Because of spherical geometry
let me explain
The Philippines are south<span> of Florida - why is flying </span>north<span> to Alaska a short-cut? The answer is that Florida, Alaska, and the Philippines are collinear locations in spherical geometry (they lie on a great circle). Another odd property of spherical geometry is that </span>the sum of the angles of a triangle is always greater then 180°. Small triangles, like those drawn on a football field, have very, very close to 180°. Big triangles, however, (like the triangle with veracities: New York, L.A. and Tampa) have significantly more than 180°.
Spherical geometry is a plane geometry on the surface of a sphere. In a plane geometry, the basic concepts are points and lines. In spherical geometry, points are defined in the usual way, but lines are defined such that the shortest distance between two points lies along them. Therefore, lines in spherical geometry aregreat circles. A great circle is the largest circle that can be drawn on a sphere. The longitude lines and the equator are great circles of the Earth. Latitude lines, except for the equator, are not great circles. Great circles are lines that divide a sphere into two equal hemispheres.
this is the long answer:
Spherical geometry is used by pilots and ship captains as they navigate around the globe. Working in spherical geometry has some non-intuitive results.
Answer: A bag can weigh 13.77 ounces and not need to be repacked.
Step-by-step explanation:
Since we have given that
Mean = 12.08 ounces
Standard deviation = 1.03 ounces
Bags in the upper 5% are too heavy and must be repackaged.
Using the standard normal table.
z = 1.645
So,
Hence, A bag can weigh 13.77 ounces and not need to be repacked.
Answer:
{x = 1/7
,y = 1
Step-by-step explanation:
Solve the following system:
{-5 y = -5 | (equation 1)
{7 x + 6 y = 7 | (equation 2)
Swap equation 1 with equation 2:
{7 x + 6 y = 7 | (equation 1)
{0 x - 5 y = -5 | (equation 2)
Divide equation 2 by -5:
{7 x + 6 y = 7 | (equation 1)
{0 x+y = 1 | (equation 2)
Subtract 6 × (equation 2) from equation 1:
{7 x+0 y = 1 | (equation 1)
{0 x+y = 1 | (equation 2)
Divide equation 1 by 7:
{x+0 y = 1/7 | (equation 1)
{0 x+y = 1 | (equation 2)
Collect results: Answer: {x = 1/7
,y = 1
<span>The length of AC is 8 units
The angle CDB is 67°
Since ABCD is a rectangle, that means that all of the angles are 90 degrees and that line segment AB is parallel to line segment CD. The line segment BD is a diagonal of the rectangle. The line segment AC is also a diagonal of the rectangle so it has the same length as given for segment BD which is 8. The angle ABD is the angle between the horizontal line and the diagonal. The angle CDB is also the angle between a horizontal line and the diagonal. So it also has the same measurement so it too is 67°.</span>