Mathematics: The perimeter of a square is increasing at a rate of 555 meters per hour. At a certain instant, the perimeter is 303030 meters. What is the rate of change of the area of the square at that instant (in square meters per hour)

IDK but there is a cool app called photomath and Cymath...

The perimeter of a square is increasing at a rate

Ответ:

trixxytang

27.06.2021

Mathematics

$21,022,706.3\ m^2/hr$

Step-by-step explanation:

Given

The rate of change of perimeter of a square is increasing at a rate of $555\ m^3/hr$

At a certain instant, the perimeter is $303030\ m$

At this instant side of square is

$\Rightarrow a=\dfrac{303030}{4}\\\\\Rightarrow a=75,757.5\ m$

Rate of change of perimeter is

$\Rightarrow \dfrac{dp}{dt}=4\dfrac{da}{dt}\\\\\Rightarrow 555=4\dfrac{da}{dt}\\\\\Rightarrow \dfrac{da}{dt}=138.75\ m/hr$

At this instant, rate of change of the area of the square is

$\Rightarrow A=a^2\\\Rightarrow \dfrac{dA}{dt}=2a\dfrac{da}{dt}\\\\\Rightarrow \dfrac{dA}{dt}=2\times 75757.5\times 138.75\\\\\Rightarrow \dfrac{dA}{dt}=21,022,706.3\ m^2/hr$

0,0(0 оценок)

The perimeter of a square is increasing at a rate of 555 meters per hour. At a certain instant, the perimeter is 303030 meters. What is the rate of change of the area of the square at that instant (in square meters per hour)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question