Problem 1 (Reducible Expression). The goal of this problem is to identify the redexes, if any, in the given
expressions. To identify a redex, you should highlight the ( x. t ) part of the redex in yellow and the t’
part of the redex in blue. Here are two examples.

For each of the following, identify the redexes, if any:
1. x ( x. x x ) ( x. x x ) x
2. ( x. ( x. x ) x ) ( x. x ) x
3. ( x. ( x. x ) x ) x. ( x. x ) x
4. ( x. x ( x. x ) x ) x. x ( x. x ) x
5. x ( x. x ( x. x ) x ) (x. x ( x. x ) x ) x
6. x. x. x x. x. x x x
7. ( ( x. y. ( y. x ) x. x x ) ) ( ( x. ( y. x ) ) x. x x )
8. ( x. ( x. ( x. x ) x ) x ) ( ( x. x ) ( x. x ) ( x. x ) )
9. x ( x. ( y. x ) x. x x ) ( x. ( y. x ) x. x x ) ( ( x. ( y. x ) ) x. x x )
10. ( x. ( y. x ) x. x x ) ( ( x. ( y. x ) ) x. x x )

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.