GingerAle

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 #2
avatar+2511 
+4

Solution:

This post has an explanation of the physics by Sir Alan and an example by Heureka.

 

Here is a reproduction of  Heureka’s math, using the data from this question.

 

\(\begin{array}{rcl} I &=& \frac{P}{4\cdot \pi\cdot r^2} \qquad P = 23\ \text{watt} \qquad r = 19\ 500\ 000\ m\\ I &=& \frac{23}{4\cdot \pi\cdot 19500000^2} \\ \\ I &=& 4.8\cdot10^{-15}\ \frac{W}{m^2}\\ \end{array}\)

 

Closest answer from list:  5 x 10−15 W/m2

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It’s usually not necessary to reinvent the wheel, but you must be careful not to inflate the tire on the wheel with hot air from a blarney bag. 

28 нояб. 2017 г.
 #2
avatar+2511 
+4

The relative quantity of sunlight is principal in determining the start of a biochemical processes that cause deciduous trees to shed their leaves. Ambient temperature decreases also affect this process, but to a lesser extent. A sudden freeze will slow or totally stop the leaf-shedding process, because the cold temperatures will slow the chemistry or destroy the altered cells that cause this process.  In extreme cases, the leaves will remain on the tree until springtime, when new growth pushes the old, dead leaves off the tree. A significant percentage of leaves are often naturally shed every year in the spring, anyway.   

 

Casual observations often hide and confuse the causes and effects in nature. Incidental and   coincidental events are often thought to be the cause, when they are neither the cause nor the effect. Consider animals that grow a “winter coat.” It is often thought the lower temperatures of fall cause this because this helps keep the animal warm in the winter. While that does keep the animal warmer, it is a reduction in sunlight, not temperature changes, that triggers the biological mechanism. As daylight time diminishes, many animals will start to grow thicker coats, and some will grow lighter-colored coats that eventually become completely white. This process “reverses” as the days become longer.

 

Several biochemical changes occur in the brain with seasonal sunlight reduction –the most notable being the reduction of serotonin. A reduction in serotonin initiates behavior changes and produces an undercoat of hair or fur in many mammals. If your pet dog or cat is growing a “winter coat” out of season, then this may indicate a reduction of serotonin caused by aberrant brain chemistry. A prescription for an SSRI (selective serotonin reuptake inhibitors) by a veterinarian will usually correct the off-season winter coat and related behavior changes.

 

It’s important to note these processes, leaf fall and winter coats, actually starts in the summertime. After the first day of summer, the days begin to shorten, and this starts the process. Seasonal daylight changes are very consistent, unlike weather patterns, which change from year to year, and can trend in a warming direction for decades before reversing and trending toward the colder temperatures. This has always been the case, despite the doomsayers of anthropomorphic global warming.   The evolutionary processes that establishing these processes are much more biased toward stable daylight ratios than temperature changes.

 

 

GA

26 нояб. 2017 г.
 #10
avatar+2511 
+5

Here’s the correct presentation. Previously, I transposed the number and modulus divisor.

An excess consumption of fermented bananas might be a major contributing factor in the cause.  I’ve left the previous presentation as a monument to my error (The math is fine). This is an extremely rare event: this is only the second time I’ve made a mistake.surprise  The first time was when I thought I made a mistake, but I didn’t, so I was wrong in thinking I did. smiley

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\(\begin{array}{rcll} n &\equiv& {\color{red}231} \pmod {{\color{green}3331}} \\ n &\equiv& {\color{red}1247} \pmod {{\color{green}1361}} \\ \text{Set } m &=& 3331\cdot 1361 = 4533491\\ \\ \end{array} \)

 

\(\begin{array}{rcll} n &=& {\color{red}231} \cdot {\color{green}1361} \cdot \underbrace{ \underbrace{ \underbrace{ \underbrace{ [ {\color{green}1361}^{\varphi({\color{green}3331})-1} \pmod {{\color{green}3331}} ] }_{=\text{modulo inverse 1361 mod 3331} } }_{=1361^{3330-1} \mod {3331} }}_{=1361^{3329} \mod {3331}}}_{=1980} + {\color{red}1247} \cdot {\color{green}3331} \cdot \underbrace{ \underbrace{ \underbrace{ \underbrace{ [ {\color{green}3331}^{\varphi({\color{green}1361})-1} \pmod {{\color{green}1361}} ] }_{=\text{modulo inverse 3331 mod 1361} } }_{=3331^{1360-1} \mod {1361} }}_{=3331^{1359} \mod {1361}}}_{=552}\\\\ n &=& {\color{red}231} \cdot {\color{green}1361} \cdot [ 1980] + {\color{red}1247} \cdot {\color{green}3331} \cdot [552] \\ n &=& 622494180+ 2292873864\\ n &=& 2915368044\\\\ && n\pmod {m}\\ &=& 2915368044\pmod {4533491} \\ &=& 333331\\\\ n &=& 333331+ k\cdot 4533491\qquad k \in Z\\\\ \mathbf{n_{min}} & \mathbf{=}& \mathbf{333331} \end{array} \)

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25 нояб. 2017 г.