By separating variables, ﬁnd the solution of the following initial value problems in explicit form: 1. y′ = 2x/(y + x2 y), y(0) = −2. 2. y′ = xy3 (1 + x2 )−1/2 , y(0) = 1. 3. y′ = 3x2 /(3y2 − 4), y(1) = 0. (Leave solution as a cubic equation for y.) 4. y′ = (2 − ex )/(3 + 2y), y(0) = 0. 5. Find the solution of the following initial value problem with x = x(t) and x = dx/dt: ˙ x + 2x = te−2t , ˙ 6. Consider the initial value problem: 2 1 x + x = 1 − t, ˙ 3 2 x(0) = x0 . x(1) = 0.

Find the value of x0 for which the solution touches, but does not cross, the t-axis. 7. Find the value of x0 for which the solution of the initial value problem x − x = 1 + 3 sin t, ˙ remains ﬁnite as t → ∞. 8. Consider the initial value problem 3 x − x = 3t + 2et , ˙ 2 x(0) = x0 . x(0) = x0

Find the value of x0 that separates solutions that grow positively as t → ∞ from those that grow negatively. How does the solution that corresponds to this critical value of x0 behave as t → ∞? 9. A home buyer can aﬀord to spend no more than $800/month on mortgage payments. Suppose that the interest rate is 9% and that the term of the mortgage is 20 years. Assume that interest is compounded continously and that payments are also made continuously. (a) Determine the maximum amount that this buyer can aﬀord to borrow. (b) Determine the total interest paid during the term of the mortgage. 10. A sky diver weighing 82 kg (including equipment) falls vertically downward from an altitude of 1500 meters, and opens the parachute after 10 sec of free fall. Assume that the force of air resistance is k1 |v|, with k1 = 1.65 kg/s, when the parachute is closed and k2 |v|, with k2 = 26.4 kg/s, when the parachute is open. (a) Find the speed of the sky diver when the parachute opens. (b) Find the distance fallen before the parachute opens. (c) What is the limiting velocity vL after the parachute opens? (d) Determine how long the sky diver is in the air after the parachute opens. (e) Sketch the graph of velocity...

...
Laboratory Activities
Exercise 1: Prefixes, Suffixes and Root Words Commonly Used in Biology
Protocol:
Example #1: Biology = study of life Example #2: Hypotonic = below tonicity
Biological Terms
Literal Meaning
Phagocytosis
To eat bag, sac, condition
Chlorophyll
Green leaf
Zoology
Study of animals
Haploid
Single
Diploid
Two, double
Exocytosis
Outside cell condition
Hypertonic
Above, over tonic
Metaphase
Change, after phase
Unicellular
One, single pertaining to
Multicellular
Many...

...CS 4320/5320 Homework 1
Fall 2014
Due September 17, 2014
This assignment is due on Wednesday, 9/17/2014 at 11:59pm. It is out of 65 points and counts for 10% of
your overall grade.
You must work on this homework in groups of 2 or 3 students. You should make one CMS submission
for your entire group, and everyone in the group will receive the same grade.
To complete the code portions of this assignment, you will need to install both MySQL
(http://dev.mysql.com/downloads/mysql/) and...

...ECON 6032 International Trade and Foreign Direct Investment Prof. Larry Qiu
Assignment 1
Due on March 4 (Session B) and March 5 (Session A) in Class
Ricardian Model
1. Suppose that each worker in the home country can produce three cars or two
televisions. Assume that Home has four workers.
a. Graph the production possibilities frontier for the home country.
b. What is the no‐trade relative price of cars at Home?
2....

...Corporate Finance Home Wok
Chapter 4
Q1: Simple Interest versus compound Interest First City Bank pays 9 percent simple interest on its savings account balances, whereas Second City Bank pays 9 percent interest compounded annually. If you made a $5,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years?
A: First City Bank: 5000*(1+10*0.09)=9500
Second City Bank: 5000*(1+0.09)10=11837
11837-9500=2337
So we will earn more...

...Evolution by Anthropology
Evolution can be explained religiously and scientifically. Scientifically evolution is the process by which different kinds of living organisms are thought to have developed from earlier forms during the history of the earth. One of the first scientists to introduce evolution in a scientific manor was Lamarck and his theory of inheritance for acquired characteristics. One of the reason’s Lamarck’s theory failed was because he wasn’t able to incorporate different...

...Homework #1 Solutions 3.1 a. Let X1 =the number of hours of process 1 used X2 =the number of hours of process 2 used The objective is to minimize the cost of producing the three products A, B and C. The constraints are on the demand of each product. Min 4X1 + X2 subject to 3X1 + X2 ≥ 10 (A’s demand) X1 + X2 ≥ 5 (B’s demand) X1 ≥ 3 (C’s demand) X1 , X2 ≥ 0 (nonnegativity) b. From the graph we can see that the isocost line just leaves the feasible region where the demand for C and B intersect....

...1. Which of the following is a financial asset?
An experienced and hardworking sales force.
A trademark
A bank loan agreement [correct]
Undeveloped land
2. Capital structure refers to the mix of a firm’s long-term debt financing and equity financing. Suppose that a firm has $4 billion debt. The market values the firm’s 100 million (equity) shares at $60 per share. Earnings per share is $5. Dividend per share is $1.What is the fraction of equity in the firm’s capital structure?
40%
60%...

...ACTG 351 HW #1 Answers 1. Curtiss Construction Company, Inc. entered into a fixed-price contract with Axelrod Associates on July 1, 2011, to construct a four-story office building. At that time, Curtiss estimated that it would take between two and three years to complete the project. The total contract price for construction of the building is $4,000,000. The building was completed on December 31, 2013. Accumulated contract costs incurred, estimated costs to complete the contract, accumulated...