diagonal of a square increases at a rate of 3 m/s. How fast is the area changing when the side of the square is 6 m?

Q: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how…

A: A 12 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4ft/s.

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

A: Suppose that the radius of circular pattern is “r” and area of the pattern is “A” then, The area of…

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

A:

Q: Car A leaves a parking lot at 9 am and travels eastward at the rate of 60 kph. Another vehicle, car…

A:

Q: A 10​-foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

A: The given data can be expressed in a right triangle as shown below.

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

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

Q: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

A: A 25-foot ladder is leaning against a wall and the base begins to fall away from the wall. When the…

Q: Suppose the sides of a cube are expanding at a rate of 2 inches per minute, How fast is the volume…

A:

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: A 25-ft ladder is leaning against a wall. If we push the ladder toward the wall at a rate of 1…

A: Given that

Q: the

A:

Q: A 15-foot ladder is leaning against a wall. If we pull the ladder away from the wall 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: We have to find the area of rectangle increasing

Q: A ladder 8 m long leans against a model home. If the bottom of the ladder slides away from the…

A: Given- A ladder 8 m long leans against a model home. If the bottom of the ladder slides away from…

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

A:

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

A: Please see the answer below.

Q: How fast is the circumference of a circle changing if the radius is changing at the rate of 3 mm/s?

A: Solution

Q: The sides of a cube are increasing at a rate of 1cm/s. How fast is the diagonal of the cube changing…

A: Explanation: Given that,  The sides of a cube are increasing at a rate of 1cm/s. The objective is to…

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: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how…

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: A perfectly spherical balloon is losing volume at a rate of 3 in3 per sec. How fast is the balloon’s…

A:

Q: An isosceles triangular water trough is 5 meters long, 3 meters across the top, and 2 meters deep is…

A: Where we see the application of derivatives to solve the given problem

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: stone dropped into a pond sends out a circular ripple whose radius increases at a constant 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: A 14 ft ladder is leaning against a wall. If the top of the ladder slides down the wall at a rate of…

A: Definition used -                Related rate -  These are the problems in which we know one of…

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

A:

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

A: Since, we have been given that all edges of a cube are expandingat a rate of 8 centimeters per…

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

A: Given,

Q: Sand flows out of an hourglass at a rate of 4 cubic inches per second and forms a conical pile. How…

A: Write the expression for volume of cone take the derivative with respect to time t than put the all…

Q: Two cars start moving from the same point. One travels south at 84 mi/h and the other travels west…

A:

Q: A 5-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away…

A: Given: Length of the ladder, l=5 ft. Distance between wall and the bottom of the ladder, x=4 ft…

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: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: A 13 feet ladder is leaning against the wall. The top slips down the wall at a rate of 2 ft/s. The…

Q: A ladder 20 feet long is leaning against a vertical wall. The base of the ladder is pulled away from…

A: First we formulate an equation involving two variables x and y by using  the Pythagorean theorem…

Q: A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing. The length…

A: Given: A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing.The…

Q: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

A:

Q: A rectangle is expanding such that its length is always 4 times its width. If the width is…

A: Let's find.

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

A: The volume of water trough = Area × Length Area of trapezium = 12×Sum of parallel sides×height…

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: a 10-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A:

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: A 25 -foot ladder is leaning against a vertical wall​ when Jack begins pulling the foot of the…

A:

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

A: