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Let η and ξ be two independent normal random variables with mean 1 and variance 2. Which of the

following statements is correct?

◦ η + ξ and η − ξ are uncorrelated and independent

◦ η + ξ and η − ξ are uncorrelated, but not independent

◦ η + ξ and η − ξ are correlated, but independent

◦ η + ξ and η − ξ are correlated and not independent

◦ None of the statements is correct

A square metal plate with a length af0.20 m and with a charge of 9.7x 10 C.

Find the electric field of the square metal plate.

A manufacturer wants to build a spring that takes a force 10 N (in negative direction) to compress it 0.2 m from the equilibrium position. The spring should be able to stretch 0.5 m from the equilibrium position.

As a mechanical engineer, you were asked to present how much work should be done to stretch the spring.The presentation shall include important components of the problem, complete and correct computations and a logical and organized explanation.

Hints:

First, create a force function F(x) by finding the spring constant k in F(x) = kx where F(x) is the force and x is the position from the equilibrium.

Then, calculate work ustng the concept of the definite integral.

If a variable force F(x) moves an object in a positive direction along the x-axis from point a to point b, then the work done on the object is W = ∫ ^b a F(x) dx