Given a cube with sides x inches, let x(t) = t + 2. What is the instantaneous rate of %3D change of the volume, with respect to time, of the cube at t = 1 second?

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Q: O. At what rate is the vertex angle of a right circular cone changing when the radius is 3 ft and…

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Q: 2. How can you relate the rate of change for the surface area of a cube (dSA/dt) as compared with…

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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…

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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 volume of a cone of radius r and height h is given by V=1/3pir^2h. If the radius increases at a…

A: Volume of a cone = πr2h3 , Where r= radius of a cone and h= height of a conedrdt= 0.5cm/sec , dhdt=…

Q: A spherical snowball is melting in such a way that its volume is decreasing at a rate of 2 cm / min.…

A: Given-  dVdt=-2cm3/min (negative sign indicates that it is decreasing). To find- The rate of radius…

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Q: A right trianglewith dimensions of X = 3 cm and y =4cm.if Cx) is increasing at arate of 2 cml sec…

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Q: As a spherical raindrop falls, it reaches a layer of dry air and begins to evaporate at a rate that…

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Q: 3. Water is flowing into a vertical cylindrical tank at the rate of 24 cubic ft. /min. if the radius…

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Q: The height h and radius r of the base of a straight circular cone are varying at constant rates of…

A: Topic:- application of derivatives

Q: 2. Find the rate of change of a volume V of a cube with respect to (a) the length w of a diagonal of…

A: Consider a cube of a side a , and diagonals z and w  We know that Pythagorean theorem , Hypotenuse 2…

Q: The radius of a star(spherical) was r=a and was observed to increase by 0.01%. Use a linear…

A: Given data is : Radius(r) of a star (spherical) is increase by 0.01% To find the percentage of…

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: A designer develops a cylindrical box with a fixed height of 15 cm. Calculate the instantaneous rate…

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Q: 1. If the motor on a motorboat is started at t = 0 and the boat consumes gasoline at the rate of 6 –…

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Q: 1. We are inflating a spherical balloon. At what rate is the volume of the balloon changing when the…

A: Since you have asked multiple question (1&2) we will solve the first question for you. . If you…

Q: The volume V of a right circular cone of radius r and height h is given by V = 1/3 πr2h. a) What is…

A: Simply take derivative with respect to given variable considering other as constant.

Q: 12) A vertical cylinder is leaking wader at a rate I ft3% If the cylinder har a height of 10t Sec.…

A: Volume of cylinder = πr2h  r= radius of cylinder  h= height of cylinder

Q: 15. Gas is being pumped into a spherical balloon at the rate of 10 cubic inches per second. When the…

A: NOTE: Refresh your page if you can't see any equations. . here we have the diameter is 30 inches so…

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

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Q: A flag is raised vertically from a pole at a constant rate of 1m/s. A point B on the ground level…

A: Given: Vertically raising speed of flag at constant rate=1 m/s……1Horizontal distance from flagpole…

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Q: As an orange grows, the rate of change of the radius r of the orange is inversely proportional to…

A: Given query is to find differential equation.

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 4…

A: Given problem:- The radius r and height h of a cylinder are changing with time. At the instant in…

Q: a. If a snowball melts so that its surface area decreases at a rate of 1 cm²/min, find the rate at…

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Q: ) A snowball is melting at a rate of 1 cm3 per second. If it remains spherical, how fast is the…

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Q: A cube is expanding in such a way that the length of its diagonal is increasing at a rate of 5…

A: Let y be the diagonal, x be the length of an edge and V be the volume of the cube at any time t.…

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

A: Let x be the legth of a side and S be the surface area of the cube We know that   S=6x2 Given that…

Q: dV If the volume of the cube increases at the rate of 15 m² / sec, then the value of is dt

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Q: The radius of a sphere is decreasing at a rate of 1/4 cm/s. At what rate is the volume decreasing if…

A: The radius of a sphere is decreasing at a rate of 14cm/s.The radius is 2cm.

Q: A spherical balloon is deflated at a rate of 10 cm3 s-1. Find the rate change of the surface area…

A: given: A spherical balloon is deflated at a rate of 10 cm3s-1. we have to find the rate change of…

Q: 15. Water is being poured at the rate of 150 cm³/s into an inverted cone with a diameter of 3 meters…

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Q: Consider a rectangular metal box without a top lid which, because of being heated, is increasing in…

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Q: The area A(t) of a circular shape is growing at a constant rate. If the area increases from 97 to…

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Q: The sides of a cube increase at a rate of R cm/s. When the sides have a length of 2 cm, the rate of…

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Q: Find the rate of change of volume at the t= 2 sec If ri=2t-1 hisim hi=3ť-t r2= 3t+1 h2=2m h2=4t-1…

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Q: A spherical balloon has been poked with a needle and air is seeping out at a rate of 2cm³ /hr. Find…

A: The volume of the spherical balloon is decreasing at the rate of 2 cm3/hr. We have to find the rate…

Q: The diameter of a spherical balloon that is being filled with air is increasing at the rate of 3…

A: the volume of the sphere is given by ..............(1)

Q: In every sphere of radius r it is true that its volume V is given by V =ar³ , A snowball is melting…

A: volume of snowball (sphere);V=43πr3differentiating w.r.t. time t;dVdt=-4π3(3r2) drdtdVdt=-4πr2…

Q: The diameter of a sphere is 5(2x+ 5), the rate of change of its surface area with respect to x is

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Q: A flag is raised vertically from a pole at a constant rate of 1 m/s. A point B on the ground is…

A: solution:- draw a right angle triangle:-

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.