19. The constant acceleration of a ball in freefall is a(t) =-9.8 meters per second squared. Use calculus to find a formula for the position s(t) of the ball given v(0) = +15 meters per second and s(0) =5 meters.

Q: 2. To the discrete population model for P with constant birth and death rates add a constant…

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Q: The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV =…

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Q: 4. Solve the initial value problem. dy a. = 3e* →, y = 6, when x = 0. dx %3D %3D

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Q: 1. Show that if you differentiate both sides of x2 + 2y³ = 6, the result is 2x + 6y2 = 0. Then solve…

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Q: Use differential approximations in the following problem. A company will sell N units of a product…

A: Given, Number of sell units of product after spending $x thousand in advertising, as given by…

Q: If the brakes on a car give the car a constant negative acceleration of 24 mfe2, where i is a…

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Q: 3. A 3-kg mass is attached to a spring having spring constant k = 300 N/m. At time t = 0, the mass…

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Q: A large tank originally contains 1000 litres in which 5 kilograms of salt is dissolved. Pure water…

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Q: A materials scientist is experimenting with a new material with which to make beverage cans. She…

A: From the given plots, the scatterplot shows a perfect negative relationship between the variables.…

Q: The amount of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a…

A: Given the amount of nitrogen dioxide present in the atmosphere on a certain day is modelled as…

Q: 4. Find the positive root of the equation correct to 3 decimal places, using Newton-Raphson method…

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Q: a) A capacitor (C) which is connected with a resistor (R) is being charged by supplying the constant…

A: Given : E = ∫0∞P(t) dt  ,   P(t) = 5Re-tRC2×R

Q: Find the approximate height of the curve y = x3 – 2x2 + 7 at the point where x = 2.98. (SOLVE BY…

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Q: Suppose now that the person begins walking away from the light pole at a constant rate of 0.6 meters…

A: In triangle △ADE and △ABC1. ∠A is common2. ∠ACB = ∠ADE        (90°)△ADE  ≈ △ABC  (AA similarity…

Q: of the differential equati

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Q: A force of 7 lb is required to hold a spring stretched 9 in. beyond its natural length. How much…

A: Given the force is 7lb and spring is stretched to 9 in. We know that 12 inches is equal to 1 feet,…

Q: Find the Bolution to Hhe initial value problem - Please Write the folution with the computer.

A: Solution of Linear Differential Equation with Constant Coefficients: The general form of linear…

Q: (12 Use differentials to est imate fl-2.01) it fCx): x/T-x.

A: We need to find differential estimate. NOTE- As per Bartleby's guidelines we can only solve one…

Q: f (x) = y = x³ +x– 10 = 0

A: Using Newton raphson method.

Q: Use differential approximations in the following problem.   A company will sell N units of a product…

A: A company will sell N units of a product after spending​ $x thousand in​ advertising, as given by…

Q: 2. A ball is dropped from a 20-foot building with a constant acceleration due to gravity of 9.8m/s².…

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Q: From the Newton's law of cooling, the cooling rate of a body is proportional to the difference…

A: We will use variable separable method to solve the differential equation.

Q: For an ideal gas, the pressure is related to temperature and volume by the formula 8.31T . If your…

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Q: A type of sugar in the blood, also known as glucose, which is one of the major sources of energy, is…

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Q: 3x =2 when x= What is the particular solution to the given differential equa

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Q: 3) For an ideal gas, the pressure is related to temperature and volume by the formula 8.31T V . If…

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Q: 14. In the theory of relativity, the mass of a particle with velocity v is то m where m, is the mass…

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Q: 4. Over the time interval 1 <t< 9, a particle moves along a straight line with a velocity of v(t) 18…

A: Her distance never be negative so we take Absolute value when curve below x axis

Q: 8. The length, width, and height of a rectangular box are measured as 80 cm, 50 cm, and 60 cm,…

A: Consider the length, width and height of rectangular box be l, w and h respectively. l=80 cmw=50…

Q: 8. The acceleration of a particle moving along x-axis at time t is defined by a=4t-12. At t=0, the…

A: Given: The acceleration of a particle moving along x‐axis at time t is defined by a=4t-12. At t=0,…

Q: According to the ideal gas law, the pressure P, temperature T, and volume V of a confined gas are…

A: To find out the change in pressure using the differentials.

Q: (d) The GoldPlus Company determines that the marginal cost for their Aiibe 64GB flash drive is given…

A: Given that : Marginal Cost Function is : dCdx=-0.02x+6. We can achieve Total cost function by…

Q: 2. A ball is dropped from a 20-foot building with a constant acceleration due to gravity of 9.8m/s².…

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Q: The Ideal Gas Law relates the pressure P, temperature T, and volume Vof an ideal gas via the…

A: The relation among the pressure P, temperature T, and volume Vof an ideal gas is given by P = T/V.

Q: 4. Suppose an object with initial velocity v, = 0 ft/s and (constant) mass m slug is accelerated by…

A: Given vN =Ftm      and    VE=Fctm2c2+F2t2

Q: 8. The velocity of a particle moving along a straight line at time t is given by v(t) = 2t – 2t3/2 –…

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Q: Solve the differential eqution y'-y=7e^x

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Q: Suppose now that the person begins walking away from the light pole at a constant rate of 0.6 meters…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: B. Solve the following problems using differentials and linear approximations. Show complete…

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Q: 5. Find the General and Particular solution of 2 = 3y ; y = 3, when x = 0 dy dx

A: We have dydx=3y Now, we can write this as: dyy=3dx Now, integrate both sides: ∫dyy=∫3dx⇒lny=3x+C…

Q: A spring of constant k=8 N/m hanging from the ceiling is placed at its lower end with an object of…

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Q: 4) For an ideal gas, the pressure is related to temperature and volume by the formula 8.317 P = If…

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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: 2. Solve the following problem 10 (хи — 2x2 — 5и?)dt max | 0, dx = x + 3u, x(0) = 6, x(10) free dt

A: We will use Euler-Lagrange equation to solbe the optimization problem.

Q: Consider an animal population P(t) with constant death rate 8 = 0.01 (deaths per animal per month)…

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Q: I Solve the differential equatons 2ydx = 3xy°dx + xdy when x = 2, y=-2 2.

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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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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.