Assume that a rectangle with sides x and y is expanding with time. Let y = 2x and x(t) = 2t + 5. What is the rate of change of the area when t = 2? -72 dt dA dt 72 = 84 dt O 4 = 60

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A: The value of each integral given the area over the given integral  ∫abf(x) dxFrom x=a  to 0 the area…

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A: For the given sphere: Rate of expansion of radius r=30 cm/min……1At t=0, r=10 cm……2Surface area, say…

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Q: Of a rectangle are chonging at the tates of 1m/s and 2m/s. Sides its When its sides are 30 m and Ao…

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Q: 22. The surface area of a right circular cylinder of height 2 feet and radius r feet is given by…

A: Given: The surface area of a right circular cylinder of height 2 feet and radius r feet is given by…

Q: Use the differential dV to estimate the change in volume of a sphere when the radius changes from 9…

A: ddxxn=n xn-1

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

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Q: O Use differentials to approximate the increase in the area of a soap bubble when its volume…

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

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

Q: The radius of a circular oil slick expands at a rate of 5 m/min. (a) How fast is the area of the oil…

A: Given,  drdt = 5 m/minArea(A) = πr2       dAdt=2πrdrdta) r = 25m    dAdt=2π255          =  785.4…

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Q: #Ś A spherical balloon is filled with helium at a rate of 200 cmsec.At the moment when the radius is…

A: we have to find the rate change of surface area of the spherical balloon

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Q: Calculate the rate of change of escape velocity vesc = (2.82 × 107)r−1/2 m/s with respect to…

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Q: a

A: y = 3x Area = y*x A = 3x2 A(t) = 3x(t)2

Q: At noon, a city park manager starts filling a swimming pool. IfV(t) is the volume of water (in ft3)…

A: Given that a city park manager is filling his swimming pool. Volume of the swimming pool is V=43πr3.…

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Q: Assume that the radius r of a sphere is expanding at a rate of 80 cm/min. The volume of a sphere is…

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Q: Use the differential dV to estimate the change in volume of a cube when the side length changes from…

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Q: Use the differential dV to estimate the change in volume of a cube when the side length changes from…

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Q: Determine whether the following statements is true or false, and explain why.

A: Answer: False.

Q: A triangular trough is 3.6 meters long, 1.2 meters 0.9 meter wide at the top as shown in the figure…

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Q: A closed box is in the shape of a rectangular solid with dimensions x, y, and z. Suppose each…

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Q: Assume that the radius ? of a sphere is expanding at a rate of 40 cm/min. The volume of a sphere is…

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Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 20cm³ /s. How…

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Q: A spherical balloon is being inflated. (a) Find a general formula for the instantaneous rate of…

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Q: Use the differential dV to estimate the change in volume of a cube when the side length changes from…

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Q: 3. A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At…

A: Diagonal of Square = √2 * Side Perimeter of Square = 4* Side Area of Square = (Side)^ 2

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Q: Water is flowing into a vertical cylindrical tank at the rate of 5 cu ft/min. If the- radius of the…

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Q: Assume that the radius r of a sphere is expanding at a rate of 10in./min. The volume of a sphere is…

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Q: A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute. (a) Find the…

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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: A sphere is expanding with time. Assume that the volume of the sphere is V = (4pi * r ^ 3)/3; r(t) =…

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Q: 2. A spherical balloon is being inflated. Find the rate of increase if the surface area (S = 4ar')…

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Q: Assume that a rectangle with sides x and y is changing with time. Let y = 2x and x(t)=t^2 What is…

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

Q: Find the rate of change of the volume (V) of a sphere with respect to its radius (r) when r = 4. 4π…

A: You must have idea about basics of derivatives. The rate of anything is basically the derivative…

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Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 40 m s1. How…

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Q: Find the total differential of z = In(x + y), x = w, y= w?. By how much will z change if w increases…

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Q: Water flows into a cylindrical tank through pipe 1 at the rate of 25 ft/s and leaves through pipes 2…

A: Water flow into a cylindrical tank through pipe 1 is 25 ft/sec rate.  And pipe 2 is 10 ft/sec. And…