. Area of a Balloon A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 2 cm/s. Express the surface area of the balloon as a function of time t (in seconds).

Q: A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The…

A: Here, the given concentration function is: C(x)=0.9x2 where x is the distance away from the plant in…

Q: A spherical balloon is being inflated. The radius of the balloon is increasing at the rate of 9…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: d) An ice cube of 16 cm3 is melting on a mesh as shown below. Each side of the ice cube is melting…

A: We have to use derivative as rate of change

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A: From the given problem: The total perimeter of the window = 24feet So,…

Q: A coal-burning electrical generating plant emits sulfur dioxide into the surrounding air. The…

A: We will solve the following.

Q: A coal-burning electrical generating plant emits sulfur dioside into the surrounding air. The…

A:

Q: A cube has an edge if 4 ft the edge is Increasing at the rate of 6 feet per minute. Express the…

A:

Q: Weather Bots is a manufacturer of neoprene weather balloons. As the 350-gram spherical balloon is…

A: (B) Given: The radius is decreasing with the rate ,drdt=2 π feet per second. Radius of balloon is…

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Q: Disappearing Mothball The rate at which the volume of a mothball evaporates from solid to gas is…

A: The rate of evaporation = Rate of decrease in volume of mothball is directly proportional to the…

Q: An object of mass m is dropped from a hovering helicopter. The air resistance is proportional to the…

A: Given: An object of mass m is dropped from a hovering helicopter. The air resistance is proportional…

Q: 8 feet 9. As shown in the figure to the right, water is draining from the conical tank with height…

A: Given information: The height of the conical tank is 12 feet and the diameter is 8 feet. (a) To…

Q: The radius r of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of…

A:

Q: The radius r of a sphere is increasing at a rate of 6 inches per minute. (a) Find the rate of change…

A: In this question, we need to find the rate of change of volume.

Q: 5. This box has a length x and a width that is 4 times its length. The volume is 500 cm. Find a…

A: Given length is xWidth is 4 times length = 4*xVolume is 500 cm3We know that volume of a cuboid is…

Q: Consider the rectangle shown in the figure.(a) Find the area of the rectangle as a function of x.(b)…

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Q: A police helicopter is flying due north at 100 mi/h and at a constant altitude of ; mi. Below, a car…

A: Let the car be at a distance x from the point where helicopter crosses highway. The height at which…

Q: 2. The height, h, in meters, of a car above the ground as a Ferris wheel turns can be modelled using…

A:

Q: Weather Bots is a manufacturer of neoprene weather balloons. As the 350-gram spherical balloon is…

A:

Q: A cylindrical can is to hold 1 liter, or 1000 cubic centimeters, of oil. Express the surface area of…

A: given: A cylinderical can is to hold 1 liter, or 1000 cubic centimeters, of oil. we have to express…

Q: A reservoir discharge water through sluices as a depth h meter below the water surface, has a…

A: We will use first backward difference operator , ∇fx=fx-fx-h let ya-h,ya,ya+h......... be the…

Q: The average rate of change of a function f between x c and x = d is average rate of change = d-c

A: Explanation of the answer is as follows

Q: The function f (t) = 900(0.992)* represents the change in a quantity over t days. What does the…

A:

Q: The attached figure shows water running into a container in the shape of a cone. The radius of the…

A: Given:Radius of the cone r=6 feetHeight of the cone h=12 feetVolume of the cone  V=13πr2h

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A: To find the average of below function from t = 0 to t = 10.

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A: Given, We have to find the rate of change of pressure with respect to volume at V = 10 L   and V =…

Q: The radius r of a circle is increasing at a rate of 7 centimeters per minute. Find the rate of…

A:

Q: Use the function of a function rule to determine the rate of change of volume a being filled by…

A: Given Radius of changes water at 0.6cm/sRadius of sphere=6cm

Q: Weather Bots is a manufacturer of neoprene weather balloons. As the 350 gram spherical balloon is…

A: For the above given data  Radius of balloon at t = 4.5 minutes  is calculated using tangent line…

Q: A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate…

A:

Q: Snowflakes land randomly on a small area of the ground at a rate of 16 per minute. Let X be the…

A: Solution

Q: An object dropped from rest from the top of a tall building on Planet X falls a distance of d(t)=…

A: The distance equation is given by,

Q: A cube has an edge of 4 feet. The edge is increasing at the rate of 2 feet per minute. Express the…

A:

Q: a spherical weather ballon is being inflated. the radius of the balloon is increasing as the rate of…

A:

Q: A cube has an edge of 3 feet. The edge is increasing at the rate of 6 feet per minute. Express the…

A: Given data: Edge of cube is 3 feet. Edge is increasing at the rate of 6 feet per minute. Let m be…

Q: Consider the rectangle shown in the figure. 1 (-x, e-x?2) (x, e-2) (a) Find the area of the…

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Q: The altitude ( of a right triangle is always hvice the base ,D Find the rate of change of the area A…

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Q: The function f (t) = 2300(0.25)* %3D represents the change in a quantity over t decades. What does…

A: We will put values of t from 0, 1 and 2 and notice the pattern that gives us the rate of change

Q: A Spherical ballon is being filled with air. The radius of the Sphere {nitially is Ift & is grawing…

A: Given: A spherical balloon is being inflated with air. The radius of the sphere initially is 11 ft…

Q: A stone is dropped into a lake, creating a circular ripple thattravels outward at a speed of 60…

A: (a) Express the radius of this circle as a function of thetime t(in seconds).

Q: The radius r of a circle is increasing at a rate of 4 centimeters per minute. (a) Find the rate of…

A:

Q: The radius r of a circle is increasing at a rate of 2 centimeters per minute. (a) Find the rate of…

A: we have given, The radius r of circle is increasing at the rate of 2 cm per min. i.e.  dA /dt=2

Q: A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute. (a) Find the…

A:

Q: An airplane flying at an altitude of 6 miles passes directly over a radar antenna. When the airplane…

A: This question is based on application of Derivative.

Q: A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate…

A:

Q: A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the…

A:

Q: A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 9…

A:

Q: During the Apollo 14 mission, Alan Shepard hit a golf ball on the Moon. The function h(t) =18&-0.8r…

A:

Q: Water flows into and out of a storage tank. A graph of the rate of change r(t) of the volume of…

A: To estimate the amount of water in the tank four days later by using Midpoint rule.