Figure 2 shows a water trough which is uniform with length y cm and has a...

  

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Figure 2 shows a water trough which is uniform with length y cm and has a cross-section made up of a semi-circle of radius x cm. The trough has no top. The volume of the trough is 64000 cm. a) Find an expression for y in terms of x. b) Show that the outside surface area, A, is given by 128000 A = #x + c) Use to find the value of x which gives the minimum surface area. d) Confirm that your value of x is a minimum. e) Find the minimum outside surface area of the trough. [2] [3] [5] [3] [2] x cm->> Figure 2 y cm Figure 2 shows a water trough which is uniform with length y cm and has a cross-section made up of a semi-circle of radius x cm. The trough has no top. The volume of the trough is 64000 cm. a) Find an expression for y in terms of x. b) Show that the outside surface area, A, is given by 128000 A = #x + c) Use to find the value of x which gives the minimum surface area. d) Confirm that your value of x is a minimum. e) Find the minimum outside surface area of the trough. [2] [3] [5] [3] [2] x cm->> Figure 2 y cm

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Given the question and the accompanying diagram lets tackle each part step by step a Find an expression for y in terms of x The volume of the trough is given as 64000 cm and the crosssection is a semi... View the full answer