{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# math370 - CARLETON UNIVERSITY FINAL EXAMINATION MATH 1005 A...

This preview shows pages 1–2. Sign up to view the full content.

CONCORDIA UNIVERSITY Department of Mathematics & Statistics Course Number Section(s) Mathematics MATH 370/MAST 330 01 Examination Date Time Pages Final December 2000 3 hours 2+1 Instructor Course Examiner Pawel G´ora Special Instructions: Calculators permitted. Table of Laplace transforms provided (page 3). Lined paper booklets. MARKS: marks for each problem are shown in front of the problems. Maximum total is 100. MARKS 1) Solve the following equations: 3 (a) xyy = 1 - x 2 , y (1) = 1. 4 (b) ( x 2 + y 2 )d x - xy d y = 0 . 7 (c) x d y d x + 2 y = x 4 . 4 (d) ( x 2 + y 2 + 2 x )d x + 2 xy d y = 0 . 7 (e) y x d x + ( y 3 - ln x )d y = 0 , by finding an integrating factor. 7 2) Find the family orthogonal to the family of curves ( x - c ) 2 + y 2 = c 2 . 7 3) A tank contains 100 gal pure water. Brine containing 2 lb salt per gallon is added to the tank at the rate of 5 gal/min. a) How much salt is present after 20 min if the well stirred mixture runs out at 6 gal/min. b) Find the maximum number of pounds of salt the tank will contain and the number of minutes needed to reach the maximum value.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern