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
X² + mx + m A perfect square trinomial is where:x² - is the square of the first term binomialmx - is twice the product of the binomials first and last termm - is the square of the last term binomial
x² + mx + m = (x + 1)²
(x + 1)² ⇒ (x+1)(x+1) = x(x+1) +1(x+1) ⇒ x² + x + x +1 = x² + 2x + 1
Answer:
correct option is C. 3.7 km
Step-by-step explanation:
given data
A to Port B = 4.7 km
lighthouse = N73°E
lighthouse = N31°E
solution
we get here first 
B and
here
A = 90 - 73 = 17°
B = 73 - 31 = 42°
and
sum of all angle 180° so
A +
17° + 42° + C = 180°
solve it we get
C = 121°
Now we use here sin law that is
........................2
put here value and we get
solve it we get
b = 3,7 km
so correct option is C. 3.7 km
To answer this we would need the expressions given.
