An open box is made from a metal sheet with dimensions 12 cm by 28 cm...

 

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An open box is made from a metal sheet with dimensions 12 cm by 28 cm as illustrated below in A up to open Let x be the length of the corner that is cut out. This will be the height of the box. [0] 28 cm (c) 12 cm 28 - 2x (a) Show that the volume of the box is given by v = 4x³ 80x² + 336x 12 - 2x (4 marks) dV (b) Find and hence find the dimensions that give the maximum volume. What is the dx maximum volume? (8 marks) Consider a box having a volume of 250 cm³ that was made from the above metal sheet with dimensions 12 cm by 28 cm. To two decimal places estimate the length, x, of the square corner that was cut away. Hint the answer is between x = 0.9cm and x = 1cm. An open box is made from a metal sheet with dimensions 12 cm by 28 cm as illustrated below in A up to open Let x be the length of the corner that is cut out. This will be the height of the box. [0] 28 cm (c) 12 cm 28 - 2x (a) Show that the volume of the box is given by v = 4x³ 80x² + 336x 12 - 2x (4 marks) dV (b) Find and hence find the dimensions that give the maximum volume. What is the dx maximum volume? (8 marks) Consider a box having a volume of 250 cm³ that was made from the above metal sheet with dimensions 12 cm by 28 cm. To two decimal places estimate the length, x, of the square corner that was cut away. Hint the answer is between x = 0.9cm and x = 1cm.

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