Answered: The area A of a circle is increasing at…

The area A of a circle is increasing at a constant rate of 2cm's-. If the area of the circle is given by A = Tr2, what is the rate of change of the radius when the radius is 4cm? %3D

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter10: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 444RE: Researchers recorded that a certain bacteria population grew from 100 to 300 in 8 hours. At this...

See similar textbooks

Related questions

Q: A spherical balloon is inflated and its volume increases at a rate of 30 in3 /min. (a). What is the…

A: Given that, The spherical balloon is inflated and its rate of change of volume is; dVdt=30 (in3min)…

Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a) Find the rate of change…

Q: Find the rate of change. Cube root 3√x with respect to x when x = 1, 8, 27

A: Consider the given: fx=x3ddxfx=ddxx3ddxfx=ddxx13ddxfx=13x13-1ddxfx=13x23

Q: A cylindrical box has a fixed height of 12 inches. Find the rate of change of volume with respect to…

Q: The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the…

A: Write the expression for the volume of the sphere and take the derivative then substitute the given…

Q: The radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of…

Q: The area of a rectangle with one of its sides s is A(s) = 6s². What is the rate of change of the…

A: Differentiate both sides of the equation, with respect to s to establish a relation between the…

Q: The area of a square with side s is A(s) s². What is the = rate of change of the area of a square…

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

Q: the radius of a circle is increasing at a constant rate of 100 meters per second. at what rate is…

A: First of all, consider the area for the circle.Then differentiate on both sides of equation w.r.t…

Q: ick is increasing at a rate of 3 meters per minute. How quickly is the area changing when the oil…

Q: The volume of a sphere is increasing at a rate of 8 cubic cm/sec. Find the rate of change of its…

A: Let V be the volume of the sphere which is given in the question as,

Q: The radius of a circle is increasing at the rate of 4 cm/s. How fast is the area of the circle…

A: Given, The radius of a circle is increasing at the rate of 4 cm/s. And the radius is 5 cm…

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 4 ft/min.…

A: Area of a circle of radius r is given by A = πr2 ...(1) Differentiate with respect…

Q: The sides of an equilateral triangle are increasing at the rate of 3cm/min. Find: a.)the rate of…

Q: The radius of a spherical balloon is decreasing at a rate of 2 - in/sec. Which of the following is…

A: As we know that the expression for the volume of the sphere: v=43πr3 Where; ''r'' is the radius of…

Q: For a certain animal, the surface area S of the body is related to the body's weight W according toS…

A: The surface area S of the body is related to the body's weight W according to S is:

Q: The radius of a circle is increasing at a constant rate of 8 centimeters per minute. At the instant…

Q: The length L of a rectangle is decreasing at a rate of 2 cm/sec while the width is increasing at a…

A: Let L be the length of the rectangle and W be the width of the rectangle. then we have ,…

Q: The volume of a cube decreases at a rate of 0.6 ft° /min. What is the rate of change of the side…

A: Since you have not mentioned I am answering 2nd Question. Given:Volume of a cube decreases at a rate…

Q: The radius of a circle is increasing at the rate of 0.7 cm/s.whats is the rate of increase of its…

Q: A triangle with constant base b and height h is changing with time where h(t) = 2t – 3. What is the…

Q: The area of a square is decreasing at a rate of 158 square centimeters per second. At the time when…

A: Area of square =(side)2 perimeter of square = 4(side) let side of square= x cm

Q: The radius of a circle is increasing at the rate of 0.7 cm/s. what is the rate of

Q: A triangle with constant base b and height h is changing with time where h(t) = 3t + 1. What is the…

Q: The radius of a circle is increasing at the rate of 0.7 cm/c.what isthe rate of oncreasing of its…

A: Differentiate circumference wrt t

Q: The area of a circle is decreasing at a rate of 17 square inches per second. At the time when the…

A: The given question can be solved as shown in step2.

Q: The pressure exerted by a certain Iiquid at 0 given point varies directly as the depth of the point…

A: Given pressure of liquid at a point is directly proportional to the depth of the surface at the…

Q: A square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

Q: A rectangle has a length that is increasing at a rate of 10 mm per second with the width being held…

A: We have to find rate of change of area .Information is given below:

Q: The area of a circle increases at a rate of 6 cm /s. a. How fast is the radius changing when the…

A: Area of circle of radius r inA=πr2→dAdr=2πrdrdt→2πrdrdt=6 [∵dAdr=6cm2/sec] -(1)

Q: The volume of a cube with sides of lengths is given by=s. Find the rate of change of volume with…

Q: Find the rate of change. Area of a square with respect to its side s when s = 5

A: To find the rate of change of the area of square with respect to its side s.

Q: The radius of a right circular cone is increasing at 3 cm/min whereas the height of the cone is…

Q: A circle has an initial radius of 50 ft. when the radius begins decreasing at the rate of 3 ft/min.…

A: Area of a circle is given byDifferentiating the function of area with respect to time:

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at a rate of 2 ft>min.…

A: Let r be the radius of the circle.The initial radius is given by r = 50 ft.Given that, the radius…

Q: At a temperature of 20°C, the volume V (in liters) of 1.33 g of o, is related to its pressure p (in…

A: As per guideline we have to solve one question Please repost other question again

Q: An ice cube that is 3 cm on each side is melting at the rate of 2 cubic cm per min. How fast is the…

Q: The area of a circle increases at a rate of 6 cm /s. a. How fast is the radius changing when the…

Q: The area of a square with sides of length s is given by A = s2 . Find the rate of change of the area…

A: The area of a square with sides of length s is given by , A=s2. To find the rate of change of area…

Q: The area of a circle is increasing at a rate of 96 square feet per minute. At the time when the…

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 ft/min.…

A: Given information:

Q: The radius r of a sphere is increasing at a rate of 8 inches per minute. Find the rate of change of…

Q: The radius of a right circular cylinder is given by square root t + 9 and its height is 1/9…

A: GivenThe radius of a right circular cylinder and height is given by

Q: The area of a square is increasing at a rate of 56 square meters per minute. At the time when the…

Q: A heated circular plate has a radius of 24 in. What is the rate of change of the plate's radius if…

A: To find the rate of change of plate's radius

Q: The surface area of a cube with sides of length x is given by S = 6x2 . Find the rate of change of…

Q: The volume of a sphere is increasing at a rate of 8 cm3/sec. Find the rate of change of the radius…

A: Given : V= 32π/3 cm3 dV/dt = 8 cm3 /sec

Q: The area of a square with side s is A(s) = s². What is the rate of change of the area of a square…

A: We are given : The Area of a square with side s is A(s) =s2

Question

100%

The area A of a circle is increasing at a constant rate of 2cm's-. If the area of the circle is given by
A = Tr2, what is the rate of change of the radius when the radius is 4cm?
%3D

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Chain Rule$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

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?
If you travel 100 miles in two hours, then your average speed for the trip is Average speed=_________=________
Find the slope ofthe line in Figure l.
Researchers recorded that a certain bacteria population grew from 100 to 500 in 6 hours. At this rate of growth, how many bacteria will there be 24 hours from the start of the experiment?
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?
Researchers recorded that a certain bacteria population grew from 100 to 300 in 8 hours. At this rate of growth, how many bacteria will there be in 24 hours?