5. The number of hours of daylight varies throughout the course of a year. In the Northern Hemisphere, the longest day is June 21, and the shortest is December 21. The average length of daylight is 12 h, and the variation from this average depends on the latitude. The graph below shows the number of hours of daylight at different times of the year for various latitudes. 20 18 16 14 12 Hours 10 60°N 8 50° N 40°N 30° N 20°N 2 Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. In Philadelphia (40°N latitude), the longest day of the year has 14 h 50 min of daylight, and the shortest day has 9 h 10 min of daylight. a. Find a sine function L that models the length of daylight as a function of t, the number of days from January 1. Explain how you determined the values of your constants. b. An astronomer needs at least 11 hours of darkness for a long exposure astronomical photograph. On what days of the year are such long exposures possible? Explain how you got your answer.

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Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.