The maximum flow rate of a standard shower head is about 3.4 gpm (12.9 l/min) and can be reduced to 2.75 gpm (10.5 l/min) by switching to a low-flow shower head that is equipped with flow controllers. consider a family of four with each person taking a 6-minute shower every morning. city water at 15°c is heated to 55°c in an oil water heater whose efficiency is 65 percent and then tempered to 42°c by cold water at the t-elbow of the shower before being routed to the shower head. the price of heating oil is $2.80/gal and its heating value is 146,300 kj/gal. assuming a constant specific heat of 4.18 kj/kg·°c for water, determine the amount of oil and money saved per year by replacing the standard shower heads by the low-flow ones. (round the final answers to one decimal place.)

newton's first law of motion

d. air pressure decreases as altitude increases.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.