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- #hn. Don't provide handwriting solutionFind value of x,y,zSuppose you are climbing a hill whose shape is given by the equationz= 1000−0.01x2−0.02y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (50, 80, 847). The positive x-axis points east and the positive y-axis points north. (a) If you walk northwest, will you start to ascend or descend? At what rate? (b) In what direction is the slope largest? Why?
- use differentials to estimate the amount of metal in a cylindrical can that is 12cm high and 8cm in diameter if the metal on the top and bottom is 0.09cm thick and the metal on the sides is 0.01cm thick.Differentiate. y = 3 x In xthe side of a sqaure is 10 cm. find the approximately, by using differential, the increase in the area if the side is increased by 0.02 cm.
- Soln of linear diff equation with constant coefficientUse differentials to estimate (2.03)4Find the work done by the gas with an initial volume of 3 cubic feet and a pressureof 1000 pounds per square foot expands to the volume of 4 cubic feet(Assume that the pressure is inversely proportional to the volume).