The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. if two light sources, one four times as strong as the other, are placed 14 ft apart, how far away from the stronger light source should an object be placed on the line between the two sources so as to receive the least illumination? (round your answer to two decimal places.)

from the weaker source

Explanation:

The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source:

  first source

  second source (stronger)

If the illumination is the same for the two sources:

We solve to find d:

from the weaker source

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards