Verify that all members of the family y = (3)1/2 (c - x2)-1/2 are solutions of the differential equation. (b) Find a solution of the initial-value problem. y' = (xy^3)/3 text(, ) y(0) = 3 y(x) =

Can somebody 1. what is the formula for finding the vertical distance between two points on a coordinate plane?

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)

The sum of the speeds of two trains is 720.2 mph. if the speed of the first train is 7.8 mph faster than the second train, find the speeds of each.