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Solnce55 [7]
3 years ago
8

The differential equation below models the temperature of an 88°C cup of coffee in a 24°C room, where it is known that the coffe

e cools at a rate of 1°C per minute when its temperature is 74°C. Solve the differential equation to find an expression for the temperature of the coffee at time t. (Let y be the temperature of the cup of coffee in °C, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 88°C.) dy dt = − 1 50 (y − 24)
Physics
1 answer:
densk [106]3 years ago
3 0

Answer:

y = 24+64\cdot e^{-150\cdot t}

Explanation:

Let solve the differential equation by separating corresponding variables:

\int\limits^t_0\, dt = -\frac{1}{150} \int\limits^y_{y_{o}} \frac{dy}{y-24}

The solution of this equation is:

t = -\frac{1}{150}\cdot (\ln|y-24|-\ln |y_{o}-24|)

The explicit form of the temperature as a function of time is:

\ln |y-24|=-150\cdot t + \ln |y_{o}-24|

y-24 = C\cdot e^{-150\cdot t}

The value of the integration constant is:

C = 64

The complete expression is:

y = 24+64\cdot e^{-150\cdot t}

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MrMuchimi

Answer:37^{\circ} North of west

Explanation:

Given

40,000-ton luxury line traveling 20 knots towards west and

60,000 ton freighter traveling towards North with 10 knots

suppose v is the common velocity after collision

conserving momentum in west direction

20\times 40,000=(20,000+60,000)v\cos \theta

suppose the final velocity makes \theta angle with x axis

v\cos \theta =10----1

Conserving Momentum in North direction

10\times 60,000=80,000\times v\sin\theta

v\sin \theta =\frac{15}{2}----2

divide 1 and 2

\tan \theta =\frac{3}{4}

\theta =37^{\circ}

so search in the area 37^{\circ} North of west to find the ship

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3 years ago
How much thermal energy is created when a 3000 kg suv brakes to a stop from 20 m/s on a level road?
JulsSmile [24]

Answer:

b. 600,000 J

Explanation:

Applying the law of conservation of energy,

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Q' = 1/2(mv²)............... Equation 1

Where Q' = Thermal energy, m = mass of the suv, v = velocity of the suv.

From the question,

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Substitute these values into equation 1

Q' = 1/2(3000×20²)

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Hence the right option is b. 600,000 J

5 0
3 years ago
Một nười thả 420g chì ở nhiệt độ 100°C và 260g nước ở nhiệt độ 58°C làm cho nước nóng lên tới 60°C . Cho nhiệt dung riêng của nư
vlabodo [156]
Hey what language is this?
6 0
3 years ago
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Dahasolnce [82]
The bowling ball is at rest, so it only has gravitational potential energy.

Ug = mgy
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Need any more help?
6 0
3 years ago
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A ball is projected upward at time t=0.0s, from a point on a roof 90m above the ground. The ball rises, then falls and strikes t
chubhunter [2.5K]
As v becomes zero at the highest point, i prefer considering different travelling directions so it will become less complicated.
dont forget to add the total time up .

also to master the skills, write down the "uvsat" may help (thats the way i found it easier to handle problems)

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3 years ago
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