A falling object weighs 160 lbs. Beginning from the differential equation, find the object's velocity after 15 seconds in ft/sec and the terminal velocity assuming:

Q: A bacteria colony begins with a population of 120 and quadruples in size every 1.5 days.   If the…

A: Given initial population = 120  So, for t=0, P=120  Using that we get: Quadruples in size every 1.5…

Q: Form the differential equation by elimanating the arbitary constant A,Bvfrom y=Ae7x+Be-7x

A:

Q: A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential…

A: The surface area of a sphere of radius r is:

Q: The population y(t) grows continuously and follows an exponential behavior over time. Its…

A: We have to find the differential equation to describe growth of population y(t).

Q: Glucose is added intravenously to the bloodstream at the rate of q units per minute, and the body…

A:

Q: A lake containing 2.4 x 10° liters of water is polluted with 2 mg/L of arsenic. A freshwater stream…

A: Given, a lake containing 2.4×109 liters of water is polluted with 2 mg/L of  arsenic. A freshwater…

Q: what is the Non-exact differential equation?

A:

Q: A spring is stretched 175 mm by an 8-kg block. If the block is displaced 100 mm downward from its…

A:

Q: Find the differential equation by rlimaniting the arbitary constants from

A:

Q: Find the differential equation of straight lines with slope and x –intercept equal.

A: Recall:  The equation of straight line is y=mx+b where, m=slope, b=y-intecept   Given, slope and x…

Q: A certain drug is being administered intravenously to a hospital patient. Fluid containing 5 mg/cm3…

A:

Q: An investor deposits $8000 into an account that pays 6% compounded continuously and then begins to…

A:

Q: In 2007, (when t = 0), world solar photovoltaic (PV) market installations were 2826 megawatts and…

A: Consider the given information. The initial value (t=0) is 2826. And the rate is 48%. St=S01+rt And,…

Q: From the differential equation by eliminationg the arbitary constant A,B from y=Ae7x+Be-7x

A:

Q: Form the differential equation by elimanating the arbitary constant A,B fror V=Ae7x+Be-7x

A: y = Ae7x + Be-7x

Q: y" – y' = sint Solve the general solution of the differential equation by the method of change of…

A:

Q: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

Q: Solve the differential equation with clear steps

A: Given, system of differential equation is dxdt=3x-y-zdydt=x+y-zdzdt=x-y+z We can write it as in…

Q: he population y(t) of a certain microorganism grows continuously and follows an expo uadrupling time…

A: In this question, the concept of derivatives is applied. Derivative We can use a derivative to…

Q: Develop the corretor-predictor formula fer solving differential equation.

A:

Q: Write the differential equation satisfied by y = Cekt.

A: Given equation is              y=Cekt

Q: What is the differential equation given functions?

A:

Q: Assume that a population P of wolves in a region is proportional to the area A of the region. Does…

A:

Q: Find a differential equation whose general solution is y = cie®t + cze¬,

A: The complimentary function of the differential equation if the root of the auxiliary equation are…

Q: If the number of fruit flies F increases at a rate that is proportional to the number of flies…

A:

Q: The change of Turkey's population (N) over time (t) is proportional to the current population. In…

A: Note: It is assumed that the population of 2021 is being asked this question.   The general solution…

Q: The growth rate of population of a city is known to be equal to 20% of the current…

A: According to the given information it is required to find the number of years it will take to double…

Q: The management at a certain factory has found that the maximum number of units a worker can produce…

A: Lets suppose that the rate of change of performance with respect to time is dNdt (a) The required…

Q: From the differential equation by eliminationg the arbitary constant A,B from y=Ae/x+Be¬-7x +Be-7x

A: To form the differential equation by eliminating the arbitrary constant

Q: To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t)…

A:

Q: Assume that the rate of evaporation for water is proportional to the initial amount of water in a…

A: Here, given that rate of change of evaporation is proportional to the initial amount of water.…

Q: Assume that a population P of wolves in a region is proportional to the area A of the region. Does…

A: This question is about application of derivative

Q: A body weighing 24 lb stretches a vertical spring 1 foot beyond its natural length. The spring is…

A:

Q: A culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to be…

A: given: A culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to…

Q: EQUATION

A:

Q: In a city of a fixed population of " people , the rate of change (with respect to time t) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to time…

Q: y² = 14eax-

A: Given y2=14eax

Q: Find the relative error in the computed area of an equilateral triangle due to an error of 3 percent…

A: To find the relative error in measuring the area of equilateral triangle where the edge is measured…

Q: By first finding an integrating factor, solve this differential equation. Give your answer in the…

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 at…

Q: A man is walking at a rate of 1.5 m/s toward a street light which is 5 m above the level ground. At…

A:

Q: The rate of change of the population p of bacteria at time t is proportional to the population at…

A:

Q: From the differential equation by elimanating arbitary constants  y=ax3+bx2

A:

Q: Derive a differential equation that expresses the height h of the water at any time t in the conical…

A: Firstly let's determine the velocity of water flowing out of the orifice, v. Consider that the…

Q: Assume an object's weight, W, is proportional to its height, H. Does it make sens use differential…

A: This question is about application of derivative

Q: Essay, elaborate the procedure in solving a homogenous differential equation.

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Q: What does it mean for a function to be a solution to a differential equation?

A: A function is said to be a solution of differential equation if it satisfies the differential…

Q: When is an equation considered as a solution of  differential equation?

A:

Q: A small cannonball with mass 9 kilograms is shot vertically upward with an initial velocity of 130…

A: we have m=9, v=130, k=0.0025, g=-9.8

Q: After a murder has been committed, the body, which was originally at 37°C, cools according to…

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.