A baseball diamond is a square 90 feet on a side. A player runs from first base to second base at a rate of 15 feet per second. At what rate is the player's distance from third base decreasing when the player is halfway between first and second base? We've already set part of this problem up. If we let x be the distance between the player and second base, and y be the distance between the player and third base, then = - 15 feet per second, and will tell us what we want to know. Use the picture to find a relationship that will help you answer the question.

 

 

 

so I got the answer - 6.71 after some 10-15 minutes of working around....... lmao and it says wrong

 

 

 

The correct answer is: 6.71 feet per second. The relationship here comes from the Pythagorean theorem, . If we differentiate that with respect to t, we get . Plugging in = - 15 and solving for gives = - 6.71 feet per second. This rate is negative, because the distance is decreasing. The question, however asked, "How fast is the distance decreasing," so the answer is, "The distance is decreasing by 6.71 feet per second."(Watch out if you didn't get a negative rate here!)

related rates are fun

I don't get it. You're not asking a question, right?

no. he's just talking about the wording of the question.