1. **Stating the problem:** We are given that the force of attraction $F$ between two bodies varies directly as the product of their masses $m_1$ and $m_2$, and inversely as the square of the distance $d$ between them. 2. **Formula and explanation:** This means we can write the relationship as: $$F = k \frac{m_1 m_2}{d^2}$$ where $k$ is the constant of proportionality. 3. **Find the constant $k$ using given values:** Given $F=20$, $m_1=25$, $m_2=10$, and $d=5$, substitute these into the formula: $$20 = k \frac{25 \times 10}{5^2} = k \frac{250}{25} = 10k$$ Solving for $k$: $$k = \frac{20}{10} = 2$$ 4. **Expression for $F$ in terms of $m_1$, $m_2$, and $d$:** Substitute $k=2$ back into the formula: $$F = 2 \frac{m_1 m_2}{d^2}$$ 5. **Find the distance $d$ when $F=30$, $m_1=7.5$, and $m_2=4$:** Use the formula: $$30 = 2 \frac{7.5 \times 4}{d^2} = 2 \frac{30}{d^2} = \frac{60}{d^2}$$ Multiply both sides by $d^2$: $$30 d^2 = 60$$ Divide both sides by 30: $$d^2 = 2$$ Take the square root: $$d = \sqrt{2} \approx 1.414$$ **Final answers:** - Expression for $F$: $$F = 2 \frac{m_1 m_2}{d^2}$$ - Distance $d$ when $F=30$, $m_1=7.5$, $m_2=4$: $$d = \sqrt{2} \approx 1.414$$