: Suppose that the temperature of a cup of coffee t minutes after it is poured is given by 1 T(t) = 26 + 80e kt, where k = . Find the average temperature of the coffee during the first 35 minutes after it is poured.

Q: The number of visitors P to a website in a given week over a 1-year period is given by P(t)= 122 +…

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Q: From 2010 through 2019, the revenue per snare fin $) tor stark Industries can be modeled by 2. 2. R…

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Q: b) Find the temperature u(x,t) from the heat equation in a laterally insulated copper bar 80 cm long…

A: b) Given :-  The temperature ux,t from the heat equation in a laterally insulated copper bar 80 cm…

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: 1) Determine f(x) given its rate of change, and that satisfies the given initial conditions: f'(t) =…

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Q: The size P of a small herbivore population at time t (in years) obeys the function  P(t)e^0.28t if…

A: The size P of a small herbivore population at time t (in years) obeys the function When P(t)=4000…

Q: Solve the IVP d3 t3X(t) - 9x(t) = 18 e-3t dt x(0) =8 x'(0) = 9 x"(0) = 0 then find x(0.5) accurate…

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Q: Find the particular solution for f(x) with the given initial conditions. f''(x) = 4x3 and f'(1) = 5…

A: Given,           f''x=4x3  and f'1=5  and f0=50

Q: If a ball is thrown straight up into the air with an initial velocity of 55 ft/s, it's height in…

A: i) Answer(i): 15 ft/s

Q: The velocity in m&gt;s of an object moving alonga line over the time interval [0, 6] is v(t) = t2 +…

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Q: Show that g(t) = t / ( t+1 ) takes on the value 0.499 for some tin [0, l].

A: To show that g(t)=tt+1takes on the value 0.499 for some t in [0, 1]. We use intermediate value…

Q: If P0 is the initial population at t = 0 and k depends on the rate of growth, then the formula for…

A: Given, P0 is the initial population at t = 0 and k depends on the rate of growth Population usually…

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

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Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

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Q: If a ball is thrown straight up into the air with an initial velocity of 60 ft/s, its height in fe…

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Q: A car drives down a road in such a way that its velocity (in m/s) at time t (seconds) is…

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Q: A series circuit consists of a resistor with R = 20 Q, a capacitor with C = 0.01 F, and a decaying…

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Q: The population of a culture of cells grows according to the function P(t)=60t/t+1, where t is…

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Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1)- = 3, x(2) = 0 dt

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Q: Suppose that the net energy generated by a solar panel in a small town up to time t in a day…

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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: Suppose the height of a spacecraft at time 1 is given by f () = 27 E1 for 0 <15 3. Find an…

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Q: 2.1 Suppose that f (t) = 3t + 2 – 12t. а. What is the average rate of change of f(t) over the…

A: Given : f(t) = 3t + 2 - 12t To find : a. What is the average rate of change of f(t) over the…

Q: Suppose that the temperature of a cup of coffee t minutes after it is poured is given by: T(t) = 23…

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Q: A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be…

A: N(t) = 2t3 + 3t2 − 4t + 1,000 represent the turtle population at the end of the year t.  The turtle…

Q: The population of a city (in millions) at time t (in years) is P(t) = 2.1e0.007" , where t = 0 is…

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Q: The population of a city (in millions) at time t (in years) is P(t) = 2.6e0.002t where t = 0 is the…

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Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

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Q: 3. Assume that the level of nitrogen dioxide present in the atmosphere on a certain June day in city…

A: The level of nitrogen dioxideN(t)=0.05t3t-64+53  0≤t≤8

Q: Assume that the average temperature for the year in a particular city is 54 with a high of about 80…

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Q: 5. Suppose T(t) represents the outdoor temperature, in degrees Fahrenheit, t hours after 8 AM.…

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Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1) - 3, г (2) — 0 dt

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Q: The number of visitors P to a website in a given week over a​ 1-year period is given by…

A: Given: Pt=125+t-80e0.02t; t∈1,52 We know that given functiony=fx is increasing and decreasing in the…

Q: Q2 The rate of heat transfer of a body can be express as: dT = -k(T – Ta) dt where T= temperature of…

A: Using Euler's method we can find the solution, the initial values are t0 = 0 and T0 = 90°C The…

Q: Find the temperature function T(t) if th

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Q: If the position of a particle on the x-axis at time t is-5t", then the average velocity of the…

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Q: If s(t) is the position on the x-axis of a particle at time t, then the quantitys(t + h)−s(t) / h…

A: If s(t) is the position on the x-axis of a particle at time t,

Q: A pump allows water to flow into a pool at the rate of r (t) = 2t liters per minute, where t is the…

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Q: A particle moves along the x-axis so that at time t≥0 its position is given by x(t)=2t3+3t2−36t+50.…

A: given, A particle moves along the x-axis so that at time t≥0 its position is given by…

Q: The population of a city (in millions) at time tt (in years) is P(t)=2.7e0.002tP(t)=2.7e0.002t,…

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Q: A 50-gal barrel is filled completely with pure water. Saltwater with a concentration of 0.3 Ib/ga…

A: Given, The amount of salt in the barrel at time t is given by…

Q: (a) In a city, the temperature ('F) in t hours after 9 a.m. is modelled by the function…

A: The mean temperature is given by the average temperature in a period of 0,12.

Q: Suppose that the amount of phosphorus in a lake at time t, denoted by P(t), follows the equation dP…

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Q: A particle moves along the X-axis so that at time t>0 its position is given by x(t)= 2t3 +…

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

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Q: Consider a poputation Piti satistying the extinction expiosion equation-ap - bP. where B= aPis the…

A: Given- Consider a population Pt satisfyinf the extinction explosion equation dPdt = aP2 - bP, where…

Q: A particle moves along the x- axis so that its position at the time t is given by x(t) = 21 – 9t²…

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Q: Suppose a metal cube is heated to a temperature of 100˚C uniformly throughout the cube and then…

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