A. Imagine a particle free to move in the x direction. Which of the following wavefunctions would be acceptable for such a particle? In each case, give your reasons for accepting or rejecting each function. 1. ψ(x)=x2 
2. ψ(x)=1/x 
3. ψ(x)=e^−x2.

b. Imagine a particle confined to move on the circumference of a circle ('a particle on a ring'), such that its position can be described by an angle ϕ in the range 0−2π.. Which of the following wavefunctions would be acceptable for such a particle? In each case, give your reasons for accepting or rejecting each function.

1. cosϕ
2. sinϕ
3. cos(0.9ϕ).

Astudent creates a model of a closed ecosystem by filling a glass tank half full with water, then adding 10 snails and two small aquatic plants. the next day, all the snails are dead. what is the most likely cause of their death?

The chart shows the costs and shipping times for materials that a company needs to build a new product. which describes the best trade-off if the company needs to start building their product within the next two years? they should order the domestic materials because it is always best to choose the fastest shipping time. they should order the imported materials because it is always best to choose the lowest cost for materials. since the shipping time is longer, they should order the domestic materials because the additional cost is worth it to get the materials in time. even though the shipping time is longer, they should order the imported materials because they are less expensive and should arrive in plenty of time to build the product.

Using the free-body diagram, calculate the net force acting on the sled. is the sled in a state of dynamic equilibrium?