Power p is the rate at which energy e is consumed per unit time. ornithologists have found that the power consumed by a certain pigeon flying at velocity v m/s is described well by the function p(v)=16v−1+10−3v3 j/s. assume that the pigeon can store 5×104 j of usable energy as body fat. find the velocity vp min that minimizes power consumption. (use decimal notation. give your answer to two decimal places.)

Explanation:

P(v) = 16 / v + 10⁻³ v³

differentiating on both sides

dP / dt = - 16 / v² + 3 x 10⁻³ v²

For maxima and minima , the condition is

dP / dt = - 16 / v² + 3 x 10⁻³ v²  = 0

v² = 160 / 3 x 10²

v² = 73 m/s

v = 8.54 m /s

To know the condition of minima

again differentiating

d²P / dt² = - 16 x -2 / v² + 6 x 10⁻³ x v

= 32 / v³ + 6 x 10⁻³ x v

= + ve quantity

So at v_p =  8.54 m /s , power consumption will be minimum .

c.is a substance that requires a small amount of energy per gram to raise its temperature; has strong cohesive forces between molecules.

explanation:

a colorless, transparent, odorless liquid that forms the seas, lakes, rivers, and rain and is the basis of the fluids of living organisms.

a lot of it means it can be "burned" for energy and sold at one price. if it is scarce, the price will go up