DM1/DO1 = (6 × 3.14 × 0.38 × 10⁻⁴ × 7.90 × 10² × (cos 24° - cos 43.8°)) / ((17.5)² (22.10)²); x = 1 / (17.5)²; DM1 - DM1/DO1 = x (c - sin 24°)

Steps to Solve

1. Evaluate the trigonometric functions

Calculate the values of $\cos 24^\circ$ and $\cos 43.8^\circ$ using a calculator.

• $\cos 24^\circ \approx 0.9135$
• $\cos 43.8^\circ \approx 0.7245$

2. Calculate the numerator for DM1/DO1

Substitute the values into the numerator: $$ \text{Numerator} = 6 \times 3.14 \times 0.38 \times 10^{-4} \times 7.90 \times 10^2 \times (0.9135 - 0.7245) $$ Calculating $(0.9135 - 0.7245) \approx 0.1890$, then compute the whole numerator.

3. Calculate the denominator for DM1/DO1

Calculate the denominator: $$ \text{Denominator} = (17.5)^2 \times (22.10)^2 $$ Calculate $(17.5)^2 \approx 306.25$ and $(22.10)^2 \approx 488.41$, then compute the product.

4. Calculate DM1/DO1

Now compute the fraction: $$ DM1/DO1 = \frac{\text{Numerator}}{\text{Denominator}} $$

5. Find x

Use the value of $DM1/DO1$ to find $x$: $$ x = \frac{1}{(17.5)^2} $$

6. Set up the final equation for DM1

Substitute $x$ and $DM1/DO1$ into the equation: $$ DM1 = DO1 \times (x (c - \sin 24^\circ)) $$ Calculate $\sin 24^\circ \approx 0.4067$ and substitute this value into the equation.