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3 years ago

What is the arc length when theta= 2pi/5 and the radius is 6 cm?

1 answer:

4 0

$\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ \cline{1-1} r=6\\ \theta =\frac{2\pi }{5} \end{cases}\implies s=6\cdot \cfrac{2\pi }{5}\implies s=\cfrac{12\pi }{5}\implies s\approx 7.54$

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A = s^2

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3 years ago

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A) The differential equation comes from the fact that the rate of temperature change is proportional to the difference in temperatures.
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B) Find general solution by separating variables and integrating $\int\frac{dT}{T-52} = \alpha \int dt \\ ln (T-52) = \alpha t + C \\ T = C e^{\alpha t} +52$ :

C) Initial condition is t=0, T = 87
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3 years ago