d Calculate r:(t) - r2(t)] and r:(t) x r2(t)] first by differentiating [ri(t) × r2(t)] first by differentiating dt dt the product directly and then by applying the formulas d [r:(t) · r2(t)] = r1(t) · dr2 dri r2(t) and dt dt dt dr2 dr1 x r2(t). dt d [ri(t) × r2(t)] = r:(t) × dt dt ri(t) = cos(t)i + sin(t)j + 8tk, r2(t) = 7i + tk d [r1(t) · r2(t)] dt d [r(t) x r2(t)] = dt

d Calculate r:(t) - r2(t)] and r:(t) x r2(t)] first by differentiating [ri(t) × r2(t)] first by differentiating dt dt the product directly and then by applying the formulas d [r:(t) · r2(t)] = r1(t) · dr2 dri r2(t) and dt dt dt dr2 dr1 x r2(t). dt d [ri(t) × r2(t)] = r:(t) × dt dt ri(t) = cos(t)i + sin(t)j + 8tk, r2(t) = 7i + tk d [r1(t) · r2(t)] dt d [r(t) x r2(t)] = dt

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 20EQ

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A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.
For T:R5R3 and nullity(T)=2, find rank(T).

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