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Consider the following. r(t) = (9− t)i + (7t − 6)j + 4tk, P(8, 1, 4) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. s(t) = √ 42 (t-1) X Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) 5s 20 (8-) + (+¹) + (+4)** +1 42 √42 42 r(t(s)) = (b) Find the point 5 units along the curve (in the direction of increasing t) from P. 5 5 20 (x, y, z) = nos - (( - ) + ( + 1) + (+4)*) 8 i+ 42 42 42

Consider the following. r(t) = (9− t)i + (7t − 6)j + 4tk, P(8, 1, 4) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. s(t) = √ 42 (t-1) X Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) 5s 20 (8-) + (+¹) + (+4)** +1 42 √42 42 r(t(s)) = (b) Find the point 5 units along the curve (in the direction of increasing t) from P. 5 5 20 (x, y, z) = nos - (( - ) + ( + 1) + (+4)*) 8 i+ 42 42 42

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Consider the following. r(t) = (9 t)i + (7t − 6)j + 4tk, P(8, 1, 4) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. 42 (t-1) X s(t) = Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) S 5s 20 = (8 - √ ₁2 ) + ( + ¹) + ( √2 + 4) k 42 42 42 r(t(s)) (b) Find the point 5 units along the curve (in the direction of increasing t) from P. 5 ( (8 - √5₁2)₁ + ( √√₁2 + ¹) ₁ + ( 4) k × ) 42 42 (x, y, z) = 20 √42 +4k
Transcribed Image Text:Consider the following. r(t) = (9 t)i + (7t − 6)j + 4tk, P(8, 1, 4) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. 42 (t-1) X s(t) = Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) S 5s 20 = (8 - √ ₁2 ) + ( + ¹) + ( √2 + 4) k 42 42 42 r(t(s)) (b) Find the point 5 units along the curve (in the direction of increasing t) from P. 5 ( (8 - √5₁2)₁ + ( √√₁2 + ¹) ₁ + ( 4) k × ) 42 42 (x, y, z) = 20 √42 +4k
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