Prove that each of the following languages is decidable by constructing a turing machine that decides it and showing that this construction is correct. hint: you may use any of the turing machines constructed in class as a subroutine of your turing machine. a. = {⟨ ⟩ |⊆ }

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.

Find v1, the speed of the fluid in the left end of the main pipe. express your answer in terms of h1, h2, g, and either a1 and a2 or γ, which is equal to a1a2.

What is the magnitude of the gravitational force acting on the earth due to the sun?