Evaluate the rate of change of the Area if the area of the circle is given by A= 6 r² when dr 7 and r = 2 dt

Q: Find the rate of change in the area (A) of a circle with respect to its radius (r) when r = 9. 9TT…

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

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Q: The length of a rectangle is given by 4t + 9 and its height is √t, where t is time in seconds and…

A: Given:

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: The length of a rectangle is given by 2t + 5 and its height is Vt, where t is time in seconds and…

A: In the given question the length and height of the rectangle are given:   The area of the rectangle…

Q: The area of a rectangle with one of its sides s is A(s) = 6s². What is the rate of change of the…

A: Differentiate both sides of the equation, with respect to s to establish a relation between the…

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

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Q: What is the rate of change of the area of acircle (A = pai r2) with respect to the radius when the…

A: The radius of a circle is r=3 units. The formula for area of circle is given by A=πr2

Q: The area of a square with side s is A(s) s². What is the = rate of change of the area of a square…

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

A: Given:The radius r of a sphere is increasing at a rate of 6 inches per minute.

Q: Find the average rate of change of the area of a circle with respect to its radius r as r changes…

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Q: The formula for the volume of a right cylinder is V = ar²h. Find the rate of change of the volume…

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Q: The volume of a sphere is increasing at a rate of 8 cubic cm/sec.  Find the rate of change of its…

A: Let V be the volume of the sphere which is given in the question as,

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: The length of a rectangle is given by 2t + 3 and its height is √t, where t is time in seconds and…

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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: What is the average rate of 5. If f (t) = -3t + 7t, describes the movement of a whale in meters.…

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

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Q: The radius R of a circle is increasing at the rate of 1 cm per sec. How fast is the area changing…

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Q: A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. Find the…

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Q: A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change…

A: Given that spherical snow ball melts at a rate proportional to its surface areaShow that rate of…

Q: A balloon's volume is increasing at 15 ft /sec at the same moment as its surface area is increasing…

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Q: A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute. (a) Find…

A: Given: Rate of change of volume of spherical balloon is dVdt=800cm3/min. (a) To find: Rate of change…

Q: Assume a circle is expanding with time, where r = t + 2. What is the formula for the rate of change…

A: Given: r = t + 2   We know that the area of the circle: A = π r2   where r is radius.

Q: What is the rate of change of the volumeof a ball (V = (4>3)pr3) with respect to the radius…

A: The volume of a ball with radius r is given by V=43πr3 Recall that the rate of change is given by…

Q: The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and…

A: Formula:  Area=length times height A(t)=t(6t+5)

Q: If the area of a healing wound changes at a rate given approximately by dA 4 for 1 <t<10 is in days…

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Q: The radius of a sphere is increasing at the rate of 2 meters per se of change of the volume with…

A: Given: The radius of a sphere is increasing at the rate of 2 meters per second.

Q: where t is time in seconds and the dimensions

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Q: A cylindrical box has a fixed height of 12 inches. Find the rate of change of volume with respect to…

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Q: The area of a square with sides of length s is given by A = s'. Find the rate of change of the area…

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Q: The area of a square with sides of length s is given by A = s². Find the rate of change of the area…

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Q: The longer base of an isosceles trapezoid is one more than 1/3 of the shorter base. If the altitude…

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

A: Given: The surface area of the cube : S=6x2 To find : Rate of change of surface area with respect to…

Q: Find the rate of change of area of the circle with respect to its radius, in ft2/ft, when the radius…

A: We have to find the rate of change of area of the circle with respect to its radius in ft2/ft. Also…

Q: The volume of a cube with sides of lengths is given by=s. Find the rate of change of volume with…

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Q: The radius of a right circular cylinder is given by sqrt(t+7) and its height is 2 (sqrt(t)), where t…

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Q: The volume of a cube with sides of length s is given by V = s3. Find the rate of change of volume…

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Q: What is the rate of change of the area of a circle (A =πr2) with respect to the radius when the…

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

Q: A square with side x cm, is changing with time where x(t) = 4t – 2. What is the rate of change of…

A: Given: A square with side x. changing with time is given as, xt=4t-2. The objective is to find the…

Q: The area of a square with sides of length s is given by A = s2 . Find the rate of change of the area…

A: The area of a square with sides of length s is given by , A=s2. To find the rate of change of area…

Q: The volume of a sphere is expanding where r = 2t. What is the rate of change in volume with respect…

A: First substitute the value of r=2t in volume ,and then differentiate it for finding the rate of…

Q: Find the rate of change of the surface area of a hemisphere with respect to its radius. a. When the…

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Q: What is the rate of change of the area of a circle (A = pair2 ) with respect to the radius when the…

A: It is required to calculate the rate of change of area of circle with respect to radius when radius…

Q: Let A be the area of a circle with radius r that is increasing in size with respect to time. If the…

A: We have to find rate of change of the radius when radius is 6 cm and rate of change of area is given…

Q: How can you relate the rate of change for the surface area of a cube (dSA/dt) as compared with its…

A: we know that surface areaS.A. and volumeV of cube is given by S.A.=6l2…

Q: The area of a square with sides of length s is given by A = s2. Find the rate of change of the area…

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Q: A heated circular plate has a radius of 24 in. What is the rate of change of the plate's radius if…

A: To find the rate of change of plate's radius

Q: The area of a square with side s is A(s) = s². What is the rate of change of the area of a square…

A: We are given :  The Area of a square with  side s is A(s) =s2

Exponential Growth Model

The relation that represents an exponential function is: