It’s rational, for a number to be rational you have to be able to write it as a fraction and you can write 0.515115111511115111115... as a fraction.
Answer:
y2 = C1xe^(4x)
Step-by-step explanation:
Given that y1 = e^(4x) is a solution to the differential equation
y'' - 8y' + 16y = 0
We want to find the second solution y2 of the equation using the method of reduction of order.
Let
y2 = uy1
Because y2 is a solution to the differential equation, it satisfies
y2'' - 8y2' + 16y2 = 0
y2 = ue^(4x)
y2' = u'e^(4x) + 4ue^(4x)
y2'' = u''e^(4x) + 4u'e^(4x) + 4u'e^(4x) + 16ue^(4x)
= u''e^(4x) + 8u'e^(4x) + 16ue^(4x)
Using these,
y2'' - 8y2' + 16y2 =
[u''e^(4x) + 8u'e^(4x) + 16ue^(4x)] - 8[u'e^(4x) + 4ue^(4x)] + 16ue^(4x) = 0
u''e^(4x) = 0
Let w = u', then w' = u''
w'e^(4x) = 0
w' = 0
Integrating this, we have
w = C1
But w = u'
u' = C1
Integrating again, we have
u = C1x
But y2 = ue^(4x)
y2 = C1xe^(4x)
And this is the second solution
Answer:
Option b
Step-by-step explanation:
Given that a researcher measures IQ and weight for a group of college students.
In general, we think that the weight has nothing to do with IQ of a person and hence not correlated.
But if we go deep, we find that after a certain weight, the person becomes lazy and inactive with a chance to have reduced IQ
Weight gain causes also health problems including less activity of both brain and body and hence there is a chance for less IQ
So we find that as weight increases iq decreases and when weight decreases, IQ increases.
Thus we can say that there is a negative correlation but not necessarily near to one.
Hence option b is right
