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gizmo_the_mogwai [7]
2 years ago
13

The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 8 cm/s. When the length is

8 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Mathematics
1 answer:
iVinArrow [24]2 years ago
7 0

Answer:

Step-by-step explanation:

A = lw \nl\frac{\dA}{\dt} =\frac{\dA}{\text{d}l}\frac{\text{d}l}{\dt} + \frac{\dA}{\text{d}w}\frac{\text{d}w}{\dt} =w\frac{\text{d}l}{\dt} + l\frac{\text{d}w}{\dt} \nll = 20 \text{ cm} \;\; \frac{\text{d}l}{\dt} = 8 \text{ cm/s} \;\;w = 10 \text{ cm}, \;\;  ]\frac{\text{d}w}{\dt} = 3 \text{ cm/s} \nl\frac{\dA}{\dt} =(  10 \text{ cm} )( 8 \text{ cm/s} ) + (  20 \text{ cm} )( 3 \text{ cm/s} )  =140 \text{ cm}^2\!\text{/s}


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