Re: Smarter Scots


Chicmac wrote:
Custos Custodum wrote:
On Wed, 3 May 2006 22:11:36 +1200, "Mad Prof" <mad@xxxxxxx> wrote:


"uNkulunkulu" <izulu@xxxxxxxxxx> wrote in message
news:k0Z5g.63407$wl.19314@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

"Mad Prof" <mad@xxxxxxx> wrote in message
news:e39cv8$j2h$1@xxxxxxxxxxxxxxxx
Are Scots any smarter than other nations? We often laugh at the Yanks
who's
knowledge of geography is sadly lacking but if you went on the streets
of
a
major Scottish town and asked a person at random to point to say 'South
Dakota' or Luxemberg on a map would they be able to do it? I doubt it.
Ask
them to solve a simple algebra problem

sin(x)+x^2=0

As this equation ha a trigonometric function (sin(x)) it has to be a
trigonometric problem and not algebraic. At first glance it is obvious to
those with even a smattering of high school maths that the answer can not
be
zero unless x=0


Fraid not - that is the trivial solution - there is also another solution.
You can see this by drawing the graph of sin(x) and x^2 and looking at the
intersections.(one of which is your solution at x=0) But other than a
graphical solution how to find x?

I don't think it can be solved algebraically - you have to resort to
numerical methods such as successive approximation or truncated
series. Alternatively you can learn to use a programmable calculator
and get the result x = -0.8767 to 4 decimal places.
Actually it can very simply, since the question does not specify
radians, (which you have understandably assumed).

So if I choose to use degrees.

Then it can immediately be seen that the solution in that instance must
be <<1.

This allows us to make the small angle approximation, where sin x = x
where x is in radians and x<<1 radian.

there are 57.3 degrees in a radian, therefore if we are working in
degrees with a very small angle then the approximation means that


x/57.3 = x^2

so x=1/57.3 = 0.000345 approx.

Chic

Oops, I forgot the neg. sign.

x/57.3 =-x^2

x= -0.000345

.

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