Imagine a spherical balloon filled with gas whose volume V is increasing at a constant rate of 3 m³/min. How fast is the radius r of the balloon increasing at the moment when the surface area S of the balloon is 27 m²? You do not need to simplify your answer, but you do need to provide NOTE: You may need the following formulas for the volume V and surface rea S of a sphere of radius r: units. V = πr³ and S = 4är². 3

Q: Consider the following function. f(x) = - Use a graphing utility to graph f on the interval [-2, 2].…

A: Given f(x)= -52x2 ∴ f'(x)= ddx-52x2=-5x We know, slope of f(x) is given by f'(x)

Q: A horizontal clothesline is tied between 2 poles, 12 meters apart. When a mass of 5 kilograms is…

A: Equate vertical and horizontal components of tension and force and then solve for tension.

Q: The parameters of a tidal mill are the blade length of 2.5 m, the tidal current of 13 knots, and the…

A: Given, The length of blade (r)=2.5 m The tidal current =13 knots Power consumed by blade(Cp of…

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A: The volume of a square pyramid is calculated using the formula: V=13b2h, where b is the length of…

Q: The formula for the volume of a right cylinder is V = ar²h. Find the rate of change of the volume…

A:

Q: The Volume (V) of a cone varies jointly as its height (h) and the square of its radius (r). Find the…

A:

Q: The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume…

A: Disclaimer:Since you have posted a question with multiple sub-parts, we will solve first three sub…

Q: The Mosteller formula for approximating the surface area, S, in m2, of a human is given by S= /hw…

A: Using partial differentiation on the above multivariable function

Q: The hull speed (in knotts) of any watercraft is given by V = 1.34-L¹/2 where L is the length of the…

A:

Q: Show the solution and draw the figure. The height and base radius of a right circular cylinder are…

A: Topic:- application of derivatives

Q: Give your answer accurate to 3 decimal places. The area of an equilateral triangle is decreasing at…

A:

Q: Water is flowing into a conical cistern at the rate of 8 m³/min. If the height of the nverted cone…

A: A. 3.64 m/sec

Q: A car is initially traveling at 50.0 km/h. The brakes are applied and the car stops over a distance…

A: Topic:-

Q: A snow ball, in the shape of a sphere, is melting so that its surface area is decreasing at a rate…

A:

Q: 30. Speed of a rocket At t sec after liftoff, the height of a rocket is 312 ft. How fast is the…

A:

Q: Given the function if possible find h(2)

A: We have to find the value of h(2) for the given function, h(x)

Q: Aryan filled a hemisphere box with water at the rate 15 cm3 s-1. Find the rate of change of the…

A: Given, Aryan filled a hemisphere box with water at the rate 15 cm3 s-1

Q: After 30 minutes from start of filling water inside the cylindrical tank, it was filled by 33…

A: In 1 minute , the water filled in the tank is:= 0.1 L And,  After 30 minutes,…

Q: Give your answer accurate to 3 decimal places. Gas is escaping from a spherical balloon at the rate…

A: Given: