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Brums [2.3K]
2 years ago
9

The rate at which the temperature is dropping is 6t 5t2 degrees Celsius per hour t hours after sundown. How much had the tempera

ture decreased between sundown and 3 hours after sundown
Mathematics
1 answer:
Whitepunk [10]2 years ago
5 0

Using a differential equation, it is found that the temperature dropped 72 degrees Celsius between sundown and 3 hours after sundown.

<h3>What is the differential equation that describes the temperature in t hours after sundown?</h3>

The rate at which the temperature is dropping is 6t + 5t^2 degrees Celsius per hour t hours after sundown, hence the <em>differential equation</em> is:

\frac{dT}{dt} = 6t + 5t^2

Applying <em>separation of variables</em>, we find the solution as follows:

\frac{dT}{dt} = 6t + 5t^2

dT = (6t + 5t^2) dt

\int dT = \int (6t + 5t^2) dt

T(t) = \frac{5t^3}{3} + 3t^2 + T(0)

In which T(0) is the temperature at sundown.

In 3 hours, the change will be of:

C = T(3) - T(0) = \frac{5t^3}{3} + 3t^2|_{t = 3}

Hence:

\frac{5(3)^3}{3} + 3(3)^2 = 45 + 27 = 72

The temperature dropped 72 degrees Celsius between sundown and 3 hours after sundown.

You can learn more about differential equations at brainly.com/question/24348029

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¿Qué interés produce s/ 72,000 al 5% anual en 1 año, 1 mes, 10 días?
PtichkaEL [24]

Answer: 3,988.8

Usaremos la fómula: I = C * i * n

I = 72 000 * 0.05 * (1 año + 1 mes + 10 día)

I = 72 000 * 0.05 * (1 + 0.08 + 0.0028)

I = 72 000 * 0.05 * 1.108

3,988.8

Step-by-step explanation:

Podemos obtener el interés que produce un capital con la siguiente fórmula:  

I = C * i * n

Ejemplo: Si queremos calcular el interés simple que produce un capital de 1.000.000 pesos invertido durante 5 años a una tasa del 8% anual. El interés simple se calculará de la siguiente forma:

I = 1.000.000 * 0,08 * 5 = 400.000

Si queremos calcular el mismo interés durante un periodo menor a un año (60 días), se calculará de la siguiente forma:

Periodo: 60 días = 60/360 = 0,16            

I = 1.000.000 * 0,08 * 60/360 =  13.333

Espero te ayude :3

3 0
3 years ago
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Answer:

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Step-by-step explanation:

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so just substitute in and simplify:

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