A circular cylinder, open at one end, has radius r cm and external surface area 27\pi cm^{3}. (i) Show that the volume of the cylinder, V cm^{3}, is given by V=\frac{\pi}{2}(27r-r^{3}).
(ii) Given that r can vary, find the stationary value of V and determine whether this value is a maximum or a minimum.

6.(q^9)^2 a. 2q^18 b. q^18 c. q^81 d.q^11 7.(6q^6)^-4 a. 6q^1296 b. 1296q^2 c. 1/1296q^24 d. 6q^-24 8. what is the value of 12x^-3 y^-1 for x = -1 and y = 5? a. -12/5 b.-10 c.-0 d.5/12 9. (y^-5)^10y^10 a. y^-60 b. y^60 c. y^-150 d. y^150 find the simplified form of each expression. 10. (4/7^5)^2 a.8/14^10 b.16/49^25 c.16/49y^10 d.8/14y^25 11. determine if the number 3.43 times 10^-6 is written in scientific notation. if not, explain. a. yes; the number is written scientific notation. b. no; the first factor is not a number between 1 and 10. c. no; it is not written as a number times a power of 10

The rectangle shown has a perimeter of 108 cm and the given area. its length is 6 more than five times its width. write and solve a system of equations to find the dimensions of the rectangle.

Ametal rod is 2/5 meters long. it will be cut into pieces that are each 1/30 meters long. how many pieces will be made from the rod?