# Math Wrod Problem

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1. A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimentions of the cross-section if the carrying capacity of the trough is to be a maximum.

2. A sheet of cardboard 18 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

• Math Wrod Problem -

A long strip of copper 8 inches wide is to be made into a rain gutter by turning up the sides to form a trough with a rectangular cross section. Find the dimentions of the cross-section if the carrying capacity of the trough is to be a maximum.

If x = the width, then the height y = (8 - x)/2

The volume of the crossection is therefore V = x(8 - x)/2 = 4x - x^2/2

Setting the first derivitive dv/dx = 4 - x = 0, x = 4 making y = 2

2. A sheet of cardboard 18 in square is used to make an open box by cutting squares of equal size from the corners and folding up the sides. What size squares should be cut to obtain a box with largest possible volume?

If the squares are x by x, the volume becomes V - (18 - 2x)(18 - 2x)

Can you take it from here?

• Math Wrod Problem -

if a boy gives his sister 2 of his years to make her twice his age, then he gives her 3 years to make her three times his age, how old are both of the kids

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