a) Approximately 40° for depression and 5° for elevation; b) it relates to the height of the observer; c) none. Step-by-step explanation: (a) Angles of depression and elevation: The angle of depression is roughly 40°, while the angle of elevation is around 5°. (b) The angles depend on the observer's height. A taller individual will have a smaller angle of elevation paired with a larger angle of depression. (c) None of the angles can reach or exceed 99°, since they are components of a right triangle. If one angle is a right angle, both of the others must be lesser than 90°.
Part 1) The radius of the circle is r=17 units. Part 2) The points (-15,14) and (-15,-16) are situated on this circle. Step-by-step explanation: Step 1 Find the radius of the circle. We know that the distance from the center of the circle to any point on its circumference equals the radius of the circle. The formula to determine the distance between two points is equal to......we have (-7, -1) and (8, 7) substitute... Step 2 Determine the y-coordinate of point (-15,y). The standard form of the circle's equation is given by... where (h,k) represents the center, and r is the radius. Replace the values, substituting x=-15 in the equation... square root both sides... ultimately, we find two solutions: point (-15,14) and point (-15,-16) refer to the attached figure for a clearer understanding of the problem.
Answer: 11, 13
Explanation:
We need to identify two consecutive integers whose product is 143. If we let x represent the larger of the two integers, the smaller integer can be expressed as (x-2). Their product equals 143, which gives us
By solving the equation:
this results in a second-order equation with two real roots: x=13 and x=-11. We disregard the negative outcome, leaving us with x=13. Hence, the two numbers are
x=13
x=13-2=11
