Explain how to find the length of the curve. Question list K r(t) = (f(t), g(t), h(t)>, for a stsb. Question 1 O A. L = 1 f(t) 2 + g(1) 2 + h(1)2 at Question 2 a b OB. L= 12(f' (1)2 + g' (1)2 + h" (1)2) at Question 3 a OC. L= VF' (t ) + g'(t ) + h'(t ) dt Question 4 b Question 5 OD. L = / F' (1)2 + g' (1)2 + h' (1)? at aFind the length of the following two-dimensional curve. Question list K r(t) = (6 cost + 6t sin t,6 sint - 6t cost) , for 0sts Question 1 L = O Question 2 (Type an exact answer, using it as needed.) Question 3 Question 4 Question 5Find the length of the following three-dimensional curve. Question list K r(t) = (sin t, cost, 61) , for 0 sts 5 Question 1 L= (Type an exact answer, using radicals as needed.) O Question 2 Question 3 O Question 4 Question 5Find the length of the following two-dimensional curve. Question list K r(t) = (3 cost,3 sint) , for 0 sts I Question 1 Set-up the integral that gives the arc length. Question 2 L= dt Question 3 (Type exact answers.) Question 4 O Question 5Homework: Section 14.4 Question 9, 14.4.45 HW Score: 0%, 0 of 10 points th E Homework Part 1 of 14 Points: 0 of 1 Save Let the curve C be described by r(t) = (a cost, b sint, c sin t), where a, b, and c are real positive numbers. Question list K a. Assume that C lies in a plane and show that C is a circle centered at the origin provided a =b+ c. b. Find the arc length of the circle. c. Assuming that the curve lies in a plane, find the conditions under which Question 6 r(t) = (a cost+ b sint, c cost + d sint, fcost + g sint) describes a circle. Then find its arc length. Question 7 a. It is given that C lies in a plane and a = b + c . For C to be a circle centered at the origin, what must be true? O A. The sum of the components of r(t) must equal the radius. Question 8 O B. The sum of the components of r(t) squared must equal the square of the radius. O C. The sum of the squares of the components of r(t) must equal the radius. Question 9 O D. The sum of the squares of the components of r(t) must equal the square of the radius O Media 1Question list K Use a calculator to approximate the length of the following curve. Simplify the arc length integral as much as possible before finding an approximation. Write the arc length integral and simplify as much as possible. Choose the correct answer below. Question 6 2 O A. L= 1412 (12 + 121) dt 0 Question 7 2 OB. L=2 (12 + 11) at Question 8 0 N O C. L = 2 tv+ + 121 dt Question 9 0 O D. L = t# + 125 dt O Media 1 nFind the length of the following two-dimensional curve. Question list K 12 ( 2t + 1 )" 3/2 r(t) = 2 ' for 0 sts 18 3 Question 3 O Question 4 L = (Type an exact answer, using radicals as needed.) Question 5 O Question 6 Question 7K For the following trajectory, find the speed associated with the trajectory and then find the length of the trajectory on Question list the given interval. r(1) = (413, -13, 713 ), for Ost57 O Question 3 The speed associated with the trajectory is O Question 4 (Type an exact answer, using radicals as needed.) Question 5 O Question 6 Question 7For the following trajectory, find the speed associated with the trajectory and then find the length of the trajectory on Question list K the given interval. - - - -.. . .. r(t) = (5e sint, 5 e ' cost, 5e ), for 0 sts In 2 Question 6 The speed associated with the trajectory is (Type an exact answer, using radicals as needed.) Question 7 Question 8 Question 9 Media 1