Answer :
Answer:
The area of the circular ripple after t second is
A =25π t²
where A is in cm².
Step-by-step explanation:
Given that,
Circular ripple that travels outward at a speed of 5 cm per second.
It means that, the radius of the circular ripple increases at a seed 5 cm/ s.
Therefore the radius of the circular ripple after t seconds is
r(t)= 5t
where r(t) is in cm.
We know ,
The area of a circular object is = π r²
The area of the circular ripple after t second is
A= π(5t)²
=25πt²
where A is in cm².
The area, A. of the circle in terms of the number of seconds, t, that have passed since the ball hits the lake is A(t)= 25t²π
The formula for calculating the area of the circular ripple as a function of time is expressed as:
A(t) = πr(t)²
Given that the ripple travels outward at a speed of 5 cm per second, hence;
r(t) = 5tcm/s
Substitute the radius into the formula to have:
A(t) = π(5t)²
A(t)= 25t²π
Hence the area, A. of the circle in terms of the number of seconds, t, that have passed since the ball hits the lake is A(t)= 25t²π
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