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I would like to thank the anonymous answerer for participating.  The reason that yours is not correct is that you have assumed a constant velocity of 5m/s.

The velocity is not constant.  In the beginning the downward velocity is 0.

Then as the lid falls it gets faster because it is accelerating at approx 9.8m/s² (That is gravity)

I am going to do it using calculus.

$$\\
When\:\: t=0,\:\: y=1.2m,\:\: \dot{y}=0 \\\\
\ddot{y}=-9.8m/s^2 \:\:(gravity)\\\\
\dot{y}=-9.8t+c_1\qquad \mbox{But since y dot=0 when t=0,} c_1=0}\\\\
\dot{y}=-9.8t\\\\
y=\frac{-9.8t^2}{2}+c_2 \qquad \mbox{substituting you get }c_2=1.2}\\\\
y=\frac{-9.8t^2}{2}+1.2\\\\
\mbox{Find t when x=0}\\\\$$

$$\begin{array}{rll}
0&=&\frac{-9.8t^2}{2}+1.2\\\\
0&=&-9.8t^2+2.4\\\\
9.8t^2&=&2.4\\\\
t^2&=&\frac{2.4}{9.8}\\\\
t&=&\sqrt{\frac{2.4}{9.8}}\\\\
t&=&0.4948\\\\

\end{array}$$

$$\mbox{The lid will shatter in 0.495 seconds}$$

Thank you Rosala,

Do you know what the origins of the saying is. Why does it mean that, do you know?

Thank you Alan and Chris,

I would not have had a clue about any of this question.

I am completely unfamiliar with graphs like these which actually surprises me.

I am only familiar with the diagonal hyperbolas with no squared terms.  

Sure, I'll try to keep it as simple for you as possible

Suppose you have two goods, eg. apples and pears.

Then a utility curve describes what combinations of goods you're indifferent between.

For example, you might like 4 pears and 2 apples just as much as you like 2 pears and 4 apples or 3 pears and 3 apples. All these 'bundles' of pears and apples which you find equally attractive are described on one curve called a utility curve. Now every single curve is given a number. This one might for example have the number 2. Now suppose we have a bundle of 6 pears and 3 apples. Let's assume that you like 6 pears and 3 apples more than 4 pears and 2 apples but you like eg. 3 pears and 6 apples just as much. Then this bundle is on another utility curve with for example the number 4. The higher the number associated with the curve, the more you like all the bundles on the curve. Now if we graph all these curves in one set of axis, we can , given the prices and your income, determine which bundle you prefer most to spend your money on. For example it might be that with €5 you can buy either 6 pears and 3 apples or 2 pears and 4 apples. Since we know that 6 pears and 3 apples lies on the utility curve with number 4 and 2 pears and 4 apples lies on the utility curve with number 2, we know that you like 6 pears and 3 apples better and should therefore buy that combination.

Now the most regular kind of utility curves are the ones you see in the first graph.

'what economists think my utility curve looks like'

The second one clearly leans towards 'stuff I don't really need to buy' (That stuff you buy which you think is awesome but end up using way to little)

And the third one, well... I think you can figure that one out yourself.

It's not like I can make sense of that 

Reinout can you please explain the joke for those who dont know a bit about economics!

i knew!

Melody "i smell the coal burning"means that someone is feeling jealous!

Yes that is true Rosala.

DragonSlayer will you please stop giving your own posts lots of points.  

It is definitely not a good look!

And I have responded to LOTS of your messages.  

I've not come across the term "covertices" before either Melody.  However, it is clear that they are the vertices of the hyperbola obtained by interchanging the signs of the x and y terms.  See graph below:

Thank you David.  

Rosala, what does "I can smell the coal burning" mean? 

That is a really good answer anonymous!    

CPhill has just gone one little step further by rationalising the denominator.  

Math activities - holiday entertainment.

NinjaDevo 5/7/14

Thank you Ninja.

This site should be added to the puzzles somewhere.

I don't understand this Chris, could you please explain it to me.

What is a covertice?

I did the graph.

Yes you did you said "mum"  

Ninja gives excellent answers!

Fri/Sat 5/7/14

♬                                        ♬ ♬ MELODY ♬ ♬

Sum and product of quadratic roots

Here is another approach.  I suspect that this is how it was meant to be done.

Given the quadratic equation 

$$ax^2+bx+c=0\qquad \mbox{the sum of the roots is } \frac{-b}{a} \mbox{ and the product of the roots is } \frac{c}{a}$$

so

$$2x^2-5x-7=0\qquad r+s= \frac{5}{2}\:\: \mbox{ and }\:\: rs=\frac{-7}{2}$$

Now

$$\dfrac{r}{s}+\dfrac{s}{r}\\\\
=\dfrac{r^2+s^2}{rs}\\\\
=\dfrac{r^2+s^2+2rs-2rs}{rs}\\\\
=\dfrac{(r+s)^2-2rs}{rs}\\\\
=\dfrac{(\frac{5}{2})^2-2\times \frac{-7}{2}}{\frac{-7}{2}}\\\\
=\dfrac{\frac{25}{4}+ \frac{14}{2}}{\frac{-7}{2}}\\\\
=\dfrac{\frac{25}{4}+ \frac{28}{4}}{\frac{-7}{2}}\\\\
=\frac{53}{4}\times\frac{-2}{7}\\\\
=\frac{53}{2}\times\frac{-1}{7}\\\\
=\frac{-53}{14}\\\\
=\:-3\frac{11}{14}$$

I gave you "points" anyway....just a slight mistake....I make 'em all the time!!!  Your approach was correct and that's sometimes more important than just getting the  "right" answer.....

Oh i see, my factoring was off.

Thanks CPhill.

I think you have the right idea, ND....let's look at the factoring once more...

2x^2 - 5x - 7 = (2x -7) (x + 1)

So the roots are 7/2 and -1

So

(7/2)/(-1) + (-1)/(7/2) =

-7/2 - 2/7   =  -(7/2 + 2/7) = - (49 + 4)/14  = -53/14

I think that might be it ......

Nothing to say......!

BTW thank god ND ur bomb isnt real or else it would b**w up all the answers!