The sides of a square decrease in length at a rate of 1 m/s. At what rate is the area of the square changing when the sides are 5 m long? At what rate are the lengths of the diagonals of the square changing?

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 5 cm/min.…

A:

Q: each side of a square increases at a rate of 1.5cm/sec .also find the rate at which the area of the…

A: Given,   Each side of a square increases at a rate of 1.5 cm/sec

Q: a 17 foot tall ladder is leaning against a vertical wall and its base is on level ground. The top of…

A: We have to find at what rate is the top of the ladder sliding down the wall when it is 8 feet above…

Q: A Ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How…

A: the height is given byh = 10 sin (pi * t) + 10dh/dt = 10 cos (pi * t) * pi

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

A: Given: Length of a ladder which rests against a vertical wall is 10 ft. Let the distance between…

Q: A stone is thrown vertically upward with a velocity of 40 feet per second from the top of a tower…

A: Given that - A stone is thrown vertically upward with a velocity of 40 feet per second from the top…

Q: A light is hung 6 meters above a straight horizontal path.  If a man 2 meters tall is walking toward…

A:

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: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2…

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

A: all details are given in below. please check it

Q: A trough of water is 8 meters in length and its ends are in the shape of isosceles triangles whose…

A: Given:- A trough of water is 8 meters in length and its ends are in the shape of isosceles triangles…

Q: The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the rate…

A: Given,dAdt=-4 cm2/minA=100cm2Let,x=side of the equilateral triangle find dxdt when dAdtis decreased…

Q: 2. please help, they canceled class due to virus can't contact teacher.

A:

Q: Water is poured into a conical tank 6 m across the top and 8 m deep at the rate of 10 m3min. How…

A:

Q: A kite 30 m above the ground moves horizontally at a speed of 10 m/min. At what rate is the angle…

A:

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: The sides of a square increase in length at a rate of 5 m/sec. a. At what rate is the area of the…

A: We apply chain rule of differentiation. Area of the square is: A= s2.  Where s is the side of a…

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 volume of a cube is increasing at the rate of 21 cc/min. At what rate is its surface area…

A: The volume of a cube is increasing at rate, dVdt = 21 cc/min To evaluate: The rate at which the…

Q: the

A:

Q: A baseball diamond has the shape of a square with sides 90 feet long, suppose the player is running…

A: It is given that a baseball diamond has the shape of square with side 90 feet long. Construct the…

Q: The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area…

A: let side of triangle = x    Given

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

A:

Q: An equilateral triangle initially has sides of length 20 ft when each vertex moves toward the…

A: We have given an equilateral triangle intially has sides of length 20ft and each vertex moves toward…

Q: Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two…

A: Let the sides of rectangle be x and y   since, two parallel sides are increasing at the rate of…

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

A: →cosθ = BaseHypotenuse→sinθ = 1-cos2θ→dcosθdθ = -sinθ

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: If the volume of a different sphere is increasing at a rate of 24 cubic inches per minutes and the…

A:

Q: A cone-shaped tank of water is leaking water at a constant rate of 3 m³/hour. If the base radius of…

A: Using volume  of cone and applications of derivative idea we solve this

Q: The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the rate…

A: Given that  The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute.…

Q: The height of a right circular cylinder is 50 inches and decreases at the rate of 4 inches per…

A: Topic = Volume

Q: Two parallel sides of a rectangle are increasing in length at the rate of 2 in/sec while the other…

A: Given: The two parallel sides of a rectangle are increasing in length at the rate of 2 in/sec. The…

Q: If the sides of an equilateral triangle are increasing at a rate of 6 m/min. How fast is the area of…

A:

Q: A ladder 3.9 m long is placed in a vertical plane which is at right angle to the vertical wall, the…

A: Given :                     The height of the ladder = 3.9m                     Let x…

Q: A 12-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A: A 12-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the…

A: let the side of the square is a meter, and the area is A given that da/dt=3m/sec a. a=15m area of…

Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

A:

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

A:

Q: A baseball diamond has the shape of a square with sides 90 ft long, as shown. A player is running…

A: A baseball diamond has the shape of a square with sides 90 feet long. A player running from second…

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

A: To determine the rate of change of angle between the ladder and the ground.

Q: A kite 100ft  above the ground moves horizontally at a speed of 8ft/s  At what rate is the angle…

A: Let x= horizontal distance L= length of string,  Then a rough sketch of the problem is as follows:

Q: A light is hung 7m above straight horizontal path. If a man 2meters tall is walking toward a light…

A:

Q: The volume of a cube is increasing at the rate of 1200 cm³ / min at the instant its edges are 20 cm…

A:

Q: The sides of a square increases in length at a rate of 3 m/sec. At what rate is the area of the…

A:

Q: How many kilometers can a train moving at an average velocity of 25 m/s southwest be displaced in 2…

A: Given, average velocity of train = 25 m/s 2 hours = 2x60x60 = 7200 seconds

Q: . A kite 100 ft above the ground moves horizontally at aspeed of 8 fts. At what rate is the angle…

A: At what rate is the angle between the stringand the horizontal decreasing when 200 ft of string has…

Q: The side of a square sheet is increasing at rate of 4 cm per minute ,At what rate is the area…

A:

Q: Water flows at the rate of 2000 cubic cm per second into a vertical cylindrical tank 120 cm in…

A: Let height of cylindrical tank is "h". Diameter is 120 cm. So, Radius would be r=1202=60 cm Volume…

Q: A ladder 20 ft. long leans against a vertical wall. If the top slides downward at the rate of 2…

A: