12. A cube's surface area increases at the rate of 72 in?/sec. At what rate is the cube's volume changing when the edge length is x = 3 in?

Q: 4. A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate…

A:

Q: 4. A baseball diamond is a square 90 ft on a side. A player runs from first base to second base at…

A:

Q: 3. The radius of a spherical balloon is increasing at the rate of 2 cm per minute. How fast is the…

A:

Q: 2. A spherical snowball melts at a rate of 367T in /sec. At what rate is the radius of the snowball…

A:

Q: 1. A paper cup has the shape of a cone with height 12 cm and radius 4 cm (at the top). If water is…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 8. If a snowball melts so that its surface area decreases at a rate of 4 cm2 /min , find the rate at…

A:

Q: 2. A balloon in the shape of a sphere is being inflated at the rate of 100 cm/sec. a. At what rate…

A: a)  Given that the balloon is in the shape of sphere and it is being inflated at the rate of…

Q: 2)The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume…

A: Given,  The radius of a sphere decreases at the rate of 1 m/sec  We have to find the rate at which…

Q: Water is dripping into a hemispherical bowl with a radius of 8 cm at a rate of 1 cubic cm per…

A:

Q: If the volume of a cube is decreasing at a rate of 24 in sec, then find the rate at which the length…

A:

Q: 16.Suppose that the dimensions of a cylinder change at constant rates: the radius of the base is…

A: Use the derivative and substitute the given values.

Q: A cube’s surface area increases at the rate of 72 in2/sec. At what rate is the cube’s volume…

A: Given:

Q: The radius of the base of a right circular cone is decreasing at the rate of 4 cm/min, and the…

A:

Q: 11. A snowball melts so that its surface area decreases at a rate of 0.5 cm/min. Find the rate at…

A:

Q: 8. The radius of an inflating balloon in the shape of a sphere is changing at a rate of 3cm/sec. At…

A:

Q: 9. When a particular plate of metal is heated in an oven, its radius increases at the rate of…

A:

Q: The original 24 m edge length x of a cube decreases at the rate of 3 m/min. a. When x = 4 m, at what…

A:

Q: 11. If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at…

A:

Q: 9) A spherical snowball is melting in such a way that its volume is decreasing at a rate of 3cm /…

A: Let, r=radius  V=volume Given that dV/dt= 3 , we have to find dr/dt=? at r=12 cm Volume and radius…

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

A: Here  radius of bubble is given and rate of change of radius of bubble is also given

Q: 2) The radius of a sphere decreases at the rate of 2 m/sec. Find the rate at which the volume…

A:

Q: 3.) A conical tank is 10ft across the top and 12 ft. deep. If oil is poured into the tank at the…

A:

Q: The original 24 m edge length x of a cube decreases at the rate of 5 ​m/min.   a. When x=5m, at what…

A:

Q: The volume of a cube decreases at a rate of 12.1 m/sec. Find the rate at which the side of the cube…

A: we have to find the rate change of a side of cube

Q: 1. A spherical balloon is being inflated so that the volume is increasing at the rate of 5 ft.³ per…

A:

Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: 1. We are inflating a spherical balloon. At what rate is the volume of the balloon changing when the…

A: Since you have asked multiple question (1&2) we will solve the first question for you. . If you…

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

Q: Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up…

A:

Q: 20. The length of a rectangle is increasing at a rate of 5 cm/sec and the width is decreasing at a…

A:

Q: If the sides of a square increase in length at a rate of 3 in/s, then the rate of change of the…

A: Let the side length of a square be x Now, Side length increases at a rate of 3in/s. That is, dxdt=3…

Q: 7. A spherical balloon is being filled in such a way that the surface area is increasing at a rate…

A:

Q: 3. The volume of a cube is increasing at the rate of 6 cm³/min. How fast is the surface increasing…

A:

Q: 2. The radius of a sphere is decreasing slowly at the rate of 2 cm/week. How fast is the volume…

A: Consider the given information. The volume of the sphere is defined as, V=43πr3

Q: 11. At what rate is the volume of the cube changing if the edge is 8 cm and is changing at 4 cm/s?

A: As we know that; The expression for the volume of the cube with the edge length ''a'' is: v=a3…

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 4 m, at what…

A: As Given :                   The length x of Cube decrease at a rate of 2 m/min.…

Q: 4. The radius of a sphere decreases at a rate of 3 m/sec. Find the rate at which the surface area…

A: Surface area of sphere is given by: A=4 π r2 Find the rate at which the surface area decreases when…

Q: 3. The area of a circular inkblot starts from zero and grows at a constant rate of 4n cm/minute.…

A: Use the derivative and formula for area of circle.

Q: 4. Water is running out of a conical tank 3 m across the top and 4 m deep at the rate of 2 m3 /min.…

A: given  h = 4 m  (Note: measurement of h is always taken from bottom) r = (3 ÷ 2 ) = 1.5 m dVdt = 2…

Q: 2) The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume…

A:

Q: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

A: If the original 24 m edge length x of a cube decreases at the rate of5 m/min, when x = 3 m at what…

Q: The radius of a right circulare cylinder is increasing at the rate of 3 in/sec, while the height is…

A: To determine the change of rate of the volume of cylinder.

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Volume of sphere: V = 43πr3, where r is radius of sphere. Surface area of sphere: S = 4πr2, where r…

Q: 1. The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: I have stated the used formulas in the solution

Q: The original 24 m edge length x of a cube decreases at the rate of 4 m/min. a. When x = 3 m, at what…

A: Given query is to find rate of change of surface are and volume when rate of chnage edge length is…

Q: 1. The volume of a cube decreases at a rate of 12 m/sec. Find the rate at which the side of the cube…

A: This question is related to application of derivatives.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.