south polar region experiences six months long winter night while it is the six months long day in the north polar region
Answers
For us, the Sun rises in the East and sets in the West. But at the poles, there are no directions. From the North Pole, whichever way we look it is South, and from the South Pole, whichever way we look, it is North. There is no Sunrise or Sunset at the polar regions as we experience at lower latitudes. The Sun appears above the horizon in Summer and makes a 360° circle in the sky - over a period of 187 days at the North Pole 90° North latitude. And in winter, the Sun is below the horizon for 163 days of darkness and 24 days of semi-darkness when the Sun is just below the horizon. It's not exactly six months of darkness/sunlight at the poles. (In Svalbard, Norway, the northernmost inhabited region of Europe, there is no sunset from approximately 19 April to 23 August, and no sunrise between November 14 and January 29.) Needless to mention, when it is summer in the Northern hemisphere, it is winter in the South.
A solstice happens when the sun's zenith is at its furthest point from the equator.
The December Solstice or Winter Solstice occurring on or about 21st December when the Sun reaches its most southerly declination of -23.5 degrees. In other words, when the North Pole is tilted furthest to 23.5 degrees away from the Sun. The Sun is directly overhead of the Tropic of Capricorn in the Southern Hemisphere during the December Solstice.It is called Winter Solstice in the Northern Hemisphere, where it is the shortest day of the year. In the Southern Hemisphere, it is the Summer Solstice and the longest day of the year. Some people call today the first day of winter. Now you can see why the North pole is in darkness and the South pole in sunlight.On the June solstice or the summer solstice, occurring on or about 21st June, the sun is visible throughout the night, in all areas from just south of the Arctic Circle to the North Pole - Land of the Midnight Sun. On the other side of the planet, south of the Antarctic Circle there's Polar Night, meaning no Sunlight at all on the June Solstice.On the equinox, the Sun is directly over the equator making the day and night approximately equal. The March equinox - 20th March - is when the Sun is apparently moving towards the summer solstice, and the September equinox - 20th September - is when the Sun is apparently moving towards the winter solstice.
Answer:
ANSWER EXPLANATION: If the polynomial p(x) is divided by a polynomial of the form x+k (which accounts for all of the possible answer choices in this question), the result can be written as
p(x)
x+k
=q(x)+
r
x+k
where q(x) is a polynomial and r is the remainder. Since x+k is a degree-1 polynomial (meaning it only includes x1 and no higher exponents), the remainder is a real number.
Therefore, p(x) can be rewritten as p(x)=(x+k)q(x)+r, where r is a real number.
The question states that p(3)=−2, so it must be true that
−2=p(3)=(3+k)q(3)+r
Now we can plug in all the possible answers. If the answer is A, B, or C, r will be 0, while if the answer is D, r will be −2.
A. −2=p(3)=(3+(−5))q(3)+0
−2=(3−5)q(3)
−2=(−2)q(3)
This could be true, but only if q(3)=1
B. −2=p(3)=(3+(−2))q(3)+0
−2=(3−2)q(3)
−2=(−1)q(3)
This could be true, but only if $q(3)=2)
C. −2=p(3)=(3+2)q(3)+0
−2=(5)q(3)
This could be true, but only if q(3)
D. −2=p(3)=(3+(−3))q(3)+(−2)
−2=(3−3)q(3)+(−2)
−2=(0)q(3)+(−2)
This will always be true no matter what q(3) is.
Of the answer choices, the only one that must be true about p(x) is D, that the remainder when p(x) is divided by x−3 is -2.