The height of the cone is measured as 9.3 cm and the radius as 3.2 cm....

 

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The height of the cone is measured as 9.3 cm and the radius as 3.2 cm. Each measurement could be off by as much as 0.1 cm. Using differentials, estimate the maximum possible error in calculating the volume of the cone. a) 7.301 cm² d) *3.191 cm b) -7.298 cm e) 4.188 cm¹ Use differentials to approximate the volume of material needed to manufacture a cone of radius 2 cm, height 8 cm and wall thickness 0.21 cm. a) = 3.96 cm³ d) = 37 cm² b) e) 5.28 cm² = 8.79 cm³ c) *7.305 cm' b) 16°C e) 25°C c) = 7.92 cm³ Suppose that the temperature of the water at the point on a river where a nuclear power plant discharges its hot waste is given by T(x,y)=2x+5y+2xy-20, where x represents the temperature of the river water (in degrees Celsius) before it reaches the power plant and y is the number of megawatts (in hundreds) of electricity being produced by the plant. If input water temperature is 10°C and number of megawatts produced is 6 (in hundreds), find the approximate change in temperature of the output water, if input water temperature changes by 1 degree, while number of megawatts remains constant at 6 (600 megawatts of electricity produced). a) 17°C d) 14°C c) 19°C The height of the cone is measured as 9.3 cm and the radius as 3.2 cm. Each measurement could be off by as much as 0.1 cm. Using differentials, estimate the maximum possible error in calculating the volume of the cone. a) 7.301 cm² d) *3.191 cm b) -7.298 cm e) 4.188 cm¹ Use differentials to approximate the volume of material needed to manufacture a cone of radius 2 cm, height 8 cm and wall thickness 0.21 cm. a) = 3.96 cm³ d) = 37 cm² b) e) 5.28 cm² = 8.79 cm³ c) *7.305 cm' b) 16°C e) 25°C c) = 7.92 cm³ Suppose that the temperature of the water at the point on a river where a nuclear power plant discharges its hot waste is given by T(x,y)=2x+5y+2xy-20, where x represents the temperature of the river water (in degrees Celsius) before it reaches the power plant and y is the number of megawatts (in hundreds) of electricity being produced by the plant. If input water temperature is 10°C and number of megawatts produced is 6 (in hundreds), find the approximate change in temperature of the output water, if input water temperature changes by 1 degree, while number of megawatts remains constant at 6 (600 megawatts of electricity produced). a) 17°C d) 14°C c) 19°C

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