$$100^2sin\dfrac{4p\dfrac{i}{7}}{2}\cdot100=\dfrac{4000000i^2nps}{14}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}100^2sin\frac{4p\frac{i}{7}}{2}\cdot100& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10000sin\frac{4p\frac{i}{7}}{2}\cdot100 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10000sin\frac{\frac{4ip}{7}}{2}\cdot100 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10000sin\frac{4ip}{14}\cdot100 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{40000i^2nps}{14}\cdot100 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{4000000i^2nps}{14}\end{aligned} $$ | |
| ① | i-i=0i |
| ② | Multiply $4p$ by $ \dfrac{i}{7} $ to get $ \dfrac{ 4ip }{ 7 } $. Step 1: Write $ 4p $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 4p \cdot \frac{i}{7} & \xlongequal{\text{Step 1}} \frac{4p}{\color{red}{1}} \cdot \frac{i}{7} \xlongequal{\text{Step 2}} \frac{ 4p \cdot i }{ 1 \cdot 7 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4ip }{ 7 } \end{aligned} $$ |
| ③ | Divide $ \dfrac{4ip}{7} $ by $ 2 $ to get $ \dfrac{ 4ip }{ 14 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{4ip}{7} }{2} & \xlongequal{\text{Step 1}} \frac{4ip}{7} \cdot \frac{\color{blue}{1}}{\color{blue}{2}} \xlongequal{\text{Step 2}} \frac{ 4ip \cdot 1 }{ 7 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4ip }{ 14 } \end{aligned} $$ |
| ④ | Multiply $10000ins$ by $ \dfrac{4ip}{14} $ to get $ \dfrac{ 40000i^2nps }{ 14 } $. Step 1: Write $ 10000ins $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 10000ins \cdot \frac{4ip}{14} & \xlongequal{\text{Step 1}} \frac{10000ins}{\color{red}{1}} \cdot \frac{4ip}{14} \xlongequal{\text{Step 2}} \frac{ 10000ins \cdot 4ip }{ 1 \cdot 14 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 40000i^2nps }{ 14 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{40000i^2nps}{14} $ by $ 100 $ to get $ \dfrac{ 4000000i^2nps }{ 14 } $. Step 1: Write $ 100 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{40000i^2nps}{14} \cdot 100 & \xlongequal{\text{Step 1}} \frac{40000i^2nps}{14} \cdot \frac{100}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 40000i^2nps \cdot 100 }{ 14 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4000000i^2nps }{ 14 } \end{aligned} $$ |