Final answer:
The length of the curve can be found using the arc length formula and the integral of the derivatives of the x, y, and z components of the curve.
Step-by-step explanation:
The length of a curve can be found using the arc length formula. In this case, the curve is defined by the function r(t) = 5t, 3 cos(t), 3 sin(t). To find the length of the curve, we need to use an integral.
Using the arc length formula, the length of the curve can be found by evaluating the integral of the square root of the sum of the squares of the derivatives of the x, y, and z components of the curve. In this case, the integral would be:
L = ∫√(25 + 9 cos²(t) + 9 sin²(t)) dt This integral can be evaluated using various integration techniques, such as substitution or integration by parts, to find the length of the curve.