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
We know that
If a system has at least one solution, it is said to be consistent.
When you graph the equations, both equations represent the same line
so
the system has an infinite number of solutions
If a consistent system has an infinite number of solutions, it is dependent.
<span>
therefore
the system is </span>consistent, dependent and <span>equivalent
</span><span>
the answer is
</span>equivalent
Answer:
<u>option 1</u>
Step-by-step explanation:
The question is as shown in the attached figure.
From the figure, we can deduce that:
∠U ≅ ∠X and ∠W ≅ ∠Z and ∠V ≅ ∠Y
So, ΔUWV similar to ΔXZY
But it is required to know " How can the triangles be proven similar by the SSS similarity theorem? "
So, we need to prove the corresponding angles are proportion
With the help of the previous corresponding angles.
So, we need to show that the ratios 
are equivalent.
So, the answer is <u>option 1</u>
Well what I would do is split the 40% into 20% so from 40% to 20% that is /2. So 32/2=16 so 20% of a number is 16, we know there is 5, 20% in 100% so multiply 16 and 5 which gives you 80. Now 25% of 80 is the same as 80*.25 or 80/4 which is 20
Your Answer 20
