Approximately how many asteroids that are 0.98 km in radius would it take to make a planet which has a radius of 6420.0 km

It'd take approximately 6543 asteroids.

Explanation:

In order to calculate the number of asteroids needed to make that planet we first need to determine the volume of each object. To do this we will consider them as spheres and apply the appropriate formula:

The number of asteroids needed are given by the division of planet's volume by the asteroid's volume.

It'd take approximately 6543 asteroids.

the first american roller coaster was the mauch chunk switchback railway, built in the mountains of pennsylvania in the mid-1800s. the track, originally built to send coal to a railway, was reconfigured as a "scenic tour."

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.