Given:
distance from the projector lens to the image, di
projector lens focal length, f
distance from the transparency to the projector lens, do
thin lens equation: 1/f = 1/di + 1/do
do = 4 inches
di = 8 feet
convert feet to inches, for uniformity.
1 foot = 12 inches
8 feet * 12 inches/ft = 96 inches
1/f = 1/96 inches + 1/4 inches
Adding fractions, denominator must be the same.
1/f = (1/96 * 1/1) + (1/4 * 24/24)
1/f = 1/96 + 24/96
1/f = 25/96
to find the value of f, do cross multiplication
1*96 = f * 25
96 = 25f
96/25 = f
3.84 = f
The focal length of the project lens is 3.84 inches
Explanation:
Given
initial velocity(v_0)=1.72 m/s

using 
Where v=final velocity (Here v=0)
u=initial velocity(1.72 m/s)
a=acceleration 
s=distance traveled

s=0.214 m
(b)time taken to travel 0.214 m
v=u+at


t=0.249 s
(c)Speed of the block at bottom

Here u=0 as it started coming downward

v=1.72 m/s
To solve the exercise it is necessary to keep in mind the concepts about the ideal gas equation and the volume in the cube.
However, for this case the Boyle equation will not be used, but the one that corresponds to the Boltzmann equation for ideal gas, in this way it is understood that

Where,
N = Number of molecules
k = Boltzmann constant
V = Volume
T = Temperature
P = Pressure
Our values are given as,




Rearrange the equation to find V we have,



We know that length of a cube is given by

Therefore the Length would be given as,



Therefore each length of the cube is 3.44nm
11.3 Electromagnetic spectrum (ESADK)
EM radiation is classified into types according to the frequency of the wave: these types include, in order of increasing frequency, radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.