The side of a cube decreases at a rate of 2.5m/s. Find the rate at which the surfacearea decreases when the side is 10 m

Q: 1. The side of a cube decreases at a rate of 2.5m/s. Find the rate at which the surfacearea…

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Q: B. How rapidly will the water level inside a vertical cylindrical tank if we pump the water out at…

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

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Q: If a snowball melts so that its surface area decreases at a rate of 1cm /min, find the rate at which…

A: Diameter= DRadius = r =D/2Surface area = A= 4pi*r^2Given dA/dt= -1 cm^2/min (negative because…

Q: The base radius, r, of a cylinder is decreasing at a rate of 0,2cm/s while its height, h, is…

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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 acceleration of a Maserati is proportional to the difference between 250 km/h and the velocity…

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Q: 3) Determine the speed of change of volume of a rectangular parallelepiped, knowing that the edges…

A: Let the length of base edges and vertical edge are x, y and z respectively such that dxdt = +2…

Q: The side of a cube decreases at a rate of 8 m/sec. Find the rate at which the volume changes, when…

A: given that a side of cubedecreases at a rate of 8m/sfind the rate at which the volume changes when…

Q: The lengths of the edges of a cube are increasing at a rate of 1 ft/min. At what rate is the surface…

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Q: A spherical drop of liquid evaporates at a rate proportional to its surface area. If a given drop…

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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: If the length of the edge of a cube is increasing at a rate of 3cm/s, how fast is the volume of the…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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

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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…

A: Solve using increasing & decreasing function.

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 volume of the sphere is increasing at the rate of 6cm^3/hr. At what rate is its surface area…

A: Given that the volume of the sphere is increasing at the rate of 6  cm^3/hr. We have to find the…

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

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

A: Topic:- application of derivatives

Q: The side of a cube is increasing at a rate 7m/s, then the rate at which the volume of the cube…

A: Let s be the side of the cube in meter and V be the volume of the cube and t be the time in…

Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

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: Find the rate of change of the total surface area of a cylinder of radius r and height h, when the…

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Q: If the radius r of a sphere is expanding at a rate of 15 cm/min, find the rate at which the volume…

A: We have given radius of a sphere is expanding at a rate of 15 cm/min. So drdt=15 cm/min As Volume of…

Q: The pressure exerted by a certain Iiquid at 0 given point varies directly as the depth of the point…

A: Given pressure of liquid at a point is directly proportional to the depth of the surface at the…

Q: The volume of water in a hemispherical bowl of radius 30cm is given by V =36x2 – x³ ) where x - X cm…

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Q: The side of a cube increases at a rate of 2.5m/s. Find the rate at which the surface area increases…

A: As we know that; The expression of the surface area of the cube is: As=6a2        ....(1) Where;…

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: A cube is expanding at the rate of change 64 m³/s. What is the rate of change of its surface area…

A: This question is based on application of derivative.

Q: A man 2m tall is walking at the rate of 2m/s away from a lamp post 7m high. At what rate is the tip…

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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: Radius of the funnel r=8 cm. Height of the funnel h= 16 cm. rate of change of volume…

Q: 3) If a spherical snowball melts so that its surface area decreases at a rate of 1 cm? he rate at…

A: It is given that a spherical ball melts so that its surface area decreases at a rate of 1 cm2 per…

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 edge of a cube decreases at a rate of 1.5m/s. Find the rate at which the surface area decreases…

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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: The velocity, in feet per second, of a running rodent is modeled by v(t) = 5√t − 2t. What is the…

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Q: The original 24 m edge length x of a cube decreases at the rate of 2 m/min. a. When x = 4 m, at what…

A: As Given :                   The length x of Cube decrease at a rate of 2 m/min.…

Q: The kinetic energy K of a mass is proportional to the square of its velocity y. If K = 12,960 joules…

A: To determine the kinetic energy.

Q: The side of a cube is increasing at a rate 9m/s, then the rate at which the volume of the cube…

A: The function f(t) is a rule that associates or fixes a number to the particular point t. The…

Q: The volume of a cube is increasing at a rate of 64 in ³/sec. At what rate is the length of each edge…

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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: The radius of a sphere decreases at a rate of 4 m/s. when the radius is 7 m, then the rate at which…

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Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Given: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when…

Q: The radius of a sphere decreases at a rate of 5 m/s. when the radius is 7 m, then the rate at which…

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Q: The diameter of a steel ball is measured to be 16 cm, with a maximum error of 0.3 cm. Estimate the…

A: The relation between the radius, r, and the diameter, l, can be defined by the equation: r=l2. It is…

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.