How fast is the volume of this box increasing when the edge is 8 inches?

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

A: Surface area of cube = 6x2Where x is the edge of the cube

Q: A trough is 10 ft long and its ends have the shape of isosceles triangles that are 2 ft across at…

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Q: # 3) Each side of a square is increasing at a rate of 6cm/s. At what rate is the area of the square…

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Q: A ladder 10 feet long is resting against a wall. If the bottom of the ladder is sliding away from…

A: Let the base be x  And the perpendicular be y and length of ladder=10 feet   dxdt=1 feet/sec…

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

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

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Q: Find the length of the edge of the cube, if an edge is increasrd by 6 dm, another edge has a 12 dm…

A: Let the edge of the cube be:  x

Q: A hypothetical cube grows so that the length of its sides are increasing at a rate of 4 ft/min. How…

A: As we know that the volume of the cube is: V=a3 Where, 'a' is the side of the the cube.   Given: a=4…

Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: It would be best to express length, width, and area as functions of time. I’ll set x = width, y =…

Q: Each side of a square is increasing at a rate of 8 cm/s. At what rate is the area of the square…

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

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Q: The volume of  a cube is increasing at a rate of 9 feet3/sec . how fast is the surface area…

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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: We have to find the area of rectangle increasing

Q: A bacterial culture quadruples in size every 4 days. We began with 200 mg. How much culture will…

A: Given: Initial size of bacterial culture is 200 mg. Since the culture quadruples in size every 4…

Q: Each side of a square is increasing at a rate of 5 cm/s. At what rate is the area of the square…

A: Let,

Q: 3. Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Area of the square is increasing at a rate of  48cm2/sec.

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

A: We need to find reat of change of area.

Q: 1.The volume of a cube is increasing at the rate of 6cm³/min. How fast is the surface area…

A: Given : rate of change of volume of cube : dV/dt = 6 cm^3 /min  To find : rate of change of surface…

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 length of a rectangle is increasing at the rate of 2 feet per second, while the width is…

A: Let length = x feet and width = y feet  Given that dx/dt= 2 and dy/dt= 1

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: If the volume of a cube is increasing at a rate of 24 in'/min and each edge is increasing at 2…

A: The volume of cube is given by V=a3 where a edge of cube. Given that volume of cube increasing at a…

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: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the volume…

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Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

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Q: A man walks across a bridge at a rate of 4 fps as a boat passes directly beneath him at 8 fps. If…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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

A: It is the application of Derivative.

Q: A hypothetical square grows so that the length of its diagonals are increasing at a rate of 8…

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Q: A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at its…

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Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

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Q: If the tank is completely full, how much is overflowing if 530 GPM is being taken off the bott

A: Given: Let the rate of filling be Qin = 1250 GPM  the rate of draining be Qdrain = 530 GPM Because…

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: A ladder 20 feet long rests against a vertical wall. If the bottom of the ladder slides away from…

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Q: A 30-foot ladder is leaned up against a 2-story building with 8-foot floors. The bottom of the…

A: Consider the diagram below with marked information: Speed of change in base is 6 feet per second.

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

A: To find how fast the volume changing  when edge is 5cm and 12cm :

Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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Q: The volume of a cube is increasing at a rate of 64 in ³/sec. At what rate is the length of each edge…

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Q: The top of a 18 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate…

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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: Given Volume of cube increasing at a rate of 68 in3/ secTo the rate of change of length of each edge…

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: Consider the sides of the function of time:  The Area is increasing by 49 cm2/s The side increasing…

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: All edges of a cube are expanding at a rate of 3 centimeters per second. (a) How fast is the volume…

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Q: . A small metal bar, whose initial temperature was 20° C, is dropped into a large container of…

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Q: Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the square…

A: Given:Each side of a square is increasing at a rate of 3 cm/s. At what rate is the area of the…

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: The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of…

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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: Let the length of the rectangle be:  l  cm Let the width of the rectangle be:  w  cm

Q: rectangle has one side of 11 cm. How fast is the area of the rectangle changing at the instant when…

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Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.