10. If an initially resting object is accelerating with a constant power, then its acceleration a(t) is given by a(t) k m/s², where k is a constant'. Find the displacement of the object t seconds after the start.

Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)xy is an…

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Q: E. Solve tne differential Equotions ☺ Czxy + xln3x)dy + .(xtyJ dx =0 when x =3, y=2

A:

Q: b) Use Euler's method to obtain a numerical solution of the differential equation dy y = 4 - dx with…

A: given             y' = 4 - y/x     and y(1) = 3, we have to find

Q: Q.5.Suppose that a projectile is launched straight upwad from the initial position with initial…

A: Given data:- The given initial velocity, v0>0 The given differential equation, dvdt=-g1+ρgv2…

Q: 14. A particle moves along the x-axis so that its acceleration at any time t is a(t) = 2t - 7. If…

A: Given that, A particle is moving along the x-axis so that its acceleration at time t is a(t) = 2t…

Q: A tank contains 50-liters of brine in which 20 grams of salt is dissolved. Pure water is being…

A: Given: Let the rate of pumping in, Rin = 5 L / min Let the rate of pumping out, Rout = 4 L / min

Q: 3. Given the function y = (x² + 1)-1 + 3, suppose x decreases from 1 to 0.9. Find the absolute and…

A: We will find out the required solution.

Q: 16. Suppose the radius r, height h, and volume V of a dh related to dt dV cylinder are functions of…

A: Given: A cylinder with radius, r and height, h. The formula for the volume (V) of the cylinder is…

Q: There is considerable evidence to support the theory that for some species there is a minimum…

A: Given- There is considerable evidence to support the theory that for some species there is minimum…

Q: Give an example of birthrates Ai >0 such that a birth process (Xt)t>0 with birthrates di, i20…

A: The example of birthrates should follow Poisson's distribution where λi are the birthrates, since…

Q: Find the differential equations for each family of curves under the following conditions: c)…

A:

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A:

Q: Suppose that a quantity y = y(t) increases at a rate that is proportional to the square of the…

A: Given that a quantity y=y(t) increases at a rate that is proportional to the square of the amount…

Q: 6. Write down the differential, dy, of y = e3x.

A: to find the differential of y=e3x

Q: A clamped beam of length 3 is modeled by: y(4) = 24, y(0) = y'(0) = 0, y(3) = y'(3) = 0. Solve the…

A: The given differential equation is y4=24, with y0=y'0=0 and y3=y'3=0 Now we integrate the given…

Q: 1 1 LGt-5- At²est + Ceisinh Dt = [(s – 1)3 ' s² + 2s – 5]

A:

Q: 3: The dimensions of a rectangular box are measured to be 75 cm, 60 cm, and 40 cm, and each…

A:

Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A: First rearrange terms in the given ordinary differential equation  dyy=0.5+sint5dt since it is…

Q: Suppose that the heat conduction in a rod of length Lis described by the equation ku- hu, 0 0, at…

A:

Q: 1 So 2t en + e-2t ezt - e-at dt

A:

Q: 1. The position of a particle at time t (s) is s(t) = V12 +1 m. Com- pute its average velocity over…

A: Given, The position of a particle at time t seconds is s(t)=t2+1 meter.  To find the average…

Q: A tank initially contains 400 gal of fresh water. At time t= 0, a brine solution with a…

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: Lake Taal has a volume of 458 cubic km, and its rate of inflow and outflov are both 175 cubic…

A:

Q: A useful new product is introduced into an isolated fixed population of 1,000,000 people, and 100 of…

A: If x denotes the number of people who adopted the product at time t, measured in then we have the…

Q: Suppose that a population grows according to the unlimited growth model described by the dy = 0.15y…

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Q: 2 Solvehe initial value problems below. dy dt

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

Q: The differential equation corresponds to Newton's law of cooling is O a. dT L = k(M – T) dt O b. OY…

A: According to the given information, it is required to select the correct option.

Q: Explain why the initial Value problem dy/dx=x-cos(y); y(1)=pi has a unique solution. For that…

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Q: Verify that y(t) = ceat solves the differential equation for unlimited growth, y' = ay, with initial…

A: Given Differential Equation : y1 = ay , y(0) = C i.e. dydt =ayie  dyy = adt Integratinh both side we…

Q: 1. Suppose that y = x³ + 4x. Suppose we increase x from 3 to 3.02. Use differentials to estimate the…

A:

Q: The differential equation for cooling of a cup of coffee is given by dT dt = -(T – Tenu)/T where T…

A: final answer is  T = 200 C at t =5 minutes detailed solution with explanation is given below

Q: A jar contains 100 mL of a certain substance which, when heated to t degrees Celsius contains E(t) =…

A: the given function for the thermal energy is E(t)=2.3t2-4.5 and as the thermometer is accurate to…

Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: Solve the following Initial Value Problem. dy/dt=sec^2(t)-sin(t), y(pi/4)=1 y=??????????????????

A: Given that: dydt=sec2t-sint, yπ4=1

Q: According to the Ideal Gas Law, the pressure P, temperature T, and volume V of a confined gas are…

A: We have to use differentials to approximate the percentage change in pressure if the temperature of…

Q: A 16-lb weight is attached to the lower end of a coil spring sus-pended from the ceiling and having…

A:

Q: NUTES -3x PG. 8 Problem q: y" =94iyse",y2s e3*

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Q: 1. Eliminate the arbitrary constants on the given equation: y = A + Be*

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 16. Use differentials (that is, linear approximation) to approximate: V3.9 – e0.05

A:

Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: 8. Use a linear approximation or differentials to estimate the value of v15, knowing the exact value…

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Q: Suppose we have a pendulum clock that uses a slightly damped pendulum to keep time (that is, b is…

A: At first we will derive a direct relationship between θ and m then from that we will observe how θ…

Q: 2) If a particle is moving in a straight line, and its distance away from its starting place (in…

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Q: The position xft) of an object of mass m that is attached to a vertical spring with restitution…

A:

Q: (1/4) Estimate the value of 82 a. approximation b. differentials

A: To estimate the value of 8214 by using a approximationb differentials

Q: If y = 5x2 + 2x + 9 , find the value of the differential dy as x changes from 3 to 3.1

A: Given, y = 5x2 + 2x + 9Differentiating with respect to x;dydx = 10x + 2At x = 3, dydxx = 3 = 10×3 +…

Q: 3) 1 Use an integrating factor to solve dy - by 25/4 = X with y(i)=-2

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Q: 4. (a) Solve the initial value problems, dy = sin t + 1; yE)=; dt (b) Evaluate V1 – x² dx. |

A: