12545 Rayleigh distribution Want solution in 3 hrs

A random variable y has a Rayleigh distribution, if and only if its probability distribution is given by: f(y)=2(alpha)y^(-alpha y^2) , y>0 and alpha>0 f(y)=0 , elsewhere a) Show that mean=(1/2)*squareroot(pie/alpha) b) Show that the variance =(1/alpha)*(1-pie/4)

Break-even analysis

1. Air Filter, Inc., sells its products for $6 per unit. It has the following costs: Rent $100,000 Factory labor $1.20 per unit Executive salaries $89,000 Raw material $.60 per unit Separate the expenses between fixed and variable cost per unit. Using this information and the sales price per unit of $6, compute the break-even point

Stopping distances maths A2

The brakes of a train can produce a retardation of 1.7ms-2. If the train is travelling at 100km h-1 and applies the brakes what distance does it travel before stopping? (have done this part and got the correct answer of 227m). I am stuck on the part below. If the driver applies the brakes 15m too late to stop at the station then what speed is the train travelling when it passes through that station?

Particle Questions

See attached file for full problem description. Need help on 2b, 3.

Particle Question

5. A particle P is acted on by three forces F1, F2 and F3, where F1 = (2i – 5j)N and F2 = (4i – 4j). Given that P is in equilibrium, a. find F3 in terms of i and j The force F3 is now removed and P moves under the action of F1 and F2 alone. b. Find to 3 s.f. the magnitude of the resultant force acting on P. c. Find, in degrees, to 1 d.p., the angle between the resultant force acting on P and the vector j.