A cylindrical tank as shown in Figure Q 1 is initially filled with water to a height, ho (m). The tank has a constant cross section area, A (m2). Water flows out of the tank through a valve at the bottom. The volumetric flow rate, F (m³/hr.) through the valve is proportional to the height ho.5 of water in the tank, F = R where R is the resistance with units of hr./m?. ho A Figure Q 1 (i.) Develop a model for the height of the water in the tank as a function of time, h(t). (ii.) Calculate the integration constant, if the tank is initially filled to 10 m and A= 5 m? and R= 1 hr./m? (ii.) Calculate the height of water in the tank,.

Q: The bending moment M of a beam of length l at a distance x from one end is given by M = Wx(l – x)/2,…

A:

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

A:

Q: A woltage V across a resistance R generates a current I = V/R. If a constant voltage of 17 volts is…

A: Given, Voltage, V=17 volts Resistance, R=5 ohms The rate of change of resistance with respect to…

Q: A spherical snowball melts at a rate of 16 in / sec. when the radius is 2 in, then the radius of the…

A: The formula for  volume of sphere is: V=43πr3 Given that dVdt=16 in3/secr=2

Q: Ex. 1. A shot of mass m, is fired from a gun of mass m2 with velocity v relative to the gun; show…

A:

Q: 1. Water is flowing into a vertical cylindrical tank at the rate of 24 ft3/min. If the radius of the…

A: As per guidelines, we are supposed to solve only first two questions. Please repost other questions…

Q: A tank initially holds 10 gal of fresh water. At t=0, a brine solution containing lb of salt per…

A: We have to find amount and concentration.

Q: A ball having mass m falls from a tower with heigh h from the ground. The velocity of the ball…

A:

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A:

Q: 39. The conical watering pail in Figure 17 has a grid of holes. Water flows out through the holes at…

A:

Q: A droplet has a mass of 2.9 x 10-13kg and a charge of +e. In what vertical electric field would the…

A:

Q: The conical watering pail with height 0.45 m and radius 0.15 m has a grid of holes. Water flows out…

A: Since multiple questions given , firs question is answered step by step. Please repost for more help…

Q: A standard cell has an emf "E" of 1.2 volts. If the resistance "R" of the circuit is increasing at…

A:

Q: The radius of a sphere increases at a rate of 3m/sec. Find the rate at which the surface area…

A: given that radius of a sphere increases at a rate of 3m/sec find the rate  when radius is 9m

Q: a.A surfboard 9 ft. long stands on the ground and leans against a wall. Due to a strong external…

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

Q: dv If the volume of the cube increases at the rate of 15 m / sec, then the value of is dt dv dV a) =…

A: Find the value value of rate of increase of volume of a cube

Q: Suppose the length of rod, L = 50 cm is immersed in steam until its temperature is throughout u, =…

A:

Q: A parachutist of mass m falls from rest in the Earth's gravitational field and is subjected to mg…

A:

Q: When a switch is closed in a circuit containing a battery E,a ersistance R and an inductance L,the…

A:

Q: 19. A conical glass whose radius is 5m and altitude 12m is being filled at the rate of 10 m. How…

A: For conical glass, Radius r=5 m, Height h=12 m, Rate of filling dVdt=10 cm3/s.

Q: A force of 7 lb is required to hold a spring stretched 9 in. beyond its natural length. How much…

A: Given the force is 7lb and spring is stretched to 9 in. We know that 12 inches is equal to 1 feet,…

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: According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot…

A: We need to find error.

Q: 3. If the temperature in a room is given by T(x, y, z) = xyz, at what rate will the temperature felt…

A:

Q: a. Water is flowing into a conical tank at a constant rate of 3 cubic meters per second. The cone…

A: The answer is given by using volume formula of cone. The answer is given as follows:

Q: The volume of a cube decreases at the rate of 74 m³/ sec. The rate at which the side of the cube…

A:

Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A: Here, given that the volume is constant. So, dVdt=0⇒ddtπr2h=0⇒πh 2rdrdt+r2dhdt=0⇒h 2rdrdt+r2dhdt=0…

Q: Suppose that the temperature T (x, y, z) of a spherical metal part satisfies, for each point (x, y,…

A: In equation we are equating two sides left hand side and right hand side. It contains variable,…

Q: A piston is seated at the top of a cylindrical chamber with radius 7 cm when it starts moving into…

A: This is application of derivative problem

Q: If a snowball melts so that its surface area decreases at a rate of 2 cm2/min, find the rate at…

A:

Q: Collars A and B of same mass m are moving towards each other with velocities shown in Fig. Ex.…

A: Solution:

Q: A spherical snowball of radius r cm has surface area S cm?. As the snowball gathers snow, its radius…

A: First let us find the rate of increase of radius. When t=4, r = 20 cm, (From the graph given) When t…

Q: B. The dimensions of a rectangular solid at a given instant (to) are (a = 13 cm), (b = 9 cm) and (c…

A:

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

A:

Q: An object of mass m falling near the surface of the earth is retarded by air resistance proportional…

A:

Q: The depth of an under proportional to the tim meters (m) of the came

A: Given that, The depth of the camera under the water is proportional to the time. We have to fill up…

Q: What is the position at time t of a car that is accelerating at a rate of 5 meters per second…

A: To determine the position of the car from the given data. (note that s =20 when t=2, not as given)

Q: For many species of fish, the allometric relationship between the weight W and the length L is…

A: Here the given that, the allometric relationship between the weight W and the length L is…

Q: A particle that moves along a straight line has velocity v(t) = t?e meters per second after t…

A: The displacement -velocity -time equation is given by, dsdt=v(t) The displacement during the first t…

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 3…

A:

Q: The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a…

A: Height is given by ht=3 sin 2πt→1instantaneous velocity=dhdt⇒Differentiate eqn 1 , w.r.t 't' , we…

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: 11. A snowball melts so that its surface area decreases at a rate of 0.5 cm²/min. Find the rate at…

A: Here we use the concept of derivatives.

Q: Assume a spring is oscillating and the length of the spring can be described as sin (t) L (t)=- What…

A:

Q: 1. The volume of a cube decreases at a rate of 12 m/sec. Find the rate at which the side of the cube…

A: This question is related to application of derivatives.

Q: f the measurement of the side of a cube is increased from 5 cm to 5.2 cm, the approximate increase…

A: Side of cube is increased from 5 to 5.2

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.