A. 4 cm behind the mirror
<span> For any mirror, </span><span><span>so</span><span>si</span>=<span>f^2</span></span>. Therefore, by plugging in the values, you get <span>18<span>si</span>=144. 144/18 = 8, so </span><span><span>si</span>=8</span>
<span> The focal point is located 12 cm from the mirror, and </span><span>si</span><span> is the distance of the image from the focal point, so the image is 4 cm from the mirror. The mirror is convex, so then the focal point and the image are both behind the mirror.</span>
If we are talking on the force being exerted by a segment of a rope of lenght R on the right on a point M which is being also pulled from the Left by a segment of rope R as shown in the figure attached. Then we invoke Newton's Third Law:
"Any force exerted by an object (in this case a segment of the rope) also suffers a equal and opposite force".
If we pick

whis is the tension exerted by the right segment then the left segment will also exert an equal and opposite force so we have that
To solve the problem it is necessary to apply the concepts related to the conservation of energy through the heat transferred and the work done, as well as through the calculation of entropy due to heat and temperatra.
By definition we know that the change in entropy is given by

Where,
Q = Heat transfer
T = Temperature
On the other hand we know that by conserving energy the work done in a system is equal to the change in heat transferred, that is

According to the data given we have to,




PART A) The total change in entropy, would be given by the changes that exist in the source and sink, that is



On the other hand,



The total change of entropy would be,



Since
the heat engine is not reversible.
PART B)
Work done by heat engine is given by



Therefore the work in the system is 100000Btu
I don’t know what the angle is in your diagram so I used the angle from the vertical.