A rectangle has a length of 7 inches and a width of 8 inches, whose sides are changing. The length is increasing by 7 in/sec and the width is growing at a rate of 2 in/sec. How fast is the area changing?

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Q: At a certain instant the dimensions of a rectangle are 8 and 12 feet, and they are increasing at the…

A: At a certain instant the dimensions of a rectangle are: Length L=8 feetWidth W=12 feet

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A: GivenAll edges of a cube are expanding at a rate of 9 centimeters per second

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A: First we have to differentiate expression of volume with respect to time.

Q: Water is poured into a conical paper cup at the rate of 3/2 in/sec (similar to Example 4 in Section…

A: I will use the formula V=13πr2h and differentiation method to solve this problem.

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

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A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

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A: Given that the diameter= 100 mm So the radius is=r=1002=50 mm Given that the radius of a sphere is…

Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 3…

A: Given that:Rate of increase of radius, drdt=3 ft/s

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A: Let A1 and A2 be the areas of the inner and outer circles at any instant and 'A' be the area between…

Q: 2. please help, they canceled class due to virus can't contact teacher.

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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: The volume of  a cube is increasing at a rate of 9 feet3/sec . how fast is the surface area…

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Q: A spherical snow ball is being made so that its volume is increasing at the rate of 8 ft /min. What…

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Q: The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the…

A: Let be the volume and r be the radius of the sphere respectively.

Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

A: Volume of sphere= =43πR3 where R is the Radius of the sphere.

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Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: To calculate the required rate of change using partial derivatives

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Q: All edges of a cube are expanding at a rate of 2 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 2 centimeters per second.

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Q: The volume of a cube is increasing at a rate of 9 cubic centimeters per second .How fast is the…

A: Solution:-

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Q: The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the…

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Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

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Q: A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant…

A: Given: A stone dropped into a still pond sends out a circular ripple whose radius increases at a…

Q: All edges of a cube are expanding at a rate of 7 cm per second. How fast is the surface area…

A: Given that all edges of a cube are expanding at a rate of 7 cm per second. Let the edge of a sphere…

Q: at a certain instant, the dimensions of a rectangle are 8 and 12 feet and they are inreasing at the…

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Q: A cone with an altitude of 50 cm has its base radius changing at the rate of one millimeter per…

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Q: A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 2…

A: Given ,  A stone dropped in a pond sends out a circular ripple whose radius increases at a constant…

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Q: The volume of a cube is increasing at the rate of 6 cm/min. How fast is the surface area increasing…

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Q: The radius of a sphere is increasing at a rate of 4 meters per minute. When the radius is 11 meters,…

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Q: as a balloon in the shape of a sphere is being blown up, the volume is increasing at the rate of 4…

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Q: A comet loses material when it gets close to the Sun at a rate of 100 cubic meters per minute.…

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Q: The sides of a square increases in length at a rate of 3 m/sec. At what rate is the area of the…

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Q: All edges of a cube are expanding at a raete of 6 centimeters per second. How fast is the surface…

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Q: A spherical iron ball 8 in. in diameter is coated with a layer of ice of uniform thickness. If the…

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Q: The volume of a cube is increasing at the rate of 9 cm3 /  sec. How fast is the surface area…

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Q: All edges of a cube are expanding at a rate of 6 centimeters per second. (a) How fast is the surface…

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