Verify that ϕ(x)=2(1−cex), where cis an arbitrary constant, is a one-parameter family of solutions to dydx=y(y−2)2.Graph the solution curves corresponding to c=0,±1,±2using the same coordinate axes.

Both the red and blue line segments stretch from the center of the circle to a point on the circle. the length of the blue segment is 5. how long is the red line segment?

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions: y < 4x − 8 y is greater than or equal to negative 5 over 2 times x plus 5 part a: describe the graph of the system, including shading and the types of lines graphed. provide a description of the solution area. (6 points) part b: is the point (5, −8) included in the solution area for the system? justify your answer mathematically. (4 points)

Which property was used to simplify the expression? 3c+9 +4c=3c+4c+9