Consider the system x' = rx + x3 - x5, which exhibits a pitchfork bifurcation.

a. Find the algebraic expressions for all teh fixed points as r varies

b. Sketch the vector fields as r varies. Be sure to indicate all the fixed points and their stability

c. Calculate rs, the parameter value at whcih the nonzero fixed points are born in a saddle-node bifurcation

Geometry answer picture question pls . reason and statements

Drag the tiles to the correct boxes to complete the pairs. match the cart-coordinates with their corresponding pairs of y-coordinates of the unit circle

Researchers were interested in whether relaxation training decreases the number of headaches a person experiences. they randomly assigned 20 participants to a control group or a relaxation training group and noted the change in number of headaches each group reported from the week before training to the week after training. which statistical analysis should be performed to answer the researchers' question?