1. **Stating the problem:** Simplify the expression $$Fy = -10 - 9 \times 10^{-9} \cdot r \cdot \frac{3 \cdot r_0 y}{4 \pi \cdot 10^{-9} \times 10^{-4}} \div (36 \pi)$$.
2. **Rewrite the expression clearly:**
$$Fy = -10 - 9 \times 10^{-9} \cdot r \cdot \frac{3 r_0 y}{4 \pi \times 10^{-9} \times 10^{-4}} \times \frac{1}{36 \pi}$$
3. **Simplify the denominator inside the fraction:**
$$4 \pi \times 10^{-9} \times 10^{-4} = 4 \pi \times 10^{-13}$$
4. **Rewrite the fraction:**
$$\frac{3 r_0 y}{4 \pi \times 10^{-13}} = 3 r_0 y \times \frac{1}{4 \pi \times 10^{-13}} = \frac{3 r_0 y}{4 \pi} \times 10^{13}$$
5. **Substitute back:**
$$Fy = -10 - 9 \times 10^{-9} \cdot r \cdot \frac{3 r_0 y}{4 \pi} \times 10^{13} \times \frac{1}{36 \pi}$$
6. **Combine constants:**
$$9 \times 10^{-9} \times 10^{13} = 9 \times 10^{4}$$
7. **Rewrite:**
$$Fy = -10 - r \cdot \frac{3 r_0 y}{4 \pi} \cdot \frac{9 \times 10^{4}}{36 \pi}$$
8. **Simplify the fraction with constants:**
$$\frac{9 \times 10^{4}}{36 \pi} = \frac{9}{36} \times \frac{10^{4}}{\pi} = \frac{1}{4} \times \frac{10^{4}}{\pi} = \frac{10^{4}}{4 \pi}$$
9. **Substitute:**
$$Fy = -10 - r \cdot \frac{3 r_0 y}{4 \pi} \times \frac{10^{4}}{4 \pi} = -10 - r \cdot 3 r_0 y \times \frac{10^{4}}{16 \pi^{2}}$$
10. **Final simplified form:**
$$Fy = -10 - \frac{3 \times 10^{4}}{16 \pi^{2}} \cdot r r_0 y$$
Simplify Force Expression 70069B
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.