A hot bowl of soup is served at a dinner party. It starts to cool according to Newton's Law of Cooling so that its temperature at time t is given by T(t) = 64 + 145e-0.05t

Q: At time t, the position of a body moving alongthe s-axis is s = t3 - 6t2 + 9t m. Find the body’s…

A: We find v and a using the first and second derivative of s. We use the power rule.

Q: A 20-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3…

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Q: The amount of trash G(t), in tons per year, produced by a town is projected to continue growing…

A: Here we do integration

Q: a. Find the rock's velocity and acceleration at time t. b. How long does it take the rock to reach…

A: Since you have posted multiple subparts question in this question so I have solved first three…

Q: 12. The velocity of a particle at time t is given by the function v(t) = t³ – sint + 2, what is the…

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Q: A particle moves along the x-axis so that at time t>=0, the acceleration of the particle is a(t) =…

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Q: A car starts from rest at time t = 0 and accelerates at –0.6t + 4 meters/sec2 for 0 <t< 12. How long…

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Q: Help A certain object moves in such a way that its velocity (in m/s) after time t (in s) is given by…

A: Consider the provided velocity equation,

Q: The concentration C (in milligrams per milliliter) of a drug in a patients bloodstream T hours after…

A: The concentration C (in milligrams per milliliter) of a drug in a patients bloodstream T hours after…

Q: Certain radioactive material decays in such a way that the mass remaining after t years is given by…

A: Given, m(t)=175e−0.02t ∴ The mass at time t=0 = 175e0 = 175 grams

Q: a weight is bouncing up and down on a spring with height h(feet) after t seconds,  given by h(t)=…

A: We will use derivative to find acceleration equate it to given value

Q: Solve the initial-value problem for y as a function of r. (81 - a) dy = 1, y(0) = 7 da Question…

A: Differential equation problem....

Q: (a) Suppose a stone is dropped from a height of 200 ft. Its position at time tis s(t)=-12t? +200…

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Q: Jane is taking a history class. The teacher states that the population of a country is shrinking at…

A: Given data: Size of the population, P = 10e0.5t

Q: A population of insects increases at a rate 290+10t+0.3t^2 insects per day (t in days). Find the…

A: Let P stand for population. Hence, dP/dt =  290+10t+0.3t2  Hence, dP = (290+10t+0.3t2)dt So, in…

Q: A model for the basal metabolism rate, in kcal/h, of a young man is R(t) = 85 - 0.19 cos(xt/12),…

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Q: A particle moves along the x-axis so that at time t 0 its position is given by a(t)= t° – t² - 5t.…

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Q: Solve the initial-value problem for a as a function of t . da (t – 13t + 42)- = 1, (t > 7, ¤(9) = 0)…

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Q: The size P of a small herbivore population at time t​ (in years) obeys the function P(t)=600e0.25t…

A: Simply substitute P = 1200 and solve for t using Lograthim.

Q: An automobile of mass M=5400 kg is moving at a speed of 30 m/s The engine is disengaged suddenly at…

A: As per the question we have to calculate the following integral : Integral of 5400v/(8.276v2 + 2000)…

Q: A 50-gallon barrel is filled completely with pure water and then salt water with a concentration of…

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Q: A particle moves along the x-axis so that at any time t > 0, its acceleration is given by a(t)=…

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

Q: If a cup of coffee has temperature 89°C in a room where the ambient air temperature is 25°C, then,…

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Q: At time t, the position of a body moving along the s-axis is s=3- 212 + 120t m. Find the body's…

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Q: If a cup of coffee has temperature 95°C in a room where the temperature is 20°C, then, according to…

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Q: The number of cells in a bacteria population is given by P(t) = 1200 - 2 where t is measured in…

A: The number of cells in a bacteria population is given by, Pt=12002t

Q: Solve the initial value problem for x as a function of t.. dx (? - 15t + 56). = 1 for (t> 8), x(9) =…

A: Given that      (t2-15t+56)(dx/dt) = 1 for (t&gt;8), x(9)=0 Here we have to find the initial value…

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A: The solution of above question is written below.

Q: A particle starts at time t-0 and moves along the x-axis so that its position at any time tz 0 is…

A: The position of the particle at any time t is: x(t)=t-132t-3x(t)=2t4-9t3+15t2-11t+3

Q: A particle moves along the x axis with its position at time t given by x(t) = (t + a)(t - b) where a…

A: Basics of differentiation are used.

Q: At time t, the position of a body moving alongthe s-axis is s = t3 - 6t2 + 9t m. Find the body’s…

A:

Q: At which times is the particle instantaneously motionless

A: Concept: The velocity is figured out by dividing the distance by the time taken to travel that same…

Q: A tank in the form of a right circular cylinder standing on end is leaking water through a circular…

A: We begin by combining all the constants as follows: Ah=π·0.52=0.785 ft2Aw=π·(2)2=12.566 ft2…

Q: A rock dropped from a state of rest at time t = 0 on the planet Ginormon travels a distance s(t) =…

A: Distance travelled is st=15.2t2. Compute the velocity. vt=s't=15.2t2'=215.2t=30.4t

Q: The figure shows an 11-foot ladder leaning against a wall. (a) Use the Pythagorean theorem to find…

A: Answer

Q: A particle starts at time t=0 and moves along the x-axis so that its position at any time tz 0 is…

A:

Q: The period T of a pendulum of length L is T = (2 √L)/√g, where g is the acceleration due to gravity.…

A: Given: The period T of a pendulum of length L is, T=2πLg A pendulum is moved from the Canal Zone,…

Q: At time t20, the acceleration of a particle moving on the x-axis is a(t)=t+sint. At t = 0, the…

A: To find the value of t , when velocity is equal to zero , Given that : a(t) = t + Sin(t) And…

Q: A particle moves along the x-axis with its position at time t given by x(t) - (t- a)(t - b), where a…

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Q: Let C(t) be the concentration of a drug in the bloodstream. AS the body eliminates the drug, C(t)…

A:

Q: A population grows at a rate P'(t) = 500te-0.2t P(t) is the population after t months. What is the…

A: Population growth at a rate P’(t) = 500te-0.2t2 Where P(t) is the population after t months Evaluate…

Q: Starting with an initial value of P(0)=55, the population of a crow community grows at a rate of…

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Q: Laboratory department detects the concentration C of impurity of an oil purifier changes with time t…

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Q: A car slows down with an acceleration of a(t nd t is measured in seconds. ) Determine the position…

A: Acceleration of the car a(t)=-15 ft/s2 v(0) = 60 ft/s s(0) = 0  a) We have to determine the position…

Q: An object moving in a straight line with an initial velocity of 65 m/s undergoes an acceleration of…

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Q: A model that describes the population of a fishery in which harvesting takes place at a constant…

A: It is given that, dP/dt=kP-h Where k and h are positive constants.

Q: If you invest P dollars in a bank account at an annual interest rate of r%, then after t years you…

A: The rate of change is the percentage change in any quantity over a specified time interval.…