Alan

There are 7 turning points so p must be 8.

Treat this as follows:   \(x = 2+\frac{1}{1+\frac{1}{x}}\)

or   \(x =2+\frac{x}{1+x}\)

Rearrange this to obtain a quadratic equation in x and solve for x (only the positive solution will apply).

Think of the planes as being at the vertices of a right-angled triangle, where the right-angle is where they intersect.

The initial distances of the two planes from the intersection point are x1 and x2 respectively, They have velocities v1 and v2.

Then the following four equations apply:

v1 = x1/2

v2 = x2/2

v2 = v1 + 100

x1² + x2² = 1000²

Solve these simultaneous equations to find the velocities.

Variants of this question keep popping up!

What do you mean by "....etc"?  I see no repetition (which there needs to be if the number is rational).

As follows:

\(\frac{2}{3}\frac{3}{4}...\frac{n}{n+1}=\frac{1}{50}\)  Succesive numerators and denominators cancel each other except for the very first numerator and the very last denominator, leaving \(\frac{2}{n+1}=\frac{1}{50}\)

Hence n+1 = 2*50   or n+1 = 100 and n = 99.  Sum = 199

probability none will speak p0 = (3/4)⁶  

probability exactly one will speak p1 = 6*(1/4)*(3/4)⁵ 

probability at least two will speak p2 = 1 - p1 - p0

You can crunch the numbers

As follows:

Like so

The question mark will be the mean of the three test values, namely (5.8 + 6.2 + 7.9)/3, with the result rounded to one decimal place.

In the first instance try plotting the diameters on the x-axis and the corresponding mean values on the y axis.