The original 24 m edge length of a cube decreases at the rate of 2 m divided by two minutes When x=1 m, at what rate does the cube’s surface area change and when x=1 m, at what rate does the cubes volume change ?

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

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Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/ sec. At what rate is a side of the ice…

A: We know that volume of a cube is given by V=a3 here V=volume of cube ,a=edge of cube Rate of change…

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Let y be height of wall upto ladder and x be distance between bottom of wall and bottom of ladder…

Q: The volume of a cube is decreasing at a rate of 24 cubic inches per minute. At the instant when an…

A: Given that  The volume of a cube is decreasing at a rate of 24 cubic inches per minute.…

Q: A trough filled with liquid is 2 m long and has a cross section of an isosceles trapezoid 30 cm wide…

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Q: The volume of a cube is increasing at a rate of 64 in/sec. At what rate is the length of each edge…

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Q: A cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is…

A: Given: The trough is being filled with water at the rate of 0.3 m3/min, dVdt=0.3 m3/min

Q: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

Q: The volume of an ice cube is decreasing at a rate of 1.5 cm³/sec. At what rate is a side of the ice…

A: option A is correct detailed solution with explanations given below

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

A: The objective is to find the rate at which the length of each edge of the cube is changing when the…

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…

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Q: The side of an equilateral triangle is increasing at the rate of 3 cm/s. What is the rate at which…

A: We can solve the given problem by using the following concept of differentiation. Let f(x) be the…

Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

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: The lower base of a trapezoid is 8 m. If its height is increasing at the rate of 0.5m/sec while its…

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Q: The length of the rectangle is increasing at a rate of 5cm/s and its width is decreasing at a rate…

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…

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Q: Each side of a square is increasing at a rate of 6 cm/s. At  what rate is the area of the square…

A:

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A: The derivative represents the rate of change. Since given that, the length of a rectangle is…

Q: The length of a rectangle is increasing at a rate of 4cm/s and its width is increasing at a rate of…

A: The length of a rectangle is increasing at a rate, dldt = 4 cm/s The width of a rectangle is…

Q: The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the…

A: Let the length of the ladder is L.

Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Each side of a square is increasing at a rate of 6 cm/s. To determine the rate at which the area of…

Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 1 m, at what…

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Q: The radius of a right circular cone is increasing at a rate of 5 inches per second and its height is…

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Q: The area of a rectangle remains 30 cm2. One side of the rectangle is expanding at a rate of 1 cm/s.…

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Q: If the ocean is opening at a rate of 3 cm/year., how wide will the ocean be in 100 million years in…

A: If the ocean is opening at a rate of 3 cm/year, then we have to find how much wide will the ocean be…

Q: When the lid is left off an ink bottle, the ink evaporates at a rate of 2.5 x 20 "cm" bottle…

A: Given that: Rate at which ink evaporates=2.5×10-6cm3s and Total volume of ink in the bottle is 36…

Q: A piece of wire of length 12 cm was cut into two pieces. The first was folded to form an equilateral…

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Q: The top of a ladder slides down a vertical wall at a rate of 1.5 m/s. At the moment when the bottom…

A:

Q: Water flows out of a hemispherical tank at a rate which is 4 times the square root of its depth. If…

A: GIVEN: Radius of the tank is 8 ft

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

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Q: The volume of a cube is increasing at a rate of 68 in3/sec. At what rate is the length of each edge…

A: Related rates of changes –                 The related rate of change is finding the rate of change…

Q: The top of a ladder that is 5 m long slides down a vertical wall at a rate of 2 m/s. At what rate…

A: Given :Length of ledder=5m

Q: The lengths of the edges of a cube are increasing at a rate of 8 ft/min. At what rate is the surface…

A:

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: The top of a ladder slides down a vertical wall at a rate of 0.15m/s. At the moment when the bottom…

A: We have given; the rate of change when ladder slides down i.e 0.15m/s The rate of change when it…

Q: A cylindrical pool has a height of 8 feet and radius of 6 feet. How fast is the volume (in cubic…

A: Volume of cylindrical shape V=πr2h ------------------(1)

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: Given: S the surface area of the cube, x the length of the cube and the length x of the cube…

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

A: It is given that, the volume of a cube is increasing at the rate of 6 cm3/min.   The objective is to…

Q: as a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4…

A: Volume of the sphere Shape ballon: V = 4/3ℼr3   (r = radius)   Now differentiate with respect to L,…

Q: A conical tank 20 feet in diameter and 30 feet tall (with vertex down) leaks water at a rate of 5…

A: To find the rate of water

Q: How long (in hours) would it take to fill a city water tank that has an inside diameter of 120 feet…

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Q: The length of a rectangle is increasing at a rate of 2 ft/s, and its width is increasing at a rate…

A: Here we have, The length of a rectangle is increasing at a rate of 2 ft/s, and its width is…

Q: A cone shaped icicle has an initial radius of 10 inches and a height of 15 inches. Once the height…

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 volume of a cube is increasing at a rate of 56 in/sec. At what rate is the length of each edge…

A: Given that the volume of a cube is increasing at a rate 56 in3/sec and the edges are 8 in. long. It…

Q: The volume of a cube is increasing at arate of 9 cubic feet per second.   how fast is the surface…

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Q: A tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in…

A:

Q: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

A: Given: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…