The area of a sector in a circle is given by the formula: A=1/2 r^2 theta, where r is the radius and theta is the central angle measured in radians. Find the rate of change of theta with respect to r if a remains constant. what is the rate when r = 3?

The rate of change of θ with respect to r, when r = 3 is given by

(dθ/dr) = - 0.148 A

Step-by-step explanation:

A = r²θ/2

And we need to find the rate if change if θ with respect to r if A is constant, then we make θ the subject of formula

θ = 2A/r²

Then we differentiate this with respect to r

θ = 2Ar⁻²

dθ/dr = - 4 Ar⁻³

(dθ/dr) = - 4 A / (r³)

When r = 3

(dθ/dr) = - 4 A / (3³) = - 4A/27 = - 0.148 A