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Consider the following. r(t) = (5 t)i + (6t - 5)j + 7tk, P(4, 1, 7) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. s(t)=√86 (t-1) Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) s(t) s(t) 6s(t) √86 √86 r(t(s)) = 4- 86 (x, y, z) = i+ 11 + +71 + X (b) Find the point 4 units along the curve (in the direction of increasing t) from P. 4 -( (4- √ 86 )₁ + ( 11 + 24 4 286 )₁ +7(1 + √56)* ) k √86 86

Consider the following. r(t) = (5 t)i + (6t - 5)j + 7tk, P(4, 1, 7) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. s(t)=√86 (t-1) Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) s(t) s(t) 6s(t) √86 √86 r(t(s)) = 4- 86 (x, y, z) = i+ 11 + +71 + X (b) Find the point 4 units along the curve (in the direction of increasing t) from P. 4 -( (4- √ 86 )₁ + ( 11 + 24 4 286 )₁ +7(1 + √56)* ) k √86 86

Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Conic Sections
Section8.2: More Parabolas And Some Circles
Problem 63.1PS
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Consider the following. r(t) = (5 t)i + (6t - 5)j + 7tk, P(4, 1, 7) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. √86 (t-1) s(t) = Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) S r(t(s)): - = - s(t) √86 i+ 11 + 6s(t) √86 j+71+ s(t) √86 k X (b) Find the point 4 units along the curve (in the direction of increasing t) from P. 4 24 4 (x, y, z) > -( (1 - √ ²56 )¹ + (11 + 355 )³ + 7 (¹ + √5) * 4- 1 k √86 86
Transcribed Image Text:Consider the following. r(t) = (5 t)i + (6t - 5)j + 7tk, P(4, 1, 7) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. √86 (t-1) s(t) = Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) S r(t(s)): - = - s(t) √86 i+ 11 + 6s(t) √86 j+71+ s(t) √86 k X (b) Find the point 4 units along the curve (in the direction of increasing t) from P. 4 24 4 (x, y, z) > -( (1 - √ ²56 )¹ + (11 + 355 )³ + 7 (¹ + √5) * 4- 1 k √86 86
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