An airplane flying horizontally at a constant altitude of 5 km passes directly over a radar station. Determine the speed of the plane if it is known that the distance between the radar and the plane is increasing at a rate of 900 km/hr and the horizontal distance between the radar and the plane is 12 km. uses the properties of derivatives to solve the rate of change problem

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Answer to a math question An airplane flying horizontally at a constant altitude of 5 km passes directly over a radar station. Determine the speed of the plane if it is known that the distance between the radar and the plane is increasing at a rate of 900 km/hr and the horizontal distance between the radar and the plane is 12 km. uses the properties of derivatives to solve the rate of change problem

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Seamus

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s^2 = x^2 + 5^2

\frac{d}{dt}(s^2) = \frac{d}{dt}(x^2 + 5^2)

2s \frac{ds}{dt} = 2x \frac{dx}{dt}

s \cdot 900 = x \cdot \frac{dx}{dt}

s = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13 \ \text{km}

13 \cdot 900 = 12 \cdot \frac{dx}{dt}

\frac{dx}{dt} = \frac{13 \cdot 900}{12}

\frac{dx}{dt} = 975 \ \text{km/hr}

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