Two spheres are cut from a certain uniform rock. one has radius 4.10 cm. the mass of the other is eight times greater.

8.2 cm

Explanation:

mass of one sphere = m

mass of other sphere = 8 m

Radius of first sphere = r = 4.10 cm

let the radius of another sphere is R

As we know that mass = volume x density

Let the density of the rock is d.

density of rock remains same.

density of small sphere = density of big sphere

mass of small sphere / volume of small sphere =

mass of big sphere / volume of big sphere

R = 2 r

R = 2 x 4.10 = 8.2 cm

Thus, the radius of big sphere is 8.20 cm.  

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

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.