(3) \( P=\frac{N+2}{D} \) (4) \( A=P+\frac{P R T}{100} \) (5) \( v^{2}=u^{2}+2 a s \) (6) \( s=\frac{n}{2}(a+l) \) (7) \( S=2 \pi r(r+h) \) (8) \( k=\frac{b r t}{v-b} \) (9) \( S=4 \pi r^{2} \) (18) \( V=\pi h^{2}\left(r-\frac{h}{3}\right) \) (11) \( L=\frac{W h}{a(W+P)} \) (12) \( \frac{L}{E}=\frac{2 a}{R-r} \) (17) \( T=\frac{m u^{2}}{K}-5 m g \) (14) \( D=\frac{\overline{3 h}}{2} \) (1p) \( t=\frac{3 p}{r}+s \) (1) \( \frac{a}{p}-\frac{b}{q}=c \) \[ H=\frac{m\left(v^{2}-u^{2}\right)}{2 g x} \]

Did you know? Many of the equations listed above have deep roots in physics and mathematics, tracing back to the early researchers and scientists. For instance, the equations of motion that describe \( v^{2} = u^{2} + 2as \) were formulated by Galileo in the 16th century and later refined by Newton. These fundamentals set the groundwork for modern kinematics and allow us to predict how objects move under various forces, which is a cornerstone of both physics and engineering! In real life, these equations aren't just ink on paper; they have incredible applications! For example, the formula \( S = 2 \pi r(r + h) \) for surface area applies to everyday objects, like designing a soda can or calculating paint needed for a cylindrical wall. Understanding these formulas empowers architects, engineers, and even graphic designers to create efficient designs that prevent wastage and improve functionality, transforming theoretical knowledge into practical applications!