Differentiation - The change of perimeter = dP/dt= 40/7m/h
What is differentiation?
Finding a function's derivative, or rate of change, is the process of differentiation in mathematics.
what is area?
It is the quantity, in other words, that counts the number of unit squares that cover the surface of a closed figure.
let the area of the square be "A" of sides "S"
area of the square
A = S²
differentiating with respect to "t" time
dA/dt = d(S²)/dt
= dA/dt = 2S*ds/dt
dA/dt=2S*ds/dt
=20m²/h
since we are given dA/dt=20
2Sds/dt=20
and at that instant A=49m sq.
=S²=49
since A=s²
S=√49
=±7
S=7
2SdS/dt=2*7ds/dt =20
ds/dt=20/14
=10/7
The perimeter of the square
P=4S
dP/dt =4dS/dt
=4*20/14
=4*10/7
thus the change of perimeter = dP/dt= 40/7m/h
to learn more about differentiation visit:
https://brainly.com/question/25081524
#SPJ4