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January 29, 2015

January 29, 2015

Posted by **Anonymous** on Sunday, April 5, 2009 at 8:54pm.

D(t)=12+Asin(((2pi)/(365))(t-80))

where A depends only on the latitude (and not t). for latitude 30 degress, A is about 2.3

1. When is the number of hours of daylight the greatest?

2.When is the number of hours of daylight the least?

3. When is the number of hours of daylight increasing at a rate of 2 minutes per day?

4. when is the number of hours of daylight decreasing at a rate of 2 min per day?

Can any one help me with any of these?

thanks a lot!

- 11th grade-Calculas -
**bobpursley**, Sunday, April 5, 2009 at 9:05pmTake the derivitive of D with respect to t. Set to zero, solve for the solutions. Those will be max/min day lengths. You can use the second derivitative to find out which.

for 3,4, set dD/dt equal to 2/60 and solve for t.

- 11th grade-Calculas -
**Anonymous**, Sunday, April 5, 2009 at 9:37pmwait to take the derivative, should i multiple out the stuff inside the ()?

- 11th grade-Calculas -
**Jacob**, Thursday, April 23, 2009 at 10:51pmdD/dt = A(2pi/365)*cos [(2pi/365)*(t-80)]

=0 for maximum or minimum

(2pi/365)*(t-80) = n*pi/2

when n=1 gives maximum , then (t-80) = 365/4, for minimum n = 3

and t-80 = 3*365/4

(3) = dD/dt = +2/60

(4) = dD/dt = -2/60

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