Asnowball is melting at a rate of 324π mm3/s. at what rate is the radius decreasing when the volume of the snowball is 972π mm3?

The rate at which the radius of the snowball is decreasing when the volume of the snowball is 972π mm³ is 1mm/s

The snowball in question is spherical in nature. The formula for finding the volume of the snowball is expressed as:

The rate at which the volume is decreasing is expressed as:

Given the following parameters

V = 972π mm³

Get the radius of the ball;

Get the rate at which the radius is decreasing:

Hence the rate at which the radius of the snowball is decreasing when the volume of the snowball is 972π mm³ is 1mm/s

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compass can be used day and night, cloudy or sunny

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.