**Problem Statement:** 4. Let the function \( v(t) = \frac{6 \sqrt[3]{t}}{4t + 1} \) be the volume, in cm\(^3\), of a balloon at time \( t \), in seconds. At what rate is the volume of the balloon changing with respect to time when \( t = 8 \)? Is the balloon inflating or deflating at this time? **Explanation:** - The function \( v(t) \) represents the volume of the balloon in cubic centimeters as a function of time \( t \) in seconds. - To determine the rate at which the volume is changing, calculate the derivative of \( v(t) \) with respect to \( t \), denoted as \( v'(t) \). - Evaluate \( v'(t) \) at \( t = 8 \). - The sign of \( v'(8) \) will indicate whether the balloon is inflating (positive rate) or deflating (negative rate) at \( t = 8 \).

Q: 2) Is A P Q R a right angle triangle P(-5,3) Q(-7,8) R(3, 12) and it. name

A:

Q: Water is leaking out the bottom of a hemispherical tank of radius 9 feet at a rate of 3 cubic feet…

A: As we know The volume of segment of height h in a hemisphere of radius r is

Q: Related rates. A spherical snow ball is melting in the following way:at the instant when its radius…

A: Given, Radius= r = 12 cm Rate of change of radius= dr/dt= - 5 cm/hour Volume of the sphere =V=…

Q: The volume V of a right circular cylinder of height 7 m and radius r m is V = V(r) = 7ar. Find the…

A:

Q: Q-4-A leak in a spherical balloon filled with gas allows the gas to leak at a rate of 3.5 m³ /min .…

A: Given that,       a leak in a spherical balloon filled with gas allows the gas to leak at a rate of…

Q: Morphine is administreted to a patient intravenously at a rate of 2.5 mg per hour. About 34,7% of…

A:

Q: A tank contains 420 liters of fluid in which 30 grams of salt is dissolved. Pure water is then…

A: