1 If a spherical drop of liquid evaporates at a rate proportional to its area, if initially its radius is 1/20 inches, and if in 15 minutes the radius is 1/40 inches, find the radius r in terms of the time t.

Q: Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: 1. A 25 feet long ladder is leaning against a wall and sliding toward the floor. If the foot of the…

A:

Q: A culture of yeast grows at a rate proportional to its size. If the initial population is 4000 cells…

A: Let's find.

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: Assuming continuous compounding P=P0eKt P→Population at moment in time P0→initial Population…

Q: 2. Suppose that at some time t the mass of the tumor, M(t), is between 0 and K. What is the sign of…

A: We need to find sign of rate of change of M.

Q: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2…

A:

Q: Suppose the population of a colony of ants grows at the rate P'(t) = 1 +   5 /(√ t + 1)   If…

A: Given, P'(t) = 1 + 5t+1 when t = 120 hours  then P(t) = 250  Thenm  when t = 0 hours then P(t) = ?

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A:

Q: A company estimates that its revenue grows continuously at a rate given by R'(t)= 2e^2t, where t is…

A: By Using simple integration

Q: The value of a computer t years after purchase is v(t) = 4000e , At what rate is the computer's…

A: we need to find rate of change with respect to time of v(t)

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: The radioactive Isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A:

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: Given expression is PV1.4=C   ......1 Where P is pressure, V is volume and C is constant.  Pressure…

Q: and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this mom

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Q: The upper end of the ladder 5 m long leans against a vertical wall. Suppose the foot of the ladder…

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Q: 1. A honeybee population starts with 100 bees and increases at a rate of f'(t) bees per week. What…

A:

Q: Assume that the radius r of the cylinder below is decreasing at a rate of 2 m/s, and that its height…

A:

Q: Solve the following problems. 1. A ladder 7.5 meters long is leaning against the wall of a house.…

A: In the question we have to find the rate at which ladder is sliding down.

Q: A vertical cylinder having a circular base of radius ‘r’ and a height of 12 m is filled with water…

A: The cylinder is filled with water at the rate of 1 m/min. To Find: If the depth of water in the…

Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

Q: A weight W is attached to a rope 50 ft long which passes over a pulley at P, 20 ft above the ground.…

A: Given: - A weight W is attached to a rope 50 ft, long which passes over a pulley at P, 20 ftabove…

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate (in…

A: Let the diameter be D cm and radius be r cm  The surface area S of the the sphere in term of…

Q: (A1) A ladder 11 feet long rests againt a certical wall. if the bottom of the ladder slides away…

A:

Q: A forester finds that a certain type of forest tree grows in such a way that its height h(t) after t…

A:

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

A:

Q: Suppose a quantity described by the function y(t) = y0ekt, where t is measured in years, has a…

A: yt=y0ekt The quantity has a doubling time of 20 years. That is, yt=2y0 when t=20.

Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Here we have a population of fruit flies that changes at a rate of g(t)=-4e0.04t…

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

A: Topic = Differential equation

Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

A: We have to determine the time necessary for the number of bacteria to triple.

Q: Solve parts a,b, and c.

A: Here we need to apply some basic concepts of derivatives to find the answers

Q: [2] The rate of growth of the bacterial population is proportional to the number of bacteria present…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: 18. A light is on the top of a 4-meter tall pole and a 1.5-meter tall person is walking away from…

A:

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A:

Q: 4. A culture initially has No number of bacteria. After one hour the number of bacteria is measured…

A: Given: N0= Initial number of bacteria After one hour the number of bacteria is measured to 32N0 Rate…

Q: The volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t =…

A: Given that the volume of sphere is increasing at a rate proportional to the reciprocal of its…

Q: A tank holds 59 gallons of water. Initially, at t=0, a solution containing 1/8 lb/gal of a chemical…

A: This is a mixing problem and at any time the amount of salt in in tank is (total salt in - total…

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

A:

Q: 7. If the rate of growth of a bacteria population is modeled by r(t) = 8e2t-1 thousand bacteria per…

A: Introduction: When a function is given, we determine the average value by integrating the function.…

Q: 1. A man on a wharf, whose hand is 8.2 m above the level of the water surface is pulling a rope tied…

A:

Q: Suppose that copper is being projected to be extracted from a certain mine at a rate given by P'(t)…

A:

Q: 1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles…

A: As per our guidelines we are supposed to answer only one question. I am solving the first one Kindly…

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: Given: The population of a community is known to increase at a rate proportional to the number of…

Q: A 14-foot ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate…

A:

Q: If oil leaks from a tank at a rate of  r(t) gallons per minute attime t , what does ∫0120 r(t) dt…

A: Oil leaks from a tank at a rate of  r(t) gallons per minute at time t.

Q: 5. A ladder 20 ft long leans against a vertical building. If the top of the ladder slides down at a…

A: Given query is to find the speed at which bottom of the ladder is sliding.

Q: 1 A 5 m ladder is leaning against a wall of a house. The bottom of the ladder is pulled away from…

A: Let the bottom of the ladder is x meters away from the wall and the top of ladder is at distance y…

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.