A child throws a stone into a sull lake causing a circular ripple to spread outw

Question

A child throws a stone into a sull lake causing a circular ripple to spread outward If the radius of the ripple increases at a constant rate of 3/4 meters per second, how fast is the area of the disturb water increasing when its radius is 15 meters? 6.For the function f(x) = x^3 + 3x^2 - 4, use your knowledge of derivatives to determine (a) the intervals on which f(x) is increasing/decreasing (b) the (x.y) coordinates of local extrema Identify each as a maximum or mm,mum intervals of concavity and (x, y) coordinates of inflection points.

Explanation / Answer

Here we have given that rate of change in radius dr/dt = 3/4 = 0.75 m/sec

And it is asked that dA/dt where r=15 m given,

so we use chain rule here i.e.

dA/dt= dA/dr x dr/dt = 0.75(dA/dr)

Now as the area of the circle A = pi r^2

so on differentiating it with respect to r, we get it as

dA/dr = pi (d/dr)(r^2 ) = pi (2r)

and at r=15

dA/dr= 2 x 3.14 x 15 = 94.2 m^2/m

so by above chain rule, we have

dA/dr = 94.2 x 0.75 = 70.65

so area is changing at the rate of 70.65 m^2 per second.

This is the answer of question 5.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.