Maths problem you can put you head around

[Instillingererno]

Try calculate the area of the black area under the triangle:

 

All help is allowed (it might seem easier than it really is)

 

 

The answer for those who are curious;; (don't cheat!);

Spoiler

 

[Guest]

Is this cheaing

https://www.sketchandcalc.com/

[Instillingererno]

Just now, dexxterlab97 said:

Is this cheaing

https://www.sketchandcalc.com/

go right ahead, just put the answer as a spoiler

[TheRandomness]

This shouldn't be in general discussion. How's it related to tech?

I managed to get to

Spoiler

Finding the area of the circle, but because I only just learnt how to do shit like <I forgot the word>

I have no clue what to do next

[Instillingererno]

Just now, TheRandomness said:

This shouldn't be in general discussion. How's it related to tech?

I managed to get to

  Reveal hidden contents

Finding the area of the circle, but because I only just learnt how to do shit like <I forgot the word>

I have no clue what to do next

Its related to tech in the way you need a computer to calculate it, you can't do it accurately on your own

[TheRandomness]

2 minutes ago, Instillingererno said:

Its related to tech in the way you need a computer to calculate it, you can't do it accurately on your own

Well, you can if you accidentally memorised enough of pi.. 3.141592653589793238462643383279502884

I need to learn more. 

[Instillingererno]

Just now, TheRandomness said:

Well, you can if you accidentally memorised enough of pi.. 3.141592653589793238462643383279502884

I need to learn more. 

it's not really the circles that are the problem. If the question was to calculate the area outside the circles it would be easy but when taking the triangle into consideration it becomes much harder

[TheRandomness]

Just now, Instillingererno said:

it's not really the circles that are the problem. If the question was to calculate the area outside the circles it would be easy but when taking the triangle into consideration it becomes much harder

Yeah, I know enough of circle theorem but not enough of the slicing the circles part. 

[Instillingererno]

Just now, TheRandomness said:

Yeah, I know enough of circle theorem but not enough of the slicing the circles part. 

ah, for the top right?

[TheRandomness]

2 minutes ago, Instillingererno said:

ah, for the top right?

Yeah

[Instillingererno]

Just now, TheRandomness said:

Yeah

That is a hard one, if you look at my solution you will see its the most complicated part of the calculation

[TheRandomness]

3 minutes ago, Instillingererno said:

That is a hard one, if you look at my solution you will see its the most complicated part of the calculation

If I had my maths book I'd probably be able to solve it...

[Shakaza]

A somewhat accurate estimation can be had by taking the area of the rectangle, subtracting the area of the two circles, and dividing by 2, and the answer comes to be around 21.46. Not correct, but pretty close. I don't really care to bother working it out with a computer, so I give it my best guess with my own brain.

[Instillingererno]

1 minute ago, Shakaza said:

A somewhat accurate estimation can be had by taking the area of the rectangle, subtracting the area of the two circles, and dividing by 2, and the answer comes to be around 21.46. Not correct, but pretty close. I don't really care to bother working it out with a computer, so I give it my best guess with my own brain.

is somewhat good enough?

[Instillingererno]

2 minutes ago, TheRandomness said:

If I had my maths book I'd probably be able to solve it...

by hand?

[TheRandomness]

8 minutes ago, Instillingererno said:

by hand?

Yeah. Long division and multiplication works (so does a calculator, but still)

[Instillingererno]

2 minutes ago, TheRandomness said:

Yeah. Long division and multiplication works (so does a calculator, but still)

How would you calculate the circle sector

[Dash Lambda]

The area of one circle is 25pi, so the area of a corner is 25(1-pi/4).

For the upper corner, to make it easier on myself, I'll just integrate (x/2 - root(25 - (x-5)^2)) over x=[8, 10] to get 5(3 - 5arctan(1/2)).

 

So the total area is 75(1 - pi/4) + 5(3 - arctan(1/2)) = approx. 19.504

 

I wish I'd made that cleaner, but that was just me doing it quickly.

 

EDIT:

57 minutes ago, Instillingererno said:

Its related to tech in the way you need a computer to calculate it, you can't do it accurately on your own

Oh, it's on. I'll do that integral by hand when I get back, but I need to go out for a bit.

[Shakaza]

26 minutes ago, Dash Lambda said:

The area of one circle is 25pi, so the area of a corner is 25(1-pi/4).

For the upper corner, to make it easier on myself, I'll just integrate (x/2 - root(25 - (x-5)^2)) over x=[8, 10] to get 5(3 - 5arctan(1/2)).

 

So the total area is 75(1 - pi/4) + 5(3 - arctan(1/2)) = approx. 19.504

 

I wish I'd made that cleaner, but that was just me doing it quickly.

 

EDIT:

Oh, it's on. I'll do that integral by hand when I get back, but I need to go out for a bit.

Mmm, Calculus. Been a while since I've done any, so I forget some of what I've learned, but it's my favorite type (division? brand? kind?) of math.

[Instillingererno]

32 minutes ago, Dash Lambda said:

The area of one circle is 25pi, so the area of a corner is 25(1-pi/4).

For the upper corner, to make it easier on myself, I'll just integrate (x/2 - root(25 - (x-5)^2)) over x=[8, 10] to get 5(3 - 5arctan(1/2)).

 

So the total area is 75(1 - pi/4) + 5(3 - arctan(1/2)) = approx. 19.504

 

I wish I'd made that cleaner, but that was just me doing it quickly.

 

EDIT:

Oh, it's on. I'll do that integral by hand when I get back, but I need to go out for a bit.

can't wait

[Shakaza]

1 hour ago, Instillingererno said:

is somewhat good enough?

For me in this particular scenario it is. If it were a question on the AP Calculus test, for example, I would give it my all, but right now I don't really care that much.

[almondhive]

I was staring at the image of the circles and thinking how could it be done and it lulled me to sleep. Best powernap of today. 

[Instillingererno]

17 minutes ago, almondhive said:

I was staring at the image of the circles and thinking how could it be done and it lulled me to sleep. Best powernap of today. 

Glad to help

[Dash Lambda]

I'm back~

 

I could've gone to 3 decimal places to get the same result as I did earlier, but the Taylor series was taking long enough and I was kind'a tired of arithmetic. I like math, but arithmetic's boring.

 

This still took me too long though...

It's been probably a couple months since I finished Calc. 3, I'm out of practice. I hate that I have to wait for another semester to start the next class -I just want to do Diff. Eq. already ;-;

 

Anyway, here's the page:

[Bhav]

To me it seems the problem area is the bit on the bottom left. Thats the only thing that makes it overly complicated.