In lab 2 we consider the van der Pol equation, x 00 + µ(x 2 − 1)x 0 + x = 0. (a) Show that at the critical point x = 0, the linearized system is that given in the lab, x 0 = y, y 0 = −x + µy. (b) Solve the system for µ = 0, µ = 0.1, and µ = 3. (c) For each of these, sketch, by hand, the phase portraits for the system. Be careful to note how they differ.

Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. the punch has 2 liters of ginger ale. part a: write an equation using one variable that can be used to find the total number of liters of cranberry juice and ginger ale in the punch. define the variable used in the equation and solve the equation. hint: 0.8x represents the number of liters of cranberry juice in the punch. (5 points) part b: how many liters of cranberry juice are present in the punch? show your work.

Does the problem involve permutations or? combinations? do not solve. the matching section of an exam has 4 questions and 7 possible answers. in how many different ways can a student answer the 4 ? questions, if none of the answer choices can be? repeated?

What are the equivalent ratios for 24/2= /3= /5.5=108/ = /15