Consider the function f (x comma y comma z )equals4 x squared plus 3 y squared plus 3 z squared plus 3, the point p(1 comma 0 comma 3 ), and the unit vector bold uequalsleft angle negative startfraction 1 over startroot 2 endroot endfraction comma 0 comma negative startfraction 1 over startroot 2 endroot endfraction right angle . a. compute the gradient of f and evaluate it at p. b. find the unit vector in the direction of maximum increase of f at p. c. find the rate of change of the function in the direction of maximum increase at p. d. find the directional derivative at p in the direction of the given vector.

Using the given data table, calculate the acceleration of the skateboarder. you can use either form of the equation below?

Which articulations allow for greatest range of motion?

When temperature of a substance increases, of its particles increase resulting in more between particles. real world applications of thermal expansion absolute zero (-273 degrees c) is the lowest possible temperature on the kelvin scale. it is a measure of where a substance has no kinetic energy. heat is a process of the . energy flows spontaneously from a object to a until equilibrium is reached. heat is measured in heat is transferred throughis a method of heat transfer that occurs between particles of matter that are in direct contact with each other. are poor conductors that impede / reduce the rate of heat transfer. is a method of heat transfer that occurs in fluids (non-solids) by means of currents. real world application of convectiona method of heat transfer through electromagnetic waves. when energy moves from one object to another inside a closed system, no energy is or in the system in the transaction. systems will spontaneously move to a state of organized energy or high disorder over time called