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:$3(2y-1)$

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 $3(2y-1)$