Some birds fly more slowly over water than over land. A bird flies at constant rate of 6 km/h over water and 10 km/h over land. To minimize the total flying time between the shore of one island and its nest, the bird will chose a path similar to the one represented in the diagram below. Given the measurements in the diagram, write the total time to fly from the island to the nest, as a function of the angle a between the direct line from one shore to the other and the flying line. Use optimization techniques to find the angle of flight that will ensure the shortest amount of time necessary for the bird to fly from the island to the nest.

Please answer all steps and questions on the paper.

a and b are two points in the third-dimenson. Show the equation that describes the set of points that are the same distance away from a and b.

The roller coaster is 80 feet above the ground at a horizontal position of 110 feet from the boarding station.The roller coaster is at a height of 100 feet above the ground as it descends the hill and reaches a horizontal position of 170 feet from the boarding station.The roller coaster levels off at a height of 80 feet above the ground at a horizontal position of 200 feet from the boarding station, then resumes dropping.A drawing of a section of the roller coaster with points marked at 110 comma 80, 170 comma 100, and 200 comma 80.Using the height of 80 feet as a baseline (because that is also the height the roller coaster is when it levels off), determine the rule for the polynomial function representing the height of the roller coaster,  h open parentheses x close parentheses, at a horizontal position of x feet from that of the boarding station. This rule can be left in factored form. Fill in the blanks to report your result as follows. a should be written as an integer or…