GingerAle

You seem amazed that Alan derived the correct solution.  He usually does. You’ll get used to it, if you stay around for awhile.

What really should amaze you is the massive and diverse amount of non-calculus math that Alan’s calculus solution replaces.   

For relatively complex questions, the official solutions presented by AoPS professors often and usually consists of extended trigonometric functions, and/or finite and infinite arithmetic and geometric sequences, and/or elaborate generating functions, connected together using linear and non-linear algebra techniques.   

Sometimes these methods are the only way to solve a problem. But if there is a calculus solution, learning these (laborious) methods will greatly enhance your understanding and appreciation of what the calculus is actually doing. 

GA

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I know what you mean ...

When I set the ambiguity filter to 0.5, the question changed to: How do you thin out the population of an overcrowded school?   

Solution: Put a road through the school. The slowest students and those who do not pay attention will be the first to go. 

(It’s easy to misapply Occam’s Razor)

GA

--. .-

Solution:

After using a babble translator with an ambiguity filter setting of 0.6

and applying novacula Occami: lex parsimoniae (Ocham's razor: law of parsimony)

I find that ...

...This is solvable by using the Secant-Tangent Product Theorem

(Total secant segment length)*(external secant segment length) = (length of tangent segment)²

Bridge portion of the road (circle portion secant length) = 5 km

Road from the bridge to where the new road will be (external portion of secant length) = 4 km

Sum of above lengths (extended secant length) = 9 km

External portion times extended length = (4*9) =36 (Square of Tangent length)

Tangent length = sqrt(36)=  6 km (How long the road will be constructed)

GA

--. .-

Do you still think abcde...bs served a big pile of BULLSHIT as an early Christmas present?

CPhil finally extracted the Roman Zero from Sisyphus’ bolder.

A new link is created after saving changes on a Desmos graph.

You will need to post this new link. 

GA

--. .-

abcde...bs wrote:

I just played with the numbers until the circles overlapped, and I got a=5, b=3, c=15, and d=15

This is the correct solution set ... But me thinks you are serving a big pile of  BULLSHIT as an early Christmas present...

Your graph loads with A = 5; B = 1; C = 3; D = 9 producing two non-intersecting circles that are tangent to different points on the x-axis when y = 0. Setting A, B, C, D to the solution numbers also produces two non-intersecting circles ... meaning your equations are worthless.

For sure, I’d like to see your solution method... using your presented equations. If it is doable, this would be analogous to traveling from New Jersey to Florida via the North Pole.  

...While you’re at the North Poll, you should ask Father Christmas for a muckrake for Christmas, because you will have to do a massive amount of muckraking to present a valid solution with this bullshit. 

GA

--. .-

 Hi Ron,

I just doubled checked; your cat’s name is available for use on this forum, and so is Ron [catname].

The moronic post above is consistent with the themes of with our forum’s new Village Idiot –the syntax is a little different from his style. Our village idiot usually signs his name–even when posting as a guest. So maybe it’s his brother, Crooked.   

I doubt anyone with a functional brain (who knows you) would think you wrote that. ...Your style is more Gracie Allen. 

LoooooooooooL