Consider an elastic string of length L whose ends are held fixed. The string is set in motion with no initial velocity from an initial position u(x, 0) = f(x). Let L = 10 and a = 1 in parts (b) and (c). (A computer algebra system is recommended.) f(x) = 2x L , 0 ≤ x ≤ L 2 , 2(L − x) L , L 2 < x ≤ L (a) Find the displacement u(x, t) for the given initial position f(x). (Use a to represent an arbitrary constant.)

Efficient homemakers ltd. makes canvas wallets and leather wallets as part of a money-making project. for the canvas wallets, they need two yards of canvas and two yards of leather. for the leather wallets, they need four yards of leather and three yards of canvas. their production unit has purchased 44 yards of leather and 40 yards of canvas. let x be the number of leather wallets and y be the number of canvas wallets. draw the graph showing the feasible region to represent the number of the leather and canvas wallets that can be produced.