Question 564756
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I am @ikleyn.   Hello again.  
This  'n2'  is my second nickname,  which I created to place here my response to  Edwin's objections.



- - - - - Here I discuss Edwin's arguments, disprove them - - - - 
- - - - - - and give the final answer to this problem - - - - - -



It is really interesting point,  deserving a discussion.


<pre>
So, in my solution I got x = 917.4239296, 4x = 4*917.4239296 = 3669.696, and I rounded it to 3670,
                                               following standard rounding rules.

                                          3x = 3*917.4239296 = 2752.272, and I rounded it to 2752,
                                               following standard rounding rules.

Now the product (4x)*(3x) is  3670*2752 = 10099840, and it is less than 10.1 million.



So, {{{highlight(highlight(nothing))}}} prevents me from claiming that 3670 is the {{{highlight(highlight(correct))}}} number of pixels across the camera.



On contrary, if I take the number 3669, then the product  (4x)*(3x)  will be 3669*2752 = 10097088,  
which means that I loose many (2752) pixels for nothing (due to using wrong conception).
</pre>

This analysis shows that &nbsp;3670 &nbsp;is &nbsp;{{{highlight(highlight(BETTER))}}} &nbsp;answer than &nbsp;3669.


Then we account for greater number of pixels, &nbsp;still being within &nbsp;10.1 &nbsp;million of pixels.


Thus, you see that the pair &nbsp;(x,y) = (3660,2752) &nbsp;is &nbsp;BETTER &nbsp;than the pair &nbsp;(x,y) = (3669,2752).


For completeness, &nbsp;let's consider the pair &nbsp;(3659,2753). &nbsp;&nbsp;It produces the product

3659*2753 = 10100757, &nbsp;which is greater than &nbsp;10.1 &nbsp;million of pixels, &nbsp;and therefore does not work in this problem.


So, this analysis shows that the pair &nbsp;(3670,2752) &nbsp;provides the &nbsp;BEST &nbsp;possible answer in this problem.



<U>ANSWER</U>.  &nbsp;&nbsp;3670 &nbsp;is &nbsp;THE &nbsp;{{{highlight(highlight(UNIQUE))}}} &nbsp;correct possible number of pixels across the camera in this problem,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;on contrary to &nbsp;Edwin's &nbsp;INCORRECT &nbsp;answer &nbsp;3669.



//////////////////////////////////////////////



Regarding next Edwin's declaration about "ikleyn frowns on the use online technology",
I'm just embarrassed to comment on it.


At this forum, I was, probably, first, who started using online computing tools.
I was first who started using here online calculator www.reshish.com for solving 
word problems on linear systems of equations for 3x3- matrices.


I used this online solver many times for word problems and especially to show/demonstrate
Gauss-Jordan step by step procedure and so on.


I was first at this forum who systematically used online solvers for statistical calculations 
(Binomial distribution and Normal distribution).


I used the online plotting tool DESMOS uncounted number of times to create quickly plots 
demonstrating functions or as a solver for finding their intersections, when Desmos works 
as a solver for non-linear equations and systems of equations.
Every time as I used it, I instructed and encouraged visitors to use this online plotting tool and calculator.


So, I don't really know, who of the tutors at this forum uses online tools and calculators more than me,
and who more than me at this forum makes visitors familiar with these tools and calculators.


It seems very strange, if Edwin does not know it, visiting this forum so often.



So, the statement by Edwin is far from to be true: as far as the heaven is far from earth. 


I never stated that I am against using online technology.
My professional activity during my working years was creating computer programs for numerical 
modelling processes in Engineering and Continuum Mechanics. It was the theme of my PhD dissertation. 
Programming for computers is another half of my mind.


Edwin came up with this conception, in order for easy disprove it and to present me as a kind of conservative idiot.
In my view, it is unacceptably low level making discussion.


Simply in this &nbsp;{{{highlight(highlight(CONCRETE))}}} &nbsp;problem the equations are so &nbsp;{{{highlight(highlight(simple))}}} &nbsp;and so &nbsp;{{{highlight(highlight(primitive))}}} &nbsp;that
using online calculators seems to be inappropriate &nbsp;&nbsp;(brings a slight smile).
Much simpler technique is to reduce the Edwin' system of equations to trivial quadratic equation 
and take a square root, as I did.


Edwin's position is in one step from to claim replacing the multiplication table by online calculators.


My position is that using online calculators is good to replace routine job, 
which does not develop the student' mind.


But every time, when mental exercises are useful (in this case - reducing the system 
of two equations to one primitive quadratic equation in one single variable and solving it by taking square root), 
it is a sin for a teacher and a sin for a student not to take advantage of such an opportunity.



This method of teaching as "setting up the equations, not solving them", as Edwin suggests,
is a method of producing mentally retarded disabled people at the exit of the high school.