13 Related Rates

13 Related Rates - 13. RELATEDRATES 1. 2 2

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13. RELATED RATES 1. The variables  x  and  y  are related by the equation of a circle  . 14 8 4 2 2 = + + + y x y x (a) [4 marks] Find the value of  dx dy  at the point (1, 1). __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[2 marks] Given that  x  is increasing at the rate of 0.2 units per second at the point (1, 1), find the  corresponding rate of change of  y . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET: Calculus 74 13. Related Rates
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2. Oil is being poured into a tank at the rate of 50 cubic metres per minute.  The shape of the tank is such that  the relationship between the volume,  V , in cubic metres, and the depth,  h , in metres, of the oil in the tank is  . 0 400 3 2 = - h V Find the rate at which the depth of the oil is increasing when there are exactly 20 cubic metres of oil in the  tank. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET: Calculus 75 13. Related Rates
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3. In the seas of planet CALC the speed of sound 
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13 Related Rates - 13. RELATEDRATES 1. 2 2

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