Two ships leave port at the same time. One sails south at \( 21 \mathrm{mi} / \mathrm{h} \), and the other sails east at \( 28 \mathrm{mi} / \mathrm{h} \). Find a function that mod the distance \( D \) between the ships in terms of the time \( t \) (in hours) elapsed since their departure. \( D(t)=\square \)

To find the distance \( D(t) \) between the two ships as a function of time \( t \), we can use the Pythagorean theorem. The southbound ship travels at \( 21 \) mi/h, so after \( t \) hours, it has traveled \( 21t \) miles south. The eastbound ship travels at \( 28 \) mi/h, so it has traveled \( 28t \) miles east. The distance \( D \) between the ships is given by: \[ D(t) = \sqrt{(21t)^2 + (28t)^2} \] Simplifying this: \[ D(t) = \sqrt{441t^2 + 784t^2} = \sqrt{1225t^2} = 35t \] So, the function you're looking for is: \[ D(t) = 35t \]