vt) - 180(1 - e 02)

Q: A 100-gal tank is initially full of water containing 10 lb of salt in solution. The tank will…

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Q: 3. According to Hooke's law, the force F required to stretch a spring x units beyond its natural…

A: We have to find the value of spring constant and weight.

Q: I started an experiment with 500 cells of bacteria in a petri dish. After 6 hours, my bacteria…

A: I started an experiment with 500 cells of bacteria in a petri dish. After 6 hours, my bacteria…

Q: 32. For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is…

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Q: . First-order chemical reactions In some chemical reactions, the rate at which the amount of a…

A: Here the derivative of y is just a multiple of the function, then y is an exponential function in…

Q: A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is…

A: Given, The downward velocity of the sky diver at time t is given by v(t) = 170(1 − e−0.15t) t is…

Q: Electricity In a series resistance-capacitance DC circuit, the instantaneous charge Q on the…

A: Given : Instantaneous charge Q is given by equation Qt =CV1-e-tRC Where C, V, and R are constants.…

Q: A culture initially has Po number of bacteria. At t = 2 hour the number of bacteria is measured to…

A: We will find out the required doubling time.

Q: The combined electrical resistance R of the resistances R, and R2 connected in 1 R1 1 parallel , is…

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Q: Calculus 11th Edition - Ron Larson Chapter 4.1 - Antiderivatives and Indefinite Integration Please…

A: From the given differential equation we separate P and t, then integrate both sides c= integrating…

Q: A rumor spreads through a school. Let y(t) be the fraction of the population that has heard the…

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Q: Newton's law of cooling states that the rate of cooling of an object is proportional to the…

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Q: By Newton's universal law of gravitation the free-fall acceleration a of a body, such as the…

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Q: A large tank contains 50 gallons of water into which 5 pounds of salt has been dissolved. A solution…

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Q: A sky diver jumps from a height above the ground. The air resistance she experiences is proportional…

A:

Q: In an experiment, a test tube containing a chemical is immersed in a water bath. At 1 = 0, the…

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Q: - Sky Diving A sky diver jumps from a reasonable height above the ground. The air resistance she…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: . Sky Diving A sky diver jumps from a reasonable height above the ground. The air resistance she…

A: Hey, since there are multiple subparts are posted, we will answer first three subparts.

Q: After 2 hours, the population of a culture of bacteria has increased by 50%. If the rate of growth…

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Q: Newton's law of cooling says that the rate of cooling of an object is proportional to the difference…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Radium decomposed at a rate proportional to the quality of radium present. Suppose that it is found…

A: Given- In 25 years approximately 1.10% of a certain quantity has decomposed. To find- To determine…

Q: A skydiver weighs 125 pounds, and her parachute and equipment combined weigh another 35 pounds.…

A: According to the problem, we have

Q: The rate of change of the population of the city is proportional to the population P at any time t…

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Q: The growth rate of a certain bacteria is known to ve proportional to the amount present. 5000…

A: We have to use P=Poektwhere: P = population Po = initial population k = proportionality constant t =…

Q: (c) Coal is extracted from a mine at a rate that is proportional to the amount of coal that remains…

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Q: Number of 3 9. 12 Bouquets Price ($) 9. 18 27 36 How can you find the constant of proportionality…

A: Consider the given table. Here it is observed that, the price is direct proportional to the number…

Q: 3. The air resistance of a free falling body with mass m is assumed to be proportional to its…

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Q: A 5000 L tank is initially filled with pure water.  A copper sulfate (salt) solution of 100g/L flows…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of salt at time t…

Q: Initially 59 grams of radioactive substance was present. After 5 hours the mass had decreased by…

A: Given query is to find the amount remaining after 22 hours.

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

A: In this exercise we have to create distant function but all the value is constant so we use the…

Q: 1. Transport through a cell membrane Under some conditions, the result of the movement of a…

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Q: Bacteria are often grown on agar plates and form circular colonies. The area of a colony is…

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Q: :) Coal is extracted from a mine at a rate that is proportional to the amount of co that remains in…

A:

Q: The half-life of the radioactive isotope Carbon-14 is about 5730 years. Part (a)-Find N in terms of…

A: Given problem:- The half-life of the radioactive isotope Carbon-14 is about 5730 years. Use the…

Q: By Newton's universal law of gravitation the free-fall acceleration a of a body, such as the…

A:

Q: Tank A has a volume of 50 liters. Tank B has a volume of 80 liters. At t = 0, tank A contains 3…

A: Given:-       Tank A has a volume of 50 liters. Tank B has a volume of 80 liters. At t = 0, tank A…

Q: A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is…

A:

Q: 3 The rate of cooling of a body can be expressed as dT = -k(T – T,), dt Where T is temperature of…

A: It is given that dTdt = -kT-Ta and we know k = 0.154 and Ta = 24 degrees Celsius.

Q: If a tank holds 4800 gallons of water, which drains from the bottom of the tank in 32 minutes, then…

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Q: The rate of change of the population of a city is proportional to the population P at any time t (in…

A: In this question we are given with the initial population and we have to find the population after…

Q: Air circulation. In a room containing 20,000 ft^3 of air, 600 ft^3 of fresh air flows in per minute,…

A: Let y be the amount of fresh air at any time t. The room contains 20,000 ft3 of fresh air and 600…

Q: Poiseuille's Law states that the volume, V, of blood flowing through an artery in a unit of time at…

A: Given query is to find the increase in radius to get the 50% increase in volume.

Q: A particle moves along a line so that its velocity at time t is v(t) = t^2 - 2t - 8 measured in…

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Q: Newton's law of cooling states that the rate of cooling of an object is proportional to the…

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Q: 2. A man with a parachute jumps out of a hovering helicopter at height H. During the fall, the man's…

A: The mathematical model for motion is provided by Newton’s second law, F = ma, with a skydiver of…

Q: A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is…

A: We will find the velocities.

Q: Hooke's Law states that the force F needed to keep a spring stretched x units beyond its natural…

A:

Q: A thermometer reading is 60oF at 3:00AM and a Civil Engineering student takes it outside where the…

A: Given: At 3:00 AM, thermometer reading = 60°F The outside air temperature = 20°F At 3:10 AM,…

Q: A truck is hired to transport goods from a factory to a warehouse. The driver's wages are figured by…

A: Let the driver's wage is W and the amount of gasoline is  G. The speed at which the truck is driven…

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.