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Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), xx seconds after Amir threw it, is modeled by: h(x)=(x2)2+16h(x) = -(x - 2)^2 + 16. How many seconds after being thrown will the ball hit the ground?

Full solution

Q. Amir stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), xx seconds after Amir threw it, is modeled by: h(x)=(x2)2+16h(x) = -(x - 2)^2 + 16. How many seconds after being thrown will the ball hit the ground?
  1. Understand the problem: Understand the problem.\newlineWe need to find the time when the ball hits the ground. This happens when the height h(x)h(x) is equal to 00.
  2. Set up the equation: Set up the equation to solve for xx when h(x)=0h(x) = 0.0=(x2)2+160 = -(x - 2)^2 + 16
  3. Solve for x: Solve the equation for x.\newlineFirst, move the terms around to isolate the squared term.\newline(x2)2=16(x - 2)^2 = 16
  4. Take square root: Take the square root of both sides of the equation.\newlinex2=±16x - 2 = \pm\sqrt{16}
  5. Find positive solution: Solve for xx.x=2±4x = 2 \pm 4
  6. Find positive solution: Solve for xx.x=2±4x = 2 \pm 4Find the positive solution for xx since time cannot be negative.x=2+4x = 2 + 4x=6x = 6

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