1. A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5 m?/sec at what rate is the radius decreasing when the area of the sheet is 12 m2?

Q: O. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

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Q: A conical shaped heap of sand is growing (picture sand being added from above at its peak). If the…

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Q: 11. If the base of a triangle is constantly 4 cm, find the rate at which the area of the triangle is…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 2)The radius of a sphere decreases at the rate of 1 m/sec. Find the rate at which the volume…

A: Given,  The radius of a sphere decreases at the rate of 1 m/sec  We have to find the rate at which…

Q: 11. A snowball melts so that its surface area decreases at a rate of 0.5 cm/min. Find the rate at…

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Q: 8. The radius of an inflating balloon in the shape of a sphere is changing at a rate of 3cm/sec. At…

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Q: A cylindrical column is (3m) high and (0.2m) radius, if the radius of the column increases at a rate…

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Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A: When length is:= 5 ft; When width is:= 2 ft; Rate of increasing length= 3 ft/s; Rate of increasing…

Q: 10. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

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Q: 11. If the original 24 m edge length x of a cube decreases at the rate of 5 m/min, when x = 3 m at…

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Q: An inverted conical water tank with a height of 12ft and a radius of 6ft ft is drained through a…

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Q: 1) A baseball diamond is a square whose sides are 90ft long. Suppose that a player running from…

A: Given : Side of Baseball diamond square =90 ft. Drawing the diagram of the whole situation,

Q: Can i get help with this problem step by step

A: The surface area of the cube, S = 6x2 The volume of the cube, V = x3 We have given dS/dt = 72.

Q: 9) A spherical snowball is melting in such a way that its volume is decreasing at a rate of 3cm /…

A: Let, r=radius  V=volume Given that dV/dt= 3 , we have to find dr/dt=? at r=12 cm Volume and radius…

Q: How fast is the surface area of a circular oil spill in the ocean changing when the radius is 10ft…

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

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: 2. The radius of a sphere decreases at the rate of 5 m/sec. Find the rate at which the volume…

A: Given that the Radius of sphere decreases at the rate of 5m/sec and radius is 5 m

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: 1. A spherical balloon is being inflated so that the volume is increasing at the rate of 5 ft.³ per…

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Q: 16. If the radius of a circle is increasing at the rate of 4 cm/s, find the rate of the increase in…

A: Given radius of a circle is increasing at the rate of 4 cm/sec.

Q: 5. A trough is 6m long and its ends have the shape of isosceles triangles that are 1m across at the…

A: The solution is given below in the next step:

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

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Q: 2)The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume…

A: We need to find the rate at which volume decrease when radius is 3m

Q: Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up…

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Q: A cylinder is leaking water but you are unable to determine at what rate. The cylinder has a height…

A: Given, Radius is 2m, height is 2m. Height is decreasing at 10 cm/min when height is 1m.

Q: 20. The length of a rectangle is increasing at a rate of 5 cm/sec and the width is decreasing at a…

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Q: If the sides of a square increase in length at a rate of 3 in/s, then the rate of change of the…

A: Let the side length of a square be x Now, Side length increases at a rate of 3in/s. That is, dxdt=3…

Q: )1. A spherical balloon is being inflated so that the volume is increasing at the rate of 5 ft.' per…

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: 15) The volume of a sphere is increasing at a rate of 6 cm³/sec. Find the rate of change of its 4T…

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

A: we know that the volume of the sphere                       V=43πr3                          (1)

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

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Q: (5) A conical water tank with vertex down has a radius of 10 ft at the top and is 24 ft high. If…

A: we know that, the volume of conical shape, V = 1/3πr^2h  so after defernciate this, we will solve…

Q: 1 A conical tank (with vertex down) is 12 feet across the top and 12 feet deep. If water is flowing…

A: "Since you have asked multiple questions we will solve the first question for you". If you want any…

Q: 1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute,…

A: The given question can be solved as shown in step2.

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: Suppose the area A of a particular rectangle increases at a rate of 2 cm^2/sec and the width w of…

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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: 3. The area of a circular inkblot starts from zero and grows at a constant rate of 4n cm/minute.…

A: Use the derivative and formula for area of circle.

Q: 1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles…

A: As per our guidelines we are supposed to answer only one question. I am solving the first one Kindly…

Q: 2) The radius of a sphere decreases at the rate of 4 m/sec. Find the rate at which the volume…

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Q: Solve the following related rates problems. 3. A tank of water in the shape of a cone is being…

A: The cone is a solid which has a circular base and comes to a point at the top similar in shape to an…

Q: 3. A water tank has the shape of an inverted circular cone with base radius 4 m and height 8 m. If…

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Q: 1. The width of a rectangle is increasing at a rate of 2 cm/sec, while the length increases at 3…

A: I have stated the used formulas in the solution

Q: 2. A tank of water in the shape of a square pyramid is leaking water at a constant rate of 4…

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Q: 1 A 5 m ladder is leaning against a wall of a house. The bottom of the ladder is pulled away from…

A: Let the bottom of the ladder is x meters away from the wall and the top of ladder is at distance y…

Q: 1. The volume of a cube decreases at a rate of 12 m/sec. Find the rate at which the side of the cube…

A: This question is related to application of derivatives.

Q: A flag is raised vertically from a pole at a constant rate of 1 m/s. A point B on the ground is…

A: solution:- draw a right angle triangle:-