You are mixing water with ice in an insulated container. The temperature of the ice is initially below its freezing point. The following are given:

the amount of heat absorbed by the ice if heated to its melting point: 6400 J,
the amount of heat absorbed by the ice if it all melts (which includes the heat needed to bring the ice to its melting point): 14,100 J,
the amount of heat given off by the water if cooled to its freezing point: 1800 J, and
the amount of heat given off by the water if it all freezes (which includes the heat needed to bring the water to its freezing point): 5200 J .
Based on this information, at equilibrium, which phases are present?

You are mixing water with ice in an insulated container. The temperature of the ice is initially below its freezing point. The following are given:

the amount of heat absorbed by the ice if heated to its melting point: 6400 ,
the amount of heat absorbed by the ice if it all melts (which includes the heat needed to bring the ice to its melting point): 14,100 ,
the amount of heat given off by the water if cooled to its freezing point: 1800 , and
the amount of heat given off by the water if it all freezes (which includes the heat needed to bring the water to its freezing point): 5200 .
Based on this information, at equilibrium, which phases are present?

ice only
water only
both ice and water

Explanation:

According to the given information ; Heat needed by to come to melting point = 6400J

Heat given by water to come to 0 degree celsius = 5200J

Since 6400J is more than 5200 J , as such the ice will nit completel melt. and also, the amount of heat released by water is not enough to melt the ice, it implies that the ice will still remain since 6400J > 5200J, therefore both ice and water will still remain at equilibrium.

i'm on my way to history not a mistory.

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.