Given the equation of a parabola, . Find the coordinates of the focus, in (x, y) form.

Find the area of the region enclosed by one loop of the curve 

The curve C is given parametrically by

Given a point with polar coordinates 

If the following argument is invalid, create a counterexample chart.  If the following argument is valid, create a formal proof. ***********************************************************You can copy and paste these for your answer: For a CE Chart: b k p q For a Proof: Statements: Reasons: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) (delete any you don’t need)

Supply the reasons that match the statements in the proof for the following VALID argument.  The statements are listed in order below. Statements:1) ~(p V ~z)2) ~p ^ z3) ~p4) z5) n –> ~z6) ~n 7) ~n –> p8) p9) p V ~z

Let  and  be a premises.  Then the truth value of    is:

If  is a premise and b is false, then  must be ____________.

Use the TF Method to determine if the following argument is valid or invalid.  Create a proof or counterexample chart in the next question.

As a plate becomes more rectangular than square, the two-way action increases and a one-way system spanning the shorter direction develops because the shorter plate strips are stiffer and carry a lesser portion of the load. (1 pt)