Problems XII
- The salary of a man is increased by 30% every two years beginning January 1, 2001. Counting from that date, at which year will his salary just exceed twice the original salary?
- The main business of research mathematics is _____?
- The sum of any real numbers and its additive inverse is _____?
- The product of any non-zero real number and its multiplicative inverse is _____?
- If n, m and k are integers and n . m = k then n and m are said to be _____ of k?
- The point which is equidistant from (-3,0) and (1,4) and a distance of 5 from (-1,7) is _____?
- The segment from (-1,4) to (2,-2) is extended three times its own length. The terminal point is _____?
- Point P(x,y) moves with a distance from point (0,1) one-half of its distance from line y = 4, the equation of its locus is _____?
- Two vertices of a triangle ar (3,5), (1,4) and the area is 1 the locus of the third vertix is _____?
- Two circles of radius 4 are drawn with centers at (2,1), (-1,-3). The equations of their common tangents are _____?
- The ordinates of the ellipse x2/a2 + y2/b2 = 1 are true ______ times those of the circle x2 + y2 = a2?
- The hyperbola 7x2 - 9y2 = 63 has a distance between directrices of _____?
- The equation of the circle which intersects x the circles x2 + y2 + x - y = 2; x2 + y2 = 5, and passes point (-2,2) is _____?
- The angle between two lines whose direction components are (2,1,-1) and (1,-1,-2) is _____?
- The area of a kite with vertices at (4,0,7), (5,1,-1), (0,-4,3) and (1,-3,7) is _____
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