For the reaction a b c→d e, the initial reaction rate was measured for various initial concentrations of reactants. the following data were collected: trial [a] (m) [b] (m) [c] (m) initial rate (m/s) 1 0.20 0.20 0.20 6.0×10−5 2 0.20 0.20 0.60 1.8×10−4 3 0.40 0.20 0.20 2.4×10−4 4 0.40 0.40 0.20 2.4×10−4

Three out of five seniors remain undecided about a college major at the end of their senior year.

The initial tableau of a linear programming problem is given. use the simplex method to solve it. x 1 x 2 x 3 s 1 s 2 z 1 2 4 1 0 0 8 3 4 1 0 1 0 10 minus3 minus12 1 0 0 1 0 the maximum is nothing when x 1equals nothing, x 2equals nothing, x 3equals nothing, s 1equals3, and s 2equals0. (be sure to simplify to lowest terms if necessary.)

5.a fishing rod is formed from a composite material of 0.5 kg of glass fibers embedded in a matrix of 0.5 kg of epoxy resin. the glass fibers are assumed to be long, continuous and unidirectional. to achieve a greater stiffness it is proposed to use a different composite that is comprised of long continuous carbon fibers that will be embedded in a matrix of 0.5 kg of epoxy resin. if the modulus of elasticity of the carbon fiber composite is 10% greater than the elastic modulus of the glass fiber composite, estimate the mass of carbon fibers that will be used to make the carbon fiber composite. assume the applied tensile stress is parallel to the direction of the long axis of the fibers. the epoxy resin, glass fiber, and carbon fiber have an elastic modulus of 5, 86, and 350 gpa respectively and a density of 1100, 2500, and 1800 respectively.