If a clock is set to Greenwich Mean Time and the Sun is observed to reach its zenith at 10:00 A.M., what is the longitude?

Mathematics

1 answer:

Rasek [7]3 years ago

3 0

Answer:

The answer to the question is

30 ° east of Greenwich Mean Time

Step-by-step explanation:

To solve this we have the given variables

Current Greenwich Mean Time = 10.00 AM

Location of the Sun at the current longitude = zenith

Supposed correct time when clock is at zenith = 12 noon or 12.00 pm

Time difference, or correction required = 10.00 a. m. - 12 p. m. = 2 hours leading

As there are 24 hours in a day one hour of the difference in time is equivalent to 360/24 or 15 ° and as the Sun is already at its zenith at the location then the location is eastwards of Greenwich Mean time that is,

15 ° × 2 = 30 ° east of Greenwich Mean Time

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50+51+52+...+101=...<br>Can you help me? I do not understand

Dmitriy789 [7]

Suppose

$S=50+51+52+\cdots+100+101$

At the same time, we can write

$S^*=101+100+99+\cdots+51+50$

Note that $S=S^*$ (just reverse the sum). Let's pair the first terms of $S$ and $S^*$ , and the second, and the third, and so on:

$S+S^*=(50+101)+(51+100)+(52+99)+\cdots+(100+51)+(101+50)$

Now, each grouped term in the sum on the right side adds to 151. There are 52 grouped terms on that same side (because there are 50 numbers in the range of integers 51-100, plus 50 and 101), which menas

$S+S^*=52\cdot151$