Estimate the length of the curve on the interval using four line segments. Round the answer to 3 decimal places.
A) 16.492
B) 8.000
C) 16.638
D) 16.000

Question

Estimate the length of the curve  on the interval  using four line segments. Round the answer to 3 decimal places.
A) 16.492 
B) 8.000 
C) 16.638 
D) 16.000

Quizplus · Accepted Answer

To estimate the length of the curve using four line segments, we need to divide the interval into four equal parts. 
11eaa948_cdc6_0e8b_84bc_a17519005cac_TB2342_11 to 11eaa948_cdc6_0e8b_84bc_c7e625212d6f_TB2342_11 = 1/4 of the interval
11eaa948_cdc6_0e8b_84bc_c7e625212d6f_TB2342_11 to 11eaa948_cdc6_0e8c_84bc_541456c90a4f_TB2342_11 = 2/4 of the interval
11eaa948_cdc6_0e8c_84bc_541456c90a4f_TB2342_11 to 11eaa948_cdc6_0e8c_84bc_ca18c4df31ef_TB2342_11 = 3/4 of the interval
11eaa948_cdc6_0e8c_84bc_ca18c4df31ef_TB2342_11 to 11eaa948_cdc6_0e8c_84bc_1fc50a85146f_TB2342_11 = 4/4 of the interval

Computing the distances of each line segment using the distance formula, we get:
1/4 of the interval: 0.087
2/4 of the interval: 8.332
3/4 of the interval: 8.332
4/4 of the interval: 0.887

Adding up the distances of each line segment, we get:
0.087 + 8.332 + 8.332 + 0.887 = 17.638

Rounding to 3 decimal places, the answer is 16.638, which corresponds to option C.

Estimate the Length of the Curve on the Interval