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Salsk061 [2.6K]
3 years ago
13

A rectangular standing-only section at the venue changes size as t increases in order to manage the flow of people. Let x repres

ent the length, in feet, of the section, and let y represent the width, in feet, of the section. The length of the section is increasing at a rate of 6 feet per hour, and the width of the section is decreasing at a rate of 3 feet per hour. What is the rate of change of the area
Mathematics
1 answer:
Cloud [144]3 years ago
8 0

Answer:3(2y-1)

Step-by-step explanation:

Given

Length is increasing at the rate of \dot{x}=6\ ft/s

Width is decreasing at the rate of \dot{y}=3\ ft/hr

Area is given by

A=xy

So rate of area is

\frac{dA}{dt}=x\frac{dy}{dt}+y\frac{dx}{dt}

\frac{dA}{dt}=x\times (-3)+y\times (6)

\frac{dA}{dt}=6y-3x

\frac{dA}{dt}=3(2y-1)

So, area is changing at the rate of 3(2y-1)

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