The diameter of a sphere is 5(2x+ 5), the rate of change of its surface area with respect to x is

Q: The length of a rectange is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A:

Q: For the function y = x2 , find the instantaneous rate ofchange of y with respect to x when x = 3.

A: The instantaneous rate of change of y with respect to x is given by dy/dx

Q: James is pumping air into a spherical balloon at a rate of : бст3 What is the rate of change of the…

A: Find the rate of change in the question by doing the derivative with respect to time after…

Q: The volume of a sphere is increasing at a rate of 4 cm3/sec. Find the rate of change of its surface…

A: We will use derivative as rate of change

Q: Is the rate of change of a cube's volume linearly proportional to the rate of change of its side?

A: Rate of change of volume of cube

Q: The width of a rectangle increases at a rate of 2 cms. The length is five times its width. Find the…

A:

Q: A spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm / min.…

A: Given-  dVdt=-2cm3/min (negative sign indicates that it is decreasing). To find- The rate of radius…

Q: The radius of a spherical balloon is increasing at a rate of 4 centimeters per minute. How fast is…

A: We have to find

Q: Find the instantaneous rate of change of 7. y = (x + 1)*(x – 3) at a = 1.

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Q: What is the rate of change of y = In x at x = 10?

A: Explanation: Given that,  y=lnx   Concept Used: To find the rate of change we will find the…

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: What is the rate of change of the volume of a ball (V = (4/3)πr3) with respect to the radius when…

A: Given: volume v=43πr3 for finding rate of change of volume with respect to radius r, we…

Q: An inverted conical tank with a height of 6 feet and a diameter of 4 feet that was filled with water…

A: It is given that, the height and diameter of the conical tank is 6 feet and 4 feet, respectively.Let…

Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the…

A: Let be the volume and r be the radius of the sphere respectively.

Q: What is the rate of change of y with respect to x for this function?

A:

Q: What is the rate of change of the volumeof a ball (V = (4>3)pr3) with respect to the radius…

A: The volume of a ball with radius r is given by V=43πr3 Recall that the rate of change is given by…

Q: If f(x) = 12x2 - x', what is the rate of change of f'(x) at (2, 40)? %3D Need Help? Watch It

A: Rate of change of f'(x)

Q: The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of…

A: We need to find reat of change of area.

Q: Let  x(V) = V1/3  be the length of the side of a cube in terms of its volume. As V decreases, does…

A: V is decreasing that is dv/dt is negative  Let dv/dt =-k where k is constant.

Q: Find the rate of change of the total surface area of a cylinder of radius r and height h, when the…

A:

Q: A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, t…

A:

Q: The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and…

A: Formula:  Area=length times height A(t)=t(6t+5)

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

A:

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: The derivative represents the rate of change. Since given that, the length of a rectangle is…

Q: The length of a rectangle is increasing at a rate of 4cm/s and its width is increasing at a rate of…

A: The length of a rectangle is increasing at a rate, dldt = 4 cm/s The width of a rectangle is…

Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

A:

Q: A designer develops a cylindrical box with a fixed height of 15 cm. Calculate the instantaneous rate…

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Q: A balloon has just been inflated. Calculate the instantaneous rate of change by which the area…

A: Introduction: A geometric shape with a sphere-like appearance. In three dimensions, the sphere is…

Q: The height h of a right circular cylinder is twice its radius r. Find the rate of the volume V of…

A: The volume of the right circular cylinder is given as: V=πr2h where 'r' is the radius of the cone…

Q: What will be the rate of change of the surface of the sphere when the radius of the sphere is 5.00…

A: Given; Radius= 5cm And time rate of change in Radius is= π/2.

Q: The length of a rectangle is increasing at a rate of 7cm/s and its width is increasing at a rate of…

A:

Q: Find x0 given that the rate of change of y =2x2+x-1 with respect to x at x=x0 is 4

A: giveny =2x2+x-1 rate of change=4rate of change=dydxdydx=4x+1

Q: Find the average rate of change of g(x) = – 4x° + 5 from x = – 4 to x = 3 3 %3D - -

A:

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A:

Q: The radius r of a sphere is increasing at a rate of 4 inches per minute.

A:

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A:

Q: The length of a rectangle is increasing at a rate of 9 cm/s and it’s width is increasing at a rate…

A: Rectangle: It is a polygon with four side and opposite sides are equal.  Also. the all the four…

Q: A spherical balloon is deflated at a rate of 10 cm3 s-1. Find the rate change of the surface area…

A: given: A spherical balloon is deflated at a rate of 10 cm3s-1. we have to find the rate change of…

Q: A spherical balloon is being deflated at the rate of 10 cm/s. What is the rate of change for the…

A:

Q: The side of a square is increasing at the rate of 0.2 cm/sec . Find the rate of increase of the…

A: we know that the perimeter of the square is with side x is                        P=4x…

Q: The length of a rectangle is increasing at a rate of 2 ft/s, and its width is increasing at a rate…

A: Here we have, The length of a rectangle is increasing at a rate of 2 ft/s, and its width is…

Q: What is the rate of change of the area of a circle (A = pair2 ) with respect to the radius when the…

A: It is required to calculate the rate of change of area of circle with respect to radius when radius…

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: Let the length of the rectangle be:  l  cm Let the width of the rectangle be:  w  cm

Q: The radius of an air bubble is increasing at the rate of 1/2 cm/s.At what rate is the volume of the…

A:

Q: How can you relate the rate of change for the surface area of a cube (dSA/dt) as compared with its…

A: we know that surface areaS.A. and volumeV of cube is given by S.A.=6l2…

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 radius of a sphere is increasing at a rate of 4mm/s.How fast is the volume increasing when the…

A: Given that the radius of a sphere is increasing at a rate of 4mm/s. That is, Now consider the…

Q: Find a formula for the average rate of change of f (x) = x^3 over [2, x] and use it to estimate the…

A: We use the average rate of change formula

Q: The radius of a sphere is decreasing at a rate of 2 centimeters per second. At the instant when the…

A: Write the equation of the surface area of sphere solve it as per given in step 2