Final answer:
To find the value of c when x = 17, we need to integrate the given function and then use a specific value of x to solve for the integration constant C. Without additional information or a boundary condition, we cannot find the exact value of C.
Step-by-step explanation:
To find the value of c when x = 17 in the equation dc/dx = (16/3) * (16x/9), we need to integrate the function dc/dx with respect to x.
Firstly, let's integrate the right-hand side of the equation: ∫(16/3) * (16x/9) dx. Simplifying the constants gives us (256/27) ∫ x dx, which upon integration provides us with (256/27) * (x^2/2) + C, where C is the integration constant.
Now, to solve for C, we need a boundary condition or additional information about the value of c when x is a specific value. If no such condition is provided, we cannot determine the exact numerical value of C; we can only express c as a function of x with an unknown constant.
Based on the information given, it seems that some important details might be missing for the exact computation. If additional information is provided, such as the initial condition, then we could substitute x = 17 to find c.