Suppose a metal cube is heated to a temperature of 100˚C uniformly throughout the cube and then placed in a room where the air is kept constantly 50˚C. Suppose we find from this measurement that T=80˚C, when t = 10 minutes. Find k.

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: The simplest model of malaria assumes that the mosquito population is at equi- librium and models…

A: The transmission dynamics of infectious disease is modeled through a first-order differential…

Q: A particle that moves along a straight line has velocity v ( t ) = t 2 e − 5 t v ( t ) = t 2 e - 5 t…

A: →v(t) = ds(t)dt→Use integration by parts.

Q: Note : m=0 d. Nuclear cells fission every (m+1) hours, how many seconds does it take 12 cells to…

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Q: If a cup of coffee has temperature 94°C in a room where the ambient air temperature is 19°C, then,…

A: To find: The average temperature of the drink C during the first 26 minutes.  Given: The temperature…

Q: The speed, s, of an accelerating object moving on a strait line is given by the formula: s = so +…

A: The initial speed is 10 m/s and the speed at time t is 16 m/s, so s0=10 m/s and s=16m/s. The time…

Q: 12. Find the time required for an object to cool from 300°F to 250°F by evaluating 300 10 1 t= dT In…

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Q: During a certain 21-hour period, the temperature at time t (measured in hours from the start of the…

A: During a certain 21-hour period, the temperature at time t (measured in hours from the start of the…

Q: A 80-kg cyclist on a 19-kg bicycle starts coasting on level ground at 30 m/sec. Use v = vo e (-k/m)t…

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Q: : Suppose that the temperature of a cup of coffee t minutes after it is poured is given by 1 T(t) =…

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Q: Answer the following as detailed as possible. 2. The tank shown below contains 80 lbs of salt…

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

A: It is given that, the velocity (v) of a car in m/s at time t in seconds is given  by the expression

Q: When a switch is closed in a circuit containing a battery E,a ersistance R and an inductance L,the…

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Q: Suppose that the population P of mussels in Lake Erie t months after January 612 2015 is given by…

A: Given: The population P of mussels in Lake Erie t months after January 2015 is given by Pt=6t26t+8.…

Q: During a certain 24-hour period, the temperature at time t (measured in hours from the start of the…

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Q: In Winter an aluminum beam was brought from the outside cold into a machine shop where the…

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

A:

Q: With time t in seconds, the velocity of a bicycle, in feet per second, is given by At) = 4t. How far…

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Q: The curved. surface of a rod of length (l) is against the flow of heat. If bot of ends of the rod…

A: Given heart equation is ∂2u∂x2=1c2∂u∂t Since c2=1 So heat equation will be ∂u∂t=∂2u∂x2…

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: A body whose temperature is 50°F is placed in a warming oven whose temperature is 100°F. After 5…

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Q: 11) A brake company is testing their brakes. When the brakes are pressed fully, it creates a…

A: When the brake is applied then  deceleration a = - 25 ft/s2 Car travelling speed v = 100 ft/s Let…

Q: The marriage rate in a certain country in 1990 was 0.95%, and there were about 351,000 marriages…

A: 1990 corresponds to t=0 So, M0= 351000 And r= 0.95% = 0.0095 So the model is:

Q: In the given question as follows, assume the accleration of the object is a(t)= 32 feet per second…

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Q: The period T of a simple pendulum is given by T=2π√L/g where L is the length of the pendulum and g…

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Q: Suppose that the rate at which the concentration of a drug in the blood changes with respect to time…

A: Given:The rate of change of concentration of a drug in blood with respect to time t is

Q: = 4000 1 0 代 50 50

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Q: Suppose that the rate of consumption of a natural resource is c'(t), where c'(t) = ke". Here t is…

A: Given, c' (t) = kert Here, t is the time in years, r is a constant and k is the consumption when t=…

Q: On a particular summer day the temperature function in Celsius is given by (T(t +7) T(t) = 20 + 8…

A: Note : As per our guidelines we are supposed to answer only one question. Since you have asked…

Q: This question is designed to be answered with a calculator. An object's velocity is given by v(t) =…

A: Given,          An object's velocity is given by vt=0.5t+3t-1t-52 , where t is time,          in…

Q: The population of two different species are given by P1 P1 = 3 ln(t) + 10 || and P2. , where t is…

A: The population of two different species are given by P1=3lnt+10 And P2=6lnt+2 Where, t measured in…

Q: to the South Coast Air Quality Management District, the level of nitrogen dioxide, a brown gas that…

A: Here,  A(t)=0.03t3(t-7)4+60.2, 0≤t≤7

Q: The population of a city (in millions) at time t (in years) is P(t) = 2.4e0.007t When will the…

A: find the value of t when population is double from what it is when time is zero.substitute value of…

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: 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 body falls in a medium offering resistance proportional to the speed at any time "t". If the…

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Q: Suppose for a life aged 40, we know 1–t40+t = 0.01 · (1 – t), te [0, 1]. t e [0, 1]. Calculate

A: Given: q40+t1-t=0.01×1-t        t∈0,1

Q: Set up an I.V.P. and solve using the following: Suppose a large mixing tank initially holds 500…

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Q: A pitcher of buttermilk initially at 25°C is to be cooled by setting it on the front porch, where…

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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: If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t…

A: The average velocity of an object is the ratio of the changes in object position and time taken by…

Q: In a circuit with an inductor of inductance L, a resistor with resistance R and a variable voltage…

A: t 1.00 1.01 1.03 1.1 i 3.10 3.12 3.18 3.24 Backward difference approximation of first order…

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

A: vt=3t12+4

Q: Suppose that a change in biomass B(t) at time t during the interval [0,5] follows the dB equation…

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Q: If a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then…

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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 v(t) =…

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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.