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 force will determine the acceleration.

How do the measurements of charge at the different locations on the sphere compare to each other? the charge measurements are different at all locations on the sphere. the charge measurements are virtually not the same at all locations on the sphere except for the charge at the very top and at the very bottom that are equal. the charge measurements are virtually the same at all locations on the sphere except for the charge at the very top. at the top, the conductive sphere has a small disk that is made of different material. the charge measurements are the same at all locations on the sphere. what happens to the charge on the conductive sphere when it is connected to a source of charge such as the electrostatic voltage source? nothing will happen because no charge goes around the surface of the sphere. the charge on the conductive sphere spreads out over the surface of the sphere; being greater in some specific locations on the sphere. the charge on the conductive sphere spreads out uniformly over the surface of the sphere. the charge on the conductive sphere spreads out non-uniformly over the surface of the sphere.

Classify each possible hypothesis about a medicinal aloe vera plant as falsifiable or non-falsifiable. aloe vera gel is the best natural skin moisturizer. aloe vera gel can heal wounds by boosting cell renewal. aloe vera juice tastes better than carrot juice. drinking aloe juice can reduce the risk of lung cancer.