Answer:
Width: 12 ft
Maximum area: 144 ft²
Step-by-step explanation:
A = 24x – x²
A = –x² + 24x
A = –(x² – 24x)
A = –(x² – 24x + 144) + 144
A = –(x – 12)² + 144
Therefore, the maximum area of 144 ft² occurs at x = 12 ft.
Answer:
Step-by-step explanation:
A way to find the inverse function is to swap the x and y (f(x)) in the equation.
We can check that it is an inverse function by using a property of inverse functions:
If we plug in the f(x) function into the variable x of the inverse function, we should end up with x
It checks out!
Answer:
Step-by-step explanation:
You should start by
Answer:
The Moon's orbit around Earth has a sidereal period of 27.3 days. During each synodic period of 29.5 days, the amount of visible surface illuminated by the Sun varies from none up to 100%, resulting in lunar phases that form the basis for the months of a lunar calendar. The Moon is tidally locked to Earth, which means that the length of a full rotation of the Moon on its own axis causes its same side (the near side) to always face Earth, and the somewhat longer lunar day is the same as the synodic period. That said, 59% of the total lunar surface can be seen from Earth through shifts in perspective due to libration.[17]
The most widely accepted origin explanation posits that the Moon formed about 4.51 billion years ago, not long after Earth, out of the debris from a giant impact between the planet and a hypothesized Mars-sized body called Theia. It then receded to a wider orbit because of tidal interaction with the Earth. The near side of the Moon is marked by dark volcanic maria ("seas"), which fill the spaces between bright ancient crustal highlands and prominent impact craters. Most of the large impact basins and mare surfaces were in place by the end of the Imbrian period, some three billion years ago. The lunar surface is relatively non-reflective, with a reflectance just slightly brighter than that of worn asphalt. However, because it has a large angular diameter, the full moon is the brightest celestial object in the night sky. The Moon's apparent size is nearly the same as that of the Sun, allowing it to cover the Sun almost completely during a total solar eclipse.
Answer:
39 degrees.
Step-by-step explanation:
We want an angle x such that 0 < x < 360 and angle x is coterminal with an angle of measure 399 degrees.
so x = 399 - 360 = 39 degrees
