2. A's age exceeds B's by n years, and is as much below mas B's is above p. Find their ages and in terpret your result when (1) n is negative. (2) n is greater than m+p. 3. Which is greater and by how much, the diagonal of a square or the perpendicular of an equilateral triangle equal in area to the square? 4. A circle is inscribed in an equilateral triangle, and a second circle to touch the first and two sides of the triangle, and a third circle to touch the second circle and the same two sides, and so on ad inf. Find the sum of the areas of all the circles. 5. The attraction at the surface of a planet varies directly as the mass and inversely as the square of the radius of the planet. The earth's radius is 4000 miles and the moon's 1100; and the moon's mass is oneseventy-fifth that of the earth. How much would at man, who weighs here 150 lbs., weigh if taken to the moon ? 6. Three equal circles are inscribed in an equilateral triangle so as to touch the sides of the triangle and each other. Find their common radius. 7. Describe Peaucellier's cell and prove that the tracing point moves in a straight line. 8. Prove that the circumradius of a triangle is abc R = ; and show that if the centres of the three escribed circles be joined the area of the triangle so formed is R (a+b+c). 9. If a, b denote the sides of a parallelogram and the angle between them, one diagonal is double the other when 10. Find the form and area of the largest rectangle which can be inscribed in a given semicircle. |