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ira [324]
3 years ago
9

The length and width of a rectangle are measured as 31 cm and 28 cm, respectively, with an error in measurement of at most 0.1 c

m in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Mathematics
1 answer:
MissTica3 years ago
5 0

Answer:

\Delta A = 5.9\,cm^{2}

Step-by-step explanation:

The area of an rectangle is given by the following formula:

A = w\cdot h

Where:

w - Width, in centimeters.

h - Height, in centimeters.

The differential of the expression is derived hereafter:

\Delta A  = \frac{\partial A}{\partial w} \cdot \Delta w + \frac{\partial A}{\partial h}\cdot \Delta h

\Delta A = h \cdot \Delta w + w \cdot \Delta h

\Delta A = (31\,cm)\cdot (0.1\,cm) + (28\,cm)\cdot (0.1\,cm)

\Delta A = 5.9\,cm^{2}

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