All Answers 359395 Answers

Yes, I guess I would!

The centripetal force required to keep the car from skidding is given by

$$F=m\frac{v^2}{r}$$

where m is the mass of the car, v is it's speed and r is the curve radius.

The frictional force is

$$F=\mu mg$$

where μ is the coefficient of friction and g is gravitational acceleration.

So equating these two forces we have:

$$\frac{v^2}{r}=\mu g\\\\
v=\sqrt{\mu gr}$$

I'll let you put in the numbers.

My experience is that the scientific community in the UK adopted the US approach to billions and trillions a long time ago!

Melody said:  I'd never remember the alt number in a million years!

You would if you used it a lot!!

It is also possible that the equation in question is meant to be:

$$e^{-0.2x}-e^{-0.75x}=0.25$$ 

In this case there are two solutions as can be seen from the graph below:

These solutions can be obtained numerically.  A simple iterative approach is to write the equation in the following form:

$$x_{n+1}=\frac{-1}{0.2}ln(0.25+e^{-0.75x_n})$$ 

Then let x0 = 1, say, and use the formula above to iterate several times.  The result is:

x ≈ 6.812073

By rewriting the iteration formula as:

$$x_{n+1}=\frac{-1}{0.75}ln(e^{-0.2x_n}-0.25)$$

we can iterate to the other solution:

x ≈ 0.6023554654

Thanks Alan,

I'd never remember the alt number in a million years!

From here you can get the degree symbol by selecting Insert, Special character and choosing the degree symbol ° (2nd row, fifth character from the right).

More generally, you can type Alt 0176 from the keyboard's numeric pad ° (you have to hold down the Alt key while typing the 0176).

Incidentally, Melody, to get out of superscript mode just select superscript again!

I don't understand.  Do you want to give a specific example?

I can't edit pages from the old forum so I'll start a new post!  

CPhill's challenge puzzle    (12May14)

It is just a superscript zero.  What do you want it for.  i mean is it just for presentation or something you want to type into a calculator or what?

You can highlight the zero. Go to the drop down format and choose superscript.  Trouble is this has a bit of a bug - it is hard to get out of superscript mode.  you can leave it till your whole post is written and then superscript it after  that works ok.

or

I nealy always use LaTex say you want 36degrees. I would open the latex box and type in 36^0 then close it again. $$36^0$$  You can do the same thing in Math(input) I believe. It looks like it is not in line properly but it straightens up when you 'publish' your post!

Melody......Here's a problem that I ran into some time ago:

Show that

(1/2)*(3/4)*(5/6)*(7/8)*..............*(97/98) *(99/100) <  (1/10)

It's "tricky" ......but simple.......all at the same time.

Maybe some of the members  - or even, non-members - would like to try their hand at proving it !!

One word of warning.......your calculator won't do you any good on this one !!!

And ....as a "silly" problem...see if some of the users can figure THIS one out!!

Show that:    sinx / n  = 6

Hi daniavm,

Admin has advised me that this problem is fixed.

We are sorry about any inconvenience that was caused. 

I'll blame it on them !!!

or just

$$e^{-13}=\frac{1}{e^{13}}$$

or just 

$$-4\frac{2}{3}$$

Your smiling cool characters tend to tell a different story.      Are they the 3 stoogers?

There are 360 degrees in a revolution and 

There are $$2\pi$$  radians in a revolution.

Angles can be measured in either degrees or radians.

I do.  I don't like improper fractions.  They are just not 'proper'.  lol

Have a look at how I wrote it using LaTex.  It is easy.  Give it a go, at least for fractions and indices.

Chris is completely correct.

If tan x = 0.76 then cos x must equal

 $$cosx\approx \pm \frac{100}{125.6}\\


cosx\approx \pm 0.7962$$

Therefore the question is nonsense

See diagram.

No...I actually DIDN'T touch it!!

Honest!!!

Ghosts in the Machine - again!!

You could leave it as a mixed number.......I don't have any particular prejudices against either one!!!

Thanks for that answer, I made exactly the same mistake recently!

$${{\mathtt{81}}}^{{\mathtt{2}}} = {\mathtt{6\,561}}$$

because

$${\mathtt{81}}{\mathtt{\,\times\,}}{\mathtt{81}} = {\mathtt{6\,561}}$$

I believe that this question is nonsensical.......

Consider that tan^-1 (.76) = 37.234833981575°

And cos-1 (.22) = 77.29096700560°

And using the "identity" 

tan (x) * cos(x) = sin(x) , we get

.76 * .22 = .1672

Which means that sin(x) = .1672

And sin^-1 (.1672) = 9.625060859216°

Which leads to the strange "identity" that

tan 37.234833981575° =   sin 9.625060859216° / cos 77.29096700560°

Which, in fact, IS true, if we're willing to let "x" represent three different things at once !!

                           $$\frac{4008}{1000}$$