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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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The experimental probability of an event is the ratio of the number of outcomes that favored the event to the total number of outcomes in the experiment.

In the question, we are given that Jake tossed a paper cup 50 times and recorded the position how it landed, which is shown in the table:

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We are asked to determine the experimental probability of each outcome.

The number of outcomes, when the landing is open-sided up is 1.

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Thus, the experimental probability of each event is as follows:

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