Pregunta
You might need: Calculator A hovercraft takes off from a platform. Its height (in meters), \( x \) seconds after takeoff, is modeled by: \( h(x)=-3(x-3)^{2}+108 \) How many seconds after takeoff will the hovercraft land on the ground? seconds
Ask by Owen Haynes. in the United States
Feb 22,2025
Solución de inteligencia artificial de Upstudy
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The hovercraft lands 9 seconds after takeoff.
Solución
To find when the hovercraft lands, we set the height equal to 0:
-3(x - 3)² + 108 = 0
Step 1: Isolate the squared term. Subtract 108 from both sides:
-3(x - 3)² = -108
Step 2: Divide both sides by -3:
(x - 3)² = 36
Step 3: Take the square root of both sides:
x - 3 = ±6
Step 4: Solve for x:
x = 3 + 6 = 9 or x = 3 - 6 = -3
Since time cannot be negative, we disregard x = -3.
Thus, the hovercraft lands 9 seconds after takeoff.
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Simplifique esta solución The Deep Dive
To find out when the hovercraft lands on the ground, we set the height function \( h(x) \) equal to 0: \[ 0 = -3(x-3)^{2} + 108 \] Solving for \( x \): 1. Rearranging gives us \( 3(x-3)^{2} = 108 \). 2. Dividing by 3: \( (x-3)^{2} = 36 \). 3. Taking the square root: \( x-3 = 6 \) or \( x-3 = -6 \). 4. So, \( x = 9 \) or \( x = -3 \). Since time cannot be negative, the hovercraft will land on the ground \( 9 \) seconds after takeoff. 9 seconds.
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