Consider the following word problem. define a variable, write a function to be optimized and use calculus to find the extrema an art lover is looking at a painting that is 6 feet high and hanging on a wall so that the bottom of the painting is 2 feet above her eye level. how far from the painting should she stand so that the angle subtended at her eye by painting is as large as possible

Which of the following describes something an engineer would probably do first when developing new technology meant to reduce ocean pollution? o a. evaluate the benefits and challenges of using certain chemicals to purify water. o b. research new scientific findings in regard to ocean cleanup. o c. identify the need to reduce ocean pollution. o d. research what has been done in the past to clean up oceanic oil residue.

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 710 n/m. it is initially at rest on an inclined plane that is at an angle of θ = 23° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. a) what is the block's initial mechanical energy? b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

Which of the following correctly describes what happens when an atomic bomb explodes? small pieces of fissionable material are joined and form a body with a mass greater than the critical mass, the relative number of neutrons escaping decreases, and a chain reaction and explosion result. large pieces of fissionable matter are brought together quickly and form a body with a mass smaller than the critical mass, the relative number of escaping neutrons increases, and a chain reaction and explosion result.