In a simple electric circuit, Ohm's law states that V=IRV=IR, where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. Assume that, as the battery wears out, the voltage decreases at 0.03 volts per second and, as the resistor heats up, the resistance is increasing at 0.04 ohms per second. When the resistance is 100 ohms and the current is 0.03 amperes, at what rate is the current changing?

Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: Solution :-

Q: Two capacitors with capacitance of 6 μF and 4 μF are connected in series across a 100 V dc source.…

A: Question- Two capacitors with capacitance of 6 μF and   4 μF are connected in series across a 100 V…

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Q: Suppose that 2 J of work is needed to stretch a spring fromits natural length of 30 cm to a length…

A:

Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: We will find out the required time.

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A:

Q: A boat with its load weighs 1,435 N. If the force exerted upon the boat by the motor in the…

A: F=72- 2vma = 72- 2v14359.81 dvdt=72-2v∫(146.3) dv72-2v=∫ dtt=-146.32ln(72-2v)+Cv=0 at…

Q: A van is 5 km due north of a pus at 2:00 PM. if the van is traveling northward at the rate of 60 kph…

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Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands…

A: Using the similarity of triangles.

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Q: A Plane (Plane A) travels North at a speed of 800 kph. after 15 minutes, another plane (plane B)…

A: Planes are moving same direction :

Q: Suppose that 3 J of work is needed to stretch a spring from its natural length of 24 cm to a length…

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Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 32 cm to a length…

A:

Q: A 200g-tank holds 100 gallons of fresh water upon first. At t = 0, a 5 gal/min salt solution…

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Q: A parachutist whose mass is 65 kg drops from a helicopter hovering 1500 m above the ground and falls…

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Q: Let a metallic rod 20 cm long be heated to a uniform temperature of 100° C. Suppose that at t = 0,…

A: Your answer is dependent on x, position from left end, and is the sum of infinity series.

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands…

A:

Q: A 10-ohm resistor and a 5-Henry inductor are connected in series with a voltage source rated at 20…

A: use ohms law and Kirchhoff law for finding the right option.

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Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

A: we know the work needed to stretch the spring W=12kx2 where x is the elongation. x=xf-xi=45-30=15…

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A: Given ,dydt=-2ft/s     negative sign because as ladder is slipping down, y decreasesby Pythagor…

Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

A:

Q: A tank contains 4000 liters (L) of a solution consisting of 120 kg of salt dissolved in water. Pure…

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Q: A roast turkey is removed from an oven when its temperature has reached 185°F and is placed on a…

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Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. (a) her shadow on the…

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Q: 2. Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a…

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Q: A tank contains 1000 liters (L) of a solution consisting of 170 kg of salt dissolved in water. Pure…

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Q: A body of unknown temperature is placed in a refrigerator at a constant temperature of 0° F. If…

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Q: A scuba tank holds 2.6 ㎥ of compressed air. A diver at a shallow depth uses about 0.002 ㎥ per breath…

A: Total compressed air in scuba tank = 2.6 m^3 Compressed air used per breath is 0.002 m^3 Breath…

Q: Find the general solution of the ODE.

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Q: Tank A contains 402 litres of brine holding 123 N of dissolved salt, and tank B contains 402 litres…

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Q: Consider a scenario in which a 20ft tall lamppost lights up a street. (a) A 5ft tall woman stands…

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A: Proceed as shown below

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Image is attached with detailed solution.

Q: A tank contains 1000 liters (L) of a solution consisting of 195 kg of salt dissolved in water. Pure…

A: Solution is given below:

Q: Two cars are traveling along a straight-line in the same direction, the lead car at 25.0 m/s and the…

A: Consider the given: Initial Speed of the lead car (uL)=25.0 m/sFinal Speed of the lead car (vL)=0…

Q: Suppose that the fish population P(t) in a lake is attacked by a disease at time t = 0, with the…

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Q: Tank A contains 407 litres of brine holding 181 N of dissolved salt, and tank B contains 407 litres…

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Q: A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32…

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Q: A tank initially holds 80 gal of a brine solution containing of salt per gallon. At t=0, another…

A:

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.