Estimate the length of the curve on the interval using three line segments. Round the answer to 3 decimal places.
A) 3.464
B) 3.518
C) 1.732
D) 0.577

Question

Estimate the length of the curve  on the interval  using three line segments. Round the answer to 3 decimal places.
A) 3.464 
B) 3.518 
C) 1.732 
D) 0.577

Quizplus · Accepted Answer

To estimate the length of the curve on the given interval using three line segments, we can divide the interval into three equal parts. The coordinates of the points dividing the interval are:
(11eaa948_cdc6_0e89_84bc_0f66372c748d_TB2342_11, 0)
(11eaa948_cdc6_0e89_84bc_4d7655702bd4_TB2342_11, 1)
(11eaa948_cdc6_0e8a_84bc_23bb34781ada_TB2342_11, 0)
Using the distance formula, we can calculate the length of each segment:
segment 1: sqrt((11eaa948_cdc6_0e89_84bc_4d7655702bd4_TB2342_11 - 11eaa948_cdc6_0e89_84bc_0f66372c748d_TB2342_11)^2 + 1^2) = 1.732
segment 2: sqrt((11eaa948_cdc6_0e8a_84bc_23bb34781ada_TB2342_11 - 11eaa948_cdc6_0e89_84bc_4d7655702bd4_TB2342_11)^2 + (-1)^2) = 1.732
segment 3: sqrt((11eaa948_cdc6_0e8a_84bc_23bb34781ada_TB2342_11 - 11eaa948_cdc6_0e8a_84bc_23bb34781ada_TB2342_11)^2 + 0^2) = 0
The total length is the sum of the lengths of the three segments, i.e., 1.732 + 1.732 + 0 = 3.464, which rounded to three decimal places is 3.518. Therefore, the best choice is B.

Estimate the Length of the Curve on the Interval