The length of a rectangle is increasing at a rate of 4cm/s and its width is increasing at a rate of 2cm/s. When the length is 20cm and the width is 10cm, how fast is the area of the rectangle increasing?

Q: The sides of a square are increasing at the rate of 2 inches per minute. How fast is the Area…

A: Given The side of square is increasing at rate of 2inches per minute.  The area of a square with…

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

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Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

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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: Each side of a square is 6 ft and is increasing at a rate of 2 ft per second. How fast is the area…

A: By differentiating equation of area of square with respect to time and substituting the value of…

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: The width of a rectangle increases at a rate of 2 cms. The length is five times its width. Find the…

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Q: Each side of a square is increasing at a rate of 2 cm/s. At what rate is the area of the square…

A: Let the side of the square be 'x' cm. Therefore the area of the square is given by: A=x2

Q: A 10-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

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

A:

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

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

A:

Q: The length of a rectangle is increasing at a rate of 3 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 5 cm/s and its width is increasing at a rate of…

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

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

A:

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: Consider the given situation, Let the length of the rectangle be ‘l’ and breadth be ‘b’.Area of…

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 boat is pulled into a dock by a rope attached to it and passing through a pulley on the dock…

A: This problem is based on the application of differentiation.  First we have to write an equation in…

Q: The volume of a cube is increasing at a rate of 9 cubic centimeters per second .How fast is the…

A: Solution:-

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

A:

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

A:

Q: The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of…

A: We know for rectangle, Area (A) = Length (l) × width (w) So, rate of change of area, (dA/dt) =…

Q: A 5 meter long ladder is leaning against a wall. If the bottom of the ladder is being pushed towards…

A: Let AB is h=5 m long ladder leaning against the wall AC. Distance between the bottom of the ladder…

Q: The sides of the square are increasing at a rate of 3 cm per second . When the sides are 5cm long ,…

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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:

Q: A 13-ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of…

A:

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

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:

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

A: Rectangle: It is a polygon with four side and opposite sides are equal.  Also. the all the four…

Q: The side of a cube is increasing at a rate of 2 mm/s. How fast is the volume Q4. - increasıng when…

A: To find  How fast is the volume of a cube increasing.

Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches per…

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

A: Given oil is spilled from tank and it flowing  in a circular path with increasing radius of 2m/s .…

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

A: Area of a rectangle = length× width Rate of change with respect to time is D/Dt

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: The width of a rectangle increases at 2 in per sec, and the length decreases at 3 in per sec. How…

A:

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 ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given:-  Ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.125m/s. At the moment when the bottom…

A:

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

A:

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

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

Q: The volume of a cube is increasing at the rate of 2 cubic inches per minute. How fast is the surface…

A:

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 have to find

Exponential Growth Model

The relation that represents an exponential function is: