Respuesta :
The relation between perimeter and radius is P = 2 pi r
dP/dr = 2pi
dP/dt = 3
when r = 2 dr/dt = dP/dt * dr/DP = 3 * 1/2pi = 0.477 m/s
dP/dr = 2pi
dP/dt = 3
when r = 2 dr/dt = dP/dt * dr/DP = 3 * 1/2pi = 0.477 m/s
The rate at which the radius is changing is [tex]\frac{3}{2\pi }[/tex] m/s.
We have a circle of radius r which is formed when a stone is dropped in it such that the perimeter of the circle is increasing at 3 m/s.
We have to find out at what rate is the radius of the circle increasing.
What is the perimeter of the circle with radius r ?
The perimeter of the circle with radius r is -
Perimeter = 2[tex]\pi[/tex]r
According to the question -
rate of change of perimeter of circle with respect to time is = 3 m/s
Mathematically, we can write it as -
[tex]\frac{dp}{dt} =[/tex] 3 m/s
Differentiating the perimeter with respect to time, we get -
[tex]\frac{d}{dt} 2\pi r =[/tex] 3
2[tex]\pi[/tex] [tex]\frac{dr}{dt}[/tex] = 3
[tex]\frac{dr}{dt}[/tex] = [tex]\frac{3}{2\pi }[/tex] m/s
Hence, the rate at which the radius is changing is [tex]\frac{3}{2\pi }[/tex] m/s.
To solve more questions on rate measurement, visit the link below -
https://brainly.com/question/11965077
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