Final answer:
To find the arc length of the curve x = 15t, y = 8t - 6, we use the arc length formula and evaluate the integral.
Step-by-step explanation:
The curve is given by the equations x = 15t and y = 8t - 6. To find the arc length of the curve on the given interval, we need to use the arc length formula. The arc length formula is given by:
s = ∫ √(dx/dt)² + (dy/dt)² dt
Substituting the given equations into the formula, we have:
s = ∫ √(15)² + (8)² dt
s = ∫ √225 + 64 dt
s = ∫ √289 dt
s = ∫ 17 dt
s = 17t + C
To find the arc length on the interval from t = 0 to t = T, we evaluate the integral at the given limits:
s = 17T - 17(0)
s = 17T