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Mathematical Methods — Question 19

QCAA 2020, Paper 2 · 7 marks

Q19 · 2020 · Technology-activeComplex unfamiliar7 marks

QUESTION 19 (7 marks)

Consider the following information when completing this question. The length of a curve y=f(x)y=f(x) over the interval [a,b][a,b] is ∫ab1+(dydx)2 dx.\int_a^b\sqrt{1+\left(\frac{dy}{dx}\right)^2}\,dx. You are driving along a road with a vertical distance above sea level DD (in metres) given by the function D(x)=300+ln⁡(x2−3x+e),D(x)=300+\ln(x^2-3x+e), where xx is the horizontal distance from an initial point of measurement (in kilometres) at sea level. Assume that if xx is positive you are east of the initial point of measurement and if xx is negative you are west of the initial point of measurement. You start your drive along the road at a horizontal distance of 10 kilometres west of the initial point of measurement and drive until you are at a horizontal distance of 10 kilometres east of the initial point. Determine the time you spend driving downhill, if you drive downhill at an average speed of 40 km/h.
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