Find d/dt [r(t) · u(t)] and d/dt [r(t) × u(t)] in two different ways.
r(t) = ti + 2t2j + t3k, u(t) = t4k

(a) d/dt [r(t) · u(t)]
(i) Find the product first, then differentiate.
(ii) Apply the properties of the derivative.

(b) d/dt [r(t) × u(t)]
(i) Find the product first, then differentiate.
(ii) Apply the properties of the derivative.

The correct choice is c

Answerthe energy required is 1.60 × 10⁻¹⁸ j, to three significant figures.explanationwe define electric potential as the ratio electric potential energy to the charge,    then the following gives us the potential difference,      the formula  may be on your formula sheet.the change in electric potential energy would be the energy that would needed to move it from point a to point b. solving for that, we get    using q = 8.00  × 10⁻¹⁹ c and  δv = 2.00 v, we get    the energy required is 1.60 × 10⁻¹⁸ j, to three significant figures.

C. it comes from the core of the earth.