That was a misleading question! Misleading because "dedicated" can mean two different things in English! Luckily, in Hebrew they get a "dedicated" word for each one! ;D

So - "dedicated" in a "dedicated parent" is very different from a "dedicated server"!

In Hebrew, the first one would stem from the root מ.ס.ר , meaning "to hand over," "to give," or "to deliver." Why? Because a dedicated person is ready to give all his abilities to a task or to a person he is dedicated to. :)

Here are some examples:
⮞ Who doesn't know that he is a most dedicated person -
מי לא יודע שהוא בן אדם מסור ביותר (audio #1)
⮞ Teachers are usually very dedicated to their jobs -
מורים בדרך כלל מאד מסורים לעבודה שלהם (audio #2)
⮞ There is no creature more dedicated to humans than a dog -
אין ייצור יותר מסור לבן אדם מכלב (audio #3)

Now, the meaning that we used in the sentence in question - "sent to a dedicated server" is completely different! It stems from another root - י.ע.ד (like in the word יעד - yaad - destination). Why? Because a dedicated object or service is something that is made to serve one very specific purpose, or - יעד.

Here are the examples of this second meaning:
⮞ This version has an external graphic card and 30 GB of dedicated memory -
GB לגרסה הזאת יש כרטיס גרפי חיצוני וזכרון ייעודי של 30 (audio #4)
⮞ This program has a dedicated server that is performing the actions that need to be done for the system to function properly -
לתוכנה הזאת יש שרת ייעודי שמבצע את הפעולות שצריך בשביל התפקוד התקין של כל המערכת. (audio #5)
⮞ After the exam the learners will be directed to the dedicated classrooms that match their abilities -
לאחר הבחינה הלומדים ייכוונו לכיתות ייעודיות התואמות את הכישורים שלהם. (audio #6)