Final answer:
Height of volcano above sea level is 4205m.
Step-by-step explanation:
Step 1
Height of volcano below sea level: 5998m
Step 2
Total height of volcano below and above sea level:
10203m
Step 3
Subtract height of volcano below sea level from total height of volcano to get height of volcano above sea level:
10203 - 5998
Step 4
Subtract the terms:
10203 - 5998 = 4205
35 sec
because 5:00-4:30=30
30+5=35
The question is:
Check whether the function:
y = [cos(2x)]/x
is a solution of
xy' + y = -2sin(2x)
with the initial condition y(π/4) = 0
Answer:
To check if the function y = [cos(2x)]/x is a solution of the differential equation xy' + y = -2sin(2x), we need to substitute the value of y and the value of the derivative of y on the left hand side of the differential equation and see if we obtain the right hand side of the equation.
Let us do that.
y = [cos(2x)]/x
y' = (-1/x²) [cos(2x)] - (2/x) [sin(2x)]
Now,
xy' + y = x{(-1/x²) [cos(2x)] - (2/x) [sin(2x)]} + ([cos(2x)]/x
= (-1/x)cos(2x) - 2sin(2x) + (1/x)cos(2x)
= -2sin(2x)
Which is the right hand side of the differential equation.
Hence, y is a solution to the differential equation.
I don't know if this is right or if you're teacher will allow this, but
you could put that as 7(x+8) because if you were to turn it into a solved thing, it would become 7x+56.
I don't know if this is right though.