The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing at a rate of ... 3 cm per second. When the length is 4 cm and the width is 5 cm, how fast is the area of the rctangle changing at that instant?

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Q: At a certain instant the dimensions of a rectangle are 8 and 12 feet, and they are increasing at the…

A: At a certain instant the dimensions of a rectangle are: Length L=8 feetWidth W=12 feet

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

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

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A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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

A: Let the length be: l Let the width be: w

Q: and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this mom

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Q: The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: The rate of increase of the width of a rectangle i.e. dwdt=2 cm/sec The rate of increase of the…

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

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

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Q: The width of a rectangle is increasing at a rate of 5 cm/sec, while the length increases at 6…

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Q: At noon Person A is 15 km east of person b. person A is walking west at 3km/h, and person b is…

A: initially A and B apart 15 km apart that  person A moves towards west at rate (da/dt) = 3 km/hr…

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Q: 1. If the radius of a spherical balloon is increasing at the rate of 3 cm/s, which of the following…

A: We are only allowed to solve one question at a time so we will answer only the first question.…

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: At what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 2 cm/s?

A: To find the rate at diagonal of a cube is increasing

Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Now in triangle ABC, by using Pythagorean theorem, we get

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: 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: 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 spherical balloon is inflated at a rate of 10 cm3>min. At what rate is the diameter of the…

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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 flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

Q: The length of a rectangle is increasing at a rate of 7cm/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 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) =…

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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

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A: From the given information, draw a picture.

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

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Q: D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a…

A: Make a diagram according to the situation.

Q: Initially filled with water, a conical reservoir is 24 ft deep and 12 ft across the top. Water goose…

A: Solution: Consider the given that conical reservoir 24ft (h) deep and 12ft across the top that is…

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 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 20-ft ladder is leaning against a wall, and the top of the ladder is sliding down the wall at a…

A: We have been given a 20ft ladder which is leaning against a wall and is sliding down the wall AD.…

Q: A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.  How fast does the tip of…

A: Given that, A 6-ft man walks away from a 16-ft high lamp post at the rate of 4 ft/s.

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: 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: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Given that,  'L' be the length of a diagonal of a rectangle whose sides have lengths x and y, and x…

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: 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

Q: A flag is raised vertically from a pole at a constant rate of 1 m/s. A point B on the ground is…

A: solution:- draw a right angle triangle:-