A spherical balloon is inflating with helium at a rate of 200x min How fast is the balloon's radius increasing at the instant the radius is 5 ft? Write an equation relating the volume of a sphere, V, and the radius of the sphere, r. (Type an exact answer, using t as needed.) Differentiate both sides of the equation with respect to t. dV dr dt dt (Type an exact answer, using t as needed. Type an expression using r as the variable.) The balloon's radius is increasing at a rate of at the instant the radius is 5 ft. (Simplify your answer.)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.