A balloon is deflating at a constant rate of 12 cm3 per second. When the volume of the balloon is 4.5T cm³, what is the rate of change of the surface area? Note that for the balloon the surface area S and the volume V are given by: S = 47r2 and V = 3

Q: Suppose a snowball remains spherical while it melts, with the radius r shrinking at 2 inch(es) per…

A:

Q: The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rates of…

A:

Q: The length of a rectangle is given by 4t + 9 and its height is √t, where t is time in seconds and…

A: Given:

Q: A rectangle has width w inches and height h inches, where the width is twice the height. Both w and…

A: It is given that, a rectangle has width w inches and height h inches, where the width is twice the…

Q: The length of a rectangle is given by 2t + 5 and its height is Vt, where t is time in seconds and…

A: In the given question the length and height of the rectangle are given:   The area of the rectangle…

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: A rectangular water tank is being filled at the constant rate of 35lt/s. The base of the tank has…

A: From the above information,  A rectangular water tank is filled at the constant rate, dVdt=35 lt/sec…

Q: The length of a rectangle is given by 4t - 3 and its height is 2t, where t is time in seconds and…

A: Given the rectangle whose length and height are given L=4t−3H=2t3

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 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: A​ hot-air balloon is 190 ftabove the ground when a motorcycle​ (traveling in a straight line on a…

A: Let x be the horizontal distance from balloon to motorcycle, y be the vertical distance from the…

Q: If the rate of change of the side length of an equilateral triangle is 2br / sec, what is the rate…

A: Please rate and feel free to ask any query about any part of the question.  I have used applications…

Q: Find the rate of change of area of the square in m/s with respect to its side when the sides, s, is…

A:

Q: The length of a rectangle is given by 2t + 3 and its height is √t, where t is time in seconds and…

A:

Q: 4. A beach ball is deflating at a constant rate of 10 cubic centimeters per second. When the volume…

A: NOTE: You have posted multiple questions we have given answer to the first question if there is a…

Q: How do you solve?

A: Given, Side of square= x x(t)= 3t+1 Therefore, Area= (3t+1)*(3t+1) A(t)= 9t²+6t+1

Q: The volume V of a right circular cylinder is given by the formula V = 1/3ar h where r is the radius…

A:

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: Given a cylinder surmounted on both ends by a hemisphere, find the rate of change of its volume with…

A: Given:     Cylinder is surmounted by hemisphere at both ends.And height of cylinder is 5 meter.

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

A:

Q: To determine drug dosages, doctors estimate a person’s body surface area (BSA) (in meters squared)…

A: Solution:Given     BSA=hm60To calculate  the rate of change of BSA with respect to mass for a person…

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: The radius of a sphere decreases at the rate of 4 m/s. when the radius is 10m, then the rate of…

A: We will find the rate of change in surface area as following .

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: If the area of a healing wound changes at a rate given approximately by dA 4 for 1 <t<10 is in days…

A:

Q: The area A of a circle is increasing at a constant rate of 2cm's-. If the area of the circle is…

A:

Q: where t is time in seconds and the dimensions

A:

Q: The volume of. a cube decreases at a rate of 0.5 ft?/min. what is the rate of change of the side…

A: Application of derivative

Q: Suppose that D = √x² + y² is the length of the diagonal of a rectangle whose sides have lengths x…

A: To find the formula for the rate of change of D with respect to x, differentiate D=x2+y2, using the…

Q: The radius of a right circular cylinder is given by √(t + 2) and its height is 1/2√t, where t is…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

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: A population of ladybugs begins with 50 ladybugs and increases at a rate of l'(t) ladybugs per week.…

A: A population of ladybugs begins with 50 ladybugs and increases at a rate of l'(t) ladybugs per week…

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

A:

Q: The radius of a right circular cylinder is given by sqrt(t+7) and its height is 2 (sqrt(t)), where t…

A:

Q: The volume of a cube with sides of length s is given by V = s3. Find the rate of change of volume…

A:

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: 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 kinetic energy K of a mass is proportional to the square of its velocity y. If K = 12,960 joules…

A: To determine the kinetic energy.

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 rectangular water tank is being filled at the  constant rate of 351t/s. The base of the tank has…

A:

Q: The sides of a cube increase at a rate of R cm/s. When the sides have a length of 2 cm, the rate of…

A:

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:

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

A:

Q: The length of a rectangle is increasing at a rate of 9 in./s, while its width is decreasing at 2…

A:

Q: It follows from Poiseuille's Law that blood flowing through certain arteries will encounter a…

A: Given  R(x) = 0.25(1 + x)4

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

A:

Q: Given the function f(x) = x which of the following is a valid formula for the instantaneous rate of…

A: The given function fx=x23 The instantaneous rate of change is given by limh→0fa+h-fah