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 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.

Using differentials the maximum error in the calculated area of the rectangle wi’ould be 5.9 cm

The area formular of a rectangle is :

Maximum error can be defined thus :

Δmax = (L × Δe) + (W × Δe)

Δmax = (31 × 0.1) + (28 × 0.1)

Δmax = 3.1 + 2.8

Δmax = 5.9 cm

Hence, the maximum error in the calculated area value is 5.9 cm.

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Step-by-step explanation:

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

Where:

- Width, in centimeters.

- Height, in centimeters.

The differential of the expression is derived hereafter:

 x +   y = 29

5x + 2y = 100

Step-by-step explanation:

Has 29 problems

then

x + y = 29

x be the number of worth 5 points questions:

5x

y be the number of worth 2 points questions

2y

the total both worth is 100 points

then:

5x + 2y = 100

x + y = 29          5x + 2y = 100