# The number of minutes of daylight per day, L(d) at 40 degrees North latitude is modeled by…?

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The number of minutes of daylight per day, L(d) at 40 degrees North latitude is modeled by the function:

a) take dL(d)/dd = 2π/366 * 167.5cos[2π/366 *(d-80)]

you have a max when this equals zero, or when the argument of the cos =π/2

set 2π/366 *(d-80)=π/2 and solve for d; d=171.5, or the 171.5 th day of the year or June 20, no shock…summer solstice in the northern hem

b) the average of a continuous function f(x) is ∫f(x)dx/L

where L is the length of the interval, here, integrate your function L(d) from 1 to 366 and divide by 366

c) take the number in b) and mult by 366

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# The number of minutes of daylight per day, L(d) at 40 degrees North latitude is modeled by…?

The number of minutes of daylight per day, L(d) at 40 degrees North latitude is modeled by the following equation: L(d)=12(1+sin((2pi/365)(d-172))) where d is the day of the year. Use this equation to find the number of minutes of daylight on June 21, the summer solstice.

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## The amount of daylight per day varies by latitude

The amount of daylight per day varies depending on how far north or south of the equator a location is. Places located closer to the equator will have more daylight hours than places located further away from the equator. This is because the Earth’s tilt causes the sun to be higher in the sky during the summer months for locations closer to the equator. Conversely, locations further away from the equator will have less daylight hours during the summer months.

The amount of daylight also changes throughout the year as the Earth orbits around the sun. During the summer months, there are more daylight hours because the Earth is closer to the sun. During the winter months, there are less daylight hours because the Earth is further away from the sun.

## The number of minutes of daylight per day is modeled by the equation L(d)= 15(d-93.5)+2640

The number of minutes of daylight per day, L(d) at degrees North latitude is modeled by the equation L(d)= 15(d-93.5)+2640.

This equation tells us that the number of minutes of daylight per day varies depending on the latitude at which you are located. The further north you are, the fewer minutes of daylight you will have each day.

If you want to maximize your daylight hours, you should plan to travel to locations near the equator where the days are longest. Conversely, if you want to minimize your daylight hours, you should plan to travel to locations near the poles where the days are shortest.

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## The graph of the equation L(d)= 15(d-93.5)+2640

The graph of the equation L(d)= 15(d-93.5)+2640 is a representation of the number of minutes of daylight per day at different degrees of latitude. The x-axis represents latitude, and the y-axis represents the number of minutes of daylight.

As you can see from the graph, the number of minutes of daylight increases as you move closer to the equator. At latitude 0 degrees (the equator), there are 24 hours of daylight per day. This is because the Earth’s axis is perpendicular to the sun’s rays at the equator. As you move away from the equator, the Earth’s axis starts to tilt away from the sun, and so the amount of daylight decreases.

At latitudes above 66.5 degrees (the North Pole), there is 24 hours of darkness per day, because the sun is always below the horizon.

This equation can be used to estimate how many minutes of daylight you will get at any given latitude. For example, at latitude 30 degrees North, you can expect to get about 14 hours of daylight per day.

## How the number of minutes of daylight per day changes as the latitude changes

The number of minutes of daylight per day, L(d) at degrees North latitude is modeled by the following equation:
L(d) = {24 x 60}/{π x cos^-1[sin(23.5) sin(360(d+10)/365)]} – {12 x 60}

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As the latitude increases, the number of minutes of daylight per day decreases. This is because the sun is lower in the sky at higher latitudes. The angle between the sun and the horizon is smaller, so there is less time for the sun to be above the horizon.

## Conclusion

The number of minutes of daylight per day, L(d) at 40 degrees North latitude is modeled by the following equation: L(d) = 24 * sin (2 * pi * d / 365). From this equation, we can see that the amount of daylight varies throughout the year, with the longest days occurring around summer solstice and the shortest days occurring around winter solstice. This simple model provides a good approximation for the variation in daylight across the year, making it a useful tool for planning purposes.