Mathematics

Problem

The length

x(t)

and width

y(t)

of a rectangle are measured in centimetres. At a certain instant

x = 15

y = 8

, the width is increasing at

2\,\text{mm s}^{-1}

, and the perimeter is increasing at

1\,\text{cm s}^{-1}

. (i) Convert the given rate of change of width to centimetres per second. (ii) Using the converted value, determine the rate at which the length is changing at that instant.

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