A rectangular steel plate expands as it is heated. Find the rate of change of area with respect to temperature T when the width is 1.6 cm and the length is 2.6 cm if d l divided by dt equals 1.1 times 10 Superscript negative 5 Baseline cm divided by degrees Upper C and dw divided by dt equals 8.9 times 10 Superscript negative 6 Baseline cm divided by degrees C. Round to one decimal place.

The variation rate is 4.07 × 10⁻⁵ cm²/ºC

Step-by-step explanation:

The relationship of the change in length as a function of the temperature, which are given in this problem can be written by the expression for the area of a rectangle

a = L × W

Differentiating both sides,

=

= W + L

The values they give us are

= 1.1 × 10⁻⁵ cm/ºC

= 8.9 × 10⁻⁶ cm/ºC

W = 1.6  cm

L= 2.6 cm

Substituting the values and calculating

= (1.6 × 1.1 × 10⁻⁵) + (2.6 × 8.9 × 10⁻⁶)

= (1.76 × 10⁻⁵) + (2.31 × 10⁻⁵)

=  4.07 × 10⁻⁵ cm²/ºC

The variation rate is 4.07 × 10⁻⁵ cm²/ºC

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step-by-step explanation: