As part of their end-of-semester project, students in a science class are asked to devise a temperature scale. The diagram below shows the work of two of the students, Paul and Simon. \( P_1 = +14.0^\circ P \) and \( P_2 = +125^\circ P \) correspond to the melting point of ice and boiling point of water respectively on the Paul scale, while \( S_1 = -9.0^\circ S \) and \( S_2 = +75.0^\circ S \) correspond to the melting point of ice and boiling point of water on the Simon scale. Assume that each division represents a degree on both scales.**Diagram:**- Two thermometers are shown side by side labeled "Paul" and "Simon."- The Paul scale has \( P_1 \) at the melting point and \( P_2 \) at the boiling point.- The Simon scale has \( S_1 \) at the melting point and \( S_2 \) at the boiling point.- Both scales show equal divisions from melting to boiling points.**Questions:**(a) **How many degrees on the Simon scale correspond to \( 1^\circ P \) on the Paul scale?** - \( 1^\circ P = 0.75 \) \( \circ S \)(b) **If a particular temperature measurement reads \( +50.0^\circ P \) on the Paul scale, what would this same temperature measurement read on the Simon scale?** - \( T_S = 37.8 \) **Additional Question:**- Are the numerical values of the melting point of ice the same on the two scales? \( \circ S \)

(a) Equate the interval between melting and boiling point 125°P-14.0°P=75.0°S--9.00°S111°P=84°S1°P=84°S111=0.756°SEquate the segment ratios in both scales to find a relation between two scales P-P1P2-P1=S-S1S2-S1P-14.0°P125°P-14.0°P=S--9.00°S75.0°S--9.00°SS+9°S=P-1411184°SS=P-1411184°S-9°S(b) Substitution S=50.0-1411184°S-9°S=18.24°S≈18.2°S