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maks197457 [2]
3 years ago
13

Let r(t)=⟨t2,1−t,4t⟩. calculate the derivative of r(t)⋅a(t) at t=5, assuming that a(5)=⟨−4,4,−5⟩ and a′(5)=⟨−5,9,3⟩

Mathematics
1 answer:
erastovalidia [21]3 years ago
6 0
\mathbf r(t)=\langle t^2,1-t,4t\rangle
\implies\mathbf r'(t)=\langle 2t,-1,4\rangle

\dfrac{\mathrm d(\mathbf r(t)\cdot\mathbf a(t))}{\mathrm dt}\bigg|_{t=5}=\mathbf r'(5)\cdot\mathbf a(5)+\mathbf r(5)\cdot\mathbf a'(5)
=\langle10,-1,4\rangle\cdot\langle-4,4,-5\rangle+\langle25,-4,20\rangle\cdot\langle-5,9,3\rangle
=(-40-4-20)+(-125-36+60)
=-165
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