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Anit [1.1K]
3 years ago
13

According to Newton's law of cooling, the rate at which an object's temperature changes is directly proportional to the differen

ce in temperature between the object and the surrounding medium. If T(t) represents the temperature of the object (CC) at time t (in hours), and T5 represents the constant temperature of the surrounding medium, then the differential equation best describing the rate of change in the temperature of the object is:
Physics
2 answers:
adelina 88 [10]3 years ago
7 0

Answer:

dT/dt = k[T5 - T]

Explanation:

DT/dt represents rate of change in temperature for Celsius degrees per hour. Its proportional to the difference in temperature between the object and the Surrounding medium. This means either dT/Dt =k (T-TS) or dT/dt=k(TS-T) with k being some positive constant of proportionality which depends on the object.

We can see that dT/dt = k(T-T5) has temperature increasing when the temperature of the object T is greater than the surrounding medium (T5).

The equation dT/dt=k(T5-T) has the temperature increasing when the object (T) is less than the temperature of the surrounding medium. Therefore the differential equation best describing the rate of change in temperature of the object is dT/dt=k(T5-T) for some positive constant of proportionality k.

Kryger [21]3 years ago
4 0

Answer:

dT(t)/dt = k[T5 - T(t)]

Explanation:

Since T(t) represents the temperature of the object and T5 represents the temperature of the surroundings, according to Newton's law of cooling, the rate at which an object's temperature changes is directly proportional to the difference in temperature between the object and the surrounding medium, that is dT(t)/dt ∝ T5 - T(t)

Introducing the constant of proportionality

dT(t)/dt = k[T5 - T(t)]

which is the desired differential equation

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Given that average speed is distance traveled divided by time, determine the values of m and n when the time it takes a beam of
emmainna [20.7K]

Answer:

5,2

Explanation:

From the question we are told that:

Speed of light C=3.0×10^8 m/s.

Generally the equation for Average Speed is mathematically given by

V_{avg}=\frac{d}{t}

Where

d=Distance between the Earth and the sun

d=1.5*10^11m

Therefore

t=\frac{d}{V_{avg}}

t=\frac{1.5*10^11m}{3.0×10^8 m/s.}

t=5*10^2s

Since m and n is given in the form of

m*10^n

Therefore

m=5 & n=2

5,2

3 0
3 years ago
B. Projectile on cliff (range)
dimulka [17.4K]

Answer:

x = 41.28 m

Explanation:

This is a projectile launching exercise, let's find the time it takes to get to the base of the cliff.

Let's start by using trigonometry to find the initial velocity

         cos 25 = v₀ₓ / v₀

         sin 25 = Iv_{oy} / v₀

         v₀ₓ = v₀ cos 25

         v_{oy} = v₀ sin 25

         v₀ₓ = 22 cos 25 = 19.94 m / s

         v_{oy} = 22 sin 25 = 0.0192 m / s

let's use movement on the vertical axis

         y = y₀ + v_{oy} t - ½ g t²

     

when reaching the base of the cliff y = 0 and the initial height is y₀ = 21 m

         0 = 21 + 0.0192 t - ½ 9.81 t²

         4.905 t² - 0.0192 t - 21 = 0

         t² - 0.003914 t - 4.2813 =0

we solve the quadratic equation

        t = \frac{ 0.003914\  \pm \sqrt{0.003914^2 + 4 \ 4.2813 }   }{2}

        t = \frac{0.003914 \ \pm 4.13828}{2}

        t₁ = 2.07 s

        t₂ = -2.067 s

since time must be a positive scalar quantity, the correct result is

        t = 2.07 s

now we can look up the distance traveled

         x = v₀ₓ t

         x = 19.94  2.07

         x = 41.28 m

5 0
3 years ago
single goose sounds a loud warning when an intruder enters the farmyard. Some distance from the goose, you measure the sound lev
Goryan [66]

Answer:

The sound level of the 26 geese is  Z_{26}= 96.15 dB

Explanation:

From the question we are told that

    The  sound level is Z_1 =  81.0 \ dB

     The number of geese is N = 26

Generally the intensity level of sound is mathematically represented as

        The intensity of sound level in dB  for one  goose is mathematically represented as

                       Z_1 = 10 log [\frac{I}{I_O} ]

Where I_o is the  threshold level of intensity with value  I_o = 1*10^{-12} \  W/m^2

            I is the intensity for one goose in W/m^2

For 26 geese the intensity would be  

          I_{26} = 26 * I

   Then  the intensity of 26 geese in dB is  

              Z_{26} = 10 log[\frac{26 I }{I_o} ]

               Z_{26} = 10 log (\ \ 26 *  [\frac{ I }{I_o} ]\ \ )

               Z_{26} = 10 log (\ \ 26  \ \ ) *   (\ \  10 log [\frac{ I }{I_o} ]\ \ )

 From the law of logarithm we have that

              Z_{26} = 10 log 26 +  10 log [\frac{I}{I_0} ]

                    = 14.15 + 82

                    Z_{26}= 96.15 dB

               

               

           

4 0
3 years ago
Why is cloning done before an investigation begins??
svlad2 [7]

Answer:Purpose of Cloning

A forensic image of a hard drive captures everything on the hard drive, from the physical beginning to the physical end. ... Hard drives are susceptible to failure. Having two clones gives an investigator one to examine and one to fall back on.Therapeutic cloning involves creating a cloned embryo for the sole purpose of producing embryonic stem cells with the same DNA as the donor cell. These stem cells can be used in experiments aimed at understanding disease and developing new treatments for disease.

Explanation:

hope this helps have a nice night lo❤️❤️❤️l

3 0
3 years ago
A stone is dropped from the
ICE Princess25 [194]
  • Height=h=500m
  • Acceleration=g=10m/s^2
  • Initial velocity=u=0
  • Speed of sound=c=340m/s
  • TIME TAKEN BY STONE TO HIT WATER=t
  • Time taken by sound to hear back=T

Now

\\ \sf\longmapsto h=ut+\dfrac{1}{2}gt^2

\\ \sf\longmapsto h=0t+\dfrac{1}{2}10t^2

\\ \sf\longmapsto 500=5t^2

\\ \sf\longmapsto t^2=100

\\ \sf\longmapsto t=10s

Now

\\ \sf\longmapsto h=cT

\\ \sf\longmapsto T=\dfrac{h}{c}

\\ \sf\longmapsto T=\dfrac{500}{340}

\\ \sf\longmapsto T=1.47\approx 1.5s

Total time:-

\\ \sf\longmapsto T_{net}=t+T=10+1.5=11.5s

8 0
2 years ago
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