what is the length of $\\widehat{acd}$?\neither enter an exact answer in terms of $\\pi$ or enter your…

Explanation:

Step1: Identify the radius of the circle

The segment $PB$ represents the radius $r$. $$r = 3$$

Step2: Determine the central angle of arc $ACD$

The angle consists of $\angle APB$ (right angle), $\angle APD$, and $\angle DPC$ (vertical to $\angle APB$). $$\theta = 90^{\circ} + 35^{\circ} + 90^{\circ} = 215^{\circ}$$

Step3: Apply the arc length formula

The formula for arc length $L$ is $\frac{\theta}{360^{\circ}} \cdot 2\pi r$. $$L = \frac{215}{360} \cdot 2 \cdot \pi \cdot 3$$

Step4: Simplify the expression

Calculate the exact value in terms of $\pi$. $$L = \frac{215}{360} \cdot 6\pi = \frac{215}{60}\pi = \frac{43}{12}\pi$$

Step5: Calculate the decimal value

Round the result to the nearest integer. $$L \approx 11.257$$

Answer:

$\frac{43}{12}\pi$ or 11