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:

step-by-step explanation:

f

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.