The radius of a sphere decreases at a rate of 3 meters per second. Find the rate at which the surface area changes when the radius is 15 m.

Q: The side of a cube increases at the rate of 11 m/sec. Find the rate at which the volume of the cube…

A: givenside of cube(a)=5mdadt=11m/secVolume of cube (v)=a3differentiating with respect to…

Q: At JCS Construction Plant, cement mixture is falling off a metal conveyor and onto an inverted…

A: Given: Cement mixture is falling off a metal conveyor and onto an inverted conical pile at a rate of…

Q: The radius of a sphere decreases at a rate of 1 m/se decreases when the radius is 15 m

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of  6cm/min.…

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Q: Can the distance traveled by a particle ever be less than its displacement? When are they equal?

A: No, the magnitude of the displacement is always less than or equal to the distance traveled.

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

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Q: 8. If a snowball melts so that its surface area decreases at a rate of 4 cm2 /min , find the rate at…

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 10 cm/min.…

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Q: If a ball of candy is covered in chocolate and is melting so that its surface area decreases at a…

A: To find: The rate at which diameter decreases when diameter is 10 cm. Given: The rate of surface…

Q: If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at…

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

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Q: The side of a cube decreases at a rate of 9 m/sec. Find the rate at which the volume changes, when…

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Q: A water tank has the shape of an inverted circular cone with base radius 2 m and height 4 m. If…

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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: Given a cylinder surmounted on both ends by a hemisphere, find the rate of change of its volume with…

A: Given:     Cylinder is surmounted by hemisphere at both ends.And height of cylinder is 5 meter.

Q: If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at…

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Q: If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at…

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Q: A kite 100 ft above the ground moves horizontally at aspeed of 8 ft/s. At what rate is the angle…

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Q: The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute. Find the rate…

A: Given that  The area of an equilateral triangle is decreasing at a rate of 4 sq. cm. per minute.…

Q: The height of a right circular cylinder is 50 inches and decreases at the rate of 4 inches per…

A: Topic = Volume

Q: The side of a cube decreases at a rate of 9 m/sec Find the rate at which the volume changes, when…

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Q: The side of a cube decreases at a rate of 7 m/sec. Find the rate at which the volume changes, when…

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Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

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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: a water tank has the shape of an inverted circular cone with a base radius of 2m and a height of 4m.…

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Q: Water flows into a conical tank at a rate of 2 ft3>min. If the radius of the top of the tank is 4…

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Q: a of 3 inche tall and has a radius of 2 inches How fast does the water level rise when the water is…

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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: water is running out of a conical funnel at the rate of 1 cu inches per second. If the radius of the…

A: This question is related to application of derivatives.

Q: Find the rate of change of volume of a sphere with respect to its surface area when the radius is 2…

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Q: The area of an equilateral triangle is decreasing at a rate of 3 cm^2/min. Find the rate (in…

A: We want to find the rate (in centimeters per minute) at which the length of a side is decreasing…

Q: A kite, 120 ft above the ground, is moving horizontally at the rate of 10 ft/sec. At what rate is…

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Q: A baseball diamond has the shape of a square with sides 90 ft long, as shown. A player is running…

A: A baseball diamond has the shape of a square with sides 90 feet long. A player running from second…

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm4/min, find the rate at…

A: Note that snowball has a shape of sphere.

Q: The lengths of the edges of a cube are increasing at a rate of 8 ft/min. At what rate is the surface…

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Q: an oil spill is spreading in a circle at a rate of 316.7in/sec2. at what rate is the radius changing…

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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: Given,Surface area is decreasing at rate = 3 cm2 per minDiameter of the snowball (d) = 11 cm

Q: A conical tank 20 feet in diameter and 30 feet tall (with vertex down) leaks water at a rate of 5…

A: To find the rate of water

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

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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: Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12rcm³ /s. If…

A: Given-  dVdt=12π cm3sec.,R=8 cm and H=16 cm To find- depth of sand after 15seconds and the rate of…

Q: If a snowball melts so that its surface area decreases at a rate of lcm²/min, find the rate at which…

A: Snowball represents a sphere So , Surface Area of sphere is 4πr2.  And , d=2r.  Using this we solve…

Q: The flow rate of water via a 50mm dia. pipe is shown in the table below, into a storage tank with a…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.