Probability : Rayleigh Distributions

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(pi/alpha) b) Show that the variance =(1/alpha)*(1-pi/4)

Break-even Point

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

Newton's Equations of Motion

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?

Modeling a Box as a Particle

See attached file for full problem description. Need help on 2b, 3. 2. A box of mass m is placed on a plane, which is inclined at an angle a to the horizontal, where tan a The plane is rough and the coefficient of friction between the box and the plane is . The box is kept in equilibrium on the plane by applying a horizontal force of magnitude P to it, acting in a vertical plane containing a line of greatest slope of the plane, as shown above. Given that P has the smallest possible, value which will enable the box to remain in equilibrium, a draw a diagram, showing all the forces acting on the box, and indicating clearly the direction in which they act, b find P in terms of m and g. ... click for more

Particles, Forces and Vectors

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.