A sphere is expanding with time. Assume that the volume of the sphere is V = (4pi * r ^ 3)/3; r(t) = t ^3+ 2 What is the formula for the rate of change of the volume of the balloon with respect to time

A sphere is expanding with time. Assume that the volume of the sphere is V = (4pi * r ^ 3)/3; r(t) = t ^3+ 2 What is the formula for the rate of change of the volume of the balloon with respect to time

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 1SE: Can the average rate of change of a function be constant?

See similar textbooks

Related questions

Q: Water is draining from a cylindrical tank of water at a rate of 3 m / min . If the radius of the…

Q: Let V(t) be the volume, in cubic inches of a balloon that is being filled with air after 't seconds.…

A: The derivative of a real valued function interprets the rate of changing of the function. It has a…

Q: ifferentials to estimate the amount of paint needed to apply a coat of paint 0.05cm thick to a…

Q: The volume of a cone of radius r and height h is given by V=1/3pir^2h. If the radius increases at a…

A: Volume of a cone = πr2h3 , Where r= radius of a cone and h= height of a conedrdt= 0.5cm/sec , dhdt=…

Q: Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of…

Q: A rectangle is inscribed in the ellipse 16 x2 + 81 y2 = 1296 Find the rate of change of the…

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.1 cm/min. At what is…

A: The diameter of the snowball is decreasing at a rate of 0.1 cm/min. So, the decreasing rate of…

Q: A box with a square base has the sides of the base increasing at 6 m/sec and the height of the box…

Q: 6. A hemispherical water tank, shown below has a radius of 6 meters and is losing water. The area of…

A: Given A = 12πh - πh2where h = depth at a time , h = 3 meterA = area Given dhdt = -12meterminwe want…

Q: Use differentials to estimate the amount of paint needed toapply a coat of paint 0.05 cm thick to a…

Q: Use differentials to estimate the amount of metal in a closed cylindrical tin can with diameter 8 cm…

A: Answer

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?
A box with a square base has the sides of the base increasing at 6 m/sec and the height of the box is increasing at 3 m/sec. The rate of change of the rectangle's volume when the base sides are = 5m and the height = 6m, is
A spherical snowball is melting so that its diameter is decreasing at rate of 0.1 cm/min. At what is the rate is the volume of the snowball changing when the diameter is 13 cm? The volume is changing at a rate of cm/min
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05cm thick to a hemispherical dome with a diameter of 50m.
The volume of a cone of radius r and height h is given by V=1/3pir^2h. If the radius increases at a rate of 1/2cm/sec and the height increases at a rate of 1/4cm/sec, then how fast is the volume changing when the height is 9cm and the radius is 6cm?
A rectangle is inscribed in the ellipse 16 x2 + 81 y2 = 1296 Find the rate of change of the area of the rectangle with respect to xRate of Change of Area with respect to x =
Use differentials to estimate the amount of metal in a closed cylindrical tin can with diameter 8 cm and height 12 cm if the metal on the top and the bottom is 0.2 cm thick and the metal on the sides is 0.1 cm thick.
Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 5.5 mi-/hr. How rapidly is radius of the spill increasing when the area is 10 mi? ? The radius is increasing at mi/hr.
All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the volume changing when each edge is 3 centimeters and 10 centimeters? (a) 3 centimeters cm3/sec(b) 10 centimeters cm3/sec
Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 9 cubic feet per minute. If the pool has radius 7 feet and height 11 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 8 feet?
A ball is inflated at a rate of 200x cubic inches per second. Find the rate at which the radius is increasing at the time when the radius is 5 inches. (The volume of a ball is V = rate =
The surface area of the sphere is decreasing at the rate of 20 cm^2/sec when the radius is 15 cm. Calculate the rate of change of the radius Calculate the rate of change of the volume at this instant