Math Is Fun Forum

Hi;

I thought I'd try Excel's Goal Seek, and managed to solve this thread's cubic and a couple of others I tested it on:

The two extra cubics have 3 roots each, and to find them I entered into column D the initial x values that I'd predetermined and stored in Column C, those values being:
(a) a high initial value to try to find the highest x;
(b) a low initial value to try to find the lowest x;
(c) half the sum of the resulting highest & lowest x values from (a) & (b) to find the remaining x (not sure if that's a good idea generally, but it worked for these equations).

Then I ran Goal Seek (individually for the equations in rows 2, 3, 5-7 & 10-12) with the respective Goal Seek boxes filled from columns E & D as per the image example.

Btw, to increase Goal Seek's precision (quite a necessary step for good accuracy with this method), I first set 'Maximum Change' in Excel's File/Options/Formulas/'Enable iterative calculation' to 0.000000000000001, which gave accuracy to 14 decimal places for this thread's cubic: i.e., x ≈ -2.09144638072228 (the last few digits aren't displayed in the image).

The above cubics are the only ones I've tried this Goal Seek method on...

Yes, I can...as part of the following Imgur web page (a screen capture):

However, while your link works for me now, I've found from your other posts that your web page links only work for a limited time, if at all.

Hi Bob;

If the temptation for me to replace my PC & laptop with a 'smart'phone becomes too overpowering for me, please jump in and save me!!

Right now, I don't feel the least bit tempted.

You asked me a question and I obliged with my response so that you weren't left wondering in the absence of one, and I simply stated my reason for being unable to assist...

Hi Bob;

I use a PC, and so maybe my experience differs from how the OP's device works (or can work) with Imgur, but this is what I've observed and got:

The OP's address isn't to the image itself...it's only to the Imgur web page with the image on it (amongst other things).

An image address has an image format extension, such as PNG, JPEG...which isn't the case with the OP's 'https://imgur.com/a/MMz2Kir'.

Solution:
I copied the OP's url into my browser's address bar, right-clicked the image that appears on the resulting Imgur page, selected 'Copy image address' from the drop-down menu, and then pasted that address into MIF (in 'img' tags nested inside 'hide' tags)...which gives me:

You'll see that the image address is very different from that of the OP's.

Maybe my method would work for the OP on his device...

Hi CurlyBracket;

Question 6: How many children do they have?

They have 3 children.

Hi CurlyBracket;

Yes, I like that method.

Just a comment re the puzzle wording:

I know what you meant with it, but, in a strict interpretation of the wording, answering the second question could have been a bit awkward if there was a tie...and there are 3 scenarios with at least one winner in which a tie occurs.

Here are some interesting links about L'Hôpital's Pulley Problem:
     Simple Geometric Solutions to De L'Hôpital's Pulley Problem
     Optimization – L'Hôpital's Pulley Problem
     Proof of length of line segment x

Shouldn't that read CBE, Bob?

But maybe placing the letter of the vertex angle of an isosceles triangle in the middle is just a habit of mine...similar idea to the order in naming angles.

Hi Jeremy & Bob,

The maths is beyond me, but I wanted to try graphically, drew this up in Geogebra, and got ED ≈ 51.90438 to 5 decimal places.

I moved C (radius 100 - BC) along circle A (radius 40) to get the largest ED (approx).

Is that anywhere near the mark?

Hi Median Joe;

I opened my Excel file in LibreOffice Calc, and it ran perfectly...including the Goal Seek function.