Dart problem

on3winyoureyes

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On a game show, you get to throw a dart at a circle of radius 50 inches. If you miss, you get to throw again until you hit the circle. How much money you win is determined by finding the product of the x and y coordinates of the point you hit. You want to determine the coordinates of the point that will maximize your winnings.

Part a says to write the equation(s) you will be working with in this problem.

Part b says Use calculus to determine the coordinates of any point on the circle that will give you the largest possible money winnings. Round to the nearest hundredth. Note:that point must be ON the circle not outside or inside the circle

So I think we'd use the equations x^2+y^2=50^2 and A=xy because it's a circle and the product part but I'm not sure about part b
 
On a game show, you get to throw a dart at a circle of radius 50 inches. If you miss, you get to throw again until you hit the circle. How much money you win is determined by finding the product of the x and y coordinates of the point you hit. You want to determine the coordinates of the point that will maximize your winnings.

Part a says to write the equation(s) you will be working with in this problem.

Part b says Use calculus to determine the coordinates of any point on the circle that will give you the largest possible money winnings. Round to the nearest hundredth. Note:that point must be ON the circle not outside or inside the circle

So I think we'd use the equations x^2+y^2=50^2 and A=xy because it's a circle and the product part but I'm not sure about part b
What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting

Hint: Approaching this simply, your Amount of winnings is A=xy and y=\(\displaystyle \sqrt{2500\, -\, x^2}\) and you want to maximize A. Of course, we might also consider that possibly we meant A = |xy| and y=\(\displaystyle \pm\sqrt{2500\, -\, x^2}\) and that solutions could be flipped, i.e. if (x,y)=(a,b) is a solution, so is (b,a).
 
On a game show, you get to throw a dart at a circle of radius 50 inches. If you miss, you get to throw again until you hit the circle. How much money you win is determined by finding the product of the x and y coordinates of the point you hit.
Without knowing how the coordinate plane is related to the circle, there is no way to know how to maximize the points. Is there maybe a picture that goes with this exercise? Are you maybe supposed to center the circle at the origin, so the conflict will be between "playing it safe" (aiming toward the middle, so you're sure to hit, but you won't get many points) and "going for it" (aiming toward the edge to maximize points, but then maybe missing the circle entirely)? Or something else? Thank you! ;)
 
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