If the rate change of the length of the circle circumference with time is (T/2) m/sec. What is the rate change of the circle area with time at the moment which the circle radius = 6 m?

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 3 ft/min.…

A: The given data is: Initial radius ri=50 ft Radius is decreasing at the rate of drdt=3ft/min To find…

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: What is the rate of change of the areaof a circle (A = pr2) with respect to the radius when the…

A: To find the rate of change of the area of a circle with respect to the radius when the radius is…

Q: Find the rate at which the surface area of the water changes when the water is 10 ft high if the…

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Q: Suppose you have a square that is 300 ft on each side.  Also suppose the length is increasing at the…

A: Given that a square that is 300 ft on each side and the length is increasing at the rate 3ft/sec,…

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

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

A: The volume of the cylinder is given by V=πr2h, where V=volume of the cylinder r=radius of the…

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

A: We will use derivative as rate of change

Q: Find the rate of change of the volume of a cone with a constant height of 5 m with respect to radius…

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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: 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, Radius of circle (r)=3 inchesRate of change of radiusdrdt=0.01 inches/sec We know that,…

Q: A 15-meter ladder is resting against a vertical wall. if the bottom of the ladder is being pushed…

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Q: The surface area of a sphere increases at a rate of 90 m/sec. Then the rate at which the radius…

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Q: The radius r of a circle is changing at the rate of -2/π m/sec. At what rate is the circle’s area…

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Q: A large weather balloon is being inflated with air at the rate of 0.9 ft3 per minute. Find the rate…

A: Given a large weather balloon is being inflated with air at the rate of 0.9 ft3 per minute. Volume…

Q: The radius of a circle is increasing at the rate of 4 cm/s. How fast is the area of the circle…

A: Given,           The radius of a circle is increasing at the rate of 4 cm/s. And the radius is 5 cm…

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 4 ft/min.…

A: Area of a circle of radius r is given by  A = πr2                ...(1) Differentiate with respect…

Q: The radius of a circle is changing at the rate of -2/pai  m/sec. At what rate is the circle’s area…

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Q: If the rate of change of the surface area of a sphere with respect to its radius is 16pi sq cm, find…

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Q: A balloon is rising vertically over a point A on the ground at the rate of 15 ft/sec. A point B on…

A: Let the distance of the balloon from point B be denoted as p. The balloon, points A and B form a…

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: A man of 2 mts tall is approaching a lamp post at the rate of 0.5m/sec.if the lamp post is situated…

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Q: The radius of a circle is increasing at the rate of 0.7 cm/s. what is the rate of

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Q: The radius of a circle is increasing at the rate of 0.7 cm/c.what isthe rate of oncreasing of its…

A: Differentiate circumference wrt t

Q: A 15-meter ladder is resting against a vertical wall, If the bottom of the ladder is being pushed…

A: Let ladder AB, l=15 m, Ladder is pushed horizontally at the rate of 1.5 m/s, ⇒dydt=1.5 We need to…

Q: The radius of a sphere decreases at a rate of 3 meters per second. Find the rate at which the…

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Q: A 5​-foot-tall woman walks at 4ft/s toward a street light that is 25ft above the ground. What is the…

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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: 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 radius of a circle is increasing at the rate of 0.7 cm/sec.what is the rate of increase of its…

A: The radius of a circle is increasing at the rate drdt= 0.7 cm/sec r = radius of the circle

Q: A conical tank that is 14 ft across the entire top and 12 ft deep is leaking water. The radius of…

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Q: The radius of a circle is changing atthe rate of -2/paiA m/sec. At what rate is the circle’s area…

A: Let the radius of the circle be r. Then the area (A) of the circle is: A=πr2 Differentiating with…

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

A: We can find the answer as below using the given data.

Q: The radius of a sphere decreases at a rate of 8 m/sec. Find the rate at which the surface area…

A: It is given that the radius of sphere decreases at a rate of 8 m/sec. So, drdt=-8. The radius is r=3…

Q: What will be the rate of change of the surface of the sphere when the radius of the sphere is 5.00…

A: Given; Radius= 5cm And time rate of change in Radius is= π/2.

Q: If a ladder of length 20ft which is leaning against a vertical wall has its upper end sliding down…

A: Given : Length of the ladder = 20 ft

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 circle has an initial radius of 50 ft. when the radius begins decreasing at the rate of 3 ft/min.…

A: Area of a circle is given byDifferentiating the function of area with respect to time:

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at a rate of 2 ft>min.…

A: Let r be the radius of the circle.The initial radius is given by r = 50 ft.Given that, the radius…

Q: A weather balloon is rising vertically at the rate of 2 m/sec. An observer is standing on the ground…

A: The diagram of the given question will be as follows Given: dydt=2 m/s To find: dxdt

Q: A yellow balloon, spherical in shape is inflated with a rate of 100 cm3 /sec. Calculate the rate at…

A: Given

Q: A triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant.…

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Q: Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. Find the rate…

A: given: Air is being pumped into a spherical balloon at a rate of 4.5 cubic feet per minute. we have…

Q: A spherical balloon is being inflated at a rate of 9(pi)cm^3/sec. At what rate is its radius…

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Q: Find the rate of change of the ice circle's area towards the start of spring if the initial radius…

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Q: A conical cistern of height 5 ft and 7 ft across the top is being filled at a rate of 5 ft3/s while…

A: A conical cistern is given whose height is 5 ft and diameter at the top is 7 ft. A conical cistern…

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 man walks along a straight path at a speed of 4ft/s. A spotlight is located on the ground 20ft…

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Q: E. If the rate change of the length of the circle circumference with time is (n/2) m/sec. What is…

A: Given:- The rate change of the length of the circle circumference with time is (π/2) m/sec. To…

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 ​ft/min.…

A: Given information:

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

A:

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 surface area of a cube with sides of length x is given by S = 6x2 . Find the rate of change of…

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