#$&*
MTH 279
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Test 1
** **
I noticed that the date for the first test is approaching, so I went to the Testing page that I had previously bookmarked during orientation:
http://vhmthphy.vhcc.edu/tests/
to get a sneak peek at what the test may be structured like. However, I did not see MTH 279 as one of the subjects with posted tests. Have I perhaps bookmarked the wrong page or misunderstood some instructions about the test?
Thank you in advance for any information.
@&
It appears that the information posted at your site is incorrect.
Tests for this course are sent to your proctor.
Email me Monday to be sure I have sent copies of your tests to your proctor.
Here is a sample test:
Form 2
Test #1
Signed by Proctor or Attendant, with Current Date and Time: ______________________
If picture ID has been matched with student and name as given above, Attendant please sign here: _________
Instructions:
Test is to be taken without reference to text or outside notes.
No calculator is necessary for most of the problems on this test. A scientific calculator without memory is permitted, and is sufficient for problems that require calculation of the values of transcendental functions. Graphing calculators may not be used.
Test is to be taken on blank paper or testing center paper.
Test is to be taken in one sitting.
Please place completed test in Dave Smith's folder, OR mail to Dave Smith, Science and Engineering, Va. Highlands CC, Abingdon, Va., 24212-0828 OR email copy of document to dsmith@vhcc.edu, OR fax to 276-739-2590. Test must be returned by individual or agency supervising test. Test is not to be returned to student after it has been taken.
Directions for Student:
Completely document your work. Show all steps and explain all reasoning, using the methods covered in the course. There are convenient formulas for the solutions of certain types of equations, but you are expected to solve using basic techniques and principles. If on a problem you bypass appropriate solution methods using formulas, you can expect at best partial credit for that solution.
Unless test is to be faxed or sent as PDF or other electronic means, please write on one side of paper only, and if possible staple test pages together.
1. Solve the following equation:
(2 x y^3 + cos(x)) dx = - (3 x^2 y^2) - sin(y)) dy
2. The population of fish in a tank is expected to grow exponentially when the population is low compared to the carrying capacity of the tank, to decline when the population exceeds carrying capacity, and when close to the carrying capacity to approach that limiting value exponentially.
Suppose the carrying capacity is 1000, the initial population is 30 and the initial rate of change of population is 2 fish / week. Set up and solve the logistic differential equation, including initial conditions, that models the population of this tank as a function of time.
3. Solve the equation
y ‘ = -1/2 x y^5, y(0) = 1 / 2
4. Solve the following equation:
y’ – t y /4 = e^(2 t) , y(0) = -3
5. The given equation is separable and is easily solved. Find its solution.
y ‘ = y^2 x, y(1 ) = 1
Sketch a direction field for this equation on the t interval [ 1 , 1.6 ], breaking this interval into three equal segments and using a scale for the y variable which is appropriate to the solution.
Sketch your solution curve, as well as a solution curve through each of the initial points (1, .5 ) , (1 ,1.5 ) and (1 , 2).
6. Solve the following equation without using separation of variables:
y ‘ – 3 cos(t) y = 0 , y(0) = 3
7. A 2% saline solution flows at 2 gallons / minute into a 200 gallon tank, initially full of a 6% saline solution. Thoroughly mixed water is pumped from the tank at 1 gallon / minute.
What is the concentration of salt in the tank as a function of time?
How long after the initial instant will the concentration be 3%, and how much of this solution will be in the tank?
What is the limiting value of the concentration, and at what time will the concentration be closest to that limit?
*@