The pressure distribution on a rectangular steel plate supporting a load is modelled by the function:...

 

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The pressure distribution on a rectangular steel plate supporting a load is modelled by the function: where x and y are in meters. (a) Calculate the gradient of the pressure function. Hence, determine the rate of change of pressure at the point (0, 1) in the direction of u = i - 2j. (b) P(x, y) = 70-(x - 1)-(y 2) (MPa) (c) (6 marks) If the dimensions of the plate is not known, determine the location on the plate where the pressure is maximum and calculate this pressure. Show that this pressure is both a local and global maximum. (10 marks) If the plate is 1 m long by 2 m wide, such that 0x 1,0 y 2, determine the minimum pressure on the plate. State any theorems used, if any. The pressure distribution on a rectangular steel plate supporting a load is modelled by the function: where x and y are in meters. (a) Calculate the gradient of the pressure function. Hence, determine the rate of change of pressure at the point (0, 1) in the direction of u = i - 2j. (b) P(x, y) = 70-(x - 1)-(y 2) (MPa) (c) (6 marks) If the dimensions of the plate is not known, determine the location on the plate where the pressure is maximum and calculate this pressure. Show that this pressure is both a local and global maximum. (10 marks) If the plate is 1 m long by 2 m wide, such that 0x 1,0 y 2, determine the minimum pressure on the plate. State any theorems used, if any.