Two word problems on Present Value

1. Income from a precious metals mining operation has been decreasing uniformly for 5 years. If income in year 1 was $100,000 and it decreased by $10,000 per year through year 5, the present worth of the income at 10% per year is closest to? A. $310,500 B. $352,200 C. $379,100 2. Income from sales of a certain oil additive has been averaging $100,000 per year. At an interest rate of 18% per year, the present worth of the income for 5 years is closest to? A. $312,700 B. $328,400 C. $335,100

mat lab

A thin glass pipe with the internal diameter of 3 mm was probed into a heart tissue (membrane) and air pressure was plied thriugh the pipe to expand the membrane. Assuming its thickness to be negligible, the circular arc of the bulged membrane was to be 3.6mm (see picture below). Find the volume of the excessive space between the end of the glass pipe and piece of membrane. (See attached file for full problem description)

Prove a theorem relating to complex solutions of a polynomial eqn

(See attached file for full problem description and equations) --- Prove that if p is a polynomial with real coefficients, and if is a (complex) solution of P(E)z = 0, then the conjugate of z, the real part of z, and the imaginary part of z are also solutions. Note: This is from a numerical analysis course, and here P(E) refers to a polynomial in E, the "shift operator" for a sequence. Please show all steps in your solution method! Thanks! ---

Recurrence Relation

attached

A thin glass pipe with the internal diameter of 3 mm was probed into a heart tissue (membrane) and air pressure was plied through the pipe to expand the membrane. Assuming its thickness to be negligible, the circular arc of the bulged membrane was to be 3.6mm (see picture below). Find the volume of the excessive space between the end of the glass pipe and piece of membrane. Need a solution in matlab.

A thin glass pipe with the internal diameter of 3 mm was probed into a heart tissue (membrane) and air pressure was plied through the pipe to expand the membrane. Assuming its thickness to be negligible, the circular arc of the bulged membrane was to be 3.6mm (see picture below). Find the volume of the excessive space between the end of the glass pipe and piece of membrane. Need a solution in matlab.