A hovercraft takes off from a platform. Its height (in meters), x seconds after takeoff, is modeled by h(x)=-(x-11)(x+3) How many seconds after takeoff will the hovercraft land on the ground? seconds

Question

A hovercraft takes off from a platform. Its height (in meters),  x seconds after takeoff, is modeled by  h(x)=-(x-11)(x+3) How many seconds after takeoff will the hovercraft land on the ground? seconds

Bytelearn · Accepted Answer

Given height function: We are given the height function h(x) = -(x-11)(x+3). To find out when the hovercraft will land on the ground, we need to determine when the height h(x) is equal to 0.Set height function equal: Set the height function equal to zero and solve for x: 0 = -(x-11)(x+3)Expand and simplify equation: Expand the equation: 0 = -x^2 - 3x + 11x + 33Solve quadratic equation: Simplify the equation by combining like terms: 0 = -x^2 + 8x + 33Substitute values into formula: To find the x values when the hovercraft is on the ground, we need to solve the quadratic equation -x^2 + 8x + 33 = 0. This can be done by factoring, completing the square, or using the quadratic formula. Since the equation does not factor easily, we will use the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a), where a = -1, b = 8, and c = 33.Calculate discriminant: Substitute the values of a, b, and c into the quadratic formula: x = [-8 ± sqrt(8^2 - 4(-1)(33))] / (2(-1))Calculate square root: Calculate the discriminant (the part under the square root): Discriminant = 8^2 - 4(-1)(33) = 64 + 132 = 196Substitute square root: Take the square root of the discriminant: sqrt(196) = 14Calculate possible solutions: Substitute the square root back into the quadratic formula: x = [-8 ± 14] / -2Identify meaningful solution: Calculate the two possible solutions for x: x1 = (-8 + 14) / -2 = 6 / -2 = -3 x2 = (-8 - 14) / -2 = -22 / -2 = 11Since time cannot be negative, the solution x = -3 seconds is not physically meaningful for this problem. Therefore, the hovercraft will land on the ground 11 seconds after takeoff.

A hovercraft takes off from a platform. Its height (in meters), $x$ seconds after takeoff, is modeled by $h(x) = -(x-11)(x+3)$ How many seconds after takeoff will the hovercraft land on the ground? $\text{seconds}$

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A hovercraft takes off from a platform. Its height (in meters), x x x seconds after takeoff, is modeled by h(x)=−(x−11)(x+3) h(x) = -(x-11)(x+3) h(x)=−(x−11)(x+3) How many seconds after takeoff will the hovercraft land on the ground? seconds \text{seconds} seconds

A hovercraft takes off from a platform. Its height (in meters), $x$ seconds after takeoff, is modeled by $h(x) = -(x-11)(x+3)$ How many seconds after takeoff will the hovercraft land on the ground? $\text{seconds}$