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A-modules over A-algebras and Hochschild cohomology for by Ladoshkin M.V.

By Ladoshkin M.V.

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Solve for X: 12. - 5x + 1 = 0. /12 + 3a: - x = 4. Find the equation of the line that passes through (-1, 2) and is perpendicular to the line through (2, 8) and (7, 1 ) . 13. Find the set of x such that —; x(x 14. The perimeter of an isosceles right triangle is 12. r-r-; r-r- > 0 . + 1)(x - 1) Find the length of the hypotenuse. 15. If u varies directly as xy and inversely as z and if u = 2 when x = 1, y = 2, and z = 3, find u if x = 2, y = 3, and z = 4. In Problems 16-20 f(x) 16. Find (/ ° g) = -== and g (x) Vx = 4# + 1.

Graph the ellipse when k = 4. 16. For what values of k is this the equation of a circle? 17. Graph the following hyperbola and find its asymptotes: 2 2 1 54 CHAPTER TEST 5D 1. Consider two line segments, one with endpoints (-2, 7) and (-3, 4 ) , the other with endpoints (1, 0) and (5, 2 ) . Find the midpoint of the line segment whose endpoints are the midpoints of the two given line segments. 2. Let AB be a line segment on which the coordinates of A are Let C be the midpoint of AB. and let D be the (4, 3) .

44 CHAPTER TEST 4D In Problems 1-5 simplify. 1. log 64 2 2. 3. log 9 1/3 1 log T 9 3 4. log 216 3S 5. log 36 216 In Problems 6-8, if log 5 = a: and log 7 = y, the given logarithm in terms of x and 6. log(35) evaluate y. 2 7 10 · ^έ 8. 4 In Problems 9 and 10 use logarithms to evaluate the given expression. 9. 10 . 82) 2 (3 ·91>3 In Problems 11 and 12 write each expression as a single logarithm. 11. 2 log(x + y) - — log{x - y) 12. log x + log y _ log x - log y 4 ~ 8 13. Suppose we invest an amount of money at 10 percent per year compounded annually.

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