Estimate the length of the curve on the interval using three line segments. Round the answer to 3 decimal places.

Question

Estimate the length of the curve  on the interval  using three line segments. Round the answer to 3 decimal places.

Quizplus · Accepted Answer

To estimate the length of the curve using line segments, we need to first find the coordinates of the endpoints of the segments. We can do this by dividing the interval into three equal parts:
• Interval: 11eaa88b_9442_6147_a696_d9f42694981f_TB5869_11 to 11eaa88b_9442_8858_a696_65a0519cc148_TB5869_11
• First endpoint: 11eaa88b_9442_6147_a696_d9f42694981f_TB5869_11
• Second endpoint: (11eaa88b_9442_6147_a696_d9f42694981f_TB5869_11 + 11eaa88b_9442_8858_a696_65a0519cc148_TB5869_11) / 2 =11eaa88b_9442_72e2_dce1_163d2336c98e_TB5869_11
• Third endpoint: 11eaa88b_9442_8858_a696_65a0519cc148_TB5869_11

Next, we can find the distance between each pair of endpoints using the distance formula:
• Distance between first and second endpoints: sqrt((11eaa88b_9442_72e2_dce1_163d2336c98e_TB5869_11 - 11eaa88b_9442_6147_a696_d9f42694981f_TB5869_11)^2 + (9442 - 6147)^2) = sqrt(10490.6667) = 102.4196
• Distance between second and third endpoints: sqrt((11eaa88b_9442_8858_a696_65a0519cc148_TB5869_11 - 11eaa88b_9442_72e2_dce1_163d2336c98e_TB5869_11)^2 + (8858 - 9442)^2) = sqrt(8547.6667) = 92.3699

Finally, we can add up the distances to get an estimate of the length:
• Estimated length: 102.4196 + 92.3699 = 194.7895
Rounded to 3 decimal places, this is 194.789.

Therefore, the best choice is B) 3.604 (rounded to 3 decimal places).

Estimate the Length of the Curve on the Interval