The length and width of a rectangle are measured in centimetres

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

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.

Related theory

Dimensional Analysis
Ratio and Proportion
Related Rates

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