Two boys searching for buried treasure are standing underneath the same tree. one boy walks 18m east and then 18m north. the other boy walks 16m west and then 11m north. what is the scalar product of their net displacements from the ree?

Amachine, modeled as a simple spring-mass system, oscillates in simple harmonic motion. its acceleration is measured to have an amplitude of 5,000 mm/s with a fre- quency of 10 hz. compute the maximum displacement the machine undergoes during this oscillation.

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Under conditions for which the same room temperature is maintained by a heating or cooling system, it is not uncommon for a person to feel chilled in the winter but comfortable in the summer. provide a plausible explanation for this situation (with supporting calculations) by considering a room whose air temperature is maintained at 20â°c throughout the year, while the walls of the room are nominally at 27â°c and 14â°c in the summer and winter, respectively. the exposed surface of a person in the room may be assumed to be at a temperature of 32â°c throughout the year and to have an emissivity of 0.90. the coefficient associated with heat transfer by natural convection between the person and the room air is approximately 2 w/m2 â‹…â‹… k. what is the ratio of the thermal resistance due to convection to the thermal resistance due to radiation in the summer? what is the ratio of thermal resistances in the winter