If a cube has sides of length express S, the total surface are of the cube, i terms of Find the rates of change of the surface area with respect to I wher I = 3 inches and I = 5 inches

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

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Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

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Q: The length x of a rectangle is decreasing at a rate of 5cm/seconds and the width y increasing at a…

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Q: The height of a right circular cone is increasing at 4 cm/sec and the radius is decreasing at 1.5…

A: Recall:  Volume of right circular cone, V=13πr2h Given, dhdt=4 cm/sec, drdt=-1.5 cm/sec  To find,…

Q: A cylinder has a height equal to its radius. Find the rate of change of volume V with respect to…

A: volume of cyclinder v =pi r2 h --1 given height =radius  h=r

Q: The volume of a cube decreases at a rate.1 of 15 m/sec. Find the rate at which the side of the cube…

A: It is given that the volume of a cube is decreasing at a rate of 15 m/sec. It is known that volume…

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: Water is flowing at the rate of 2 m3/min into a tank in the form of an inverted cone having an…

A: The given question can be depicted as follows:Now, the volume of a cone is given by V = 13πr2h

Q: The volume of a sphere is increasing at a rate of 8 cubic cm/sec.  Find the rate of change of its…

A: Let V be the volume of the sphere which is given in the question as,

Q: A tank of water in the shape of a cone is being filled with water at a rate of 3 m3/sec. The base…

A: To find: The rate of change of depth of water in the tank, when the height is 9 m. Given: The radius…

Q: A small plane flies horizontally on a line 400 m directly above an observer with a speed of 70 m/s.…

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Q: A cylindrical column is (3m) high and (0.2m) radius, if the radius of the column increases at a rate…

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Q: A drum of oil in the shape of a cone is leaking oil at a constant rate of 3cm / hour. The base…

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Q: The Volume (V) of a cone varies jointly as its height (h) and the square of its radius (r). Find the…

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Q: According to the special theory of relativity, the mass of an object moving at speed v is given as…

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Q: Find the rate of change of the area of a square with respect to the length z of a diagonal. What is…

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Q: A large conical tank of height H being filled with water by a hose at the top of the tank at a rate…

A: given: A large conical tank of height H=9 feet and radius R=3 feet is being filled with water by a…

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: The temperature at a point in a ball with conductivity K is inversely proportional to the distance…

A: We know:

Q: The radius of a circle is increasing at the rate of 0.7 cm/c.what isthe rate of oncreasing of its…

A: Differentiate circumference wrt t

Q: The length l of a rectan-gle is decreasing at the rate of 2 cm/sec while the width w is increasing…

A: (a)Given:

Q: 2. A tank with a shape of a cone is 20 feet deep and has a diameter of 10 feet at the top. Water is…

A: Given; Diameter = 10 feet  Height = 20 feet

Q: The length l of a rectangle is decreasing at the rate of 2 cm/sec while the width w is increasing at…

A: Given:The length of rectangle is decreasing at rate 2cm/sec  The width  of rectangle is…

Q: The linear density of a cable wire is the rate of change of its mass with respect to its length. A…

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Q: The time rate of change of the radius of a sphere is 1/2π, when its radius is 5 cm , find the rate…

A: According to the question, we have to find the rate of change of surface area of the sphere with…

Q: A tank of water in the shape of a cone is leaking water  at a constant rate of  4ft^3/hr. The base…

A: Given : The initial conditions are,  cone is leaking water at a constant rate of 4ft^3/hr.  The base…

Q: 2. The radius and lateral area of a right circular cylinder change at the rates of 1 cm/s and -2…

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Q: The longer base of an isosceles trapezoid is one more than 1/3 of the shorter base. If the altitude…

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Q: water is running out of a conical funnel at the rate of 1 cu inches per second. If the radius of the…

A: This question is related to application of derivatives.

Q: A tank of water in the shape of a cone is being filled with water at a rate of 12 m3/sec. The base…

A: Consider the given information about cone. Base radius of the cone R=26 m Height of the cone H=8 m…

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

A: see below the answer and calculation

Q: A water tank has the shape of an inverted circular cone (point down) with a base of radius 6 feet…

A: solution:- we have to find dh/dt?

Q: The radius of a circle is increasing at a constant rate of 0.2 meters per second. What is the rate…

A: At the instant when the perimeter of the circle is 20π, then p=2πr20π=2πrr=10 m

Q: The temperature at a point in a ball with conductivity K is inversely proportional to the distance…

A:

Q: (a) Water is flowing out at the rate of 6 m / min from a reservoir shaped like hemispherical bowl of…

A: Given: The depth of the water is denoted as y. The radius of the water is denoted as r. The volume…

Q: The side of an equilateral triangle is increasing at a rate of 3 m/sec, then the rate at which its…

A: Let the side of an equilateral triangle be x cm.∴ Area of equilateral triangle, A = √3/4x2…

Q: the radius r of a right circular cylinder with fixed height of 48 inches is increasing. Find the…

A: NOTE: Refresh your page if you can't see any equations. . the volume of the cylinder is given by…

Q: A conical tank has height 3 m3 m and radius 2 m2 m at the base. Water flows in at a rate of 2…

A:

Q: The side of a square is increasing at the rate of 0.2 cm/sec . Find the rate of increase of the…

A: we know that the perimeter of the square is with side x is                        P=4x…

Q: The altitude of a triangle is increasing at a rate of 1 cmminwhile the area of the triangle is…

A: Givendhdt=1cm/mindAdt=2cm2/minA=100cm2h=10cm

Q: A right circular cylinder has a 4 inch diameter and is filling with water at a constant rate.  The…

A: Consider the volume of right circular cylinder V. Differentiate it w.r.t time t.…

Q: The radius r of a right circular cylinder with a fixed height of 48 inches is increasing. Find the…

A: The solution for the above question is as shown below.

Q: The centripetal force of an object of mass m is given by F(r)=mv2r, where v is the speed of rotation…

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Q: 2. The height and volume of a right circular cone change at the rates of 1 cm/s and -2 cm^3/s,…

A: Let's find.

Q: 2. The volume and radius of a right circular cylinder change at the rates of 1 cm^3/s and -2 cm/s,…

A: Given : Radius = 2cm, height = 1 cm Rate of change of radius is 2 cm/s and rate of change of volume…

Q: The volume V of a right circular cone of radius r and height h is given by V = Tr²h. Find a formula…

A: To find the instantaneous rate of change:

Q: A right circular cylinder has a fixed height of 4m. Find the rate of change of its volume V with…

A: Let h and r denote the hieght and radius of base of the cylinder.1

Q: A right triangle with legs of lengths x and y has its area given by the following. If the rate of…

A: Area of a right triangle is given by A = 12xy Rate of change of x is 2 units per minute i.e., dxdt =…

Exponential Growth Model

The relation that represents an exponential function is: