How much greater is the light-collecting area of a 6-meter telescope than a 3-meter telescope? how much greater is the light-collecting area of a 6- telescope than a 3- telescope? two times four times six times

Four times

Explanation:

The amount of light collected by a telescope is proportional to the area of the telescope:

However, the area of the telescope is given by

where R is the radius. This means that the amount of light collected is proportional to the square of the radius of the telescope:

(a similar argument is valid for the diameter, since radius and diameter are proportional to each other).

In the example, the radius of the 2nd telescope is twice (6 m) as the radius of the first telescope (3 m): this means that the amount of light collected will increase by a factor of

So, by a factor 4.

a longitudinal wave moves energy that is to the direction of the wave’s movement. - true