A pebble is dropped into a calm pond, causing ripples in the form of concentric circles, as shown. The radius r of the outer ripple is increasing at a constant rate of 1 foot per second. When the radius is 4 feet, at what rate is the total area A of the disturbed water changing?

Q: The base radius, r, of a cylinder is decreasing at a rate of 0,2cm/s while its height, h, is…

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Q: O. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

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Q: The side of a cube is increasing at a rate of 5cm/sec, find the related change in surface area wher…

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Q: If the radius of a sphere is increasing at a constant rate of 2 cm/sec, then the volume 3 is…

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Q: 11. If a snowball melts so that its surface area decreases at a rate of 1 cm/min, find the rate at…

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Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: We have given change in edge with respect to time is 2cm/sec.  We have to find the changes in…

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10…

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Q: A vertical cylinder is leaking water at a rate of 3 m/sec. If the cylinder has a height of 10 m and…

A: The volume of the cylinder is given by V=πr2h, where V=volume of the cylinder r=radius of the…

Q: A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius…

A: Rate of Radius of outer ripple increasing = 1 ft/sec                    Radius = 4 feet

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10…

A: Given: Rate of change of volume = 10ft3/min Diameter of the base of the cone is approximately three…

Q: The legs of an isosceles right triangle increase in length at a rate of 6 m/s a. At what rate is the…

A: Let, l be the length of a legth of a leg of an isosceles right triangle, h be the length of the…

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: 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: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate (in…

A:

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: We have to find the rate of change of surface area.

Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at…

A: Solve using increasing & decreasing function.

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate (in…

A: we have to find the rate change in diameter

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in…

A:

Q: Consider a pool shaped like the bottom half of a sphere, that is being filled. The radius of the…

A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm/min, find the rate (in…

A: Given  Decreasing rate of surface area = 3cm2/min To find: the rate of decreasing of diameter when…

Q: A plane flying parallel to the ground at a height of 4 km passes over a radar station R. A short…

A: NOTE: Refresh your page if you can't see any equations. . here we have y=4 when s=5, s'=300 km/h

Q: The volume of a cube is increasing at a rate of 60 in3/sec. At what rate is the length of each edge…

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Q: The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in…

A: Rate of increase of radius of a spherical ball,drdt= 2 cm/min Radius of the ball = 9 cm

Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 8 centimeters per second.a To determine how fast is…

Q: The volume of a sphere is increasing at the rate of 6 cm3/hr. at what rate is its surface area…

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Q: The volume V of a right circular cone of radius r and height h is given by V = 1/3 πr2h. a) What is…

A: Simply take derivative with respect to given variable considering other as constant.

Q: 3) If a spherical snowball melts so that its surface area decreases at a rate of 1 cm? he rate at…

A: It is given that a spherical ball melts so that its surface area decreases at a rate of 1 cm2 per…

Q: Find the rate at which the volume of a right circular cylinder of constant altitude 10 ft changes…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16…

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Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 10…

A: Given that dVdt=10, h=15 find dhdt r=radius of base at time t h= height at time t V= volume of cone…

Q: If the radius of a sphere is increasing at a constant rate of 3 cm/sec, then the volume is…

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Q: The edge length of a cube is 12 cm and increasing at a rate of 2 m. How fast is the Surface Area of…

A: Given dx/dt=2cm/hr X=12cm

Q: The fixed sides of an isosceles triangle are of length 6 cm. (See the figure.) If the sides slide…

A: Given: The fixed sides of an isosceles triangle are of length 6 cm and the sides slide outward at a…

Q: A spherical snowball of radius r cm has surface area S cm?. As the snowball gathers snow, its radius…

A: First let us find the rate of increase of radius. When t=4, r = 20 cm, (From the graph given) When t…

Q: A spherical snowball is melting in such a way that its surface area decreases at the rate of 1…

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Q: D A child is rolling a spherical snowball with an outer 1) Tayer of ice so that the volume Of the…

A: As per bartleby answering guidelines we are supposed to answer only first question in case of…

Q: A cube is expanding in such a way that the length of its diagonal is increasing at a rate of 5…

A: Let y be the diagonal, x be the length of an edge and V be the volume of the cube at any time t.…

Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: The radius of a sphere is decreasing at a rate of 14cm/s.The radius is 2cm.

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: paper cup has the same shape of a cone with the height of 8cm and a radius 3cm (at the top). If…

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Q: All edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast is the surface…

A: From the given data: The rate of expanding of a cube is 4cm/sec

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: All edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast is the surface…

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Q: Suppose that the radius of a circular water pool is expanding at a rate of 2 meters per hour, when…

A: Given:

Q: How fast is the surface area of a cu

A: Given that : Edge of a cube = 30 cm Th edge changing at the rate of 3 mm per second.

Q: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: Given : 1) Oil spills from a ruptured tanker and spreads in a circular pattern.             2)…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.