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1 answer:
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Answer:
1.190390345 degrees.
Explanation:
As stated in the problem that the angle between the two curves is also the angle between slopes of the two cures at the point of intersection, which is 1 (when we set two equation equal and solve for x).
We know, if you don't you could verify it for yourself and it will be a nice mathematical exercise for you, that when there are two lines with slopes and
then the angle between them and their two slopes has following relationship.
where
is angle between the two lines.
As it is clear that we can easily get the angle between the two curves if we know slopes at that point, which you will see in second is very straight forward to calculate.
Slopes are simply derivatives evaluated at the point of intersection and the two derivatives are 16x and
, substituting x =1 we get,
and
.
Now put and
in this relationship, rearrange and solve for angle, it will come out to be
= 1.190390345 degrees.
that is our angle that we want to know between the two cures at the point of their intersection.
As per Weins displacement law the wavelength of light for which we get the peak of the graph is always inversely proportional to the temperature.
So we can say
So here if temperature becomes more cool then wavelength will increase
here we know that
It means the hottest star out of all three is star 3
and coolest star is star 1
now if we star 2 becomes cooler then it means its temperature will go near to star 1 and hence it will more look like to star 1.
So correct answer is
it will look more like Star 1