Daylight-latitude relationships The table gives the numbers of minutes of daylight occurring at various latitudes in the northern hemisphere at the summer and winter solstices.
Latitude | Summer | Winter |
0° | 720 | 720 |
10° | 755 | 685 |
20° | 792 | 648 |
30° | 836 | 604 |
40° | 892 | 548 |
50° | 978 | 462 |
60° | 1107 | 333 |
(a) Which of the following equations more accurately predicts the length of day at the summer solstice at latitude L?
(1) D1 = 6.096L + 685.7
(2) D2 = 0.00178L3 − 0.072L2 + 4.37L + 719
(b) Approximate the length of daylight at 35° at the summer solstice.
Volume of a box From a rectangular piece of metal having dimensions 24 inches by 36 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides.
(a) Determine an equation for the volume V of the box in terms of x.
(b) Use a table utility to approximate the value of x within ±0.1 inch that will produce the maximum volume.
Constructing a box A cardboard box with an open top and a square bottom is to have a volume of 25 ft3. Use a table utility to determine the dimensions of the box to the nearest 0.1 foot that will minimize the amount of cardboard used to construct the box.
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