2. The length s of each side of an equilateral triangle is increasing at a rate of 13 feet per hour. Find the rate of change of the area when s = 41 feet. (Formula A =V %3D

Q: Given the area of a circle A=πr^2, find the rate of change of diameter d if dA/dt=3cm/min and the…

A: To find: The rate of change of the diameter d. Given: The rate of change of area is dAdt=3…

Q: QUESTION 1 The radius of semicircle is increasing at the rate of 0.8 cm/s, calculate the rate of…

A:

Q: At what rate is the distance between the planes changing? mph (b) How much time does the controller…

A:

Q: centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 8…

A: The volume of a pyramid isBh3 , where B is the area of the base and h is the height of full pyramid.…

Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per…

A:

Q: One side of a triangle is increasing at a rate of 7 cm/s and a second side is decreasing at a rate…

A: From the given, the sides a and b of the triangle is 29 cm and 36 cm, respectively. The gievn angle…

Q: 31) As the zoom lens in a camera moves in and out, the size of the rectangular image changes. Assume…

A:

Q: An inverted conical water tank with a height o 6 ft and a radius of 3 ft is drained through a hole…

A: Given, height of conical tank 6 ft and radius 3 ft.

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: Topic- application of derivatives

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A: The volume of a square pyramid is calculated using the formula: V=13b2h, where b is the length of…

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A: Given query is to find the rate of change of height of water.

Q: (b) Use the given formulas for the volume and area (displayed above the diagram) to rewrite the…

A:

Q: A 25-foot ladder is leaning against a house, as shown in the figure below. 25 ft sec +X→ If the base…

A: a). Put x = 15, we get b). Put x = 24, we get

Q: The radius, r, of a circle is decreasing at a rate of 4 cm/sec. Find the rate of change of the area,…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per…

A: dv/dt = 45 cm3/second side is 2 cm height is 5 cm side/height = 2/5 side (s) = 2h/5 volume of…

Q: For what values of x is the instantaneous rate of change of the graph of y = sin x equal to 0? O and…

A: See solution below

Q: The area bounded by a curve, the X-axis, a fixed ordi- nate, and a variable ordinate is proportional…

A:

Q: The lengths of the edges of a cube are increasing at a rate of 9 ft/min. At what rate is the surface…

A: Total surface area of cube S = 6x2 Where x is length of the side of cube. we have given x = 19 ft.…

Q: The base of a triangle is shrinking at a rate of 6cm/s and the height of the triangle is increasing…

A: The rate of change of the area with respect to time is the derivative of the area function with…

Q: The length of a rectangle is increasing at a rate of 12 in./s, while its width is decreasing at 2…

A:

Q: 31. The rate of change of the circumference of a circle when its radius increases at 1 cm/min is Зп…

A: The solution is given in the next step.

Q: The depth or water in a cyclindrical tank 4m in diameter is increasing at the rate of 0.7 m/min.…

A: Volume of cylindrical tank, V= πr2h Here, r= 2

Q: 21. For the camera and rocket shown in Figure 3.4.5, at what rate is the camera-to-rocket distance…

A: Given that the distance between camera and launching pad is 3000 ft., the distance between launching…

Q: A triangle with constant base b and height h is changing with time where h(t) = 2t – 3. What is the…

A:

Q: A triangle has a base that is increasing at a rate of 18 mm per minute with the height being held…

A: Area of the triangle is given by;A = 12 ×base×height

Q: If the radius of a circle increases at the rate of 0.01 inch/sec, find the rate of change of the…

A: We have to find the rate of change of area when the radius is 3 inches and when the radius increases…

Q: Sand is being dropped at the rate of 5 n3/min onto a conical pile. If the height of the pile is…

A:

Q: The edge of a square is increasing at the rate of 3 cm / sec. At what rate is the area of the square…

A: Here is the question of application of derivatives So here let's assume that, Side of square = x…

Q: The length l of a rectan-gle is decreasing at the rate of 2 cm/sec while the width w is increasing…

A: (a)Given:

Q: 20. If a point R on the unit circle moves along the circle at the rate of 1 unit per second, then…

A: Given: A point R on the unit circle moves along the circle at the rate of 1 unit per second. To find…

Q: The radius of a sphere decreases at the rate of 4 m/s. when the radius is 10m, then the rate of…

A: We will find the rate of change in surface area as following .

Q: One side of a triangle is increasing at a rate of 6 cm/s and a second side is decreasing at a rate…

A:

Q: The radius of a circle is decreasing at a constant rate of 8 feet per second. At the instant when…

A: The radius of a circle is decreasing at a constant rate = drdt=-8 ft/s Area of circle A = 16π ft2

Q: The radius of a circle is increasing at a constant rate of 0.2 meters per second What is the rate of…

A: Given that the radius of a circle is increasing at a constant rate of 0.2 meters per second. To find…

Q: An inverted pyramid is being filled with water at a constant rate of 65 cubic centimeters per…

A:

Q: The edge of a cube decreases at a rate of 1.5m/s. Find the rate at which the surface area decreases…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: 1. Find the rate of change of the area of a circle with respect to its radius when the radius is 3…

A: Authoring guidelines:…

Q: A pool of water with surface area of 0.6 hectares has a uniform dept of 3M a pipe drain the pool at…

A:

Q: 1. A biker is 50 meters away from a pole. The biker starts to ride south parallel to the pole at a…

A: Solution is given below:

Q: An inverted pyramid is being filled with water at a constant rate of 55 cubic centimeters per…

A: Given: speed of waterdVdt=55 cm3second, b1=b2=6cm, h=13cm

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in…

A:

Q: An inverted pyramid is being filled with water at a constant rate of 60 cubic centimeters per…

A:

Q: The area of a circle increases at a rate of 5 cm2 /s. a. How fast is the radius changing when the…

A: Definition used -              Area of the circle  -                                   A =πr2…

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:

Q: Water is being drained from a conical reservoir (vertex down) at the rate of 3 cubic feet per…

A: Given the volume flow rate of water is: 3 cubic feet per second. Consider the height of the cone is…

Q: 18. If the radius of the circle increases at the rate of 0.01 cm per second, find the rate of change…

A: Topic:- Application of Derivative  Correct option = a

Q: The volume V=r° of a spherical balloon changes with the radius. a. At what rate (ft°/ft) does the…

A: Consider the given equation: V=43πr3 Where V is the volume and r is the radius. Differentiating the…

Q: The sides of a cube increase at a rate of R cm/s. When the sides have a length of 2 cm, the rate of…

A:

Exponential Growth Model

The relation that represents an exponential function is: