The circumference of the base of a cylinder is 245 mm. A similar cylinder has a base with circumference of 60 mm. The
oral area of the larger cylinder is 210 mm
What is the lateral area of the smaller cylinder?

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

If x+y+z=0 what is the value of [tex] {x}^{3} + {y}^{3} + {z}^{3} [/tex]

For the sequence [tex]a_{n} = 2n/(n+1)[/tex], what is the value of [tex]a_{10}[/tex]