The question relates to application of sine functions.

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Sunsets are later in the summer than in the winter. For planning a sunset dinner cruise through the 30 000 islands, the cruise planners may find the time, t, in hours (on a 24 hour clock) of the sunset on the nth day of the year using the equation (calculator needs to be in degree mode):

t = 1.75sin0.986(n-80)+18.43

Determine the time of the sunset on Shera's birthday of July 26, the 207th day of the year.

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Answer:
7:52 p.m.

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How do I solve this problem?
Do I need to graph the equation or can I just solve it from doing the calculation?
When I substitute 207 in the (n-80) and solve for it, I get 203.75

n = 207 in this case. So the formula becomes

t = 1.75*sin (0.986*127)+18.43
= 1.75 *0.8169 + 18.41
= 19.84 hrs
= 19:50 militsry time = 7:50 PM

Thanks, I just realized what I have done wrong... I forgot to multiple 1.75 with sin

I keep getting 22.25

And before, I had my calculator in radian mode ... now I have it in degree mode

To solve this problem, you can use the given equation and substitute the value of n with 207 (which is the 207th day of the year, representing Shera's birthday).

The equation is: t = 1.75sin(0.986(n-80)) + 18.43

To begin, calculate (n-80):
(n-80) = 207 - 80 = 127

You mentioned that when you substituted 207 for (n-80), you obtained 203.75. However, it seems like there was a mistake in your calculation. The correct value should be 127, not 203.75.

Next, substitute the calculated value of (n-80) back into the equation:

t = 1.75sin(0.986 * 127) + 18.43

To solve this equation, you can use a calculator that is set to degree mode. Multiply 0.986 by 127, and then find the sine of the result. Finally, multiply the sine result by 1.75, and add 18.43 to get the final time value.

Evaluating this expression should give you the time of the sunset on Shera's birthday, which, according to the given answer, is 7:52 p.m.