Sunspots The area of a circular sunspot is growing at a rate of 1,200 km^2/sec. a. How fast is the radius growing at the instant when it equals 10,000 kilometers?  b. How fast is the radius growing at the instant when the sunspot has an area of 64,000 square kilometers?  (Use the area formula to determine the radius at the instant)

Q: A board 10 feet long slides down a wall. At the instant the bottom end is 8 feet from the wall, the…

A: Pythagoras theorem: Hypotenuse2=Base2+Perpendicular2 Product rule of differentiation: (fg)'=fg'+gf'…

Q: Optimization: • A meteor (spherical in shape) enters earth's atmosphere and starts burning up in…

A: A is the area of the meteor , which is a surface area of sphere A=4πr2 sq.units Given that,…

Q: To evaluate the possibility of using pyramid-shaped vessel, the rate of change of the dimensions…

A: This question can be solved by using rate of change of physical quantities.

Q: the trough is being filled with water at a rate of 0.2m3/min0.2m3/min

A:

Q: Sand falls from a conveyor belt at the rate of 10 m3/min onto the top of a conical pile. The height…

A: It is given that rate of volume increases and the relationship between height and radius is also…

Q: Two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3 cm / sec.…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 8100 cubic centimeters per min at the…

A: I am attaching image so that you understand each and every step.

Q: Water is leaking out of an inverted conical tank at a rate of 11700 cubic centimeters per min at the…

A: Let's find rate of water is being pumped into the tank.

Q: Liquid feed at a rate of 8 L/min is introduced into a cylindrical tank with a bottom area of 335…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 7900.0 cubic centimeters per min at…

A:

Q: Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their…

A:

Q: A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away…

A: Lets make the figure

Q: A hemispherical tank of radius 1.75 m is full of water. It is connected with a pip which emoties it…

A: It is known that the radius of hemisphere, r=1.75m

Q: Water is flowing at the rate of 50 m3/min from a shallow concrete conical reservoir (vertex down) of…

A: Water is flowing at rate of 50 m3/ min from a shallow concrete conical reservoir of base radius 45 m…

Q: To evaluate the possibility of using pyramid-shaped vessel, the rate of change of the dimensions…

A: Volume of pyramid = 1/3 * base area * height

Q: Water is leaking out of an inverted conical tank at a rate of 7600 cubic centimeters per minute at…

A:

Q: The circumference of a sphere was measured to be 84 cmwith a possible error of 0.5 cm.(a) Use…

A:

Q: Water is flowing at the rate of50 m3/min from a shallow concrete conical reservoir (vertexdown) of…

A:

Q: MY A board 20 feet long slides down a wall. At the instant the bottom end is 16 feet from the wall,…

A:

Q: A projectile is fired straight upward with an initial velocity of 100 m/s from the top of a building…

A: (a)

Q: Water is flowing at the rate of50 m3/min from a shallow concrete conical reservoir (vertexdown) of…

A: Given that, water is flowing at the rate of 50 m3/min from a shallow concrete conical reservoir…

Q: A spherical balloon is losing air at the rate of 4 cubic centimeters per minute. How fast is the…

A:

Q: double integral.

A: We have to solve the given integral ∫∫Rx cosy dA where R is the triangular region.

Q: Water stored in an inverted right circular cone leaks out at a constant rate of 2 ft3 per day. The…

A:

Q: he rate (liters per minute) at which water drains from a tank recorded at half-minute intervals. Use…

A: Given interval is half minute width is 0.5 First we find out the area using left end points. Start…

Q: A hollow cone has height 5 feet and radius 2 feet. The vertex of the cone is pointed down so that it…

A:

Q: Water flows from a storage tank at a rate of 700 − 7t liters per minute. Find the amount of water…

A:

Q: Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular…

A:

Q: 6. A thin circular plate made of gold changes size when heated, but remains in a circular shape. The…

A: Let r be the radius of the circular plate.Then, the area, A=πr2Given that dAdt=2 cm2/min

Q: When I circular played in metal is heated in the oven it’s radius increases at a rate of 0.01…

A: We use application of derivatives to find rate of change of area of circle.

Q: A board 20 feet long slides down a wall. At the instant the bottom end is 16 feet from the wall, the…

A:

Q: = trapezoidal rule to approximate the integral

A:

Q: 1. A stone is dropped into a still pond. Concentric circular ripples spread out and radius of…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 10,000 cm3/min at the same time that…

A:

Q: Water flows from a storage tank at a rate of 300 – 7t liters per minute. Find the amount of water…

A:

Q: 3) Sand falls from a conveyor belt at a rate of 10 m’ / min onto the top of a conical pile. The…

A: Differentiate volume wrt t

Q: 3. Water flows from a storage tank at a rate of (500 – 5t) liters per minute. Find the amount of…

A:

Q: A ladder 10 meters long leans against a vertical wall. The lower end of the ladder is pulled away…

A: Let x= distance of the lower end from the wall y= height of the top of the ladder Given that dx/dt=…

Q: dx xVa² -x²

A: Given that integral. :  dx/[x(√a2 -x2)]. We find solution of this integration by using general…

Q: Photic zone In contrast to the situation described in the pre- vious exercise, in parts of New York…

A: The Beer Lambert law states that the amount of light that penetrates to a depth of x meters in an…

Q: Water is being drained at a rate of 50 m3/min from a concrete conical reservoir (vertex down). The…

A:

Q: Sand falls from a conveyor belt at a rate of 9m3/min onto the top of a conical pile. The height of…

A:

Q: A ball is inflated at a rate of 200x cubic inches per second. Find the rate at which the radius is…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 7500.0 cubic centimeters per min at…

A: Here I am attaching image so that you understand each and every step.

Q: Sand falls from a conveyor belt at a rate of 10 m° / min onto the top of a conical pile. The height…

A:

Q: Water is leaking out of an inverted conical tank at a rate of 12800.0 cubic centimeters per min at…

A: Given that       Water is leaking out of an inverted conical tank at a rate of 12800 cubic…

Q: Water flows from a storage tank at a rate of (500 − 5t) liters per minute. Find the amount of water…

A: Given: 500-5t

Q: 2. [Growth of a tumor] When the radius of a spherical tumor is 6 mm, it is growing at a rate of 0.1…

A: To determine how fast the volume is changing.

Q: Water at the rate of 10 cm3/ min is pouring into the leaky cistern whose shape is a cone 16 cm. deep…

A:

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.