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# Suppose you use this formula to model the sunrise, where t is the time after midnight and m is the number of months after January 1st.

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Suppose you use this formula to model the sunrise, where t is the time after midnight and m is the number of months after January 1st. What happens on September 1st? (Hint: September is the ninth month. Substitute the appropriate value for m and solve for t(m)).

t(m) = 1.665 sin π/6 (m+3) + 5.485

A. The sun rises at the zero hour (midnight)

B. The sun rises at about 5:29 am

C. The sun rises at about 3:00 am

D. The sun rises at about 5:45 am

Dec 14, 2015

#1
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Suppose you use this formula to model the sunrise, where t is the time after midnight and m is the number of months after January 1st. What happens on September 1st? (Hint: September is the ninth month. Substitute the appropriate value for m and solve for t(m)).

t(m) = 1.665 sin π/6 (m+3) + 5.485

I assume:
$$\begin{array}{lrcll} & t(m) &=& 1.665 \cdot \sin{ \left( \frac{\pi\cdot (m+3)}{6} \right) }+ 5.485 \\\\ m = 9 & t(9) &=& 1.665 \cdot \sin{ \left( \frac{\pi\cdot (9+3)}{6} \right) }+ 5.485 \\ & t(9) &=& 1.665 \cdot \sin{ \left( \frac{\pi\cdot (12)}{6} \right) }+ 5.485 \\ & t(9) &=& 1.665 \cdot \sin{ ( 2 \pi ) }+ 5.485 \qquad \sin{ ( 2 \pi )} = 0\\ & t(9) &=& 1.665 \cdot 0 + 5.485 \\ & t(9) &=& 5.485 \\\\ & t(9) &=& 5:[(5.485-5)\cdot 60]\ \mathrm{am} \\ & t(9) &=& 5:[29.1]\ \mathrm{am} \end{array}$$

B. The sun rises at about 5:29 am Dec 14, 2015

#1
+15

Suppose you use this formula to model the sunrise, where t is the time after midnight and m is the number of months after January 1st. What happens on September 1st? (Hint: September is the ninth month. Substitute the appropriate value for m and solve for t(m)).

t(m) = 1.665 sin π/6 (m+3) + 5.485

I assume:
$$\begin{array}{lrcll} & t(m) &=& 1.665 \cdot \sin{ \left( \frac{\pi\cdot (m+3)}{6} \right) }+ 5.485 \\\\ m = 9 & t(9) &=& 1.665 \cdot \sin{ \left( \frac{\pi\cdot (9+3)}{6} \right) }+ 5.485 \\ & t(9) &=& 1.665 \cdot \sin{ \left( \frac{\pi\cdot (12)}{6} \right) }+ 5.485 \\ & t(9) &=& 1.665 \cdot \sin{ ( 2 \pi ) }+ 5.485 \qquad \sin{ ( 2 \pi )} = 0\\ & t(9) &=& 1.665 \cdot 0 + 5.485 \\ & t(9) &=& 5.485 \\\\ & t(9) &=& 5:[(5.485-5)\cdot 60]\ \mathrm{am} \\ & t(9) &=& 5:[29.1]\ \mathrm{am} \end{array}$$

B. The sun rises at about 5:29 am heureka Dec 14, 2015