To solve this problem it is necessary to apply the concepts related to intensity as a function of power and area.
Intensity is defined to be the power per unit area carried by a wave. Power is the rate at which energy is transferred by the wave. In equation form, intensity I is

The area of a sphere is given by

So replacing we have to

Since the question tells us to find the proportion when

So considering the two intensities we have to


The ratio between the two intensities would be

The power does not change therefore it remains constant, which allows summarizing the expression to

Re-arrange to find 



Therefore the intensity at five times this distance from the source is 
Answer:
The radius of the gold nucleus is 7.1x10⁻¹⁵m
Explanation:
The nearest distance is:
(eq. 1)
Where
z = atomic number of gold = 79
e = electron charge = 1.6x10⁻¹⁹C
k = electrostatic constant = 9x10⁹Nm²C²
energy of the particle = 32 MeV = 5.12x10⁻¹²J
At the potential energy is zero, all the energy will be kinetic energy:

Where
m = 4 mp = mass of proton

Replacing in equation 1

Imagine an object is moving in one dimension on a number line, and for this we'll say that the numbers on the line are a metre apart. If the object moves from 2 m to 7 m, the change in position is 7-2=+5 metres. But if the object moves back from 7 m to 2 m, the change in position is 2-7=-5 metres. since

, and time is always positive, velocity will be positive in one direction and negative in the other direction.
Answer:
The temperature is 90.4°C
Explanation:
See the attached for explanation