testreview1 - t b What happens to the temperature of the...

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Math 2090 fall 2009 Test review for Exam1 1. Find the orthogonal trajectories of the family of curves, where c is an arbitrary constant. 2. Obtain the general solution to each of the following first order differential equations. (a) (b) (c) (d) (e) 3. Solve the following IVP problems. (a) Where (b) 4. It is known that a certain object has constant of proportionality in Newton’s law of cooling. When the temperature of this object is F, it is placed in a medium whose temperature is changing in time according to . a) Using Newton’s law of cooling, determine the temperature of the object at time
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Unformatted text preview: t . b) What happens to the temperature of the object as? Is it reasonable? 5. 6. Using ERO (elementary row operations) to reduce the given matrix to RREF (reduced row echelon matrix). Show your work. Then determine the rank of the matrix. 7. Determine the solution set to the given system of equations. \ 8. Determine all values of the constant k for which the following system has (a) no solution , (b) an infinite number of solutions, and (c) a unique solution. 9. Find (if it exists) the inverse of the given matrix by using the Gauss-Jordan method. ....
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