3. A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At what rate is the perimeter changing? (b) At what rate is the area changing at the moment the side length is 10 in?

Q: 2. Sand is being dropped at the rate of 10ft.3/min into a conical pile. If the height of the pile is…

A:

Q: Suppose the edges of a cube are increasing at a constant rate of 8 m/hr. Then, the volume of the…

A:

Q: Suppose that a spherical balloon is being inflated and the radius of the balloon is increasing at a…

A: The increasing rate of radius of ballon is

Q: The edges of a cube are expanding at a rate of 5cm per second. How fast is the volume changing when…

A:

Q: The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is…

A: Given that, drdt=1.1 in/s and dhdt=-2.7 in/s. Also, it is given that r=102 in. and h=162 in. It is…

Q: At a certain instant the dimensions of a rectangle are 8 and 12 feet, and they are increasing at the…

A: At a certain instant the dimensions of a rectangle are: Length L=8 feetWidth W=12 feet

Q: All edges of a cube are expanding at a rate of 9 centimeters per second. (a) How fast is the volume…

A: GivenAll edges of a cube are expanding at a rate of 9 centimeters per second

Q: Suppose that a given moment, the radius of a right circular cylinder is 2 cm and increasing at a…

A:

Q: A conical vessel 12 cm deep and with a radius of 6 cm at the top, is being filled with water. If the…

A: A conical vessel 12 cm deep and with a radius of 6 cm at the top. That is, the height of the cone is…

Q: 3. Water is flowing out of a cylindrical storage tank at a rate of 2 m3/min. If the tank has a…

A:

Q: A cube has sides that are increasing at a rate of 10 cm/s. At what rate is the volume increasing…

A: Valur=?

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

A:

Q: 8. The volume of a right circular cylinder is 60 cm³ and is increasing at 2 cm³/min at a time when…

A: Given:                                 Volume of a right circular cylinder V…

Q: A spherical balloon has a radius r that is increasing at a rate of 3 cm/s. At what rate is the…

A:

Q: A cancer tissue is in the shape of a sphere whose radius is increasing at the rate of 2 mm per day.…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. A water tank is in the form of an inverted right circular cone h feet deep and d feet wide across…

A: At any time t, let the height of the water be h ft and the radius of the cone formed by the volume…

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

A:

Q: A sperical snowball is melting in such a way that its volume is decreasing at a rate of 1 cm^3/min.…

A: Volume of the sphere formula:‘r’ is the radius of the sphere

Q: Suppose that a mothball loses volume by evaporation at a rate propotional to its instataneous area.…

A:

Q: A spherical balloon is being deflated at a rate of 80 cm3/min. At what rate is the radius decreasing…

A:

Q: A trough whose cross section is an equilateral triangle is 6 m long and 2 m wide across the top. If…

A: Solve by diagram and using formulas of equilateral triangle

Q: Find the rate of change. Volume of a cube with respect to its sides when s = 5

A: The volume of a cube with side s is V=s3 Differentiate with respect to s dVds=ddss3=3s2

Q: At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 2 cm/s?

A: To find the rate at diagonal of a cube is increasing

Q: 5. The volume of a cube is increasing at a rate of 10 cm³/min . How fast is the surface area…

A: Given:- The volume of a cube is increasing at a rate of 10 cm³/min. To find:- How fast is the…

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: To calculate the required rate of change using partial derivatives

Q: A rectangle is expanding such that its length is always 4 times its width. If the width is…

A:

Q: 1. Water is flowing into a vertical cylindrical tank at the rate of 24 cu. ft. per min. If the…

A: Given , Water is flowing into vertical tank at rate if 24 cu .ft . per min. Radius of tank is 4ft.…

Q: 2. Suppose that the bottom of a conical shaped tank of water has been ruptured. At the instant when…

A:

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: let the side of the square is a meter, and the area is A given that da/dt=3m/sec a. a=15m area of…

Q: 1. Suppose that oil spills from a container and spreads in a circular pattern. If the radius of the…

A:

Q: 3. Water is flowing out of a cylindrical storage tank at a rate of 2m/min. If the tank has a radius…

A:

Q: Assume a pink paint spill spreads in a circular pattern whose radius increases at a rate of 2 in/s.…

A:

Q: Suppose that a tumor in a person’s body has a spherical shape and that treatment is causing the…

A: we know that the volume of the sphere                       V=43πr3                          (1)

Q: 2. A cylindrical plastic container with a radius of 15 cm is being filled with orange juice at a…

A:

Q: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: Given that all edges of a cube are expanding at a rate of 7 cm per second. Let the edge of a sphere…

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

A:

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

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

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: 2. All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the volume…

A:

Q: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant rate. At…

A: Given: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant…

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: A rectangle is expanding such that its length is always 4 times its width. If the width is…

A: Let's find.

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: A spherical balloon has a radius r that is increasing at a rate of 3 emfs. At what rate is the…

A: Given: drdt=3πcm/s   To find: dvdt when r=10

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

A: Given , Bacterial cell is in spherical shape.Let radius be 'r' μm . ∴ Volume of cell, v v = 43π…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.