Please answer these two questions ASAP, no need for explanations just showing the working out is totally fine. Instead of using dy/dx please use y' or y" instead thanks.

(VECTORS/CALCULUS)

7. (a) Use Newton's method ONCE with an initial guess of To = 2 to find an approxi- mation to the solution of x2 = 2- 20. (Newton's method for solving f(x) = 0: In+1 = In - f(In) for n = 0, 1, 2, ...) f' (In ) (4 marks) (b) The perimeter P of an square is related to its area A by P2 = KA where k = 16. Suppose that the area A of a given square increases by 4%. Use calculus to find the approximate percentage change in P. (4 marks)8. A large cylindrical drum is to be constructed with the dimensions shown at right. The (cir cular) top and bottom of the drum are to be constructed using metal which costs $10 per square metre' while the curved sides are to be constructed using metal which costs $40 per square metre. The required volume of h the drum is 1r m3. Determine the dimensions r and h which minimise the cost of construction of the drum. (Make sure you explain why your 30- lution is a (global) minimum.)