A Course in Algebra by Yun Fan

By Yun Fan

This quantity is predicated at the lectures given through the authors at Wuhan collage and Hubei collage in classes on summary algebra. It provides the basic suggestions and simple houses of teams, earrings, modules and fields, together with the interaction among them and different mathematical branches and utilized features.

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A Course in Algebra

This quantity is predicated at the lectures given through the authors at Wuhan college and Hubei collage in classes on summary algebra. It offers the basic recommendations and uncomplicated homes of teams, jewelry, modules and fields, together with the interaction among them and different mathematical branches and utilized features.

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7. Find the equation of the circle with center (3, - 1 ) . If P is one endpoint of a diameter of the circle and Q is the other endpoint, find the coordinates of Q. 8. Choose a point R on the circle, different from P and Q. Prove that PQE is a right triangle. , 0, {(a, center (c, 9. 2x2 b) } , {circle of radius r with d)}). + 2y2 + 2Ax - 20y + 123 = 0 10. x2 + y2 - 10tf + 6z/ + 35 = 0 11. 2 2 + 8x - 14y + 62 = 0 x + y In Problems 12 and 13, given the equation of the parabola, find the vertex, the axis, and the direction the parabola opens.

Let C be the midpoint of AB and let D be the midpoint of AC. If the coordinates of D are (2, 3/2), find the coordinates of B. Problems 3-5 concern a circle with a point P, coordinates (0, 0 ) , inside. The point P bisects a chord of the circle and thus determines the chord. 3. Find the equation of the circle with center (1, -1) and radius 4. 4. Find the equation of the line through P that is perpendicular to the chord. 5. Find the length of the chord. In Problems 6-8 the point P with coordinates (1, - 2 ) , is on the circle in question.

Find (f ° f) "1 (x) . 14. Find (/_1 o/" 1 ) (J;) . 15. Find the equation of the line that passes through (2, 3). and is perpendicular to the line through (1, 2) and (3, 5 ) . 27 CHAPTER TEST 3D 16. If I determine where fix) x2 x < 0 x 0 < x < 1 1 X > 0 is increasing, decreasing, and constant. 17. The force of attraction between two bodies is inversely proportional to the square of the distance between them. Find the constant of proportionality if the force is 12 and the distance is 10. 18. Use the horizontal line test to determine whether fix) - x3 + 1 is a one-to-one function.

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