Other Math Answers

How do standard algorithms differ from student-invented strategies? Explain the benefits of invented strategies over standard algorithms (give at least two valid points).

A short run cost function for an entrepreneur is q³- 8q² + 30q + 60. Determine the price at which the entrepreneur cases production in an ideal market. Also, derive the supply function.

Consider the upward motion of a particle under gravity with a velocity of projection u_o and resistance mkv². Show that the velocity V at the time t and distance x from point lf projection are related as

2gx/V_t² = ln[(u_o²+V_t²)/(V²+V_t²)], where k=g/V_t²

Suppose that monopolist has a demand function p1= 100-Q1 , p1=80-Q1 , C=6Q1+6Q2. How much should be sold in the market? What are corresponding prices? Find total profit?

Write the limitations of the Malthusian model of population growth.

Give one example each from the real world for the following, along with justification,

for your example:

(i) A non-linear model

(ii) A stochastic model

(iii) A linear, deterministic model.

In a population of lions, the proportionate death rate is 0.55 per year and the

proportionate birth rate is 0.45 per year. Formulate a model of the population. Solve

the model and discuss its long term behavior. Also, find the equilibrium point of the

model.

Find the equilibrium price in a perfectly competitive market with the supply function S(p)=(-p² +4)/3and the demand function D(p)= -p+2.Using the static criterion of Walras, determine whether the price is stable or not.

Consider the blood flow in an artery following Poiseuille’s law. If the length of the

artery is 3 cm, radius is 7×10^-3 cm and driving force is 5×10³ dynes/cm² then using blood viscosity, μ = 0 × 027 poise, find the

(i) velocity u( y) and the maximum peak velocity of blood, and

(ii) shear stress at the wall of the artery.

A body is falling free in a vacuum. The fall is necessarily related to the gravitational

acceleration g and the height h from which the body is dropped. Use dimensional

analysis to show that the velocity V of the falling body satisfies the relation V/√(gh)=constant.