Final answer:
The equation of the transformed function with a period of 10π is V = tan(0.1x). The horizontal stretch of the tangent function is achieved by dividing the input variable by the stretch factor.
Step-by-step explanation:
The graph of the function V = tan(x) has a period of π, which means it repeats every π units along the x-axis. When the function is horizontally stretched so that its period becomes 10π, we are effectively stretching the graph by a factor of 10 along the x-axis. To achieve this horizontal stretch, we need to divide the variable inside the tangent function by the stretch factor, which gives us the transformed function V = tan(0.1x). This is because the period of the tangent function is given by π/b where y = tan(bx), and in order for the period to be 10π, we solve for b in 10π = π/b, yielding b = 0.1.