the current in an electric circuit is given by di Ri +L==0 dt 18- where R=10 ohm and L=0.2 henry when time t=0, current i=4 amper Find the current value when time t=0.02 seconds.

Q: where w(t) is measured in 74 (c) The grain in the silo is spoiling at a rate modeled by w(t) = 32 ·…

A: c) To find : The amount of grain remain unspoiled in the silo at time t=8 Given that : The amount of…

Q: The rate at which ice is melting in a pond is given by R (t) = V1+ 2', where Ris measured in cubic…

A: We use substitution method to solve integration to find out amount of ice melting in first 5 minutes

Q: 12. Find the time required for an object to cool from 300°F to 250°F by evaluating 300 10 1 t= dT In…

A:

Q: A mass attached to a vertical spring has position function given by s(t) = 3 sin(4t) where t is…

A:

Q: Lets assume that y(t) represents how many fish are harvested in month t. Solve dy/dt =1/(y+yt2) with…

A: The given differential equation is: dydt=1y+yt2 and y0=4 Here t in month To find approximately how…

Q: A materials scientist is experimenting with a new material with which to make beverage cans. She…

A: From the given plots, the scatterplot shows a perfect negative relationship between the variables.…

Q: The range R of a projectile is shown below, where v, is the initial velocity in meters per second…

A:

Q: A 80-kg cyclist on a 19-kg bicycle starts coasting on level ground at 30 m/sec. Use v = vo e (-k/m)t…

A:

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

A:

Q: A rectangular swimming pool 10 ft wide by 20 ft long and of uniform depth is being filled with…

A: Given that, Width of rectangular swimming pool = 10 ft Length of rectangular swimming pool = 20 ft…

Q: A car starts from rest at time t = 0 and accelerates at – 0.61 + 4 meters/sec? for 0 <t< 12. How…

A: Given: a = -0.6t+4 and velocity at t= 0 is 0 Since, dvdt=a, here v is the velocity and a is the…

Q: A model for the basal metabolism rate, in kcal/h, of a young man is R(t) = 85 - 0.19 cos(xt/12),…

A:

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

A:

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

A:

Q: In Winter an aluminum beam was brought from the outside cold into a machine shop where the…

A:

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: Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6…

A: Two cars are travelling to each other.

Q: Water is being drained from a spout in the bottom of a cylindrical tank. According to the…

A: Given  , Rate if drain: dV/dt = - 1.8L/min By integrating the equation we get the volume.

Q: The barometric pressure p (in inches of mercury) at an altitude x miles above sea level satisfies…

A:

Q: The impedance Z (ohms) in a series circuit is related to the resistance R (ohms) and reactance X…

A: Given,

Q: where h is the height of the water, t is time (in sec) and g is gravitational acceleration = 9.8…

A:

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: Q1: A conical tank with 3 m height, and 1.2 m radius initially is filled with water. If the water…

A: Given: Let H and R be the height and radius of the conical tank respectively. H=3 m R=1.2 m Let V be…

Q: A sailboat is running along a straight course with thewind providing a constant forward force of 50…

A: Given: A sailboat is running along a straight course with thewind providing a constant forward force…

Q: The position of a moving particle is given by s(t) = t2 – 2t + 6 on the interval 0 <t < 6, - where…

A: We will solve the following.

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

A: Instantaneous velocity of a particle is the velocity at a particular time.

Q: A 32-lb weight stretch a spring 2ft. At t = 0, the mass is released 1 ft above the cquilibrium…

A: The solution is given below

Q: A tank initially holds 10 gal of fresh water. at t=0, a brine solution containing 1/2 lb of salt per…

A: Given that, A tank initially holds 10 gal of fresh water. At t=0, a brine solution containing 1/2 lb…

Q: The velocity of a sky driver t seconds after jumping is given by v(t)=80(1−e-0.02t), measured in…

A:

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A:

Q: dV = 0.6t · cos(0.08t² – 1) , where V(t) is in dt 10) The rate of change in the volume of a tank is…

A:

Q: The power consumed in an electrical resistor is given by P = watts. Use R differentials to…

A: The electrical power is given as P=E2R Differentiate with respect to R dPdR=R×dE2dR-E2×dRdRR2…

Q: The position of a vibrating spring after t seconds is given by f(t) = (1/2) cost − (1/5) sin t…

A: The given position of a vibrating spring is ft=12cost-15sint, where t is the time in seconds.…

Q: A ball is thrown upward from a height of 3.6 m at an initial speed of 63 m/sec. Acceleration…

A:

Q: A mass-spring system is subjected to a single external force F (t) = sin (t), which acts for 0≤t≤2π…

A: Given mass-spring system is subjected to a single external force F (t) = sin (t), which acts for…

Q: If f(t)=2t+sin(t) describes the length of an oscillating spring in m/s, what is the instantaneous…

A: Solution is written in below steps.

Q: A tank with capacity of 300 gal of water originally contains 200 gal of water with 100 lb of salt in…

A:

Q: A mass-spring system is subjected to a single external force F (t) = sin (t), which acts for 0≤t≤2π…

A: Given a mass-spring system is subjected to a single external force F (t) = sin (t), which acts for…

Q: The bacteria concentration in a reservoir varies as C 3e-1.4t + e-0.2t Using Newton- %D Raphson…

A:

Q: It takes 50J of work to stretch a spring 0.2m from its equilibrium position. How much work is needed…

A:

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

A:

Q: The following figure shows the velocity, in cm/sec, of a particle moving along a number line.…

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Q: The volume V of a sphere of radius r changes over time t. a. Find an equation relating dV&gt;dt to…

A:

Q: An 11-m beam is subjected to a load, and the shear force follows the equation V(x) = 5 +0.25x² where…

A: Note:- As per our guidelines, we can answer the first of this problem as all the methods are…

Q: Find the antiderivative of the given derivative. ds 14(4? – 1)3 dt S =

A:

Q: A cyclist rides down a long straight road at a velocity (in m/min) given by v(t) = 400 – 20t, for…

A: Solve the following

Q: It takes 15 J of work to stretch a spring 0.2 m from its equilibrium position. Find the spring…

A:

Q: The acceleration, a, of a particle is given by a = 5- 6t Given that the initial displacement at t=0…

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…

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.