.

chris3000 1 year ago

My grandparents get on my nerves so bad. My grandma is evil, greedy and selfish. She takes half my grandpa's money which me and my mom need for food, medicine, supplies and other requirements for our daily lives.

chris3000 1 year ago

It is the start of a new fresh year, 2024!

PuzzleFan 1 year ago

I had a wonderful holiday Chris, thanks for asking. We sat near the fireplace and read some books and ate some cake. It was cold some nights, we had to bundle up under the blankets.

chris3000 1 year ago

Well, did everyone have an enjoyable, relaxing Christmas this year? We certainly did, me and my mother. We played some board games and ate some Christmas cookies.

chris3000 1 year ago

I just realized I'm almost at Level 77!

suhangha-2 1 year ago

Top member ranked 5!

john96 1 year ago

Is everybody ready for the Christmas spirit, we need to start shopping early before the crowd gets out, it's cold up here in Iceland.

suhangha-2 1 year ago

Oh, I missed it: e^i music is in base 12, the real-part as acoustic piano, and the imaginary-part as marimba / harp. I'm making a build app project (while learning Java) and I'm using this self-composed song as bg music

SPOILER

public void onProgressChanged(SeekBar seekBar, int progress, boolean fromUser)

float (marimba volume) = (float) Math.round(144 * Math.cos(progress * Math.PI / 144)) / 144;
float (harp volume) = (float) Math.round(144 * Math.sin(progress * Math.PI / 144)) / 144;

@(Chris || John || PF): are you tried build apk project (if you learned Java not JS)?

chris3000 1 year ago

Yes, I had a great weekend, we got 3-4 inches of rain and had an isolated tornado. Luckily it didn't do too much damage, just knocked the power out for an hour.

john96 1 year ago

It's been a nice peaceful Saturday here in Iceland. Y'all had a good day/night?

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niimporta 15 years ago

Here you can post EVERYTHING you wan't.
So, let's GO!

**!!Knobs are allowed, but only if you use them with parsimony!!**

Ideas to post:

Pictures of the editor of levels
Something about games
Interesting stuff (like The canopener has been invented 42 years after the can)
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Or not funny histories
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and more..
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Do what U wan't, but don't insult!
And no flooding, we don't want to get drowned in messages (flooding = posting big messages)

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