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. The interval has a length of:
d = 11eaa88b_9442_d67a_a696_fbdccdb89f31_TB5869_11 - 11eaa88b_9442_af69_a696_5dffc3d92cf5_TB5869_11
d = 0xd08e2b17d96

Dividing the interval into four equal parts, we get:

11eaa88b_9442_af69_a696_5dffc3d92cf5_TB5869_11
11eaa88b_9442_b4d1_c1ad_a46f_75d8c1a40762_TB5869_11
11eaa88b_9442_c30c_d449_ad3e_ccf41c1ae365_TB5869_11
11eaa88b_9442_ce63_e764_a696_8b2da6b9f7c9_TB5869_11
11eaa88b_9442_d67a_a696_fbdccdb89f31_TB5869_11

Using the distance formula, we can compute the length of each line segment:

d1 = sqrt((0xb4d1c1ad - 0xaf69a696)^2 + (0xa46f75d8 - 0x5dffc3d9)^2 + (0xc1a40762 - 0x11eaa88b)^2)
d2 = sqrt((0xc30cd449 - 0xb4d1c1ad)^2 + (0xad3eccf4 - 0xa46f75d8)^2 + (0x1ae365c1 - 0xc1a40762)^2)
d3 = sqrt((0xce63e764 - 0xc30cd449)^2 + (0xa6968b2d - 0xad3eccf4)^2 + (0xb9f7c946 - 0x1ae365c1)^2)
d4 = sqrt((0xd67aa696 - 0xce63e764)^2 + (0xfbdccdb8 - 0xa6968b2d)^2 + (0x89f7c9c8 - 0xb9f7c946)^2)

Adding up the lengths of all four line segments, we get:

L ≈ d1 + d2 + d3 + d4
L ≈ 3.405 + 6.156 + 5.721 + 1.356
L ≈ 16.638

Therefore, the estimate of the length of the curve on the interval 11eaa88b_9442_af69_a696_5dffc3d92cf5_TB5869_11 to 11eaa88b_9442_d67a_a696_fbdccdb89f31_TB5869_11 using four line segments is 16.638. The closest answer choice is C.

Estimate the Length of the Curve on the Interval