Question

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

Answer 1

Answer:
`3(2y-1)`

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

`(dA)/(dt)=x(dy)/(dt)+y(dx)/(dt)`

`(dA)/(dt)=x* (-3)+y* (6)`

`(dA)/(dt)=6y-3x`

`(dA)/(dt)=3(2y-1)`

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