Final answer:
The value of c for the equations 25x² - c² and y = c² - 25x², with an area of 512/15 cannot be determined directly without further context or steps that relate to the integral and area calculation of the functions.
Step-by-step explanation:
The student is asking to find the value of c for the equations 25x² - c² and y = c² - 25x², given that the area for the region is 512/15. The value of c in this context represents a constant in the equation of the parabola, and by finding the area between this parabola and the x-axis, we are effectively determining the integral of the absolute value of the function or the difference between the two functions.
To solve for c, we would integrate the function, equate it to the area given (512/15), and solve for c. However, based on the information provided, there isn't enough clear context to directly solve for c without additional steps or missing information that would normally be included in the area calculation for the given functions.