The side of the base of a square prism is decreasing at a rate of 7 km/min and the height of the prism is increasing at a rate of 10 km/min. At a certain instant, the base's side is 4 km and the height is 9 km. What is the rate of change of the surface area of the prism at that instant?

Q: Suppose the edges of a cube are increasing at a constant rate of 8 m/hr. Then, the volume of the…

A:

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

A: topic - application of derivatives

Q: The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is…

A: Given that, drdt=1.1 in/s and dhdt=-2.7 in/s. Also, it is given that r=102 in. and h=162 in. It is…

Q: if the base of triangle is constantly 4 cm find the rate at which the area of the triangle is…

A:

Q: A conical vessel 12 cm deep and with a radius of 6 cm at the top, is being filled with water. If the…

A: A conical vessel 12 cm deep and with a radius of 6 cm at the top. That is, the height of the cone is…

Q: There is a constant outflow of a liquid into a inverted conical vessel 15 m deep and 7.5 m in…

A: Find the rate of change of volume of water in the cone, with respect to time:…

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: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

Q: The radius of the base of a right circular cone is decreasing at the rate of 4 cm/min, and the…

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: Water is being poured at the rate of 27 m³/min. into an inverted conical tank that is 12-meter deep…

A: Given that a canonical tank that had radius is 6meter and height is 12 meter and dh/dt= 1/6…

Q: A sperical snowball is melting in such a way that its volume is decreasing at a rate of 1 cm^3/min.…

A: Volume of the sphere formula:‘r’ is the radius of the sphere

Q: Water is being released from a conical reservoir (vertex down) 20 ft in radius and 40 ft deep at a…

A: Use similar triangle to shoe that  r/20 = h/40 where r and h are the radius and height of water in…

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

A: Given that, Let length of the ractangle is L and the width is W and area is A. Then according to the…

Q: a) Water is flowing into a leaky cistern at the rate of 31.4 cu ft./min. The cistern is a right…

A: Given that  The water is flowing into a leaky cistern at the rate of 31.4 cu ft./min ⇒dVdt=31.4…

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: A trough whose cross section is an equilateral triangle is 6 m long and 2 m wide across the top. If…

A: Solve by diagram and using formulas of equilateral triangle

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

A:

Q: A balloon, in the shape of a right circular cylinder, is being inflated in such a way that the…

A:

Q: The lower base of a trapezoid is 8 m. If its height is increasing at the rate of 0.5m/sec while its…

A:

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

A: Topic = Volume

Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: To calculate the required rate of change using partial derivatives

Q: The sides of a square increase in length at a rate of 4 m/sec. a. At what rate is the area of the…

A: Area of square = a2 Where a is length of side of square.

Q: A vertical cylinder is leaking water at a rate of 8m^3/sec. if the cylinder has a height of 10m and…

A: In a vertical cylinder water is leaking at a rate of 8 m3/sec. dVdt=8 Height of the cylinder is 10…

Q: The volume of a cube increases at a constant rate of 135 ft°/ sec. The rate at which the side of the…

A:

Q: The radius of a right circular cone is increasing at a rate of 5 inches per second and its height is…

A:

Q: Find how fast the area of a triangle increases as the length of the base of the triangle increases…

A: (a) We need to find dAdb where A is the area of the triangle and b is the base of the triangle.

Q: 2) A person is standing 350 feet away from a model rocket that is fired straight up into the air at…

A:

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: Given that radius =7 ft dVdt=9 cubic ft per minutefind dhdt Also V=πr2h

Q: A 100-ft long cable of diameter 4 in. is subsequently submerged in seawater. Due to corrosion, the…

A: Given that diameter is 4 inches and height is 100 feet. And rate of decrease in area is 750 in2yr.…

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

A:

Q: The radius of the base of a cylinder is increasing at a rate of 1 m/h and the height of the cylinder…

A: Given,         The radius of the base of a cylinder is increasing at a rate of 1 m/h and the height…

Q: A spherical drop of liquid evaporates at a rate proportional to tis surface area. If a given drop…

A: Given: The drop evaporates to 18 of its volume in 5 minutes

Q: The radius of a right circular cylinder is increasing at the rate of 8 in/sec while the height is…

A: Given- drdt=8 in/sec and dhdt=-3 in/sec To Find- The rate of the volume changing when r= 7 in and…

Q: A plane flying horizonrally at an altitude of 1 mi and a speed of 500 mi/h passes directly over a…

A: given that plane is flying horizontally at an altitude of 1mi speed=500 mi/h find the rate at which…

Q: A trough filled with water is 2m long and has a cross section in the shape of an isosceles trapezoid…

A:

Q: The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing…

A: Let,  r - radius of the right circular cone h-Height of the right circular cone  V- Volume of the…

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A:

Q: A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30…

A:

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

A:

Q: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant rate. At…

A: Given: An inverted conical tank 10 m high and 3 m radius at the top fills with water at a constant…

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: The radius of a right circulare cylinder is increasing at the rate of 3 in/sec, while the height is…

A: To determine the change of rate of the volume of cylinder.

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: A tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in…

A:

Q: A bacterial cell is spherical in shape. If the radius of the cell is increasing at the rate of 0.01…

A: Given , Bacterial cell is in spherical shape.Let radius be 'r' μm . ∴ Volume of cell, v v = 43π…

Q: A horizontal trough is 16m long, and its ends are isosceles trapezoids with an altitude of 4m, a…

A: The derivative is also called the rate of change of a quantity with respect to time. The volume of 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: All the edges of a cube are expanding at a rate of 1/6 cm/sec. Determine the rate of change of the…

A: