PLEASE WRITE CLEARLY AND EXPLAIN EVERY DETAIL TO EACH STEP PRECISELY PLEASE FOR BOTH QUESTIONS PLEASE DON'T SKIP ANY DETAILS QUESTION 1 Suppose that the number of hours of daylight on a given day in Seattle is modeled by the function 3 75cos( 6) 12 25, with t given in months and t 0 corresponding to the winter solstice What is the average number of daylight hours in a year At which times t 1 and t 2 , where 0 t 1 t 2 12, do the number of daylight hours equal the average number Write an integral that expresses the total number of daylight hours in Seattle between t 1 and t 2 Compute the mean hours of daylight in Seattle between t 1 and t 2 here 0 t 1 t 2 12, and then between t 2 and t 1 and show that the average of the two is equal to the average day length QUESTION 2 As implied earlier, according to Kepler's laws, Earth's orbit is an ellipse with the Sun at one focus The perihelion for Earth's orbit around the Sun is 147,098,290 km and the aphelion is 152,098,232 km By placing the major axis along the x axis, find the average distance from Earth to the Sun The classic definition of an astronomical unit (AU) is the distance from Earth to the Sun, and its value was computed as the average of the perihelion and aphelion distances Is this definition justified

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jul 05, 2024

PLEASE WRITE CLEARLY AND EXPLAIN EVERY DETAIL TO EACH STEP PRECISELY PLEASE FOR BOTH QUESTIONS PLEASE DON'T SKIP ANY DETAILS. QUESTION 1 Suppose that the

PLEASE WRITE CLEARLY AND EXPLAIN EVERY DETAIL TO EACH STEP PRECISELY PLEASE FOR BOTH QUESTIONS PLEASE DON'T SKIP ANY DETAILS.

QUESTION 1

Suppose that the number of hours of daylight on a given day in Seattle is modeled by the function 3.75cos(/6)+12.25, with t given in months and t=0 corresponding to the winter solstice.

What is the average number of daylight hours in a year?
At which times t₁ and t₂, where 0 t₁< t₂< 12, do the number of daylight hours equal the average number?
Write an integral that expresses the total number of daylight hours in Seattle between t₁ and t₂.
Compute the mean hours of daylight in Seattle between t₁and t₂here 0 t₁< t₂< 12, and then between t₂and t₁and show that the average of the two is equal to the average day length.

QUESTION 2

As implied earlier, according to Kepler's laws, Earth's orbit is an ellipse with the Sun at one focus. The perihelion for Earth's orbit around the Sun is 147,098,290 km and the aphelion is 152,098,232 km.

By placing the major axis along the x-axis, find the average distance from Earth to the Sun.
The classic definition of an astronomical unit (AU) is the distance from Earth to the Sun, and its value was computed as the average of the perihelion and aphelion distances. Is this definition justified?